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https://web2.0calc.com/questions/convert-2-e-pi-i-6-to-rectangular-form | +0
# Convert $2 e^{\pi i/6}$ to rectangular form.
0
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Convert $$2 e^{\pi i/6}$$ to rectangular form.
Jan 4, 2019
#1
+99333
+2
This is probably the easiest question you have ever asked.
But why would I answer it?
https://web2.0calc.com/questions/let-a-and-b-be-real-numbers-the-complex-number-4
Jan 4, 2019 | 2019-03-25 06:44:33 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9839164018630981, "perplexity": 3186.50769751088}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-13/segments/1552912203755.18/warc/CC-MAIN-20190325051359-20190325073359-00348.warc.gz"} |
https://freshbiostats.wordpress.com/2013/09/ | Featured
# FreshBiostats birthday and September-born famous statisticians
With the occassion of the 1st birthday of FreshBiostats, we want to remember some of the great statisticians born in September and that have contributed to the “joy of (bio)stats”.
Gerolamo Cardano Pavia, 24 September 1501 – 21 September 1576 First systematic treatment of probability Caspar Neumann Breslau, 14 September 1648 – 27 January 1715 First mortality rates table Johann Peter Süssmilch Zehlendorf, 3 September 1707 – 22 March 1767 Demographic data and socio-economic analysis Georges Louis Leclerc (Buffon) Montbard, 7 September 1707 – Paris, 16 April 1788 Premier example in “geometric probability” and a body of experimental and theoretical work in demography Adrien-Marie Legendre Paris, 18 September 1752 – 10 January 1833 Development of the least squares method William Playfair Liff, 22 September 1759 – London, 11 February 1823 Considered the founder of graphical methods of statistics (line graph, bar chart, pie chart, and circle graph) William StanleyJevons Liverpool, 1 September 1835 – Hastings,13 August 1882 Statistical atlas – graphical representations of time series Anders Nicolai Kiaer Drammen, 15 September 1838 – Oslo, 16 April 1919 Representative sample Charles Edward Spearman London, 10 September 1863 – 17 September 1945 Pioneer of factor analysis and Spearman´s Rank correlation coefficient Anderson Gray McKendrick Edinburgh, September 8, 1876 – May 30, 1943 Several discoveries in stochastic processes and collaborator in the path-breaking work on the deterministic model for the general epidemic Maurice Fréchet Maligny, 2 September 1878 – Paris, 4 June 1973 Contributions in econometrics and spatial statistics Paul Lévy 15 September 1886 – 15 December 1971 Several contributions to probability theory Frank Wilcoxon County Cork, 2 September 1892 – Tallahassee, 18 November 1965 Wilcoxon rank-sum tests, Wilcoxon signed-rank test Mikhailo Pylypovych Kravchuk Chovnytsia, 27 September 1892- Magadan, 9 March 1942 Krawtchouk polynomials, a system of polynomials orthonormal with respect to the binomial distribution Harald Cramér Stockholm, 25 September 1893 – 5 October 1985 Important statistical contributions to the distribution of primes and twin primes Hilda Geiringer Vienna, 28 September 1893 – California, 22 March 1973 One of the pioneers of disciplines such as molecular genetics, genomics, bioinformatics,… Harold Hotelling Fulda, 29 September 1895 – Chapel Hill, 26 December 1973 Hotelling´s T-squared distribution and canonical correlation David van Dantzig Rotterdam, 23 September 1900 -Amsterdam, 22 July 1959 Focus on probability, emphasizing the applicability to hypothesis testing Maurice Kendall Kettering, 6 September 1907 – London, 29 March 1983 Random number generation and Kendall´s tau Pao-Lu Hsu Peking, 1 September 1910 – Peking, 18 December 1970 Founder of the newly formed discipline of statistics and probability in China
It is certainly difficult to think of the field without their contributions. They are all a great inspiration to keep on learning and working!!
Note: you can find other interesting dates here.
Update: and Significance´s timeline of statistics here.
Any author you consider particularly relevant? Any other suggestions?
Featured
# Infographics in Biostatistics
Although the history of Infographics according to Wikipedia does not seem to mention Fritz Kahn as one of the pioneers of this technique, I would like to start this post mentioning one of the didactic graphical representations of this Jewish German doctor, who was highly reputed as a popular science writer of his time.
Apart from his fascinating views of the human body in the form of machines and industrial processes, I am particularly attracted by his illustration below, summarising the evolution of life in the Earth as a clock in which the history of humans would not take more than a few seconds…
Image extracted from the printed version of the article “Fritz Kahn, un genio olvidado” published in El País, on Sunday 1st of September 2013.
What could be understood by some as a naive simplification of matters requires, in my opinion, a great deal of scientific knowledge and it is a fantastic effort to communicate the science behind very complex mechanisms.
This and more modern infographic forms of visualisation represent an opportunity for statisticians –and more specifically biostatisticians-, to make our field approachable and understandable for the wider public. Areas such as Public Health (see here), Cancer research (find examples here and here), and Drug development (see here) are already using them, so we should not be ashamed to make of these “less rigorous” graphical representations an important tool in our work.
Note: There are plenty of resources available online to design a nice infographic in R. For a quick peek into how to create easy pictograms, check out this entry in Robert Grant´s stats blog. Also, the wordcloud R package will help you visualising main ideas from texts…
We will soon show a practical example of these representations in this blog, keep tuned!
Featured
# An example of Principal Components Analysis
The last post that I published was about two techniques of Multivariate Analysis: Principal Component Analysis (PCA) and Correspondence Analysis (CA). In this post I will show a practical example of PCA with R. Let’s go!
We are going to work with Fisher’s Iris Data available in package “datasets”. This data, collected over several years by Edgar Anderson was used to show that these measurements could be used to differentiate between species of irises. That data set gives the measurements in centimeters of the variables sepal length and width and petal length and width, respectively, for 50 flowers from each of 3 species of iris. The species are Iris setosa, versicolor, and virginica.
You can load the Iris data and examine this data frame with:
```data(iris)
str(iris); summary(iris[1:4])
pairs(iris[1:4],main="Iris Data", pch=19, col=as.numeric(iris\$Species)+1)
mtext("Type of iris species: red-> setosa; green-> versicolor; blue-> virginica", 1, line=3.7,cex=.8)
```
We will use “prcomp” R function to carry out the analysis, which is similar to “princomp” function.
As we said in the last post, PCA is used to create linear combinations of the original data that capture as much information in the original data as possible. For that and before starting with PCA is convenient to mention some particularities of this methodology.
In the prcomp function we need indicate if the principal components are calculated through correlation matrix (with standardized data) or covariance matrix (with raw data). We will standardize our variables when these have different units and have very different variances. If they are in the same units both alternatives are possible. In our example all variables are measured in centimetres but we will use the correlation matrix for simplicity’s sake.
```#To examine variability of all numeric variables
sapply(iris[1:4],var)
range(sapply(iris[1:4],var))
# maybe this range of variability is big in this context.
#Thus, we will use the correlation matrix
#For this, we must standardize our variables with scale() function:
iris.stand <- as.data.frame(scale(iris[,1:4]))
sapply(iris.stand,sd) #now, standard deviations are 1
```
Now applied the prcomp() function to calculate the principal components:
```#If we use prcomp() function, we indicate 'scale=TRUE' to use correlation matrix
pca <- prcomp(iris.stand,scale=T)
#it is just the same that: prcomp(iris[,1:4],scale=T) and prcomp(iris.stand)
#similar with princomp(): princomp(iris.stand, cor=T)
pca
summary(pca)
#This gives us the standard deviation of each component, and the proportion of variance explained by each component.
#The standard deviation is stored in (see 'str(pca)'):
pca\$sdev
```
In order to decide how many principal components should be retained, it is common to summarise the results of a principal components analysis by making a scree plot, which we can do in R using the “screeplot()” function:
```#plot of variance of each PCA.
#It will be useful to decide how many principal components should be retained.
screeplot(pca, type="lines",col=3)
```
From this plot and from the values of the ‘Cumulative Proportion of Variance’ (in summary(pca)) we can conclude that retaining 2 components would give us enough information, as we can see that the first two principal components account for over 95% of the variation in the original data.
```#The loadings for the principal components are stored in:
```
This means that the first two principal component is a linear combination of the variables:
$PC1 = 0.521*Z_1 - 0.269*Z_2 + 0.580*Z_3 + 0.564*Z_4$
$PC2 = -0.377*Z_1 - 0.923*Z_2 - 0.024*Z_3 - 0.066*Z_4$
where $Z_1, \ldots, Z_4$ are the standardization of original variables.
The weights of the PC1 are similar except the associate to Sepal.Width variable that is negative. This component discriminate on one side the Sepal.Width and on the other side the rest of variables (see biplot). This one principal component accounts for over 72% of the variability in the data.
All weights on the second principal component are negative. Thus the PC2 might seem considered as an overall size measurement. When the iris has larger sepal and petal values than average, the PC2 will be smaller than average. This component explain the 23% of the variability.
The following figure show the first two components and the observations on the same diagram, which helps to interpret the factorial axes while looking at observations location.
```#biplot of first two principal components
biplot(pca,cex=0.8)
abline(h = 0, v = 0, lty = 2, col = 8)
```
To interpret better the PCA results (qualitatively) would be useful to have the opinion of an expert in this area, as sometimes is somewhat confusing. I encourage you to participate! | 2019-07-20 01:39:03 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 3, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4106080234050751, "perplexity": 1418.0973999777318}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-30/segments/1563195526401.41/warc/CC-MAIN-20190720004131-20190720030131-00211.warc.gz"} |
https://kluedo.ub.uni-kl.de/frontdoor/index/index/year/2005/docId/1612 | ## Wavelet Deformation Analysis for Spherical Bodies
• In this paper we introduce a multiscale technique for the analysis of deformation phenomena of the Earth. Classically, the basis functions under use are globally defined and show polynomial character. In consequence, only a global analysis of deformations is possible such that, for example, the water load of an artificial reservoir is hardly to model in that way. Up till now, the alternative to realize a local analysis can only be established by assuming the investigated region to be flat. In what follows we propose a local analysis based on tools (Navier scaling functions and wavelets) taking the (spherical) surface of the Earth into account. Our approach, in particular, enables us to perform a zooming-in procedure. In fact, the concept of Navier wavelets is formulated in such a way that subregions with larger or smaller data density can accordingly be modelled with a higher or lower resolution of the model, respectively.
Author: Willi Freeden, Volker Michel urn:nbn:de:hbz:386-kluedo-13697 Schriften zur Funktionalanalysis und Geomathematik (9) Preprint English 2004 2004 Technische Universität Kaiserslautern 2005/02/17 Cauchy-Navier-GleichungCauchy-Navier equation Dirichlet-Problem ; Elastische Deformation ; Kugel ; Mehrskalenanalyse; Neumann-Problem ; Skalierungsfunktion ; Wavelet-Analyse zur Veröffentlichung angenommen durch "International Journal on Wavelets, Multiresolution and Information Processing" Fachbereich Mathematik 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik 33-XX SPECIAL FUNCTIONS (33-XX DEALS WITH THE PROPERTIES OF FUNCTIONS AS FUNCTIONS) (For orthogonal functions, see 42Cxx; for aspects of combinatorics see 05Axx; for number-theoretic aspects see 11-XX; for representation theory see 22Exx) / 33Fxx Computational aspects / 33F05 Numerical approximation and evaluation [See also 65D20] 42-XX FOURIER ANALYSIS / 42Cxx Nontrigonometric harmonic analysis / 42C40 Wavelets and other special systems 74-XX MECHANICS OF DEFORMABLE SOLIDS / 74Bxx Elastic materials / 74B05 Classical linear elasticity 86-XX GEOPHYSICS [See also 76U05, 76V05] / 86Axx Geophysics [See also 76U05, 76V05] / 86A20 Potentials, prospecting Standard gemäß KLUEDO-Leitlinien vor dem 27.05.2011
$Rev: 13581$ | 2015-03-28 04:02:59 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4323396384716034, "perplexity": 6180.1152741578435}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-14/segments/1427131297195.79/warc/CC-MAIN-20150323172137-00211-ip-10-168-14-71.ec2.internal.warc.gz"} |
https://www.cell.com/biophysj/fulltext/S0006-3495(18)31160-3 | Article| Volume 115, ISSUE 12, P2395-2402, December 18, 2018
• Top
# Adhesion of Active Cytoskeletal Vesicles
Open AccessPublished:October 22, 2018
## Abstract
Regulation of adhesion is a ubiquitous feature of living cells, observed during processes such as motility, antigen recognition, or rigidity sensing. At the molecular scale, a myriad of mechanisms are necessary to recruit and activate the essential proteins, whereas at the cellular scale, efficient regulation of adhesion relies on the cell’s ability to adapt its global shape. To understand the role of shape remodeling during adhesion, we use a synthetic biology approach to design a minimal experimental model, starting with a limited number of building blocks. We assemble cytoskeletal vesicles whose size, reduced volume, and cytoskeletal contractility can be independently tuned. We show that these cytoskeletal vesicles can sustain strong adhesion to solid substrates only if the actin cortex is actively remodeled significantly. When the cytoskeletal vesicles are deformed under hypertonic osmotic pressure, they develop a crumpled geometry with deformations. In the presence of molecular motors, these deformations are dynamic in nature, and the excess membrane area generated thereby can be used to gain adhesion energy. The cytoskeletal vesicles are able to attach to the rigid glass surfaces even under strong adhesive forces just like the cortex-free vesicles. The balance of deformability and adhesion strength is identified to be key to enable cytoskeletal vesicles to adhere to solid substrates.
## Introduction
Giant unilamellar vesicles have proven to be an excellent model system to study basic processes of cellular adhesion (
• Albersdörfer A.
• Feder T.
• Sackmann E.
Adhesion-induced domain formation by interplay of long-range repulsion and short-range attraction force: a model membrane study.
,
• Cuvelier D.
• Nassoy P.
Hidden dynamics of vesicle adhesion induced by specific stickers.
,
• Goennenwein S.
• Tanaka M.
• Sackmann E.
• et al.
Functional incorporation of integrins into solid supported membranes on ultrathin films of cellulose: impact on adhesion.
,
• Reister-Gottfried E.
• Sengupta K.
• Smith A.S.
• et al.
Dynamics of specific vesicle-substrate adhesion: from local events to global dynamics.
,
• Sackmann E.
• Smith A.S.
Physics of cell adhesion: some lessons from cell-mimetic systems.
,
• Lipowsky R.
• Rouhiparkouhi T.
• Weikl T.R.
• et al.
Domain formation in cholesterol-phospholipid membranes exposed to adhesive surfaces or environments.
,
• Franke T.
• Lipowsky R.
• Helfrich W.
Adhesion of lipid membranes induced by CrCl 3.
). The interactions involved in the formation of adhesion domains and the fundamental differences between cell-cell and cell-substrate adhesion have been identified (
• Smith A.S.
• Sengupta K.
• Sackmann E.
• et al.
Force-induced growth of adhesion domains is controlled by receptor mobility.
). Recently, it has been shown that adhering vesicles act as force generators and that the adhesion process itself is sufficient to induce traction forces on a surface (
• Murrell M.P.
• Voituriez R.
• Gardel M.L.
• et al.
). The adhesion forces can be well controlled by the membrane composition of the vesicle and surface functionalization (
• Bernard A.-L.
• Guedeau-Boudeville M.-A.
• di Meglio J.-M.
• et al.
Strong adhesion of giant vesicles on surfaces? dynamics and permeability.
). During adhesion strengthening, the adhesion forces pull on the membrane, dampen its fluctuations, and thus increase the membrane tension (
• Rädler J.O.
• Feder T.J.
• Sackmann E.
• et al.
Fluctuation analysis of tension-controlled undulation forces between giant vesicles and solid substrates.
). An increase in adhesion strength above a critical value causes the membrane tension to reach its critical lysis tension, leading to vesicle bursting (
• Lipowsky R.
• Seifert U.
). Under conditions of specific adhesion, the lateral forces from the surface come from the attraction between the membrane-bound receptors and ligands on the surface. In going from an unbound state to a bound state, the vesicles undergo significant shape transformations (
• Rädler J.O.
• Feder T.J.
• Sackmann E.
• et al.
Fluctuation analysis of tension-controlled undulation forces between giant vesicles and solid substrates.
,
• Lipowsky R.
• Seifert U.
,
• Bruinsma R.
• Behrisch A.
• Sackmann E.
Adhesive switching of membranes: experiment and theory.
,
• Seifert U.
• Lipowsky R.
). This adhesion-induced shape transformation has been successfully explained by free energy minimization in the framework of the Helfrich theory of elastic cells (
• Capovilla R.
• Guven J.
,
• Helfrich W.
Elastic properties of lipid bilayers: theory and possible experiments.
). Thus far, insight into the adhesion process through the model system lacks involvement of membrane-cytoskeletal coupling. What has already been established is that binding the cortex to the membrane causes dampening of membrane fluctuations and increases the membrane tension for both cells and vesicles (
• Diz-Muñoz A.
• Fletcher D.A.
• Weiner O.D.
Use the force: membrane tension as an organizer of cell shape and motility.
,
• Loiseau E.
• Schneider J.A.
• Bausch A.R.
• et al.
Shape remodeling and blebbing of active cytoskeletal vesicles.
). But how this would influence the adhesion process is yet to be explored.
Here, we elucidate the role of the presence of a cytoskeletal cortex on the adhesion process in biomimetic systems. The specific adhesion of vesicles to a glass surface is mediated by biotin and streptavidin as the ligand-receptor pair. We observe that for a given ligand-receptor density for which cortex-free vesicles show strong adhesion, cytoskeletal vesicles burst. We show that the observation of bursting cytoskeletal vesicles compared to stably adhered cortex-free vesicles is due to the need for a vesicle to deform to accommodate with the surface so that it can gain in adhesion, which in turn requires excess membrane area. However, a significant amount of the excess membrane area in cytoskeletal vesicles is pinned to a rigid cortex and hence not available for the deformations to gain adhesion energy. The adhesion process relies on the availability of excess membrane area.
Because the coupling of cytoskeleton to the membrane is opposing the vesicle deformation to gain adhesion, we provide the cytoskeletal vesicles with excess membrane area by applying additional hypertonic stress. Under the reduced volume condition, the vesicles can then develop large deformations. Our experiments show that only active remodeling of the cortex can provide the required excess membrane area to deform and gain adhesion energy. Using myosin motors, we induce active remodeling in actin cortex. Under hypertonic stress, the weakly adhered active cytoskeletal vesicles make a transition from weak adhesion to strong adhesion regime without rupturing their membrane. Hence, we show that active remodeling of the cortex is thus an important component to enable the adhesion of cytoskeletal vesicles.
## Materials and Methods
### Reagents
Egg L-α-phosphatidylcholine lipids were ordered from Sigma-Aldrich (St. Louis, MO) (P3556) in powder form and dissolved at 50 mg/mL in a chloroform/methanol mixture (9:1, v/v). 1,2-dioleoyl-sn-glyero-3-[(N-(5-amino-1-carboxypentyl)iminodiacetic acid)succinyl) (nickel salt) lipids (Ni-NTA) (790404 C); 1,2-distearoyl-sn-glycero-3-phosphoethanolamine-N-biotinyl(polyethylene glycol)-2000] (ammonium salt) (880129 C) and PEG2000PE (880160 C) lipids were ordered from Avanti Polar Lipids (Alabaster, AL). The mineral oil was from Sigma-Aldrich (M3516), and the silicone oil (viscosity 50 centistokes) was from Roth (4020.1). Decane was from Sigma-Aldrich (D901). Biotinylated bovine serum albumin (BSA) (A8549) and streptavidin (S4762) were also purchased from Sigma-Aldrich.
### Proteins
Proteins were purified according to previously published protocols. G-actin (
• MacLean-Fletcher S.
• Pollard T.D.
Identification of a factor in conventional muscle actin preparations which inhibits actin filament self-association.
,
• Spudich J.A.
• Watt S.
The regulation of rabbit skeletal muscle contraction. I. Biochemical studies of the interaction of the tropomyosin-troponin complex with actin and the proteolytic fragments of myosin.
) and muscle myosin II (
• Margossian S.S.
• Lowey S.
Preparation of myosin and its subfragments from rabbit skeletal muscle.
) were purified from rabbit skeletal muscle. The fragment of Xenopus laevis anillin spanning amino acids 1–428 (
• Kinoshita M.
• Field C.M.
• Mitchison T.J.
• et al.
Self- and actin-templated assembly of mammalian septins.
), excluding the myosin binding site, was cloned into a pET-28a vector and purified from Escherichia coli with histidine (His) tags on both termini. Anillin is a monomer with two F-actin binding sites that enables it to bundle the actin filaments (
• Field C.M.
• Alberts B.M.
Anillin, a contractile ring protein that cycles from the nucleus to the cell cortex.
,
• Piekny A.J.
The myriad roles of Anillin during cytokinesis.
). Anillin 1–428 was stored at −80°C in buffer with 25 mM imidazole (pH 6), 25 mM KCl, 4 mM MgCl2, 1 mM EGTA, and 1 mM 1,4-dithiothreitol. The His tag on the two termini of anillin couples the actin to the Ni-NTA (nitrilotriacetic acid) lipids in the membrane.
### Buffer solution
We mixed the solution to be encapsulated on ice immediately before vesicle production. The reaction mix that was encapsulated inside the vesicle contained 1.5 μM anillin, 0.1 μM myosin II, 10 μM G-actin, 10 mM imidazole, 1 mM MgCl2, 1 mM ATP, 1 mM EGTA, 30 mM KCl, 2 mM dithiothreitol, 300 mM sucrose, and 0.5 μM Alexa Fluor 488 phalloidin. The pH of the final inside solution was 7.2. The outside solution for production of vesicles consisted only of glucose dissolved in Millipore water (Merck Millipore, Burlington, MA). The osmotic pressure of the outside solution was adjusted to be 10–15 milliosmoles (mOsm) higher than the protein mix to form stable vesicles.
### Vesicle production
Vesicles were produced using continuous droplet interface crossing encapsulation (cDICE) (
• Abkarian M.
• Loiseau E.
• Massiera G.
Continuous droplet interface crossing encapsulation (cDICE) for high throughput monodisperse vesicle design.
). Briefly, this method consists of a cylindrical rotating chamber successively filled with a glucose solution to collect the vesicles, a lipid-in-oil solution to saturate the oil-water interfaces, and decane as the continuous phase in which droplets were produced. The protocol to disperse the lipids in the oil solution published elsewhere (
• Claudet C.
• In M.
• Massiera G.
Method to disperse lipids as aggregates in oil for bilayers production.
) was modified to encapsulate proteins inside the vesicles (
• Loiseau E.
• Schneider J.A.
• Bausch A.R.
• et al.
Shape remodeling and blebbing of active cytoskeletal vesicles.
). The lipid-in-oil mix contained 14% (v/v) mineral oil, 80% (v/v) silicon oil, and 6% decane. Lipids from stocks solutions (in chloroform) were first dissolved in decane and then oil (silicon + mineral) were added to give the final lipid concentration of 0.5 mM.
The reaction mix containing the cytoskeletal elements was injected through a glass capillary tube by inserting the capillary’s tip (diameter of 20 μm) in decane. Because of the shear force droplets detach from the tip and are then carried by the centrifugal force through the lipid-in-oil solution, where they were first coated by a lipid monolayer and then by a second lipid monolayer while crossing the oil-water interface. The two monolayers zipped together to form a bilayer. Vesicles were collected in the glucose solution, which was sucked with a micropipette once the chamber was stopped. For the process to succeed, the osmolarity of the encapsulated solution has to be 10–15 mOsm lower than the outside. The whole process was completed in a cold room maintained at 5°C to prevent fast polymerization of the cytoskeleton. We produced vesicles in a span of 2 min. Although cDICE is a high-yield method resulting in hundreds of vesicles under most conditions, encapsulating proteins at high concentrations (10 μM actin and up to 1.5 μM anillin) resulted in a decrease of the yield. At the highest protein concentrations, a 100-μL sample contained ∼50 vesicles with diameters ranging from 15 to 30 μm. Large vesicles with a diameter of 40 μm were produced using capillaries with tip diameters larger than 20 μm. The lipid bilayer of the vesicles consisted of egg L-α-phosphatidylcholine with 10 mol % Ni-NTA and 1 mol % biotinylated PEG2000 lipids.
BSA-biotin and streptavidin were used to functionalize the coverslips to specifically adhere the vesicles. The stocks and working solutions of BSA, BSA-biotin, and streptavidin were all prepared in 1× phosphate-buffered saline (PBS) containing 2.7 mM KCl and 137 mM NaCl with pH 7.4 at room temperature (P4417; Sigma-Aldrich). To functionalize the coverslips, they were first incubated for 20 min at room temperature with a mix of 1 mg/mL BSA-biotin and 1 mg/mL BSA in different ratios, followed by a couple washes with 1× PBS and then further incubation with 0.5 mg/mL streptavidin. Three different v/v ratios (70:30, 50:50, and 35:65) of 1 mg/mL BSA-biotin and 1 mg/mL BSA were used in our experiments to vary the ligand density at the surface. PEG-biotin lipids in the membrane were kept at 1 mol % for the strong adhesion. After streptavidin binding, the coverslips were rinsed with the external buffer of the vesicle suspension to avoid any osmotic pressure changes caused by the PBS. Because the external buffer is just glucose in water, 5 μM KCl was added to the buffer to screen short-range repulsive electrostatic interactions and allow biotin-streptavidin binding.
In addition to lowering the percentage ratio of BSA-biotin and BSA, we also added 0.5 mol % PEG2000 lipids into the vesicle membrane to lower the adhesion strength between the coverslip and the membrane.
### Deflating protocol
Vesicles were deflated by adjusting the surrounding osmotic pressure in a diffusion chamber. The chamber consisted of two compartments made of flat o-rings and separated by a membrane (Merck Millipore) with a pore size of 0.22 μm. The o-rings used were of 20 mm in diameter and 2 mm in thickness.
The vesicles were confined in the bottom compartment, and their surrounding osmotic pressure was changed by adding glucose buffer in the top compartment. The osmotic pressure equilibrates in both chambers via glucose diffusion through the polycarbonate membrane separating the two compartments. The increase in osmotic pressure in the bottom compartment was followed by harvesting aliquots from the top compartment every 10 min. After the osmotic pressure measurement, which took around 30 s, the aliquots were put back in the top chamber to avoid volume differences. The calibration chart can be seen in Fig. S1.
### Imaging and analysis
Vesicles were imaged with a Leica Microscope DMI3000 B and a 63× numerical aperture 1.3 oil immersion objective for bright-field microscopy and epifluorescence, in combination with a Hamamatsu ORCA-ER camera (Hamamatsu, Japan).
Confocal images were acquired using Leica TSC SP5 and a 63× numerical aperture 1.4 oil immersion objective. The three-dimensional (3D) reconstruction using the confocal stack was done using Imaris Software. Kymographs were prepared from the time-lapse images of the vesicles sedimented on passivated surface in epifluorescence using a Fiji (
• Schindelin J.
• Arganda-Carreras I.
• Cardona A.
• et al.
Fiji: an open-source platform for biological-image analysis.
) plugin. We always used the closed chambers to image the vesicles to avoid large scale drifts and convection.
## Results and Discussion
### Cytoskeletal vesicles
Our model system is a giant unilamellar vesicle containing a cross-linked actin cortex anchored to its inner leaflet. The His-tagged anillin is responsible for both cross-linking the actin and coupling the actin network to the Ni-NTA lipids that are incorporated into the membrane. We call the vesicle that has an actin cortex a cytoskeletal vesicle, as shown in Fig. 1, a and b. Protein encapsulation occurs during vesicle preparation using the cDICE method adapted for this system (
• Loiseau E.
• Schneider J.A.
• Bausch A.R.
• et al.
Shape remodeling and blebbing of active cytoskeletal vesicles.
). By adding myosin motors to the network, we added contractility and hence activity. Depending on the presence or absence of motor proteins, we call cytoskeletal vesicles active vesicles or passive vesicles, respectively. The actin cortex is formed by encapsulating 10 μM of G-actin and 1.5 μM of anillin at 4°C. We induced contractility into the cortex by adding an additional 0.1 μM of myosin motors into the reaction mix. The amount of anillin inside the vesicle and mol % of Ni-NTA needed to form an actin cortex has been characterized in depth in previously published work (
• Loiseau E.
• Schneider J.A.
• Bausch A.R.
• et al.
Shape remodeling and blebbing of active cytoskeletal vesicles.
). The active vesicles were observed having dynamic deformations (Fig. 1 c; Videos S1 and S2), unlike the passive and cortex-free vesicles. These deformations are due to the active stress generated by the myosin motors in actin cortex. Myosin motors are known to create sliding motion between the actin filaments. It is this sliding of the filaments and tension in the membrane that causes dynamic shape changes in case of the active vesicles (Fig. S2). The characteristic timescale over which we observed the active shape changes is much larger than the timescale of membrane fluctuations. The active cortex pushes and pulls on the lipid bilayer, causing tiny vertices to appear on the vesicle surface approximately once every 20 s (Video S2). In contrast, the membrane fluctuations in the cortex-free vesicles are of a much higher frequency, 2 s−1, as is evident from the kymograph in Fig. 1 d. No microscopic membrane fluctuations, as observed in the cortex-free vesicles, were seen in the cytoskeletal vesicles. This can be best seen by comparing the kymographs shown in Fig. 1 d. The kymographs were obtained from the line intensity profiles taken across a section of the membrane from the epifluorescence time-lapse recording of the vesicles with labeled membrane. The absence of the microscopic fluctuations can be attributed to anchoring of the elastic actin cortex to the membrane, which kills the high-amplitude fluctuation modes. These observations already indicate that the excess membrane area is strongly coupled to the actin cortex and is no longer free for shape transformations in cytoskeletal vesicles.
The specific adhesion strength between the vesicle and the functionalized glass surface can be controlled by tuning the ligand-receptor density between the two. We used biotin-streptavidin as a ligand-receptor pair to make vesicles adhere to the glass (Fig. 1 e). We used two different ligand densities at the glass surface by coating the glass with BSA-biotin and BSA mixed at two different volume ratios, 70:30 and 50:50. The membrane was doped with 1 mol % PEG-biotin lipids to make the vesicles bind to streptavidin on the glass surface.
We observed that for both ligand densities the cortex-free vesicles bind to the rigid glass surface and adopt a spherical cap shape (Fig. 2 a). 5% of vesicles get leaky but maintain their shape, as can be seen in Fig. S3. We excluded all the leaky vesicles from further analysis. As per the previously published theoretical estimates, a vesicle with a constant volume adopts a spherical cap shape under strong adhesion conditions (
• Bernard A.-L.
• Guedeau-Boudeville M.-A.
• di Meglio J.-M.
• et al.
Strong adhesion of giant vesicles on surfaces? dynamics and permeability.
). It has also been shown that the contact angle provides a measure for the adhesion strength (
• Steinkühler J.
• Agudo-Canalejo J.
• Dimova R.
• et al.
Modulating vesicle adhesion by electric fields.
,
• Gruhn T.
• Franke T.
• Dimova R.
• Lipowsky R.
Novel method for measuring the adhesion energy of vesicles.
,
• Murrell M.
• Pontani L.L.
• Sykes C.
• et al.
Spreading dynamics of biomimetic actin cortices.
). We adopted the same approach for concluding if a vesicle is strongly adhered or not. Therefore, if a vesicle makes an acute angle (<90°) with the surface, we call it a strong adhesion; otherwise, we consider the adhesion weak. We used Fiji to determine the contact angles from the 3D projections of the confocal stacks as can be seen in Fig. S4. On a glass surface coated with a mix of 70% BSA-biotin and 30% BSA, all cytoskeletal vesicles burst within a minute after making contact with the surface. The passive vesicles have their membrane area bound to the cortex which makes it difficult for the lateral forces to pull the excess membrane area to gain in adhesion energy. In the case of the active vesicles, the contractile forces in the cortex increase membrane tension, leading to a membrane rupture under adhesion.
On lowering the ligand density on the surface (50% BSA-biotin and 50% BSA), we observed that some size selection occurs and cytoskeletal vesicles with a longest chord length shorter than 20 μm are stable for more than 30 min. We used the longest chord length as a way to determine the vesicle size because the vesicles deviate from a spherical shape when they make contact with the surface. Fig. 2, b and c show the bottom slice from the z-stack of active vesicles that did not burst against the vesicles that burst after making contact with the surface, respectively. Vesicles that burst after contact with the surface form an irregular supported bilayer visible only in the bottom-most slice of the z-stack (Fig. 2 d). Our observations show that the vesicles that do not burst after 30 min of contact with the glass surface form contact area with a diameter ≤14.4 $±$ 1.9 μm (mean $±$ SD; n = 20). Bigger vesicles form a larger contact area before they burst, which can be seen in the footprint of the active vesicles that burst in Fig. 2 c. One possible reason for the observed size dependency is the local curvature of the vesicles at the contact area, which determines accessibility of the binding partners. The accessibility of the binding partners increases with decreasing curvature (increasing radius) and hence the attractive forces between the vesicle and the glass surface. The increased attraction will consequently lead to increased lateral forces. Because the limiting parameter here would be the deformability of the vesicle and the membrane is bound to the cortex underneath, we conclude that the elasticity of the cortex limits the spreading dynamics. In the case of vesicles with diameters >20 μm, the large membrane curvature generates lateral forces, which increase the membrane tension beyond the lysis limit, causing the cytoskeletal vesicles to burst.
The finding that the cytoskeletal vesicles burst, whereas cortex-free vesicles are able to adhere at a similar ligand-receptor density, can be attributed to the difference in the availability of excess membrane. Cortical coupling has already been reported to limit available excess area and thus limits the vesicle’s ability to form membrane tubes under hydrodynamic flow (
• Guevorkian K.
• Manzi J.
• Sykes C.
• et al.
Mechanics of biomimetic liposomes encapsulating an actin shell.
). To increase adhesion, a vesicle needs to deform, which is only possible at the cost of excess membrane area and increase in the membrane tension. Membrane tension limits gain in adhesion once the excess membrane area has been consumed. Owing to the coupling of membrane to the cortex, the excess membrane area is not freely available to make deformations in cytoskeletal vesicles. Therefore, the increase in contact area beyond the cutoff (∼15 μm) causes the lysis of the membrane in these vesicles. In the next series of experiments, we aimed to increase the available excess area by applying hypertonic osmotic stress to enable the strong adhesion of cytoskeletal vesicles.
### Deformation of cytoskeletal vesicles under hypertonic osmotic stress
Because the limiting parameter for creating adhesion is a lack of excess membrane area, we applied a hypertonic osmotic stress using a two-level diffusion chamber (Fig. 3 a) to deflate the vesicles to a reduced volume of ν = 0.6 (40% volume loss). The reduced volume is defined by the ratio between the volume of liquid present in the deformed vesicle and the volume enclosed by a sphere with the same surface area. We compare the deformations of passive and active vesicles in the nonadhering state under hyperosmotic pressure to pinpoint the effect of myosin motors on shape adaptations. Cortex-free vesicles show the well-described morphological deformations predicted by the minimization of curvature energy of the lipid membrane (
• Käs J.
• Sackmann E.
Shape transitions and shape stability of giant phospholipid vesicles in pure water induced by area-to-volume changes.
,
• Sackmann E.
• Duwe H.P.
• Engelhardt H.
Membrane bending elasticity and its role for shape fluctuations and shape transformations of cells and vesicles.
,
• Seifert U.
Configurations of fluid membranes and vesicles.
) (Fig. 3 b; Video S3). In contrast, the passive cytoskeletal vesicles remain mostly spherical for up to a 10% increase in the osmotic pressure without changing their volume (Fig. 3 c). Because the volume of the passive vesicle does not change significantly, we estimate that the resulting applied pressure reaches 0.11 atm. The reduced volume and the vesicle shape remain almost the same as the surrounding osmotic pressure increases from 450 to 500 mOsm (Fig. 3, c and d). Increasing the osmotic pressure further leads to a further compressive stress buildup and finally to an abrupt deformed shape change (∼6% radius decrease). After this abrupt deformation, when the pressure reaches 520 mOsm, the cortex stability again resists further deformations until the pressure exceeds 540 mOsm (Fig. 3 c) and a second sudden shape change occurs. After the second sudden event of cortex shape change, the radius of the vesicle starts decreasing monotonically as external pressure increases.
In contrast to these discontinuous deformations of the passive cytoskeletal vesicles, the presence of 0.1 μM of myosin motors enable vesicles to adapt continuously to the osmotic pressure change. Indeed, the myosin contractile activity pulls on the membrane, and the limiting parameter to deformation is now the membrane tension of the vesicle. We observe a continuous remodeling of vesicle shape, without any sudden instabilities (Fig. 3 b). The final equilibrium shape of both passive and active vesicles is comparable (Fig. 3 c). Both vesicle types show a complex morphology with many invaginations, resembling a crumpling transition of an elastic shell (Fig. 3 c at point III; Fig. S5; Video S4), as predicted for spherical elastic shells submitted to a constant compressive rate (
• Vliegenthart G.A.
• Gompper G.
Compression, crumpling and collapse of spherical shells and capsules.
).
### Adhesion of cytoskeletal vesicles under hypertonic osmotic stress
Because adhesion depends on the availability of excess area, we tested the adhesion process of active and passive cytoskeletal vesicles having diameters larger than 20 μm under hypertonic stress. To avoid immediate bursting of vesicles, we slightly reduced the adhesion strength between the membrane and the glass by adding 0.5 mol % PEG2000 lipids to the membrane and by coating the glass with a mix of 35% biotin-BSA and 65% BSA instead of a 50:50 mix. Cytoskeletal vesicles are still unstable and observed to burst even under the lower adhesion strength. Because of the lower density of adhesion molecules on the surface and the presence of PEG lipids in the bilayer, vesicle adhesion slows down and the membrane rupture is delayed by around 10–15 min. Because assembling of the diffusion chamber takes ∼1–2 min, the cytoskeletal vesicles are under hypertonic stress and start to deflate long before they can reach the previously observed lysis point. To estimate the contact angle in a nondeflated state, we performed control experiments. In the control experiments, we acquired z-stacks of 20 vesicles in the first 10 min of the adhesion process under no osmotic stress. Fig. 4, a and b represent the typical shape of a cortex-free and a cytoskeletal vesicle in the nondeflated state, respectively. A z-stack of a cytoskeletal vesicle before deflation can be seen in Video S5. We found no difference between the shapes of passive and active vesicles before deflation, and the average contact angle was found to be around 122° for all the different types of vesicles. We chose the glucose concentration in the top chamber to be 570 mOsm higher than the bottom chamber to get larger deformations in a shorter time than the nonattached vesicles. The reduced vesicle volume in this case was around 48%. In 60 min, the solution in the two compartments reached equilibrium (calibration plot in Fig. S1) and we started imaging.
We observed that the deflated cytoskeletal vesicles (both active and passive) remain stably adhered to glass even after 2 h of coming in contact with the glass without any observable bursting events. We observed cortex-activity-dependent shape transformations in cytoskeletal vesicles under hypertonic stress. After a volume reduction of around 48%, passive vesicles became strongly and irregularly deformed (Fig. 4 d; Video S6), whereas all adhered active vesicles adopted the shape of a smooth spherical cap (Fig. 4 e; Video S7). We observed that after deflation, the contact angle and shape of the active vesicles are identical to those of cortex-free vesicles (Fig. 4, c, e, and f; Video S8). The identical shape transformation and change in contact area exhibited by the cortex-free vesicles and the active cytoskeletal vesicles after deflation suggest that excess membrane area is created by active deformation of the vesicles to increase adhesion to the surface and to reduce the contact angle. For both cortex-free vesicles and active cytoskeletal vesicles, the contact angle changes from ∼122° in the nondeflated state to ∼70° in the deflated state, as shown in Fig. 4 f. Thus, active remodeling of the cortex is needed to get the desired shape transformations that can lead to a gain in the adhesion area. Passive vesicles lack the ability to actively remodel their cortex and hence just crumple under the osmotic pressure change.
The resulting shapes of the passive vesicles in nonadhered and adhered conditions are indistinguishable. It demonstrates that under experimental conditions presented here, adhesive forces alone are not sufficient to induce a shape change in the passive elastic shell. The contact angle of passive vesicles could not be determined after deflation because of its highly deformed random shape near the surface. A comparison between the shape acquired by a weakly adhered passive and an active vesicle after 48% volume reduction can be seen in Video S8.
As discussed in the previous section, passive vesicles show abrupt changes in their shape caused by the sudden crumpling of the elastic actin cortex. For nonadhering passive vesicles, we observed that the cortex crumples only when the osmotically induced deformation forces are sufficiently high (Fig. 3 b). In comparison, the attractive forces from the small adhesion zone are too small to induce any shape remodeling in passive vesicles. Consequently, any excess area resulting from deflation remains trapped as randomly distributed invaginations and is not available to increase the adhesion area.
In the case of active cytoskeletal vesicles, the presence of myosin motors develops activity in the cortex and enables cortical remodeling. The osmotic pressure and the adhesion forces both are able to induce deformations. During adhesion-area formation, the osmotic pressure continuously yields sufficient excess area, which is then continuously pulled laterally by the adhesive molecules. Excess area of the osmotically induced deformations is thus made available for adhesion by the motor activity. Our experiments show that the availability of excess membrane area depends on the ability of the actin cortex to remodel actively.
## Author Contributions
R.M., E.L., and A.R.B. planned the experiments. R.M. and E.L. performed the experiments and analyzed the data. R.M., E.L., and A.R.B. wrote the article.
## Acknowledgments
Research was supported by the German Science Foundation (DFG) via the SFB863 and the Nanosystems Initiative Munich.
## Supporting Material
• Document S1. Supporting Materials and Methods and Figs. S1–S5
## References
• Albersdörfer A.
• Feder T.
• Sackmann E.
Adhesion-induced domain formation by interplay of long-range repulsion and short-range attraction force: a model membrane study.
Biophys. J. 1997; 73: 245-257
• Cuvelier D.
• Nassoy P.
Hidden dynamics of vesicle adhesion induced by specific stickers.
Phys. Rev. Lett. 2004; 93: 228101
• Goennenwein S.
• Tanaka M.
• Sackmann E.
• et al.
Functional incorporation of integrins into solid supported membranes on ultrathin films of cellulose: impact on adhesion.
Biophys. J. 2003; 85: 646-655
• Reister-Gottfried E.
• Sengupta K.
• Smith A.S.
• et al.
Dynamics of specific vesicle-substrate adhesion: from local events to global dynamics.
Phys. Rev. Lett. 2008; 101: 208103
• Sackmann E.
• Smith A.S.
Physics of cell adhesion: some lessons from cell-mimetic systems.
Soft Matter. 2014; 10: 1644-1659
• Lipowsky R.
• Rouhiparkouhi T.
• Weikl T.R.
• et al.
Domain formation in cholesterol-phospholipid membranes exposed to adhesive surfaces or environments.
Soft Matter. 2013; 9: 8438-8453
• Franke T.
• Lipowsky R.
• Helfrich W.
Adhesion of lipid membranes induced by CrCl 3.
EPL. 2006; 76: 339-345
• Smith A.S.
• Sengupta K.
• Sackmann E.
• et al.
Force-induced growth of adhesion domains is controlled by receptor mobility.
Proc. Natl. Acad. Sci. USA. 2008; 105: 6906-6911
• Murrell M.P.
• Voituriez R.
• Gardel M.L.
• et al.
Nat. Phys. 2014; 10: 163-169
• Bernard A.-L.
• Guedeau-Boudeville M.-A.
• di Meglio J.-M.
• et al.
Strong adhesion of giant vesicles on surfaces? dynamics and permeability.
Langmuir. 2000; 16: 6809-6820
• Rädler J.O.
• Feder T.J.
• Sackmann E.
• et al.
Fluctuation analysis of tension-controlled undulation forces between giant vesicles and solid substrates.
Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics. 1995; 51: 4526-4536
• Lipowsky R.
• Seifert U.
Mol. Cryst. Liq. Cryst. 1991; 202: 17-25
• Bruinsma R.
• Behrisch A.
• Sackmann E.
Adhesive switching of membranes: experiment and theory.
Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics. 2000; 61: 4253-4267
• Seifert U.
• Lipowsky R.
Phys. Rev. A. 1990; 42: 4768-4771
• Capovilla R.
• Guven J.
Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 2002; 66: 041604
• Helfrich W.
Elastic properties of lipid bilayers: theory and possible experiments.
Z. Naturforsch. C. 1973; 28: 693-703
• Diz-Muñoz A.
• Fletcher D.A.
• Weiner O.D.
Use the force: membrane tension as an organizer of cell shape and motility.
Trends Cell Biol. 2013; 23: 47-53
• Loiseau E.
• Schneider J.A.
• Bausch A.R.
• et al.
Shape remodeling and blebbing of active cytoskeletal vesicles.
• MacLean-Fletcher S.
• Pollard T.D.
Identification of a factor in conventional muscle actin preparations which inhibits actin filament self-association.
Biochem. Biophys. Res. Commun. 1980; 96: 18-27
• Spudich J.A.
• Watt S.
The regulation of rabbit skeletal muscle contraction. I. Biochemical studies of the interaction of the tropomyosin-troponin complex with actin and the proteolytic fragments of myosin.
J. Biol. Chem. 1971; 246: 4866-4871
• Margossian S.S.
• Lowey S.
Preparation of myosin and its subfragments from rabbit skeletal muscle.
in: Methods in Enzymology. Structural and Contractile Proteins Part B: The Contractile Apparatus and the Cytoskeleton. Volume 85. Academic Press, 1982: 55-71
• Kinoshita M.
• Field C.M.
• Mitchison T.J.
• et al.
Self- and actin-templated assembly of mammalian septins.
Dev. Cell. 2002; 3: 791-802
• Field C.M.
• Alberts B.M.
Anillin, a contractile ring protein that cycles from the nucleus to the cell cortex.
J. Cell Biol. 1995; 131: 165-178
• Piekny A.J.
The myriad roles of Anillin during cytokinesis.
Semin. Cell Dev. Biol. 2010; 21: 881-891
• Abkarian M.
• Loiseau E.
• Massiera G.
Continuous droplet interface crossing encapsulation (cDICE) for high throughput monodisperse vesicle design.
Soft Matter. 2011; 7: 4610-4614
• Claudet C.
• In M.
• Massiera G.
Method to disperse lipids as aggregates in oil for bilayers production.
Eur. Phys. J. E Soft Matter. 2016; 39: 9
• Schindelin J.
• Arganda-Carreras I.
• Cardona A.
• et al.
Fiji: an open-source platform for biological-image analysis.
Nat. Methods. 2012; 9: 676-682
• Steinkühler J.
• Agudo-Canalejo J.
• Dimova R.
• et al.
Modulating vesicle adhesion by electric fields.
Biophys. J. 2016; 111: 1454-1464
• Gruhn T.
• Franke T.
• Dimova R.
• Lipowsky R.
Novel method for measuring the adhesion energy of vesicles.
Langmuir. 2007; 23: 5423-5429
• Murrell M.
• Pontani L.L.
• Sykes C.
• et al.
Spreading dynamics of biomimetic actin cortices.
Biophys. J. 2011; 100: 1400-1409
• Guevorkian K.
• Manzi J.
• Sykes C.
• et al.
Mechanics of biomimetic liposomes encapsulating an actin shell.
Biophys. J. 2015; 109: 2471-2479
• Käs J.
• Sackmann E.
Shape transitions and shape stability of giant phospholipid vesicles in pure water induced by area-to-volume changes.
Biophys. J. 1991; 60: 825-844
• Sackmann E.
• Duwe H.P.
• Engelhardt H.
Membrane bending elasticity and its role for shape fluctuations and shape transformations of cells and vesicles.
Faraday Discuss. Chem. Soc. 1986; 81: 281-290
• Seifert U.
Configurations of fluid membranes and vesicles. | 2023-03-25 08:06:08 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 2, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.47599029541015625, "perplexity": 10396.887838554514}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296945317.85/warc/CC-MAIN-20230325064253-20230325094253-00065.warc.gz"} |
https://community.wolfram.com/groups/-/m/t/2285459 | Any example of periodic columns in asymmetrical 1D cellular automata?
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Does anyone know of or is able to track down a 2-color, 1-D cellular automaton admitting an aperiodic initial configuration and a ruleset that is asymmetrical, and which has at least one (but not infinitely many) columns that are periodic or eventually periodic?I realize that sounds like a lot, so a word on motivation. It's still unproven whether or not the center column of Rule 30 ever becomes periodic. (It doesn't, but a proof is elusive.) This would be a generalized attack on the problem, showing that whole class doesn't exist. There are a couple of examples out there of rules that do have a central column which eventually or immediately cycles while other columns remain aperiodic (e.g. Rule 150), but every single one that I've seen has a symmetrical ruleset, meaning any symmetrical initial configuration can only reach states with the same axis of symmetry.To keep things reasonable, I limit us to 2 colors (read: cell states) since if we add a third, there are no doubt uninteresting solutions which paint a line of the third color down the center, and then ignore it while carrying on processing actively with the other two colors. That said, I think we can allow range to be arbitrarily large without a similar pitfall, so rulesets could draw from e.g. the 5 cells above them instead of the typical 3, although going too high might turn out similarly unhelpful.As additional clarification, such a CA would need to be on an open grid, not a torus. Periodic tiling in the initial row is fine so long as there's some finite, aperiodicity-seeding deviation from it at some point, e.g. the $0^\infty10^\infty$ classic start for Rule 30.In short, I'm wondering if anyone knows of any example where an asymmetrical ruleset could maintain a periodic column, or has any thoughts on this issue as to why such an arrangement is or is not plausible. My guess is that such examples do not exist or are very rare, partially based on having searched some and not found any, but I'd love to have someone else try their hand at finding one.And again, another way to state the main constraint is that there must be one or more periodic columns along with aperiodic columns occurring both somewhere left and somewhere right of the periodic column—one whole side devolving into periodicity is not what we're after. | 2021-06-19 14:53:49 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.49366629123687744, "perplexity": 686.2368274135173}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-25/segments/1623487648373.45/warc/CC-MAIN-20210619142022-20210619172022-00262.warc.gz"} |
https://www.physicsforums.com/threads/lim-x-inf-of-x-a-x-a-x-e.84089/ | # Lim(x->inf) of ((x+a)/(x-a))^x = e
#### techtown
lim(x-->inf) of ((x+a)/(x-a))^x = e
I started this problem and quickly became stuck, the question asks for what value of "a" is the following true:
lim(x-->inf) of ((x+a)/(x-a))^x = e
I took the natural log of both sides to start and got this:
lim(x-->inf) of x*ln((x+a)/(x-a)) = 1
I've tried going on from here but nothing in the end makes sense and i don't know any other way to start the problem; any help is appriciated, thanks.
Last edited:
#### Maxos
The text is wrong:
$$\lim_{\substack{x\rightarrow 0}}f(x) = 1 , \forall a \in \mathbb{R}$$
whereas
$$\lim_{\substack{x\rightarrow \infty}}f(x) = e^{2a}$$
Ok?
Last edited:
#### techtown
ah, yes, i did mean for x to go to infinity; but how did you get e^2a?
#### Maxos
$$\lim_{\substack{ x \rightarrow \infty}} {(\frac {x+a}{x-a})}^x = \lim_{\substack{ x \rightarrow \infty}} {(1+ \frac {2a}{x-a})}^x = \\ \lim_{\substack{ y \rightarrow \infty}} {(1+ \frac {2a}{y})}^{y+a}=$$
$$\lim_{\substack{y \rightarrow \infty}} {(1+ \frac {2a}{y})}^y {(1+ \frac {2a}{y})}^a = \\ \lim_{\substack{y\rightarrow \infty}}{(1+ \frac {2a}{y})}^y = e^{2a}$$
Last edited:
#### techtown
thank you, i think i have it now
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• Solo and co-op problem solving | 2019-10-18 10:50:59 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4525240957736969, "perplexity": 4959.132137409411}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-43/segments/1570986682037.37/warc/CC-MAIN-20191018104351-20191018131851-00434.warc.gz"} |
https://www.jefkine.com/deep/2016/08/01/initialization-of-deep-feedfoward-networks/ | # Initialization Of Deep Feedfoward Networks
Mathematics Behind Neural Network Weights Initialization - Part Two: In this second of a three part series of posts, we will attempt to go through the weight initialization algorithms as developed by various researchers taking into account influences derived from the evolution of neural network architecture and the activation function in particular.
## Introduction
Deep multi-layered neural networks often require experiments that interrogate different initialization routines, activations and variation of gradients across layers during training. These provide valuable insights into what aspects should be improved to aid faster and successful training.
For Xavier and Bengio (2010) [1] the objective was to better understand why standard gradient descent from random initializations was performing poorly in deep neural networks. They carried out analysis driven by investigative experiments that monitored activations (watching for saturations of hidden units) and gradients across layers and across training iterations. They evaluated effects on choices of different activation functions (how it might affect saturation) and initialization procedure (with lessons learned from unsupervised pre-training as a form of initialization that already had drastic impact)
A new initialization scheme that brings substantially faster convergence was proposed. In this article we discuss the algorithm put forward by Xavier and Bengio (2010) [1]
Earlier on, Bradley (2009) [2] found that in networks with linear activation at each layer, the variance of the back-propagated gradients decreases as we go backwards in the network. Below we will look at theoretical considerations and a derivation of the normalized initialization.
### Notation
1. $f$ is the activation function. For the dense artificial neural network, a symmetric activation function $f$ with unit derivative at $0\,(i.e\, f'(0) = 1)$ is chosen. Hyperbolic tangent and softsign are both forms of symmetric activation functions.
2. $z^i$ is the activation vector at layer $i$, $z^i = f(s^{i-1})$
3. $s^i$ is the argument vector of the activation function at layer $i$, $s^i = z^{i-1}w^i + b^i$
4. $w^i$ is the weight vector connecting neurons in layer $i$ with neurons in layer $i+1$.
5. $b^i$ is the bias vector on layer $i$.
6. $x$ is the network input.
From the notation above, it is easy to derive the following equations of back-propagation
The variances will be expressed with respect to the input, output and weight initialization randomness. Considerations made include:
• Initialization occurs in a linear regime
• Weights are initialized independently
• Input feature variances are the same $( =Var[x])$
• There is no correlation between our input and our weights and both are zero-mean.
• All biases have been initialized to zero.
For the input layer, $X \in \mathbb{R}^{m \times n}$ with $n$ components each from $m$ training samples. Here the neurons are linear with random weights $W^{(in\rightarrow 1)} \in \mathbb{R}^{m \times a}$ outputting $S^{(1)} \in \mathbb{R}^{n \times a}$.
The output $S^{(1)}$ can be shown by the equations below:
Given $X$ and $W$ are independent, we can show that the variance of their product can be given by:
Considering our inputs and weights both have mean $0$, Eqn. $(3)$ simplifies to
$X_i$ and $W_i$ are all independent and identically distributed, we can therefore show that:
%
Further, lets now look at two adjacent layers $i$ and $i'$. Here, $n_i$ is used to denote the size of layer layer $i$. Applying the derivative of the activation function at $s_k^i$ yields a value of approximately one.
\begin{align} f'(s_k^{i}) \approx 1, \tag {4} \end{align} \
Then using our prior knowledge of independent and identically distributed $X_i$ and $W_i$, we have.
%
$Var[W^{i'}]$ in Eqn. $5$, is the shared scalar variance of all weights at layer $i'$. Taking these observations into consideration, a network with $d$ layers, will have the following Eqns.
We would then like to steady the variance such there is equality from layer to layer. From a foward-propagation point of view, to keep information flowing we would like that
%
From a back-propagation point of view, we would like to have:
%
For Eqns. $(8)$ and $(9)$ to hold, the shared scalar variances $n_{i'}Var[W^{i'}]$ in Eqn. $(5)$ should be $1$. This is the same as trying to ensure the variances of the input and output are consistent (realize that the technique used here helps avoid reducing or magnifying the signals exponentially hence mitigating the exploding or vanishing gradient problem):
As a compromise between the two constraints (representing back-propagation and foward-propagation), we might want to have \begin{align} \forall (i), \quad \frac{2}{n_{i} + n_{i+1}} \tag {12} \end{align}
In the experimental setting chosen by Xavier and Bengio (2010) [1], the standard initialization weights $W_{i,j}$ at each layer using the commonly used heuristic: \begin{align} W_{i,j} \sim U \left[ -\frac{1}{\sqrt n}, \frac{1}{\sqrt n} \right], \tag {13} \end{align}
where $U \left[ -\theta, \theta \right]$ is the uniform distribution in the interval $\left(-\theta, \theta \right)$ and $n$ is the size of the previous layer (the number of columns of $W$).
For uniformly distributed sets of weights $W \overset{iid}{\sim} U \left[ -\theta, \theta \right]$ with zero mean, we can use the formula $\left\{ x \sim U[a,b] \implies Var[x] = \frac{(b-a)^2}{12} \right\}$ for variance of a uniform distribution to show that:
Substituting Eqn. $(14)$ into an Eqn. of the form $nVar[W] = 1$ yields:
The weights have thus been initialized from the uniform distribution over the interval \begin{align} W \sim U \left[ -\frac{\sqrt 3}{\sqrt {n}}, \frac{\sqrt 3}{\sqrt {n}} \right] \tag{15} \end{align}
The normalization factor may therefore be important when initializing deep networks because of the multiplicative effect through layers. The suggestion then is of an initialization procedure that maintains stable variances of activation and back-propagated gradients as one moves up or down the network. This is known as the normalized initialization \begin{align} W \sim U \left[ -\frac{\sqrt 6}{\sqrt {n_{i} + n_{i+1}}}, \frac{\sqrt 6}{\sqrt {n_{i} + n_{i+1}}} \right] \tag{16} \end{align}
The normalized initialization is a clear compromise between the two constraints involving $n_{i}$ and $n_{i+1}$ (representing back-propagation and foward-propagation), If you used the input $X \in \mathbb{R}^{m \times n}$, the normalized initialization would look as follows: \begin{align} W \sim U \left[ -\frac{\sqrt 6}{\sqrt {n + m}}, \frac{\sqrt 6}{\sqrt {n + m}} \right] \tag{17} \end{align}
### Conclusions
In general, from Xavier and Bengio (2010) [1] experiments we can see that the variance of the gradients of the weights is the same for all the layers, but the variance of the back-propagated gradient might still vanish or explode as we consider deeper networks.
### Applications
The initialization routines derived here, more famously known as “Xavier Initialization” have been successfully applied in various deep learning libraries. Below we shall look at Keras a minimalist, highly modular neural networks library, written in Python and capable of running on top of either TensorFlow or Theano.
The initialization routine here is named “glorot_” following the name of one of the authors Xavier Glorot [1]. In the code snippet below, glorot_normal is the implementation of Eqn. $(12)$ while glorot_uniform is the equivalent implementation of Eqn. $(15)$
### References
1. Glorot Xavier, and Yoshua Bengio. “Understanding the difficulty of training deep feedforward neural networks.” Aistats. Vol. 9. 2010. [PDF]
2. Bradley, D. (2009). Learning in modular systems. Doctoral dissertation, The Robotics Institute, Carnegie Mellon University.
3. Wikipedia - Variance: “Product of independent variables”. | 2019-02-17 06:19:57 | {"extraction_info": {"found_math": true, "script_math_tex": 63, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 18, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8735844492912292, "perplexity": 1098.3777317654612}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-09/segments/1550247481624.10/warc/CC-MAIN-20190217051250-20190217073250-00101.warc.gz"} |
https://itprospt.com/qa/311137/how-do-you-write-each-fraction-or-mixed-number-as | 1
# How do you write each fraction or mixed number as a decimal: 3/11?
## Question
###### How do you write each fraction or mixed number as a decimal: 3/11?
How do you write each fraction or mixed number as a decimal: 3/11?
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https://boyslife.org/games/write-a-funny-caption/164893/write-a-funny-caption-for-this-photo-102/?replytocom=1800359 | What’s going on in this picture? What is that “shark” saying, doing or thinking?
If you can think of a funny caption for this photo, just post it in the comment form at the bottom of this page. After we approve it, your funny caption will be on this page for everyone to read.
1 Comment on Write a Funny Caption For This Photo
1. Bow down to the king of the ocean! | 2020-08-05 02:39:47 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8525754809379578, "perplexity": 1275.510731540902}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-34/segments/1596439735906.77/warc/CC-MAIN-20200805010001-20200805040001-00282.warc.gz"} |
https://meangreenmath.com/2020/07/20/engaging-students-finding-points-on-the-coordinate-plane-4/ | # Engaging students: Finding points on the coordinate plane
In my capstone class for future secondary math teachers, I ask my students to come up with ideas for engaging their students with different topics in the secondary mathematics curriculum. In other words, the point of the assignment was not to devise a full-blown lesson plan on this topic. Instead, I asked my students to think about three different ways of getting their students interested in the topic in the first place.
I plan to share some of the best of these ideas on this blog (after asking my students’ permission, of course).
This student submission comes from my former student Tiger Hersh. His topic, from Pre-Algebra: finding points on the coordinate plane.
A2 : How could you as a teacher create an activity or project that involves your topic?
To find a point on a 2-D coordinate plane we would need to have an x-axis and y-axis. Many things in the real world could act as a coordinate plane and that could also be used to create an activity or project. One of those things could be where the students could use a Nerf gun and fire it at a wall with a coordinate plane. This activity would not only be engaging for students but also help them understand how to plot the points on a coordinate plane, but also show students how to find the point on the coordinate plane.
Students will group up and take turns firing darts at a wall that would have a coordinate plane on it. Each group will have different color darts to indicate where each group has plotted their point. Each student in each group will fire two darts at the coordinate plane; After each student has finished plotting their points they will approximate the point and record it down on their worksheet.
Curr1 : How can this topic be used in your students’ future courses in mathematics or science?
Plotting points on a 2-D coordinate plane is used in almost every future course in mathematics. You can observe the usage of 2-D coordinate planes in Geometry, Algebra 1, Algebra 2, Pre-Cal, and so on.
In Geometry you can plot the points of a triangle on the coordinate plane to then find the distance between them with the distance formula or you could find the midpoint between each point using the midpoint formula. These are only some examples that plot points on the 2-D coordinate plane.
In Algebra 1/2 you can see that you can find the slope between two points using the slope equation. You can also use this concept to plot points for equations that involve the slope-intercept form, polynomials, the unit circle, shapes, etc. The points that are plotted could also show what is happening over a period of time and also give us an idea what the equation is trying to tell us.
In Pre-cal you plot points on a coordinate plane in the equation $x^2+y^2=1$ to form the unit circle and also plot points when you have to rotate or transform a shape or equation.
Cul1 : How has this topic appeared in pop culture (movies, TV, current music, video games, etc.)?
The game Starcraft 2 is a real-time strategy (RTS) game where you have to build an economy to fuel an army and beat the opponent by destroying their infrastructure, economy, or army. Interestingly when you build your building you notice that you are building on a 2-D coordinate plane.
The game itself is in its own 2-D coordinate plane where you have to plan where to move at certain points and also place your buildings at certain points to either block off a ramp or create a concave for your units so that they are able to deal more damage towards the opponent. There are also times in the game where you have to keep in mind about key parts in the map where your opponent is, where your next bases are, where proxies are, and where to set up counter attacks on your opponent. | 2020-10-22 09:43:13 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 1, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4195619821548462, "perplexity": 436.59753793991536}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-45/segments/1603107879362.3/warc/CC-MAIN-20201022082653-20201022112653-00353.warc.gz"} |
https://www.physicsforums.com/threads/kinematics-question-using-vectors.932046/ | # Kinematics question using vectors
Tags:
1. Nov 19, 2017
### Ofir12
A child is in danger of drowning in the river. The river has a current of 2.5 km/hr . The child is 0.6 km from the shore. A rescue boat with speed 20.0 km/hr (with respect to the water) ,located 0.8km downstream, sets off from the shore.
What would be the optimum angle (shore -> boat ) to reach the child as fast as possible ?
And how long will it take to the boat to reach him?
I'm not sure if this is the correct way to draw this :
3. The attempt at a solution
a = 0.6 km
b = 0.8 km
v = 20.0km
u = 2.5km
c = √(a² + b²)
how do I find the angle?
I feel a little bit lost, your help is appriciated.
Thanks.
Last edited: Nov 19, 2017
2. Nov 19, 2017
### haruspex
The optimum angle or some angle in the diagram? For reference, it would be handy to label some points, like B for launch point of boat, etc.
What are your thoughts on the optimisation?
3. Nov 19, 2017
### Ofir12
I'm not sure if this is the right way to draw this, and how to approach the question.
I know that i'm looking for an angle between 2 vectors (shore and boat).
Actually they didn't mention the word "optimum" in the question, they just asked what is the angle. (I assumed that it should be optimum, buy maybe im wrong)
4. Nov 19, 2017
### Delta²
Well this problem is kind of strange for me as to what the problem wants. If the boat isn't allowed to change angle during its trip, then there is only one possible angle (there will be a system of two equations with two unknowns, the angle and the time , this system might have one solution or none) for which the boat reaches the child.
I suggest for starting, that you assume that $\theta$ is the angle. Find the velocities $v_x$ and $v_y$ of the boat, and make two equations for the distance travelled $s_x$ and $s_y$ in each axis. | 2017-12-17 02:47:56 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.49496695399284363, "perplexity": 752.0215099914288}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-51/segments/1512948592846.98/warc/CC-MAIN-20171217015850-20171217041850-00342.warc.gz"} |
http://mathhelpforum.com/advanced-algebra/175539-abelian-normal-group.html | # Math Help - abelian normal group
1. ## abelian normal group
Let $G$ be a group of order $3825$. Prove that if $H$ is a normal subgroup of order $17$ in $G$ then $H \leq Z(G)$, where $Z(G)$ represents the center of $G$.
(Please do not use sylow's or cauchy's theorems.)
2. Originally Posted by abhishekkgp
Let $G$ be a group of order $3825$. Prove that if $H$ is a normal subgroup of order $17$ in $G$ then $H \leq Z(G)$, where $Z(G)$ represents the center of $G$.
(Please do not use sylow's or cauchy's theorems.)
If you don't want Sylow and Cauchy theorems, then I suppose you want even less semidirect
products and stuff, thus the question is: what do you want? What stuff is allowed or wanted by you?
Tonio
3. Is there a nice way to do this if the Sylow theorems are allowed? I can't see anything short of a group classification argument.
4. Originally Posted by roninpro
Is there a nice way to do this if the Sylow theorems are allowed? I can't see anything short of a group classification argument.
Indeed, I feel as though the simplest way to do this is to note that it is of the form $p^2q$ with $p,q$ prime and $q\notequiv 1\text{ mod }p$ and thus abelian...that said the only ways I know how to prove this are Sylow's theorems or rep. theory.
5. Just noting the arithmetic: $3825=3^2\cdot 5^2\cdot 17$.
6. Originally Posted by abhishekkgp
Let $G$ be a group of order $3825$. Prove that if $H$ is a normal subgroup of order $17$ in $G$ then $H \leq Z(G)$, where $Z(G)$ represents the center of $G$.
(Please do not use sylow's or cauchy's theorems.)
(*) If H is a subgroup of G, then the factor group $N_G(H)/C_G(H)$ is isomorphic to a subgroup of Aut H (Hungerford, "Algebra", p92).
By assumption, $N_G(H)=G$. Since H is a group of order 17, H is isomorphic to the cyclic group of order 17, i.e., $C_{17}$. Thus, |Aut(H)|=16.
Now, $|G/C_G(H)|$ divides both 16 and 3825 by Lagrange's theorem and (*), it follows that $|G/C_G(H)|=1$. Can you conclude from here? | 2016-07-31 01:45:30 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 33, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9046382904052734, "perplexity": 144.17823667378173}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-30/segments/1469258948335.92/warc/CC-MAIN-20160723072908-00069-ip-10-185-27-174.ec2.internal.warc.gz"} |
https://meishi-restaurant.nl/12280/how-is-nickel-extracted-from-nickel-ore/ | how is nickel extracted from nickel ore
# how is nickel extracted from nickel ore
### How Is Nickel Extracted? Reference
Nickel is extracted from ores via the Mond process, in which nickel oxides are purified through multiple steps into pure nickel metal. It is placed with hydrogen and carbon monoxide gases at 122 degrees Fahrenheit, which converts it to impure nickel. This impure nickel then reacts with the carbon monoxide, becoming nickel tetracarbonyl.
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### Nickel: smelting, producing-Metalpedia
Nickel is recovered through extractive metallurgy: it is extracted from its ores by conventional roasting and reduction processes that yield a metal of greater than 75% purity. In many stainless steel applications, 75% pure nickel can be used without further purification, depending on
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### Nickel processing Britannica
Nickel processing, preparation of the metal for use in various products. Although it is best known for its use in coinage, nickel (Ni) has become much more important for its many industrial applications, which owe their importance to a unique combination of properties. Nickel has a relatively high
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### Lateritic nickel ore deposits - Wikipedia
Extraction. Nickel laterites are a very important type of nickel ore deposit. They are growing to become the most important source of nickel metal for world demand (currently second to sulfide nickel ore deposits). Nickel laterites are generally mined via open cut mining methods. Nickel is extracted from the ore by a variety of process routes.
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### US3953200A - Nickel extraction process - Google Patents
A process for extracting nickel from a low-grade nickel complex ore. The process features simultaneously grinding and leaching of the ore with an aqueous ammoniacal leach solution. US3953200A - Nickel extraction process - Google Patents nickel ore
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Cited by: 29
### Extraction of Nickel - QS Study
Extraction of Nickel . Main ore is Pentlandite; Nickel is extracted from ores through the Mond procedure, in which nickel oxides are purified throughout several steps into pure nickel metal. It is placed with hydrogen and carbon monoxide gases at 122 degrees Fahrenheit, which converts it to impure nickel.
More
### Nickel processing - Extraction and refining Britannica
Nickel processing - Nickel processing - Extraction and refining: The extraction of nickel from ore follows much the same route as copper, and indeed, in a number of cases, similar processes and equipment are used. The major differences in equipment are the use of higher-temperature refractories and the increased cooling required to accommodate the higher operating temperatures in nickel
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### Nickel - Wikipedia
Nickel is obtained through extractive metallurgy: it is extracted from the ore by conventional roasting and reduction processes that yield a metal of greater than 75% purity. In many stainless steel applications, 75% pure nickel can be used without further purification, depending on the impurities.
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Group: group 10
### Copper Nickel Solvent Extraction
Nickel and copper were co-extracted from ammoniacal ammonium sulfate leach liquors (pH-9.5) with LIX 64N extractant in a oratory-size mixer-settler continuous circuit. Three extraction stages resulted in >99-pct extraction of nickel, substantial copper extraction, and essentially no cobalt extraction
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### Nickel Ore - an overview ScienceDirect Topics
Nickel salts, such as nickel chloride, nickel sulfate, and nickel nitrate, are also produced. Stated the sources and forms of natural occurrence of nickel, it is easy to reconcile that the commonly used extraction processes of nickel from its ores are carried out with roasting followed by reduction.
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Nov 16, 2011 Nickel Extraction koreahiho. Loading Unsubscribe from koreahiho? Froth Flotation of Ultramafic Nickel Ore - No Pre-treatment - Duration: 1:11. Salah Uddin 102,855 views.
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: koreahiho
### Extraction of Nickel Nickel Ore Mining Mining
Oct 16, 2019 Extraction of Nickel. This introduces the extraction of nickel process and characteristics of laterite nickel ore dressing, highlights the nickel ore crushing, washing in the nickel production process design.. 1 Description of nickel ore. The laterite nickel ore is complex in composition and can be roughly divided into two types: limonite type and silicon magnesium-nickel type.
More
### Extraction of Nickel and Cobalt from Sulfide Ores
The present study proposes a new smelting process for limonitic nickeliferous laterite ore in order to separate nickel and cobalt from the ore and produce a nickel matte at lower smelting
More
### Direct extraction of nickel and iron from laterite ores
Carbonyl method of extraction of Ni and Fe from laterite ore was applied to several types of ores. • Ore reduction with hydrogen gas was compared with reduction by CO/CO 2 gas mixture.. Extraction of nickel and iron was done at elevated pressure and temperature.
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### Extraction of Nickel - QS Study
Extraction of Nickel . Main ore is Pentlandite; Nickel is extracted from ores through the Mond procedure, in which nickel oxides are purified throughout several steps into pure nickel metal. It is placed with hydrogen and carbon monoxide gases at 122 degrees Fahrenheit, which converts it to impure nickel.
More
### (PDF) Nickel extraction from nickel matte
Nickel extraction from nickel matte. which could easily be adapted to take this nickel intermediate giving them significant potential benefits especially as nickel laterite ore grades diminish
More
### How is Nickel Mined - Want to Know it
Nickel is often extracted from its ore by roasting at high temperatures. In some cases this is enough to separate the nickel in other cases strong chemicals are used to separate the ore. Nickel is also refined using electro refining. In this process the ore is placed in a nickel
More
### Nickel Ore - an overview ScienceDirect Topics
Nickel salts, such as nickel chloride, nickel sulfate, and nickel nitrate, are also produced. Stated the sources and forms of natural occurrence of nickel, it is easy to reconcile that the commonly used extraction processes of nickel from its ores are carried out with roasting followed by reduction.
More
### A New Process for Cobalt Nickel Separation
excellent cobalt-nickel separation primary leach liquor by Cyanex 272. However, manganese extraction from the leach liquor along with cobalt could not be avoided, thus increasing the cost of the process. For sulphide ores, there is another alternative; if the ore can be concentrated by flotation, matte smelting is used instead of leaching.
More
### NICKEL AND COBALT ORES: FLOTATION
The usual method of nickel extraction from sulRde ores is through the production of nickel matte after enriching the nickel content of the ore. This is com-monly carried out by magnetic separation, Sotation, or a combinationof both after the ore is comminuted to below 200 m in size. The enrichment depends
More
### Nickel Mining and Processing: Everything you Need to Know
Nickel mining occurs through extractive metallurgy, which is a material science that covers various types of ore, the washing process, concentration and separation, chemical processes and the extraction
More
### Extracting Nickel Metal From US Nickels - YouTube
Oct 09, 2017 Hey Everyone, In this WEEKS EPISODE OF BMS THAT IS SO ON-TIME, I try to extract the nickel metal out of US Nickels using hydrochloric acid. As it turns out, I run into a major problem.
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### Extractive Metallurgy: Extraction of Lateritic Nickel Ore
Dec 23, 2008 Extraction of Lateritic Nickel Ore (Hydrometallurgical Route) Genesis And Types Of Nickel Laterites. Usually, nickel ore type in the world are sulphide and oxide minerals. In East Indonesia, we often see nickel oxide mineral that is called nickel laterite. Lateritic nickel ores formed by intensive tropical weathering of ultramafic rocks above
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### Nickel - wwwchem.uwimona.edu.jm
nickel deposits in the world. Extraction of Nickel In 1899 Ludwig Mond developed a process for extracting and purifying nickel. The so-called "Mond Process" involves the conversion of nickel oxides to pure nickel metal. The oxide is obtained from nickel ores by a series of treatments including concentration, roasting and smelting of the minerals.
More
### Nickel Mining and Processing: Everything you Need to Know
Nickel mining occurs through extractive metallurgy, which is a material science that covers various types of ore, the washing process, concentration and separation, chemical processes and the extraction
More
### NICKEL AND COBALT ORES: FLOTATION
The usual method of nickel extraction from sulRde ores is through the production of nickel matte after enriching the nickel content of the ore. This is com-monly carried out by magnetic separation, Sotation, or a combinationof both after the ore is comminuted to below 200 m in size. The enrichment depends
More
### CN102268537A - A method of extracting cobalt from nickel
The invention discloses a method for extracting cobalt and nickel from laterite-nickel ore, which comprises the following steps of: performing roasting preprocessing on the laterite-nickel ore; blending the roasted material with water to obtain pulp; directly adding ion exchange resin for leaching and adsorbing the nickel and cobalt; separating the ion exchange resin from the ore pulp; eluting
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### Enhanced methods for nickel recovery from low-grade ores
Sep 06, 2017 Nickel Extraction from Bleed Streams with SX. Another method for extraction of nickel from the bleed stream is the use of solvent extraction (SX). Copper-selective solvents can be chosen, and many steps are followed to get nickel and copper powder from the bleed.
More
### nickel extract from ore - pavages
Nickel - Extraction and Purification - Mond Process. The Mond process, sometimes known as the carbonyl process is a technique created by Ludwig Mond in 1890 to extract and purify nickel. The process was used commercially before the end of the 19th century. It is done by converting nickel oxides (nickel combined with oxygen) into pure nickel.
More
### Nickel and its extraction
May 03, 2018 HYDROMETALLURGICAL APPROACHES: (Cu₈Ni₁₆Fe₁₀)→Limonite (FeO(OH).nH₂O) • Solvent Extraction Electrowinning approach to lateritic ore beneficiation, is a hydrometallurgical method that relies on leaching, extractants, and electrowinning to produce nickel from ore Heap leaching is an industrial mining process to extract precious
More
### Synchronous extraction of nickel and copper from a mixed
Mar 10, 2018 In this study, ammonium sulfate roasting technique was used to process a typical Chinese mixed oxide-sulfide nickel ore to extract copper and nickel directly in a relatively low temperature range (300500 °C) under the condition of inletting oxygen gas.
More
### Nickel: Learn How To Trade Precious Metals at Commodity
Nickel occurs in ore bodies, and breaking down these ore bodies to extract nickel expends energy. Producing nickel requires ample supplies of coal, electricity and crude oil. Mines and blast furnaces utilize energy to extract nickel ores from the ground and process it into nickel. These costs can have a big effect on primary production.
More
### How is Nickel Mined - Want to Know it
Nickel is often extracted from its ore by roasting at high temperatures. In some cases this is enough to separate the nickel in other cases strong chemicals are used to separate the ore. Nickel is also refined using electro refining. In this process the ore is placed in a nickel
More
### Nickel Geoscience Australia
Nickel is a hard silver-white metal with a high melting point and can withstand very low temperatures. Nickel is rarely found in the earth in its pure form; it mixes well with other metals to make many useful alloys. Nickel is malleable and ductile (can be beaten and drawn out into a wire) and is rust-resistant.
More
### Nickel - Agiboo CTRM
Nickel mined from lateritic ore is mined from various depths beneath the surface using large earth-moving equipment. The other nickel containing type of ore, sulfidic ore, is usually found in combination with copper ore and is mined underground. Nickel from lateritic ore is extracted
More
### Extraction of Nickel and Cobalt from Sulfide Ores
The present study proposes a new smelting process for limonitic nickeliferous laterite ore in order to separate nickel and cobalt from the ore and produce a nickel matte at lower smelting
More
### Extraction of Nickel Nickel Ore Mining Mining
Oct 16, 2019 Extraction of Nickel. This introduces the extraction of nickel process and characteristics of laterite nickel ore dressing, highlights the nickel ore crushing, washing in the nickel production process design.. 1 Description of nickel ore. The laterite nickel ore is complex in composition and can be roughly divided into two types: limonite type and silicon magnesium-nickel type.
More
### (PDF) Nickel extraction from nickel matte
Nickel extraction from nickel matte. which could easily be adapted to take this nickel intermediate giving them significant potential benefits especially as nickel laterite ore grades diminish
More
### Nickel Mines, Nickel Extraction Process, Nickel Recovery
Copper- Nickel Ore Flotation Process. When process copper-sulfide nickel ore, collector and frother will be used in order to better results. A basic principle of copper-sulfide nickel ore process is that it is better to let copper assimilate into nickel ore rather than the opposite. For it is easier to recovery cooper from nickel concentrate.
More
### Nickel and its extraction
May 03, 2018 HYDROMETALLURGICAL APPROACHES: (Cu₈Ni₁₆Fe₁₀)→Limonite (FeO(OH).nH₂O) • Solvent Extraction Electrowinning approach to lateritic ore beneficiation, is a hydrometallurgical method that relies on leaching, extractants, and electrowinning to produce nickel from ore Heap leaching is an industrial mining process to extract precious
More
### Enhanced methods for nickel recovery from low-grade ores
Sep 06, 2017 Nickel Extraction from Bleed Streams with SX. Another method for extraction of nickel from the bleed stream is the use of solvent extraction (SX). Copper-selective solvents can be chosen, and many steps are followed to get nickel and copper powder from the bleed.
More
### A New Process for Cobalt Nickel Separation
excellent cobalt-nickel separation primary leach liquor by Cyanex 272. However, manganese extraction from the leach liquor along with cobalt could not be avoided, thus increasing the cost of the process. For sulphide ores, there is another alternative; if the ore can be concentrated by flotation, matte smelting is used instead of leaching.
More
### Nickel: Learn How To Trade Precious Metals at Commodity
Nickel occurs in ore bodies, and breaking down these ore bodies to extract nickel expends energy. Producing nickel requires ample supplies of coal, electricity and crude oil. Mines and blast furnaces utilize energy to extract nickel ores from the ground and process it into nickel. These costs can have a big effect on primary production.
More
### nickel extract from ore - pavages
Nickel - Extraction and Purification - Mond Process. The Mond process, sometimes known as the carbonyl process is a technique created by Ludwig Mond in 1890 to extract and purify nickel. The process was used commercially before the end of the 19th century. It is done by converting nickel oxides (nickel combined with oxygen) into pure nickel.
More
### Indonesian nickel ore export ban implications for nickel
Sep 04, 2019 Likewise, while it is probable that we will need to reduce out Chinese nickel in NPI production from the current forecast of 516 kt, this could still prove conservative depending on how much ore
More
### EXTRACTION OF NICKEL AND COBALT FROM LATERITIC
of the ore sample. The atmospheric leaching experiments were conducted on the 70% limonitic 30% nontronitic ore mixture obtained from the Gördes open pit mine. Considering the similar studies from literature and highest nickel and cobalt extraction into account, the process parameters optimized as; leaching at 104°C
More
### Processing of Nickel Laterite Ores on the Rise
Lateritic Nickel Ore Processing. While sulfide nickel ores are processed via upgrading to concentrates and then smelting, this approach is not applicable to laterite ores. A variety of approaches are availe to process nickel laterite ores, with the most prevalent approaches explained below.
More
### EU Challenges Indonesian Nickel Ore Export Ban to WTO
Sep 25, 2019 Initially, ore exports were originally banned in 2014. In 2017, Indonesia announced that it was in a position to allow nickel ore to be exported-only those with a nickel content of less than 1.7 per cent. China’ laterite nickel mines are all dependent on imports, mainly from the
More
### How is Nickel Mined - Want to Know it
Nickel is often extracted from its ore by roasting at high temperatures. In some cases this is enough to separate the nickel in other cases strong chemicals are used to separate the ore. Nickel is also refined using electro refining. In this process the ore is placed in a nickel
More
### from what mineral do we extract nickel
extraction of nickel from its ore - Mining. Jan 15, 2013 Extractive Metallurgy: Extraction of Lateritic Nickel Ore Dec 20, 2008 Usually, nickel ore type in the world are sulphide and oxide minerals In East Indonesia, we often see nickel oxide mineral that is called nickel laterite »More detailed.
More
### metal - Extraction of nickel from its ores -
Nickel can be extracted directly from its ore by reduction by hydrogen or carbon monoxide at elevated temperature at $600\ \mathrm{^\circ C}$ to $650\ \mathrm{^\circ C}$: $$\ce{NiO + H2 -> Ni + H2O}$$ $$\ce{NiO + CO -> Ni + CO2}$$ Also, it can be extracted by treatment with dilute sulfuric acid following by
More
### Nickel - Extraction and Purification - Mond Process
Mond Process. The Mond process, sometimes known as the carbonyl process is a technique created by Ludwig Mond in 1890 to extract and purify nickel. The process was used commercially before the end of the 19th century. It is done by converting nickel oxides (nickel combined with oxygen) into pure nickel.
More | 2020-02-25 12:47:17 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.49685782194137573, "perplexity": 8918.265610438842}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-10/segments/1581875146066.89/warc/CC-MAIN-20200225110721-20200225140721-00247.warc.gz"} |
http://mathhelpforum.com/number-theory/101227-number-theory-primes.html | 1. ## Number theory(Primes)
*Determine whether the following assertions are true or false. if true, prove the result, and if false, give a counter example
2. If p is a prime and p/(a^2+b^2) and p/(b^2+c^2) then p/(a^2-c^2).
2. Hint : if $p|a,\: p|b$ then $p|(a\pm b)$
3. ## help me pls
oh bruno, i don't really get it..can u help me
4. If $p|a,\: p|b$ then $a=pm,\: b=pn$. Then $a \pm b = pm \pm pn = p(m \pm n)$, so $p|(a \pm b)$.
Now how can you get $a^2-c^2$ from $a^2+b^2$ and $b^2+c^2$?
5. ## primes
i'm still blurred...sorry i still don't get it. oh..is it true? is it the final answer or do i need to elaborate it further?
6. Exactly one minute has gone by between my post and your call for more help. Perhaps taking five minutes to try to understand wouldn't do any harm.
If you can't even judge by yourself whether this is the answer or not, you might want to go back to your textbook. Do you even understand the statement of the problem?
7. Maybe this will help:
We will use some substitution, let $a^2=x, \ b^2=y$ and $c^2=z$
So we have $p|x+y$ and $p|y+z$
Note that $a^2 - c^2= x-z$, so we are trying to see if $p|x-z$
In case Bruno's proof confused you because he used $a$ and $b$ also, I'll put it here again with different letters, and with abit more detail.
If $p|g$ and $p|h$ then there exists $m$ and $n$ such that $g=pm$ and $h=pn$. So $g \pm h = pm \pm pn = p(m \pm n)$.
Note that the $\pm$ just means that it works for both addition and subtraction.
Now, $m \pm n$ is just an integer, which we can designate as $l$. So, $g \pm h = p(m \pm n) = pl$. Since $l$ exists, by definition $p|g \pm h$
What Bruno is asking is that if we let $x+y=g$ and $y+z=h$, is there a way we can add or subtract $g$ or $h$ so that we get $x-z$ | 2013-05-23 17:30:34 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 35, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8466748595237732, "perplexity": 264.48849478668734}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2013-20/segments/1368703635016/warc/CC-MAIN-20130516112715-00012-ip-10-60-113-184.ec2.internal.warc.gz"} |
https://socratic.org/questions/why-is-benzene-planar-and-cyclohexane-is-non-planar | # Why is benzene planar and cyclohexane nonplanar?
Dec 2, 2015
Short answer: Benzene is planar because its carbon atoms are ${\text{sp}}^{2}$ hybridized, and cyclohexane is nonplanar because its carbon atoms are ${\text{sp}}^{3}$ hybridized.
#### Explanation:
Benzene
The structure of benzene is
Each carbon atom is bonded to three other atoms, so it is ${\text{sp}}^{2}$ hybridized: trigonal planar with all bond angles equal to 120°.
The interior angles of a regular hexagon are 120°.
This exactly matches the ${\text{sp}}^{2}$ bond angles, so benzene can be planar with no angle strain.
Cyclohexane
The structure of cyclohexane is
Each carbon atom is bonded to four other atoms, so it is ${\text{sp}}^{3}$ hybridized: tetrahedral with all bond angles equal to 109.5°.
If the carbon atoms in cyclohexane were arranged as a planar hexagon, the bond angles would have to be 120°.
This would introduce a large amount of angle strain (and other types of strain) into the molecule.
The molecule can relieve this strain if it puckers into a three-dimensional chair shape.
This brings the bond angles back to 109.5 ° and minimizes all the strains in the molecule. | 2019-05-20 15:46:25 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 5, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.3682063817977905, "perplexity": 3140.9629742501306}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-22/segments/1558232256040.41/warc/CC-MAIN-20190520142005-20190520164005-00047.warc.gz"} |
http://crsl.ciiz.pw/material-derivative-matlab.html | Material Derivative Matlab
Set the "material properties"… that is, all the constants that appear Matlab (uses Matlab syntax too). Discover How to Solve Your Computational Problem Contact sales Explore featured MATLAB and Simulink capabilities through videos, examples, software reference. Ferziger/Peric, ch 1 Cohen/Kundu ch4 White ch 4 4 14-Feb. Notice: Undefined index: HTTP_REFERER in /home/yq2sw6g6/loja. Often for loops can be eliminated using Matlab’s vectorized addressing. In her essay, Reaching Beyond Skills to Cognitive Development in Teaching Quantitative Thinking with MATLAB, Risa Madoff describes how helping students move beyond syntax to solve geologic problems can engage them in the material and accelerate their learning progress. Substituting Equation into and by separating the contributions of entropy flux and entropy production terms due to heat conduction and the evolution of phase fields, that is,. Failure Analysis Engineer Element Materials Technology June 2019 – Present 5 months. where Λ is the growth rate, and D t = ∂ t + v · ∇ is the material derivative. Solving PDE involving boundary condition with partial derivatives with respect to space and time. Elastic modulus (E) is a measure of the stiffness of a material under compression or tension, although there is also an equivalent shear modulus. , 3D-PTV, tomographic PTV and. Take the operation in that definition and reverse it. 1 Derivation Ref: Strauss, Section 1. This is one of over 2,200 courses on OCW. Recall from your first calculus course (differential calculus) the following idea. M&P, materials and processes ==> 材料及び工程 M&QA, maintainability and quality assurance ==> 整備可能性品質保証 M&R Maintenance And Repair ==> 维修. One thing to note is that for the form you want, you need to explicitly define y as a function of x. The Nelder{Mead method attempts to minimize a scalar-valued nonlinear func-tion of nreal variables using only function values, without any derivative information (explicit or implicit). The internal energy in this way is not much better, because we usually do forget about some parts of it (oscillational modes, rest mass, binding energies, etc). Lecture 17 - Material Time Derivative Content: 2. matlabnb (Matlab notebooks) Other formats are Wikis: gwiki (Googlecode), cwiki (Creole), mwiki (MediaWiki) plain (pure ascii) pandoc (various Markdown formats) Slides. In the simplest case, this prediction is the current location. Cavitation growth and collapse are analyzed in three different. Note: This page uses common physics notation for spherical coordinates, in which is the angle between the z axis and the radius vector connecting the origin to the point in question, while is the angle between the projection of the radius vector onto the x-y plane and the x axis. These constitute the simplest nonlinear convective terms allowed by rotational symmetry. Ideal flow concepts of velocity potentials and stream functions are introduced and applied to simple planar flows. Active contour initialization Inspired by previous work [9] we utilize the computed optical flow field Á to perform a cluster analysis of the registered phase images using k-means clustering [10]. PERFECTLY MATCHED LAYERS FOR TIME-HARMONIC ACOUSTICS IN THE PRESENCE OF A UNIFORM FLOW∗ E. where the second time derivative is included to cover also Newton’s equation. Brancik, Programs for fast numerical inversion of Laplace transforms in Matlab language environment, in: Sbornik 7. The nth Derivative is denoted as n n n df dx fnnxfx,i. This is one of over 2,200 courses on OCW. • The maximal directional derivative of the scalar field f(x,y,z) is in the direction of the gradient vector ∇f. The mapping function is generally nonlinear, but its derivative at a point is linear with respect to small changes in position. be first introduced to mathematical software. The simplest constitutive equation for a solid material or tissue is the linear elastic constitutive equation. as in the material derivative in fluid mechanics). See Circuit Model for an example of choosing the best-form mathematical model to avoid using Derivative blocks in your models. We defined the chemical potential as the variational derivative of the total energy and its flux as the minus gradient of the potential. in the Eulerian system, D. Click Download or Read Online button to get matlab blues in pdf book now. Next, let's look at an example where we can demonstrate the technique introduced above. where Λ is the growth rate, and D t = ∂ t + v · ∇ is the material derivative. , 3D-PTV, tomographic PTV and Shake-the-Box), employing both the instantaneous velocity and the velocity material derivative of the sparse tracer particles. by Laplace and Fourier transform methods, or in the form of a power series) is either. Jump to navigation Jump to search. Join GitHub today. Material derivative: rate of change in time following uid particle expressed in Euler coordinates. Students use MATLAB to analyze an oceanographic data set collected in an estuary on a class boat trip, and put it into context using time-series data downloaded from online sources. Global Markets - Derivative & Investment Product Structuring Banca IMI settembre 2019 – Presente 3 mesi. Syllabus and introduction. These MATLAB materials are based upon work supported by the National Science Foundation under Grants Nos. Kinematics is the study of motion without regard to the forces that bring about the motion. But, if you don't happen to find yourself pining to know the volume of a parallelepiped, you may wonder what's the use of the scalar triple product. GitHub is home to over 28 million developers working together to host and review code, manage projects, and build software together. 1, "Heat flow in a bar; Fourier's Law", I do not explain any physics or. nth order derivative in matlab. Bisection Method in MATLAB Code:. pdf), Text File (. Read honest and unbiased product reviews from our users. Fluid kinematics are presented along with the justification for the material derivative. In the simplest case, this prediction is the current location. The material derivative of a the global minimum value of χ 2 within the parameters bounds using the trust-region reflective method implemented in Matlab 7. Note: The latter type of boundary condition with non-zero q is called a mixed or radiation condition or Robin-condition, and the term Neumann-condition is then reserved for the case q = 0. MATLAB Scripts D D. Compressible and incompressible flows, vorticity, Euler’s equations, potential flows and (boundary) integral equations. The first spatial derivative of string displacement yields slope waves. Professor of Mathematics; Director of Graduate Programs; PI of the NSF-RTG project Randomized Numerical Analysis; Research area: numerical analysis. fp = @(x) 1 + 4/3*x^(1/3); % First-order derivative of f! x0 = 1; % Initial guess! Newton's Method MATLAB Implementation Author: Bruno Abreu Calfa Created Date:. Kleiser Mathematics, Mechanical and Process Engineering ETH Zuric h November 21, 2013 c. Partial differential equations are useful for modelling waves, heat flow, fluid dispersion, and. The frequency dependence comes about because when a time-varying elec-tric field is applied, the polarization response of the material cannot be instantaneous. I could not find any good resource online to explain clearly to me the difference between a normal derivative and a total derivative and why my solution here was wrong. These constitute the simplest nonlinear convective terms allowed by rotational symmetry. From zero to Matlab over the course of a mere six weeks. So D(u) is simply the diffusion. For the ground substance of the annulus fibrosus the investigation was based on experimental data taken from the literature. Matlab toolbox which we developed in recent years for numerical solution of the FRO equations. This leads to the following de nition. A temperature probe is moving through the flow at velocity u, and it records the material derivative. Analytic Solutions of Partial Di erential Equations MATH3414 School of Mathematics, University of Leeds 15 credits Taught Semester 1, Year running 2003/04. 3 Vorticity, Circulation and Potential Vorticity. DocOnce has strong support for writing slides, see the slides demo for examples. Ramamurtham - Strength of material - Dhanpat Rai Publication. The master balance. For example, at time t. Local conservation of mass implies that the material derivative of the density vanishes, i. The fiber volume faction of the composite is assumed to be 13%, which is commonly seen in large area additive manufacturing applications [ 7 , 22 , 23 ]. A fluid element, often called a material element. The material derivative in (2) is discretized using semi-Lagrangian methods to remove stability constraints on advection [27,28]. In the past we’ve used the fact that the derivative of a function was the slope of the tangent line. 5 The Stagnation Concept 55. These constitute the simplest nonlinear convective terms allowed by rotational symmetry. 331 (3/23/08) Estimating directional derivatives from level curves We could find approximate values of directional derivatives from level curves by using the techniques of the last section to estimate the x- and y-derivatives and then applying Theorem 1. This MATLAB function interpolates a numerical solution returned by pdepe at new query points xq, and returns the interpolated values of the solution u and their partial derivative dudx. In addition, formulas are developed to impose upper and lower bounds for the bubble parameters, thereby allowing the use of larger time steps. The derivative of y (s, t) with respect to t is denoted by y · (s, t) and its physical meaning is the moving speed of the edges or the centerline of the belt along the y axis observed at a fixed s. In the form expected by pdepe, the left boundary condition is. That is, the path follows the fluid current described by the fluid's velocity field u. m function and run in Matlab. It is easier, however,. Next, we create the state vector x, in this case x contains only two components, y and y dot which we have designated as x1 and x2. Material derivative Although it is usually most convenient to use Euler coordinates, we still need to consider the rate of change of quantities following a uid particle. Users need Matlab installed, Visual C++, and Excel. Notes on Atmospheric Physics Arnaud Czaja1 Physics Department & Grantham Institute for Climate Change, Imperial College, London. And this page and the next, which cover the deformation gradient, are the center of that heart. The material derivative in (2) is discretized using semi-Lagrangian methods to remove stability constraints on advection [27,28]. INSTRUCTOR: I want to illustrate the important notion of stiffness by running ode45, the primary MATLAB ODE solver, on our flame example. Introduction Computational Fluid Dynamics (CFD) is the emerging field of fluid mechanics in which fluid flow problems are solved and analyzed using computational methods and numerical algorithms. When called, it performs the following task: Initializes the instrument using programmed parameters such as integration time, scans to average, smoothing and digitizer timing. In the process, we will. Additionally, there are 4 Matlab assignments. Find helpful customer reviews and review ratings for Modeling Derivatives Applications in Matlab, C++, and Excel at Amazon. Scribd is the world's largest social reading and publishing site. Integrate and Differentiate Polynomials Open Live Script This example shows how to use the polyint and polyder functions to analytically integrate or differentiate any polynomial represented by a vector of coefficients. Hencky strain has some com-. in an inviscid flow: (1) where p is the pressure, u is the velocity vector, ρ is the fluid density, and D/Dt is the material derivative, i. In Matlab we can define symbolic variables with the commands sims. Note that to take the derivative of a constant, you must first define the constant as a symbolic expression. We describe here the development of a CSD package in MATLAB called PMAD. MIT OpenCourseWare is a free & open publication of material from thousands of MIT courses, covering the entire MIT curriculum. The analysis of structures made of hyperelastic materials is necessarily nonlinear. Finally, the MATLAB code to obtain updated curvature (spatial and material) and its derivatives is presented. Although FEATool currently does not include support for evaluating 2nd order derivatives, the open design of the source code makes this easy to support simply by including the following i_eval case in the sf_line_H3 m-file definition (for more regarding custom finite element shape functions in MATLAB script code see the previous post on. Note: This page uses common physics notation for spherical coordinates, in which is the angle between the z axis and the radius vector connecting the origin to the point in question, while is the angle between the projection of the radius vector onto the x-y plane and the x axis. Need to change the extension ". Notice how the slope of each function is the y-value of the derivative plotted below it. The differential approach provides point‐by‐point details of a flow pattern as oppose to control volume. Computing Derivatives 153 MATLAB is started just like any other. That is, the path follows the fluid current described by the fluid's velocity field u. From then on, fractional calculus has been developed, which is a generalization of the commonly used integer-order differentiation and integration. The dimensionless shearing stress of the fluid motion is expressed in the form of first order linear differential equation given as follows:. material time derivative and the reference configuration time derivative leads to the ALE equations, (2. Part 8: Differentiation. Designed for those who need to learn how micromechanical approaches can help understand the behaviour of bodies with voids, inclusions, defects, this book is perfect for readers without a programming background. 2 The material derivative The continuity equation contains the “time-derivative” of the fluid density. This function will take in arguments t, y, and k and output the variable dy. f '' evaluates to Derivative [2] [f]. Singer and Pytel - Strength of materials - Harper and row Publication. Professor of Mathematics; Director of Graduate Programs; PI of the NSF-RTG project Randomized Numerical Analysis; Research area: numerical analysis. To do this, we can again use the symbolic toolbox in MATLAB. 1 Basic Concepts This chapter deals with numerical approximations of derivatives. int ABSTRACT The direct numerical simulation (DNS) of the laboratory experiment of Plumb and McEwan (1978) exhibits wave reflec-tion, wave interference, wave-mean flow interaction and wave breaking. Beer and Johnston - Strength of materials - CBS Publication. Nagel, [email protected] Higher Order Derivative Divided contact [email protected] Find Euler-Lagrange Equation for Spring. Derivative and Integration. Although the flux is continuous, the partial derivative may have a jump at a material interface. The material derivative is a total derivative, that depends on time and space. The entire book utilizes Matlab, C++, and Excel. In the following sequence of steps, to isolate the time derivative of porosity , material derivatives ( ) are used. 1 Introduction This appendix lists MATLAB scripts that implement all of the numbered algorithms presented throughout the text. LEGENDRE‡§ Abstract. the derivative of the (n-1)st derivative, fxn 1. In addition, some examples using Matlab toolkits are used: Chapter 1 makes use of the Fixed-Income Toolkit. Pid controller basics pdf. Additionally, there are 4 Matlab assignments. Its popularity derives in part from the fact that it is unstable without control, that is, the pendulum will simply fall over if the cart isn't moved to balance it. Chapter 7: Numerical Differentiation 7–19 • To estimate the second derivative we simple apply one of the above algorithms a second time, that is using the backward difference The MATLAB diff Function • To make computing the numerical derivative a bit easier, MATLAB has the function diff(x) which computes the. Find materials for this course in the pages linked along the left. ChE 312 Atomic structure, semiconductor materials, solar cells, Transistors and Process Sequence of Fabrication, Control of Microcontamination, Microlithography, Doping, Etching, Oxidation, Chemical Vapour Deposition and Reactor Design, Classification and Electrical, Mechanical Properties of Polymer, Polymer Catalysis and Molecular Chemistry, Flow Behaviour and Polymer Processing, Polymer Blends and Composites, Applications of Polymers (Exchange Resin etc. This leads to the following de nition. However, if we instead had f(x(t),y(t),z(t),t) then df/dt is the sum of the partial derivatives because of chain rule. Announcements Last updated: April 26, 2004. mat extension, in the current directory. The nth Derivative is denoted as n n n df dx fnnxfx,i. Students use MATLAB to analyze an oceanographic data set collected in an estuary on a class boat trip, and put it into context using time-series data downloaded from online sources. The purpose of this paper is to determine the Mooney-Rivlin parameters in order to evaluate the stress and strain state of rubber structures using the finite element method. The differential approach provides point‐by‐point details of a flow pattern as oppose to control volume. where Λ is the growth rate, and D t = ∂ t + v · ∇ is the material derivative. An example of a one-dimensional dynamical system is a mass on a string. For an example of such simplification, see More Examples. Schneiders 0 0 Department of Aerospace Engineering , TU Delft, Delft , The Netherlands A method is proposed to reconstruct the instantaneous velocity field from time-resolved volumetric particle tracking velocimetry (PTV, e. The Material Derivative. material in the text; rather, it is to present the capabilities of MATLAB as they are needed by someone studying the text. We use these results for formulating a linearized updating algorithm for curvature and its derivatives when the configuration of the curve acquires a small increment. Its popularity derives in part from the fact that it is unstable without control, that is, the pendulum will simply fall over if the cart isn't moved to balance it. The surface derivatives which appear in the formulas – can be computed analytically using some identities stated in [29, section 3] or [45, section 3] which link surfaces derivatives on to surface derivatives on The discrete analogue of the integration by parts formula used in the proof of proposition 3. eing surfaced being a matrix coding code, nowadays the MATLAB is one of the successful multi-paradigm computing surroundings for various complicated numerical computations and simulations. APP MTH 4102 - Fluid Mechanics - Honours North Terrace Campus - Semester 1 - 2019 (Maple and Matlab) in solution methods. 6truein} \setlength{\oddsidemargin}{-. To do this, we can again use the symbolic toolbox in MATLAB. The Saturn V rocket used in the Apollo 11 spacecraft is employed to provide better understanding of a real-life scenario. The numerical value returned by MATLAB is somewhat less than half the area of a square 2 units on a side. Often for loops can be eliminated using Matlab’s vectorized addressing. 1 Physical derivation Reference: Guenther & Lee §1. 3 - Proportional-Derivative Control. The Material global ELF ELK. The MATLAB codes written by me are available to use by researchers, to access the codes click on the right hand side logo. The purpose of this paper is to determine the Mooney-Rivlin parameters in order to evaluate the stress and strain state of rubber structures using the finite element method. The boundary conditions can be classified as follows. Students will apply their knowledge to solve relevant problems in the field of asset pricing and by implementing models on Matlab through weekly homework assignments. eing surfaced being a matrix coding code, nowadays the MATLAB is one of the successful multi-paradigm computing surroundings for various complicated numerical computations and simulations. We derive the isogeometric configuration sensitivity of the Mindlin plates by using the material derivative and adjoint approaches. A temperature probe is moving through the flow at velocity u, and it records the material derivative. We will restrict the analysis to. In my experience Mathematica is quite popular among physicists, especially for theoretical work. El-Bary, On dual-phase-lag thermoelasticity theory with memory-dependent derivative, Mechanics of Composite Materials Structures 24(11) (2017), 908–916. The numerical integration invoked by the combination of double and int is native, not to MATLAB, but to MAPLE, from which MATLAB's symbolic routines are borrowed. Designed for those who need to learn how micromechanical approaches can help understand the behaviour of bodies with voids, inclusions, defects, this book is perfect for readers without a programming background. Material derivative Although it is usually most convenient to use Euler coordinates, we still need to consider the rate of change of quantities following a uid particle. The dimensionless shearing stress of the fluid motion is expressed in the form of first order linear differential equation given as follows:. M&P, materials and processes ==> 材料及び工程 M&QA, maintainability and quality assurance ==> 整備可能性品質保証 M&R Maintenance And Repair ==> 维修. Such a descrip-tion is appropriate under many but not all circumstances. Introduction to computational errors analysis, floating-point representation, computational arithmetic, numerical solving techniques, linear and nonlinear algebraic equation system solving techniques, polynomial and spline interpolation techniques, least squares fitting , eigenvalue approximation techniques, numerical derivation techniques, numerical integration techniques, including gaussian. is carried out to test the dynamic inside the catalyst pellet using the partial differential equation (pde) solver in Matlab 2014 software. Built into any numerical fluid simulation should be the continuity equation, which ensures mass conservation in the system @⇢ @t + ~r ⇧(⇢~v) = @⇢ @t +~v⇧ ~r⇢+⇢~r ⇧~v = D⇢ Dt +⇢r~ ⇧~v = 0. A state-of-the-art simulation software is developed to perform first-order sensitivity analysis for composite manufacturing problems using the DDM. Singer and Pytel - Strength of materials - Harper and row Publication. The final value of t is 2 over y naught, and I'm. Os conteúdos de Docsity são complemente acessíveis de qualquer versão English Español Italiano Srpski Polski Русский Português Français. The first argument to any of the MATLAB ODE solvers is the name of a function that specifies the. Schneiders 0 Fulvio Scarano 0 Jan F. In the Lagrangian reference, the velocity is only a function of time. The matrix equation for the discretization is defined in terms of the two velocity components and pressure, and then solved using the direct ‘backslash’ solver in MATLAB. If f is differentiable at some point x, then this is the linear transformation that best approximates f for points close x, and is known as the derivative or the differential of f at x. Elastic modulus (E) is a measure of the stiffness of a material under compression or tension, although there is also an equivalent shear modulus. It is assumed that not all students have the prerequisite background. Mechanical energy flow rate keyword after analyzing the system lists the list of keywords related and the list of websites with related content, in addition you can see which keywords most interested customers on the this website. The material derivative computes the time rate of change of any quantity such as temperature or velocity (which gives acceleration) for a portion of a material moving with a velocity, $${\bf v}$$. The LHS of the Equation (10) accounts for a density change of fluid, gas, and hydrate phase. The barotropic vorticity equation The barotropic vorticity equation describes the evolution of a homogeneous (constant density), non-divergent, incompressible flow on the surface of the sphere. derivative of the. We will restrict the analysis to. Also, there are several of you that have some experience with MATLAB and by working in groups we can help each other. The differential approach provides point‐by‐point details of a flow pattern as oppose to control volume. In particular, MATLAB software will be used in this course. The material derivative of transcript density D (expressed in arbitrary unit mm-1 min-1) was calculated from the continuity equation. The master balance. CE597 – Environmental Fluid Mechanics Purdue University, School of Civil Engineering Spring Semester 2012 General course information GENERAL COURSE DESCRIPTION This course presents the basic fluid mechanics of numerous environmental flows in oceans, rivers, lakes, and the. A material derivative is the time derivative - rate of change - of a property following a fluid particle P'. The product and chain rules apply to matrix derivatives as well. 1 Basic Concepts This chapter deals with numerical approximations of derivatives. We will show that two types of solutions are possible, corresponding. Whether you've loved the book or not, if you give your honest and detailed thoughts then people will find new books that are right for them. In fluid mechanics, there are generally three routes of work in the field, three ways to conduct experiments. Matlab toolbox which we developed in recent years for numerical solution of the FRO equations. Such a matrix is called the Jacobian matrix of the transformation (). Big D-derivative notation is used in fluid dynamics to denote the derivative "when moving with the flow", see Material derivative. (The story is more complicated than this but when we say f is"differentiable"we mean ∇f represents the derivative, to be discussed a little later. FINITE ELEMENT : MATRIX FORMULATION Georges Cailletaud Ecole des Mines de Paris, Centre des Mat´eriaux UMR CNRS 7633 Contents 1/67. Partial differential equations contain partial derivatives of functions that depend on several variables. diff_forward, a MATLAB program which interactively uses forward differences to estimate the derivative of a function f(x), using a stepsize h. This MATLAB construction with the square brackets takes a vector y, adds another value to it, making it one element longer and puts the resulting y out back in y out. Hydrodynamic Stability of Newtonian and Non-Newtonian Fluids Julian Mak The program used for computations are MATLAB D=Dt material derivative @[email protected]+ uru. 7) We can demonstrate this concept of the numerical derivative with a simple MATLAB script. Matlab toolbox which we developed in recent years for numerical solution of the FRO equations. And then, the iteration process is repeated by updating new values of a and b. The derivative of y (s, t) with respect to t is denoted by y · (s, t) and its physical meaning is the moving speed of the edges or the centerline of the belt along the y axis observed at a fixed s. Full text of "Stephen Senturia Microsystem Design" See other formats. The material derivative is a Lagrangian concept but we will work in an Eulerian reference frame. Chapter 6 - Flow visualization - streamlines, streamfunctions and velocity potential. Production of typical P/M components (with flow charts), self lubricated bearing, cemented carbides, cermets, refractory metals, electrical contact materials, friction materials, and diamond impregnated tools, friction plate, clutch plate, commutator brushes. Paris Area, France • Priced derivative products (exotic swaps, basket swaps, quanto commodity swaps and cross currency swaps) on crude oil and refined products such as Brent, WTI, Diesel, Gasoil, Fuel, Cracks. ( to be implemented in Matlab or similar scientific The Material Derivative 2. Unofficial ERRATA and Commentary for Continuum Mechanics for Engineers–3rd ed. Comp chem is really cool but also somewhat limiting compared to other areas. We use these results for formulating a linearized updating algorithm for curvature and its derivatives when the configuration of the curve acquires a small increment. In the simplest case, this prediction is the current location. The material derivative is accordingly modified to include an advection correction, inhomogeneous and anisotropic diffusion terms and a multiplicative noise contribution. The initiative of developing the MATLAB code is to study the PCM performance, and the number of extra features similar to other whole building simulation tools is very minimal. is the material derivative. Material Derivative. We describe here the development of a CSD package in MATLAB called PMAD. f ' is equivalent to Derivative [1] [f]. Note: The latter type of boundary condition with non-zero q is called a mixed or radiation condition or Robin-condition, and the term Neumann-condition is then reserved for the case q = 0. Discrete wavelet transform algorithms written for multivariate analysis and classification of complex materials. A new approach, using an outlet condition in the form of a material derivative, termed Material Derivative Boundary Condition (MDBC), is introduced and a numerical model to solve convection. considering a material derivative as the outlet BC was yet constructed. , 3D-PTV, tomographic PTV and Shake-the-Box), employing both the instantaneous velocity and the velocity material derivative of the sparse tracer particles. In the past we’ve used the fact that the derivative of a function was the slope of the tangent line. normE from my model but I do not know what that would be called. pdf), Text File (. discrete or lattice description, of the material undergoing phase separation. So D(u) is simply the diffusion. Stanford Libraries' official online search tool for books, media, journals, databases, government documents and more. The program selects the step size in time to resolve this. (5) where I is the identity matrix and the strain components are as follows, e ( x , t n )=[ e xx ( x , t n ) e xy ( x , t n ); e yx ( x , t n ) e yy ( x , t n )]. This tutorial is designed to provide the reader with a basic understanding of how MATLAB works, and how to use it to solve problems in linear algebra and multivariable calculus. A financial instrument, traded on or off an exchange, the price of which is directly dependent upon the value of one or more underlying securities, equity indices, debt instruments, commodities, other derivative instruments, or any agreed upon pricing index or arrangement. ( to be implemented in Matlab or similar scientific The Material Derivative 2. Derivative is generated when you apply D to functions whose derivatives the Wolfram Language does not know. However I was told that this solution could not be applied to this question because I should be solving for the total derivative. The Truesdell rate is simply the time derivative of the pull back of the Kirchhoff stress with the deformation gradient, pushed forward by the deformation gradient multiplied by J (or J^-1 I forget which) - in other words, it is basically th Lie derivative of the Kirchhoff stress upto a mutiple of j or J^-1. Chapter 3 - Kinematics: Lagrangian vs. Then, equation (12) becomes. simply write down Newton’s second law, F = m~a, as a function of the total derivative (referred to as material derivative in [1]). Notice that if x is actually a scalar in Convention 3 then the resulting Jacobian matrix is a m 1 matrix; that is, a single column (a vector). Note that the above conservation laws implies that the rate of change of the advective (material) derivative of the momentum equals the gradient of pressure. MATLAB can find the derivative of symbolic expressions. Discover How to Solve Your Computational Problem Contact sales Explore featured MATLAB and Simulink capabilities through videos, examples, software reference. In the Lagrangian reference, the velocity is only a function of time. Watch Queue Queue. The material derivative is accordingly modified to include an advection correction, inhomogeneous and anisotropic diffusion terms and a multiplicative noise contribu- tion. 1D Heat equation and a finite-difference solver Guillaume Ri et MARETEC IST 1 The advection-diffusion equation The original concept applied to a property within a control volume V from which is derived the integral advection-diffusion equation states as {Rate of change in time} = {Ingoing − Outgoing fluxes} + {Created − Destroyed}: (1). This is my script in MATLAB so far:. In the lecture entitled Maximum likelihood - Algorithm we have explained how to compute the maximum likelihood estimator of a parameter by numerical methods. MATLAB has capabilities for both numerical and symbolic calculations. This should be very simple. Dt [f, x 1, …, Constants-> {c 1, …}] specifies that the c i are constants, which have zero total derivative. Introduction Model 1: constant normal velocity Model 2: linear velocity Model 3: exponential velocity Conclusions Polishing Lead Crystal Glass Universita degli Studi di Firenze. Rotation Tensor, Stretch Tensors. El-Karamany and A. Some basic oceanographic knowledge is required, and data sets are provided to students as. 2 molecule. • Using matrix-specific built-in functions such as rref, ones, diag and eig. PERFECTLY MATCHED LAYERS FOR TIME-HARMONIC ACOUSTICS IN THE PRESENCE OF A UNIFORM FLOW∗ E. Finally, the MATLAB code to obtain updated curvature (spatial and material) and its derivatives is presented. In the Lagrangian approach we keep track of its original position (Xi) and follow its path which is described by xi(Xi,t). The material derivative is accordingly modified to include an advection correction, inhomogeneous and anisotropic diffusion terms and a multiplicative noise contribution. Matlab - Essential Training. It is also called the advective derivative, derivative following the motion, hydrodynamic derivative, Lagrangian derivative, material derivative, particle derivative, substantial derivative, substantive derivative (Tritton 1989), Stokes derivative (Kaplan 1991, pp. Please help me to run my code of dynamic energy and material balance equation for batch reactor in s function. This looks like it's indeed just a non-linear diffusion equation. When m = n, the Jacobian matrix is square, so its determinant is a well-defined function of x, known as the Jacobian determinant of f. Levy 5 Numerical Differentiation 5. A new approach, using an outlet condition in the form of a material derivative, termed Material Derivative Boundary Condition (MDBC), is introduced and a numerical model to solve convection. A detailed description of this model along with step-by-step instructions to simulate the coil can be found in the Model Gallery. The following projects are integrated with the material covered in courses MTH. and , where is the metric tensor. To “drive” the various algorithms, one. It is unique since it provides full working Matlab Source Code The second part of Interest Rate Derivatives Explained covers volatility and term structure modelling For the material and questions contact [email protected] Jibin Kumar (@jibinkumarr) | Twitter Read more. It can serve as lecture notes for a graduate level course in continuum mechanics for engineers interested in the subject. Find materials for this course in the pages linked along the left. Uses for MATLAB include matrix calculations, developing and running algorithms, creating user interfaces (UI) and data visualization. Numerical models for the formation of marine gas hydrate : constraints on methane supply from a comparison… Davie, Matthew K. but using excel, Matlab, or a pocket calculator and a graphing paper) an exponential prole that seems to t each of the proles reasonably well at depth ranges from 500m to the ocean bot- tom. edu 734-936-0502. The Material global ELF ELK. MATLAB, which stands for Matrix Laboratory, is a very powerful program for performing numerical and symbolic calculations, and is widely used in science and engineering, as well as in mathematics. , Dρ/Dt = 0, which, in turn, implies that along any streamline ρ is constant. A meme page to check every time MatLab crashes a dot is for partial time derivatives, not total ones (e. The material derivative of a the global minimum value of χ 2 within the parameters bounds using the trust-region reflective method implemented in Matlab 7. in the Eulerian system, D. Use Git or checkout with SVN using the web URL. 1 General Considerations Of interest is water flowing in a channel with a free surface, which is usually referred to as open channel flow. In the lecture entitled Maximum likelihood - Algorithm we have explained how to compute the maximum likelihood estimator of a parameter by numerical methods. Subsequently, the axial and torsional vibration of rods and lateral vibration of strings and beams will be examined with techniques presented for the calculation of normal modes and natural frequencies, free and forced vibration response. Assuming a steady current field, the material derivative D/Dt is following a water column through the region. M&P, materials and processes ==> 材料及び工程 M&QA, maintainability and quality assurance ==> 整備可能性品質保証 M&R Maintenance And Repair ==> 维修. This appears to be consistent with our plot. Users need Matlab installed, Visual C++, and Excel. Physical models (transport equations, energy and entropy principles). 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PARTITION BY
Ranking functions
17. Ranking Functions – Exercise 3
Window Frames
Analytic Functions
PARTITION BY ORDER BY
Order of Evaluation
Finished!
## Instruction
Excellent! This is the next-to-last exercise for ranking functions.
## Exercise
Show the first and last name of the customer who bought the second-most-recently-purchased GiftCard. Show the payment date also. Assume that an individual rank is assigned for each gift card purchase.
### Stuck? Here's a hint!
Use a CTE:
WITH Ranking AS (...) SELECT ...
And pick the row with Rank = 2. | 2018-12-14 20:30:56 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.1752047836780548, "perplexity": 11607.32967543768}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-51/segments/1544376826306.47/warc/CC-MAIN-20181214184754-20181214210754-00511.warc.gz"} |
https://www.bartleby.com/solution-answer/chapter-51-problem-57e-calculus-an-applied-approach-mindtap-course-list-10th-edition/9781305860919/finding-a-cost-function-in-exercises-5558-find-the-cost-function-for-the-given-marginal-cost-and/6ee2d63c-6360-11e9-8385-02ee952b546e | Chapter 5.1, Problem 57E
### Calculus: An Applied Approach (Min...
10th Edition
Ron Larson
ISBN: 9781305860919
Chapter
Section
### Calculus: An Applied Approach (Min...
10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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# Finding a Cost Function In Exercises 55–58, find the cost function for the given marginal cost and fixed cost. See Example 8. Marginal Cost Fixed Cost ( x = 0 ) d C d x = 1 50 x + 4 $750 To determine To calculate: The cost function for the marginal cost dCdx=120x+4 that have a fixed cost of$750.
Explanation
Given Information:
The marginal cost is dCdx=120x+4 and the fixed cost is \$750.
Formula used:
The sum rule of basic integration [f(x)+g(x)]dx=f(x)dx+g(x)dx.
The simple power rule of integration xndx=xn+1n+1+C.
Calculation:
Consider the marginal cost, dCdx=120x+4.
Integrate the provided marginal cost, use the sum rule of basic integration [f(x)+g(x)]dx=f(x)dx+g(x)dx.
dCdxdx=(120x+4)dxC(x)=120xdx+4dx=1201x12dx+41dx=120x12dx+41dx
Use the simple power rule of integration xndx=xn+1n+1+C
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Mathematics For Machine Technology | 2019-12-06 23:04:17 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.47964170575141907, "perplexity": 8060.404030755555}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-51/segments/1575540491491.18/warc/CC-MAIN-20191206222837-20191207010837-00402.warc.gz"} |
https://www.physicsforums.com/threads/two-particles-in-a-magnetic-field.64976/ | # Two particles in a magnetic field
1. Feb 25, 2005
### sony
Illustration:
http://home.no.net/erfr1/images/2.jpg
"A particle, X with mass m and charge q starts with an inital velocity zero, and follows the red path indicated on the drawing. It follows a half circle when entering the magnetic field.
A new particle, Y with mass m(same) and charge 2q starts from the same place as X. Is the following true og untrue:
1. The force on Y is double the force on X in the electric field.
2. The force on Y is double the force on X in the magnetic field.
3. The time Y uses on the half circle is half the time X uses.
1. Fex=qE and Fey=2qE. So that's true.
2. Fmx=qvB = q*sqrt(qU/m) * B.
And Fmy = qvb = 2q * sqrt(2qU/m) * B. So this statement is false.
3. I don't get this.
It's half a circle, so v=Pi*r/T
And I have tried the formula: v^2/r = 4Pi^2*r / T^2
But everything I use involves either v, or r og both. And the radius of Y has to be smaller right? Since the mag. force on Y is the biggest. But I don't know the radius! And the speed is such an ugly expression, and I always end up with the square root of an expression, so the difference can't be 1/2.
The book says that statement 3 is true...
Thanks
Last edited by a moderator: Apr 21, 2017
2. Feb 25, 2005
### dextercioby
$$T_{X}=\frac{\pi r_{X}}{v_{x}}$$ (1)
$$T_{Y}=\frac{\pi r_{Y}}{v_{Y}}$$ (2)
$$r=\frac{mv}{qB}$$ (3)
Use (3) for the 2 particles and then combine with (1) & (2) to reach the result.
Daniel.
3. Feb 25, 2005
### sony
Aaaah! Thank you. So the speed is ruled out and I get:
Tx= Pi*m/qB
Ty=1/2 * Pi*m/qB
Ty=1/2Tx
I can't believe I spent so much time on this :). Stupid me.
Thanks! | 2017-08-20 23:08:16 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7852068543434143, "perplexity": 1720.100612295656}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-34/segments/1502886106996.2/warc/CC-MAIN-20170820223702-20170821003702-00655.warc.gz"} |
https://gateway.ipfs.io/ipfs/QmXoypizjW3WknFiJnKLwHCnL72vedxjQkDDP1mXWo6uco/wiki/Change_of_variables.html | # Change of variables
In mathematics, a change of variables is a basic technique used to simplify problems in which the original variables are replaced with functions of other variables. The intent is that when expressed in new variables, the problem may become simpler, or equivalent to a better understood problem.
Change of variables is an operation that is related with substitution. However these are different operations, as it can be seen when considering differentiation (chain rule) or integration (integration by substitution).
A very simple example of a useful variable change can be seen in the problem of finding the roots of the sixth order polynomial:
Sixth order polynomial equations are generally impossible to solve in terms of radicals (see Abel–Ruffini theorem). This particular equation, however, may be written
(this is a simple case of a polynomial decomposition). Thus the equation may be simplified by defining a new variable x3 = u. Substituting x by into the polynomial gives
which is just a quadratic equation with solutions:
The solutions in terms of the original variable are obtained by substituting x3 back in for u:
Then, assuming that x is real,
## Simple example
Consider the system of equations
where and are positive integers with . (Source: 1991 AIME)
Solving this normally is not very difficult, but it may get a little tedious. However, we can rewrite the second equation as . Making the substitution reduces the system to Solving this gives or Back-substituting the first ordered pair gives us , which easily gives the solution Back-substituting the second ordered pair gives us , which gives no solutions. Hence the solution that solves the system is .
## Formal introduction
Let , be smooth manifolds and let be a -diffeomorphism between them, that is: is a times continuously differentiable, bijective map from to with times continuously differentiable inverse from to . Here may be any natural number (or zero), (smooth) or (analytic).
The map is called a regular coordinate transformation or regular variable substitution, where regular refers to the -ness of . Usually one will write to indicate the replacement of the variable by the variable by substituting the value of in for every occurrence of .
## Other examples
### Coordinate transformation
Some systems can be more easily solved when switching to polar coordinates. Consider for example the equation
This may be a potential energy function for some physical problem. If one does not immediately see a solution, one might try the substitution
given by .
Note that if runs outside a -length interval, for example, , the map is no longer bijective. Therefore should be limited to, for example . Notice how is excluded, for is not bijective in the origin ( can take any value, the point will be mapped to (0, 0)). Then, replacing all occurrences of the original variables by the new expressions prescribed by and using the identity , we get
.
Now the solutions can be readily found: , so or . Applying the inverse of shows that this is equivalent to while . Indeed we see that for the function vanishes, except for the origin.
Note that, had we allowed , the origin would also have been a solution, though it is not a solution to the original problem. Here the bijectivity of is crucial. Note also that the function is always positive (for ), hence the absolute values.
### Differentiation
Main article: Chain rule
The chain rule is used to simplify complicated differentiation. For example, to calculate the derivative
the variable x may be changed by introducing x2 = u. Then, by the chain rule:
so that
where in the very last step u has been replaced with x2.
### Integration
Difficult integrals may often be evaluated by changing variables; this is enabled by the substitution rule and is analogous to the use of the chain rule above. Difficult integrals may also be solved by simplifying the integral using a change of variables given by the corresponding Jacobian matrix and determinant. Using the Jacobian determinant and the corresponding change of variable that it gives is the basis of coordinate systems such as polar, cylindrical, and spherical coordinate systems.
### Differential equations
Variable changes for differentiation and integration are taught in elementary calculus and the steps are rarely carried out in full.
The very broad use of variable changes is apparent when considering differential equations, where the independent variables may be changed using the chain rule or the dependent variables are changed resulting in some differentiation to be carried out. Exotic changes, such as the mingling of dependent and independent variables in point and contact transformations, can be very complicated but allow much freedom.
Very often, a general form for a change is substituted into a problem and parameters picked along the way to best simplify the problem.
### Scaling and shifting
Probably the simplest change is the scaling and shifting of variables, that is replacing them with new variables that are "stretched" and "moved" by constant amounts. This is very common in practical applications to get physical parameters out of problems. For an nth order derivative, the change simply results in
where
This may be shown readily through the chain rule and linearity of differentiation. This change is very common in practical applications to get physical parameters out of problems, for example, the boundary value problem
describes parallel fluid flow between flat solid walls separated by a distance δ; µ is the viscosity and the pressure gradient, both constants. By scaling the variables the problem becomes
where
Scaling is useful for many reasons. It simplifies analysis both by reducing the number of parameters and by simply making the problem neater. Proper scaling may normalize variables, that is make them have a sensible unitless range such as 0 to 1. Finally, if a problem mandates numeric solution, the fewer the parameters the fewer the number of computations.
### Momentum vs. velocity
Consider a system of equations
for a given function . The mass can be eliminated by the (trivial) substitution . Clearly this is a bijective map from to . Under the substitution the system becomes
### Lagrangian mechanics
Main article: Lagrangian mechanics
Given a force field , Newton's equations of motion are
.
Lagrange examined how these equations of motion change under an arbitrary substitution of variables , .
He found that the equations
are equivalent to Newton's equations for the function , where T is the kinetic, and V the potential energy.
In fact, when the substitution is chosen well (exploiting for example symmetries and constraints of the system) these equations are much easier to solve than Newton's equations in Cartesian coordinates. | 2022-05-25 08:08:03 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9363476037979126, "perplexity": 441.943199793281}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-21/segments/1652662580803.75/warc/CC-MAIN-20220525054507-20220525084507-00217.warc.gz"} |
http://physics.stackexchange.com/tags/particle-physics/new | # Tag Info
## New answers tagged particle-physics
0
Classical electrodynamics has a lagrangian for the classical fields, see discussion here . The photon is an elementary particle and does not have a classical existence. Here is on page 5 the Lagrangian for a photon
2
Here is a (partial?) list of new hadrons discovered at LHC experiments $\chi_b(3P)$: a $b\overline{b}$ bound state, discovered by ATLAS in 2011 $\Xi_b(5945)^0$: a $bsu$ bound state, discovered by CMS in 2012 $\Xi_b^\prime(5935)^-$ and $\Xi_b^\star(5955)^-$: $bsd$ bound states, discovered by LHCb in 2014 $P_c(4380)$ and $P_c(4450)$: $c\overline{c}uud$ ...
2
The common hypothesis supposes that there is a slight asymetry in a transformation (i.e., slightly more likely in one direction than the other), which is called the "violating CP symmetry" (occuring in the weak interaction). See wikipedia "baryon asymmetry" and "CP violation".
1
Let me start by examining your last line about kinetic and potential energies. Potential energy is NOT a property of matter. But kinetic energy IS! Here is a short derivation of why kinetic energy is a property of matter: $E=mc^2$ in rest frame of the particle. But if you switch to a different inertial frame in which the particle is moving at speed v, $E' ... 2 Recent particles, which were confirmed by CERN, are pentaquarks and also it has been observed that the Bs0 meson decay in 2 muons. Both of these though had been theoretically predicted long ago. 0 When right handed neutrinos are introduced, they imply$L$violation through their Majorana nature. Their decay into lepton and Higgs doublets $$N\,\longrightarrow l\,\Phi^\dagger$$ violates the lepton number (since$N$has zero lepton number being Majorana). These decays take place out of thermal equilibrium, therefore a net lepton asymmetry is produced. ... 0 The history of attempting to solve, overcome the conundrum that wave particle duality presents is fraught with inventive thought experiments. But in every case a fault has been found in the reasoning. In your proposed experiment you define a phosphorus 'particle' that's able to illuminate itself, and thus no interference involved in observing the particle as ... 4 The Large Hadron collider was closed for a year and more for an upgrade in energy from 7 to 14 TeV. They have started runs in the summer but there is nothing solidly announced, though there are some exciting hints , which need more statistics. 2 1) You can of course write down these amplitudes in any basis you choose, as long as you take into account matrix elements of the CKM and PMNS matrix. 2) There is indeed a difference here, neutrinos are produced exclusively by the weak interaction, whereas quarks can be pair produced by the strong (or electric) force, or produced by weak decays. 3) in ... 0 Only charged particles can be deflected: electrons, protons, and other charged hadrons and mesons. Light and X-ray can't. 1 To make it short, you need "proper" Mass/Energy Eigenstates and "proper" flavour Eigenstates. The mixing theory means that you have real coherent states. This works very well since the mass differences of Neutrinos are extremely small and the Energy is high. For the charged leptons this is not the case. For an electron to turn into a Tau it needs a lot of ... -3 Identification of particles and anti-particles Good question. It's nice to see somebody thinking about physics. Shame it's an old question, but hey ho, it's never too late for physics. The identification of an electron as a particle and the positron as an antiparticle is a matter of convention. We see lots of electrons around us so they become ... 1 Here is one possible way to evaluate this expression using FeynCalc: << FeynCalc` SUNF[a1, a2, a3] SUNF[a4, a2, a7] SUNF[a7, a8, a1] SUNF[a5, a6, a3] * SUNF[a9, a4, a5] SUNF[a8, a9, a6] // SUNSimplify[#, Explicit -> True, SUNNToCACF -> False] & // Simplify and the answer is: 1/4 SUNN^3 (-1 + SUNN^2) i.e. what the OP got from doing the ... 7 Free neutrons are unstable, and decay to a proton, electron, and electron antineutrino with a half life of about 10 minutes. https://en.wikipedia.org/wiki/Neutron In most cases, the electron escapes but the proton captures another electron from its environment, making a hydrogen atom composed of one proton, one electron (and no neutrons.) In some rare cases ... 1 Depending on the way you look at them, there are several kind of kaons:$K^0$and$\overline{K^0}$are the kaons produced by strong interaction. They have a definite isospin and strangeness quantum numbers made respectively of$d\bar{s}$and$\bar{d}s$. However they can oscillate meaning that they transform spontaneously in each other:$K^0 \leftrightarrow ...
16
There is a misconception in your question, specifically: how does a neutron weigh more than itself plus 2 extra particles It doesn't. A hydrogen atom is composed only of a proton and an electron, but no neutron. Hydrogen is shown diagrammatically shown below: Image Source If a neutron were included, then it becomes the isotope of hydrogen, ...
0
The way to approach the problem initially is to consider what you know about the reaction $$n \longrightarrow \mathrm{p}^+ + \mathrm{e}^- + \bar{\nu}_e \,.$$ Because of the relativity principle we can consider the reaction in the rest-frame of the neutron without loss of generality and we know that both (three-)momentum and energy are conserved. ...
0
In Richard Beth's Mechanical Detection and Measurement of the Angular Momentum of Light, bright light from a mercury arc lamp was circularly polarized and passed through a half-wave plate (which reverses the sense of circular polarization) attached to a torsion pendulum. A bit of clever experimental design sent the light through the half-wave plate twice so ...
2
Yes and it already happened. http://physicsworld.com/cws/article/news/2012/mar/19/neutrino-based-communication-is-a-first From the arXiv:1203.2847 Beams of neutrinos have been proposed as a vehicle for communications under unusual circumstances, such as direct point-to-point global communication, communication with submarines, secure communications ...
-2
If you look at the standard model you will only find gluons. This is very clear and should settle any doubts. (Pions are a historical relic of the middle of the twentieth century which only provide an approximation.)
2
What happens to a particle and antiparticle that collide? The 511keV/c² electron is typically converted into a 511keV photon, and the 511keV/c² positron is converted into another 511keV photon. However it needn't be a 1:1 conversion. Check out positronium where you can read that the triplet state's leading decay is to three gammas. That's three photons, ...
2
"Matter can never be destroyed, so what happens to those particles? Do they just disappear? Where does the mass go?" It's not true that "matter can never be destroyed". According to classical understanding, yes, mass was always conserved and was never destroyed. But that's not entirely correct. The meaning of the well known equation $E=mc^2$ is that energy ...
3
The following diagram and explanation from Cornell University's page A Brief Introduction to Particle Physics may be of help: (Note, as correctly mentioned by @HDE in the comments, the term 'mini Big Bang' is a bit misleading, but the main point remains as @Jon Custer mentioned in the comments: The mass gets converted into energy. And energy can be ...
2
So let's start from the relations you gave and transform one of them from ket to bra. $$\left|i\right> = \mathcal{ CPT}\left | \bar{i}\right>$$ $$\left<f\right| = \left< \bar{f}\right| (\mathcal{ CPT})^{\dagger}$$ Using the CPT invariance condition, $\left(\mathcal{ CPT} \right)T \left(\mathcal{ CPT}\right)^{-1}= T^{\dagger}$, It is easy ...
1
I'll give you some points here. If you just treat $K_\alpha$-rays as a transition from principal number 2 to 1, $\Delta E \approx \frac{3}{4}Z^2$ Hartree, which has unit of keV when $Z>10$. Use characteristic Moseley's law, check http://en.wikipedia.org/wiki/Moseley%27s_law setting $k_1, k_2$ appropriately and using $\Delta E = h \Delta f=hf_{\text ... 1 To start with what are identical to each other are the elementary particles of the standard model. of particle physics. When complex composites of these particles are built this complete identity starts differentiating. In interacting with each other quantum numbers enter and energy states. One proton may be indistinguishable from another proton , but a ... 1 Particle antiparticle potential/hypothetical pairs exist in vacuum as a mathematical description, necessary for calculations of interactions between elementary particles. These mathematically annihilate and reappear within the heisenberg uncertainty principle.In the Hawking radiation case the virtual pairs at the event horizon have a probability one of ... 3 The quote is correct but a bit misleading. The statement "In doing so it also liberates particles known as neutrinos" includes electrons also which are the other particle that is released in neutron decay, and is the way that beta decays were discovered. The neutrino was discovered because neutron decay showed a three body momentum spectrum for the ... 1 Setting $$\theta := \theta_1 + \theta_2$$, the momentum of the Higgs boson (candidate) with respect to the lab $$\| \textbf p_{lab}[~H~] \| = \| \textbf p_{lab}[~\gamma_1~] \| ~\text{Cos}[~\theta_1~] + \| \textbf p_{lab}[~\gamma_2~] \| ~\text{Cos}[~\theta_2~] = (E_{lab}[~\gamma_1~] ~ \text{Cos}[~\theta_1~] + E_{lab}[~\gamma_2~] ~ ... 0 How does a molecule form? At the most general level the idea is that there exist lower energy states with the atoms in the molecule closer to each other, and the original joint state of the atoms had a nonzero ability to transition into that lower energy state and give up some energy. The rest is really some thermodynamics. If everything is hot and dense ... 2 You're question is interesting because it is connected to the notion of elementary particle. As mentioned by anna v, the elementary particles (fermions) of the standard model have very specific properties under the symmetry of the standard model (SU(2)_L\times U(1)_Y \times SU(3)_c): they lie in the fundamental representation of the group, which in ... 11 How can the unstable particles of the standard model be considered particles in their own right if they immediately decay into stable particles? Here I will only consider elementary, non composite particles. All the hadronic resonances are composite particles of quark antiquark combinations as well as the neutron . The standard model of particle ... 4 Inmediately is not really true, there is some proportionality. Sorry I am not answering directly about "the standard model", this is quarks and leptons. But they will fit the general pattern, you will see. Let me first consider all the "particles" listed in the particle data group file. Most of the particles decaying via photons have a half-live about ... 2 How can the unstable particles of the standard model be considered particles in their own right if they immediately decay into stable particles? Nobody has an issue calling the electron a particle. Ditto for a neutron. It's stable in a nucleus, and the fact that a free neutron decays in circa 15 minutes doesn't much matter. It's similar for a muon, ... 4 I think the most direct answer to this would be the fact that a heavier particle can decay into many different lighter particles for different reactions. The abundance of occurence of these relations are const. Again the same heavy particle can be created in multiple types of collisions of various different lighter particles. Thus we cannot say that the ... 24 Take for example an electron and a muon. The muon is unstable because it decays into an electron and two neutrinos in about 2\mus. But a muon is not in some sense an excited electron. Both particles are excitations in a quantum field and they are both as fundamental as each other. The electron is stable only because there is no combination of lighter ... 2 Your question seems quite general, but perhaps you're confused about what "decay" is. When we say something "decays" we don't always mean that it's somehow "breaking up" into it's constituent parts. In fact, we hardly ever do. The heavier particles aren't really "transient interplay of the stable forms", unless I misunderstand, and that isn't something that ... 3 The intrinsic parity of a pair of particles is the product of the intrinsic parities of the particles. The convention is that that matter particles have positive parity and antiparticles have negative parity, so a pair of matter particles should have positive intrinsic parity. However that's not quite the entire story, because electrons must obey the ... 4 I expect you are familiar with the Big Bang model, seen here . It is a mathematical model using mathematical solutions from General Relativity and the Standard Model of particle physics . The BB developed to describe astronomical observations and the SM developed to describe particle physics observations. The SM describes how particles/nature behaves as ... 10 You say: Now, when we talk about energetically favourably bound systems, they have a total mass-energy less than the sum of the mass-energies of the constituent entities. and this is perfectly true. For example if we consider a hydrogen atom then its mass is 13.6ev less than the mass of a proton and electron separated to infinity - 13.6eV is the ... 4 This happens because of a property of the strong force, called Asymptotic Freedom. This causes the interaction between quarks to get asymptotically weaker as the distance between them decreases. This is the reason why quarks are always found in a bound state and are not freely available in nature. The strong force confines quarks to a region where they ... 2 Your mistake is coming from your treatment of the orbital angular momentum in the case of a 3 body-decay. You have to take into account the orbital angular momentum between 2 pions L_1 and the orbital angular momentum L_2 between the third pion and the barycenter of the first 2 pions. The conservation of the total angular momentum imposes that$$\vec{1} ... 3 The best solutions of the challenge are available in these papers: http://jmlr.org/proceedings/papers/v42/ 0 Since you asked this question there have been a couple of confirmation of exotic particles which consist of four or more quarks. For example, Z(4430) recently observed in LHCb, was already discovered by Belle long time ago. This exotic particle has a$c\bar{c}d\bar{u}\$ quark structure. This would lead us to think how color confinement would be satisfied? As ...
1
You are right saying that the only advantage of the higher lumi accelerator will be to operate for a shorter amount of time. Indeed you can build up the same statistics just running longer at a lower lumi. But if you contextualize this, you find out important consequences. With physics programmes that already extend over decades, a factor 10 less luminosity ...
1
The textbook An Introductory Course of Particle Physics by Palash B. Pal offers a (slightly unsatisfactory) answer. The author writes that Such symmetris are often called horizontal symmetries. The name is a pictorial reminder to the list of quark fields in Eq. 17.1: transformations in this group act horizontally in this arrangement. I don't have the ...
0
I'm not actually a high-energy guy, and my knowledge of jets is all second hand, but I did do a graduate summer school on the topic one year. If I recall correctly... Jet energy is the total energy of particles making up the jet. Jet energy resolution is the experimental limit on how well that quantity can be known. You'll note that both of these ...
1
Is there any size of photon if so what is it? The photon is an elementary particle among the others which form a basis for the standard model of particle physics. The Standard Model of elementary particles (more schematic depiction), with the three generations of matter, gauge bosons in the fourth column, and the Higgs boson in the fifth. The ...
5
A photon is a unit ("quantum") of excitation of the quantum electromagnetic field. Thinking roughly of the quantum field as a vast collection of quantum harmonic oscillators, each oscillator corresponding to a mode of vibration of the field, we specify the quantum field's state by stating how many quantums above the QHO ground state each mode oscillator is ...
Top 50 recent answers are included | 2015-10-13 09:10:15 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7745004892349243, "perplexity": 515.916430588355}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-40/segments/1443738004493.88/warc/CC-MAIN-20151001222004-00230-ip-10-137-6-227.ec2.internal.warc.gz"} |
https://math.meta.stackexchange.com/questions/1127/wysiwyg-for-math-formulas | # WYSIWYG for math formulas?
Is there any website or tool that allows you to create math formulas visually which can then be pasted on this website?
I'm looking for something like the equation editor in Microsoft Word or Google Docs.
• Have you seen this? – J. M. is a poor mathematician Nov 12 '10 at 23:59
• @J.M.: nope, that's a pretty useful website. Still not entirely WYSIWYG, but it's a step in the right direction. – Senseful Nov 13 '10 at 1:58
• I'm working on a project that does exactly this. It's not ready yet but I'll report back when it is. If you want a preview, check out hristo.oskov.com/Kamma (I recommend using Chrome) – Hristo Mar 25 '11 at 3:54
• Maybe this comparison at Wikipedia might be useful for you. – Martin Sleziak May 4 '12 at 16:53
• We need a WYSIHYD editor for copy-pasted homework. – user127096 Mar 16 '14 at 15:45
• LyX is almost a WYSIWYG editor to generate document parsed by TeX engine. You can create a math environment with Ctrl+M, type the formula with help of a GUI, and then copy the whole environment. This place the TeX code of the formula into the clipboard.
• MathType also support copy-as-TeX when you have enabled it.
• Mathematica has the TeXForm[] function to convert its expression into TeX code, but it will have nonstandard commands.
Almost all my questions, answers and comments here have been created in version 4.10 of MacKichan Software's Scientific WorkPlace (SWP). The latest version is 5.5.
Here is an example
which generates the following code
\frac{1}{4}<\left( x-\frac{5}{2}\right) ^{2}<\frac{9}{4}\Leftrightarrow \frac{1}{2}<\left\vert x-\frac{5}{2}\right\vert <\frac{3}{2}
enclosed in \frac{1}{4}<\left( x-\frac{5}{2}\right) ^{2}<\frac{9}{4}\Leftrightarrow \frac{1}{2}<\left\vert x-\frac{5}{2}\right\vert <\frac{3}{2}
and a quote from the site:
You can create, edit, and typeset mathematical and scientific text more easily than ever before. The software is based on an easy-to-use word processor that completely integrates writing mathematics and text in the same environment. With the built-in computer algebra system, you can perform computations right on the screen.
These are some free version I found on the web that works well enough.
I found another one here http://camdenre.github.io/src/app/html/EquationEditor
I found an okay one here http://visualmatheditor.equatheque.net/ | 2020-02-24 02:36:10 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5678527355194092, "perplexity": 2508.988874519314}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-10/segments/1581875145869.83/warc/CC-MAIN-20200224010150-20200224040150-00090.warc.gz"} |
https://tex.stackexchange.com/questions/411780/using-apa6-how-do-i-get-the-date-to-appear-on-the-title-page-after-the-authors | # Using apa6, how do I get the date to appear on the title page after the authors
I've tried using: \data{\today}
but no date is printed on the title page.
The only way I can get a date on the title page is by putting \today between the \begin{document} and \maketitle, i.e.: \begin{document} \today \maketitle
This puts a date at the upper-left on the title page.
Thanks
Use the macro note
\documentclass[]{apa6}
\title{Title}
\author{John Doe}
\affiliation{University}
\note{\today}
\usepackage{lipsum}
\begin{document}
\maketitle
\lipsum[1-2]
\end{document} | 2020-11-27 08:32:40 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9642379879951477, "perplexity": 3959.711435222605}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-50/segments/1606141191511.46/warc/CC-MAIN-20201127073750-20201127103750-00317.warc.gz"} |
https://byjus.com/question-answer/the-quadratic-equation-x-2-ax-12-can-be-factorised-where-one-of-the-roots/ | Question
# The quadratic equation, $${x}^{2}+ax+12$$ can be factorised , where one of the roots $$k$$, is a negative integer. Then the possible value of $$k$$ is?
A
13
B
12
C
6
D
7
Solution
## The correct options are B $$-12$$ C $$-6$$Since the above equation has real roots and the product of the roots is positive, hence either both the roots are positive or both the roots are negative. However, it is given that one of the root is negative, hence both the roots are negative. Therefore the possible roots are $$(\pm1,\pm12),(\pm2,\pm6),(\pm3,\pm4)$$.Maths
Suggest Corrections
0
Similar questions
View More | 2022-01-28 11:11:39 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9475274682044983, "perplexity": 219.826275155974}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-05/segments/1642320305494.6/warc/CC-MAIN-20220128104113-20220128134113-00538.warc.gz"} |
https://www.physicsforums.com/threads/consider-a-spherical-wave-show-that-e-obeys-maxwells-equations.548894/ | Consider a spherical wave Show that E obeys maxwell's equations
Homework Statement
Consider a simple spherical wave, with omega/k=c
E(r, theta, phi, t)=((A sin theta)/r)(cos(kr - omega t) -(1/kr)sin(kr - omega t)) phi-hat
i) Using Faraday's law, find the associated magnetic field B
ii) Show that E obeys the remaining three of Maxwell's equations
The Attempt at a Solution
It's part b I am stuck on. I tried to prove it obeys div E=ro/epsilon0
I tried to do div E in spherical coordinates but I don't know how to when I don't know how to differentiate it with respect to phi because the equation given for E doesn't contain phi. i also don't know how ro is related to any of the terms in the equation for E. Please help.
dextercioby | 2021-04-22 03:03:31 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8680354356765747, "perplexity": 959.7784191391423}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-17/segments/1618039560245.87/warc/CC-MAIN-20210422013104-20210422043104-00309.warc.gz"} |
https://indico.cern.ch/event/452781/timetable/?view=standard_inline_minutes | # VERTEX 2016
Europe/Rome
La Biodola, Isola d'Elba, Italy
#### La Biodola, Isola d'Elba, Italy
,
Description
The International Workshop on Vertex Detectors (VERTEX) is a major annual series of international workshops for physicists and engineers from the high energy and nuclear physics community. VERTEX provides an international forum to exchange the experiences and needs of the community, and to review recent, ongoing, and future activities on silicon based vertex detectors. The workshop covers a wide range of topics: existing and future detectors, new developments, radiation hardness, simulation, tracking and vertexing, electronics and triggering, applications to medical and other fields.
The 25th edition of the series will be held on September 26th-30th 2016 at "La Biodola", a beautiful little bay on Elba Island. Participants are expected to attend the meeting for its full duration, arriving on the island on September 25th and leaving on October 1st.
Participants
• Alberto Ciarrocchi
• Alberto Messineo
• Aldo Mozzanica
• Alessandro Iovene
• Alexander Lawerenz
• Andre Schöning
• Andreas Mussgiller
• Auguste Guillaume Besson
• Barbara Storaci
• Benjamin Schwenker
• Cameron Thomas Dean
• Caterina Deplano
• Christer Frojdh
• Cinzia Da Via
• Claudia Gemme
• Daniel Hynds
• Daniela Bortoletto
• Dave Robinson
• Davide Ceresa
• Erika De Lucia
• Ettore Zaffaroni
• Fabian Huegging
• Fabrizio Palla
• Francesco Fiori
• Francesco Forti
• Francesco Tenchini
• Franco Ligabue
• Georg Steinbrueck
• Gian Mario Bilei
• Gian-Franco Dalla Betta
• Giuliana Rizzo
• Giulio Pellegrini
• Gregor Kramberger
• Harris Kagan
• Hongbo Zhu
• Hwanbae Park
• Hyebin Jeon
• Ioana Pintilie
• Irina Rashevskaya
• Jacobo Konigsberg
• Jan Troska
• Joel Goldstein
• Katsuro Nakamura
• Kookhyun Kang
• Leo Greiner
• Leonardo Rossi
• Lorenzo Vitale
• Luca Lodola
• Lucia Lilli
• Luigi Gaioni
• Marcel Vos
• Marco Petruzzo
• Marco Verzocchi
• Maria Margherita Obertino
• Mario Rothermund
• Massimiliano Fiorini
• Matthew Noy
• Maurizio Boscardin
• Maximiliano Puccio
• Michael J. Morello
• Michael Wang
• Mikael Mårtensson
• Mohsine Menouni
• Richard Brenner
• Roberto Dell'Orso
• Sascha Epp
• Seyed Ruhollah Shojaii
• Shanzhen Chen
• Shun Ono
• Simon Kudella
• Stefania Beole'
• Stefano Bettarini
• Sven Wonsak
• Thomas Fritzsch
• Thomas Lueck
• Valentina Santina Gallo
• Valerio Re
• Will Parker
• Yasuo Arai
• Yosuke Takubo
• Yuri Gotra
Email
• Sunday, 25 September
• 17:00 19:30
Registration
• 19:30 20:00
Welcome cocktail 30m
• Monday, 26 September
• 09:00 09:45
B00-Workshop opening
Convener: Roberto Dell'Orso (Universita di Pisa & INFN (IT))
• 09:00
Welcome 15m
Speaker: Francesco Forti (Universita di Pisa & INFN (IT))
• 09:15
Highlights of the Pixel 2016 workshop 22m
The Pixel 2016 workshop was held in Sestri Levante (not far from Elba) in early September.
It is the 8th of a series that initiated in the year 2000 in Genoa and moved to US, Europe and Asia. It is the only workshop entirely dedicated to the technology of the pixel detectors and all the applications in particle and x-ray physics. In this report I'll illustrate the most significant advances which have been presented and discussed at the workshop.
Speaker: Leonardo Rossi (Sezione di Genova)
• 09:45 10:45
B01-Operational experience on current detectors
Convener: Roberto Dell'Orso (Universita di Pisa & INFN (IT))
• 09:45
ALICE ITS Operational Experience 22m
ALICE, A Large Ion Collider Experiment, is conceived to study the physics of strongly interacting matter and the properties of the Quark-Gluon-Plasma produced in ultra-relativistic heavy-ions collisions at the CERN LHC. The innermost detector of ALICE is the Inner Tracking System (ITS) which plays the essential role of primary and secondary vertex reconstruction, it is used for particle tracking and identification and contributes to the first trigger level. The ITS covers the pseudo-rapidity range |η|<0.9 and consists of six cylindrical layers of silicon detectors placed coaxially around the beam pipe. Three different technologies have been selected to equip the ITS: pixel detectors for the two inner layers, drift detectors for the two central layers and strip detectors for the outer layers. In this report the three detectors constituting the ITS are briefly described, the operational experience during Run2 is summarised with a focus on the performance of the detector compared to Run1 and on the interventions done during the long technical stop at the end of 2015.
Speaker: Caterina Deplano (Nikhef National institute for subatomic physics (NL))
• 10:15
LHCb silicon detectors: Run 2 operational experience 22m
LHCb is a dedicated experiment to study New Physics in the decays of heavy hadrons at the Large Hadron Collider (LHC) at CERN. The detector includes a high precision tracking system consisting of a silicon-strip vertex detector (VELO) surrounding the pp interaction region, a large area silicon-strip detector located upstream of a dipole magnet (TT), three stations of silicon-strip detectors (IT), and straw drift tubes placed downstream (OT). The operational experience of the silicon detectors VELO, TT and IT from LHC Run 2, the maintenance work during year end shut down, and the upgrade of operation and monitoring software will be presented. Possible operational challenges for the silicon detectors in LHC Run 2 will also be discussed, with particular emphasis on studies of the effects of radiation damage.
Speaker: Shanzhen Chen (University of Manchester (GB))
• 10:45 11:15
coffee break 30m
• 11:15 12:45
B02-Operational experience on current detectors
Convener: Leonardo Rossi (Universita e INFN Genova (IT))
• 11:15
ATLAS IBL operational experience 22m
The Insertable B-Layer (IBL) is the inner most pixel layer in the ATLAS experiment, which was installed at 3.3 cm radius from the beam axis in 2014 to improve the tracking performance. To cope with the high radiation and hit occupancy due to proximity to the interaction point, a new read-out chip and two different silicon sensor technologies (planar and 3D) have been developed for the IBL.
After the long shut-down period over 2013 and 2014, the ATLAS experiment started data-taking in May 2015 for Run-2 of the Large Hadron Collider (LHC). The IBL has been operated successfully since the beginning of Run-2 and shows excellent performance with the low dead module fraction, high data-taking efficiency and improved tracking capability. The experience and challenges in the operation of the IBL will be presented as well as its performance.
Speaker: Yosuke Takubo (High Energy Accelerator Research Organization (JP))
• 11:45
ATLAS Tracker and Pixel Operational Experience 22m
The tracking performance of the ATLAS detector relies critically on the silicon and gaseous tracking subsystems that form the ATLAS Inner Detector. Those subsystems have undergone significant hardware and software upgrades to meet the challenges imposed by the higher collision energy, pileup and luminosity that are being delivered by the LHC during Run2. The key status and performance metrics of the Pixel Detector, the Semi Conductor Tracker, and the Transition Radiation Tracker are summarised, and the operational experience and requirements to ensure optimum data quality and data taking efficiency are described.
Speaker: Dave Robinson (University of Cambridge (GB))
• 12:15
CMS Tracker operational experience 22m
The CMS Tracker was repaired, recalibrated and commissioned successfully for the second run of Large Hadron Collider. In 2015 the Tracker performed well with improved hit efficiency and spatial resolution compared to Run I. Operations successfully transitioned to lower temperatures after commissioning environmental control and monitoring. This year the detector is expected to withstand luminosities that are beyond its design limits and will need a combined effort of both online and offline team to yield the high quality data that is required to reach our physics goals. We present the experience gained during the second run of the LHC and show the latest performance results of the CMS Tracker.
Speaker: Francesco Fiori (National Taiwan University (TW))
• 12:45 16:00
lunch break 3h 15m
• 16:00 17:30
B03-Operational experience on current detectors
Convener: Richard Brenner (Uppsala University (SE))
• 16:00
STAR MAPS Vertex Detector operational experience 22m
The Heavy Flavor Tracker at the STAR experiment is a set of silicon tracking detectors at the STAR experiment at the Relativistic Heavy Ion Collider at Brookhaven National Laboratory that is designed to extend the STAR measurement capabilities in the heavy flavor domain. This system took data in Au+Au collisions, p+p and p+Au collisions at $\sqrt{s_{NN}}=$200 GeV at RHIC, during the period 2014-2016. The innermost high resolution PiXeL detector (PXL) is the first application of the state-of-the-art thin Monolithic Active Pixel Sensors (MAPS) technology in a collider environment.
The PXL detector is based on 50 μm-thin MAPS sensors with a pitch of 20.7 μm. Each sensor includes an array of nearly 1 million pixels, read out in a column parallel rolling shutter mode with an integration time 185.6 μs. The 170 mW/cm2 power dissipation allows for air cooling and contributes to reduce the global material budget to 0.4% radiation length on the innermost layer.
The experience and lessons learned from construction and operations of this novel detector will be presented in this talk. Detector performance and results from 2014 Au+Au data analysis, demonstrating the STAR capabilities of charm reconstruction, will be shown.
Speaker: Leo Clifford Greiner (Lawrence Berkeley National Lab. (US))
• 16:30
The CLAS12 Silicon Strip Detector at CEBAF 22m
The Silicon Vertex Tracker is a central tracker built for the CLAS12 experiment aiming at measuring the momentum and reconstructing the vertices of charged particles emerging from the target. The system is designed to operate at a luminosity of 1035 cm-2s-1 and to have a momentum resolution of 5% for 1 GeV tracks. The tracker is centered inside 5T solenoid magnet and has 33792 channels of Hamamatsu silicon microstrip sensors. To lower the amount of material in the tracking volume to 0.06X0 modules are assembled on the barrel using unique cantilevered geometry. The sensors have graded angle design to minimize dead areas and a readout pitch of 156 μm. Double sided module hosts three daisy-chained sensors on each side with total strip length of 33 cm. There are 512 channels per module read out by four Fermilab Silicon Strip Readout (FSSR2) chips featuring data driven architecture, mounted on a rigid-flex hybrid. We describe the detector and present performance results from tracker commissioning with cosmic muons.
Speaker: Yuri Gotra (Thomas Jefferson National Accelerator Lab)
• 17:00
Operational experience with the NA62 Gigatracker 22m
The Gigatracker is a hybrid silicon pixel detector developed for the NA62 experiment at CERN, which aims at measuring the branching fraction of the ultra-rare kaon decay K$^{+} \rightarrow \pi^{+} \nu \overline{\nu}$ at the CERN SPS. The detector has to track particles in a 75 GeV/c hadron beam with a flux reaching 1.3 MHz/mm$^2$ and provide single-hit timing with better than 200 ps r.m.s. resolution for a total material budget of less than 0.5% X$_0$ per station. The tracker comprises three 61mm×27mm stations installed in vacuum (~10$^{−6}$mbar) and cooled with liquid C$_{6}$F$_{14}$ circulating through micro-channels etched inside few hundred of microns thick silicon plates. Each station is composed of a 200$\mu$m thick planar silicon sensor bump-bonded to 2×5 custom 100$\mu$m thick ASIC, called TDCPix. Each chip contains 40×45 asynchronous pixels, each 300$\mu$m×300$\mu$m and is instrumented with 720 time-to-digital converter channels with 100 ps bin. In order to cope with the high rate, the TDCPix is equipped with four 3.2 Gb/s serializers sending out the data. Detector description, operational experience and results from the NA62 experimental runs will be presented.
Speaker: Massimiliano Fiorini (Universita di Ferrara & INFN (IT))
• 17:30 18:00
coffee break 30m
• 18:00 19:30
B04-Detectors in design and construction
Convener: Marcel Vos (IFIC Valencia (ES))
• 18:00
The DAMPE silicon tungsten tracker 22m
The DAMPE (DArk Matter Particle Explore) satellite has been successfully launched on the 17$^{th}$ December 2015. It is a powerful space detector made of the following sub systems: a double layer plastic scintillator strip detector (PSD), a silicon-tungsten tracker converter (STK), a bismuth germanium oxide imaging calorimeter (BGO) and a neutron detector (NUD). The DAMPE satellite has been designed for the identification of possible Dark Matter signatures thanks to its capability to detect electrons and photons with an unprecedented energy resolution in an energy range going from few GeV up to 10 TeV. Moreover, thanks to the measurement of the nuclei flux up to 100 TeV, the DAMPE satellite will contribute to a better understanding of the propagation mechanisms of high energy cosmic rays. Currently, the DAMPE satellite is showing excellent performances in orbit and soon the first results will be published.
In this document, a detailed description of the silicon-tungsten tracker-converter STK and its performance in orbit are reported. The tracker has been designed and developed by an international collaboration composed of groups from University of Geneva, INFN Perugia, INFN Bari, INFN Lecce and the Institute of High Energy Physics, Beijing. The STK is made of 768 single-sided AC-coupled silicon micro-strip detectors arranged in 192 ladders for a total silicon area of about 7 m$^2$, comparable to the silicon area of the AMS-02 tracker. Moreover, the STK is also used as converter thanks to the insertion of tungsten foils which allow the conversions of incoming photons in electron-positron pairs. The STK is showing a very stable behavior in orbit with excellent performances in terms of charge reconstruction and space resolution.
Speaker: Valentina Gallo (Universite de Geneve (CH))
• 18:30
Development and construction of the Belle II DEPFET pixel detector 22m
The construction of the new accelerator at the Japanese Flavour Factory (KEKB) has been finalized and the commissioning of its detector (Belle II) is planned by early 2017. This new e+e- machine ("SuperKEKB") will deliver an instantaneous luminosity of 8⋅10^35 cm−2s−1, which is 40 times higher than the world record set by KEKB.
In order to be able to fully exploit the increased number of events and provide high precision measurements of the decay vertex of the B meson systems in such a harsh environment, the Belle II detector will include a new silicon vertex detector, based on the DEPFET technology. The new pixel detector, close to the interaction point, consists of two layers of active pixel sensors. The DEPFET technology combines the detection together with the in-pixel amplification by the integration, on every pixel, of a field effect transistor into a fully depleted silicon bulk. In Belle II, DEPFET sensors thinned down to 75 μm with low power consumption and low intrinsic noise will be used.
In the talk, a general overview of latest results and the construction status will be presented.
Speaker: Benjamin Schwenker (Uni Goettingen)
• 19:00
The Belle II SVD detector 22m
The Silicon Vertex Detector (SVD) is one of the main detectors in the Belle II experiment (KEK, Japan). The SVD takes essential roles of precise decay-vertex determination and low-energy-track reconstruction in combination with the PiXel Detector (PXD). SVD consists of four-layers Double-sided Silicon Strip Detectors (DSSD) located in a cylindrical shape around the Belle II interaction point. Each layer is composed of several DSSD ladders. Considering high beam-background circumstance in Belle II, we employ the APV25 readout ASIC chip with performances of small shaping time (~50nsec) and high irradiation tolerance (over 1MGy). The most notable feature of the SVD DSSD is a “chip-on-sensor” concept, which minimizes lengths of the signal propagation from DSSD strips to APV25 and reduces noises from strip capacitance into an acceptable level.
Under the international cooperation among several institutes, the SVD is being developed toward the installation in 2018. Currently, the mass production of the SVD ladders has been started. Also we have performed an electron-beam test combined with the PXD in order to develop tracking algorithm and estimate the performance. This talk will give an overview of the SVD development status, the performance, and the prospect of the SVD assembly and commissioning until the installation.
Speaker: Katsuro Nakamura (KEK)
• Tuesday, 27 September
• 09:00 10:30
B05-Detectors in design and construction
Convener: Franco Ligabue (Universita di Pisa & INFN (IT))
• 09:00
The LCHb VELO for Phase 1 Upgrade 22m
The LHCb experiment will undergo a complete upgrade during the second long shutdown of the LHC. The detector closest to the interaction region, the Vertex Locator (VELO), will be removed and replaced with a new design. The new VELO will sit closer to the interaction point and be capable of a full 40 MHz hardware readout which will drastically increase the physics reach of LHCb, leading us from the discovery towards the precision era. This presentation will discuss the aim, design, testing and current status of the VELO Upgrade.
• 09:30
The LHCb UT for Phase 1 upgrade 22m
The planned upgrade of the LHCb detector is designed to achieve 40 MHz readout (the maximum bunch crossing rate), allowing the experiment to collect 5fb^-1 of data per year. As part of this upgrade the tracking subsystem in front of the dipole magnet will be replaced by the Upstream Tracker (UT). Data from the UT will be critical to the LHCb software trigger, allowing more rapid and reliable extrapolation of tracks from the Vertex Locator to the Downstream Tracker. In addition to rapid readout, the UT will feature improved granularity to accommodate increased occupancy.
The detector consists of 4 planes with a total area of approximately 8.5 m^2, composed of single sided silicon strip sensors. The sensors are integrated with the dedicated front-end electronics into modules assembled in a double-sided fashion on vertical structures called staves, providing mechanical support and cooling. The innermost sensors have a circular cut-out at one edge to increase the acceptance near the beam pipe, and most of the sensors feature embedded pitch-adapters to match the sensor output pitch and the front-end electronics input pitch. The dedicated front-end ASIC (SALT) provides digitization with a built-in 6-bit ADC, common mode subtraction, and zero suppression and data processing and formatting. All components of the detector are designed to maintain performance through an integrated luminosity of 50 fb^-1.
The detector will commence operation together with the rest of the upgraded LHCb experiment after the LHC LS2 shutdown, currently scheduled to end in 2020. An overview of the UT design will be given and details of the performance of prototype sensors, electronics, and mechanical components, as well as the envisaged electronics system design and readout architecture, will be presented.
Speaker: Will Parker (University of Maryland (US))
• 10:00
The upgrade of the ALICE ITS 22m
ALICE (A Large Ion Collider Experiment) is studying the physics of strongly interacting matter and in particular the properties of the Quark-Gluon Plasma (QGP), using proton--proton, proton--nucleus and nucleus--nucleus collisions at the CERN LHC (Large Hadron Collider). To fulfil the requirements of the ALICE physics program for run 3 of the LHC, a major upgrade of the experimental apparatus is planned for installation in the second long LHC shutdown. A key element of the ALICE upgrade is the construction of a new, ultra-light, high-resolution Inner Tracking System (ITS). The new ITS will significantly enhance the determination of the distance of closest approach to the primary vertex, the tracking efficiency at low transverse momenta, and the read-out rate capabilities, with respect to what achieved with the current detector. It will consist of seven detector layers based on a Si Monolithic Active Pixel Sensors with a pixel size of about 30x30 $\mu m^2$. This contribution presents the design goals and layout of the new ALICE ITS, focusing on the performance of the sensor prototypes and on the technical implementation of the main detector components.
Speaker: Stefania Beole (Universita e INFN Torino (IT))
• 10:30 11:00
coffee break 30m
• 11:00 12:30
B06-Detectors in design and construction
Convener: Gian Mario Bilei (Universita e INFN, Perugia (IT))
• 11:00
The upgrade of the CMS pixel detector for phase 1 22m
The innermost layers of the CMS tracker are built out of pixel detectors arranged in three barrel layers (BPIX) and two forward disks in each endcap (FPIX). The original CMS detector was designed for the nominal instantaneous LHC luminosity of 1 x 10^34 cm^-2 s^-1. Under the conditions expected in the coming years, which will see an increase of a factor two of the instantaneous luminosity, the CMS pixel detector will see a dynamic inefficiency caused by data losses due to buffer overflows. For this reason the CMS Collaboration has been building a replacement pixel detector which is scheduled for installation in an extended end of year shutdown during Winter 2016/2017.
The Phase I upgrade of the CMS pixel detector will operate at full efficiency at an instantaneous luminosity of 2 x 10^34 cm^-2 s^-1 with increased detector acceptance and additional redundancy for the tracking, while at the same time reducing the material budget. These goals are achieved using a new readout chip and modified powering and readout schemes, one additional tracking layer both in the barrel and in the disks, and new detector supports including a CO2 based evaporative cooling system, that contribute to the reduction of the material in the tracking volume.
This contribution will review the design and technological choices of the Phase I detector, and discuss the status of the construction of the detector and the performance of its components as measured in test beam and system tests. The challenges and difficulties encountered during the construction will also be discussed, as well as the lessons learned for future upgrades.
Speaker: Marco Verzocchi (Fermi National Accelerator Lab. (US))
• 11:30
The CMS Silicon Pixel detector for HL-LHC 22m
The LHC is planning an upgrade program which will bring the luminosity to about $5\cdot 10^{34}$cm$^{-2}$s$^{-1}$ in 2028, with the goal of an integrated luminosity of 3000 fb$^{-1}$ by the end of 2037. This High Luminosity scenario, HL-LHC, will present new challenges of higher data rates and increased radiation. In order to maintain its physics reach in the HL-LHC era, the CMS Collaboration is preparing an upgrade program of the detector known as the Phase-2 upgrade. The CMS Phase-2 Pixel upgrade will require a high bandwidth readout system and highly radiation tolerant sensors and on-detector ASICs. Several technologies for the upgrade sensors are being studied. Serial powering schemes are under consideration to accommodate significant constraints on the system. These prospective designs, as well as new layout geometries that include very forward pixel discs with acceptance extended from |eta|<2.4 to |eta|<4, will be presented together with performance estimates.
Speaker: Georg Steinbrueck (Hamburg University (DE))
• 12:00
The CMS Outer Tracker detector for HL-LHC 22m
The LHC is planning an upgrade program that foresees to increase the luminosity to about 5*10^34cm-2s-1 by 2028, and which will allow to reach an integrated luminosity of 3000fb-1 by 2037. In line with the preparations for the High Luminosity LHC (HL-LHC), the LHC experiments are preparing substantial upgrades of their detectors in order to cope with the new requirements. For the HL-LHC era CMS will replace its current outer tracker by a completely new system that will withstand the harsh operation condition and fully exploit the provided luminosity. In contrast to the existing tracker, the new system will also provide trigger information that will allow track reconstruction in the Level-1 trigger decision. The presentation will discuss the design of the future CMS outer tracker and show highlights from the ongoing R&D activities.
Speaker: Andreas Mussgiller (Deutsches Elektronen-Synchrotron (DE))
• 12:30 16:00
lunch break 3h 30m
• 16:00 18:00
B07-Detectors in design and construction
Convener: Prof. Daniela Bortoletto (University of Oxford (GB))
• 16:00
The Mu3e Pixel-Tracker 22m
The Mu3e experiment at PSI will search for the Lepton Flavor Violating Decay mu^+ -> e^+e^+e^- with an unprecedented sensitivity of 1 out of 10^16 decays. The Mu3e tracking detector has four layers of High Voltage-Monolithic Active Pixel Sensors (HV-MAPS) and exploits He-gas cooling and an ultra-light mass design with a thickness of 1 per mill of a radiation length per layer to fulfill the very stringent requirements from multiple Coulomb scattering. All registered hits are readout and reconstructed using an online event reconstruction.
The design of the MUPIX chip implementing a trigger-less readout architecture is presented
together with recent results from test beam measurements obtained with the MUPIX7 chip, which represents a fully functional small scale HV-MAPS prototype of the final sensor. The layout of the ultra-light tracker modules is described and data transmission tests using thin aluminium-kapton flex-prints are presented.
Finally an outlook is given. Possible applications of the HV-MAPS technology, in particular of the MUPIX design, for upgraded LHC experiments and track trigger applications will be discussed.
Speaker: Andre Schoening (Ruprecht-Karls-Universitaet Heidelberg (DE))
• 16:30
The ATLAS tracker pixel detector for HL-LHC 22m
The high luminosity upgrade of the LHC (HL-LHC) in 2026 will provide new challenges to the ATLAS tracker. The current inner detector will be replaced with an entirely-silicon tracker which will consist of a five barrel layer Pixel detector surrounded by a four barrel layer Strip detector. The expected high radiation levels are requiring the development of upgraded silicon sensors as well as new a front-end chip. The dense tracking environment will require finer granularity detectors. The data rates will require new technologies for high bandwidth data transmission and handling. The current status of the HL-LHC ATLAS Pixel detector developments as well as the various layout options will be reviewed.
Speaker: Claudia Gemme (Universita e INFN Genova (IT))
• 17:00
The ATLAS tracker strip detector for HL-LHC 22m
As part of the ATLAS upgrades for the High Luminsotiy LHC (HL-LHC) the current ATLAS Inner Detector (ID) will be replaced by a new Inner Tracker (ITk). The ITk will consist of two main components: semi-conductor pixels at the innermost radii, and silicon strips covering larger radii out as far as the ATLAS solenoid magnet including the volume currently occupied by the ATLAS Transition Radiation Tracker (TRT). The primary challenges faced by the ITk are the higher planned read out rate of ATLAS, the high density of charged particles in HL-LHC conditions for which tracks need to be resolved, and the corresponding high radiation doses that the detector and electronics will receive. The ITk strips community is currently working on designing and testing all aspects of the sensors, readout, mechanics, cooling and integration to meet these goals and a Technical Design Report is being prepared. This talk is an overview of the strip detector component of the ITk, highlighting the current status and the road ahead.
Speaker: Kyle James Read Cormier (University of Toronto (CA))
• 17:30
CMOS pixel development for HL-LHC 22m
CMOS pixel detectors with charge collection in an epitaxial layer (10-20 $\mu$m thick) have been developed since 2001 and have become realized in the STAR pixel detector at RICH and are also proposed for the ALICE ITS Upgrade. For the rate and radiation environment expected at the HL-LHC new approaches have been developed based on the following enabling technology features: HV add-ons that allow to use high depletion voltages (HV-MAPS); high resistivity wafers for large depletion depths (HR-MAPS); radiation hard processed with multiple nested wells to allow CMOS electronics embedded with sufficient shielding into the sensor substrate and backside processing and thinning for material minimization and backside voltage application.
R&D within for HL-LHC has started about 2010. Currently members of more than 20 groups in ATLAS are actively pursuing CMOS pixel R&D in an ATLAS Demonstrator program (sensor design and characterizations) started in 2014. The program's first goal was to demonstrate that depleted (monolithic) CMOS pixels (DMAPS) are suited for high rate, fast timing and high radiation operation at LHC. For this a number of technologies have been explored and characterized. In this presentation the challenges for the usage of CMOS pixel detectors at HL-LHC are discussed such as fast readout and low power consumption designs as well as fine pitch and large pixel matrices. Different designs of CMOS prototypes are presented with particular emphasis on timing (rate) performance and radiation tolerance.
Speaker: Fabian Huegging (Universitaet Bonn (DE))
• 18:00 19:30
B08-Poster and industry session
Wine and cheese poster and industry session
• 18:00
Wire-bonding and Assembly Studies for the Outermost Layer of Silicon Vertex Detector in the Belle-II experiment 1m
The vertex detector (VXD) for the Belle-II experiment, at the Super-KEKB in Japan, measures precisely information of vertexing and tracking. The VXD consists of a pixel detector (PXD) and a silicon vertex detector (SVD) with two and four layers, respectively, so that operates under a high luminosity environment of the Belle-II experiment. For the SVD, a novel chip-on-sensor concept, called “Origami”, is developed to reduce the multiple Coulomb scattering and capacitive noise. A wire-bonding and assembly procedures for the outermost layer of the SVD have been studied. A wire-bonding study especially for the Origami module has been performed. As changing the bonding parameters, we measure pull-forces to break the wires by pulling them and observe shape types of broken wires and bond foot prints. In addition, an issue on position precision of a tilted DSSD is found, and a shim method has been employed and studied to improve mechanical precision of the DSSD. In this paper, we present the results of wire-bonding study and introduce the shim method to solve the problem of the tilted sensor during the assembly procedures.
Speakers: Hyebin Jeon (On behalf of Belle-II SVD Collaboration) , Mr Kookhyun Kang (Kyungpook National Universiy)
• 18:01
2.5 Gb/s Simple Optical Wireless Communication System for Particle Detectors in High Energy Physics 1m
We successfully demonstrated simple and low cost 2.5 Gb/s optical wireless transmission at 10 cm distance, aiming to be employed in high-energy physics experiments using off-the-shelf VCSEL and PIN photodiode with proper ball lens. The measured tolerance to misalignment is around ±1mm at Bit Error Rate of 10-12.
Summary:
Particle physics experiments generate large amounts of data, whose transmission requires huge infrastructure of optical fibers. This increases the material budget, limits space and also introduces excessive labor cost for cables installation and management. High-speed Optical Wireless Communication (OWC) can be a viable solution to reduce the complexity of optical fiber networks for future upgrades. We are designing an OWC system for particle detectors, having as a reference application the inner tracker of Compact Muon Solenoid (CMS) operating in Large Hadron Collider (LHC) at CERN. The proposed OWC solution is not intended to completely substitute the optical fiber links, but it will be rather used to introduce the radial connectivity between silicon strip sensors.
We have designed a 2.5 Gb/s OWC link, which comprises a VCSEL (1550nm) transmitter and a PIN photodiode with ball lens at 10 cm of transmission distance. In future, this simple and low cost design may be integrated on silicon strip sensors inside CMS or other short distance links in particle detectors.
After careful design of the receiver, we achieved a tolerance to misalignment in the range of ±1mm, which is important because, only passive alignment in range of ≥±0.25 mm is acceptable in particle detector systems. In this paper, we report the design of the OWC link and detailed tolerance to misalignment study, based on different diameter lenses at the receiver. By this analysis, we designed the custom packaging for the photodiode and a 4mm ball lens. The results of this activity will also be presented in the paper.
We are aiming to deploy the OWC link in high energy physics environment therefore, we have selected VCSEL and InGaAs PIN photodiode because of their radiation tolerance [J. Troska et al, IEEE Trans on Nuclear Sci, 58, 6, Dec 2011]. Moreover, we selected fused silica and quartz glass type lenses, since they only can provide proper irradiation properties, i.e. much better than BK7 glass at 1550nm [S.M. Javed Akhtar., et al, Optical Materials, Vol 29, 12, Aug 2007].Since these glass types are still tested for lower dose in future we will plan irradiation test in order to qualify the optical components and especially the lens in environments with high radiation level.
• 18:02
Fast pattern recognition of ATLAS L1 track trigger for HL-LHC 1m
A fast hardware based track trigger for high luminosity upgrade of the Large Hadron Collider (HL- LHC) is being developed in ATLAS. The goal is to achieve trigger levels in high pileup collisions that are similar or even better than those achieved at low pile-up running of LHC by adding tracking information to the ATLAS hardware trigger which is currently based on information from calorimeters and muon trigger chambers only.
Two methods for fast pattern recognition are investigated. The first is based on matching tracker hits to pattern banks of simulated high momentum tracks which are stored in a custom made Associative Memory (AM) ASIC. The second is based on the Hough transform where detector hits are transformed into 2D Hough space with one variable related to track pt and one to track direction.
Hits found by pattern recognition will be sent to a track fitting step which calculates the track parameters . The speed and precision of the track fitting depends on the quality of the hits selected by the pattern recognition step. The figure of merit of the pattern recognition is measured by the efficiency for finding hits from high pT tracks and the power of rejecting hits from low pT tracks and fakes.
We will describe the implementation of the two methods for Silicon Tracker (SIT) for ATLAS HL- LHC upgrad and compare the performance using full event simulation with 200 event pile-up .
Speaker: Mikael Martensson (Uppsala University (SE))
• 18:03
A silicon positition sensitive detector for the AEGIS experiment 1m
The AEGIS experiment at CERN aim to measure the gravitational constant of anti-Hydrogen and in the future perform long-term anti-matter mass spectroscopy. To achieve the gravitational measurement, the AEGIS collaboration will produce a pulsed anti-Hydrogen beam for the first time and measure the deflection of the path of the antihydrogen from a straight line, after it has passed through a Moire reflectometer. A gravitational module, consisting of a silicon detector, an emulsion detector and a scintillating fibre time-of-flight detector will measure the annihilation of the anti-Hydrogen and is being developed to provide a position resolution better than 10 μm. Here we present the status of the AEGIS experiment as well as the latest results on the gravitation module, in particular new results on the silicon detector where the annihilations will take place.
Speaker: Heidi Sandaker (University of Oslo (NO))
• 18:04
Qualification of Barrel Pixel Detector Modules for the Phase 1 Upgrade of the CMS Vertex Detector 1m
To withstand the higher rates of LHC Runs 2 and 3, with expected luminosities of up to 2 x 10^34 cm^{-2} s^{-1}, the current CMS pixel detector at the LHC will be replaced as part of the CMS Phase I Upgrade during the extended winter shutdown in 2016/17. The new pixel detector features a new geometry with one additional detector layer in the barrel region (BPIX) and one additional disk in the forward region (FPIX), new digital readout chips and improved front-end electronics as well as a new CO2-based cooling system for both the barrel and forward region. An overview of the BPIX detector module production will be given, with special focus on the different stages of quality assurance. A review of the quality tests as well as the calibrations which all produced modules undergo in a temperature and humidity controlled environment will be given, together with a description of the testing setups. Exemplary, the KIT/Aachen production line and its subprocesses will be presented together with their quality and yield.
Speaker: Mr Simon Kudella (KIT - Karlsruhe Institute of Technology (DE))
• 18:05
Tracking Machine Learning Challenge 1m
The instantaneous luminosity of the LHC is expected to increase at HL-LHC so that the amount of pile-up can reach a level of 200 interaction per bunch crossing, almost a factor of 10 w.r.t the luminosity reached at the end of run 1. In addition, the experiments plan a 10-fold increase of the readout rate. This will be a challenge for the ATLAS and CMS experiments, in particular for the tracking, which will be performed with a new all Silicon tracker in both experiments. In terms of software, the increased combinatorial complexity will have to be dealt with within flat budget at best.
Preliminary studies show that the CPU time to reconstruct the events explodes with the increased pileup level. The increase is dominated by the increase of the CPU time of the tracking, itself dominated by the increase of the CPU time of the pattern recognition stage. In addition to traditional CPU optimisation and better use of parallelism, exploration of completely new approaches to pattern recognition has been started.
To reach out to Computer Science specialists, a Tracking Machine Learning challenge (trackML) has been set up, building on the experience of the successful Higgs Machine Learning challenge in 2014 (see talk by Glen Cowan at CHEP 2015). It associates ATLAS and CMS physicists with Computer Scientists. A few relevant points:
• A dataset consisting of a simulation of a typical full Silicon LHC experiments has been created, listing for each event the measured 3D points, and the list of 3D points associated to a true track. The data set is large to allow the training of data hungry Machine Learning methods : the orders of magnitude are : one million event, 10 billion tracks, 1 terabyte.
• The participants to the challenge should find the tracks in an additional test dataset, meaning building the list of 3D points belonging to each track (deriving the track parameters is not the topic of the challenge)
• A figure of merit has been defined which combines the CPU time, the efficiency and the fake rate (with an emphasis on CPU time)
• The challenge platforms allow measuring the figure of merit and to rate the different algorithms submitted.
The emphasis is to expose innovative approaches, rather than hyper-optimising known approaches. Machine Learning specialists have showed a deep interest to participate to the challenge, with new approaches like Convolutional Neural Network, Deep Neural Net, Monte Carlo Tree Search and others.
Speaker: David Rousseau (LAL-Orsay, FR)
• 18:06
4D fast tracking for experiments at the High Luminosity LHC 1m
Several efforts have been recently devoted to develop high-resolution timing detectors for tracking at the High Luminosity LHC (HL-LHC) experiments while track triggers, implemented with dedicated hardware, have been used at hadron colliders to select heavy-flavour decays. We propose a R&D project to combine the two methods and develop an innovative detector, based on accurate time and position particle hit measurements, for 4D tracking and fast track trigger. The precise measurement of the hits’ time is the key feature to operate an effective pattern recognition that guarantees a high tracking efficiency while enhancing the ghost track rejection, and to perform selective track triggering. We ultimately aim to exploit this detector in flavour physics experiments, in conditions of a high event pile-up, where sensors and front-end electronics are required to provide a hit time resolution of the order of 20 ps and a hit position resolution better than 40 $\mu$m, and are able to continuously operate in a harsh radiation environment (up to a total flux of $10^{17}$ 1-MeV neutrons equivalent per cm$^2$).
State of the art tracking pixel detectors with precise time-tagging show a time resolution of about 200 ps, and we aim to reduce this by one order of magnitude. Crucial aspects to achieve this ultimate time resolution are the optimization of pixel sensor geometries (in both 3D and planar technologies) to achieve the most uniform electric field, and the design of fast and low noise dedicated front-end ASIC. This front-end will incorporate a fast current amplifier followed by a discriminator and a time-to-digital converter, and will be developed in 65 nm CMOS technology with fault tolerant architecture which matches the radiation hardness requirements.
Feasibility studies of a 4D fast track finding system, using hits’ space and time information, has been recently presented as a possible solution for the low level track trigger of the HL-LHC experiments. The system is based on a massively parallel algorithm implemented in commercial FPGAs using a pipelined architecture and allows a precise real-time determination of the track parameters (including time) while maintaining a low fraction of reconstructed fake tracks.
The proposed detector will allow to perform flavour physics at the LHC operating at instantaneous luminosities more than one order of magnitude larger than the current ones, while guaranteeing large tracking efficiencies and a negligible ghost tracks rate.
Speaker: Massimiliano Fiorini (Universita di Ferrara & INFN (IT))
• 18:07
Readout architecture for the Pixel-Strip module of the CMS Outer Tracker Phase-2 upgrade 1m
The Outer Tracker upgrade of CMS introduces new challenges for the front-end readout electronics. In particular, the capability of identifying particles with high transverse momentum requires high speed real time communication among readout ASICs. The Pixel-Strip module needs two different readout ASICs, namely the SSA for the strip sensor and the MPA for the pixelated sensor. At each Bunch Crossing, the strip data are transmitted to the MPA which is responsible for the particle discrimination. The proposed architecture allows for a total data flow between readout ASICs of ~100 Gbps and reduces the output data flow from 1.28 Tbps to 60 Gbps per module with a total power density < 100 mW/cm$^2$.
Speaker: Davide Ceresa (CERN)
• 18:08
PixFEL: development of an X-ray diffraction imager for future FEL applications 1m
A readout channel for applications to X-ray diffraction imaging at free electron lasers has been developed in a 65 nm CMOS technology. The analog front-end circuit can achieve an input dynamic range of 100 dB by leveraging a novel signal compression technique based on the non-linear features of MOS capacitors. Trapezoidal shaping is accomplished through a transconductor and a switched capacitor circuit, performing gated integration and correlated double sampling. A small area, low power 10 bit successive approximation register (SAR) ADC, operated in a time-interleaved fashion, is used for numerical conversion of the amplitude measurement. A prototype chip has already been fabricated and characterized. A new readout chip, consisting of 32x32 square cells, has been designed to be bump bonded to a slim/active edge pixel sensor and form the first demonstrator for the PixFEL X-ray imager. The pixel pitch is 110 μm, for a total area of about 16 mm$^2$. In particular, a couple of different versions for the time variant processor have been implemented and, as compared to the prototype version, the charge preamplifier is provided with a larger range of gain settings, therefore improving the system capability to comply with photon energies in the 1 keV to 10 keV interval. This work, besides discussing in detail the readout channel and array architecture, will present the results from the chip characterization.
Speaker: Luca Lodola (INFN - National Institute for Nuclear Physics; University of Pavia)
• 18:09
Double-sided strip sensors for Limadou-CSES project 1m
Production of 60 AC-coupled double-sided silicon microstrip sensors, designed to equip the two layers of the HERD detector in the Limadou-CSES project, has been recently completed at FBK. The sensors, fabricated on 150 mm silicon wafers, have an overall size of 10.96 cm x 7.76 cm = 85.05 cm2.
Sensor testing and quality control has been performed at INFN Trieste and TIFPA. After presenting an overview of the test procedures and results, the contribution will focus on the analysis of some characteristic defects, which were severely limiting the production yield. As a result of this study, a modification of the fabrication process has been proposed, leading to an increased yield.
Speaker: Irina Rashevskaya (Universita e INFN, Trieste (IT))
• 18:10
Characterization of HV-CMOS detectors in BCD8 technology and of a controlled hybridization technique 1m
Radiation detectors built in high-voltage and high-resistivity CMOS technology are an interesting option for the large area pixel-trackers sought for the upgrade of the Large Hadron Collider experiments. A possible architecture is a hybrid design, where CMOS sensors are readout by front-electronics coupled through a thin dielectric layer. A critical requirement is the radiation hardness of both the sensor and interconnection technology up to a dose of 0.1-1 Grad, depending on the distance from the interaction region.
In this paper we present the characterization of detctors built in BCD8 technology by STMicrolectronics. The BCD8 is a 160 nm process integrating bipolar, CMOS and DMOS devices and it is mostly used for automotive application. A version with 70 V voltage capability has been tested to evaluate its suitability for the realization of CMOS sensors with a depleted region of several tens of micrometer. Sensors featuring 50×250 µm2 pixels on a 125 Ωcm resistivity substrate have been characterized showing a uniform breakdown at 70 V before irradiation, as expected by design in this technology, and a capacitance of about 80 fF at 50 V reverse bias voltage.
The response to ionizing radiation is tested using radioactive sources and an X-ray tune, reading out the detector with an external spectroscopy chain. At the nominal 50 V bias, the device can detect soft X-rays, whose ionization yield is comparable to a minimum ionizing particle in the depletion region, demonstrating the detector is suitable also for charged particle detection and tracking application.
Irradiation tests were performed up to proton fluences exceeding 5×1015 p/cm2 and they show the depletion and breakdown voltages increases with irradiation
A hybridization process for capacitive coupling has been developed. It consists of gluing the CMOS sensor to the readout electronics using a dielectric epoxy, whose thickness is controlled by SU8 pillars deposited on the readout chip surface. Uniformity of better than 100 nm on the pillar surface has been obtained. Assemblies have been performed using the ATLAS FE-I4 readout ASIC and prototype CMOS sensors. Measurements show a planarity better than 1.5 µm peak-to-peak on the 5 mm length of the HV-CMOS chip. To evaluate more precisely the achievable uniformity dummy chips of FE-I4 sizes have been made on 6-inch wafers. The measurement of the 24 capacitors on each chip is expected to achieve a precise estimation of the real thickness uniformity. The goal is to achieve less then 10% variation on the glue thickness (~0.5 µm).
Speakers: Ettore Zaffaroni (Università degli Studi e INFN Milano (IT)) , Hitesh Shrimali (IIT Mandi)
• 18:11
Testbeam results for the first real-time tracking system based on artificial retina algorithm 1m
The INFN-Retina project aims at developing a fast track finding system prototype capable to operate at 40 MHz event rate with hundreds of track per event, for the high-luminosity LHC experiments. A tracking system prototype to be tested on beam has been built as practical demonstrator. In this work, we present the testbeam results of an embedded tracking system prototype based on artificial retina algorithm, capable to reconstruct tracks in real time with a latency <1 μs and with track parameter resolutions that are comparable with the offline results. The maximal event rate that the telescope can accept is 1.1 MHz and it is determined by the Beetle readout chip. The test was carried out using a 180 GeV/c proton beam at the CERN SPS. The tracking system prototype consists of 8 planes of single-sided silicon sensors with 512 strips each and 183 μm pitch; the active area of the sensor is about 100 cm2 with 500 μm thickness.
A custom data acquisition (DAQ) board based on Xilinx Kintex 7 FPGA has been developed. It manages the readout of the ASICs, the sampling of the analog channels, and the retina algorithm implementation. The FPGA resources have been divided among the different modules of the retina architecture: approximately 10% for the switch module that routes the data to appropriate cellular units for the processing stage, 50% for the pool of engines that evaluate how well a set of hits matches with a specific track hypothesis, and 10% for the track parameter determination, keeping the rest for backup. This configuration allows to realise more than 1000 cellular units working in parallel at a clock frequency of the system greater than 200 MHz. Testbeam results will be presented and compared with simulations, in particular for the tracking performance. Perspective for the future will be also discussed.
Speakers: Jinlin Fu (Università degli Studi e INFN Milano (IT)) , Marco Petruzzo (Università degli Studi e INFN Milano (IT))
• 18:12
The CMS Pixel Luminosity Telescope 1m
The Pixel Luminosity Telescope is one of the newest additions to a number of sub-detectors dedicated to measuring the luminosity provided to the CMS experiment by the LHC. The PLT, as an independent luminometer, consists of eight 3-layer telescopes based on silicon pixel detectors placed at a high eta around the beam pipe on each end of CMS. All 16 telescopes view the interaction point under a small angle. A fast cluster counting signal from the front-end chips is used to form 3-fold coincidences in the telescopes when a particle passes all three planes. By applying the zero-counting method a bunch-by-bunch online measurement of the delivered luminosity is produced. Tracking information is used in offline analysis methods to derive corrections to the measured data by distinguishing collision products from beam halo and other accidental events caused by albedo, multiple scattered and other stray particles. The tracking information also provides an alignment of the installed telescopes. Using the CMSSW simulation framework and the experience gained during the 2015 running period, the PLT operating configuration was prepared for the high luminosity running period in 2016. The performance of the detector will be presented.
Speaker: Andreas Kornmayer (CERN)
• 18:13
A Decay Tree Fitter for the Belle II Analysis Framework 1m
The Belle II experiment at SuperKEKB is rapidly approaching its data taking phase, where it will be used to perform precision measurements of SM and new physics processes with unprecedented accuracy. At the same time, the Belle dataset (~1ab^{-1}) still presents rich possibilities for physics analyses, which can now also be performed within the Belle II Analysis Software Framework (basf2). In both of these cases, high precision reconstruction of particle observables is paramount.
Decay chains in particle physics experiments are typically reconstructed vertex by vertex, starting with final state particles and ending with the head of the decay tree. However, this means each vertex fit is blind to upstream information which could potentially improve the fit resolution.
An alternate approach, which was used with success in BaBar, involves using a least square approach, based on a Kalman filter, to extract all parameters of the decay chain simultaneously. This method is especially useful in the reconstruction of neutral or missing particles and provides access to the full covariance matrix of the decay. It is being implemented in basf2 and will be presented along with the outlook for future physics analyses.
Speakers: Dr Francesco Tenchini, Dr Francesco Tenchini (University of Melbourne)
• 18:14
THE SOFTWARE FRAMEWORK OF THE BELLE II SILICON VERTEX DETECTOR AND ITS DEVELOPMENT FOR THE 2016 TEST-BEAM AT DESY 1m
GIACOMO CARIA and PHILLIP URQUIJO, School of Physics, The University of Melbourne, VIC 3010
(on behalf of the Belle II SVD group )
In this poster, I shall give an overview of the reconstruction software for the Belle II Silicon Vertex Detector (SVD). The Belle II detector at the SuperKEKB e+e- collider in Tsukuba, Japan, aims to probe the flavour frontier, looking for new sources of CP violation. Construction will be completed in late 2018 to be ready for physics data taking. The SVD is a key component of the Belle II inner detector (Vertex Detector), comprised of four layers of double-sided silicon strip sensors. It is responsible for reconstructing trajectories of slow pions, for providing energy loss information for particle identification, and for an accurate determination of decay vertices such as those from K-short mesons. The SVD must therefore provide highly reliable, and precise charged particle hit information at an unprecedented luminosity (designed value 8 x 10^35 cm^-2 s^-1).During April 2016 the SVD and the Pixel detector systems were tested at a DESY test-beam facility in Hamburg, Germany. In this exercise the performance of hardware design, data acquisition and software framework were studied, providing much needed insight for the completion of the detector modules and for their operation in Belle II. I shall discuss SVD software framework, focusing on the aspects that have been developed for the DESY test-beam as well as some aspects of full Belle II operation: such as the treatment of data quality issues in silicon strips, calibration of the charge read-out system, and hit clustering algorithms.
Speaker: Mr Giacomo Caria (University of Melbourne)
• 18:15
An Associative Memory Chip for the Trigger System of the ATLAS Experiment 1m
The AM06 is the 6th version of a large Associative Memory chip designed in 65 nm CMOS technology. The AM06 operates as a highly parallel ASIC processor for pattern recognition in ATLAS experiment at CERN. It is the core of the Fast TracKer electronic system which is tailored for online track finding in trigger system of ATLAS experiment at the LHC. The Fast TracKer system is able to process events up to 100 MHz in real time.
AM06 is a complex chip, designed combining full-custom memory arrays, standard logic cells and IP blocks. It contains memory banks that store data organized in 18 bit words; a group of 8 words is called a “pattern”. AM06 silicon area is 168 mm2 and contains 421 millions transistors and stores 217 patterns.
Moreover AM is suitable also for interdisciplinary applications (i.e., general purpose image filtering and analysis). In future we plan to design a more powerful and flexible chip at 28 nm CMOS.
In this poster the architecture of design and the characterization results of AM06 will be presented.
Speaker: Seyed Ruhollah Shojaii (Università degli Studi e INFN Milano (IT))
• 18:16
Measurement of the hit resolution and reconstruction efficiency of the Belle-II Silicon Vertex Detector in the 2016 beam test at DESY 1m
The Belle-II experiment is a multipurpose particle detector which will
take data at the asymmetric electron positron collider SuperKEKB
operated at a design luminosity of $8\times 10^{35} cm^{-2} s^{-1}$.
Track reconstruction close to the interaction point in the Belle-II
experiment is provided by the Silicon Vertex Detector (SVD), consisting of
4 layers of double sided silicon strip detectors, and two layers of
pixel detectors (PXD). The SVD was designed to provide a high hit finding efficiency and
position resolution when operated in the high-luminosity environment
provided by the SuperKEKB collider.
In April 2016 a combined beam test of the SVD and
the PXD has been performed at DESY Hamburg to test
the full data acquisition chain which will be used
in the Belle-II experiment.
For this beam test a section of the SVD and the PXD have
been placed in a beam of high energy electrons.
Several runs of data taking have been recorded with
varying beam energies, ranging from 2 GeV up to 5 GeV, within
a magnetic field which strength was varied between 0 Tesla and 1 Tesla.
We use the data recorded at the beam test at DESY to perform
a measurement of the hit reconstruction efficiency and the resolution
of the reconstruction of hit positions of the
SVD-sensors. For this measurement we use reconstructed tracks
to predict the position of a hit on the SVD-sensor under test
and try to find reconstructed hits in the proximity of
the predicted position. Efficiencies are estimated by
counting how often a hit could be associated to
the reconstructed track. The spatial resolution of reconstructed
hits is estimated by analyzing the residuals of the
reconstructed hit positions with respect to the positions predicted by the
extrapolated track.
To avoid biases the SVD-sensor under test is not included
in the track finding and fitting procedure. The efficiency
is measured as a function of the position on the sensor.
Speaker: Mr Thomas Lück (INFN - Pisa)
• 18:17
Large Area Thinned Planar Sensors for Future High-Luminosity-LHC Upgrades 1m
Planar hybrid silicon sensors are a well proven technology for past and current particle tracking detectors in HEP experiments. However, the future high-luminosity upgrades of the inner trackers at the LHC experiments pose big challenges to the detectors. A first challenge is an expected radiation damage level of $2\cdot 10^{16}\, \mbox{n}_{\mbox{eq}}/\mbox{cm}^2$. For planar sensors, one way to counteract the charge loss and thus increase the radiation hardness is to decrease the thickness of their active area. A second challenge is the large detector area which has to be built as cost efficient as possible, i.e. it is aimed for low-cost and large-sized sensors.
The CiS research institute has accomplished a proof-of-principle run with n-in-p ATLAS-Pixel sensors where cavities are etched to the sensors back side to reduce its thickness. One advantage of this technology is that thick frames remain at the sensor edges and guarantee mechanical stability on wafer level while the sensor is left on the resulting thin membrane. During the dicing step, the frames can be removed in order to obtain completely thin sensors. For this cavity-etching technique, no handling wafers are required which represent a benefit in terms of process effort and cost savings.
The membranes with areas of up to ~$\,4\times4\,$cm² and target thicknesses of 100 and 150µm feature a sufficiently good homogeneity across the whole wafer area. The processed pixel sensors show good electrical behaviour with an excellent yield for such a prototype run. First sensors with electroless Ni- and Pt-UBM are already successfully assembled with read-out chips. The technology is currently transferred to 6” wafer size. First results of etching trials with dummy wafers with larger thinned areas will be shown as well.
Speaker: Dr Alexander Lawerenz (CiS Forschungsinstitut fuer Mikrosensorik)
• 18:18
A monolithic pixel sensor with fine space-time resolution based on silicon-on-insulator technology for the ILC vertex detector 1m
We have been developing a silicon-on-insulator (SOI) pixel sensor optimized for vertexing at the International Linear Collider (ILC) experiment. The SOI monolithic pixel detector is realized using standard CMOS circuits fabricated on a fully depleted sensor layer. We are currently designing and evaluating the prototype sensor named SOFIST. The SOFIST can store both position and timing information of the charged particles in each 20 $\times$ 20 $\mu$m pixel. The pixel circuit contains a comparator for hit-signal discrimination. If the charge signal is over the threshold voltage level, this analog signal and hit-timing information are captured to analog memory and embedded time-stamp circuits, respectively. The position resolution of the sensor is further improved by the position weighted with the charges shared among multiple pixels. The target performance of the position resolution is better than 3 $\mu$m. The sensor also has column-parallel analog-to-digital conversion (ADC) circuits and zero-suppression logic for high-speed data readout. In this presentation, we report the status of the development and evaluation of the prototype sensor.
Speaker: Mr Shun Ono (KEK)
• 18:19
Graphene and 2D Materials for Radiation Detection Devices 1m
Pixels detectors are widely used detection devices in high-energy physics experiments. For more precise and accurate measurements one would like to have faster, less noisy and smaller pixels, but current technology imposes several limits on these characteristics.
The aim of this study is to explore the applications of bi-dimensional materials such as graphene or transition metal dichalcogenide monolayers (TMDs) to address these problems. In particular, one wants to determine whether nanoelectronic devices based on 2D materials could be used to obtain built-in amplification of the pixel signal. In this work some prototype pixel sensors (50x50$\mathrm{\mu m}^2$) based on graphene and MoS$_2$ transistors are investigated by means of numerical simulations, to evaluate the expected performance. The working principle is the field-effect modulation of the channel conductivity of a 2D material-based transistor, due to the presence of ionization charges in a silicon absorber placed beneath. Several architectures were tested, and a final device of choice is presented, with a sketch of a realistic readout system and its noise figure. The conductance modulation due to incoming particles is found to be more than $30\%$ (on a baseline of $\sim10\mu$A), resulting in a strong current signal.
According to simulation results, 2D materials-based pixels show promising built-in pre-amplification and good signal quality, with $\mathrm{SNR}\sim290$ for a MIP crossing the device. Moreover, their fabrication would be in principle simple, if 2D materials fabrication technology continues to improve. More specifically, these devices would be less complex than other proposed systems such as SOI or DEPFET pixels. These aspects allow to conclude that it would be highly desirable to further study the subject, to perfect the device design, as well as to build some prototype devices to be tested with a radiation source.
Speakers: Alberto Ciarrocchi (Università di Pisa) , Francesco Forti (Universita di Pisa & INFN (IT))
• 18:20
The Monitoring System of the Belle-II Vertex Detector 1m
The Belle-II VerteX Detector (VXD) is a 6 layers silicon tracker device that will cope with an unprecedented luminosity of 8 × 10^35 cm−2s−1 achievable by the new SuperKEKB e+e− collider, now under commissioning at the KEK laboratory (Tsukuba, Japan).
All environment parameters such as temperature, humidity and radiation levels, must be constanly monitored and under certain conditions action must be promptly taken, such us interlocking the power supply or deliver an abort signal to the SuperKEKB collider.
The VXD electronics is cooled with a complex biphase CO2 system at -30° and constantly fluxed with N2 to keep the humidity as low as possible.
The temperature system is based on two different sensors, NTC thermistors and FOS (Fiber Optical Sensors) with partial overlap.
The humidity is monitored by sniffing system and precise dew-point sensors.
A radiation monitoring and beam abort system has been developed based on single-crystal diamond sensors.
The sensors will be placed in 20 key positions in the vicinity of the interaction region.
The severe space limitations require a remote readout of the sensors.
The system design will be described, along with the sensor characterization procedure and the prototype of the readout electronics.
In this contribution we present the first results of the temperature and humidity system commissioned in a Beam Test at DESY in April 2016 and the preliminary results of the radiation monitoring achieved with a prototype system during the first SuperKEKB commissiong phase in February-June 2016.
Speaker: Lorenzo Vitale (Universita e INFN, Trieste (IT))
• 18:21
A Prototype of a New Generation Readout ASIC in 65nm CMOS for Pixel Detectors at HL-LHC 1m
The HL-LHC accelerator will constitute a new frontier for particle physics after year 2024. Major experimental challenge resides in inner tracking detectors: here the dimension of sensitive area (pixel) has to be scaled down with respect to LHC detectors.
This paper describes a readout ASIC in 65nm CMOS with a matrix of 64x64 pixels each of dimension 50x50 μm2, designed by CHIPIX65 project, part of RD53 Collaboration. It is a demonstrator of a Pixel Phase 2 chip, with compact design, low power and in-time threshold below 1000e−. All IP-blocks and analog front ends are designed by CHIPIX65 project in the framework of RD53 Collaboration: they have been produced, tested and several have already proven to be radiation hard up to 5-800 Mrad. The chip implements two different analog front end designs, one with asynchronous the other with synchronous comparator designs, but with main common characteristics: compact design; ENC below 100 e- for 50 fF input capacitance; below 5 μW/pixel power consumption; fast rise time, allowing correct time-stamp; signal digitisation using Time Over Threshold; leakage current compensation up to 50nA per pixel.
All global biases and voltages are programmed in the chip periphery, for each value a 10-bits current steering global DAC is used; a band gap circuit provides a stable reference voltage. The adopted strategy is very robust, easily scalable and mismatch effects are kept to a negligible level. Bias voltages and current are monitored by a 12-bit ADC.
A novel digital architecture has been designed in order to maintain a high efficiency (above 99% ) at pixel hit rate of 3 GHz/cm2 , trigger of 1 MHz rate and latency of 12.5μsec. The digital architecture is organized into pixel regions: in order to have a very compact and low power architecture, a large pixel region consisting of 4x4 pixels has been used. A 5-bit ToT charge is stored in a centralised latency buffer: at the arrival of a trigger, a matching logic selects eventually the right memory location and sends the data to the End of Column logic. The particle inefficiency due to this architecture is about 0,1% for an area occupation of of 65% and a low power consumption. The readout is obtained using a column drain protocol with a FIFO for each pixel region column, connected to a global dispatcher FIFO that after a 8b10b encoding splits the data into 20-bit trunks and sends them to a serialiser. Data are sent out from the chip using a differential transceiver converting the CMOS into SLVS JEDEC 400mV standard. Given the small size of the chip, an output rate of 320 MHz for the serialised data can be used, but higher output rates are possible., since SER and sLVDS-TX are designed to sustain up to 1.2 Gb/s. Chip configuration is performed through fully-duplex synchronous SPI-master/slave transaction. CHIPIX65 demonstrator will be submitted in June 2016.
Speaker: Luca Pacher (Universita e INFN Torino (IT))
• Wednesday, 28 September
• 09:00 10:30
B09-Applications to medical and other fields
Convener: Giuliana Rizzo
• 09:00
R&D networks and opportunities 22m
Future Radiation Detectors and Imaging Technologies have common requirements in different fields of application. The "ERDIT" network was formed in 2014 to explore the European research and development trends and to promote exchanges from different scientific fields and different countries. The talk will present the "ERDIT" network and related collaborative activities and review the current funding opportunities dedicated to Radiation Detectors and Imaging Technologies like ATTRACT.
Speaker: Cinzia Da Via (University of Manchester (GB))
• 09:30
Applications of vertexing detectors 22m
Detector concepts originally developed for vertex applications have been further developed to address the needs of different applications outside high-energy physics. A typical example is the MEDIPIX series of detectors. The original concept was based on the Omega3 readout chip. Over the years the technology has been further developed into the MEDIPXI2 chip with energy windowing and its successor MEDIPIX3 adding charge summing to avoid spectral distortion due to charge sharing. The TIMEPIX chip introduced time-over-threshold (TOT) and time-of-arrival (TOA) concepts to identify incoming photons or particles. With its successor TIMEPIX3 TOT and TOA can be recorded simultaneously. TIMEPIX3 also uses event driven readout to increase the maximum event rate.
The different MEDIPIX/TIMEPIX chips have found applications as materials research, medical imaging, dosimetry and astronomy. This presentation will cover the characteristics of the devices and their use in different applications.
Speaker: Prof. Christer Frojdh (Mid Sweden University)
• 10:00
Vertexing and tracking in hadrontherapy 22m
Hadrontherapy represents a remarkable example of the interdisciplinary collaboration between nuclear physics and medicine. Proton and carbon ion beams are used in the clinical practice for external radiotherapy treatments achieving, for selected indications, promising and superior clinical results with respect to X-ray based radiotherapy. At the same time, the accurate dose delivery is more sensitive to the patient positioning and to anatomical variations with respect to photon therapy. In order to fully exploit the advantages of ion beams in the clinical practice, the development of novel techniques to monitor the beam range and the dose release during the patient treatment is highly demanded. Several non-invasive monitoring strategies based on tracking and vertexing of secondary radiation exiting the patient have been proposed, \textit{e.g.}, prompt gamma, charged secondaries and beta+ emitters, and will be reviewed together with future directions.
Speaker: Erika De Lucia (Istituto Nazionale Fisica Nucleare Frascati (IT))
• 10:30 11:00
coffee break 30m
• 11:00 12:30
B10-Applications to medical and other fields
Convener: Stefano Bettarini (University of Pisa and INFN (IT))
• 11:00
DepFET Direct Electron Detectors for time-resolved imaging applications 22m
Carrying out ultrafast electron diffraction (UED) experiments capturing the motion of molecules or the dynamics of biological systems at very short time scale require the availability of ultrafast, ultrabright electron sources and high performance imaging detectors. There has been tremendous progress in the field of semiconductor based X-ray detectors driven by the needs and demands of existing and upcoming fee-electron laser sources or related experiments.
While direct hit detectors are the standard choice for any application involving the detection of photons, there use is only marginally when it comes to the detection of electrons, as required in any ultrafast electron diffraction (UED) experiment or the wide field of electron microscopy applications (e.g. Transmission Electron Microscopy).
Most camera systems employed in such experiments are rather slow in terms of frame rate and use an indirect process by means of a scintillator to retrieve the electron intensity distribution by detecting the optical photons created in the scintillator.
This work reports on the development of novel ultrafast direct-electron-hit silicon detectors using DEPFET technology. These systems allow for a high signal-to-noise ratio and the capability to discriminate single electrons with high statistical probability. For UED experiments we are developing systems providing 1kHz frame rates and therefore single shot capabilities. A second (related) detector system will run at frame rates up to 80 kHz, and is mainly intended for recording the dynamics of non-periodic (biological) samples in real space and real time by use of dynamic electron microscopy.
Speaker: Sascha Epp (Max Planck Institute for the Structure and Dynamics of Matter)
• 11:30
XFEL Detector Developments 22m
In the last years a large development effort has taken place in the photon science community around the world to develop detectors for existing and upcoming X-ray free electron laser (XFEL) facilities. XFELs have very short X-ray pulses ( ~100 fs) with a very high intensity (10^12) and, depending on the facility a high repetition rate of up to 4.5 MHz. The detectors usually aim to achieve single photon sensitivity (i.e. require a very low noise) and a dynamic range of 10^4-10^5 photons. To achieve this conflicting requirements different concepts have been developed by the different groups. In this presentation I will give an overview over the different developments.
Speaker: Aldo Mozzanica (PSI)
• 12:00
Diamond detector technology; status and perspectives 22m
At present most experiments at the CERN Large Hadron Collider (LHC)
are planning upgrades in the next 5-10 years for their innermost
tracking layers as well as luminosity monitors to be able to take data
as the luminosity increases and CERN moves toward the High Luminosity-LHC
tolerant technologies than exist today. As a result this is one area of
intense research. Chemical Vapor Deposition (CVD) diamond has been
used extensively and successfully in beam conditions/beam loss monitors
as the innermost detectors in the highest radiation areas of essentially
all LHC experiments. The startup of the LHC in 2015 brought a new
milestone where the first diamond pixel modules were installed in an LHC
experiment (ATLAS) and successfully began taking data. As a result,
this material is now being discussed as a possible sensor material
for tracking very close to the interaction region and for pixelated
beam conditions/beam loss monitors of the LHC/HL-LHC upgrades where
the most extreme radiation conditions will exist.
The RD42 collaboration at CERN is leading the effort to use CVD diamond
as a material for tracking detectors operating in extreme radiation
environments. During the last three years the RD42 group has succeeded
in producing and measuring a number of devices to address specfic issues
related to use at the HL-LHC. We will present status of the RD42 project with
emphasis on recent beam test results. In particular we present the latest
results on material development, the most recent results on the independence
of signal size on incident particle rate in poly-crystalline CVD
diamond pad and pixel detectors over a range of particle fluxes up to
20 MHz/cm^2 measured, and results from first 3D diamond detectors which
produce an extremely radiation tolerant device and collect nearly all of
the charge deposited in the material. In addition we will present plans for future
use of the most recent devices.
Speaker: Harris Kagan (Ohio State University (US))
• 12:30 12:35
Group Photo 5m
We will take a group photo on the lawn in front of the Fuoco di Bosco at the end of the session
• 12:35 14:00
lunch break 1h 25m
• 15:00 19:00
Excursion
• Thursday, 29 September
• 09:00 10:30
B11-New developments and detector R&D
Convener: Cinzia Da Via (University of Manchester (GB))
• 09:00
Small pitch 3D devices 22m
The ATLAS IBL project led to an impressive progress in 3D radiation sensors, with experimental confirmation of their remarkable radiation tolerance with relatively low power dissipation, and the demonstration of medium volume productions with an acceptable yield. These accomplishments paved the way for using 3D sensors in other pixel detector systems in Phase 1 upgrades at the LHC (e.g., AFP and CT-PPS), and made them a very appealing option also for the innermost tracking layers at the HL-LHC. The latter application involves very high hit-rate capabilities, increased pixel granularity, extreme radiation hardness, and reduced material budget. Compared to existing 3D sensors, the future ones will have to be geometrically “downscaled”, involving smaller pitch (e.g., 50×50 or 25×100 μm2), shorter inter-electrode spacing (~30 μm), narrower electrodes (~5 μm), and reduced active thickness (~100 μm). The development of a new generation of 3D pixel sensors with these challenging features is under way by different groups in Europe, in collaboration with processing facilities like FBK, CNM, and SINTEF.
This talk will first review the lessons learned from existing 3D detectors. Then it will address the main design and technological issues for small pitch 3D devices. Preliminary results from the electrical and functional characterization of the first prototypes will be reported and compared to TCAD simulations.
Speaker: Gian-Franco Dalla Betta (INFN and University of Trento)
• 09:30
SOI Monolithic pixel detector technology 22m
Silicon-On-Insulator (SOI) is very fascinating technology which can be used to fabricate monolithic radiation detectors. Although there were several difficult issues to solve such as back-gate effect, sensor-circuit coupling, and radiation hardness etc., we could solve these issues by introducing buried wells, double-SOI wafer and higher dose LDD region.
We also introduced active merge technique in which NMOS and PMOS transistors are merged and share active layer and contacts. This reduced layout size less than 50% of previous design.
I will present newly developed technologies and recent developments of integration-type and counting-type detectors.
Speaker: Prof. Yasuo Arai (High Energy Accelerator Research Organization (JP))
• 10:00
Micro channel cooling solutions for silicon detectors 22m
With the advent of thinner and more precise silicon detectors for vertexing and tracking in collider experiments, the design of sufficiently thin and stable supports and services is increasingly challenging. In this contribution an overview is given of the adoption of micro-channel cooling in high energy physics. The emphasis is on a recently proposed approach to integrate the cooling channels in the silicon sensor and the connectivity of the micro-channel circuit to the overall system. Measurements are presented of the cooling performance, that can exceed the performance of more traditional systems by a large factor. The measurements are extrapolated to more realistic systems. We also discuss the impact on the mechanical stability.
Speaker: Marcel Vos (IFIC Valencia (ES))
• 10:30 11:00
coffee break 30m
• 11:00 12:30
B12-New developments and detector R&D
Convener: Maurizio Boscardin (FBK Trento)
• 11:00
Low gain avalanche devices 22m
The objective of the work presented in this talk is the development of new position sensitive detectors with low signal amplification useful also for timing applications and called Low Gain Avalanche Detector (LGAD). These new devices are based on the standard Avalanche Photo Diodes (APD) normally used for optical and X-ray detection applications.
We will present the last experimental results on 50um thin LGAD fabricated for the High Granularity Time Detector of the ATLAS experiment. We have performed a beam test at CERN with LGAD of different gain and report the measured timing resolution, comparing it with laser injection and simulations. For the 50 μm LGAD, the timing resolution measured is 30 ps.
In order to optimize the electrical characteristics of thin LGAD we performed two dimensional numerical simulations based on Sentaurus and Silvaco simulation tools and the technological steps needed for the fabrication.
In this talk we will discuss also the radiation hardness of LGAD and the methods implemented to withstand the high fluences expected in the HGTD.
Speaker: Dr Giulio Pellegrini (Centro Nacional de Microelectrónica (IMB-CNM-CSIC) (ES))
• 11:30
High fluence effects on silicon detectors: damage and defects characterization 22m
The CERN RD50 collaboration has the aim to investigate radiation hard semiconductor devices for very high luminosity colliders. This is done by looking into four key aspects: Defect/material characterization, detector characterization, new structures and full detector systems.
After the Phase II upgrade of the Large Hadron Collider (LHC) the luminosity will increase and therefore the radiation level for the silicon detectors. They have to be able to operate at fluences of up to 2E16 neq/cm$^2$. To cope with this, new semiconductor sensor technologies have been developed within the RD50 collaboration. This talk will give a brief overview of those, which include:
3D detectors, HV-CMOS pixel detectors, low gain avalanche detectors (LGAD) and sensors with slim/active edge.
Speaker: Sven Wonsak (University of Liverpool (GB))
• 12:00
Experimental techniques for defect characterization of highly irradiated materials and structures 22m
There are several applications where solid devices are exposed to irradiation. Depending on the operational conditions (type of the particles, temperature, fluence) the physical properties of the exposed device degrades differently, reaching the point of electrical failure in very harsh enviroments. The radiation damage, starting already under low irradiation fluences, get more complex with increasing the fluences due to the generation of various type of irradiation induced, electrically active, defects. Accordingly, the defect characterization becomes a more difficult and costly task, requiring several complementary techniques to understand the detailed relation between the “microscopic” reasons as based on defect analysis and their “macroscopic” consequences for device performance. In this respect, the talk will focus on the defect characterization techniques suitable for investigating highly irradiated materials/structures, employed and developed within CERN RD50 Collaboration: I-DLTS, TSC and TDRC for electrical characterization of bulk and interface defect states, HRTEM and EPR for structural and chemical identification of the radiation induced defects. Correlations with the results obtained by other techniques determining the „macroscopic” electrical properties of the devices (leakage current, effective doping, carriers trapping lifetime) will be presented as well.
Speaker: Ioana Pintilie (NIMP Bucharest-Magurele, Romania)
• 12:30 16:00
lunch break 3h 30m
• 16:00 17:30
Convener: Alberto Messineo (Universita di Pisa & INFN (IT))
• 16:00
The simulations of radiation damage effects in silicon detectors from the properties of the lattice defects has long been one of the important tasks of CERN-RD50 collaboration. As calculations often don't converge with full set of the indentified defects the simulations include either reduced number of defects or more often effective defects. Several different models were presented in the past, which gave reasonable agreement with the limited number of measured data, however often failing to describe a broader set of measurements of collected charge, leakage current and full depletion voltage. The models used within RD50 will be presented together with the comparisson of different simulation tools. A special empahasis will be given to practical aspects of simulations. Finaly the device model based on measurements whose parameters should be used as anchor points for simulations of heavly irradiated silicon detectors will be described.
Speaker: Gregor Kramberger (Jozef Stefan Institute (SI))
• 16:30
Radiation Tolerance of 65nm CMOS 22m
The High Luminosity LHC (HL-LHC) is the proposed upgrade to the LHC to be made in a long machine shutdown which should take place in the years 2023 to 2025, according to current schedule and aims increasing the luminosity of the machine up to 5.1034 cm−2s−1. The upgrade will improve statistically marginal measurements and will allow a better chance to see rare processes.
The ATLAS and CMS experiments are planning major detector upgrades to cope with the increase in beam luminosity. Pixel detectors are placed in the innermost part of the experiments and are therefore exposed to the highest fluences and highest ionizing radiation doses. Simulations show that the innermost parts of the new pixel detector will integrate a fluence of about 1016 n/cm2 (1 MeV neutron equivalent) and a Total Ionizing Dose (TID) of 1000 Mrad.
The RD-53 collaboration was established to develop the next generation of pixel readout chips needed by ATLAS and CMS at the HL-LHC. This development requires extreme rate and radiation tolerance. The 65 nm CMOS process seems to be promising for the future pixel readout chips in terms of high integration density and a first demonstrator chip containing 76 800 pixels of 50µm × 50 µm will be submitted in April 2017 .
The first part of this presentation is dedicated to the TID effects on the 65nm process. A lot of information about the 65 nm process tolerance were obtained by studying radiation effects on individual transistors and used as a way to understand the causes of failure in digital or analog designs. In fact, the radiation tolerance of 65 nm bulk CMOS devices was investigated using 10 keV X-rays up to a Total Ionizing Dose (TID) of 1 Grad and irradiation tests were performed at room temperature (25 °C) as well as at low temperature (-15 °C).
In principle, the gate oxides of advanced CMOS technologies are scaled to thinner dimensions, which should make devices highly tolerant to TID effects. However, irradiation tests showed a strong performance degradation for the small size devices. In fact, the Shallow Trench Isolation (STI) used as the field oxide for device isolation and represents the main issue when considering TID effects for scaled down technologies.
We will review the various degradations induced by the STI charge buildup. The first degradation is related to the leakage current in the irradiated NMOS devices and caused by the parasitic STI device. The second type of degradation concerns the threshold voltage shift of narrow channel devices. The effect, intitled “Radiation-Induced Narrow Channel Effect” (RINCE) was already reported for other commercial processes. Furthermore, For this 65 nm process, another effect was observed and designed as Radiation-Induced Short Channel Effect (RISCE). It is realated to the fact that degradation depends not only on the width of the channel but more degradation is observed for short channel than for long channel devices.
The effect of the bias and of the temperature during irradiation and during annealing will be discussed. In particular, high temperature annealing does not help recovering the current drive in irradiated devices. On the contrary, performance degradation is observed after high temperature annealing for PMOS devices. Very often, in irradiation qualification, the Low Dose Rate (LDR) dammage is estimated from the TID effects at a High Dose Rate (HDR) followed by high temperature annealing. For the 65 nm process, testing are carried out in order to estimate the dammage at LDR and to provide a methology for qualification and especially for the pixel detector which will function in a cooled area.
A methology for SPICE parameters extraction for radiation-induced degradation on pmos and nmos transistors is proposed. Comparison of radiation-induced leakage current, threshold shift and mobility degradation in test MOSFETs between total dose irradiation experiments and simulation results exhibits a good agreement.
The second part of this presentation is dedicated to the Single Event Upset (SEU) tolerance for the 65nm process. Indeed, for the future pixel readout chips, local and global memories are implemented to retain respectively the local pixel configuration and the global chip configuration. SEU tolerant memories are used to allow reliable operation at high beam intensities and to avoid reloading frequently the configuration data. A prototype chip has been designed where a different structures of the configuration memories based on Dual Interlocked CElls (DICE) or on Triple Redundancy Latches (TRL) were implemented.
SEU tolerance tests were carried out at CERN-PS facility with the 24 GeV protons beam. SEU measurements show that the DICE latch improves the SEU tolerance by a factor of 10 with only a small increase on the area compared to the standard latch, making the DICE suitable for pixel configuration whereas the TRL allows an improvement by a factor of 2500 but the structure consumes a higher area making it suitable only for global configuration.
Speaker: Mohsine Menouni (Centre National de la Recherche Scientifique (FR))
• 17:00
RD53 status and plans 22m
The RD53 collaboration is developing a large scale pixel front-end chip, which will be a tool to evaluate the performance of 65 nm CMOS technology in view of its application to the readout of the innermost detector layers of ATLAS and CMS at the HL-LHC. This paper will review recent results concerning radiation effects on devices and circuits in this technology, and will give a picture of the current understanding of damage mechanisms and of rad-hard design criteria. Experimental results of the characterization of two small scale readout chips will be discussed in the frame of the design work that is currently leading to the development of the large scale demonstrator chip RD53A to be submitted by the end of 2016.
Speaker: Luigi Gaioni (INFN - National Institute for Nuclear Physics)
• 17:30 18:00
coffee break 30m
• 18:00 19:30
B14-Electronics and system integration
Convener: Valerio Re (Universita e INFN, Pavia (IT))
• 18:00
Chip Development for High Time Resolution Silicon Detectors 22m
The NA62 GigaTracKer (GTK) is a hybrid pixel detector required to time MIPS to better than 200ps (RMS) with a material budget of less than 0.5% $X_0$. I will introduce the GigaTracker Readout ASIC (TDCPix) designed to respond to these requirements, giving some detail about the main challenges, the architectural choices made during the design, the measured performance of the ASIC and detector assembly, as well as what we believe limits the time resolution. If time permits, I will compare and contrast the GTK electronics with those required for the CMS HGCAL upgrade project front end electronics.
Speaker: Matthew Noy (CERN)
• 18:30
High Speed Optical and Electrical link developments 22m
The vast quantities of data being produced by modern particle physics detectors require the use of high-speed serial data transmission technologies in order to enable their successful design. This contribution will review the developments in this area that target the Phase II upgrades of the LHC experiments and may find application in other areas in the same way as their current counterparts have done. The technologies being pursued cover both optical and electrical data transmission links, with the target application typically driving choice based on balancing the pros and cons of the two approaches. The customized front-end components being developed will be described in the context of their uses within complete link systems that are not only capable of reading-out detectors but also provides the means to control them.
Speaker: Jan Troska (CERN)
• 19:00
Development of wireless data and power transmission for tracking detectors 22m
A large contribution to the total material budget of trackers come from services for data communication and power. Optimizing the material budget without large scarification of reliability is important when designing trackers.
The WADAPT (Wireless Allowing Data And Power Transmission) project investigates the feasibility for wireless data and power transmission to trackers. The project benefit from the fast growing development of wireless technology for the consumer market. The components becoming available in consumer products uses millimeter waves and capable of Gbps data transfer over short distance at low power hence possibly well suited for use in trackers. The millimeter wave transceivers and antennas are med with technology widely used in trackers. The size of the components in wireless data link is compatible with tracking detectors.
We will present results from feasibility studies of wireless data transfer in tracker environment using commercial components that are not optimized for trackers. Results will be shown on data transfer between and trough tracker layers, Bit Error Rate for a Gbps wireless data link, measurement of crosstalk between closely placed links etc.
The WADAPT project is now developing a wireless data link optimized for trackers that can be easily integrated with components currently developed for HL-LHC. We will present the plan and status of this development.
Speaker: Richard Brenner (Uppsala University (SE))
• Friday, 30 September
• 09:00 10:30
B15-Online and offline tracking and vertexing
Convener: Michael J. Morello (SNS and INFN-Pisa (IT))
• 09:00
FTK status and perspectives for track trigger in ATLAS at HL-LHC 22m
The expected instantaneous luminosities delivered by the Large Hadron Collider will place continually increasing burdens on the trigger systems of the ATLAS detector. The use of tracking information is key to maintaining a manageable trigger rate while keeping a high efficiency. At the same time, however, track finding is one of the more resource-intensive tasks in the software-based processing farms of the high level trigger system. To support the trigger, ATLAS is building and currently installing the Fast TracK Finder (FTK), a hardware-based system that uses massively parallel pattern recognition in Associative Memory to reconstruct tracks above transverse momenta of 1 GeV across the entire detector at 100 kHz with a latency of ~100 microseconds. In the first-stage of track finding, FTK compares hits in ATLAS silicon detectors against ~1 billion pre-computed track pattern candidates. Track parameters for these candidates, including goodness-of-fit tests, are calculated in FPGAs using a linear approximation, leading to nearly offline-quality efficiency and resolution with a low fake rate.
In order to prepare for the future high-luminosity environment, ATLAS is also studying upgrades to the hardware-based track trigger capabilities of the detector. The FTK++ upgrade will expand on the power of the FTK system, with newer and faster FPGAs and a significantly larger number of patterns, allowing the upstream software-based trigger system access to full-scan tracking at 100 kHz, even with an average of up to 200 overlapping proton-proton interactions.
The L1Track upgrade will use shared hardware technologies with FTK++ and provide regional tracking for confirmation of the earliest stage muon and calorimeter trigger systems, particularly for single electron triggers, with a latency of only 6 microseconds. L1Track is expected to maintain high efficiency (>= 95%) and low fake rate for tracks with transverse momenta above 4 GeV at a rate of 1 MHz. In an alternative upgrade model in which the full 1 MHz rate is passed to a computing farm, FTK++ will continue to provide the full-scan tracking at 100 MHz, and L1Track will be replaced by the EFTrack system, which will similarly provide fast regional tracking to the computing farm.
This contribution will describe the parameters of the FTK system and the status of installation and commissioning of the hardware, as well as future, longer-term, plans for hardware-based track triggers at ATLAS.
Speaker: Jahred Adelman (Northern Illinois University)
• 09:30
The CMS track trigger for the High Luminosity LHC 22m
The High Luminosity LHC is expected to deliver luminosities of 5 × 10ˆ34 cm-2s-1, with about 200 proton-proton interactions per bunch crossing, on average. For their physics program to take advantage of these high collision rates the LHC experiments need to redesign their trigger systems so that they identify charged particle tracks at the very first stage of triggering. The CMS track trigger upgrade will make use the silicon tracker detector upgrade to measure with precision, with a latency of about 5 microseconds, the transverse momenta of all charged particles, for particles with momentum above 2 GeV/c. We discuss the challenges that this project entails and different algorithmic and architectural solutions that can help overcome them. We also describe the current status and plans for these projects.
Speaker: Jacobo Konigsberg (University of Florida (US))
• 10:00
Tracking in high-multiplicity events 22m
The ALICE experiment is preparing a major upgrade of its inner silicon tracker (the Inner Tracking System) and of its Online and Offline systems for the upcoming Run3 of the LHC starting in 2021.
During its Run3, LHC will deliver Pb-Pb collisions at $\sqrt{s_{NN}} = 5.5$ TeV with a peak luminosity $L=6\times10^{27} cm^-2 s^{-1}$ and an interaction rate of 50 kHz, to be compared to the 8 kHz interaction rate currently delivered by the LHC. The aim of ALICE is to cope with such a high interaction rate improving at the same time the resolution and the efficiency of its silicon tracker.
In this context, one of the requirements for a prompt calibration of external detectors and to speed up the offline data processing is to run online the reconstruction of tracks in the Upgraded Inner Tracking System.
A new algorithm based on Cellular Automata has been developed to tackle this issue. In this algorithm the tracking is split in multiple phases to profit from data locality. At first, hit points are organised in sectors of azimuthal angle and longitudinal coordinate; then the algorithm looks for track segments within these sectors of the detector, independently. Track segments with compatible track parameters are marked as neighbours. Neighbouring track segments are then merged at the final stage using a set of rules defined by the Cellular Automaton mechanism, somewhat similar to the set of rules used in the Conway's Game of Life.
The obtained computing and tracking performance are compliant with the requirements of ALICE being able to reconstruct tracks of transverse momentum down to 100 MeV/c in events with high track density ($dN / d\eta$ up to 2000). The tracking and computing performance of this algorithm will be shown in the case of central Pb-Pb events at $\sqrt{s_{NN}} = 5.5$ TeV.
Speaker: Maximiliano Puccio (Universita e INFN Torino (IT))
• 10:30 11:00
coffee break 30m
• 11:00 12:30
B16-Online and offline tracking and vertexing
Convener: Andre Schoening (Ruprecht-Karls-Universitaet Heidelberg (DE))
• 11:00
Using precision timing information in high rate and high pileup conditions 22m
High energy particle collider experiments are facing ever more challenging conditions, operating at todays accelerators capable of providing instantaneous luminosity of 10^34 cm-2s-1 and above. The high center of mass energy, the large number of simultaneous collision of beam particles in the experiments and the very high repetition rates of the collision events pose huge challenges. They result in extremely high particle fluxes, causing very high occupancy in the particle physics detectors operating at these machines. A precise timing information with a precision of around 10 ps and below is seen as a major aid in the reconstruction of the physics events under such challenging conditions. In this talk I will review the efforts of the LHC collaborations to augment the timing performance of their detectors during future upgrade campaigns. to utilize precision timing for the event reconstruction in a high rate and high pileup environment as expected at the high luminosity LHC and at future hadron colliders. Different detector technologies allowing precision timing measurements will be discussed and their potential benefit will be illustrated with a particular focus on tracking.
Speaker: Adolf Bornheim (California Institute of Technology (US))
• 11:30
Investigating the Micron Automata Processor for HEP Pattern Recognition Applications 22m
The Micron Automata Processor is a dedicated pattern matching engine that is based on a non-Von Neumann processor architecture, and was designed primarily to satisfy the growing needs of high-speed text-based pattern search applications. We investigate its suitability for HEP pattern recognition applications, using a sample track-confirmation trigger to demonstrate a proof-of-principle. We compare its performance, in this sample application, with that of other processor architectures, including general purpose CPUs, GPUs, and custom devices based on content-addressable memories.
Speaker: Michael Wang (Fermi National Accelerator Lab. (US))
• 12:00
Tracking, calibration&alignment, and data processing in the LHCb upgrade 22m
For Run III foreseen to start in 2020, the LHCb experiment will run at an instantaneous luminosity of 2x10^33 cm-2s-1 with a fully software based trigger. A major upgrade of the detector and of data acquisition system will allow having a full readout at the collision rate of 40 MHz. LHCb is planning to have the same Run II strategy with a real-time alignment and calibration procedure and an offline-like quality reconstruction in the latest stage of the software trigger. This strategy includes the alignment of the full tracking system (both for the vertex detector and all the tracking stations) evaluated in few minutes at the beginning of each fill and the complete calibration of the PID sub-detectors for each run that corresponds to a maximum of 1 hour of data taking. The reconstruction used in Run I was optimized to fit the time constrained required by the software trigger: 45 ms and 650 ms for the first and second trigger stage.
In Run III, a total time budget of 13 ms event to take the trigger decision is foreseen.
This implies a large gain in speed in the reconstruction to be achieved. Different approaches are under study to mach this challenging goal, e.g. using parallelism in the CPU and GPU, use of machine learning to veto bad events on an early stage, optimization on different architectures.
The Run II strategy ends to have as output of the second stage of the software trigger the same quality performance as in the “offline” processing. This results in the possibility to perform analyses directly on the output of the trigger without requiring an offline reconstruction. Saving only the interesting information of the selected events reduces significantly the event size down to a factor of 10. Thus an equivalent factor higher rate of signals can be exploited in physics analyses with the same resources. During Run II, the event format has been made more flexible, which has allowed to satisfy more physics analysis requirements. In Run III, LHCb plans to use this same strategy for all the analyses with abundant signals to record the events in a reduced format that can be fed directly to the physics analysis.
The importance and the challenging of this strategy is discussed. We illustrate the operational and physics performance of the real-time alignment and calibration, the overview of the reconstruction and the real-time analysis model in Run2. Plans and different approaches under study for Run III are also presented.
Speaker: Barbara Storaci (Universitaet Zuerich (CH))
• 12:30 16:00
lunch break 3h 30m
• 16:00 17:30
B17-Vertexing at future accelerators
Convener: Fabrizio Palla (Universita di Pisa & INFN (IT))
• 16:00
The ILC Vertex Detector requirements 22m
After few decades of R&D, the International Linear Collider (ILC) project has reached a level of maturity proving the feasibility of the machine and of the detectors. The ILC physics goals cover a very wide and ambitious program including top-quark quark physics, electroweak precision measurements, direct and indirect searches beyond the Standard Model (BSM) like SUSY, dark matter manifestations, exotic particles and phenomena, etc., and an extensive Higgs physics program covering mass, couplings to fermions and bosons, quantum numbers and total width measurements. These measurements are expected to reach an unprecedented level of precision in most of the cases, which will allow probing physics BSM, since typical deviations from the Standard Model are expected to be in the order of magnitude of the ILC sensitivity.
To accomplish the ambitious physics program of the ILC, the vertex detector will be essential for providing the necessary physics performances in terms of flavor tagging, displaced vertex charge determination and low momentum tracking capabilities.
Taking advantage of the much less demanding running conditions at the ILC than at hadron colliders like LHC, the vertex detector is expected to reach particularly high performances as far as spatial resolution and material budget are concerned (typical impact parameter resolution of the order of 5 microns and material budget in the order of 0.15-0.2 % of radiation length per layer).
In addition, the particular time structure of the beams has major consequences on the specifications of the detectors and their read-out architecture. It allows to concentrate the read-out during 199 ms beamless periods separating 1 ms long bunch trains or to suppress the average power consumption by switching off (at least partially) the detectors in-between trains (the so called power pulsing).
Finally, the beam related background of the ILC, which translates into a high rate of low momentum-e-e+ pairs hitting the vertex detector, drives the expected occupancy (and the related necessary read-out speed) as well as the radiation load.
The talk will focus on the vertex detector requirements following from both the physics and the experimental constraints. Wherever different, the aspects to each detector concepts (SiD and ILD) will be discussed.
Speaker: Auguste Guillaume Besson (Institut Pluridisciplinaire Hubert Curien (FR))
• 16:30
Development of detector technologies for ILC vertexing. 22m
The physics programme at the ILC relies heavily on pure and efficient
identification of heavy-flavour quarks, requiring pixel vertex detectors
with 3-4 µm hit resolution and a material budget of 0.1-0.2% of a
Although technology choices are still several years in the future, a number
of detector concepts are currently being actively studied. I will discuss
these concepts and the associated ongoing R&D programmes, including
potential sensor technologies (CMOS, CCD, DepFet etc) as well as
mechanical and system issues.
Speaker: Joel Goldstein (University of Bristol (GB))
• 17:00
CLIC silicon pixel R&D 22m
The physics aims at the future CLIC high-energy linear e+e- collider set very high precision requirements on the performance of the vertex and tracking detectors. Moreover, these detectors have to be well adapted to the experimental conditions, such as the time structure of the collisions and the presence of beam-induced backgrounds. The principal challenges are: a point resolution of a few μm, ultra-low mass (~0.2% X0 per layer for the vertex region and ~1% X0 per layer for the outer tracker), very low power dissipation (compatible with air-flow cooling in the inner vertex region) and pulsed power operation, complemented with ~10 ns time stamping capabilities. A highly granular all-silicon vertex and tracking detector system is under development, following an integrated approach addressing simultaneously the physics requirements and engineering constraints. For the vertex-detector region, hybrid pixel detectors with small pitch (25 μm) and analog readout are explored. For the outer tracking region, both hybrid concepts and fully integrated CMOS sensors are under consideration. The feasibility of ultra-thin sensor layers is validated with Timepix3 readout ASICs bump bonded to active edge planar sensors with 50-150 μm thickness. Prototypes of CLICpix readout ASICs implemented in 65 nm CMOS technology with 25 μm pixel pitch have been produced. Hybridisation concepts have been developed for interconnecting these chips either through capacitive coupling to active HV-CMOS sensors or through bump-bonding to planar sensors. Recent R&D achievements include results from beam tests with all types of hybrid assemblies. Simulations based on Geant4 and TCAD are used to validate the experimental results and to assess and optimise the performance of various detector designs. The R&D project also includes the development of through-silicon via (TSV) technology, as well as various engineering studies involving thin mechanical structures and full-scale air-cooling tests. An overview of the R&D program for silicon detectors at CLIC will be presented.
Speaker: Daniel Hynds (CERN)
• 17:30 18:00
coffee break 30m
• 18:00 18:30
B18-Vertexing at future accelerators
Convener: Francesco Forti (Universita di Pisa & INFN (IT))
• 18:00
Vertical integration technologies for tracking detectors 22m
In the past ten years, 3D vertical integration technologies have generated a wide interest in the silicon pixel sensors and front-end electronics communities. They have the potential to lead to the fabrication of multilayer high performance devices with no dead area, where each layer is optimized for its function (particle sensing, analog signal amplification and filtering, digital memory and readout,…). This paper will review the results that the community got so far, and assess the current status of R&D work on 3D integration applied to particle detection systems. Finally, the prospects of 3D integration for the future generation of tracking detectors will be discussed.
Speaker: Valerio Re (Universita e INFN, Pavia (IT))
• 18:30 19:45
B19-Workshop closing
• 18:30
Workshop Summary 45m
Speaker: Daniela Bortoletto (University of Oxford (GB))
• Saturday, 1 October
• 09:00 11:00
Departure | 2021-05-09 12:39:16 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4145050346851349, "perplexity": 3714.73352424111}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-21/segments/1620243988986.98/warc/CC-MAIN-20210509122756-20210509152756-00635.warc.gz"} |
http://mathoverflow.net/questions/102412/conics-in-the-quadric-line-complex/102462 | # Conics in the quadric line complex
Hello, I apologize in advance if this question is misguided somehow, since my algebraic geometry is pretty shaky.
I am wondering if there is a way to understand all the conics in a generic quadric line complex $X$. Remember that $X$ is defined as the intersection of the image of the complex Grassmanian $G(2,4)$ in $P^5$ under the Plucker embedding, with a quadric hypersurface in $P^5$. Since $G(2,4)\subset P^5$ is itself a quadric, $X$ may also be viewed as a complete intersection of two quadrics in $P^5$. By "conic" I mean rational curve of degree 2.
From looking at Griffiths and Harris, I see that two sources of conics in $X$ come from viewing $X\subset G(2,4) =$ {lines in $P^3$}, and considering the subspaces $\sigma(p),\sigma(h)\subset X$, where $p$ is a point in $P^3$, $h$ is a 2-plane in $P^3$, $\sigma(p)$ is the subspace of $X$ consisting of lines in $P^3$ passing through $p$, and $\sigma(h)$ is the the subspace of $X$ consisting of lines in $P^3$ contained in $h$. I may have made a mistake, but it seems to me that the former should contribute a 3 dimensional family of conics, and the latter a 4 dimensional family of conics, in $X$. I believe 4 is the expected dimension, and I think one can show that the expected dimension is achieved in this case (here I mean complex dimensions).
Therefore, my question is: do these account for all the conics in $X$, and if so, do they fit together into a moduli space in some way? (And is there a nice way to write down the actual curves, given a nice choice of quadrics? I can try to work this out myself).
If not, is there some way to write down all the conics?
I assume this is a classical subject, and would be delighted with a reference to more information (I suppose it's even possible that I overlooked something in Griffiths and Harris, which someone more familiar with the subject might be able to let me know).
Thanks!
-
One interpretation of the quadric line complex $X$ is as the moduli space of stable, rank $2$, degree $1$ vector bundles on a genus $2$ curve $C$ (whose associated Kummer is the Kummer in G&H), cf. Newstead, "Topological Properties of Some Spaces of Stable Bundles". From this point of view, Ana-Maria Castravet has described the spaces of rational curves in $X$ of every degree (not just degree $2$), cf. "Rational families of vector bundles on curves".
-
Sorry for not getting back to you both earlier. Thanks so much for your answers! In particular, the comment to Will's answer was very helpful for me. – Sam Lewallen Aug 19 '12 at 18:42
Comment: The family of hyperplanes in $\mathbb P^3$ is $3$-dimensional, because it is isomorphic to another copy of $\mathbb P^3$.
This does not give you all the conics. The reason is simple. Every conic you constructed lies on a plane entirely contained within $G(2,4)$, so it usually lies on a plane not entirely contained in the other quadric hypersurface. But the other quadric hypersurface also contains planes! These generically fail to lie entirely in $G(2,4)$, meaning that the intersection of that plane with $G(2,4)$ is a conic in $X$ that cannot be a conic of the two types you gave.
The full family of conics consists of the intersection of $X$ with all planes that lie in the vanishing set of some nontrivial linear combination of the definition polynomials of $G(2,4)$ and the other quadric hypersurface. Only for the planes lying in the vanishing set of the defining polynomial of $G(2,4)$ can you have a nice geometric description.
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There is a nice description of every conic. Except for the two degenerate families of conics described above, every smooth conic in $\text{Grass}(2,k^4) = \text{Grass}(\mathbb{P}^1,\mathbb{P}^3)$ is the parameter space of lines (in one ruling) on a smooth quadric hypersurface in $\mathbb{P}^3$. – Jason Starr Jul 17 '12 at 15:40 | 2014-10-20 18:21:13 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8974660634994507, "perplexity": 165.14705289589074}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-42/segments/1413507443062.21/warc/CC-MAIN-20141017005723-00295-ip-10-16-133-185.ec2.internal.warc.gz"} |
https://socratic.org/questions/how-do-you-find-the-exact-value-of-arcsin-sin-2pi-3 | # How do you find the exact value of arcsin(sin((2pi)/3))?
Mar 2, 2017
$\arcsin \left(\sin \left(\frac{2 \pi}{3}\right)\right) = \frac{2 \pi}{3}$
#### Explanation:
By definition if $\sin A = x$, $\arcsin x = A$,
and substituting $x$ for $\sin A$ in $\arcsin x = A$
$\arcsin \left(\sin A\right) = A$ and hence
$\arcsin \left(\sin \left(\frac{2 \pi}{3}\right)\right) = \frac{2 \pi}{3}$ | 2020-02-23 11:22:20 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 8, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9961339831352234, "perplexity": 664.6416996446254}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-10/segments/1581875145767.72/warc/CC-MAIN-20200223093317-20200223123317-00321.warc.gz"} |
https://tex.stackexchange.com/questions/454288/question-marks-instead-of-reference-and-double-question-marks-instead-of-figure | # Question marks instead of reference, and double question marks instead of figure and table cross-references
I wrote my thesis with Sweave (R+LaTeX). Everything went fine until I bought a new computer. I copied the Sweave file (.Rnw) with all figures and tables, as well as with the bibliography (.bib).
When I compile the file on my new computer, everything is fine, text, figures, tables and layout.... BUT:
• every in-text reference is a question mark, although the bibliography at the end of the document is 100% (number, title etc).
• every cross-reference for the figures and tables is a double question mark, although the figures and tables are 100% (number, title etc).
Any idea of what is wrong?
Thanks, Elsa
\documentclass[a4paper,12pt,twoside]{book}
\usepackage[utf8]{inputenc}
\usepackage[english]{babel}
\usepackage{cite}
\usepackage[utf8]{inputenc}
\usepackage[english]{babel}
\usepackage{floatrow}
\floatsetup[table]{capposition=top}
\usepackage{colortbl}
\usepackage{fancyhdr}
\usepackage{lipsum}
\usepackage[english=usenglishmax]{hyphsubst}
\usepackage[nottoc]{tocbibind}
\usepackage{tabularx,array}
\usepackage{enumitem}
\usepackage{changepage}
\usepackage[all]{nowidow}
\usepackage{longtable}
\usepackage{scrextend}
\usepackage{amsmath}
\usepackage{etoolbox}
\usepackage{tikz}
\usepackage{titlecaps}
\usepackage{rotating}
\usepackage{nameref}
\usepackage{pdfpages}
\usepackage{xcolor}
\usepackage{color}
\usepackage{placeins}
\usepackage{pdflscape}
\usepackage{subfigure}
\usepackage{cleveref}
\usepackage{tabularx}
\usepackage[utf8]{inputenc}
\usepackage{floatrow}
\usepackage{float}
\usepackage{titlesec}
\usepackage{arydshln}
\usepackage{amsfonts,amssymb}
\setcounter{secnumdepth}{4}
\bibliographystyle{acm}
\usepackage{alphalph}
\renewcommand*{\thesubfigure}{(\alphalph{\value{subfigure}})}
\renewcommand{\chaptername}{}
\usepackage{graphicx}
\usepackage[justification=justified,format=plain]{caption}
\usepackage{afterpage}
\makeatletter
\renewcommand\@pnumwidth{2cm}
\patchcmd{\l@chapter}{\bfseries}{}{}{}
\makeatother
\begin{document}
%
%
%
\renewcommand\bibname{References}
\bibliography{TemporalPartitioning2}
\end{document}
The error I get when running bibtex is:
> This is BibTeX, Version 0.99d (MiKTeX 2.9.6840 64-bit) The top-level
> auxiliary file: Draft_PhDThesis_dec2017.aux The style file: acm.bst I
> found no \bibdata command---while reading file
> Draft_PhDThesis_dec2017.aux Warning--I didn't find a database entry
> for "Wulf" Warning--I didn't find a database entry for "Haeckel"
> Warning--I didn't find a database entry for "bioce" Warning--I didn't
> find a database entry for "Strauss" ... (There was 1 error message)
When I look at the .aux file I notice that there is no \bibdata{...} which I believe is created by \bibliography{...}. Not sure what is wrong.
I don't think the problem only lies with the bibtex and the bibliography because the cross-referencing of figures and tables is also not working properly. Unless there are two independent problems, but I don't think so.
The problem definitely lies with the installation because it works fine when I run it on my old laptop... I have not managed to find out what was wrong... if someone can someday shed some light, thanks!
• Did you compiled with bibtex? Also, have you tried to compile twice after bibtex with pdflatex? – koleygr Oct 7 '18 at 21:55
• I assume I am compiling with bibtex. All the reference information is in a .bib file (TemporalPartitioning2.bib), which is called with \bibliography{TemporalPartitioning2}. I compiled the document multiple times. However, I don't know if that has anything to do with my issue, but I get the error message that sweave.sty is not found... – Elsa Bussiere Oct 11 '18 at 8:09
• Hi @ElsaBussiere, please check this: tex.stackexchange.com/q/153193/120578 – koleygr Oct 11 '18 at 8:17
• Thanks, I resolved this problem following the instructions on the link you gave me. However, the question marks are still there... – Elsa Bussiere Oct 11 '18 at 9:37
• Please compile by using pdflatex mainFile then bibtex mainFile and again twice pdflatex mainFile... where "mainFile" is the name of your main file without extensions – koleygr Oct 11 '18 at 9:47 | 2020-09-26 08:18:20 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8557663559913635, "perplexity": 2898.687525424183}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-40/segments/1600400238038.76/warc/CC-MAIN-20200926071311-20200926101311-00386.warc.gz"} |
https://cs.stackexchange.com/questions/61127/subset-sum-like-problem-over-boolean-vectors | # Subset sum-like problem over boolean vectors
I'm interested in finding maximal solutions to the problem of finding a subset that "sums" to a specific value. The elements of the set are boolean vectors and the notion of "sum" is point-wise or.
Say you had {10, 01, 00} then there are two subsets that sum to 11: {10, 01} and {10, 01, 00}.
In particular, I want maximal solutions. So I don't care about {10, 01} if {10, 01, 00} is a solution, because {10, 01, 00} contains {10, 01}.
What algorithms are known for how to do this? Can you think of an algorithm? One way to do this would be to use the dynamic programming solution mentioned on Wikipedia (modifying it to store maximal sets of subsets rather than true/false): Pseudo-polynomial time dynamic programming solution
Is there something that beats this due to using vectors rather than integers? Or is this doomed to be just as inefficient?
• What means "pointwise or"? Does it mean to "or" the coordinates of the binary vectors? If so, I think the solution of Yuval will not work, e.g. 01+11=10, but 01 !<=10 and 11 !<= 10 – miracle173 Aug 1 '16 at 6:31
Let us say that $x \leq y$ if $x_i \leq y_i$ for all $i$. Suppose that your starting vectors are $x_1,\ldots,x_n$ and your target is $y$. If $x_i \not\leq y$ then $x_i$ cannot belong to any solution, so you can throw away all these vectors. The remaining vectors OR together to a vector $x \leq y$. If $x \neq y$ then there is no solution. Otherwise, take all remaining vectors – this is clearly the maximal solution. | 2019-08-17 22:49:41 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7271390557289124, "perplexity": 430.3971959444459}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-35/segments/1566027313501.0/warc/CC-MAIN-20190817222907-20190818004907-00046.warc.gz"} |
http://3790863534.srv040078.webreus.net/j7e1x/which-of-the-following-is-cationic-complex-2f4ae9 | This is the first report on the biodistribution of the cytofectin component of a pDNA–cationic lipid complex for which the distribution of the plasmid component has also been reported. The lability of Pd-OTf bonds in the oxidation addition complex aids in this formation. A positively charged complex ion is called a cationic complex. (A) Sodium lauryl sulphate (B) Sodium stearate (C) Cetryltrimethyl ammonium bromide (D) Sodiu Cationic definition is - of, relating to, or being a cation. Find out the solubility of $Ni(OH)_2$ in 0.1 M NaOH. Cationic lipid-mediated delivery is a fast, simple, and reproducible means for easily introducing DNA, RNA, siRNA, or oligonucleotides into eukaryotic cells. As the expression implies, the cationic and anionic compounds possess properties that when added together form insoluble complexes such as salts. The metal in this is named exactly as you would expect, with the addition of its oxidation state. Given that the ionic product of $Ni(OH)_2$ is $2 \times 10^{-15}$. The types of monomers necessary for cationic polymerization are limited to alkenes with electron-donating substituents and heterocycles. (iii) Nickel is purified by zone refining. As the expression implies, the cationic and anionic compounds possess prop-erties that when added together form insoluble complexes such as salts. Chemistry. Optimized NEET 2020: Which of the following is cationic detergent? Is the complex [CoF6] cationic or anionic if the oxidation state of cobalt ion is +3? Biology. (i) Cast iron is obtained by remelting pig iron with scrap iron and coke using hot air blast. To obtain this complex, triflates must be used as the leaving group [1]. (ii) In the extraction of silver, silver is extracted as cationic complex. The correct order of the spin-only magnetic moment of metal ions in the following low spin complexes, asked May 14, 2019 in Chemistry by Ruksar (68.7k points) jee mains 2019 +1 vote. The correct match between items of List - I and List - II is : In Wolff‐Kishner reduction, the carbonyl group of aldehydes and ketones is converted into. Note: If you aren't sure about oxidation states, you could follow this link. 33.1k SHARES. How to use cationic in a sentence. Cationic dyes = Basic dyes 4. You may need to download version 2.0 now from the Chrome Web Store. It allows the highly efficient transfection of a broad range of cell types, including adherent, suspension, and insect cells, as well as primary cultures. In contrast, anionic and cationic com-pounds that can be mixed over a wide range of ratios and provide a clear, viscous, high-foaming complex are defined as soft complexes. A cation is a positively charged ion. - Chemistry. Which one of the following is not employed as antihistamine? A coordination complex consists of a central atom or ion, which is usually metallic and is called the coordination centre, and a surrounding array of bound molecules or ions, that are in turn known as ligands or complexing agents. Another way to prevent getting this page in the future is to use Privacy Pass. Name the following coordination compounds Cationic complex ion with a bidentate from CHEMISTRY 162 at Rutgers University Potassium ferro cyanide K 4 [ F e ( C N ) 6 ] and Sodium argento cyanide N a [ A g ( C N ) 2 ] are anionic complexes. 1 answer. $Sucrose + H_20 \rightleftharpoons Glucose + Fructose$. On electrolysis of dil.sulphuric acid using Platinum (Pt) electrode, the product obtained at anode will be: Reaction between acetone and methyl magnesium chloride followed by hydrolysis will give : Which of the following oxoarid of sulphur has -O-O- linkage? Which of the following option are correct? 15. Physics. Solution for Define the following:(i) Cationic detergents(ii) Narrow spectrum antibiotics(iii) Disinfectants Coordination compound, any of a class of substances with chemical structures in which a central metal atom is surrounded by nonmetal atoms or groups of atoms, called ligands, joined to it by chemical bonds. Which of the following is an example of homoleptic complex ? • Completing the CAPTCHA proves you are a human and gives you temporary access to the web property. Reason (R) – In a bimetallic complex, the interchange of one or more ligands between the cationic and the anionic coordination entities result in coordination isomerism (a) Both A and R are correct and R is the correct explanation of A. a) Penicillin b) Furosemide c) Salicylate (aspirin) d) Hydrochlorothiazide e) Cimetidine 11.4) Infusion of p-aminohippuric acid (PAH) would reduce secretion by the proximal tubule of which of the following? ... What is the value of spin only magnetic moment of anionic and cationic part of complex
3:04 100.2k LIKES. Anionic dyes = Acidic dyes. ‘The development of both cationic and anionic exchange materials did not occur until 1935.’ ‘Synthetic small interfering RNA molecules can be introduced into cells by using reagents such as cationic lipids to promote uptake across the cell membrane.’ Books. If you are on a personal connection, like at home, you can run an anti-virus scan on your device to make sure it is not infected with malware. Learn vocabulary, terms, and more with flashcards, games, and other study tools. Assertion : For liquid dishwashing, nonionic detergents are used. The one-electron reduction of a cationic (allenylidene)[cyclic(alkyl) (amino)carbene]gold(I) complex leads to the corresponding neutral, paramagnetic, formally gold(0) complex.DFT calculations reveal that the spin density of this highly robust coinage metal complex is mainly located on the allenylidene fragment, with only 1.8 and 3.1% on the gold center and the CAAC ligand, respectively. Question By default show hide Solutions. It contains complex cation [ P t ( N H 3 ) 6 ] 2 + . Your IP: 91.234.99.207 Performance & security by Cloudflare, Please complete the security check to access. The atomic radiusis: Which of the following set of molecules will have zero dipole moment ? History of discovery. NCERT DC Pandey Sunil Batra HC Verma Pradeep Errorless. We report that the cationic phosphidozirconocene complex [(η 5-C 5 H 5) 2 Zr(PCy 2)][CH 3 B(C 6 F 5) 3] (II) reacts with azobenzene, resulting in the expedient formation of Zr complex (2) bound to a tridentate PNN ligand.This reaction proceeds by a mechanism of cooperative nucleophilic substitution of … If you are at an office or shared network, you can ask the network administrator to run a scan across the network looking for misconfigured or infected devices. Draw the three major resonance structures of the sigma complex intermediate in the reaction of acetophenone with HNO3/H2SO4 to yield o-nitroacetophenone. anion is not coordinated the complex is cationic with two molecules of from LIFESCI 001 at Brock University Please enable Cookies and reload the page. Many metal-containing compounds, especially those of transition metals, are coordination complexes. electrons from a nucleophile to form a cationic intermediate. Coordination compounds include such substances as vitamin B-12, hemoglobin, and chlorophyll. The cationic complex CoOH 2 6 2 should have how many unpaired electrons A 0 B 1 from CS 93 at University Of Arizona 11.3) Which of the following drugs is cationic (positive charge)? Identify a molecule which does not exist. 33.1k VIEWS. (a) Na [Ag (CN)2] (b) [Ag (NH3)2]Cl (c) [Ni(CO)4] (d) K4[Fe(CN)6] It contains two dyes, eosin and methylene blue, as well as the sugar lactose. • Start studying Naming of Metals: Cationic complex. 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The Power Of Yet Quotes, William Murphy I Will Wait On You, How Far Is Egypt From Israel, Ebony Mines Skyrim, Sigma Pune Careers, Prasa Vacancies Cape Town 2020, Pri Lds Church, | 2021-09-28 05:02:27 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.43244490027427673, "perplexity": 7472.2432657968275}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-39/segments/1631780060201.9/warc/CC-MAIN-20210928032425-20210928062425-00304.warc.gz"} |
http://www.gradesaver.com/textbooks/math/other-math/basic-college-mathematics-9th-edition/chapters-1-5-cumulative-review-exercises-page-378/13 | Basic College Mathematics (9th Edition)
Since multiplication and division are at the same level according to the order of operations, after finding the square root and exponent, the problem is solved from left to right like a normal problem is. 1. $\sqrt 121=11$ and $2^{3}=8$ 2. $88\div11\times8=64$ | 2017-02-21 14:28:08 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8008715510368347, "perplexity": 271.20904665418414}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-09/segments/1487501170741.49/warc/CC-MAIN-20170219104610-00491-ip-10-171-10-108.ec2.internal.warc.gz"} |
https://artofproblemsolving.com/wiki/index.php?title=2021_AIME_I_Problems/Problem_8&diff=prev&oldid=174082 | # Difference between revisions of "2021 AIME I Problems/Problem 8"
## Problem
Find the number of integers $c$ such that the equation $$\left||20|x|-x^2|-c\right|=21$$has $12$ distinct real solutions.
## Solution 1 (Piecewise Function: Analysis and Graph)
We take cases for the outermost absolute value, then rearrange: $$\left|20|x|-x^2\right|=c\pm21.$$ Let $f(x)=\left|20|x|-x^2\right|.$ We rewrite $f(x)$ as a piecewise function without using absolute values: $$f(x) = \begin{cases} \left|-20x-x^2\right| & \mathrm{if} \ x \le 0 \begin{cases} 20x+x^2 & \mathrm{if} \ x\le-20 \\ -20x-x^2 & \mathrm{if} \ -20 0 \begin{cases} 20x-x^2 & \mathrm{if} \ 020 \end{cases} \end{cases}.$$ We graph $y=f(x)$ with all extremum points labeled, as shown below. The fact that $f(x)$ is an even function ($f(x)=f(-x)$ holds for all real numbers $x,$ so the graph of $y=f(x)$ is symmetric about the $y$-axis) should facilitate the process of graphing. $[asy] /* Made by MRENTHUSIASM */ size(1200,300); real xMin = -65; real xMax = 65; real yMin = -50; real yMax = 125; draw((xMin,0)--(xMax,0),black+linewidth(1.5),EndArrow(5)); draw((0,yMin)--(0,yMax),black+linewidth(1.5),EndArrow(5)); label("x",(xMax,0),(2,0)); label("y",(0,yMax),(0,2)); real f(real x) { return abs(20*abs(x)-x^2); } real g(real x) { return 21; } real h(real x) { return -21; } draw(graph(f,-25,25),red,"y=\left|20|x|-x^2\right|"); draw(graph(g,-65,65),blue,"y=\pm21"); draw(graph(h,-65,65),blue); pair A[]; A[0] = (-20,0); A[1] = (-10,100); A[2] = (0,0); A[3] = (10,100); A[4] = (20,0); for(int i = 0; i <= 4; ++i) { dot(A[i],red+linewidth(4.5)); } label("(-20,0)",A[0],(-1.5,-1.5),red,UnFill); label("(-10,100)",A[1],(-1.5,1.5),red); label("(0,0)",A[2],(0,-1.5),red,UnFill); label("(10,100)",A[3],(1.5,1.5),red); label("(20,0)",A[4],(1.5,-1.5),red,UnFill); add(legend(),point(E),40E,UnFill); [/asy]$ Since $f(x)=c\pm21$ has $12$ distinct real solutions, it is clear that each case has $6$ distinct real solutions geometrically. We shift the graphs of $y=\pm21$ up $c$ units, where $c\geq0:$
• For $f(x)=c+21$ to have $6$ distinct real solutions, we need $0\leq c<79.$
• For $f(x)=c-21$ to have $6$ distinct real solutions, we need $21
Taking the intersection of these two cases gives $21 from which there are $79-21-1=\boxed{057}$ such integers $c.$
~MRENTHUSIASM
## Solution 2 (Graphing)
Graph $y=|20|x|-x^2|$ (If you are having trouble, look at the description in the next two lines and/or the diagram in Solution 1). Notice that we want this to be equal to $c-21$ and $c+21$.
We see that from left to right, the graph first dips from very positive to $0$ at $x=-20$, then rebounds up to $100$ at $x=-10$, then falls back down to $0$ at $x=0$.
The positive $x$ are symmetric, so the graph re-ascends to $100$ at $x=10$, falls back to $0$ at $x=10$, and rises to arbitrarily large values afterwards.
Now we analyze the $y$ (varied by $c$) values. At $y=k<0$, we will have no solutions, as the line $y=k$ will have no intersections with our graph.
At $y=0$, we will have exactly $3$ solutions for the three zeroes.
At $y=n$ for any $n$ strictly between $0$ and $100$, we will have exactly $6$ solutions.
At $y=100$, we will have $4$ solutions, because local maxima are reached at $x= \pm 10$.
At $y=m>100$, we will have exactly $2$ solutions.
To get $12$ distinct solutions for $y=|20|x|-x^2|=c \pm 21$, both $c +21$ and $c-21$ must produce $6$ solutions.
Thus $0 and $c+21<100$, so $c \in \{ 22, 23, \dots , 77, 78 \}$ is required.
It is easy to verify that all of these choices of $c$ produce $12$ distinct solutions (none overlap), so our answer is $\boxed{057}$.
## Solution 3 (Graphing)
Let $y = |x|.$ Then the equation becomes $\left|\left|20y-y^2\right|-c\right| = 21$, or $\left|y^2-20y\right| = c \pm 21$. Note that since $y = |x|$, $y$ is nonnegative, so we only care about nonnegative solutions in $y$. Notice that each positive solution in $y$ gives two solutions in $x$ ($x = \pm y$), whereas if $y = 0$ is a solution, this only gives one solution in $x$, $x = 0$. Since the total number of solutions in $x$ is even, $y = 0$ must not be a solution. Hence, we require that $\left|y^2-20y\right| = c \pm 21$ has exactly $6$ positive solutions and is not solved by $y = 0.$
If $c < 21$, then $c - 21$ is negative, and therefore cannot be the absolute value of $y^2 - 20y$. This means the equation's only solutions are in $\left|y^2-20y\right| = c + 21$. There is no way for this equation to have $6$ solutions, since the quadratic $y^2-20y$ can only take on each of the two values $\pm(c + 21)$ at most twice, yielding at most $4$ solutions. Hence, $c \ge 21$. $c$ also can't equal $21$, since this would mean $y = 0$ would solve the equation. Hence, $c > 21.$
At this point, the equation $y^2-20y = c \pm 21$ will always have exactly $2$ positive solutions, since $y^2-20y$ takes on each positive value exactly once when $y$ is restricted to positive values (graph it to see this), and $c \pm 21$ are both positive. Therefore, we just need $y^2-20y = -(c \pm 21)$ to have the remaining $4$ solutions exactly. This means the horizontal lines at $-(c \pm 21)$ each intersect the parabola $y^2 - 20y$ in two places. This occurs when the two lines are above the parabola's vertex $(10,-100)$. Hence we have \begin{align*} -(c + 21) &> -100 \\ c + 21 &< 100 \\ c &< 79. \end{align*} Hence, the integers $c$ satisfying the conditions are those satisfying $21 < c < 79.$ There are $\boxed{057}$ such integers.
Note: Be careful of counting at the end, you may mess up and get $59$.
## Solution 4 (Algebra)
Removing the absolute value bars from the equation successively, we get \begin{align*} \left|\left|20|x|-x^2\right|-c\right|&=21 \\ \left|20|x|-x^2\right|&= c \pm21 \\ 20|x|-x^2 &= \pm c \pm 21 \\ x^2 \pm 20x \pm c \pm21 &= 0. \end{align*} The discriminant of this equation is $$\sqrt{400-4(\pm c \pm 21)}.$$ Equating the discriminant to $0$, we see that there will be two distinct solutions to each of the possible quadratics above only in the interval $-79 < c < 79$. However, the number of zeros the equation $ax^2+b|x|+k$ has is determined by where $ax^2+bx+k$ and $ax^2-bx+k$ intersect, namely at $(0,k)$. When $k<0$, $a>0$, $ax^2+b|x|+k$ will have only $2$ solutions, and when $k>0$, $a>0$, then there will be $4$ real solutions, if they exist at all. In order to have $12$ solutions here, we thus need to ensure $-c+21<0$, so that exactly $2$ out of the $4$ possible equations of the form $ax^2+b|x|+k$ given above have y-intercepts below $0$ and only $2$ real solutions, while the remaining $2$ equations have $4$ solutions. This occurs when $c>21$, so our final bounds are $21, giving us $\boxed{057}$ valid values of $c$.
## Remark
The graphs of $F(x)=\left||20|x|-x^2|-c\right|$ and $G(x)=21$ are shown here in Desmos: https://www.desmos.com/calculator/i6l98lxwpp
Move the slider around for $21 to observe how they intersect for $12$ times.
~MRENTHUSIASM
## Video Solution
https://youtu.be/6k-uR71_jg0 ~mathproblemsolvingskills.com | 2022-10-02 22:21:46 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 147, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9357494115829468, "perplexity": 697.4878582488686}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-40/segments/1664030337360.41/warc/CC-MAIN-20221002212623-20221003002623-00406.warc.gz"} |
https://in.mathworks.com/help/comm/ref/comm.fmmodulator-system-object.html | # comm.FMModulator
Modulate signal using FM method
## Description
The `comm.FMModulator` System object™ applies baseband frequency modulation to a signal. For more information, see Algorithms.
To modulate a signal using the FM method:
1. Create the `comm.FMModulator` object and set its properties.
2. Call the object with arguments, as if it were a function.
## Creation
### Syntax
``fmmodulator = comm.FMModulator``
``fmmodulator = comm.FMModulator(Name,Value)``
``fmmodulator = comm.FMModulator(fmdemodulator)``
### Description
````fmmodulator = comm.FMModulator` creates an FM modulator System object.```
example
````fmmodulator = comm.FMModulator(Name,Value)` sets properties using one or more name-value arguments. For example, `'SampleRate,400e3'` specifies a sample rate of 400 kHz.```
example
````fmmodulator = comm.FMModulator(fmdemodulator)` sets properties based on the configuration of the input `comm.FMDemodulator` System object, `fmdemodulator`.```
## Properties
expand all
Unless otherwise indicated, properties are nontunable, which means you cannot change their values after calling the object. Objects lock when you call them, and the `release` function unlocks them.
If a property is tunable, you can change its value at any time.
Sample rate of the input signal in Hz, specified as a positive scalar. This property specifies the sample rate at the output of a modulator or at the input of a demodulator. The sample rate must be greater than twice the frequency deviation (that is, `SampleRate` > 2×`FrequencyDeviation`).
Data Types: `double`
Peak deviation of the output signal frequency in Hz, specified a positive scalar. The frequency deviation must be less than half the sample rate (that is, `FrequencyDeviation` < `SampleRate`/2).
The system bandwidth is BT = 2×(`FrequencyDeviation` + BM), where BM is the message bandwidth in Hz. For more information, see Algorithms.
Data Types: `double`
## Usage
### Syntax
``outsig = fmmodulator(insig)``
### Description
example
````outsig = fmmodulator(insig)` modulates the input message signal and outputs a baseband FM signal.```
### Input Arguments
expand all
Input signal, specified as a scalar or column vector.
Data Types: `double` | `single` | `fi`
Complex Number Support: Yes
### Output Arguments
expand all
Modulated baseband FM signal, returned as a scalar or column vector with complex values. The output signal has the same data type and size as the input `insig`.
## Object Functions
To use an object function, specify the System object as the first input argument. For example, to release system resources of a System object named `obj`, use this syntax:
`release(obj)`
expand all
`step` Run System object algorithm `release` Release resources and allow changes to System object property values and input characteristics `reset` Reset internal states of System object
## Examples
collapse all
Apply baseband modulation to a sine wave. Plot the sine wave and the modulated signals.
Set parameters for the example.
```fs = 1e3; % Sample rate (Hz) ts = 1/fs; % Sample period (s) fd = 50; % Frequency deviation (Hz)```
Create a sinusoidal signal with a duration of 0.5 s and frequency of 4 Hz.
```t = (0:ts:0.5-ts)'; x = sin(2*pi*4*t);```
Create an FM modulator System object™, setting the sample rate and frequency deviation.
```fmmodulator = comm.FMModulator( ... 'SampleRate',fs, ... 'FrequencyDeviation',fd);```
FM-modulate the signal and plot its real part. The frequency of the modulated signal changes with the amplitude of the input signal.
```y = fmmodulator(x); plot(t,[x real(y)])```
Apply baseband FM modulation to a white Gaussian noise source and plot the spectrum of the modulated signal.
Initialize parameters for the example.
```fs = 1e3; % Sample rate (Hz) ts = 1/fs; % Sample period (s) fd = 10; % Frequency deviation (Hz)```
Create a white Gaussian noise source with a duration of 5 seconds.
```t = (0:ts:5-ts)'; x = wgn(length(t),1,0);```
Create two FM modulator System objects, setting the sample rate and frequency deviation. Set the frequency deviation of the second FM modulator object five times higher than the first FM modulator.
```fmmod1 = comm.FMModulator( ... SampleRate=fs, ... FrequencyDeviation=fd); fmmod2 = comm.FMModulator( ... SampleRate=fs, ... FrequencyDeviation=5*fd);```
Use the FM modulators to apply FM modulation to the signal `x`.
```y1 = fmmod1(x); y2 = fmmod2(x);```
Plot the spectra of the two modulated signals. The larger frequency deviation associated with channel 2 results in a noise level that is 10 dB higher than the first channel.
```specanalyzer = spectrumAnalyzer(SampleRate=fs,ShowLegend=true); specanalyzer([y1 y2]) release(specanalyzer)```
Modulate and demodulate a sinusoidal signal. Plot the demodulated signal and compare it to the original signal.
Initialize parameters for the example.
```fs = 100; % Sample rate (Hz) ts = 1/fs; % Sample period (s) fd = 25; % Frequency deviation (Hz)```
Create a sinusoidal signal with a duration of 0.5 s and frequency of 4 Hz.
```t = (0:ts:0.5-ts)'; x = sin(2*pi*4*t);```
Create an FM modulator System object™, setting the sample rate and frequency deviation. Then, create an FM demodulator System object, using the FM modulator configuration to set the demodulator properties.
```fmmodulator = comm.FMModulator( ... 'SampleRate',fs, ... 'FrequencyDeviation',fd); fmdemodulator = comm.FMDemodulator(fmmodulator);```
FM-modulate the signal and plot the real component of the complex signal. The frequency of the modulated signal changes with the amplitude of the input signal.
```y = fmmodulator(x); plot(t,[x real(y)]) title('Input Sinusoid and FM-Modulated Signals') xlabel('Time (seconds)'); ylabel('Amplitude') legend('Input signal','Modulated signal (real component)')```
Demodulate the FM-modulated signal.
`z = fmdemodulator(y);`
Plot the original and demodulated signals. The demodulator output signal exactly aligns with the original signal.
```plot(t,x,'r',t,z,'ks') legend('Original signal','Demodulated signal') xlabel('Time (s)') ylabel('Amplitude')```
## Algorithms
A frequency-modulated passband signal, Y(t), is given as
`$Y\left(t\right)=A\mathrm{cos}\left(2\pi {f}_{\text{c}}t+2\pi {f}_{\text{Δ}}{\int }_{0}^{t}x\left(\text{τ}\right)d\text{τ}\right)\text{\hspace{0.17em}},$`
where:
• A is the carrier amplitude.
• fc is the carrier frequency.
• x(τ) is the baseband input signal.
• fΔ is the frequency deviation in Hz.
The frequency deviation is the maximum shift from fc in one direction, assuming |x(τ)| ≤ 1.
A baseband FM signal can be derived from the passband representation by downconverting the passband signal by fc such that
`$\begin{array}{c}{y}_{\text{s}}\left(t\right)=Y\left(t\right){e}^{-j2\pi {f}_{\text{c}}t}=\frac{A}{2}\left[{e}^{j\left(2\text{π}{f}_{\text{c}}t+2\text{π}{f}_{\text{Δ}}{\int }_{0}^{t}x\left(\text{τ}\right)d\text{τ}\right)}+{e}^{-j\left(2\text{π}{f}_{\text{c}}t+2\text{π}{f}_{\text{Δ}}{\int }_{0}^{t}x\left(\text{τ}\right)d\text{τ}\right)}\right]{e}^{-j2\text{π}{f}_{\text{c}}t}\\ =\frac{A}{2}\left[{e}^{j2\text{π}{f}_{\text{Δ}}{\int }_{0}^{t}x\left(\text{τ}\right)d\text{τ}}+{e}^{-j4\text{π}{f}_{\text{c}}t-j2\text{π}{f}_{\text{Δ}}{\int }_{0}^{t}x\left(\text{τ}\right)d\text{τ}}\right]\text{\hspace{0.17em}}.\end{array}$`
Removing the component at -2fc from yS(t) leaves the baseband signal representation, y(t), which is given as
`$y\left(t\right)=\frac{A}{2}{e}^{j2\pi {f}_{\Delta }{\int }_{0}^{t}x\left(\tau \right)d\tau }.$`
The expression for y(t) can be rewritten as $y\left(t\right)=\frac{A}{2}{e}^{j\varphi \left(t\right)}$, where $\varphi \left(t\right)=2\text{π}{f}_{\Delta }{\int }_{0}^{t}x\left(\tau \right)d\tau$. Expressing y(t) this way implies that the input signal is a scaled version of the derivative of the phase, ϕ(t).
To recover the input signal from y(t), use a baseband delay demodulator, as this figure shows.
Subtracting a delayed and conjugated copy of the received signal from the signal itself results in this equation.
`$w\left(t\right)=\frac{{A}^{2}}{4}{e}^{j\varphi \left(t\right)}{e}^{-j\varphi \left(t-T\right)}=\frac{{A}^{2}}{4}{e}^{j\left[\varphi \left(t\right)-\varphi \left(t-T\right)\right]}\text{\hspace{0.17em}},$`
where T is the sample period. In discrete terms,
The signal vn is the approximate derivative of ϕn such that vnxn.
## References
[1] Hatai, I., and I. Chakrabarti. “A New High-Performance Digital FM Modulator and Demodulator for Software-Defined Radio and Its FPGA Implementation.” International Journal of Reconfigurable Computing (December 25, 2011): 1–10. https://doi.org/10.1155/2011/342532.
[2] Taub, H., and D. Schilling. Principles of Communication Systems. McGraw-Hill Series in Electrical Engineering. New York: McGraw-Hill, 1971, pp. 142–155.
## Version History
Introduced in R2015a | 2022-12-07 23:32:15 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 6, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7290542721748352, "perplexity": 3081.763639163919}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-49/segments/1669446711221.94/warc/CC-MAIN-20221207221727-20221208011727-00823.warc.gz"} |
https://web2.0calc.com/questions/help_91336 | +0
# Help!
+1
203
2
+738
Moving only south and east along the line segments, how many paths are there from A to B?
MIRB16 Mar 8, 2018
#1
+20025
+1
Moving only south and east along the line segments, how many paths are there from A to B?
$$\begin{array}{|rcll|} \hline && {^{12}}C_3- {^5}C_1 {^6}C_1- {^6}C_1 {^5}C_1 \\ &=& {^{12}}C_3-2\cdot {^5}C_1{^6}C_1 \\ &=& 220-2\cdot 30 \\ &=& 220-60 \\ &=& 160 \\ \hline \end{array}$$
heureka Mar 8, 2018
#2
+738
+3
Again thanks so much
MIRB16 Mar 9, 2018 | 2018-10-20 07:33:41 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9275966882705688, "perplexity": 2325.665586997504}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-43/segments/1539583512592.60/warc/CC-MAIN-20181020055317-20181020080817-00553.warc.gz"} |
https://astrobites.org/guides/astronomy-the-electromagnetic-spectrum/radio/ | Observable from ground : Yes
### Contents
Frequency – 0 to about 1 GHz
Energy – 0 to about 4 μeV per photon
Wavelength – Infinity to about 30 cm
• Galactic – magnetic fields (synchrotron), solar activity (synchrotron), H II regions (bremsstrahlung), planetary nebulae (recombination lines), pulsars (synchrotron)
• Extragalactic – neutral hydrogen content and kinematics (hyperfine transitions), magnetic fields (synchrotron), relativistic electrons (synchrotron), jets (synchrotron), AGN (synchrotron and bremsstrahlung)
### Effect of the Galaxy
• Faraday RotationA linearly-polarized wave can be decomposed into a sum of left- and right-circularly polarized waves at the same frequency (with a zero phase difference corresponding to polarization along one of the Cartesian axes). These left and right circularly-polarized components travel at different speeds through a plasma rendered anisotropic due to a magnetic field. Upon exiting the plasma, the left- and right-circular polarization modes have picked up a net phase difference, which causes their sum to still be linearly-polarized, but along a different axis. Thus the plane of linear polarization of an em wave is rotated upon propagation through a magnetized plasma.This effect is frequency-dependent. Our Galaxy is full of ionized hot gas (H II), and is simultaneously permeated by a large-scale magnetic field. The Faraday effect due to this plasma is observed in the polarized signal from radio pulsars within our Galaxy, and on all extragalactic radio sources. How do we know what the original plane of polarization is? We don’t – so the effect is almost always studied as a function of frequency.
• Scintillation Just like stars twinkle due to turbulence in the Earth’s atmosphere, point sources (~ microarcseconds in size) of radio waves such as quasars and interstellar masers twinkle as their radio waves pass through the turbulent interstellar medium on the one hand, and the fluctuating Solar wind within the interplanetary medium, on the other hand. Both these effects, as well as scattering from dust grains in the ISM cause the sources to look larger than they really are. The term coined for this phenomenon in the optical is “seeing” – there is a “seeing” in the radio, too!
• Foreground contamination: synchrotron radiation from Galactic planeOur Galaxy emits bright synchrotron radiation (see below) from relativistic electrons gyrating in the Galactic magnetic field. This emission is strongest in the Galactic plane, where the electron density is the highest. Being a synchrotron spectrum, this radiation is stronger at low frequencies, and completely dominates the radio sky below 100 MHz.
A 22 MHz all-sky map. The dominant source is synchrotron radiation from our Galaxy. This is a foreground that needs to be modeled and removed for any precision radio measurement at low frequencies, such as the CMB (WMAP), and epoch of reionization (LOFAR).
Paradoxically, some of the most energetic phenomena in the Universe produce copious amounts of the lowest energy electromagnetic radiation – radio waves.
Continuum, or broad-band sources are visible across the radio spectrum. Increasing the bandwidth of the receiver systems improves the flux measurement of continuum sources. The signal-to-noise ratio for radio observations of continuum sources is proportional to one over the square root of the product of the integration time and the observing bandwidth.
#### Synchrotron (non-thermal)
Need: relativistic electrons, magnetic fields
The paths of charged particles are bent by the presence of magnetic fields. As their space velocity changes, they accelerate. All accelerated charged particles radiate. In the case of relativistic particles (usually electrons) spiraling in magnetic fields, the resulting emission is called synchrotron radiation. The total power radiated by a relativistic particle of Lorentz factor, ɣ in a magnetic field, B is proportional to ɣ2B2.
The detailed shape of the spectrum of synchrotron radiation is complicated, but for a power-law distribution of electrons,
N(E) ∝ E-p, the spectrum is also a power law, P(ω) ∝ ω-(p-1)/2. Physical arguments (finite total energy) require that p>1, which means that synchrotron radiation is stronger at lower frequencies.
1. Prof. Malcolm Longair’s Course Notes
Examples: supernova remnants, GRB afterglows, radio galaxies
Diagnostics for: Magnetic field magnitude and direction, relativistic electron population (Number density as a function of electron energy)
#### Bremsstrahlung (thermal)
Need: free electrons and ions, high density
Overlay of VLA 330 MHz radio contours on a UK Schmidt optical photograph of the Orion region. The radio emission is dominated by thermal bremsstrahlung from hot gas ionized by the central stars of the nebula.
The paths of charged particles are bent by the presence of other charged particles – in particular, the paths of free electrons are bent when they pass by charged ions. As their space velocity changes, they accelerate. All accelerated charged particles radiate. Thus a hot plasma, which has free electrons and ions, is able to cool by free-free- aka bremsstrahlung- (“braking”) radiation. The spectrum of the radiation is calculated by averaging over the impact parameter for all possible trajectories of the electron with respect to the ion followed by an average over the speed distributions of the electrons. The result is different for non-relativistic bremsstrahlung (aka “thermal” bremsstrahlung, with a Maxwell-Boltzmann speed distribution assumed), and bremsstrahlung from relativistic particles1 (non-thermal free-free emission)
Thus thermal bremsstrahlung is observed for any source consisting of hot plasma. The free-free emissivity scales as the square of the density, and is dominant over non-thermal (synchrotron processes) in hot, dense gas with weak magnetic fields.
1. Prof. Malcolm Longair’s Course Notes
Examples: H II regions, pulsar wind nebulae
Diagnostics for: Electron temperature and density
1 Credit: Dr Martin Kohl
### Sources of radio spectral lines
Radio spectral lines only appear at frequencies characteristic of the atomic transition responsible. The signal-to-noise ratio of spectral line observations is independent of the bandwidth, but is still inversely proportional to the square root of the integration time.
#### Recombination lines (thermal/non-thermal)
Need: partly-ionized medium
The frequency of an atomic transition from an upper level, m to a lower level, n is given by the Rydberg formula, $nu = cRZ^2(n^{-2} - m^{-2}).$ When m = n+1, the line is designated as an nα transition, while for m = n+2, m = n+3, … we have an nβ, nγ … transition. For large n and m, these frequencies fall in the radio wavebands. An analysis of the relative intensities of observed radio recombination lines yields a direct measure of the electron temperature in the source region, as well as abundances of the emitting species (just as in the optical bands).
Radio (pushing microwave) recombination lines from the star-forming region, Orion A. The booming central line is H109α, i.e. a transition between a principal quantum number from 110 to 109. Recombination lines from other species, as well as other high-n transitions of Hydrogen are visible in the same spectrum.
Examples: H II regions, planetary nebulae, nuclei of radio galaxies, hot gas in the ISM
Diagnostics for: Ionizing photon flux, electron temperature, electron density, emission measure (integral of the square of the electron density along the line of sight)
#### Hyperfine structure (thermal)
Need: neutral hydrogen *
The H I Nearby Galaxy Survey (THINGS)
In atomic hydrogen, the ground state (n = 1) state is split by coupling of the electron spin to the magnetic dipole moment of the nucleus. When the spins of the proton and electron point in the same direction, the system has a slightly higher energy (about 6 x 10-6 eV) than when the spins are anti-aligned. Transitions between the two states lead to the emission of a hyperfine line at 21 cm. The probability of any given hydrogen atom making this transition is exceedingly small (the lifetime of the upper state is 107 years), but there is so much neutral hydrogen in the universe that this transition is almost ubiquitous.
* Hyperfine transitions in other species, such as deuterium and 3He+ can also be observed.
Examples: Diffuse ISM of other galaxies, ISM of the Galaxy, neutral intergalactic medium (at z > zreionization)
Diagnostics for: Kinematics (rotation curves), total gas mass
1. The HI Nearby Galaxy Survey (THINGS)
#### Elements of a radio telescope
1. Reflective element (e.g. parabolic dish)
The reflective element focuses parallel beams of radio waves on to the active element at the focus. It also shields the feed from radiation from the ground and surroundings. The reflective element determines the shape of the primary beam of the telescope (e.g. the beam pattern of a paraboloidal dish antenna on the sky is the Airy pattern) and sets the basic restrictions on the required pointing accuracy of the telescope.
2. Active element (aka “feed”: e.g. dipole or horn antenna)
The feed is an example of a transducer – it captures radio waves traveling through the air and transforms them into electric signals on a cable. | 2021-09-27 05:01:49 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 1, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.676559567451477, "perplexity": 1516.7764291032295}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-39/segments/1631780058263.20/warc/CC-MAIN-20210927030035-20210927060035-00477.warc.gz"} |
https://www.doubtnut.com/question-answer/harry-got-350-as-his-salary-he-puts-1-nth-of-his-salary-in-his-saving-account-and-then-spends-the-re-195772055 | HomeEnglishClass 12MathsChapterHeart Of Algebra
Harry got $350 as his salary.... # Harry got$350 as his salary. He puts ((1)/(n))^(th) of his salary in his saving account , and then spends the rest of the money on buying presents for his family members. If Harry has 8 family members and he spends an amount, the same as what he saved , equally on each member, what is the value of n ?
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00:00 - 00:59question l Harry got 350 dollars as a salary he puts one buy anything of salary in his savings account and then spend the rest of the money on buying presents for his family members if Harry has eight family members and he spends an amount the same as what he speed equally on each member what is the value of your options are a pics base9 and 12 solution will be we know that had his salary is free \$50 and we are given that he saves won by another of his salary amount saved is amount saved is 1 by N H of his salary that is 1 by n x 350 and now we are given that
01:00 - 01:59he spent the rest of the money on buying presents for his family members Sohail spending our expenditure basically total expenditure total expenditure is salary - the amount saved 350 - 1 by n x 350 can be written as if we take 350 common 350 X 1 minus one upon in this is the total expenditure made by Harry and now we are given that he spent the rest of the money on buying presents for his family members if Harry has 8 family members and his pension amount the same as what he saved equal to on each member of this is his total expenditure and out of which he buys presence for his eight family members and his
02:00 - 02:59the same amount on each family member as the amount He saved sunao sunao family members total family members are it and the amount spent on each family member will be total divided upon 8 because he spending the equal amount on each family members to 350 upon 8 x minus one upon n so now we are given that he spent the same amount on each family members as what he saved so now according to question Re 5350 upon 8 x 1 -
03:00 - 03:59one upon n is equal to one point in X 350 because this was the amount saved by him one point and into 352 now 35350 get cancelled and it is being divided hair so it will be transposed to write inside and it will multiply to 1 minus one upon to eat a point in 21 is equal to 8.1 plus one upon in sunao 1 is equal to 9 point in this implies n is equal to 9 this is the value of n which we get and hence according to the options given to a r option the | 2021-12-05 23:58:07 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.30597421526908875, "perplexity": 1193.9051205171834}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-49/segments/1637964363226.68/warc/CC-MAIN-20211205221915-20211206011915-00149.warc.gz"} |
https://www.physicsforums.com/threads/gyroscopic-effect-in-a-horizontal-axis-ic-engine.717355/ | # Gyroscopic effect in a horizontal axis IC engine
1. Oct 18, 2013
### marellasunny
My tutor says Henry Ford opted for a horizontal-bed IC engine for the Model-T as this would avoid having any gyroscopic effects(normally associated with a vertical oriented engine).
My question is,how does it matter if the engine cylinders are oriented horizontally or vertically?since the crankshaft is rotating anyway and would produce a gyroscopic effect nevertheless,right?
As a extreme example of my understanding of engine gyroscopic effect,I would like to cite the rotary engine of the plane 'Sopwith Camel', which produced so much gyroscopic effect that the plane went 'up' on left turns and 'down' on right turns.But,this was because there were 8 cylinders revolving around a stationary crankshaft.
In case of the Model-T,the cylinders were stationary,so how would these produce a gyroscopic effect?
2. Oct 18, 2013
### etudiant
Interesting question.
As the crankshaft and flywheel are the only significant rotating elements that I can think of, maybe your tutor is mistaken.
Have you asked why s/he believes this? Maybe s/he was told this long ago and has never really thought about it.
3. Oct 18, 2013
### SteamKing
Staff Emeritus
The rotary aircraft engines used in WWI had 9 cylinders.
The horizontal placement of the engine in automobiles simplifies laying out the drivetrain. I don't think Ford was the first to use this layout. I think Panhard in France was the first to use the front engine - rear drive layout in about 1895.
http://en.wikipedia.org/wiki/Système_Panhard
Standing the engine on end has no benefit of which I am aware and quite a few disadvantages:
1. It obstructs forward visibility.
2. Adds another right-angle gear to the driveline
3. Complicates lubrication of the internal engine parts
4. In pre-electric starter days, makes it damned difficult to use a crank to start the engine
5. Upper cylinders would be difficult to lubricate
6. Hard to provide fuel using the simple carbs and gravity feed systems from the fuel tank.
7. Hard to cool with a conventional radiator
4. Oct 18, 2013
### Baluncore
I think this situation is one of angular momentum, not of gyroscopic effects.
A vertical axis engine would tend to cause significant directional changes to the vehicle when changing RPM or gear ratio.
5. Oct 19, 2013
### marellasunny
Why?
More specifically,does a larger gear ratio mean a greater/smaller rotational moment of inertia for the whole system? From my calculations,larger the gear ratio,smaller the overall rotational moment of inertia.
$$Gear. ratio=\frac{\omega _1}{\omega _2}$$,say 1 is the input shaft.
We know that,
$$\frac{\omega _1}{\omega _2}=\frac{n_2}{n_1}$$
where n-number of teeth on each gear [n1-number of teeth on input gear,n2-number of teeth on output gear]
omega-rpm of the gears
$$K.E_{system}=KE_1+KE_2=0.5J_1 \omega_1^2+0.5J_2(\frac{n_1}{n_2} \omega_1)^2$$
$$J_{system}=J_1+J_2$$
Therefore,greater the gear ratio,smaller the rotational moment of inertia of the whole system,right?
Q.Wouldn't a gearbox in a horizontal axis engine also have different moment of inertias at different rpms?
6. Oct 19, 2013
### marellasunny
Why?
More specifically,does a larger gear ratio mean a greater/smaller rotational moment of inertia for the whole system? From my calculations,larger the gear ratio,smaller the overall rotational moment of inertia.
$$Gear. ratio=\frac{\omega _1}{\omega _2}$$,say 1 is the input shaft.
We know that,
$$\frac{\omega _1}{\omega _2}=\frac{n_2}{n_1}$$
where [n1-number of teeth on input gear,n2-number of teeth on output gear]
omega-rpm of the gears
$$K.E_{system}=KE_1+KE_2=0.5J_1 \omega_1^2+0.5J_2(\frac{n_1}{n_2} \omega_1)^2$$
$$J_{system}=J_1+J_2$$
Therefore,greater the gear ratio,smaller the rotational moment of inertia of the whole system,right?
This now brings me to the question:
Q.How does it matter in relation to the angular momentum if the engine cylinder axis is horizontal(like a boxer engine) or vertical(like a inline 4)?
Q.How does it matter in relation to the gyroscopic effect if the engine cylinder axis is horizontal(like a boxer engine) or vertical(like a inline 4)?
7. Oct 19, 2013
### Baluncore
I think the OP has some confusion about referencing cylinder axis or crankshaft axis. It is the crankshaft that rotates and so it is the crankshaft axis that is the gyroscopic axis.
It makes no difference which way the cylinders are orientated since they reciprocate in a balanced way.
There are three simple crankshaft rotation axis orientations.
1. Traditional. In the line of the tail-shaft. When you rev the engine the car rocks sideways.
2. Transverse. When you rev the engine the car rocks less but in a front – rear way.
3. Vertical. When you rev the engine the car changes direction. Not an ideal situation. Changing gear changes RPM, therefore it changes rotational momentum and causes the vehicle to tend to change direction when changing gear.
8. Oct 19, 2013
### Baluncore
Correct. Rotary engines had an odd number of cylinders on a single fixed eccentric crank. The reason for an odd number of cylinders is that, being four stroke, the firing order could be regular. That is not possible with an even number of cylinders except with two stroke engines.
9. Oct 21, 2013
### marellasunny
Upon further clarification with the lecturer,he meant the gyroscopic effect was produced due to the flywheel.So,yes Baluncore,you were correct in saying that the crankshaft axis is the 'gyroscopic axis'.
**"Vertical crankshaft orientation axis"-is this even possible?Examples please.
10. Oct 21, 2013
### Baluncore
A great many lawn mowers are now built with a vertical crankshaft axis, examples are Victa, Flymo.
The oil seal at the bottom of the shaft is not such a problem with two stroke motor lubrication since an oil sump is not required.
There is an advantage with a gas turbine being mounted with a vertical shaft in a light motor vehicle as it would prevent wheels lifting off the ground when going around tight corners.
Last edited: Oct 21, 2013
11. Oct 22, 2013
### marellasunny
Twist to the tale,tutor says gyroscopic effects very negligible in today's drive-train format i.e with the flywheel occurring immediately after the engine.Reason given:there is no 'lever'/distance for the flywheel moment to act on and hence no gyroscopic effect.Says the only possibility is if the bearings are loose and the flywheel can move left/right.
This was contrary to my understanding that in order for the occurrence of gyroscopic moment,one needs :a.Yaw moment b.Rotating flywheel mass.
Is he right?
12. Oct 23, 2013
### AlephZero
I'm slowly coming to the conclusion that either your tutor doesn't know what he/she is talking about, or somebody's first language is not English and some terms have been translated wrongly.
13. Oct 24, 2013
### Baluncore
Your representation of your tutors opinion is hearsay. Your lack of vocabulary skills may have resulted in your tutor misunderstanding your question or in you misunderstanding their reply.
It would be more mature to approach the apparent inconsistency by asking where the misunderstandings are, rather than to make it personal by insisting the tutor is wrong. It is wise never to corner a rat. Your hostility and personal attack on a superior will alienate you from others. That would appear to be self destructive and counter to your best long term interests. To progress you need helpful allies, not enemies.
Professional etiquette requires that you respect professionals in your field. No professional is going to gang up with you against your tutor to prove your tutor wrong. If you do not respect others then you cannot expect to be invited to join that profession.
14. Oct 26, 2013
### marellasunny
Yes,thank you.I needed to be reminded of that.Conscience didn't feel right when I left the room with doubts still lingering,should have gone back and cleared them out.Hope the administrator comes-up with a category called 'ethics in academia'.
F.Y.I:I am not being sarcastic. | 2017-11-23 20:58:27 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.3665526509284973, "perplexity": 3682.4078054265933}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-47/segments/1510934806939.98/warc/CC-MAIN-20171123195711-20171123215711-00194.warc.gz"} |
http://mathhelpforum.com/algebra/219856-orthogonal-vectors-plane.html | # Math Help - Orthogonal Vectors in a plane
1. ## Orthogonal Vectors in a plane
Find two orthogonal vectors in the plane containing the points A(-5,3,-4) B(-4,-3,-1) and C(-2,5,3)
Ok so i have that
AB = <1,-6,3>
AC = <3,2,7>
AB X AC = n = determinant of the 3x3 matrix = -48i + 2j +20k
so i need u and v such that u . v = 0 and u . n = 0 and v . n =0
i have a feeling it should be easy but i can't figure it out?
2. ## Re: Orthogonal Vectors in a plane
Hey linalg123.
Hint: If you need two orthogonal vectors that lie in the plane I suggest you use one of the vectors (like AB), then given the plane normal take AB X N and get the second vector that is both orthogonal to AB and the Normal vector.
3. ## Re: Orthogonal Vectors in a plane
thanks i knew it was gonna be obvious!
4. ## Re: Orthogonal Vectors in a plane
As an alternative method, use the fact that any vector in the plane of the triangle can be expressed as some linear combination of (say) $\underline{AB} \text{ and } \underline{AC}$.
Suppose then that a suitable vector is $\alpha\underline{AB}+\beta\underline{AC}.$
For this to be perpendicular to $\underline{AB},$ its scalar product with $\underline{AB}$ has to equal zero.
The result from that allows you to write either $\alpha \text{ or } \beta$ in terms of the other.
Remember that your answer is not going to be unique, if you have a vector that is perpendicular to $\underline{AB},$ then any (non-zero) scalar multiple will also be perpendicular to $\underline{AB},$ so you don't need an actual value for $\alpha \text{ or } \beta$. | 2014-11-27 12:03:26 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 8, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7651314735412598, "perplexity": 284.1474922038317}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-49/segments/1416931008289.40/warc/CC-MAIN-20141125155648-00164-ip-10-235-23-156.ec2.internal.warc.gz"} |
http://mathhelpforum.com/calculus/113043-differentiating-functions-natural-logs-print.html | # Differentiating functions with natural logs
• November 7th 2009, 03:45 PM
iheartphysics01
Differentiating functions with natural logs
Can anyone explain to me how to do this problem?
y=ln(cos(4x))
• November 7th 2009, 03:53 PM
Scott H
Welcome to the Math Help Forum! :)
The function $y=\ln\cos (4x)$ may be differentiated by applying the Chain Rule twice, knowing that
\begin{aligned}
\frac{d}{dx}\ln x&=\frac{1}{x}\\
\frac{d}{dx}\cos x&=-\sin x\\
\frac{d}{dx}(kx)&=k.
\end{aligned}
For reference, the Chain Rule states that
$\frac{d}{dx}f(g(x))=f'(g(x))g'(x).$
• November 7th 2009, 03:53 PM
VonNemo19
Quote:
Originally Posted by iheartphysics01
Can anyone explain to me how to do this problem?
y=ln(cos(4x))
Sure!
$\frac{d}{dx}[\ln{u}]=\frac{u'}{u}$
In your problem, let $u=\cos(4x)$. This implies $u'=-4\sin{(4x)}$
So...
$\frac{d}{dx}[\ln{u}]=\frac{u'}{u}=\frac{-4\sin(4x)}{\cos(4x)}=-4\tan(4x)$
• November 7th 2009, 04:06 PM
iheartphysics01
ok thanks so much!(Happy)
i will probably be using this forum a lot! | 2016-06-30 10:02:38 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 7, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8348743915557861, "perplexity": 3791.143547253625}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-26/segments/1466783398216.41/warc/CC-MAIN-20160624154958-00105-ip-10-164-35-72.ec2.internal.warc.gz"} |
https://planetmath.org/QED | # QED
The term “QED” is actually an abbreviation and stands for the Latin quod erat demonstrandum, meaning “which was to be demonstrated.”
QED typically is used to signify the end of a mathematical proof. The symbol
$\square$
is often used in place of “QED,” and is called the “tombstone”, “Halmos symbol” or “Halmos tombstone” after mathematician Paul Halmos (it can vary in width, however, and sometimes it is fully or partially shaded). Halmos borrowed this symbol from magazines, where it was used to denote “end of article”.
Title QED Canonical name QED Date of creation 2013-03-22 12:40:14 Last modified on 2013-03-22 12:40:14 Owner mathwizard (128) Last modified by mathwizard (128) Numerical id 8 Author mathwizard (128) Entry type Definition Classification msc 00A99 Synonym Q.E.D Related topic QEDInTheoreticalAndMathematicalPhysics Related topic QCDOrQuantumChromodynamics Related topic MathematicalFoundationsOfQuantumFieldTheories Related topic QuantumOperatorAlgebrasInQuantumFieldTheories Related topic GrassmanHopfAlgebrasAndTheirDualCoAlgebras Related topic FoundationsOfQuantumFieldTheories Related topic QuantumChromod Defines Halmos symbol Defines tombstone Defines Halmos tombstone | 2018-10-22 09:40:46 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 1, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7695444822311401, "perplexity": 9759.763662609841}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-43/segments/1539583515029.82/warc/CC-MAIN-20181022092330-20181022113830-00295.warc.gz"} |
https://www.physicsforums.com/threads/two-lines-of-charge-net-electric-field.189055/ | # Two lines of charge, net electric field
1. Oct 4, 2007
1. The problem statement, all variables and given/known data
Short sections of two very long parallel lines of charge are shown, fixed in place, separated by L = 8.0cm. The uniform linear charge densities are $$+6.0\mu$$C/m for line 1 and $$-2.0\mu$$C/m for line 2. Where along the x axis shown is the net electric field from the two lines zero?
The known data is:
$$\lambda_{1} = 6 \times 10^{-6} C$$
$$\lambda_{2} = -2 \times 10^{-6} C$$
$$L = 0.08m$$
http://www.clan-dm.net/members/jen/netfield.jpg [Broken]
(sorry, scanner doesn't like big books)
2. Relevant equations
line of infinite charge: $$\frac{\lambda}{2\pi \epsilon_{0}r}$$
permittivity constant: $$\epsilon_{0} = 8.85*10^{-12}$$
3. The attempt at a solution
I didn't get very far with this one. From what I can tell, I need to sum the electric fields, and figure out when it's zero.
I started out like this:
0 = E1 + E2
E1 = -E2
Obviously, at this point substituting E for the line of infinite charge equation proved fruitless. I don't know if I'm overcomplicating, undercomplicating, or just plain clueless. Any help is appreciated. :)
Also, the given answer makes no sense to me:
$$x = \frac{\lambda_{1} - \lambda_{2}}{\lambda_{1} + \lambda_{2}}\left( \frac{L}{2} \right)$$
Last edited by a moderator: May 3, 2017
2. Oct 4, 2007
### Staff: Mentor
Call the coordinate of the zero-field point x. How would you write the distance to each line charge (in terms of x and L) so that you could use the infinite line charge equation?
3. Oct 4, 2007
I'm assuming that the 0 point is somewhere in the positive x region (because the first line has a larger charge - please let me know if my thinking is off).
With that assumption, line 1 would be L + x away from the point, and line 2 would be L/2 + x away?
Is this on the right track?
$$\frac{\lambda}{2\pi\epsilon_{0}(L + x)} = -\frac{\lambda}{2\pi\epsilon_{0}(L/2 + x)}$$
4. Oct 4, 2007
### Staff: Mentor
Good! Keep going.
Edit: Oops, looks like your equation is a bit off. See comment in next post.
Last edited: Oct 4, 2007
5. Oct 4, 2007
Ok, I algebra'd it out and got x = -3L/4.. which should give me x = -6cm. I guess that means my original assumption of 0 occurring in the positive side was incorrect?
The given answer is very confusing - why would it be in that form? I never actually came across it while finding x.
6. Oct 4, 2007
### Staff: Mentor
I think there's an error in your distances in your equation. Assuming you measure x from the origin, then the distance to line 1 will be x + L/2 and the distance to line 2 will be x - L/2.
To get that answer, solve the problem symbolically. Don't plug in numbers for L, $\lambda_1$, and $\lambda_2$.
7. Oct 4, 2007
Phew, got it. I had measured my distances in a weird way, but I fixed it now. :)
The answer should have been 8cm, correct?
Thanks so much! I have one more question about the etiquette on here. Is it bad form to post more than one question in a day? There's one other problem I'm banging my head against, but will hopefully figure out on my own.. I'm asking just in case. :)
Last edited: Oct 4, 2007
8. Oct 4, 2007
### Staff: Mentor
Yes. Good work.
Of course not! Post as many as you want. As long as you're showing your work, why not? (Better to post them in separate threads, of course.) | 2017-10-20 11:43:02 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6717392206192017, "perplexity": 1104.304773598509}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-43/segments/1508187824068.35/warc/CC-MAIN-20171020101632-20171020121632-00167.warc.gz"} |
https://discourse.pymc.io/t/question-on-how-to-model-spike-and-slab-priors/5277/2 | # Question on how to model spike and slab priors
Hi,
I am new to the pymc3 community, and I have a question on how to apply spike and slab prior on variables.
Here is my model:
Y = X\beta + \epsilon
\beta_i \sim (1-\gamma_i)N(0,0.001^2) + \gamma_i N(0,\sigma_1^2)
\gamma_i \sim \text{Bernoulli }(\pi)
\pi \sim \text{Beta}(1,1)
\epsilon \sim N(0,\sigma_e^2)
\sigma_1 \sim \text{HalfCauchy}(5)
\sigma_e \sim \text{HalfCauchy}(5)
\beta and \gamma are vectors with length = n, in other words, length(beta) == length(gamma) ==n .
I cannot find examples showing mixture on the variables, and I am not sure what I wrote is correct or not.
here is my pymc3 model:
sigma_1 = pm3.HalfCauchy('sigma_1',5)
sigma_e= pm3.HalfCauchy('sigma_e',5)
pi = pm3.Beta('pi',1,1)
gamma = pm3.Bernoulli('gamma',p = pi,shape = n)
mixture_sd = pm3.math.switch(gamma > 0.5, sigma_1, 0.001)
beta = pm3.Normal('beta',mu = 0,sigma = mixture_sd, shape = n)
mu = tt.dot(X,beta)
likelihood = pm3.Normal('y',mu = mu, sigma = sigma_e,observed = y)
The mean(posterior) for \pi and \gamma are too small to be true. The program almost always reports that all of the \beta_i comes from N(0,0.001^2).
I would really appreciate it if someone can help me on this.
Thanks
Xing
Interesting, I posted a similar question yesterday:
What you specify, can be pretty easily modeled in PyMC3:
def beta_spike_slab(shape,spike): inclusion_prop = 0.05 beta_spike = pm.Normal(‘beta_spike’, 0, spike, shape=shape) beta_slab = pm.Normal(‘beta_slab’, 10, shape=shape) gamma = pm.Bernoulli(‘gamma’, inclusion_prop, shape=shape) beta_spike_slab = pm.Deterministic(‘beta_spike_slab’,(beta_spike * (1-gamma)) + ((beta_slab * gamma))) return beta_spike_slab
but this leads to slow sampling, because it is needed to marginalize over the bernoulli distribution.
I have not found a way to do this without divergence/sampling problems, so if anyone has any ideas, I would love to hear them!
Thank you very much. In your code, did you mean
beta_slab = pm.Normal(‘beta_slab’, 0, 10, shape=shape)
In addition, did you spot anything wrong with my implementation?
Yes, that is what I meant.
What are your sampling options? Because you cannot use NUTS for discrete variables, you need to (dramatically) increase your tuning steps. When I choose
trace = pm.sample(1000, tune=12000, nuts={"target_accept": 0.99})
sigma_1 = pm.HalfNormal('sigma_1',10, shape=shape) pi = pm.Beta('pi',2,7) gamma = pm.Bernoulli('gamma',p = pi,shape = shape) mixture_sd = pm.Deterministic('mixture_sd', pm.math.switch(gamma > 0.5, sigma_1, 0.001)) beta = pm.Normal('beta',mu = 0,sigma = mixture_sd, shape = shape)
I do get the right beta coefficients with my toy dataset.
And I think the next step would be to not use match.switch, but replace it with a continous function like tt.net.sigmoid, to improve sampling, see Frequently Asked Questions
I used NUTS for the continues variables and metropolis for gamma. I found it to be very slow.
A continuous version is much faster than the discrete one. Here is the code-
def conti_spike_slab(shape):
mu_hat = 0
sigma_hat = 10
tau = 5
lambda_hat = pm.Normal('lambda_hat', mu = mu_hat, sigma = sigma_hat, shape = shape)
spike_raw = pm.Normal('spike_raw', mu = 0, sigma = 1, shape = shape)
spike = pm.Deterministic('spike',tau*spike_raw*pm.invlogit(lambda_hat))
return spike
Let me know what you guys think.
2 Likes
Perhaps the main point of the spike and slab prior is that it exactly zeros out many coefficients in the posterior samples. If you move to a continuous prior, you give that up. There are better continuous priors favoring many sparse entries. The horseshoe prior is one of them.
1 Like
Unless you’re drawing a single sample, having exact 0s is not particularly useful. And if you want the MAP why are you bothering with sampling at all? Otherwise the general process is “take the trace and ask how often this coefficient was 0” – which can be effectively read off from lambda_hat anyway.
I recently read a paper- https://royalsocietypublishing.org/doi/pdf/10.1098/rsif.2018.0572 which claims that their continuous version of spike and slab outperforms horseshoe prior, it is based on iverse logit which I implemented above.
1 Like
Interesting. I stand corrected with regard to my statement about the horseshoe - I look forward to taking a look at that paper.
1 Like
That’s a really interesting paper, will have to try it later, thanks! | 2022-06-25 19:43:13 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6644635796546936, "perplexity": 3331.0917750056037}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-27/segments/1656103036099.6/warc/CC-MAIN-20220625190306-20220625220306-00312.warc.gz"} |
https://www.gradesaver.com/textbooks/science/physics/college-physics-4th-edition/chapter-11-problems-page-429/30 | ## College Physics (4th Edition)
We can rank the waves in order of maximum transverse speed, from largest to smallest: $e \gt a \gt b = d \gt c$
The maximum transverse speed $v_m = A~\omega = A~(2\pi~f)$. The frequency is the number of cycles per second. Let $t$ be the total time shown on each graph. We can count the number of cycles in each graph to find an expression for the frequency. The amplitude is the maximum distance each point moves away from the center during each cycle. We can count the units from the center of the wave to find an expression for the amplitude for each graph. We can find an expression for the maximum transverse speed for each graph. (a) $\omega =2\pi f = \frac{(2\pi)(5)}{t} = \frac{10\pi}{t}$ $A = 3~units$ $v_m = A~\omega = (3)(\frac{10\pi}{t}) = \frac{30\pi}{t}$ (b) $\omega =2\pi f = \frac{(2\pi)(2)}{t} = \frac{4\pi}{t}$ $A = 4~units$ $v_m = A~\omega = (4)(\frac{4\pi}{t}) = \frac{16\pi}{t}$ (c) $\omega =2\pi f = \frac{(2\pi)(2)}{t} = \frac{4\pi}{t}$ $A = 2~units$ $v_m = A~\omega = (2)(\frac{4\pi}{t}) = \frac{8\pi}{t}$ (d) $\omega =2\pi f = \frac{(2\pi)(4)}{t} = \frac{8\pi}{t}$ $A = 2~units$ $v_m = A~\omega = (2)(\frac{8\pi}{t}) = \frac{16\pi}{t}$ (e) $\omega =2\pi f = \frac{(2\pi)(4)}{t} = \frac{8\pi}{t}$ $A = 4~units$ $v_m = A~\omega = (4)(\frac{8\pi}{t}) = \frac{32\pi}{t}$ We can rank the waves in order of maximum transverse speed, from largest to smallest: $e \gt a \gt b = d \gt c$ | 2020-02-19 11:34:18 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.737707793712616, "perplexity": 219.32496710526348}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-10/segments/1581875144111.17/warc/CC-MAIN-20200219092153-20200219122153-00197.warc.gz"} |
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# Bolthausen, E (1982). The Berry-Esseen theorem for strongly mixing Harris recurrent Markov chains. Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete, 60(3):283-289.
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## Abstract
Let $\xi_0,\xi_1,\cdots$ be a stationary Harris-recurrent Markov chain with state space $(E,\scr E)$, and let $f\colon E\rightarrow{\bf R}$ and $X_i=f(\xi_i)$. It is known that the sequence $X_i$, $i\geq 0$, is strongly mixing, i.e., $\alpha(n)\rightarrow 0$, where $\alpha(n)$ are the strong (or Rosenblatt) mixing coefficients. If $\alpha(n)$ decreases at a sufficiently fast rate and $f$ is suitably chosen, then a central limit theorem holds for the partial sums $\sum_{i=0}^nX_i$. The present paper gives conditions for the convergence rates to be $O(n^{-1/2})$.
## Citations
37 citations in Web of Science®
34 citations in Scopus® | 2016-07-24 20:36:25 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7871775031089783, "perplexity": 1546.3900206604621}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-30/segments/1469257824146.3/warc/CC-MAIN-20160723071024-00063-ip-10-185-27-174.ec2.internal.warc.gz"} |
https://www.chemeurope.com/en/encyclopedia/Stirling_engine.html | My watch list
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# Stirling engine
In the family of heat engines, 'Stirling engine' defines a closed-cycle regenerative hot air engine. In this context; "hot air" may be taken to include other permanent gasses, "closed-cycle" to mean the working fluid is permanently contained within the system, and "regenerative" to refer to the use of an internal heat exchanger - the regenerator.
## Background
In the conversion of heat into mechanical work, the Stirling engine has the potential to achieve the highest efficiency of any real heat engine, theoretically up to the full Carnot efficiency, though in practice this is limited by non-ideal properties of the working gas and engine materials, such as friction, thermal conductivity, tensile strength, creep, melting point, etc. Though traditionally classified as an external combustion engine the Stirling engine can run on any heat source, including solar, chemical and nuclear. There are many possible implementations of the Stirling engine most of which fall into the category of reciprocating piston engine.
In contrast to internal combustion engines, Stirling engines have the potential to be more energy efficient, quieter, and more reliable with lower maintenance requirements. They are preferred for certain niche applications that value these unique advantages, particularly in cases where the primary objective is not to minimize the capital cost per unit power ($/kW), but rather to minimize the cost per unit energy generated by the engine ($/kWh). Compared to an internal combustion engine of a given power rating, Stirling engines currently have a higher capital cost and are usually larger and heavier; therefore, the engine technology is rarely competitive on this basis alone. For some applications, however, a proper cost-benefit analysis can favor a Stirling engine over an internal combustion engine.
In recent years, the advantages of Stirling engines have become increasingly significant, given the general rise in energy costs, energy shortages and environmental concerns such as climate change. These growing interests in Stirling technology have fostered the ongoing research and development of Stirling devices. The applications include water pumping, space-based astronautics, and electrical generation from plentiful energy sources that are incompatible with the internal combustion engine, such as solar energy, agricultural waste and domestic refuse.
Another useful characteristic of the Stirling engine is that the cycle is reversible. Which means that if supplied with mechanical power, it can function as a heat pump. Experiments have been performed using wind power driving a Stirling cycle heat pump for domestic heating and air conditioning. In the late 1930s, the Philips Corporation of the Netherlands successfully utilized the Stirling cycle in cryogenic applications.[1]
### History
Stirling's air engine (as it is referred to in early text books - see hot air engine history) was invented by Reverend Dr. Robert Stirling and patented by him in 1816. When the name became simplified to Stirling engine is not known, but may be as recently as the mid twentieth century when the Philips company began to experiment with working fluids other than air - the instruction book for their MP1002CA (see below) still refers to it as an 'air engine'. The main subject of that original patent was a heat exchanger which Stirling called the "economiser" for its enhancement of fuel economy in a variety of applications. The patent also described in detail the employment of one form of the economiser in an air engine, in which application it is now commonly known as a regenerator. An engine built by Stirling was put to work pumping water in a quarry in 1818. Subsequent development by Robert Stirling and his brother James, an engineer, resulted in patents for various improved configurations of the original engine, including pressurisation which by 1845 had sufficiently increased the power output for it to successfully drive all the machinery at a Dundee iron foundry.
As well as conserving fuel, the inventors sought to create a safer alternative to the steam engines of the time whose boilers frequently exploded with dire consequences, often including loss of life. However, the need for the Stirling engine to run at a very high temperature to maximize power and efficiency exposed limitations in the materials of the day and the few engines which were built in those early years had rather short and troublesome lives. In particular, 'hot end' failures occurred more frequently than could be tolerated, albeit with far less disastrous results than a steam boiler explosion.
Though it ultimately failed as a competitor to the steam engine in the field of industrial scale prime movers, during the latter nineteenth and early twentieth centuries smaller engines of the Stirling/hot air type (the boundary between the two is often blurred as in many the regenerator is of dubious efficiency or omitted altogether) were produced in large numbers, finding applications wherever a reliable source of low to medium power was required, most commonly perhaps for raising water. These generally operated at lower temperatures so as not to tax available materials and thus tended to be rather inefficient, their major selling point being that in contrast to a steam engine, they could be operated safely by anybody capable of managing the fire in a domestic range. As the century wore on, this role was eventually usurped by the electric motor and small internal combustion engines and by the late 1930s the Stirling engine was a largely forgotten scientific curiosity represented only by toys and a few small ventilating fans.
At this time Philips, the large Dutch electrical and electronic manufacturer, was seeking to expand the market for its radio sets into areas where mains electricity was unknown and the supply of short-lived batteries uncertain. Philips’ management decided that what was needed was a low-powered portable generator and tasked a group of engineers at the company research lab (the Nat. Lab) in Eindhoven to investigate the practicalities. Reviewing various prime movers old and new, each was rejected for one reason or another until the Stirling engine was considered. Inherently quiet and capable of running from any heat source (common lamp oil “cheap and available everywhere” was favoured), it seemed to offer real possibilities. Encouraged by their first experimental engine, which produced 16 watts of shaft power from a bore and stroke of 30x25mm, a development program was set in motion.
Remarkably, this work continued throughout World War II and by the late 1940s they had an engine – the Type 10 – which was sufficiently developed to be handed over to Philips’ subsidiary Johan de Witt in Dordrecht to be ‘productionised’ and incorporated into a generator set as originally planned. The set progressed through three prototypes (102A, B, and C), with the production version, rated at 200 watts electrical output from a bore and stroke of 55x27mm, being designated MP1002CA (affectionately known as the 'Bungalow set'). Production of an initial batch began in 1951, but it became clear that they could not be made at a price that the market would support, besides which the advent of transistor radios with their much lower power requirements meant that the whole raison d'être for the set was fast disappearing. Though the MP1002CA may have been a dead end, it represents the start of the modern age of Stirling engine development.
Philips went on to develop the Stirling engine for a wide variety of applications including vehicles, but only ever achieved any commercial success with the 'reversed Stirling engine' cryocooler. They did however take out a large number of patents and amass a wealth of information relating to Stirling engine technology, which was later licensed to other companies.
It was also employed in reverse as a heat pump to produce early refrigeration.[citation needed]
## Functional description
### The engine cycle
Since the Stirling engine is a closed cycle, it contains a fixed mass of gas called the "working fluid", most commonly air, hydrogen or helium. In normal operation, the engine is sealed and no gas enters or leaves the engine. No valves are required, unlike other types of piston engines. The Stirling engine, like most heat-engines, cycles through four main processes: cooling, compression, heating and expansion. This is accomplished by moving the gas back and forth between hot and cold heat exchangers. The hot heat exchanger is in thermal contact with an external heat source, e.g. a fuel burner, and the cold heat exchanger being in thermal contact with an external heat sink, e.g. air fins. A change in gas temperature will cause a corresponding change in gas pressure, while the motion of the piston causes the gas to be alternately expanded and compressed.
The gas follows the behavior described by the gas laws which describe how a gas's pressure, temperature and volume are related. When the gas is heated, because it is in a sealed chamber, the pressure rises and this then acts on the power piston to produce a power stroke. When the gas is cooled the pressure drops and this means that less work needs to be done by the piston to compress the gas on the return stroke, thus yielding a net power output.
When one side of the piston is open to the atmosphere, the operation is slightly different. As the sealed volume of working gas comes in contact with the hot side, it expands, doing work on both the piston and on the atmosphere. When the working gas contacts the cold side, the atmosphere does work on the gas and "compresses" it. Atmospheric pressure, which is greater than the cooled working gas, pushes on the piston.
To summarize, the Stirling engine uses the temperature difference between its hot end and cold end to establish a cycle of a fixed mass of gas expanding and contracting within the engine, thus converting thermal energy into mechanical power. The greater the temperature difference between the hot and cold sources, the greater the potential Carnot cycle efficiency.
Small demonstration engines have been built which will run on a temperature difference of as little as 7 °C, e.g. between the palm of a hand and the surrounding air, or between room temperature and melting water ice. [2] [3] [4]
### Pressurisation
Most high performance Stirling engines are pressurised, that is the mean pressure of the working fluid is above atmospheric pressure. This increases the mass of working fluid processed per cycle, thus, all other things being equal, the engine produces more power. Unfortunately all other things seldom are equal, and to realise the potential of pressurisation larger heat exhangers (including the regenerator) are required. This inevitably increases dead space and possibly gas flow resistance, both of which tend to reduce power output. Like most aspects of Stirling engine design, optimisation of this aspect is a delicate balancing act between often conflicting requirements. It was experimenting with pressurisation which initially led Philips to move from atmospheric air to other gases for the working fluid. At high temperatures and pressures, the oxygen in air tended to combine with any lubricating oil that made its way past the piston seals, giving problems with clogging the heat exchangers or even the possibility of an explosion. It was later found that some gases, particularly hydrogen and helium, offered other advantages over air.
## The Stirling cycle
For a detailed description see the Stirling cycle thermodynamics section below
The idealised or "text book" Stirling cycle is a thermodynamic cycle with two isochores (constant volume) and two isotherms (constant temperature). It is the most efficient thermodynamic cycle capable of practical implementation in an engine - its theoretical efficiency equaling that of the hypothetical Carnot cycle. However technical issues limit its efficiency when applied - for instance a simpler mechanism may be favored over attaining a close fit to the theoretical cycle.
### The regenerator
In a Stirling engine, the regenerator is an internal heat exchanger and temporary store placed between the hot and cold spaces such that the working fluid passes through it first in one direction then the other. Its function is to retain within the system that heat which would otherwise be exchanged with the environment at temperatures intermediate to the maximum and minimum cycle temperatures, thus enabling the thermal efficiency of the cycle to approach the limiting Carnot efficiency defined by those maxima and minima.
The primary effect of regeneration in a Stirling engine is to greatly increase the thermal efficiency by 'recycling' internally heat which would otherwise pass through the engine irreversibly. As a secondary effect, increased thermal efficiency promises a higher power output from a given set of hot and cold end heat exchangers (since it is these which usually limit the engine's heat throughput), though, in practice this additional power may not be fully realised as the additional dead space and pumping loss inherent in practical regenerators tends to have the opposite effect.
A regenerator is difficult to design. The ideal regenerator would be: a perfect insulator in one direction, a perfect conductor in another, have no internal volume yet infinite flow area and infinite surface area. As with the hot and cold exchangers, achieving a successful regenerator is a delicate balancing act between high heat transfer with low viscous pumping losses and low dead space. These inherent design conflicts are one of many factors which limit the efficiency of practical stirling engines. A typical embodiment might consist of a stack of fine metal wire meshes, with low porosity to reduce dead space (but watch those pumping losses!), and with the wire axes perpendicular to the gas flow to reduce conduction in that direction.
The regenerator is the key feature invented by Robert Stirling and its presence or otherwise should be used to distinguish a true Stirling engine from other closed cycle hot air engines.
Many engines which have no apparent regenerator can still with some justification be called Stirling engines as, in the simple beta and gamma configurations with a 'loose fitting' displacer, the surfaces of the displacer and its cylinder will cyclically exchange heat with the working fluid providing some regenerative effect. This is most often seen in small model and LTD types where the additional flow losses and dead space associated with a separate regenerator could actually prove counterproductive and the 'no regenerator' approach is probably near optimal.
Also see: Economiser
## Engine configurations
Engineers classify Stirling engines into three distinct types. The Alpha type engine relies on interconnecting the power pistons of multiple cylinders to move the working gas, with the cylinders held at different temperatures. The Beta and Gamma type Stirling engines use a displacer piston to move the working gas back and forth between hot and cold heat exchangers in the same cylinder.
### Alpha Stirling
• An alpha Stirling contains two separate power pistons in separate cylinders, one "hot" piston and one "cold" piston. The hot piston cylinder is situated inside the higher temperature heat exchanger and the cold piston cylinder is situated inside the low temperature heat exchanger. This type of engine has a very high power-to-volume ratio but has technical problems due to the usually high temperature of the "hot" piston and the durability of its seals. (See animation here[5])
#### Action of an alpha type Stirling engine
The following diagrams do not show a regenerator, which would be placed in the pipe connecting the two cylinders. The crankshaft has also been omitted.
### Beta Stirling
• A beta Stirling has a single power piston arranged within the same cylinder on the same shaft as a displacer piston. The displacer piston is a loose fit and does not extract any power from the expanding gas but only serves to shuttle the working gas from the hot heat exchanger to the cold heat exchanger. When the working gas is pushed to the hot end of the cylinder it expands and pushes the power piston. When it is pushed to the cold end of the cylinder it contracts and the momentum of the machine, usually enhanced by a flywheel, pushes the power piston the other way to compress the gas. Unlike the alpha type, the beta type avoids the technical problems of hot moving seals. (See animation here[6])
#### Action of a beta type Stirling engine
A beta Stirling has two pistons within the same cylinder both connected to the same crankshaft. One of these is the tightly fitted power piston and the other a loosely fitted displacement piston.
### Gamma Stirling
• A gamma Stirling is simply a beta Stirling in which the power piston is mounted in a separate cylinder alongside the displacer piston cylinder, but is still connected to the same flywheel. The gas in the two cylinders can flow freely between them but remains a single body. This configuration produces a lower compression ratio but is mechanically simpler and often used in multi-cylinder Stirling engines.
### Other types
Changes to the configuration of mechanical Stirling engines continue to interest engineers and inventors. Notably, some are in pursuit of the rotary Stirling engine; the goal here is to convert power from the Stirling cycle directly into torque, a similar goal to that which led to the design of the rotary combustion engine. No practical engine has yet been built but a number of concepts, models and patents have been produced. [7] [8]
There is also a field of "free piston" Stirling cycles engines, including those with liquid pistons and those with diaphragms as pistons.
An alternative to the mechanical Stirling engine is the fluidyne pump, which uses the Stirling cycle via a hydraulic piston. In its most basic form it contains a working gas, a liquid and two non-return valves. The work produced by the fluidyne goes into pumping the liquid.
A recent development of Stirling engines are the thermoacoustic stirling engine, which looks like the beta Stirling engines but without the displacer.
## Heat sources
Virtually any temperature difference will power a Stirling engine. The heat source may be derived from fuel combustion, hence the term "external combustion engine", although the heat source may also be solar, geothermal, nuclear or even biological. Likewise a "cold source" below the ambient temperature can be used as the temperature difference (see liquid nitrogen economy). A cold source may be the result of a cryogenic fluid or iced water. In the case where a small temperature differential is used to generate a significant amount of power, large mass flows of heating and cooling fluids must be pumped through the external heat exchangers, thus causing parasitic losses that tend to reduce the efficiency of the cycle.
Because a heat exchanger separates the working gas from the heat source, a wide range of heat sources can be used, including any fuel or waste heat from some other process. Since the combustion products do not contact the internal moving parts of the engine, a Stirling engine can run on landfill gas containing siloxanes without the accumulation of silica that damages internal combustion engines running on this fuel. The life of lubricating oil is longer than for internal-combustion engines.
The U.S. Department of Energy in Washington, NASA Glenn Research Center in Cleveland, and Infinia Corporation of Kennewick, Wash., are developing a free-piston Stirling converter for a Stirling Radioisotope Generator. This device would use a plutonium source to supply heat.
## Recent commercial development
In the late 1940s, the Philips Electronics company in The Netherlands was searching for a versatile electricity generator to enable worldwide expansion of sales of its electronic devices in areas with no reliable electricity infrastructure. The company put a huge R&D research effort into Stirling engines building on research it had started in the 1930s and which lasted until the 1970s. The only lasting commercial product for Philips was its reversed Stirling engine: the Stirling cryocooler (see below).
Los Alamos National Laboratory has developed an "Acoustic Stirling Heat Engine" [9] with no moving parts. It converts heat into intense acoustic power which (quoted from given source) "can be used directly in acoustic refrigerators or pulse-tube refrigerators to provide heat-driven refrigeration with no moving parts, or ... to generate electricity via a linear alternator or other electroacoustic power transducer".
Think Nordic, an electric car company in Norway, is working with inventor Dean Kamen on plans to install Stirling engines in the Think City, an otherwise all-electric vehicle that will be commercially available at the end of 2007, at least in Europe.
Since 1988[10], Kockums shipyards have equipped submarines with Stirling engines. They are currently used on submarines of the Gotland and Södermanland classes. These engines are run on diesel and liquid oxygen and are fitted under the name Stirling AIP for air-independent propulsion.
## Stirling cycle thermodynamics
The ideal Stirling cycle consists of four thermodynamic processes acting on the working fluid ( See diagram to right):
• Points 1 to 2, Isothermal Expansion
• Points 2 to 3, Constant-Volume (aka isometric or isochoric) heat-removal
• Points 3 to 4, Isothermal Compression
• Points 4 to 1, Constant-Volume (aka isometric or isochoric) heat-addition
This ideal Stirling cycle is commonly known as a "squared-cycle", because when graphed on a Pressure-Volume plot, the rapid transitions between the processes produce a shape with corners. In a real Stirling engine, physical design constraints limit the net force on each engine component, and thus limit the maximum acceleration (or rate-of-change of velocity). Thus a real Stirling cycle in a Stirling engine requires relatively smooth motion, which is commonly sinusoidal or quasi-sinusoidal. In this case the shape of the PV-plot is quasi-elliptical. Also in a real engine cycle, the heat transfer performance of the heat exchangers ranges from 100% effectiveness in an isothermal process, to 0% effectiveness in an adiabatic process (no heat transfer). The compression and expansion processes can be modeled as a polytropic processes [11]
$\frac{P V^n = k}{}$,
where k is constant, and n is bounded by:
$1 \le n \le \frac{c_p} {c_V} \le 2$.
where cV is the specific heat capacity at constant volume (J/kgK) and cp is the specific heat capacity at constant pressure (J/kgK)
Compared to the ideal cycle, the efficiency of a real engine is reduced by irreversibilities, friction, and the loss of short-circuit conducted heat, so that the overall efficiency is often only about half of the ideal (Carnot) efficiency. [12]
• They can run directly on any available heat source, not just one produced by combustion, so they can be employed to run on heat from solar, geothermal, biological, nuclear sources or waste heat from any industrial process.
• A continuous combustion process can be used to supply heat, so most types of emissions can be greatly reduced.
• Most types of Stirling engines have the bearing and seals on the cool side of the engine; consequently, they require less lubricant and last significantly longer between overhauls than other reciprocating engine types.
• The engine mechanisms are in some ways simpler than other types of reciprocating engine types, i.e. no valves are needed, and the fuel burner system can be relatively simple.
• A Stirling engine uses a single-phase working fluid which maintains an internal pressure close to the design pressure, and thus for a properly designed system the risk of explosion is relatively low. In comparison, a steam engine uses a two-phase gas/liquid working fluid, so a faulty relief valve can cause an over-pressure condition and a potentially dangerous explosion.
• In some cases, low operating pressure allows the use of lightweight cylinders.
• They can be built to run very quietly and without an air supply, for air-independent propulsion use in submarines or in space.
• They start easily (albeit slowly, after a warm-up period) and run more efficiently in cold weather, in contrast to the internal combustion which starts quickly in warm weather, but not in cold weather.
• A Stirling engine used for pumping water can be configured so that the pumped water cools the compression space. This is, of course, most effective when pumping cold water.
• They are extremely flexible. They can be used as CHP (combined heat and power) in the winter and as coolers in summers.
• Waste heat is relatively easily harvested (compared to waste heat from an internal combustion engine) making Stirling engines useful for dual-output heat and power systems.
### Size and Cost Issues
• Stirling engine designs require heat exchangers for heat input and for heat output, and these must contain the pressure of the working fluid, where the pressure is proportional to the engine power output. In addition, the expansion-side heat exchanger is often at very high temperature, so the materials must resist the corrosive effects of the heat source, and have low creep (deformation). Typically these material requirements substantially increase the cost of the engine. The materials and assembly costs for a high temperature heat exchanger typically accounts for 40% of the total engine cost. (Hargraves)
• All thermodynamic cycles require large temperature differentials for efficient operation; however, in an external combustion engine, the heater temperature always equals or exceeds the expansion temperature. This means that the metallurgical requirements for the heater material are very demanding. This is similar to a Gas turbine, but is in contrast to a Otto engine or Diesel engine, where the expansion temperature can far exceed the metallurgical limit of the engine materials, because the input heat-source is not conducted through the engine; so the engine materials operate closer to the average temperature of the working gas.
• Dissipation of waste heat is especially complicated because the coolant temperature is kept as low as possible to maximize thermal efficiency. This increases the size of the radiators, which can make packaging difficult. Along with materials cost, this has been one of the factors limiting the adoption of Stirling engines as automotive prime movers. However, for other applications high power density is not required, such as Ship propulsion, and stationary microgeneration systems using combined heat and power (CHP).[13]
### Power and torque issues
• Stirling engines, especially those that run on small temperature differentials, are quite large for the amount of power that they produce (i.e. they have low specific power). This is primarily due to the low heat transfer coefficient of gaseous convection which limits the heat flux that can be attained in an internal heat exchanger to about 4 - 20 W/(m*K). This makes it very challenging for the engine designer to transfer heat into and out of the working gas. Increasing the temperature differential and/or pressure allows Stirling engines to produce more power, assuming the heat exchangers are designed for the increased heat load, and can deliver the convected heat flux necessary.
• A Stirling engine cannot start instantly; it literally needs to "warm up". This is true of all external combustion engines, but the warm up time may be shorter for Stirlings than for others of this type such as steam engines. Stirling engines are best used as constant speed engines.
• Power output of a Stirling tends to be constant and to adjust it can sometimes require careful design and additional mechanisms. Typically, changes in output are achieved by varying the displacement of the engine (often through use of a swashplate crankshaft arrangement), or by changing the quantity of working fluid, or by altering the piston/displacer phase angle, or in some cases simply by altering the engine load. This property is less of a drawback in hybrid electric propulsion or "base load" utility generation where constant power output is actually desirable.
### Gas Choice Issues
• Hydrogen's low viscosity, high thermal conductivity and specific heat make it the most efficient working gas, in terms of thermodynamics and fluid dynamics, to use in a Stirling engine. However, given the high diffusion rate associated with this low molecular weight gas, hydrogen will leak through solid metal, thus it is very difficult to maintain pressure inside the engine for any length of time without replacement of the gas. Typically, auxiliary systems need to be added to maintain the proper quantity of working fluid. These systems can be a gas storage bottle or a gas generator. Hydrogen can be generated either by electrolysis of water, or by the reaction of acid on metal. Hydrogen can also cause the embrittlement of metals. Hydrogen is also a very flammable gas, while helium is inert.
• Most technically advanced Stirling engines, like those developed for United States government labs, use helium as the working gas, because it functions close to the efficiency and power density of hydrogen with fewer of the material containment issues. Helium is relatively expensive, and must be supplied by bottled gas. One test showed hydrogen to be 5% absolutely (24% relatively) more efficient than helium in the GPU-3 Stirling engine.[14]
• Some engines use air or nitrogen as the working fluid. These gases are less thermodynamically efficient but they minimize the problems of gas containment and supply. The use of Compressed air in contact with flammable materials or substances such as lubricating oil, introduces an explosion hazard, because compressed air contains a high partial pressure of oxygen. However, oxygen can be removed from air through an oxidation reaction, or bottled nitrogen can be used.
## Applications
### Combined heat and power applications
Combined heat and power (CHP) is an economical source of mechanical or electrical power, which uses a heat source in conjunction with a secondary heating application, usually a pre-existing energy use, such as an industrial process. Usually the primary heat source will enter the Stirling engine heater, since that will usually be at a higher temperature than the heating application, and the "waste" heat from the engine's heater will supply the secondary heating application. The power produced by the engine is often used to run an industrial or agricultural process, which in turn creates biomass waste refuse that can be used as free fuel for the engine, thus reducing waste removal costs. The overall process is very resourceful, thus making it efficient and cost-effective overall.
WhisperGen, a New Zealand firm with offices in Christchurch, has developed an "AC Micro Combined Heat and Power" Stirling cycle engine. These microCHP units are gas-fired central heating boilers which sell power back into the electricity grid. WhisperGen announced in 2004 that they were producing 80,000 units for the residential market in the United Kingdom. A 20 unit trial in Germany started in 2006.
### Solar power generation
Placed at the focus of a parabolic mirror a Stirling engine can convert solar energy to electricity with an efficiency better than non-concentrated photovoltaic cells, and comparable to Concentrated Photo Voltaics. On August 11 2005, Southern California Edison announced [15] an agreement to purchase solar powered Stirling engines from Stirling Energy Systems [16] over a twenty year period and in quantity (20,000 units) sufficient to generate 500 megawatts of electricity. These systems, on a 4,500 acre (19 km²) solar farm, will use mirrors to direct and concentrate sunlight onto the engines which will in turn drive generators.
### Stirling cryocoolers
Any Stirling engine will also work in reverse as a heat pump: i.e. when a motion is applied to the shaft, a temperature difference appears between the reservoirs. One of their modern uses is in refrigeration and cryogenics.
The essential mechanical components of a Stirling cryocooler are identical to a Stirling engine. The turning of the shaft will compress the working gas causing its temperature to rise. This heat will then be dissipated by pushing the gas against a heat exchanger. Heat would then flow from the gas into this heat exchanger which would probably be cooled by passing a flow of air or other fluid over its exterior. The further turning of the shaft will then expand the working gas. Since it had just been cooled the expansion will reduce its temperature even further. The now very cold gas will be pushed against the other heat exchanger and heat would flow from it into the gas. The external side of this heat exchanger would be inside a thermally insulated compartment such as a refrigerator. This cycle would be repeated once for each turn of the shaft. Heat is in effect pumped out of this compartment, through the working gas of the cryocooler and dumped into the environment. The temperature inside the compartment will drop because its insulation prevents ambient heat from coming in to replace that pumped out.
As with the Stirling engine, efficiency is improved by passing the gas through a “Regenerator” which buffers the flow of heat between the hot and cold ends of the gas chamber.
The first Stirling-cycle cryocooler was developed at Philips in the 1950s and commercialized in such places as liquid nitrogen production plants. The Philips Cryogenics business evolved until it was split off in 1990 to form the Stirling Cryogenics & Refrigeration BV [17], The Netherlands. This company is still active in the development and manufacturing of Stirling cryocoolers and cryogenic cooling systems.
A wide variety of smaller size Stirling cryocoolers are commercially available for tasks such as the cooling of sensors.
Thermoacoustic refrigeration uses a Stirling cycle in a working gas which is created by high amplitude sound waves.
### Heat pump
A Stirling heat pump is very similar to a Stirling cryocooler, the main difference being that it usually operates at room-temperature and its principal application to date is to pump heat from the outside of a building to the inside, thus cheaply heating it.
As with any other Stirling device, heat flows from the expansion space to the compression space; however, in contrast to the Stirling engine, the expansion space is at a lower temperature than the compression space, so instead of producing work, an input of mechanical work is required by the system (in order to satisfy the second law of thermodynamics). When the mechanical work for the heat-pump is provided by a second Stirling engine, then the overall system is called a "heat-driven, heat-pump".
The expansion-side of the heat-pump is thermally coupled to the heat-source, which is often the external environment. The compression side of the Stirling device is placed in the environment to be heated, for example a building, and heat is "pumped" into it. Typically there will be thermal insulation between the two sides so there will be a temperature rise inside the insulated space.
Heat-pumps are by far the most energy-efficient types of heating systems. Stirling heat-pumps also often have a higher coefficient of performance than conventional heat-pumps. To date, these systems have seen limited commercial use; however, use is expected to increase along with market demand for energy conservation, and adoption will likely be accelerated by technological refinements.
### Marine engines
Kockums [18], the Swedish shipbuilder, had built at least 8 commercially successful Stirling powered submarines during the 1980s. As of 2005 they have started to carry compressed oxygen with them (see Gotland class submarine).
### Nuclear power
There is a potential for nuclear-powered Stirling engines in electric power generation plants. Replacing the steam turbines of nuclear power plants with Stirling engines might simplify the plant, yield greater efficiency, and reduce the radioactive by-products. A number of breeder reactor designs use liquid sodium as coolant. If the heat is to be employed in a steam plant, a water/sodium heat exchanger is required, which raises some concern as sodium reacts violently with water. A Stirling engine obviates the need for water anywhere in the cycle.
United States government labs have developed a modern Stirling engine design known as the Stirling Radioisotope Generator for use in space exploration. It is designed to generate electricity for deep space probes on missions lasting decades. The engine uses a single displacer to reduce moving parts and uses high energy acoustics to transfer energy. The heat source is a dry solid nuclear fuel slug and the heat sink is space itself.
### Automotive engines
It is often claimed that the Stirling engine has too low a power/weight ratio and too long a starting time for automotive applications. There have been at least two automobiles exclusively powered by Stirling engines that were developed by NASA, as well as earlier projects by Ford and American Motor Companies.
The main difficulties involved in using the Stirling engine in an automotive application are start-up time, acceleration response, shut-down time, and weight, not all of which have ready-made solutions. Many people believe that hybrid electric drive systems can bypass all of these setbacks. In November 2007, a prototype hybrid car using solid bio-fuel and a stirling engine was announced by the Precer project in Sweden. www.precer.se (in Swedish, with an English specification sheet under the PDF link).
The NASA vehicles were designed by contractors and designated MOD I and MOD II. The MOD II replaced the normal spark-ignition engine in a 1985 4-door Chevrolet Celebrity hatchback. In the 1986 MOD II Design Report (Appendix A) the results show that the highway gas mileage was increased from 40 to 58 mpg and the urban mileage from 26 to 33 mpg with no change in gross weight of the vehicle.
Start-up time in the NASA vehicle maxed out at 30 seconds, while Ford's research vehicle used an electric heater placed directly into the hot air mix to get the vehicle started in only a few seconds.
### Aircraft engines
Stirling engines hold theoretical promise as aircraft engines. They are quieter, less polluting, gain efficiency with altitude, are more reliable due to fewer parts and the absence of an ignition system, produce much less vibration (airframes last longer) and safer, less explosive fuels may be used. (see below "Argument on why the Stirling engine can be applied in aviation" or "Why Aviation Needs the Stirling Engine" by Darryl Phillips, a 4-part series in the March 1993 to March 1994 issues of Stirling Machine World)
### Geothermal energy
Some believe that the ability of the Stirling engine to convert geothermal energy to electricity and then to hydrogen may well hold the key to replacement of fossil fuels in a future hydrogen economy. [19] This belief was also founded on research conducted at Los Alamos Labs that began as a hot dry rocks research, but later calculated the near limitless energy potential from molten rock on one side of a Stirling engine and ocean water on the other. Although currently the most feasible source of commercial electrical generation is solar, very long range predictions show advances in deep drilling and development of methods to work with molten rock could yield exponential levels of clean energy generation for thousands of years.
### Low temperature difference engines
A low temperature difference (Low Delta T, or LTD) Stirling engine will run on any low temperature differential, for example the difference between the palm of a hand and room-temperature or room temperature and an ice cube. Usually they are designed in a gamma configuration, for simplicity, and without a regenerator. They are typically unpressurized, running at near-atmospheric pressure. The power produced is less than one watt, and they are intended for demonstration purposes only. They are sold as toys and educational models.
## References
1. ^ "The Philips Stirling Engine", CM Hargreaves, Chapter 2 section 4 pp63
2. ^ Palm Top Stirling Engine Quote: "...This engine is running on PALMTOP! by using heat of Palm. Then temperature difference of it is 7K..."
3. ^ Pasco model SE-8575: The visible Stirling engine (pdf)
4. ^ Working cardboard model of a stirling engine (German website translated with translate.google.com)
5. ^ Animation: keveney.com: Two Cylinder Stirling Engine
6. ^ Animation: keveney.com: Single Cylinder Stirling Engine
7. ^ Rotary Stirling Engines This site is intended to assist and support all enthusiasts who work to advance the cause of the Stirling Cycle engine. Accessed October 2006
8. ^ Rotary piston array machine Concept from Gangolf Jobb . Accessed August 2007
9. ^ Los Alamos National Laboratory: Acoustic Stirling Heat Engine Home Quote: "...More Efficient than Other No-Moving-Parts Heat Engines..."
10. ^ Kockums' pages on Stirling engines
11. ^ David Haywood: An introduction to Stirling-cycle machines (pdf)
12. ^ Israel Urieli (Dr. Iz), Associate Professor Mechanical Engineering: Stirling Cycle Machine Analysis
13. ^ 31 October, 2003, BBC News: Power from the people Quote: "...The boiler is based on the Stirling engine, dreamed up by the Scottish inventor Robert Stirling in 1816....The technical name given to this particular use is Micro Combined Heat and Power or Micro CHP..."
14. ^ osti.gov: High-power baseline and motoring test results for the GPU-3 Stirling engine
15. ^ PureEnergySystems.com: World's largest solar installation to use Stirling engine technology
16. ^ stirlingenergy.com
17. ^ Stirling Cryogenics & Refrigeration BV
18. ^ kockums.se
19. ^ The American Stirling Company Opinion on Geothermal Energy and the Stirling engine. Accessed December 2006.
### Academic References and Non-commercial Research
• David Haywood University of Canterbury NZ "Introduction to Stirling-Cycle Analysis" (PDF)
• Stirling-Cycle Research Group, University of Canterbury NZ
• Ohio University Israel Urieli
• Stirling Engine Simple Analysis
• Alpha Stirlings,
• Beta Stirlings,
• Gamma Stirlings
• Peter Fette: Stirling Engine Researcher, mirror
• Animation,
• Regenerator efficiency and simulation
• Stirling Engine with 8 cylinders, twice double acting
• Argument on why the Stirling engine can be applied in aviation, mirror
• regarding design of a Fluidyne pump 15 pages (pdf)
• Rotary piston array machine
• Martini, William (April 1978). Stirling Engine Design Manual. NASA-CR-135382. NASA. Retrieved on 2007-06-25.
• Stirling Engine Research (English). Lund University, Sweden. Retrieved on 2007-06-25.
• Herzog, Siegfried (11/01/05). Stirling Engines (English). Assistant Professor of Mechanical Engineering. Penn State University at Mont Alto. Retrieved on 2007-08-30.
• NASA Automotive Stirling Engine MOD II Design Report
• Ford patent for decreasing the start-up time of Stirling engines US 4,057,962
• Performance Calculator
• P. H. Ceperley (1979). "A pistonless Stirling engine — The traveling wave heat engine". J. Acoust. Soc. Am. 66: 1508–1513.
• Thermomechanical generator, a Stirling Engine invented by Cooke-Yarborough
• Beale Number, used for estimating the power output of a Stirling Engine
• West Number, used for estimating the power output of a Stirling Engine
• Fluidyne, a liquid-piston Stirling engine
• Stirling Radioisotope Generator, stirling engine using a radioisotope source to produce electricy for deep space missions
• Distributed Energy Resources
## Commercial manufacturers and suppliers
• Infinia Corporation - Solar and radioisotope powered engines.
• AstroMedia - Stirling engine cardboard kit, runs on a cup of coffee.
• Stirling Danmark Aps - Stirling engines designed for CHP on renewable fuels.
• Stirling-Steele Engine - Stirling Engine plans.
• Kontax Stirling Engines - Hand-held Low Temperature differential Stirling engines.
• ShinyShack.com - Low Temperature and flame driven Stirling engines.
• Thermal Engine Corporation - Stirling-powered wood stove fan.
• American Stirling Company - Power Producing Engines
• Stirling Technology, Inc. - Energy recovery ventilator technology.
• STM Power - Combined heat and power Stirling engine-generator sets.
• QRMC - Stirling engine manufacturer.
• EADS Astrium - Stirling cooler manufacturer for space applications.
• AIM Infrared Modules - Stirling cooler manufacturer.
• Carl Aero GmbH - Maker of working model Stirling engines.
• WhisperGen - Domestic Stirling-engine central heating boilers which generate electricity.
• Sunpower - "the world's leading developer of free-piston machines."
• Stirling Energy Systems - Building a 29.4% efficient, 500 MW Stirling energy plant (expandable to 850 MW), using satellite dish compound mirrors, north of Los Angeles. Larger than all other U.S. solar power projects combined.
• exergia - Solar Stirling Engines
be-x-old:Рухавік Стырлінга | 2023-02-01 02:46:38 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 2, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4894135296344757, "perplexity": 2035.1295905577256}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764499899.9/warc/CC-MAIN-20230201013650-20230201043650-00039.warc.gz"} |
http://math.stackexchange.com/questions/46450/generating-a-regular-sequence-out-of-two | # Generating a regular sequence out of two
Here is the last problem of my final exam in "Commutative algebra" which I think, no one has solved it completely, today!
Let $R$ be a commutative Noetherian ring. Let $a_1,\dots,a_n$ and $b_1,\dots,b_n$ be two regular sequences in $R.$ Prove that there is a regular sequence $c_1,...,c_n$ s.t. for each $i$, $1 \leq i \leq n$, $$c_i \in (a_1,\dots,a_i) \cap (b_1,\dots,b_i).$$
Note: I attempted to show that $c_i=a_ib_i$ is the desired one, but it seems that we can not do anything, when $i \geq 2.$
-
Your attempt does not work for the sequences $(x,y)$ and $(y,x)$ in $k[x,y]$. – Mariano Suárez-Alvarez Jun 20 '11 at 11:46
Did you learn about the notion of depth in your class? Let $I$ be an ideal in $R$, a commutative noetherian ring. We call a regular sequence $c_1, \dots, c_k \in I$ a maximal $I$-sequence if we cannot find any $i \in I$ such that $c_1, \dots, c_k,i$ is still regular. It is a surprising fact that the length of any maximal $I$-sequence is the same. This length is called the depth of $I$.
It's not at all obvious from first principles that you can define depth, but once it's well-defined your problem becomes much easier:
We do induction: the case $n=1$ is just what you said above. Now take two regular sequences $a_1, \dots, a_n$ and $b_1, \dots, b_n$. Inductively we have that there exists $c_1, \dots, c_{n-1}$ regular such that $c_i \in (a_1, \dots, a_i) \cap (b_1, \dots ,b_i)$. To finish the proof we just need to find $c_n \in (a_1, \dots, a_n) \cap (b_1, \dots ,b_n)$ that is not a zerodivisor mod $(c_1, \dots ,c_{n-1})$. The depth of both $(b_1, \dots ,b_n)$ and $(a_1, \dots, a_n)$ are $n$. Why?
Thus $c_1, \dots, c_{n-1}$ is not a maximal $(\{a_k\})$-sequence or $(\{b_k\})$-sequence. So we can extend it and both: we can find $d \in (\{a_k\})$ and $d' \in (\{b_k\})$ neither $d$ or $d'$ are zerodivisors mod $(c_1, \dots, c_{k-1})$. Thus $dd'$ is not a zero divisor either, but is in both ideals, so it's the desired element.
Bottom line: the notion of depth is really handy. Unfortunately, I don't know a really elementary proof that it's well defined (that all maximal $I$-sequences have the same length). Most proofs use cohomology-- we define a chain complex associated to the generators of the ideal, and the depth is the first place where the complex is not exact.
-
Excellent: +1. To the OP: I highly recommend that you accept this answer – zcn Jun 27 at 17:30
I just looked in Kaplansky, and he does give an elementary proof of the well-definedness of depth. You could plug that in here, and make my answer entirely elementary, but it would just look unmotivated and harder. My philosophy on regular sequences is that its always easiest to use the Koszul complex when you can. – Phil Jun 27 at 21:44 | 2014-09-22 10:18:57 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8739438056945801, "perplexity": 177.6804042173172}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-41/segments/1410657136966.6/warc/CC-MAIN-20140914011216-00325-ip-10-234-18-248.ec2.internal.warc.gz"} |
https://math.stackexchange.com/questions/793156/how-much-zeros-has-the-number-1000-at-the-end | # How much zeros has the number $1000!$ at the end?
I know that it depends of the factors of five and two.
But the number is too long to figure how much factos of five and two there are.
Any hints?
• – lhf May 13 '14 at 13:56
• – Indrayudh Roy May 13 '14 at 13:56
There are always twos a-plenty. The exponent of prime $p$ occuring in $n!$ is well-known to be $$\lfloor n/p\rfloor +\lfloor n/p^2\rfloor + \lfloor n/p^3\rfloor +\ldots$$ hence for $n=1000$ and $p=5$ we find $$\lfloor 1000/5\rfloor +\lfloor 1000/25\rfloor + \lfloor 1000/125\rfloor +\lfloor 1000/625\rfloor + \ldots= 200+40+8+1+0+\ldots=249$$ (Just to check, for $p=2$ we get $$500+250+125+62+31+15+7+3+1\gg249$$ so really more than enough)
yes it depends on $2$ and $5$. Note that there are plenty of even numbers. Also note that $25\times 4 = 100$ which gives two zeros. Also note that there $125\times 8 = 1000$ gives three zeroes and $5^4 \times 2^4 = 10^4$. Each power of $5$ add one extra zero. So, count the multiple of $5$ and it's power less than $1000$.
the number of factor 2's between 1-1000 is more than 5's.so u must count the number of 5's that exist between 1-1000.can u continue?
If a number ends with $n$ zeros than it is divisible by $10^n$, that is $2^n5^n$.
A factorial clearly has more $2$s than $5$s in its factorization so you only need to count how many $5$s are there in the factorization of $1000!$
There are $\lfloor\frac{1000}{5}\rfloor=200$ numbers below $1000$ that can be divided by $5$, but you also have to consider that there are $\lfloor\frac{1000}{5^2}\rfloor=40$ numbers divisible by $25$, $\lfloor\frac{1000}{5^3}\rfloor=8$ and $\lfloor\frac{1000}{5^4}\rfloor=1$ number divisible by $625$, for a total of $249$ zeros.
Two questions:
Can you work out which of $2$ and $5$ will be the critical one for your question? A little thought should make this obvious.
You say that "the number is too long" - but actually the number of factors can be computed quite quickly even by hand. Can you see how many factors $521$ there might be, or factors $257$ in the product? How about factors $31$? Can you apply this to your choice of $2$ or $5$?
• This seemed to me to be a hint in response to a homework question which asked for a hint. – Mark Bennet May 13 '14 at 15:15 | 2021-03-02 08:04:05 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7526788711547852, "perplexity": 220.11516878545402}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-10/segments/1614178363782.40/warc/CC-MAIN-20210302065019-20210302095019-00222.warc.gz"} |
https://codereview.stackexchange.com/questions/215823/checking-if-a-multi-dimensional-arrays-given-property-is-empty-or-not-for-the-w | # Checking if a multi dimensional array's given property is empty or not for the whole collection
This is what I am doing and it's working:
var isEmpty = true;
for(let i = 0; i< members.length; i++)
{
var member = members[i];
if(member && member[3]){
isEmpty = false;
break;
}
}
if(isEmpty) {
var somePrefix = "123 -"
for(let i = 0; i< members.length; i++)
{
var member = members[i];
if(member && member[2]){
member[3] = somePrefix + i;
}
}
}
Can this be improved? I'm simply checking if a specific property is empty for all of the collection of multi dimensional array.
Here is what's happening:
1. Checking X property is empty for all members
2. If it is, then auto populate it
• If any of the property is filled in then leave it as is
• Can I just point out that your "style" is very hard to read/uncommon. – Vera Perrone Mar 20 at 13:09
• @VeraPerrone show me how you would improve it, without that your comment isn't of much help – Mathematics Mar 20 at 15:07
## Style
• Don't forget to close the line with semicolons where appropriate.
• Use const for variables that do not change.
• Use let for variables that are scoped to the block.
• Use for of loops when you do not need the index.
• In JS the opening block delimiter { is on the same line as the associated statement. eg for(...) { // << { on same line
• Even if its an example, always write code as functions, not as flat bits of code as in your example. The function name adds additional contextual semantic meaning and forces you to write in a style more akin to real world needs.
• Use a space between
• tokens and (, eg for (, if (foo) {.
• operators and operands, eg 1 + 2, i ++
• commas and expressions, eg a, b (not that it applies in your example)
## Typescript?
You have the question tagged typescript, yet the code is pure JS. If you wanted a typescript version you have not indicated, and personally apart from better IDE integration the additional complexity of typescript does not offer any benefit over well written JS.
## Rewrites
With all things equal the best quality source code has the shortest line count.
## Cleaning up of your code
Note that because the code is written as a function I have not needed to use an intermediate to hold the abstract "empty" state of members, removing 4 lines of code.
function populateIfMembersEmpty(members, prefix = "123 -") {
for (const member of members) {
if (member && member[3]) { return }
}
for (let i = 0; i< members.length; i++) {
if (members[i] && members[i][2]) { members[i][3] = prefix + i }
}
}
## Alternatives
function populateIfMembersEmpty(members, prefix = "123 -") {
if (! members.some(member => member && member[3])) {
members.forEach((member, i) => {
if (member && member[2]) { member[3] = prefix + i }
});
}
}
or
Does a member of members on the same line need to be named, or is a symbolic representation any less meaningful?
function populateIfMembersEmpty(members, prefix = "123 -") {
if (! members.some(m => m && m[3])) {
members.forEach((m, i) => m && m[2] && (m[3] = prefix + i));
}
}
or
function populateIfMembersEmpty(members, prefix = "123 -") {
if (members.some(m => m && m[3])) { return }
members.forEach((m, i) => m && m[2] && (m[3] = prefix + i));
}
19 lines down to 4 may sound pedantic, but apply the same to a large code base and a monster source file of 10,000 lines can be a far more manageable 2,000 reducing the odds of a bug by 80%
As the only response you have so far got that has unnecessarily emphasized a confusing point, I will say your style is neither "very" hard (or hard) to read, nor is it uncommon. (Let alone "very" uncommon, meaning... unique? no! 🙄). | 2019-07-19 22:16:51 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.17975100874900818, "perplexity": 5260.155958441515}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-30/segments/1563195526359.16/warc/CC-MAIN-20190719202605-20190719224605-00184.warc.gz"} |
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# Phase-field model of pitting corrosion kinetics in metallic materials
## Abstract
Pitting corrosion is one of the most destructive forms of corrosion that can lead to catastrophic failure of structures. This study presents a thermodynamically consistent phase field model for the quantitative prediction of the pitting corrosion kinetics in metallic materials. An order parameter is introduced to represent the local physical state of the metal within a metal-electrolyte system. The free energy of the system is described in terms of its metal ion concentration and the order parameter. Both the ion transport in the electrolyte and the electrochemical reactions at the electrolyte/metal interface are explicitly taken into consideration. The temporal evolution of ion concentration profile and the order parameter field is driven by the reduction in the total free energy of the system and is obtained by numerically solving the governing equations. A calibration study is performed to couple the kinetic interface parameter with the corrosion current density to obtain a direct relationship between overpotential and the kinetic interface parameter. The phase field model is validated against the experimental results, and several examples are presented for applications of the phase-field model to understand the corrosion behavior of closely located pits, stressed material, ceramic particles-reinforced steel, and their crystallographic orientation dependence.
## Introduction
Corrosion is the gradual destruction of materials (usually metallic materials) via chemical and/or electrochemical reaction with their environment. It costs about 3.1% of the gross domestic product (GDP) in the United States, which is much more than the cost of all natural disasters combined. Localized corrosion, such as pitting corrosion, is one of the most destructive forms of corrosion; it leads to the catastrophic failure of structures and raises both human safety and financial concerns.1,2,3 Pitting corrosion of stainless steel usually occurs in two different stages: (1) pit initiation from passive film breakage4,5,6 and (2) pit growth.2,3,7,8,9,10,11,12 In this study, we focused on the development of a phase-field modeling capability to study pit growth by considering both anodic and cathodic reactions.
In the past few decades, great efforts have been made to develop numerical models for pitting corrosion. The moving interface and the electrical double layer at the metal/electrolyte interface are the two challenging problems faced by most of these numerical models. These numerical models can be divided according to the method in which a moving interface is incorporated in their models. Several steady state9,10,13,14,15,16,17,18 and transient state19,20,21,22,23,24,25,26,27,28 models have been developed over the years that did not allow for changes in the shape and dimensions of the pits/crevices as corrosion proceeds.
Recent advances in numerical techniques, such as the finite element method, the finite volume method, the arbitrary Lagrangian–Eulerian method, the mesh-free method, and the level set method have encouraged researchers to model the evolving morphology of the pits with a moving interface. Most of these modeling efforts have used a sharp interface to represent the corroding surface, which requires the matching mesh at each time step,11,29 thus increasing the errors associated with the violation of mass conservation laws and increasing the computation cost. The finite volume method models overcome this problem by creating a matching mesh as a function of the concentration of ions, but they are still unable to model complex microstructures.12,30,31 A mesh-free method, the peridynamic model, has been implemented to model pitting corrosion, but it only considered electrochemical reactions without considering the ionic transport in the electrolyte.7
Over the past three decades, the phase field (PF) method has emerged as a powerful simulation tool for modeling of microstructure evolution. PF models study the phase transformation by defining the system’s free energy, and the system’s microstructure evolution is predicted by free energy minimization. The PF approach has been extensively applied to many materials processes, such as solidification, dendrite growth, solute diffusion and segregation, phase transformation, electrochemical deposition, dislocation dynamics, crack propagation, void formation and migration, gas bubble evolution, and electrochemical processes.32
PF models assume a diffusive interface at the phase boundaries rather than a sharp one, which makes the mathematical functions continuous at the interface. A few recent attempts have been made to use the PF method to model pitting corrosion and stress corrosion cracking without the consideration of cathodic reactions, ionic transport and in particular the dependence of overpotential on metal ion concentration in the electrolyte.33,34 In reality, the transport of ionic species in the electrolyte often plays a very important role in diffusion controlled corrosion processes, and the effects of these ionic species must be incorporated to model the process adequately. In this study, a PF method is used to model pitting corrosion by considering both anodic and cathodic reactions, transport of ionic species and the dependence of overpotential on metal ion concentration in the electrolyte.
This paper is organized as follows. Firstly, we describe the system and the electrochemical reactions considered in this work followed by the construction of PF model. The total free energy of this PF model consists of three parts: bulk free energy, gradient energy and electrostatic energy. We used the KKS model35 to construct the bulk free energy and the interfacial energy. Secondly, we developed the governing equations which comprise of mass diffusion, electromigration, and chemical reaction terms, whereas the interface conditions are incorporated by introducing an order parameter that defines the system’s physical state at each material point. Thirdly, a study is included to couple the kinetic interface parameter and the system’s total overpotential. Fourthly, the PF model is validated against the experimental results and previous numerical models. Lastly, several case studies are presented to demonstrate the strength of this proposed PF model.
## Results and discussion
### The system and electrochemical reactions considered
The system studied consists of stainless steel 304 (SS304) in dilute salt water (Fig. 1). It is assumed that new passive film will not form in this system. We will consider the effects of passive film formation in a future study. In this model, the following electrochemical reactions and kinetics are considered.
For the oxidation of main metal alloy elements in SS304,
$$Fe\,\rightarrow\,Fe^{+ 2} + 2e^-$$
$$Ni\,\rightarrow\,Ni^{ + 2} + 2e^ -$$
$$Cr\,\rightarrow\,Cr^{ + 3} + 3e^ -$$
In the following, Me is used to represent the effective metal in SS304 with an average charge number of z1. The material properties of SS304 such as molar concentration in solid phase (csolid = 143 mol/L),12 saturation concentration in the electrolyte (csat = 5.1 mol/L),12 effective diffusion coefficient (D1 = 8.5 × 10−10 m2/s),12 and the average charge number (z1 = 2.19) based on Fe, Ni, Cr, and their mole fractions within the alloy (taken from Ref. 12). The above reactions can then be simplified to
$$M_e\,\rightarrow\,M_e^{z_1} + z_1e^ -$$
(1)
The anodic dissolution of the metal is assumed to follow Butler–Volmer equation,
$$i_a = i_0\left[ {\exp \left( {\frac{{\alpha _az_1F\varphi _{s,o}}}{{R_gT}}} \right) - \exp \left( { - \frac{{\alpha _cz_1F\varphi _{s,o}}}{{R_gT}}} \right)} \right]$$
(2)
where F is the Faraday constant, Rg is the gas constant, T is the temperature, φs,o is the polarization overpotential, io is the exchange current density, αa is the anodic charge transfer coefficient, αc is the cathodic charge coefficient (αc = 1 − αa). The values of the above mentioned parameters are reported in Table 1s (supplementary material).
For the hydrogen discharge reaction in Eq. (3), the corresponding rate is given in Eq. (4)
$$H^ + + e^ - \to \frac{1}{2}H_2$$
(3)
$$J_5 = J_{50}\left[ {H^ + } \right]exp\left( {\frac{{\alpha _5F}}{{R_gT}}\varphi _{s,o}} \right)$$
(4)
For reduction of water (Eq. (5)), the corresponding rate is given in Eq. (6)
$$H_2O + e^ - \to H + OH^ -$$
(5)
$$J_6 = J_{60}exp\left( {\frac{{\alpha _6F}}{{R_gT}}\varphi _{s,o}} \right)$$
(6)
Experimental values of i0, J50, J60, αa, α5, and α6 are given in Table 1s.
In this work, the following two reactions in the electrolyte are considered
$$M_e^{z_1} + H_2O\rightleftharpoons\,M_eOH^{z_1 - 1} + H^ +$$
(7)
$$H_2O\rightleftharpoons\,OH^ - + H^ +$$
(8)
The equilibrium constants of reactions in Eqs. (7) and (8) are defined as K1 and K2, respectively.
$$K_1 = \frac{{k_{1f}}}{{k_{1b}}},\,K_2 = \frac{{k_{2f}}}{{k_{2b}}}$$
where k1f, k1b, k2f, and k2b are the forward and backward reaction rates. Therefore, a total of six ion species are considered in this model,
$$M_e^{z_1} = c_1;M_eOH^{z_2} = c_2;Cl^{z_3} = c_3;Na^{z_4} = c_4;H^{z_5} = c_5;OH^{z_6} = c_6$$
where zi (i = 1, 2, ……6) are the charge numbers of the respective species (their values are given in Table 2s), and ci (i = 1, 2, ……6) are the normalized concentrations of the respective species. The normalized concentration ci is determined by Ci = Ci/Csolid for i = 1,2,…,6, where Ci represents the molar concentration of ionic species. The constants K1 and K2 can also be expressed as a function of Ci.
$$K_1 = C_2C_5/C_1,\,K_2 = C_5C_6$$
### The phase field model for corrosion
The surface of the metal is normally covered with the passive film; however, a partial breakdown in the film can occur, which may initiate pits like the one illustrated in Fig. 1. The model consists of two phases: the solid phase Me (i.e., the metal part) and the liquid phase (i.e., the electrolyte part). The driving force for metal corrosion and microstructure evolution is from the minimization of the system’s total free energy, which usually consists of bulk free energy Eb, interface energy Ei, and long-range interaction energies such as elastic strain energy Es and electrostatic energy Ee.36,37 The system’s total energy can be expressed as
$$E = E_b + E_i + E_s + E_e$$
(9)
The inclusion of elastic and/or plastic deformation in the model is completely feasible because it has been done in other systems.38,39,40 It can be even necessary to include the strain energy term if a volumetric non-compatible passive film develops during corrosion. Because the formation of a passive film will not be considered in the first stage of this work, for simplicity, the elastic strain energy is not considered here. In a later section, the effect of applied or residual stress on pitting will be studied using the concept of overpotential rather than strain energy. Now we have,
$$E = E_b + E_i + E_e$$
(10)
$$E = {\int} {\left[ {f_b\left( {c_1,\eta } \right) + \frac{{\alpha _u}}{2}\left( {\nabla \eta } \right)^2 + z_1FC_1\varphi } \right]} dV$$
(11)
where fb(c1, η), derived in the next section, is the local bulk free energy density, which is a function of the normalized concentration of the ionic species c1 and order parameter η; the second term in Eq. (11) represents the gradient energy density that contributes to the interfacial energy, in which αu is the gradient energy coefficient, which is related to physical parameters in a later section; and the third term in Eq. (11) represents the electrostatic energy density where C1 is the molar concentration of metal ion and φ is the electrostatic potential.
### Bulk free energy density
To determine the bulk free energy density fb(c1, η), we use the model proposed by Kim et al. for binary alloys.35 We chose KKS model because the model has less limitations on the interface thickness as compared to some other models such as model presented by the model by Wheeler et al.41 The detailed derivations of all functions in the KKS model were skipped here and readers are referred to the original paper.35 In KKS model, the model parameters can be analytically determined by material properties and experimental conditions for the concerned system. In KKS model, at each point, the material is regarded as a mixture of two coexisting phases, and a local equilibrium between the two phases is always assumed:
$$c_1 = h\left( \eta \right)c_s + \left[ {1 - h\left( \eta \right)} \right]c_l$$
(12)
$$\partial f_s\left( {c_s} \right)/\partial c_s = \partial f_l\left( {c_l} \right)/\partial c_l$$
(13)
where cs and cl represent the normalized concentrations of the solid and liquid phases, respectively; h(η) is a monotonously varying function from h(0) = 0 to h(1) = 1. In this study, it is assumed that h(η) = η2(−2η + 3). In Eq. (13), the free energy densities of the solid and liquid phases are expressed as fs(cs) and fl(cl), respectively. Because the concentration is considered to be a mixture of solid and liquid phases at each point, by following the same argument, the bulk free energy density of the solid and liquid phases are expressed in a similar manner,
$$f_b(c_1,\eta ) = h\left( \eta \right)f_s(c_s) + \left[ {1 - h\left( \eta \right)} \right]f_l(c_l) + wg(\eta )$$
(14)
This is a double well potential in the energy space. The height of the double well potential is w, and g(η) = η2(1 − η)2. This expression has two minima at η = 0 and η = 1, which represent the electrolyte phase and the solid phase, respectively.
For this system, fs(cs) and fl(cl) can reasonably be considered as parabolic functions.42
$$f_s\left( {c_s} \right) = A(c_s - c_{eq,s})^2$$
(15)
$$f_l\left( {c_l} \right) = A\left( {c_l - c_{eq,l}} \right)^2$$
(16)
where ceq,s = 1 and ceq,l = Csat/Csolid are the normalized equilibrium concentrations of the solid and liquid phases, respectively. The temperature-dependent free energy density proportionality constant A is considered to be equal for both the liquid and solid phases. Its value is calculated in such a manner that the driving force for the metal corrosion in the approximated resulting system is quite close to that of the original thermodynamic system.42
The evolution of phase order parameter η and metal ion concentration c1 in time and space are assumed to obey the Ginzburg–Landau (also known as Allen–Cahn)43 and Cahn–Hilliard44 equations, respectively.
$$\frac{{\partial \eta }}{{\partial t}} = - L\frac{{\delta E}}{{\delta \eta }} = L\left[ {\nabla \alpha _u\nabla \eta + h\prime \left( \eta \right)\left\{ {f_l\left( {c_l} \right) - f_s\left( {c_s} \right) - \left( {c_l - c_s} \right)\frac{{\partial f_l\left( {c_l} \right)}}{{\partial c_l}}} \right\} - wg\prime \left( \eta \right)} \right]$$
(17)
$$\begin{array}{*{20}{l}} {\frac{{\partial {\mathrm{c}}_1}}{{\partial {\mathrm{t}}}}} \hfill & = \hfill & {\nabla M\nabla \frac{{\delta E}}{{\delta c_1}} + R_1} \hfill \cr {} \hfill & = \hfill & {\nabla \left[ {D_1\left( \eta \right)\nabla c_1} \right] + \nabla \left[ {D_1\left( \eta \right)h\prime \left( \eta \right)\left( {c_l - c_s} \right)\nabla \eta } \right]} \hfill \cr {} \hfill & {} \hfill & {+ \nabla \left[ {\frac{{z_1Fc_1D_1\left( \eta \right)}}{{R_gT}}\nabla \varphi } \right]y_1\left( \eta \right) + R_1} \hfill \end{array}$$
(18)
where L is the kinetic parameter that represents the solid–liquid interface mobility, and M is the mobility of metal ions and expressed as $$M = D_1(\eta )/(\partial ^2f_b/\partial c_1^2)$$. In Eq. (18), R1 is the source and/or sink term for metal ions due to reaction (Eq. (7)), and it takes the form of (−k1fc1 + k1bc2c5)y1(u). The function y1) defined below is to ensure that reaction (Eq. (7)) occurs only in the electrolyte phase.
$${\mathrm{y}}_1\left( \eta \right) = \left\{ {\begin{array}{*{20}{l}} {1;} \hfill & {\eta \le 0} \hfill \cr {} \hfill & {0 < \eta < 0.1} \hfill \cr {0;} \hfill & {\eta \ge 0.1} \hfill \end{array}} \right.\left( {{\mathrm{linearly}}\,{\mathrm{change}}\,{\mathrm{from}}1\,{\mathrm{to}}\,0} \right)$$
(19)
### Conservation of charge
In this study, we follow Dassault’s work rather than following Guyer’s model45,46 which simplifies the model by removing the need to discretize the double layer at the metal–electrolyte interface. It allows our PF model to simulate the corrosion process from meso- to macro-length scales, as compared to Guyer’s model, which was limited to nanoscale. It is also possible to incorporate the effect of the laminar/turbulent flow of the electrolyte on the metal–electrolyte interface in case of moving electrolyte.47 Here, the conservation of charge can be expressed as
$$\frac{{\partial \rho _e}}{{\partial t}} = \nabla \left\{ {\sigma _e\left[ {1 - y_1\left( \eta \right)} \right]\nabla \varphi } \right\} + y_1\left( \eta \right)FC_{solid}{\sum} {z_i} \frac{{\partial c_i}}{{\partial t}}$$
(20)
where ρe is the charge density and σe is the electrical conductivity of the metal in the solid phase. The function [1 − y1(η)] interpolates the electrical conductivity, σe in the solid phase to zero in the electrolyte phase, where y1(η) is defined in Eq. (19). The time needed for charge accumulation across the interface due to the diffusion of ionic species is much longer than that required to achieve steady-state charge accumulation across the interface, so the conservation of charge in the above system can be considered at a steady state. The relation given in Eq. (20) is reduced to
$$0 = \nabla \left\{ {\sigma _e\left[ {1 - y_1\left( \eta \right)} \right]\nabla \varphi } \right\} + y_1(\eta )FC_{solid}{\sum} {z_i} \frac{{\partial c_i}}{{\partial t}}$$
(21)
The height of the double well potential w and the gradient energy coefficient αu can be related to the interface energy ϱ and the interface thickness l33
$${\it{\varrho }} = 4\sqrt {w\alpha _u}$$
(22)
$$l = \sqrt 2 \alpha \prime \sqrt {\frac{{\alpha _u}}{w}}$$
(23)
where α′ is a constant value determined by the order parameter u. If the interface region is defined as 0.05 < η < 0.95; the value of α′ is 2.94.35
### Transport equations for other ionic species in the electrolyte
The governing equations of the other five ionic species are the Nernst–Planck equations with chemical reaction terms. They are expressed as
$$\frac{{\partial {\mathrm{c}}_2\left( {{\boldsymbol{x}},t} \right)}}{{\partial {\mathrm{t}}}} = \nabla \left[ {D_2\left( \eta \right)\nabla c_2} \right] + \nabla \left[ {\frac{{z_2Fc_2D_2\left( \eta \right)}}{{R_gT}}\nabla \varphi } \right]y_1\left( \eta \right) + R_2$$
(24)
$$\frac{{\partial {\mathrm{c}}_3\left( {{\boldsymbol{x}},t} \right)}}{{\partial {\mathrm{t}}}} = \nabla \left[ {D_3\left( \eta \right)\nabla c_3} \right] + \nabla \left[ {\frac{{z_3Fc_3D_3\left( \eta \right)}}{{R_gT}}\nabla \varphi } \right]y_1\left( \eta \right)$$
(25)
$$\frac{{\partial {\mathrm{c}}_4\left( {{\boldsymbol{x}},t} \right)}}{{\partial {\mathrm{t}}}} = \nabla \left[ {D_4\left( \eta \right)\nabla c_4} \right] + \nabla \left[ {\frac{{z_4Fc_4D_4\left( \eta \right)}}{{R_gT}}\nabla \varphi } \right]y_1\left( \eta \right)$$
(26)
$$\frac{{\partial {\mathrm{c}}_5\left( {{\boldsymbol{x}},t} \right)}}{{\partial {\mathrm{t}}}} = \nabla \left[ {D_5\left( \eta \right)\nabla c_5} \right] + \nabla \left[ {\frac{{z_5Fc_5D_5\left( \eta \right)}}{{R_gT}}\nabla \varphi } \right]y_1\left( \eta \right) + R_5$$
(27)
$$\frac{{\partial {\mathrm{c}}_6\left( {{\boldsymbol{x}},t} \right)}}{{\partial {\mathrm{t}}}} = \nabla \left[ {D_6\left( \eta \right)\nabla c_6} \right] + \nabla \left[ {\frac{{z_6Fc_6D_6\left( \eta \right)}}{{R_gT}}\nabla \varphi } \right]y_1\left( \eta \right) + R_6$$
(28)
where R2 is the source/sink term originated from the electrochemical reaction in Eq. (7) which takes the form as [k1fc1 − k1bc2c5]y1(η). The rates of forward and backward reaction are expressed by k1f and k1b respectively. It is assumed that no electrochemical reaction occurs inside the metal part. This is ensured by y1(η) defined in Eq. (19). R5 and R6 are the source/sink terms originated from electrochemical reactions in Eqs. (7) and (8) and take the form as $$\left[ {k_{1f}c_1 - k_{1b}c_2c_5 + k_{2f} - k_{2b}c_5c_6} \right]y_1\left( \eta \right) - \left( {\frac{{J_5}}{{z_5FC_{solid}}}} \right)y_2\left( \eta \right)$$ and $$\left[ {k_{2f} - k_{2b}c_5c_6} \right]y_1\left( \eta \right) - \left( {\frac{{J_6}}{{z_6FC_{solid}}}} \right)y_2\left( \eta \right)$$ respectively. The rates of forward and backward reactions for the hydrolysis of water are represented by k2f and k2b, respectively. It should be noted that R5 and R6 have an additional term near the metal–electrolyte interface due to the cathodic reactions considered in Eqs. (3) and (5) where J5 and J6 are defined in Eqs. (4) and (6) respectively. These reaction terms are multiplied by a step function y2(η) to ensure that these reactions only happen in a small region near the metal surface.
$${\mathrm{y}}_2\left( \eta \right) = \left\{ {\begin{array}{*{20}{l}} {1;} \hfill & {0.01 \le \eta < 0.05} \hfill \cr {0;} \hfill & {\eta \ge 0.05} \hfill \cr {0;} \hfill & {\eta < 0.01} \hfill \end{array}} \right.$$
(29)
It should also be noted that, in Eqs. (25) and (26) there are no source/sink terms because it was assumed that c3 (Cl) and c4 (Na+) does not take part in any reactions. This is not true if a salt film can be formed. The effect of salt film formation will be studied in a future study.
The electrostatic potential, φ, is governed by Eq. (21) coupled with the governing Eqs. (18) and (2428). The diffusivity Di is a function of the order parameter η. As it is known, the diffusivity of ionic species differs in the metal and electrolyte phase. The diffusivities of all the ions were defined using a step function of the order parameter η. For metal ion c1, a step function as expressed in Eq. (30) is used in which the diffusivity value in metal is assumed to be γ times less than that in electrolyte. A step function as expressed in Eq. (31) is used for all other ionic species (c2, c3, c4, c5, and c6).
$${\mathrm{D}}_1\left( \eta \right) = \left\{ {\begin{array}{*{20}{l}} {D_1;} \hfill & {\eta < 0.90} \hfill \cr {} \hfill & {0.90 \le \eta \le 0.95} \hfill \cr {D_1/\gamma ;} \hfill & {\eta > 0.95} \hfill \end{array}} \right.\,\left( {{\mathrm{linearly}}\,{\mathrm{change}}\,{\mathrm{from}}\,D_1{\mathrm{to}}\,D_1/\gamma } \right)$$
(30)
$${\mathrm{D}}_{\mathrm{i}}\left( {\mathrm{\eta}} \right) = \left\{ {\begin{array}{*{20}{l}} {{\mathrm{D}}_{\mathrm{i}};} \hfill & {\eta < 0.90} \hfill \cr {} \hfill & {0.90 \le \eta \le 0.95} \hfill \cr {0;} \hfill & {\eta > 0.95} \hfill \end{array}} \right.\,\left( {{\mathrm{linearly}}\,{\mathrm{change}}\,{\mathrm{from}}\,D_i\,{\mathrm{to}}\,0} \right)$$
(31)
for i = 2,3,….,6.
### Overpotential
The overpotential is expressed as
$$\varphi _{s,o} = \varphi _m - \varphi _{m,se} - \varphi _c - \varphi _l$$
(32)
where φm is the potential in the metal phase also known as applied potential; φm,se is the standard electrode potential in the metal; and φc is the concentration overpotential expressed in (33).
$$\varphi _c = \frac{{R_gT}}{{Fz_1}}\ln\frac{{c_{1b}}}{{c_{eq,l}}}$$
(33)
The concentration of $$M_e^{z_1}$$ near the interface is,
$$c_{1b} = \left\{ {\begin{array}{*{20}{l}} {c_1;} \hfill & {\left( {\eta = 0.05} \right)} \hfill \cr {0;} \hfill & {\left( {\eta < 0.05} \right)} \hfill \cr {0;} \hfill & {\left( {\eta > 0.05} \right)} \hfill \end{array}} \right.$$
(34)
The electrostatic potential near the interface is,
$$\varphi _l = \left\{ {\begin{array}{*{20}{l}} {\varphi ;} \hfill & {\left( {\eta = 0.05} \right)} \hfill \cr {0;} \hfill & {\left( {\eta < 0.05} \right)} \hfill \cr {0;} \hfill & {\left( {\eta > 0.05} \right)} \hfill \end{array}} \right.$$
(35)
### Kinetic interface parameter and overpotential relation
In this model, the metal corrosion is described by the order parameter η. The corrosion rate is controlled by the kinetic interface parameter L. The shift in the corrosion mode from activation-controlled to diffusion-controlled can be modeled by continuous variation of the kinetic interface parameter L. The relationship between the kinetic interface parameter L and the corrosion rate is linear in the activation-controlled mode.33 From the Butler–Volmer equation, as expressed in (2), the kinetic interface parameter has an effect on overpotential similar to that of the current density, as expressed below in (36). A similar technique is also implemented in a peridynamic model, in which the interface diffusivity is directly related to the current density for Tafel relation.7
$$L = L_o\left[ {\exp \left( {\frac{{\alpha _az_1F\varphi _{s,o}}}{{R_gT}}} \right) - \exp \left( { - \frac{{\alpha _cz_1F\varphi _{s,o}}}{{R_gT}}} \right)} \right]$$
(36)
Following the method developed in Refs 7 and33 and using the experimental values for SS304 (reported in Table 1s), i0 = 1.0 × 10−6A/cm2 and αa = 0.26, we calculated L0 = 1.94 × 10−13 m3/(Js).
## 1D PF model
We implemented the PF model to simulate the corrosion evolution in 1D. The simulations are executed at T = 293.15 K (20 °C) with metal potential of 844 mV SHE (standard hydrogen electrode) (i.e., 600 mV SCE [saturated calomel electrode]) in a 1 M NaCl solution. The temperature dependence of the diffusion coefficient is governed by the Einstein relation.12 The PF simulation results for the corrosion length are then compared with the 1D pencil electrode of experimental findings.3 The simulations are performed for 400 s, and the results of the corroded length are plotted against the square root of time $$\left( {\sqrt t } \right)$$. The simulation results agree well with the experimental results, as illustrated in Fig. 2. The 1D PF model and the 1D pencil electrode experimental results show similar slopes.
A qualitative study on the concentration distribution of ionic species inside the electrolyte is performed as done in many classical numerical models for crevice and pitting corrosion.9,10,48 It is difficult to quantitatively measure the molar concentration distribution of ionic species in the electrolyte experimentally. Because such experimental data is lacking, we have discussed these concentration variations theoretically. Figure 1s (supplementary material) shows the concentration in mol/L on a logarithmic scale. The higher value of metal ions near the interface results in a slight increase in the [H+] ion concentration (i.e., a decrease in the pH value) due to strong coupling between C1, C2, and C5. The value of [H+] increases as the overpotential increases because it results in a higher production rate of metal ions and hydrolysis of metal ions. Although, this study was performed on a lower overpotential, but a small increase in C5 can still be seen in Fig. 1s (supplementary material). This increase in positive charge is neutralized by the migration of chloride ions towards the interface, as shown in Fig. 1s (supplementary material).
To investigate the effects of metal potential, several simulations were performed to show the behavior of corrosion under different metal potentials. Figure 2s (supplementary material) shows that the corrosion rate obtained for these metal potentials are of the same order of the magnitude as the experimental results.49 The experimental results plotted in Fig. 2s (supplementary material) give the maximum corrosion rates that can be achieved at the corresponding metal potential. A calibration study was also performed to achieve a corrosion rate for PF 1D model simulation close to experimental ones by varying exchange current density (i0). It was found that if the value of i0 is chosen equal to twice the reported value (i0 = 1 × 10−6 A/cm2) in Table 1s (supplementary material), then the corrosion rate agree well with the experimental values.49 For the sake of consistency, all the presented modeling results are simulated by using the same of value of i0 as reported in Table 1s (supplementary material). The overpotential for the corresponding corrosion rates are shown in Fig. 3s (supplementary material).
### PF simulations for 2D model
The 2D simulations are performed with a metal potential of 600 mV SCE (844 mV SHE). The boundary conditions and initial values are the same as described in Fig. 7s (supplementary material). To compare the 2D PF model results with the experimental ones, a 300 μm by 240 μm rectangular geometry is considered in which the metal and electrolyte parts are equally divided, as shown in Fig. 4s (supplementary material). A 60 μm wide and 20 μm deep semi-elliptical pit is assumed. The remaining surface, as shown in Fig. 4s, is considered to have a passive oxide film. Figure 4s (supplementary material) shows the concentration distribution inside the electrolyte at various time intervals. In Fig. 3, the 2D PF model results are compared with the 2D foil experiment results reported in the literature.3 The evolution of pitting depth over the time shows a trend similar to that found in the experimental results3 but with deeper pitting depths than the experimantal data. As mentioned earlier, the regrowth of passive film may be an important factor. We will include the formation of passive film in a future study. The contours of the electrostatic potential distribution for the simulations with the above conditions are shown in Fig. 5s (supplementary material).
### Case studies
#### Case study 1: Interaction of closely located pits
In reality, multiple pits can nucleate due to changes in chemistry on the metal surface, whereas most numerical models consider only the nucleation or growth of a single pit. A few efforts have been made to understand both experimentally and numerically the interaction of multiple pits.50,51 Because we have not considered pit initiation in our PF model, we apply our PF model to two narrow initial openings of 5 μm each at distances of (a) 12 μm and (b) 5 μm at an applied metal potential of 200 mV SHE. The boundary conditions and initial values are the same as those given in Fig. 7s (supplementary material). Figure 4 shows the changes in the morphology of pits with and without interaction in (b) and (a), respectively. It can be seen that without their interaction, these pits corrode at a rate similar to that at which they grow individually. After the pits interact, the chemical compositions of the ionic species change in the vicinities of the pits in the electrolyte. The interaction between the two pits can have either a positive or negative effect on pit growth.52 In this study the interaction of the two closely located pits had a positive effect which can be seen in Fig. 4 (b) at t = 6 s. The corroded material in both cases was estimated which suggested that the corrosion rate was increased in case (b). Two pits finally coalesce to form a wider pit, similar to the pits formed in real-life metallic structures (i.e., multiple pits nucleate on the corroding surface and interact with each other), which are wider.
#### Case study 2: Pitting corrosion in a stressed material
Like other alloys, stainless steel can have stressed zones (tensile and compressive). It is believed that overpotential is not uniform in the case of stressed zones, which results in different corrosion rates in different material locations and directions. The experimental findings53 show that most pits grow in locations near the scratched lines on the surface that result from mechanical polishing. These scratched lines could result in strain hardening, as revealed by electrochemical analysis.53 The experimental findings also illustrate that overpotential is not uniform in the presence of residual stresses. Gutman explained the same phenomenon with his theoretical model in which the compressive stress zone has less overpotential than the unstressed zone and the tensile stress zone.54 The overpotential is directly related to the corrosion current density. The relationship between the overpotential of the compressive stress zone (φcomp,s), the unstressed zone (φs,o), and the tensile stress zone (φtens,s) is φcomp,s < φs,o < φtens,s. It should be noted that corrosion rate in plastically deformed zones is greater than that of elastically deformed zones, due to the presence of high density dislocations in plastically deformed zones. In this study, we applied the overpotential dependence on applied/residual stress proposed by Gutman.54 According to Gutman’s model,54 residual stress of 600MPa corresponds to a change in overpotential of about 20mV in our system. Here, we model a material with both tensile and compressive stress zones, which have an overpotential difference of φcomp,s = φs,o − 20 mV and φtens,s = φs,o + 20 mV, whereas φs,o is calculated from (32). A small opening of 6 μm is considered at the material’s surface. The boundary conditions and initial values are the same as those given in Fig. 7s (supplementary material). Figure 5 shows that areas under tensile stress corrode at a faster rate than areas in the compressive stress zone. The pit morphology is closer to that of pits formed during a natural corrosion process because, in most natural scenarios, the corrosion process begins when the passive film is damaged by strain hardening of the surface. In fact, in most of these cases, multiple pits coalesce and grow faster along width than depth. This process is already illustrated in the previous case in which two closely located pits interact.
#### Case Study 3: Crystallographic plane-dependent pitting corrosion
Several studies suggested that crystallographic orientations greatly affect the propagation rates and morphology of the corroding pits.55,56,57 This dependence is usually attributed to factors such as close packing of crystal planes, reaction rate variation along different plane orientations and density of crystalline defects on micro scale. Here, we demonstrate that this PF model can be a good tool to study this phenomenon in detail. The crystal orientations affect the rate of corrosion because planes with lower atomic densities usually corrode at faster rates than planes with higher atomic densities.57 It has been reported that the corrosion rate tends to increase in the order of {111} < {110} ≤ {100}. The corrosion rate in the crystallographic plane {111} is one third of {100}.57 The scenario in which planes {110} and {100} corrode at the same rate is considered because no exact value is available for their ratio. We implemented our PF model to study the effects of the crystallographic plane orientation on pit growth. The domain geometry considered is 30 μm × 27 μm, as shown in Fig. 6. The PF simulations are performed at a lower metal potential of −400 mV SHE because it is believed that the crystallographic orientation dependence is limited to lower overpotentials when the corrosion process is activation controlled.33,58 A small opening of 6 μm is considered at the surface of the material. The initial values and boundary conditions are the same as described in Fig. 7s (supplementary material). Crystallographic planes {111}, {110}, and {100} are represented by blue, brown, and magenta, respectively, in Fig. 6, which shows that the pit shape is no longer uniform because {111} corrodes at one third the rate of the other two planes. This pit morphology illustrates the strength of our PF model under complex microstructures, with which most sharp interface models fail to cope.
#### Case Study 4: Pitting corrosion in ceramic particle–reinforced steel
Ceramic particles such as TiB2 and/or TiC are often embedded into steel to improve its stiffness, strength,59 and wear resistance.60 Although the addition of these ceramic particles improves some of the material’s mechanical properties, it has very little effect on corrosion resistance.61 In fact, these reinforcements may enhance stress corrosion cracking (SCC) because they can change the stress distribution near the pits. In case of SCC, a higher stress concentration can be resulted at the tip of a growing pit when the pit reaches a ceramic particle. Metal corrodes faster at the high tensile stress region in the vicinity of a ceramic particle. As we are not studying SCC in this study, the effect of stress concentration will not be considered here. Because the ceramic particles are far less reactive than steel, we assume that they are non-corrodible in salt solution. To ensure that the ceramic particles do not corrode in the salt solution, we considered L to be equal to zero for the ceramic particles. A small opening of 6 μm is assumed at the surface of the material. The boundary conditions and initial values are the same as those described in Fig. 7s (supplementary material). Figure 7 shows that the pit morphology changes with the presence of ceramic materials. This example elaborates the ability of this PF model to handle complex structures.
In this study, we have developed a PF model for metal corrosion with ion transport in the electrolyte and this model is used to study pitting corrosion of SS304 in salt water. It is shown that once the kinetic interface parameter is calibrated with the material’s exchange current density, the model has the potential to predict corrosion behavior over the whole range of reaction and diffusion-controlled processes. The simulation results showed that the PF model predictions agree well with the experimental results and that the model has the ability to handle complex microstructures, such as the interaction of closely located pits, the effects of stress on pitting, the effects of ceramic particles, and crystallographic plane orientation on corrosion.
## Method
Finite element method, Galerkin method,62 is used for space discretization while Backwards differentiation formula (BDF) method63 is used for the time integration of the governing partial differential Eqs (17, 18, 21, 2428). Triangular Lagrangian mesh elements were chosen to discretize the space. It was ensured that we have at least 12 mesh elements inside the diffuse interface to accurately approximate η (order parameter) and the piecewise functions based on η.
### Data availability
The data and codes supporting the findings of this study are available from the corresponding author on reasonable request.
## References
1. 1.
Sharland, S. M. A review of the theoretical modelling of crevice and pitting corrosion. Corros. Sci. 27, 289–323 (1987).
2. 2.
Ernst, P. & Newman, R. C. Pit growth studies in stainless steel foils. I. Introduction and pit growth kinetics. Corros. Sci. 44, 927–941 (2002).
3. 3.
Ernst, P. & Newman, R. C. Pit growth studies in stainless steel foils. II. Eff. Temp. Chloride Conc. Sulphate Addit. Corros. Sci. 44, 943–954 (2002).
4. 4.
Williams, D. E., Westcott, C. & Fleischmann, M. Studies of the initiation of pitting corrosion on stainless steels. J. Electroanal. Chem. Interfacial Electrochem. 180, 549–564 (1984).
5. 5.
Engelhardt, G. & Macdonald, D. D. Unification of the deterministic and statistical approaches for predicting localized corrosion damage. I. Theoretical foundation. Corros. Sci. 46, 2755–2780 (2004).
6. 6.
Laycock, N. J., Noh, J. S., White, S. P. & Krouse, D. P. Computer simulation of pitting potential measurements. Corros. Sci. 47, 3140–3177 (2005).
7. 7.
Chen, Z. & Bobaru, F. Peridynamic modeling of pitting corrosion damage. J. Mech. Phys. Solids 78, 352–381 (2015).
8. 8.
Duddu, R. Numerical modeling of corrosion pit propagation using the combined extended finite element and level set method. Computational Mechanics 54, 613-627 (2014).
9. 9.
Sharland, S. M. & Tasker, P. W. A mathematical model of crevice and pitting corrosion – I. The physical model. Corros. Sci. 28, 603–620 (1988).
10. 10.
Sharland, S. M. A mathematical model of crevice and pitting corrosion – II. The physical model. Corros. Sci. 28, 621–630 (1988).
11. 11.
Sarkar, S., Warner, J. E. & Aquino, W. A numerical framework for the modeling of corrosive dissolution. Corros. Sci. 65, 502–511 (2012).
12. 12.
Scheiner, S. & Hellmich, C. Stable pitting corrosion of stainless steel as diffusion-controlled dissolution process with a sharp moving electrode boundary. Corros. Sci. 49, 319–346 (2007).
13. 13.
Abodi, L. C. et al. Modeling localized aluminum alloy corrosion in chloride solutions under non-equilibrium conditions: steps toward understanding pitting initiation. Electrochim. Acta 63, 169–178 (2012).
14. 14.
Galvele, J. Transport processes in passivity breakdown—II. Full hydrolysis of the metal ions. Corros. Sci. 21, 551–579 (1981).
15. 15.
Galvele, J. R. Transport processes and the mechanism of pitting of metals. J. Electrochem. Soc. 123, 464-474 (1976).
16. 16.
Krawiec, H., Vignal, V. & Akid, R. Numerical modelling of the electrochemical behaviour of 316L stainless steel based upon static and dynamic experimental microcapillary-based techniques. Electrochim. Acta 53, 5252–5259 (2008).
17. 17.
Turnbull, A. & Thomas, J. A model of crack electrochemistry for steels in the active state based on mass transport by diffusion and ion migration. J. Electrochem. Soc. 129, 1412–1422 (1982).
18. 18.
Walton, J. C. Mathematical modeling of mass transport and chemical reaction in crevice and pitting corrosion. Corros. Sci. 30, 915–928 (1990).
19. 19.
Oldfield, J. W. & Sutton, W. H. Crevice corrosion of stainless steels: II. Experimental studies. Br. Corros. J. 13, 104–111 (1978).
20. 20.
Oldfield, J. W. & Sutton, W. H. Crevice corrosion of stainless steels: I. A mathematical model. Br. Corros. J. 13, 13–22 (1978).
21. 21.
Hebert, K. & Alkire, R. Dissolved metal species mechanism for initiation of crevice corrosion of aluminum: I. Experimental investigations in chloride solutions. J. Electrochem. Soc. 130, 1001–1007 (1983).
22. 22.
Watson, M. K. & Postlethwaite, J. Numerical simulation of crevice corrosion: the effect of the crevice gap profile. Corros. Sci. 32, 1253–1262 (1991).
23. 23.
Sharland, S. M. A mathematical model of the initiation of crevice corrosion in metals. Corros. Sci. 33, 183–201 (1992).
24. 24.
Friedly, J. C. & Rubin, J. Solute transport with multiple equilibrium-controlled or kinetically controlled chemical reactions. Water Resour. Res. 28, 1935–1953 (1992).
25. 25.
White, S. P., Weir, G. J. & Laycock, N. J. Calculating chemical concentrations during the initiation of crevice corrosion. Corros. Sci. 42, 605–629 (2000).
26. 26.
Webb, E. G. & Alkire, R. C. Pit initiation at single sulfide inclusions in stainless steel: III. Mathematical model. J. Electrochem. Soc. 149 (2002).
27. 27.
Gavrilov, S., Vankeerberghen, M., Nelissen, G. & Deconinck, J. Finite element calculation of crack propagation in type 304 stainless steel in diluted sulphuric acid solutions. Corros. Sci. 49, 980–999 (2007).
28. 28.
Venkatraman, M. S., Cole, I. S. & Emmanuel, B. Corrosion under a porous layer: a porous electrode model and its implications for self-repair. Electrochim. Acta 56, 8192–8203 (2011).
29. 29.
Xiao, J. & Chaudhuri, S. Predictive modeling of localized corrosion: an application to aluminum alloys. Electrochim. Acta 56, 5630–5641 (2011).
30. 30.
Scheiner, S. & Hellmich, C. Finite volume model for diffusion- and activation-controlled pitting corrosion of stainless steel. Comput. Methods Appl. Mech. Eng. 198, 2898–2910 (2009).
31. 31.
Onishi, Y., Takiyasu, J., Amaya, K., Yakuwa, H. & Hayabusa, K. Numerical method for time-dependent localized corrosion analysis with moving boundaries by combining the finite volume method and voxel method. Corros. Sci. 63, 210–224 (2012).
32. 32.
Li, Y., Hu, S., Sun, X. & Stan, M. A review: applications of the phase field method in predicting microstructure and property evolution of irradiated nuclear materials. npj Comput. Mater. 3, 16 (2017).
33. 33.
Mai, W., Soghrati, S. & Buchheit, R. G. A phase field model for simulating the pitting corrosion. Corros. Sci. 110, 157–166 (2016).
34. 34.
Mai, W. & Soghrati, S. A phase field model for simulating the stress corrosion cracking initiated from pits. Corros. Sci. 125, 87–98 (2017).
35. 35.
Kim, S. G., Kim, W. T. & Suzuki, T. Phase-field model for binary alloys. Phys. Rev. E 60, 7186–7197 (1999).
36. 36.
Chen, L. Q. Phase-field models for microstructure evolution. Annu. Rev. Mater. Res. 32, 113–140 (2002).
37. 37.
Moelans, N., Blanpain, B. & Wollants, P. An introduction to phase-field modeling of microstructure evolution. Calphad 32, 268–294 (2008).
38. 38.
Guo, X. H., Shi, S.-Q. & Ma, X. Q. Elastoplastic phase field model for microstructure evolution. Appl. Phys. Lett. 87, 221910 (2005).
39. 39.
Guo, X. H., Shi, S. Q., Zhang, Q. M. & Ma, X. Q. An elastoplastic phase-field model for the evolution of hydride precipitation in zirconium. Part I: smooth specimen. J. Nucl. Mater. 378, 110–119 (2008).
40. 40.
Guo, X. H., Shi, S. Q., Zhang, Q. M. & Ma, X. Q. An elastoplastic phase-field model for the evolution of hydride precipitation in zirconium. Part II: specimen with flaws. J. Nucl. Mater. 378, 120–125 (2008).
41. 41.
Wheeler, A. A., Boettinger, W. J. & McFadden, G. B. Phase-field model for isothermal phase transitions in binary alloys. Phys. Rev. A 45, 7424–7439 (1992).
42. 42.
Hu, S. Y., Murray, J., Weiland, H., Liu, Z. K. & Chen, L. Q. Thermodynamic description and growth kinetics of stoichiometric precipitates in the phase-field approach. Calphad 31, 303–312 (2007).
43. 43.
Ginzburg, V. L. On the theory of superconductivity. Il Nuovo Cim. (1955–1965) 2, 1234–1250 (1955).
44. 44.
Cahn, J. W. & Hilliard, J. E. Free energy of a nonuniform system. I. Interfacial free energy. J. Chem. Phys. 28, 258–267 (1958).
45. 45.
Pongsaksawad, W., Powell, A. C. & Dussault, D. Phase-field modeling of transport-limited electrolysis in solid and liquid states. J. Electrochem. Soc. 154, F122–F133 (2007).
46. 46.
Guyer, J. E., Boettinger, W. J., Warren, J. A. & McFadden, G. B. Phase field modeling of electrochemistry. II. Kinet. Phys. Rev. E 69, 021604 (2004).
47. 47.
Leblanc, P., Cabaleiro, J., Paillat, T. & Touchard, G. Impact of the laminar flow on the electrical double layer development. J. Electrost. 88, 76–80 (2017).
48. 48.
Turnbull, A. & Ferriss, D. Mathematical modelling of the electrochemistry in corrosion fatigue cracks in structural steel cathodically protected in sea water. Corros. Sci. 26, 601–628 (1986).
49. 49.
Revie, R. W. & Uhlig, H. H. Uhlig's Corrosion Handbook, 3rd edn (Wiley, Hoboken, New Jersey, 2011).
50. 50.
Budiansky, N. D., Organ, L., Hudson, J. L. & Scully, J. R. Detection of interactions among localized pitting sites on stainless steel using spatial statistics. J. Electrochem. Soc. 152, B152–B160 (2005).
51. 51.
Laycock, N., White, S. & Krouse, D. Numerical simulation of pittingcorrosion: interactions between pits in potentiostatic conditions. ECS Trans. 1, 37–45 (2006).
52. 52.
Laycock, N. J., Krouse, D. P., Hendy, S. C. & Williams, D. E. Computer simulation of pitting corrosion of stainless steels. Electrochem. Soc. Interface 23, 65–71 (2014).
53. 53.
Martin, F. A., Bataillon, C. & Cousty, J. In situ AFM detection of pit onset location on a 304L stainless steel. Corros. Sci. 50, 84–92 (2008).
54. 54.
Gutman, E. M. Mechanochemistry of Solid Surfaces. (World Scientific Publishing Company, Singapore, 1994).
55. 55.
Shahryari, A., Szpunar, J. A. & Omanovic, S. The influence of crystallographic orientation distribution on 316LVM stainless steel pitting behavior. Corros. Sci. 51, 677–682 (2009).
56. 56.
Kumar, B. R., Singh, R., Mahato, B., De, P. K., Bandyopadhyay, N. R. & Bhattacharya, D. K. Effect of texture on corrosion behavior of AISI 304L stainless steel. Mater. Charact. 54, 141–147 (2005).
57. 57.
Lindell, D. & Pettersson, R. Crystallographic effects in corrosion of austenitic stainless steel 316L. Mater. Corros. 66, 727–732 (2015).
58. 58.
Frankel, G. S. Pitting corrosion of metals: a review of the critical factors. J. Electrochem. Soc. 145, 2186–2198 (1998).
59. 59.
Akhtar, F. Ceramic reinforced high modulus steel composites: processing, microstructure and properties. Can. Metall. Q. 53, 253–263 (2014).
60. 60.
Akhtar, F. Microstructure evolution and wear properties of in situ synthesized TiB2 and TiC reinforced steel matrix composites. J. Alloy. Compd. 459, 491–497 (2008).
61. 61.
Pagounis, E. & Lindroos, V. K. Processing and properties of particulate reinforced steel matrix composites. Mater. Sci. Eng. A 246, 221–234 (1998).
62. 62.
Fairweather, G. Finite Element Galerkin Methods for Differential Equations, Lecture Notes in Pure and Applied Mathematics, vol. 34, Marcel Dekker, New York, (1978).
63. 63.
Ascher, U. M. & Petzold, L. R. Computer Methods for Ordinary Differential Equations and Differential-Algebraic Equations. Vol. 61 (Society For Industrial Applied Mathematics, U.S., Philadelphia, 1998).
## Acknowledgements
This work was supported by Research Grants Council of Hong Kong (PolyU 152140/14E).
## Author information
Authors
### Contributions
S.Q.S. conceived the idea, designed and supervised the project. T.Q.A. developed the model, performed simulations and wrote the manuscript. Z.X. and S.Q.S. also contributed in developing the model. S.Q.S., S.Y.H., Y.L. and J.L. provided critical comments and contributed to revisions of the manuscript.
### Corresponding author
Correspondence to San-Qiang Shi.
## Ethics declarations
### Competing interests
The authors declare no competing interests.
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Ansari, T.Q., Xiao, Z., Hu, S. et al. Phase-field model of pitting corrosion kinetics in metallic materials. npj Comput Mater 4, 38 (2018). https://doi.org/10.1038/s41524-018-0089-4
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Journal of The Electrochemical Society (2020) | 2021-04-14 03:55:26 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.58534175157547, "perplexity": 2186.8638086743026}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-17/segments/1618038076819.36/warc/CC-MAIN-20210414034544-20210414064544-00480.warc.gz"} |
http://www-users.math.umn.edu/~stant001/MCC2017abs/klee.html | Kyungyong Lee
Speaker: Kyungyong Lee, University of Nebraska
Title: A conjectural description for real Schur roots of acyclic quivers
Abstract: Let $Q$ be an acyclic quiver. The dimension vectors of indecomposable rigid representations are called real Schur roots. We give a conjectural description for real Schur roots of $Q$ using non-self-intersecting paths on Riemann surfaces, and prove it for certain quivers of finite types and for the quivers with three or less vertices and multiple arrows between every pair of vertices. Each of such paths gives rise to a reflection of the Weyl group of the corresponding Kac--Moody algebra and determines a real Schur root uniquely. This is joint work with Kyu-Hwan Lee. | 2018-09-24 02:12:24 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8175517916679382, "perplexity": 379.11854105117504}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-39/segments/1537267160085.77/warc/CC-MAIN-20180924011731-20180924032131-00362.warc.gz"} |
http://www.techspot.com/community/topics/my-hijackthis-log-after-using-avg-spy-virus-rootkit-scanner.83201/ | My Hijackthis Log - After using AVG Spy+Virus+Rootkit Scanner
Jul 30, 2007
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O2 - BHO: SSVHelper Class - {761497BB-D6F0-462C-B6EB-D4DAF1D92D43} - C:\Program Files\Java\jre1.6.0_02\bin\ssv.dll
O3 - Toolbar: (no name) - {014DA6C9-189F-421a-88CD-07CFE51CFF10} - (no file)
O3 - Toolbar: (no name) - {4E7BD74F-2B8D-469E-A1F6-FC7EB590A97D} - (no file)
O4 - HKLM\..\Run: [SunJavaUpdateSched] "C:\Program Files\Java\jre1.6.0_02\bin\jusched.exe"
O9 - Extra button: (no name) - {08B0E5C0-4FCB-11CF-AAA5-00401C608501} - C:\Program Files\Java\jre1.6.0_02\bin\ssv.dll
O9 - Extra 'Tools' menuitem: Sun Java Console - {08B0E5C0-4FCB-11CF-AAA5-00401C608501} - C:\Program Files\Java\jre1.6.0_02\bin\ssv.dll
That's just Adobe and Java running in the background - unless you use Java all the time there's no point in having this run - it runs automatically when it needs to be used anyway.
Hope it helps a little
3. ArroyoHighTS RookieTopic Starter
Thanks but I also really want to remove these... should I?
O2 - BHO: SDWin32 Class - {172FD220-3BF1-4B9C-B162-0278DC493EA3} - C:\WINDOWS\System32\zbopr.dll (file missing)
O2 - BHO: SDWin32 Class - {86CF160A-13F1-46DA-958D-4E11464B2420} - C:\WINDOWS\System32\cfnpw.dll (file missing)
O3 - Toolbar: &Yahoo! Toolbar - {EF99BD32-C1FB-11D2-892F-0090271D4F88} - C:\Program Files\Yahoo!\Companion\Installs\cpn\yt.dll
O9 - Extra button: AIM - {AC9E2541-2814-11d5-BC6D-00B0D0A1DE45} - C:\Program Files\AIM\aim.exe
O9 - Extra button: Real.com - {CD67F990-D8E9-11d2-98FE-00C0F0318AFE} - C:\WINDOWS\System32\Shdocvw.dll
O9 - Extra button: Messenger - {FB5F1910-F110-11d2-BB9E-00C04F795683} - C:\Program Files\Messenger\msmsgs.exe
the yahoo toolbar should have an uninstaller in Add/Remove Programs, I suggest looking there for an uninstaller, and if not well, it shouldn't be there now should it?
5. momokTS RookiePosts: 2,265
Hi,
You should remove those entries. However, do note that they are reminiscent of an infection on your system. Please do the following.
Very Important: Malware infections can possibly lead to identity theft, loss of funds from bank accounts, misuse of credit card information etc. Therefore I strongly encourage you to please read this thread HERE before deciding what course of action to take regarding your infection.
Should you decide to clean your computer, please go ahead to Viruses/Spyware/Malware, preliminary removal instructions and follow the steps given. Do follow all the instructions exactly. They will provide logs for analysis of your system so I will know how to instruct you to proceed.
Thereafter, please post fresh HijackThis, AVG Antispyware and Combofix logs as attachments into this thread. Do not copy and paste your logs if not it will be ignored and/or removed.
Also, please let me know the results of the AVG Antirootkit scan
Regards, | 2016-12-04 02:00:21 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8370367884635925, "perplexity": 12528.51037456579}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-50/segments/1480698541170.58/warc/CC-MAIN-20161202170901-00374-ip-10-31-129-80.ec2.internal.warc.gz"} |
http://www.chegg.com/homework-help/questions-and-answers/explain-unit-coefficient-oflinear-thermal-expansion-means-going-sites-i-gotthat-unit-10-6--q452904 | ## Coefficient of linear thermal expansion
Can someone explain to me what the unit of the Coefficient oflinear thermal expansion means? After going to two sites, I gotthat the unit was (10-6 / K at 20o C). Pleaseexplain what this unit means. | 2013-05-21 21:14:10 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8062025308609009, "perplexity": 2841.586009761154}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2013-20/segments/1368700563008/warc/CC-MAIN-20130516103603-00028-ip-10-60-113-184.ec2.internal.warc.gz"} |
https://physics.stackexchange.com/questions/488397/is-idempotency-rho2-rho-a-necessary-and-sufficient-condition-for-rho-t | # Is idempotency, $\rho^2=\rho$, a necessary and sufficient condition for $\rho$ to be a pure state?
I've seen some claims that idempotency ($$\rho^2=\rho$$) is necessary and sufficient to guarantee the existence of some state $$\psi$$ such that $$\rho=|\psi\rangle\langle\psi|$$, as well as claims on the trace such as here. However, I have so far been unable to prove a necessary and sufficient condition for a density matrix to represent a pure state.
It is easy to see that if $$\rho=|\psi\rangle\langle\psi|$$ then $$\rho$$ is idempotent: $$\rho^2=|\psi\rangle\langle\psi|\psi\rangle\langle\psi|=|\psi\rangle\langle\psi|=\rho$$ by normalization. However, the converse has proven more difficult I have been able to show, by expanding in a basis and noting that the eigenvalues of an idempotent matrix are either 0 or 1, that if $$\rho$$ is idempotent then $$\rho=\sum_j \lambda_j |\psi_j\rangle\langle\psi_j|$$ where each $$\lambda_j$$ is either 0 or 1. How can I complete the proof? Alternatively, is idempotency not a sufficient condition for a pure state?
• What is the spectral expansion of $\rho^2$? Compare with of $\rho$, studying the sign of $\lambda^2-\lambda$ for $\lambda\in [0,1]$... Jun 27 '19 at 5:53
• Notice that the sum of all $\lambda$ must equal $1$. Jun 27 '19 at 6:03
• That is not true - for example, $\begin{bmatrix} 1 & 0 & 0 & 0 \\ 0 & 0.5 & 0.5 & 0 \\ 0 & 0.5 & 0.5 & 0 \\ 0 & 0 & 0 & 0 \end{bmatrix}$ is idempotent and has the sum of all eigenvalues equal to 2. Are you saying that another condition needs to be imposed, that the trace must be 1 so that there can only be 1 nonzero eigenvalue? This gives me a proof that idempotency together with unit trace is a sufficient condition, at least, but is it necessary to have $tr(\rho)=1$? Jun 27 '19 at 12:05
• I now posted a complete proof. Jun 27 '19 at 12:07
THEOREM 1 If $$\rho$$ is a density matrix (i.e., a positive, unit-trace, trace-class operator, also in an infinite dimensional Hilbert space), then $$\rho$$ is a pure state iff $$\rho^2=\rho$$.
Proof. If $$\rho$$ is pure, then $$\rho^2=\rho$$. Let us prove the converse implication. Suppose that $$\rho^2 = \rho$$ ($$\rho^2$$ is trace class if $$\rho$$ is because the set of trace class operators is a $$^*$$ ideal of the $$C^*$$-algebra of bounded operators) then $$0=\rho^2-\rho = \sum_{j} (\lambda_j^2 -\lambda_j) |\psi_j\rangle \langle \psi_j|\tag{1}$$ where, from the definition of density matrix (positive unit-trace trace-class operator) $$\lambda_j \in [0,1]\tag{2}$$ and $$\sum_j \lambda_j =1\tag{3}\:.$$ Let us assume that there are at least two $$j\neq j'$$ with $$\lambda_j,\lambda_{j'}>0$$. We conclude from (2) that both $$\lambda_j^2-\lambda_j<0$$ and $$\lambda_{j'}^2-\lambda_{j'}<0$$. Since $$\langle \psi_k|\psi_h \rangle = \delta_{hk}$$, (1) leads to $$0 = \langle \psi_{j'}|0 \psi_{j'}\rangle = \lambda_{j'}^2-\lambda_{j'} <0$$ that is impossible. We conclude that the assumption that there are at least two $$j\neq j'$$ with $$\lambda_j,\lambda_{j'}>0$$ is untenable so that $$\rho = |\psi_j\rangle \langle \psi_j|$$. $$\Box$$
With a similar route one easily proves that
THEOREM 2 If $$\rho$$ is a density matrix (also in an infinite dimensional Hilbert space), then $$\rho$$ is a pure state iff $$tr(\rho^2)=tr(\rho)$$ ($$=1$$).
Proof. If $$\rho$$ is pure the thesis it trivial. Let us pass to the converse implication. Since $$\sum_j \lambda_j =1$$ and $$\lambda_j\in [0,1]$$, if more than one $$\lambda_j$$ does not vanish, every $$\lambda_j$$ is strictly less than $$1$$, so that we have in particular $$\lambda^2_j < \lambda_j$$ for all $$j$$, which implies $$\sum_j \lambda_j^2 < \sum_j \lambda_j$$. This meas that if $$tr(\rho^2) = tr(\rho)$$, then only one $$\lambda_j$$ does not vanish so that $$\rho$$ is pure. $$\Box$$
• In other words, idempotency is not sufficient, but idempotency with unit trace is, and I had overlooked the assumption of unit trace before as it was hidden in the defining properties of the density operator. Retrospectively, this makes sense because it's essentially normalization of the state. Thank you! Jun 27 '19 at 12:16
• Yes, I agree with you. Jun 27 '19 at 12:18
if $$\rho^2=\rho$$, the only eigenvalues of $$\rho$$ can be $$0$$ or $$1$$, as a matter of fact if
$$\rho|\psi\rangle=\lambda|\psi\rangle$$
then
$$\rho^2|\psi\rangle=\lambda^2|\psi\rangle=\rho|\psi\rangle=\lambda|\psi\rangle$$
hence $$\lambda^2=\lambda$$, i.e. $$\lambda\in\{0,1\}$$. Since $$\mathrm{Tr}(\rho)=1$$, $$\rho$$ can have at most one eigenvalue $$1$$, hence $$\rho=|\psi\rangle\langle \psi|$$.
Let $$\rho\ge0$$ be a positive semidefinite (finite-dimensional) operator, and consider the following three conditions:
1. $$\newcommand{\tr}{\operatorname{tr}}\tr(\rho)=1$$
2. $$\tr(\rho^2)=1$$
3. $$\rho^2=\rho$$.
Any two of the above imply the remaining one.
(1 and 2 $$\Longrightarrow$$ 3) Positivity implies that we can eigedecompose $$\rho$$ as $$\rho=\sum_k p_k P_k$$ with $$\tr(P_j P_k)=\delta_{jk}$$, $$P_j$$ orthogonal projections, and $$p_k\ge0$$. Then $$\tr(\rho)=1$$ implies $$\sum_k p_k=1$$, and $$\tr(\rho^2)=1$$ implies $$\sum_k p_k^2=1$$. These two conditions are compatible only if $$p_k=\delta_{k,1}$$, that is, if $$\rho=P_1$$ for some trace-1 projection $$P_1$$.
(1 and 3 $$\Longrightarrow$$ 2) This is obvious.
(2 and 3 $$\Longrightarrow$$ 1) Also obvious.
• I was confused at first... I'd say "any two of the above imply the remaining one". Dec 1 '20 at 12:30
• But note that condition 1. is automatically true, by definition, for a density matrix. Dec 1 '20 at 12:31
• @pglpm sure, that's why I stated the conditions for a positive semidefinite operator, not for a state
– glS
Dec 1 '20 at 13:46
• My bad, I overlooked that. Dec 1 '20 at 15:33 | 2021-09-19 08:51:00 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 80, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9662719964981079, "perplexity": 152.85385536434492}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-39/segments/1631780056752.16/warc/CC-MAIN-20210919065755-20210919095755-00492.warc.gz"} |
https://people.maths.bris.ac.uk/~matyd/GroupNames/192i1/C2xS3xC2%5E2sC4.html | Copied to
clipboard
## G = C2×S3×C22⋊C4order 192 = 26·3
### Direct product of C2, S3 and C22⋊C4
Series: Derived Chief Lower central Upper central
Derived series C1 — C6 — C2×S3×C22⋊C4
Chief series C1 — C3 — C6 — C2×C6 — C22×S3 — S3×C23 — S3×C24 — C2×S3×C22⋊C4
Lower central C3 — C6 — C2×S3×C22⋊C4
Upper central C1 — C23 — C2×C22⋊C4
Generators and relations for C2×S3×C22⋊C4
G = < a,b,c,d,e,f | a2=b3=c2=d2=e2=f4=1, ab=ba, ac=ca, ad=da, ae=ea, af=fa, cbc=b-1, bd=db, be=eb, bf=fb, cd=dc, ce=ec, cf=fc, fdf-1=de=ed, ef=fe >
Subgroups: 1832 in 674 conjugacy classes, 207 normal (17 characteristic)
C1, C2, C2, C2, C3, C4, C22, C22, C22, S3, S3, C6, C6, C6, C2×C4, C2×C4, C23, C23, C23, Dic3, C12, D6, D6, C2×C6, C2×C6, C2×C6, C22⋊C4, C22⋊C4, C22×C4, C22×C4, C24, C24, C4×S3, C2×Dic3, C2×Dic3, C2×C12, C2×C12, C22×S3, C22×S3, C22×C6, C22×C6, C22×C6, C2×C22⋊C4, C2×C22⋊C4, C23×C4, C25, D6⋊C4, C6.D4, C3×C22⋊C4, S3×C2×C4, S3×C2×C4, C22×Dic3, C22×C12, S3×C23, S3×C23, S3×C23, C23×C6, C22×C22⋊C4, S3×C22⋊C4, C2×D6⋊C4, C2×C6.D4, C6×C22⋊C4, S3×C22×C4, S3×C24, C2×S3×C22⋊C4
Quotients: C1, C2, C4, C22, S3, C2×C4, D4, C23, D6, C22⋊C4, C22×C4, C2×D4, C24, C4×S3, C22×S3, C2×C22⋊C4, C23×C4, C22×D4, S3×C2×C4, S3×D4, S3×C23, C22×C22⋊C4, S3×C22⋊C4, S3×C22×C4, C2×S3×D4, C2×S3×C22⋊C4
Smallest permutation representation of C2×S3×C22⋊C4
On 48 points
Generators in S48
(1 27)(2 28)(3 25)(4 26)(5 40)(6 37)(7 38)(8 39)(9 36)(10 33)(11 34)(12 35)(13 29)(14 30)(15 31)(16 32)(17 44)(18 41)(19 42)(20 43)(21 48)(22 45)(23 46)(24 47)
(1 32 23)(2 29 24)(3 30 21)(4 31 22)(5 36 19)(6 33 20)(7 34 17)(8 35 18)(9 42 40)(10 43 37)(11 44 38)(12 41 39)(13 47 28)(14 48 25)(15 45 26)(16 46 27)
(1 6)(2 7)(3 8)(4 5)(9 45)(10 46)(11 47)(12 48)(13 44)(14 41)(15 42)(16 43)(17 29)(18 30)(19 31)(20 32)(21 35)(22 36)(23 33)(24 34)(25 39)(26 40)(27 37)(28 38)
(1 3)(2 38)(4 40)(5 26)(6 8)(7 28)(9 31)(10 12)(11 29)(13 34)(14 16)(15 36)(17 47)(18 20)(19 45)(21 23)(22 42)(24 44)(25 27)(30 32)(33 35)(37 39)(41 43)(46 48)
(1 39)(2 40)(3 37)(4 38)(5 28)(6 25)(7 26)(8 27)(9 29)(10 30)(11 31)(12 32)(13 36)(14 33)(15 34)(16 35)(17 45)(18 46)(19 47)(20 48)(21 43)(22 44)(23 41)(24 42)
(1 2 3 4)(5 6 7 8)(9 10 11 12)(13 14 15 16)(17 18 19 20)(21 22 23 24)(25 26 27 28)(29 30 31 32)(33 34 35 36)(37 38 39 40)(41 42 43 44)(45 46 47 48)
G:=sub<Sym(48)| (1,27)(2,28)(3,25)(4,26)(5,40)(6,37)(7,38)(8,39)(9,36)(10,33)(11,34)(12,35)(13,29)(14,30)(15,31)(16,32)(17,44)(18,41)(19,42)(20,43)(21,48)(22,45)(23,46)(24,47), (1,32,23)(2,29,24)(3,30,21)(4,31,22)(5,36,19)(6,33,20)(7,34,17)(8,35,18)(9,42,40)(10,43,37)(11,44,38)(12,41,39)(13,47,28)(14,48,25)(15,45,26)(16,46,27), (1,6)(2,7)(3,8)(4,5)(9,45)(10,46)(11,47)(12,48)(13,44)(14,41)(15,42)(16,43)(17,29)(18,30)(19,31)(20,32)(21,35)(22,36)(23,33)(24,34)(25,39)(26,40)(27,37)(28,38), (1,3)(2,38)(4,40)(5,26)(6,8)(7,28)(9,31)(10,12)(11,29)(13,34)(14,16)(15,36)(17,47)(18,20)(19,45)(21,23)(22,42)(24,44)(25,27)(30,32)(33,35)(37,39)(41,43)(46,48), (1,39)(2,40)(3,37)(4,38)(5,28)(6,25)(7,26)(8,27)(9,29)(10,30)(11,31)(12,32)(13,36)(14,33)(15,34)(16,35)(17,45)(18,46)(19,47)(20,48)(21,43)(22,44)(23,41)(24,42), (1,2,3,4)(5,6,7,8)(9,10,11,12)(13,14,15,16)(17,18,19,20)(21,22,23,24)(25,26,27,28)(29,30,31,32)(33,34,35,36)(37,38,39,40)(41,42,43,44)(45,46,47,48)>;
G:=Group( (1,27)(2,28)(3,25)(4,26)(5,40)(6,37)(7,38)(8,39)(9,36)(10,33)(11,34)(12,35)(13,29)(14,30)(15,31)(16,32)(17,44)(18,41)(19,42)(20,43)(21,48)(22,45)(23,46)(24,47), (1,32,23)(2,29,24)(3,30,21)(4,31,22)(5,36,19)(6,33,20)(7,34,17)(8,35,18)(9,42,40)(10,43,37)(11,44,38)(12,41,39)(13,47,28)(14,48,25)(15,45,26)(16,46,27), (1,6)(2,7)(3,8)(4,5)(9,45)(10,46)(11,47)(12,48)(13,44)(14,41)(15,42)(16,43)(17,29)(18,30)(19,31)(20,32)(21,35)(22,36)(23,33)(24,34)(25,39)(26,40)(27,37)(28,38), (1,3)(2,38)(4,40)(5,26)(6,8)(7,28)(9,31)(10,12)(11,29)(13,34)(14,16)(15,36)(17,47)(18,20)(19,45)(21,23)(22,42)(24,44)(25,27)(30,32)(33,35)(37,39)(41,43)(46,48), (1,39)(2,40)(3,37)(4,38)(5,28)(6,25)(7,26)(8,27)(9,29)(10,30)(11,31)(12,32)(13,36)(14,33)(15,34)(16,35)(17,45)(18,46)(19,47)(20,48)(21,43)(22,44)(23,41)(24,42), (1,2,3,4)(5,6,7,8)(9,10,11,12)(13,14,15,16)(17,18,19,20)(21,22,23,24)(25,26,27,28)(29,30,31,32)(33,34,35,36)(37,38,39,40)(41,42,43,44)(45,46,47,48) );
G=PermutationGroup([[(1,27),(2,28),(3,25),(4,26),(5,40),(6,37),(7,38),(8,39),(9,36),(10,33),(11,34),(12,35),(13,29),(14,30),(15,31),(16,32),(17,44),(18,41),(19,42),(20,43),(21,48),(22,45),(23,46),(24,47)], [(1,32,23),(2,29,24),(3,30,21),(4,31,22),(5,36,19),(6,33,20),(7,34,17),(8,35,18),(9,42,40),(10,43,37),(11,44,38),(12,41,39),(13,47,28),(14,48,25),(15,45,26),(16,46,27)], [(1,6),(2,7),(3,8),(4,5),(9,45),(10,46),(11,47),(12,48),(13,44),(14,41),(15,42),(16,43),(17,29),(18,30),(19,31),(20,32),(21,35),(22,36),(23,33),(24,34),(25,39),(26,40),(27,37),(28,38)], [(1,3),(2,38),(4,40),(5,26),(6,8),(7,28),(9,31),(10,12),(11,29),(13,34),(14,16),(15,36),(17,47),(18,20),(19,45),(21,23),(22,42),(24,44),(25,27),(30,32),(33,35),(37,39),(41,43),(46,48)], [(1,39),(2,40),(3,37),(4,38),(5,28),(6,25),(7,26),(8,27),(9,29),(10,30),(11,31),(12,32),(13,36),(14,33),(15,34),(16,35),(17,45),(18,46),(19,47),(20,48),(21,43),(22,44),(23,41),(24,42)], [(1,2,3,4),(5,6,7,8),(9,10,11,12),(13,14,15,16),(17,18,19,20),(21,22,23,24),(25,26,27,28),(29,30,31,32),(33,34,35,36),(37,38,39,40),(41,42,43,44),(45,46,47,48)]])
60 conjugacy classes
class 1 2A ··· 2G 2H 2I 2J 2K 2L ··· 2S 2T 2U 2V 2W 3 4A ··· 4H 4I ··· 4P 6A ··· 6G 6H 6I 6J 6K 12A ··· 12H order 1 2 ··· 2 2 2 2 2 2 ··· 2 2 2 2 2 3 4 ··· 4 4 ··· 4 6 ··· 6 6 6 6 6 12 ··· 12 size 1 1 ··· 1 2 2 2 2 3 ··· 3 6 6 6 6 2 2 ··· 2 6 ··· 6 2 ··· 2 4 4 4 4 4 ··· 4
60 irreducible representations
dim 1 1 1 1 1 1 1 1 2 2 2 2 2 2 4 type + + + + + + + + + + + + + image C1 C2 C2 C2 C2 C2 C2 C4 S3 D4 D6 D6 D6 C4×S3 S3×D4 kernel C2×S3×C22⋊C4 S3×C22⋊C4 C2×D6⋊C4 C2×C6.D4 C6×C22⋊C4 S3×C22×C4 S3×C24 S3×C23 C2×C22⋊C4 C22×S3 C22⋊C4 C22×C4 C24 C23 C22 # reps 1 8 2 1 1 2 1 16 1 8 4 2 1 8 4
Matrix representation of C2×S3×C22⋊C4 in GL6(𝔽13)
12 0 0 0 0 0 0 12 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1
,
1 0 0 0 0 0 0 1 0 0 0 0 0 0 12 12 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1
,
12 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 12 12 0 0 0 0 0 0 1 0 0 0 0 0 0 1
,
1 0 0 0 0 0 0 12 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 12 0 0 0 0 0 12 1
,
1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 12 0 0 0 0 0 0 12
,
8 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 11 0 0 0 0 1 12
G:=sub<GL(6,GF(13))| [12,0,0,0,0,0,0,12,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1],[1,0,0,0,0,0,0,1,0,0,0,0,0,0,12,1,0,0,0,0,12,0,0,0,0,0,0,0,1,0,0,0,0,0,0,1],[12,0,0,0,0,0,0,1,0,0,0,0,0,0,1,12,0,0,0,0,0,12,0,0,0,0,0,0,1,0,0,0,0,0,0,1],[1,0,0,0,0,0,0,12,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,12,12,0,0,0,0,0,1],[1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,12,0,0,0,0,0,0,12],[8,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,1,0,0,0,0,11,12] >;
C2×S3×C22⋊C4 in GAP, Magma, Sage, TeX
C_2\times S_3\times C_2^2\rtimes C_4
% in TeX
G:=Group("C2xS3xC2^2:C4");
// GroupNames label
G:=SmallGroup(192,1043);
// by ID
G=gap.SmallGroup(192,1043);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-3,297,80,6278]);
// Polycyclic
G:=Group<a,b,c,d,e,f|a^2=b^3=c^2=d^2=e^2=f^4=1,a*b=b*a,a*c=c*a,a*d=d*a,a*e=e*a,a*f=f*a,c*b*c=b^-1,b*d=d*b,b*e=e*b,b*f=f*b,c*d=d*c,c*e=e*c,c*f=f*c,f*d*f^-1=d*e=e*d,e*f=f*e>;
// generators/relations
×
𝔽 | 2021-10-24 19:39:27 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9996659755706787, "perplexity": 3233.559574706273}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-43/segments/1634323587593.0/warc/CC-MAIN-20211024173743-20211024203743-00656.warc.gz"} |
https://www.math-only-math.com/associative-property-of-multiplication-of-complex-numbers.html | # Associative Property of Multiplication of Complex Numbers
Here we will discuss about the associative property of multiplication of complex numbers.
Commutative property of multiplication complex numbers:
For any three complex numbers z$$_{1}$$, z$$_{2}$$ and z$$_{3}$$, we have (z$$_{1}$$z$$_{2}$$)z$$_{3}$$ = z$$_{1}$$(z$$_{2}$$z$$_{3}$$).
Proof:
Let z$$_{1}$$ = a + ib, z$$_{2}$$ = c + id and z$$_{3}$$ = e + if be any three complex numbers.
Then (z$$_{1}$$z$$_{2}$$)z$$_{3}$$ = {(a + ib)(c + id)}(e + if)
= {(ac - bd) +i(ad + cb)}(e + if)
= {(ac - bd)e - (ad + cb)f) + i{(ac - bd)f + (ad + cb)e)
= {a(ce - df) - b(cf + ed)} + i{b(ce - df) + a(ed + cf)
= (a + ib){(cf - df) + i(cf + ed)}
= z$$_{1}$$(z$$_{2}$$z$$_{3}$$)
Thus, (z$$_{1}$$z$$_{2}$$)z$$_{3}$$ = z$$_{1}$$(z$$_{2}$$z$$_{3}$$) for all z$$_{1}$$, z$$_{2}$$, z$$_{3}$$ ϵ C.
Hence, multiplication of complex numbers is associative on C.
Solved example on commutative property of multiplication of complex numbers:
Show that multiplication of complex numbers (2 + 3i), (4 + 5i) and (1 + i) is associative.
Solution:
Let z$$_{1}$$ = (2 + 3i), z$$_{2}$$ = (4 + 5i) and z$$_{3}$$ = (1 + i)
Then (z$$_{1}$$z$$_{2}$$)z$$_{3}$$ = {(2 + 3i)(4 + 5i)}(1 + i)
= (2 4 - 3 5) + i(2 5 + 4 3)}(1 + i)
= (8 - 15) + i(10 + 12)}(1 + i)
= (-7 + 22i)(1 + i)
= (-7 1 - 22 1) + i(-7 1 + 1 22)
= (-7 – 22) + i(-7 + 22)
= -29 + 15i
Now, z$$_{1}$$(z$$_{2}$$z$$_{3}$$) = (2 + 3i){(4 + 5i)(1 + i)}
= (2 + 3i){(4 1 - 5 1) + i(4 1 + 1 5)}
= (2 + 3i){(4 - 5) + i(4 + 5)}
= (2 + 3i)(-1 + 9i)
= {2 (-1) - 3 9} + i{2 9 + (-1) 3}
= (-2 - 27) + i(18 - 3)
= -29 + 15i
Thus, (z$$_{1}$$z$$_{2}$$)z$$_{3}$$ = z$$_{1}$$(z$$_{2}$$z$$_{3}$$) for all z$$_{1}$$, z$$_{2}$$, z$$_{3}$$ ϵ C.
Hence, multiplication of complex numbers (2 + 3i), (4 + 5i) and (1 + i) is associative.
Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.
Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need. | 2021-05-08 22:31:51 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4830920994281769, "perplexity": 4880.630054467277}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-21/segments/1620243988927.95/warc/CC-MAIN-20210508211857-20210509001857-00390.warc.gz"} |
https://www.techwhiff.com/issue/what-is-biodiversity-an-indicator-of-a-ecosystem-health--216512 | # What is biodiversity an indicator of? A. ecosystem health B. ecosystem growth C. ecosystem decline D. ecosystem location
###### Question:
What is biodiversity an indicator of? A. ecosystem health B. ecosystem growth C. ecosystem decline D. ecosystem location
### The volume of a cylinder is 88 cubic inches. A smaller container, similar in shape, has a scale factor of 1/2.What is the volume of the smaller container?
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### A boy holding a stack of 9 identical books steps on a scale and weighs 138 pounds. The boy then holding a stack of 3 of the same books again steps on the scale and weighs 120 pounds. How much does the boy weigh?
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### Factor: a=1 d2 - 10d + 25
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### You wish to purify an ATP-binding enzyme from a crude extract that contains several contaminating proteins. To purify the enzyme rapidly and to the highest purity, you must consider some sophisticated strategies, among them affinity chromatography. Explain how affinity chromatography can be applied to the separation, and explain the physical basis of the separation
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### What was one source of tension in the Middle Colonies in the 1600s?
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### The pressure of the impinging plates could only be relieved by thrusting skyward,and forming _____ mountain A) eurasian B) HimalayaC) rockyD) ural
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### One cubic foot is equal to 7.48 gallons how many gallons of water does jose need to fill his aquarium? round to the nearest gallo
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### (18 + 7) x (11 - 7) write 3 steps then answer it and i will give u brainlyiest if u are correct
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### How did William Wordsworth organize "I Wandered Lonely as a Cloud" for readers? (5 points) I wandered lonely as a cloud That floats on high o'er vales and hills, When all at once I saw a crowd, A host, of golden daffodils; Beside the lake, beneath the trees, Fluttering and dancing in the breeze. Continuous as the stars that shine And twinkle on the milky way, They stretched in never-ending line Along the margin of a bay: Ten thousand saw I at a glance, Tossing their heads in a sprightly dance. T
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### Convert 0.0547 hectograms to ounces
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### If it was against the law to read books, i would break the law and read anyway
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### How could a teacher indicate which of the exercises on a page to do?
How could a teacher indicate which of the exercises on a page to do?... | 2022-09-26 12:44:15 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.35978376865386963, "perplexity": 2425.8629330979143}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-40/segments/1664030334871.54/warc/CC-MAIN-20220926113251-20220926143251-00631.warc.gz"} |
https://math.stackexchange.com/questions/1978215/ac-circuits-proof | # AC Circuits Proof
My circuit analysis teacher is asking us to prove for extra credit:
$sin[wt+arctan\frac{R}{\omega L}] = cos[\omega t+arctan\frac{-\omega L}{R})]$
w = omega
t = time
R = resistant
L = inductance
Ive been working at it for a couple of hours and I cannot make any headway. Would anyone be able to point me in the correct direction?
Thank you for your time
• Please learn MathJax. – Em. Oct 21 '16 at 5:35
## 1 Answer
Hints:
$\cos \theta = \sin \left(\dfrac\pi2-\theta\right)$
$\arctan x + \arctan\left(\dfrac1x\right) = \dfrac\pi2$ (if $x>0$)
$\arctan(-x) = -\arctan x$
$\cos(-\theta) = \cos\theta$
• Thank you, I think the negative in the cos's arctan is incorrect though. Without it I am able to make them equal but with it the two arctan's just cancel themselves. – nbstrong Oct 21 '16 at 16:37
• @MushinZero the negative sign in the problem is correct. I'll add another hint related to it. Let me know if you still need help with it. – tilper Oct 21 '16 at 17:17 | 2019-09-22 16:03:03 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5776691436767578, "perplexity": 550.5079150219386}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-39/segments/1568514575596.77/warc/CC-MAIN-20190922160018-20190922182018-00017.warc.gz"} |
http://lists.extropy.org/pipermail/paleopsych/2006-January/004952.html | # [Paleopsych] Edge Annual Question 2004: What's Your Law?
Premise Checker checker at panix.com
Mon Jan 23 21:14:42 UTC 2006
Edge Annual Question 2004: What's Your Law?
http://edge.org/q2004/q04_print1.html
There is some bit of wisdom, some rule of nature, some law-like
pattern, either grand or small, that you've noticed in the universe
that might as well be named after you. Gordon Moore has one; Johannes
Kepler and Michael Faraday, too. So does Murphy.
Since you are so bright, you probably have at least two you can
articulate. Send me two laws based on your empirical work and
observations you would not mind having tagged with your name. Stick to
science and to those scientific areas where you have expertise. Avoid
I am asking members of the Edge community to take this project
seriously as a public service, to work together to create a document
that can be widely disseminated, that can stimulate discussion and the
imagination.
Say the words....
Happy New Year!
John Brockman
Publisher & Editor
164 Contributors: George Dyson o Bruce Sterling o William Calvin o
Howard Gardner o James J. O'Donnell o Marc D. Hauser o David Lykken o
Irene Pepperberg o Daniel Gilbert o Joseph Traub o Roger Schank o
Douglas Rushkoff o Karl Sabbagh o Carlo Rovelli o Timothy Taylor o
Richard Nisbett o Freeman Dyson o John Allan Paulos o John McWhorter o
Kevin Kelly o Brian Goodwin o John Barrow o Marvin Minsky o Garniss
Curtis o Todd Siler o Howard Rheingold o David G. Myers o Michael
Nesmith o Arnold Trehub o Keith Devlin o Arthur R. Jensen o John
Maddox o John Skoyles o Pamela McCorduck o Philip W. Anderson o
Charles Arthur o David Bunnell o Esther Dyson o Scott Atran o Jay
Ogilvy o Steven Kosslyn o Jeffrey Epstein o Stewart Brand o Piet Hut o
Geoffrey Miller o Nassim Taleb o Donald Hoffman o Richard Rabkin o
Stanislas Dehaene o Susan Blackmore o Raphael Kasper o Alison Gopnik o
Art De Vany o Robert Provine o Stuart Pimm o Chris Anderson o Alan
Alda o Andy Clark o Charles Seife o Jaron Lanier o Seth Lloyd o John
Horgan o Robert Aunger o Ernst Pöppel o Michael Shermer o Colin
Blakemore o Scott Sampson o Verena Huber-Dyson o Gary Marcus o Rodney
Brooks o David Deutsch o Steve Grand o Paul Davies o David Finkelstein
o Richard Dawkins o J. Craig Venter o Steve Quartz o Philip Campbell o
Tor Nørretranders o Julian Barbour o Maria Spiropulu o Eberhard
Zangger o David Buss o Mark Mirsky o Lee Smolin o Nancy Etcoff o Anton
Zeilinger o Edward O. Laumann o George Lakoff o Haim Harari o Matt
Ridley o Daniel C. Dennett o W. Brian Arthur o Samuel Barondes o
Jamshed Bharucha o Ray Kurzweil o Adam Bly o Kai Krause o Dylan Evans
o Jordan Pollack o Stuart Kauffman o Niels Diffrient o Gerald Holton o
Robert Sapolsky o Izumi Aizu o Randoph Nesse o Dave Winer o Rupert
Sheldrake o Ivan Amato o Judith Rich Harris o Steven Strogatz o Sherry
Turkle o Leonard Susskind o Christine Finn o Simon Baron-Cohen o Henry
Warwick o Gino Segre o Neil Gershenfeld o Steven Levy o Paul Ryan o
Stuart Hameroff o Leo Chalupa o Terrence Sejnowski o Eduard Punset o
Paul Steinhardt o Delta Willis o Rudy Rucker o Al Seckel o Howard
Morgan o Clifford Pickover o Beatrice Golomb o K. Eric Drexler o Mark
Hurst o Art Kleiner o Yossi Vardi o Nicholas Humphrey o Martin Rees o
John Markoff o Gerd Gigerenzer o Steve Lohr o David Berreby o William
Poundstone o Dennis Overbye o Sara Lippincott o Albert-László Barabási
o David Gelernter o W. Daniel Hillis o Marti Hearst o Steven Pinker o
Lisa Randall o Gregory Benford o Allan Snyder o Mike Godwin o Dan
Sperber o Frank Tipler o Andrian Kreye o Eric S. Raymond o Brian Eno o
Antonio Damasio o Helena Cronin o Paul Ewald o Charles Simonyi o John
Rennie o Alun Anderson
[nytimes.gif]
CONNECTIONS
Finding the Universal Laws That Are There, Waiting . . .
By Edward Rothstein, January 10, 2004 [free registration required]
Nature abhors a vacuum. Gravitational force is inversely proportional
to the square of the distance between two objects. Over the course of
evolution, each species develops larger body sizes. If something can
go wrong, it will.
Such are some of nature's laws as handed down by Aristotle, Newton,
Edward Cope and Murphy. And regardless of their varying accuracy (and
seriousness), it takes an enormous amount of daring to posit them in
the first place. Think of it: asserting that what you observe here and
now is true for all times and places, that a pattern you perceive is
not just a coincidence but reveals a deep principle about how the
world is ordered.
If you say, for example, that whenever you have tried to create a
vacuum, matter has rushed in to fill it, you are making an
observation. But say that "nature abhors a vacuum" and you are
asserting something about the essence of things. Similarly, when
Newton discovered his law of gravitation, he was not simply accounting
for his observations. It has been shown that his crude instruments and
approximate measurements could never have justified the precise and
elegant conclusions. That is the power of natural law: the evidence
does not make the law plausible; the law makes the evidence plausible.
But what kind of natural laws can now be so confidently formulated,
disclosing a hidden order and forever bearing their creator's names?
We no longer even hold Newton's laws sacred; 20th-century physics
turned them into approximations. Cope, the 19th-century
paleontologist, created his law about growing species size based on
dinosaurs; the idea has now become somewhat quaint. Someday even an
heir to Capt. Edward Aloysius Murphy might have to modify the law he
based on his experience about things going awry in the United States
Air Force in the 1940's.
So now, into the breach comes John Brockman, the literary agent and
gadfly, whose online scientific salon, Edge.org, has become one of the
most interesting stopping places on the Web. He begins every year by
posing a question to his distinguished roster of authors and invited
guests. Last year he asked what sort of counsel each would offer
George W. Bush as the nation's top science adviser. This time the
"There is some bit of wisdom," Mr. Brockman proposes, "some rule of
nature, some lawlike pattern, either grand or small, that you've
noticed in the universe that might as well be named after you." What,
More than 150 responses totaling more than 20,000 words have been
posted so far at www.edge.org/q2004/q04_print.html. The respondents
form an international gathering of what Mr. Brockman has called the
"third culture" Û scientists and science-oriented intellectuals who
are, he believes, displacing traditional literary intellectuals in
importance. They include figures like the scientists Freeman Dyson and
Richard Dawkins, innovators and entrepreneurs like Ray Kurzweil and W.
Daniel Hillis, younger mavericks like Douglas Rushkoff and senior
mavericks like Stewart Brand, mathematicians, theoretical physicists,
computer scientists, psychologists, linguists and journalists....
Hartford Courant:
Edge.org Compiles Rules Of The Wise Observations Of Thinking People
January 9, 2004 By John Jurgensen, Courant Staff Writer [free
registration required]
Everything answers to the rule of law. Nature. Science. Society. All
of it obeys a set of codes...It's the thinker's challenge to put words
to these unwritten rules. Do so, and he or she may go down in history.
Like a Newton or, more recently, a Gordon Moore, who in 1965 coined
the most cited theory of the technological age, an observation on how
computers grow exponentially cheaper and more powerful... Recently,
John Brockman went looking for more laws.
..."It's interesting to sit back and watch this crowd move the
question in different directions that I hadn't intended," says
Brockman, who has been posting answers to the annual question online
since 1997... This year's results, published on edge.org, run the
gamut from brainy principles to homespun observations in the tradition
of Murphy's Law...If all this theorizing sounds a little high-flown,
it's not, says Brockman. The important questions of life aren't
restricted to an exclusive club - this just happens to be the
intellectual company Brockman keeps.
" They're not sitting around looking at their work in awe and wonder,"
he says. "They're looking at experiments and empirical results and
asking, Where do we go from here?'"
... As for choosing a favorite among the crop of submissions, Brockman
invokes a law of his own: "Nobody knows, and you can't find out."
Wall St. Journal:
SCIENCE JOURNAL By Sharon Begley, January 2 , 2004
Scientists Who Give Their Minds to Study, Can Give Names, Too
(Subscription Required)
Heisenberg has one, and so do Boyle and Maxwell: A scientific
principle, law or rule with their moniker attached.... It isn't every
day that a researcher discovers the uncertainty principle, an ideal
gas law, or the mathematical structure of electromagnetism. And ours
is the era of real-estate moguls, phone companies and others slapping
their name on every building, stadium and arena in sight.... So, John
Brockman, a New York literary agent, writer and impresario of the
online salon Edge, figures it is time for more scientists to get in on
the whole naming thing.... As a New Year's exercise, he asked scores
of leading thinkers in the natural and social sciences for "some bit
of wisdom, some rule of nature, some law-like pattern, either grand or
small, that you've noticed in the universe that might as well be named
after you."...The responses, to be posted soon on Mr. Brockman's Web
site www.edge.org, range from the whimsical to the somber, from
cosmology to neuroscience...You can find other proposed laws of nature
on the Edge Web site. Who knows? Maybe one or more might eventually
join Heisenberg in the nomenclature pantheon.
The Independent (UK)
A Week in Books: Core principles are needed in the muddled business of
books
By Boyd Tonkin, 02 January 2004
The literary agent John Brockman, who makes over significant
scientists into successful authors, has posted an intriguing question
on his Edge website. He seeks suggestions for contemporary "laws",
just as Boyle, Newton, Faraday and other pioneers gave their names to
the rules of the physical universe. (That eminent pair, Sod and
Murphy, soon followed suit.) Brockman advises his would-be legislators
to stick to the scientific disciplines, and you can find their
responses at www.edge.org.
______________________________________________________________________
______________________________________________________________________
Alun Anderson
Anderson's First Law (of the Experienced Science Journalist)
Science may be objective but scientists are not.
Anderson's Second Law (of the Experienced Science Journalist)
A scientist who can speak without jargon is either an idiot or a
genius.
Anderson's Third Law (on Subjectivity and Objectivity from the
Interface of Neuroscience and Computers)
The bigger the brain, the better the stories it fabricates for us.
Corollary
The more technology gives us the power to record and store everything,
the less it captures reality.
laws on subjectivity and objectivity from the interface of
Neuroscience and Computers
Anderson's Fourth Law (for ordinary folk)
Science can produce knowledge but it cannot produce wisdom.
Anderson's Fifth Law (Based on An Ancient Zen Saying to An Untutored
Monk Seeking Wisdom)
If you can tell the false from the true you are already a scientist.
John Rennie
Rennie's Law of Credibility
Scientists don't always know best about matters of science-but they're
more likely to be right than the critics who make that argument.
1st Corollary to the Law of Credibility
The first job of any scientific fraud is to persuade the public that
science is itself unscientific.
2nd Corollary to the Law of Credibility
Any iconoclast with a scientifically unorthodox view who reminds you
that Galileo was persecuted too...ain't Galileo.
Rennie's Law of Evolutionary Biology
The most important environmental influences on any organism are always
the other organisms around it.
Corollary to the Law of Evolutionary Biology
Species do not occupy ecological niches; they define them.
Charles Simonyi
Simonyi's Law of Guaranteed Evolution
Anything that can be done, could be done "meta".
______________________________________________________________________
Paul Ewald
Ewald's First Law
The defining characteristic of science--the one that gives sciences
its extraordinary explanatory power--is the objective use of evidence
to distinguish between alternative guesses.
Corollary 1
Most of religion is antithetical to science.
Corollary 2
Much of Western Medicine is antithetical to science.
.
Corollary 3
Quite a bit of Science is antithetical to science.
Ewald's Second Law
When the practice of medicine finally obtains a balanced perspective,
Medicine and Evolutionary Medicine will be one and the same.
______________________________________________________________________
Helena Cronin
Cronin's law of dual information storage
Adaptations stockpile information in environments as well as in genes.
The Hungarian mathematician Paul Erdos used to describe himself as a
"machine for turning coffee into theorems". In much the same way,
genes are machines for turning stars into a bird's compass;
carotenoids into males of dazzling beauty; smells into love-potions;
facial muscles into signals of friendship; a glance into uncertainty
of paternity; and oxygen, water, light, zinc, calcium and iron into
bears, beetles, bacteria or bluebells. More strictly, genes are
machines for turning stars into birds and thereby into more genes.
This reminds us that adaptations weld together two information-storage
systems. They build up a store of information in genes, meticulously
accumulated, elaborated and honed down evolutionary time. And, to
match that store, they also stockpile information in the environment.
For genes need resources to build and run organisms; and adaptations
furnish genes (or organisms) with the information to pluck those
resources from the environment. So stars and carotenoids and glances
need to be there generation after generation no less reliably than the
information carried by genes.
Thus genes and environments are not in opposition; not zero-sum; not
parallel but separate. Rather, they are designed to work in tandem.
Their interconnection is highly intricate, minutely structured; and it
becomes ever more so over evolutionary time.
And thus, without environments to provide resources, genes would not
be viable; and without genes to specify what constitutes an
environment, environments would not exist. So how could biology not be
an environmental issue? And, conversely, how could environments not
be--necessarily--a biological issue?
Cronin's law of adaptations and environments
What constitutes an organism's environment depends on the species'
What constitutes an organism's environment? The answer is that it is
the organism's adaptations that stake out which are the relevant
aspects of the world. An environment is not simply a given. It is the
typical characteristics of a species, its adaptations, that specify
what constitutes the environment for that species.
Think of it this way. Adaptations are keys to unlocking the world's
resources. They are the means by which organisms harness features of
the world for their own use, transforming them from part of the
indifferent world-out-there into the organism's own tailor-made,
species-specific environment, an environment brimming with materials
and information for the organism's own distinctive adaptive needs.
And so to understand how any species interacts with its environment,
we need to start by exploring that species' adaptations. Only through
adaptations was that environment constructed and only through
understanding adaptations can we reconstruct it.
And, similarly, within a sexually reproducing species, differences
between the sexes should be the default assumption. In particular, the
male's. On the contrary, if a rule-of-thumb default is needed, turn to
the female. After all, the 'little brown bird' is what the entire
species--males, females and juveniles--looks like before sexual
selection distorts her mate into a showy explosion of colour and song.
When it comes to environments, males perceive them as platforms for
status games. Females most certainly do not.
______________________________________________________________________
Antonio Damasio
Damasio's First Law
The body precedes the mind.
Damasio's Second Law
Emotions precede feelings.
Damasio's Third Law
Concepts precede words.
______________________________________________________________________
Brian Eno
Eno's First Law
Culture is everything we don't have to do
We have to eat, but we didn't have to invent Baked Alaskas and Beef
Wellington. We have to clothe ourselves, but we didn't have to invent
platform shoes and polka-dot bikinis. We have to communicate, but we
didn't have to invent sonnets and sonatas. Everything we do--beyond
simply keeping ourselves alive--we do because we like making and
experiencing art and culture.
Eno's Second Law
Science is the conversation about how the world is. Culture is the
conversation about how else the world could be, and how else we could
experience it.
Science wants to know what can be said about the world, what can be
predicted about it. Art likes to see which other worlds are possible,
to see how it would feel if it were this way instead of that way. As
such art can give us the practice and agility to think and experience
in new ways - preparing us for the new understandings of things that
science supplies.
______________________________________________________________________
Eric S. Raymond
Raymond's Law of Software
Given a sufficiently large number of eyeballs, all bugs are shallow.
Raymond's Second Law
Any sufficiently advanced system of magic would be indistinguishable
from a technology.
The first one is sometimes called "Raymond's Law" now, though I
originally called it "Linus's Law" when I formulated it. Second one.
Hmmm. Several people have since invented this one independently, but I
came up with it more than twenty years ago. It's a reply to Arthur C.
Clarke's Third Law, "Any sufficiently advanced technology is
indistinguishable from magic."
Raymond's Law of Consequences
The road to hell has often been paved with good intentions. Therefore,
evil is best recognized not by its motives but by its methods.
______________________________________________________________________
Andrian Kreye
Kreye's Law of Literalism
When devaluated information makes opinion an added value, the law of
literalism is permanently questioned, while remaining the last resort
of reason.
The inflation of available information has devaluated word and image
to mere content. The resulting perception fatigue is increasingly met
with the overused rhetorical tool of polarizing opinion. It's based on
an old trick used by street vendors. In the intellectual food court of
mass media, opinion appeals to reflexes just as the fried fat and
sugar smells of snackfood outlets activate age-old instincts of
hunting and gathering. In the average consumer opinion triggers an
illusion of enlightenment and understanding that ultimately clouds the
reason of literalism.
Literalism is freedom from credo, dogma and philosophical pessimism.
It's the process of finding reality driven by an optimistic faith in
its existence. It tries to transcend the limits of the word, by
permanently questioning any perception of reality.
Belief and ideology, the strongest purveyors of opinion, have long
known the language of science and reason. Creationists use secular
reasoning to demand that schools stop teaching the laws of evolution.
Right-wing radicals and religious fundamentalists of all creeds tone
down their world visions to fit into an opinionated consensus.
Economic and political forces use selective findings to present their
interests as fact.
Literalism can become an exhausting effort to defend the principles of
fact and reason in a polarized world. The complex and often boring
nature of factual reality makes it an unglamorous voice amid a choir
of sparkling witticisms and provocations. Devoid of the ecstasies and
spiritual cushioning of religion it denies age old longings. It can be
decried as heresy or simultaneously accused of treason by all sides.
It must sustain the insecurities brought on by the absence of ultimate
truth. Having been the gravitational center of enlightenment, it must
be defended as the last resort of reason.
______________________________________________________________________
Frank Tipler
Tipler's Law of Unilimited Progress
The laws of physics place no limits on progress, be it scientific,
economic, cultural, or intellectual. In fact, the laws of physics
require the knowledge and wealth possessed by intelligent beings in
the universe to increase without limit, this knowledge and wealth
becoming literally infinite by the the end of time. Intelligent life
forms must inevitably expand out from their planets of origin, and
convert the entire universe into a biosphere. If the laws of physics
be for us, who can be against us?
______________________________________________________________________
Dan Sperber
Sperber's Shudder
Thanks for the invitation, but this time I will pass: I am too much of
an anarchist: the only laws I like are scientific ones, and the idea
of some normative statement being labelled, even if just for fun,
"Sperber's Law", makes me shudder. Sorry! (But I will enjoy reading
the "laws" of other people).
______________________________________________________________________
Mike Godwin
Godwin 's Law
As an online discussion grows longer, the probability of a comparison
involving Nazis or Hitler approaches one.
______________________________________________________________________
Allan Snyder
Snyder's First Law
The most creative science is wrong, but the deception ultimately leads
to the benefit of mankind. Think Freud!
Snyder's Second Law
Everyone steals ideas from everyone else, but they do so
unconsciously. This has evolved for our very survival. It maximises
the innovative power of society.
______________________________________________________________________
Gregory Benford
Benford's Modified Clarke Law
Any technology that does not appear magical is insufficiently
______________________________________________________________________
Lisa Randall
Randall's First Law
Non-existence "theorems", which state something cannot happen, are
untrustworthy; they are only statements about what we have seen or
thought of so far. Non-existence theorems often appear in physics.
They are useful guidelines, but there are often loopholes. Sometimes
you find those loopholes by looking--and sometimes you find them by
accident through superficially unrelated research
Randall's Second Law
Studies confirming Baron-Cohen's First Law will always reflect the
bias of the investigator.
______________________________________________________________________
Steven Pinker
Pinker's First Law
Human intelligence is a product of analogy and combinatorics. Analogy
allows the mind to use a few innate ideas--space, force, essence,
goal--to understand more abstract domains. Combinatorics allows an a
finite set of simple ideas to give rise to an infinite set of complex
ones.
Pinker's Second Law
Human sociality is a product of conflicts and confluences of genetic
interests. Our relationships with our parents, siblings, spouses,
friends, trading partners, allies, rivals, and selves have different
forms because they instantiate different patterns of overlap of
ultimate interests. History, fiction, news, and gossip are endlessly
fascinating because the overlap is never 0% or 100%.
______________________________________________________________________
Marti Hearst
Hearst's Law
A public figure is often condemned for an action that is taken
unfairly out of context but nevertheless reflects, in a compelling and
encapsulated manner, an underlying truth about that person.
______________________________________________________________________
W. Daniel Hillis
Hillis' Law
The representation becomes the reality.
Or more precisely: Successful representations of reality become more
important than the reality they represent.
Examples:
Dollars become more important than gold.
The brand becomes more important than the company.
The painting becomes more important than the landscape.
The new medium (which begins as a representation of the old medium)
eclipses the old.
The prize becomes more important than the achievement.
The genes become more important than the organism.
______________________________________________________________________
David Gelernter
Gelernter's First Law
Computers make people stupid.
Gelernter'sSecond Law
One expert is worth a million intellectuals. (This law is
onlyapproximate.)
Gelernter's Third Law
Scientists know all the right answers and none of the right questions.
_________________________________________________________________
Albert-László Barabási
Barabási's Law of Programming
Program development ends when the program does what you expect it to
do--whether it is correct or not.
_________________________________________________________________
Sara Lippincott
Lippincott's Law
God is evolving. So if you're an atheist, you'd better hope that the
arrow of time only goes in one direction.
_________________________________________________________________
Dennis Overbye
Overbye's Law
"There's always a faster gun."
_________________________________________________________________
William Poundstone
Poundstone's First Law
Independent discoverers of great ideas emerge in proportion to the
time spent looking for them. The history of science is a fractal, with
co-discoverers emerging like crinkles in the Norwegian coastline.
Poundstone's Second Law
The fractal dimension of scientific discovery increases with time.
Where people once marveled at the simultaneous discovery of calculus,
we now marvel when a Nobel science prize goes to one person.
_________________________________________________________________
David Berreby
Berreby's First Law
Human kinds exist only in human minds.
Human differences and human similarities are infinite, therefore any
assortment of people can be grouped together according to a shared
trait or divided according to unshared traits. Our borders of race,
ethnie, nation, religion, class etc. are not, then, facts about the
world. They are facts about belief. We should look at minds, not
kinds, if we want to understand this phenomenon.
Berreby's Second Law
Science which seems to confirm human-kind beliefs is always welcome;
science that undermines human-kind belief is always unpopular.
To put it more cynically, if your work lets people believe there are
"Jewish genes'" (never mind that the same genes are found in
Palestinians) or that criminals have different kinds of brains from
regular people (never mind that regular people get arrested all the
time), or that your ancestors 5,000 years ago lived in the same neck
of the woods as you (never mind the whereabouts of all your other
ancestors), well then, good press will be yours. On the other hand, if
your work shows how thoroughly perceptions of race, ethnicity, and
other traits change with circumstances, well, good luck. Common sense
will defend itself against science.
_________________________________________________________________
Steve Lohr
Lohr's Law
The future is merely the past with a twist--and better tools.
Gerd Gigerenzer
Gigerenzer's Law of Indispensable Ignorance
The world cannot function without partially ignorant people.
The ideal of omniscience fuels the many disciplines and theories that
envision godlike humans. Much of cognitive science, and Homo
economicus as well, assume the superiority of a mind with complete,
veridical representations of the outside world that remain stable and
available throughout a lifetime. The Law of Indispensable Ignorance,
in contrast, says that complete information is neither realistic nor
generally desirable. What is desirable are partially (not totally)
ignorant people.
Justice is blindfolded; jurors are not supposed to know the criminal
record of the defendant; trial consultants hunt for "virgin minds"
anonymously under the veil of ignorance about the authors; trust in
experiments demands double-blind procedures; economic fairness
encourages sealed bids. The efficient market hypothesis implies that
knowledge of future stock prices is impossible, and the Greek skeptics
taught their students that they knew nothing.
When watching a pre-recorded football game, we do not want to know the
result in advance; knowledge would destroy suspense. The estimated 5
to 10% of children and their fathers who falsely believe that they are
related might not lead a happier life by becoming less ignorant;
knowledge can destroy families. And few of us would want to know the
day we will die; knowledge can destroy hope.
Zero-intelligence traders who submitted random bids and offers in
double auctions were as good as experts. Pedestrians who chose stocks
by mere name recognition outperformed market experts and the Fidelity
Growth Fund--and even more successfully when they were from abroad and
more ignorant of the stock names. Expert ball players made better
decisions about where to pass the ball when they had less time.
Recreational tennis players who had only heard of half of the
professional players in Wimbledon 2003 and simply bet that those they
had not heard of would lose predicted the outcomes of the matches
better than the official ATP-rankings and the seeding. Adam Smith's
invisible hand is a metaphor for how collective wisdom emerges from
the uninformed masses.
We can prove that situations exist in which a group does best by
following its most ignorant member rather than the consensus of their
informed majority, and we can prove that a heuristic that ignores all
information except for one reason will make better predictions than a
multiple regression with a dozen reasons. Mnemonists, who have
virtually unlimited memory, are swamped by details and find it
difficult to abstract and reason, while ordinary people's working
memory limitations maximize the ability to detect correlations in the
world. Limited memory facilitates acquisition of language, in infants
and computers alike; the more complex the species, the longer the
period of infancy.
Theories that respect the Law of Indispensable Ignorance incorporate a
more realistic picture of people as being partially ignorant.
Omniscience is dispensable.
_________________________________________________________________
John Markoff
Markoff's Law of Inversion
Technology once trickled down from supercomputers to PCs. Now new
computing technology comes to game machines first.
Corollary
The companies who make the fastest computers are the ones that make
things that go under Xmas trees.
_________________________________________________________________
Martin Rees
Rees's Law
As cosmological theories advance, they will draw more concepts from
biology.
The part of the universe astronomers can observe is probably only a
tiny part of the aftermath of 'our' big bang, which in turn may be one
of an infinity of 'bangs' in which the physics may be very different
from in ours. To analyse how our own cosmic habitat relates to this
ensemble, we'll need to draw on concepts from ecology and evolutionary
biology ('fitness landscapes', etc).
So we'll need biological ideas to understand the beginning. But
biology may control the far future too. In some 'universes' (ours
perhaps among them) life can eventually become pervasive and powerful
enough to renders the dynamics of the cosmic future as unpredictable
as that of an organism or mind.
_________________________________________________________________
Nicholas Humphrey
Humphrey's Law of the Efficacy of Prayer
In a dangerous world there will always be more people around whose
prayers for their own safety have been answered than those whose
prayers have not.
_________________________________________________________________
Yossi Vardi
Vardi's Law
Experts predictions are always correct.
[cnn.jpg]
1. A certain portion of all predictions made by experts will be
correct.
2. Human memory is short.
3. Make lot of forcasts, most of the people will remember the
correct ones.
4. A good hedge: make contradictory predictions with intervals
between them.
_________________________________________________________________
Art Kleiner
Kleiner's Law
Every organization always operates on behalf of the perceived needs
and priorities of some core group of key people. This purpose will
trump every other organizational loyalty, including those to
shareholders, employees, customers, and other constituents.
_________________________________________________________________
Mark Hurst
Hurst's Law
Any unbounded bitstream tends to irrelevance.
Bits are so easy to create, copy, and send that without some filtering
process, the worth of the entire bitstream decays
rapidly. A good example is the e-mail inbox. Many e-mail users have no
discipline about deleting or filtering their mail, and thus the bits
that flow in--spam and legimitate mail together--clutter the inbox to
an extent that the worth of the inbox overall tends to zero.
Stated another way, the worth of a bitstream is proportional to the
accuracy and usage of the filters and meta-bits applied to the
bitstream.
_________________________________________________________________
K. Eric Drexler
Drexler's First Law
Physical technology evolves toward limits set by physical law.
Drexler's Second Law
A technology approaching the limits set by physical law must build
with atomic precision.
_________________________________________________________________
Beatrice Golomb
Golomb 's Law
Everything in biology is more complicated than you think it is, even
taking into account Golomb's Law.
_________________________________________________________________
Clifford Pickover
Pickover 's Law of Mutating Conjectures
I am having difficulty formulating a law to give you. Through the
millennia, even the most brilliant minds rarely generated great and
will crumble after a time. Perhaps Edge is asking the wrong question.
Knowledge moves in an ever-expanding, upward-pointing funnel. From the
rim, we look down and see previous knowledge from a new perspective as
new theories are formed. Today's conjectures mutate, new theories
evolve, and yesterday's impossibilities become part of everyday life.
_________________________________________________________________
Howard Morgan
Morgan's First Law
To a first approximation, no deals close.
Morgan's Second Law
To a first approximation all appointments are canceled.
Morgan's Third Law
Events of probability zero happen--they are the ones that change the
world.
These laws are actually the engineering approximations to life.
_________________________________________________________________
Al Seckel
Seckel's First Law
Visual Perception is Essentially an Ambiguity Solving Process.
Most of us take vision for granted. After all, it comes to us so
easily. With normal vision we are able to navigate quickly and
efficiently through a visually rich three-dimensional world of light,
shading, texture, and color--a complex world in motion, with objects
of different sizes at differing distances. Looking about we have a
definite sense of the "real world".
In fact, our visual system is so successful at building an accurate
representation of the real world (our perception) that most of us do
not realize what a difficult task our brain is performing. Without
conscious thought, our visual system gathers and interprets complex
information, providing us with a seamless perception of our
environment. The complexities of how we perceive are cleverly
concealed by a successful visual system.
It might seem reasonable for us to assume that there is a one-to-one
mapping between the real world and what you perceive--that your visual
system "sees" the retinal image, in much the way that a digital camera
records what it "sees."
Although it seems like a useful analogy, there is no real comparison
between our visual system and a camera beyond a strictly surface
level. Furthermore, this comparison trivializes the accomplishments of
our visual system. This is because a camera records incoming
information, but our brain interprets incoming information.
Furthermore, it feels to us as if a photograph reproduces a
three-dimensional world, but it doesn't. It only suggests one. The
same visual system that interprets the world around us also interprets
the photograph to make it appear as a three-dimensional scene.
Our perceptions are not always perfect. Sometimes our brain will
interpret a static image on the retina in more than one way. A
skeleton cube, known as a Necker cube, is a classic example of a
single image that is interpreted in more than one way. If you fixate
on this cube for any length of time, it will spontaneously reverse in
depth, even though the image on the retina remains constant. Our brain
interprets this image differently because of conflicting depth cues.
The great 19th century German physicist and physiologist Hermann Von
Helmholtz first discovered the basic problem of perception over one
hundred years ago. He correctly reasoned that the visual information
from our world that is projected onto the back of the retina is
spatially ambiguous. Helmholtz reasoned that there can be an infinite
variety of shapes that can give rise to the same retinal image, as
long as they subtend the same visual angle to the eye.
However, the concept of visual ambiguity is far deeper than what
Helmholtz originally proposed, because it turns out that any one
aspect of visual information, such as brightness, color, motion, etc,
could have arisen from infinitely many different conditions. It is
very hard to appreciate this fact at first, because what we perceive
in a normal viewing environment is not at all ambiguous.
If all visual stimuli are inherently ambiguous, how does our
visual/perceptual system discard the infinite variety of possible
conditions to settle on the correct interpretation almost all the
time, and in such a quick and efficient manner? The problem basically
stated is, how does the visual system "retrieve" all of the visual
information about the 3D world from the very limited information
contained in the 2D retinal image? This is a basic and central
question of perception.
Studying the visual system only at one level will never result in a
full understanding of visual perception. Many of the underlying
mechanisms that mediate vision may be even "messier" than previously
thought, with cross-feedback from more than one level of visual
processing contributing to processing at another level. UCSD vision
scientist V.S. Ramachandran is correct when he believes that it is
time to "open the black box in order to study the responses of nerve
cells," but he is also probably right to promote his Utilitarian
Theory of Perception, which argues for a clever "bag of tricks" that
the human visual system has evolved over millions of years of
evolution to resolve the inherent ambiguities in the visual image.
Visual perception is largely an ambiguity-solving process.
The task of vision scientists, therefore, is to uncover these hidden
and underlying constraints, rather than to attribute to the visual
system a degree of simplicity that it simply does not possess.
Seckel's Second Law
Our Visual/Perceptual System is Highly Constrained.
Sometimes our perceptions are wrong. Often these errors have been
classified as illusions, dismissed by many as failures of the visual
system, quirky exceptions to normal vision.
If illusions are not failures of the visual system, then, what are
they? After all, we do categorize a number of different perceptual
experiences as "illusions". What makes them fundamentally different
than those we perceive as normal?
One difference is a noticeable split between your perception and
conception. With an illusion, your perception is fooled but your
conception is correct--you're seeing something wrong (your mis
perception), but you know it's wrong (your correct conception).
Initially, your conception may be fooled too, but at that point you
are unaware that you are encountering an illusion. It is only when
your conception is at odds with your perception that you are aware
that you have encountered an illusion.
Furthermore, in almost all pictorial illusions (where the meaning of
the image is not ambiguous), your perceptions will continue to be
fooled, even though your conception is fine, no matter how many times
you view the illusion. It does not matter how old you are, how smart
you are, how cultured you are, or how artistic you are, you will
continue to be fooled by these illusions over and over again. In fact,
you cannot "undo" your incorrect perceptions, even with extended
experiences, worldly knowledge, or training. It is more important for
your visual system to adhere to these constraints than to violate them
because it has encountered something unusual, inconsistent, or
highly constrained on how it interprets the world.
It is not my intention to cause the reader to think that visual
perception is unreliable and untrustworthy. This would be a mistake
as, for the most part, our perceptions of the world are veridical.
However, how we perceive the world is not a mirror image of reality,
but an actively and intelligently constructed one that allows us to
have the best chances for survival in a complicated environment.
_________________________________________________________________
Rudy Rucker
Rucker's Law of Morphogenesis
Most biological, social, and psychological systems are based on
interactions between an activator and an inhibitor. The patterns which
emerge depend upon the relative rates at which the activator and
inhibitor spread. Three main cases occur, depending on whether the
activator's diffusion rate is much less than, roughly equal to, or
greater than the rate at which the inhibition spreads. In these three
cases we observe, respectively, isolated patches like zebra stripes or
leopard spots, moving complex patterns like Belusov-Zhabontinsky
scrolls, or seething chaos. Applying this to the activator-inhibitor
patterns in the human brain, if you inhibit new thoughts, you are left
with a few highly stimulated patches: obsessions and fixed ideas. If
you manage to create new thought associations at about the same rate
you inhibit them, you develop creative complexity. And too high a rate
of activation leads to unproductive mania. Exercise: apply this notion
_________________________________________________________________
Delta Willis
Delta's Law
There are three sides to every story.
The Greek letter delta is a symbol for change in formulas. This
triangle can be taken personally to create a philosophy that can be
used as laws. For example, the 3 points of a triangle create a
possibility space for change. Two points in a debate provide nothing
more than a tyranny of dichotomies, whereas adding a third possibility
is always more interesting, and closer to the true complexity of life.
This rule of favoring 3s instead of 2s also works in any design to
please the eye, such as three pictures on a wall instead of two. A
couple become more interesting when they go beyond their own twosome
to create a third focal point, whether a child, a book or a business.
As Yale paleontologist Dolf Seilacher put it, Symmetry is boring. The
next time you are confronted with only two choices, create a third,
and see the possibility space expand.
_________________________________________________________________
Paul Steinhardt
Steinhardt's Law
Good science creates two challenging puzzles for each puzzle it
resolves.
Corollary 1
Contrary to some prognostications, science is not coming to an end.
Good science is growing every day.
Corollary 2
The Anthropic Principle does not resolve any puzzles andcreates no new
ones. Hence, ...
(Exercise left for the reader--fill in the blank. For hint, see
Steinhardt's Law.)
_________________________________________________________________
Eduard Punset
Punset's First Law
If fully conscious, don´t trust your brain.
The brain is very good at managing automated, unconscious processes
such as breathing, digesting or transpiring. But so far neuroscience
has not produced the slightest evidence that flipping a coin to decide
on important matters such as marriage, taking up a job, or traveling
is any worst than a formal, conscious, discriminatory decision made by
the brain. This should not surprise anybody. If we leave aside the
individual brain, and look at the evolution of social primates as a
whole, few would question that the history of civilization equals the
history of sucessive and cumulative automatization in fields such as
agriculture, industry or information. Why should it be different for
the individual brain?
Punset's Second Law
When in doubt, please ask Nature, not people. After all, this is the
This Law has to do with Darwinian Theory and Business Practice. There
is a huge amount of money to be made by just applying basic science to
ordinary business. In the Universe as a whole--according to
Physics--95% of reality is invisible. Most businessmen, however, are
convinced that 95% of what is going on in their firms, workshops or
projects can be seen at first sight. No wonder that it takes on
average over three failures for an innovation to succeed.
_________________________________________________________________
_________________________________________________________________
Terrence Sejnowski
Sejnowski's Law
For every important function that a cell needs to carry out Nature has
created a gadget to make it more efficient.
and often have hundereds of parts.)
_________________________________________________________________
Leo Chalupa
Chalupa's First Law
No matter how good or bad things are at any given point in time (in
science as in life), remember that "this too shall pass."
This is key for attaining longevity in this business...people who
"violate" or are unaware of this rule are doomed to failure. In other
words, it is vitally important how one deals with success and failure
in doing cutting edge science. Failure is the rule even among the most
successful working scientists (since 90% of grant application are
typically rejected and the top journals reject even a higher
percentage); and with respect to success, in all but a few exceptional
cases, institutional memory is exceedingly fleeting (i.e, yesterday's
superstars are unrecognized by today's grad students, postdocs, junior
faculty). So you've got to keep pitching if you want to stay in the
science game.
Chalupa's Second Law
Don't underestimate the importance of fashion in doing science.
Another key for success in science...if you're too far ahead of the
herd (with very few exception) you're not going to get funded by
NIH/NSF or published in the premier journals. This is in spite of the
fact that they claim that they fund innovative research. Anyone who
has spend as much time on grant review committees as I have will
recognize the power of this rule. In other words, there is a price to
pay for originality and every working scientist knows this is the
case.
_________________________________________________________________
Stuart Hameroff
Hameroff's Law
The sub-conscious mind is to consciousness what the quantum world is
to the classical world.
The vast majority of brain activity is non-conscious; consciousness is
"the tip of an iceberg" of neural activity. Yet the threshold for
transition from pre-, non-, or sub-conscious processes into conscious
awareness is unknown. The sub-conscious mind as revealed in dreams has
been described by Matte Blanco as a place where "paradox reigns, and
opposites merge to sameness". Reality is seemingly described by two
separate sets of laws. In our everyday classical world, Newton's laws
and Maxwell's equations accurately portray reality. However at small
scales, the bizarre laws of quantum mechanics rule: particles are
distorted in space and time (uncertainty), exist in multiple states or
locations simultaneously (superposition) and remain connected in
opposite states over distance (nonlocal entanglement). In the quantum
world "paradox reigns and opposites merge to sameness".
The boundary, or threshold between the quantum and classical worlds
(i.e. quantum state reduction, collapse of the wave function,
measurement, decoherence) remains mysterious. Early quantum theorists
attributed reduction/collapse to observation: "consciousness collapses
the wave function". Modern physics attributes reduction/collapse to
any interaction with the classical environment ("decoherence").
Neither solves the problem of isolated quantum superpositions which
are nonetheless useful in quantum computation.
In quantum computation, information may be represented as isolated
superpositions (e.g. as quantum bits--"qubits"--of both 1 AND 0) which
interact/compute by nonlocal entanglement, and eventually
reduce/collapse to classical solutions.
Based on a 1989 suggestion by Sir Roger Penrose, he and I have put
forth a specific model of consciousness involving quantum computation
in microtubules within the brain's neurons. Superpositions of multiple
possible pre-/sub-conscious perceptions or choices reach threshold for
self-collapse (by Roger's "objective reduction" due to properties of
fundamental spacetime geometry), and select/reduce to particular
classical perceptions or choices. Each reduction is a conscious event,
a series of which gives a "stream of consciousness".
The main scientific objection to our proposal has been that the brain
is too warm for quantum computation which in the technological realm
seems to require ultra cold temperatures to avoid thermal decoherence.
However recent evidence shows that quantum processes in biological
molecules are enhanced by increased temperature. Evolution has had
billion of years to solve the problem of decoherence. Consciousness
may be a particular form of quantum state reduction: a process on the
edge between the quantum and classical worlds.
_________________________________________________________________
Paul Ryan
Ryan's Law
Once the miind is freed to think positionally without orientation, a
logic of relationships naturally ensues.
_________________________________________________________________
Steven Levy
Levy's Law
The truth is always more interesting that your preconception of what
it might be.
In journalism, this means that the best practicioners should not have
the stories written out in their heads before they report them.
Preconceptions can blind you to the full, rich human reality that
awaits you when you actually listen to your subjects and approach the
material with an open mind. It wouldn't surprise me if the same tabula
rasa principle applies when scientists try to answer the big
questions.
_________________________________________________________________
Neil Gershenfeld
Gershenfeld's Law on Research
Experiments take pi times longer than planned (no matter how many
factors of pi you account for).
Gershenfeld's Law on Writing
Good [theses, papers, books] are never finished, just abandoned.
Gershenfeld's Goal
Function from form.
"Form follows function" implies that they're separable; the most
profound scientific and technological insights that I know follow from
abstracting logical functions from physical forms.
_________________________________________________________________
Gino Segre
Segre's First Law
Numbers are everything.
This is just a rephrasing of the Pythagorean credo, proclaimed 2500
years ago, that "All things are numbers". Science began with it, but
it's still worth remembering that measurements are at the base of all
science.
Segre's Second Law
Understand what the numbers mean.
One has to keep looking for a theory that will explain the numbers.
Our galaxy has a hundred billion stars and our brain has a hundred
billion neurons. Understanding our galaxy and our brain are great
challenges, but two different theories are required.
_________________________________________________________________
Henry Warwick
Warwick's First Law
Art takes you out of town, and gives you a destination. Science builds
the bus that takes you there.
destination, a wonderful place, a new way of looking at things, a deep
shift in your understanding of what it means to be human with a sense
of profundity and awe at the Creation, pointing toward a new and
better environment for living, smiling a new smile--all by altering
your consciousness in some useful and insightful way.
Cooking up the better paint or programming didn't make the better
paintmaker a better painter, or the better word processor-maker a
better writer, but the great painter required the skills of the better
paint makers and the great writer needs the tool of the trade. If we
are to go to these grand destinations, artists need the insights and
tools provided by science--the " bus" to take us there. And we need to
heed Art.
Warwick's Second Law
Art tells the jokes that science insists on explaining.
_________________________________________________________________
Simon Baron-Cohen
Baron-Cohen's Law of Sex differences in the Mind
In any random population, of those who score in the above-average
range on tests of empathizing, females will significantly outnumber
males. And of those who score in the above-average range on tests of
systemizing, males will significantly outnumber females.
Baron-Cohen's Law of Autism
What unites individuals on the autistic spectrum is impaired
empathizing in the presence of intact or even superior systemizing,
relative to non-autistic individuals of the same mental age.
_________________________________________________________________
Chritsine Finn
Finn's Law
Uncertainty is the final test of innovation.
That is, new concepts are tested best by a sudden faltering confidence
on the part of the innovator operating in an almost-liminal,
almost-sure intellectual state.
Does not the palpible quiver preceding the sudden rush of certainty
give that
final kick to real innovation?
This is especially good for interdisciplinary areas, where unusual
conjunctions
generally involve more maverick trip-wire than usual.
_________________________________________________________________
Leonard Susskind
Susskind's Rule of Thumb
My rule has to do with pardigm shifts--yes, I do believe in them. I've
been through a few myself. It is useful if you want to be the first on
your block to know that the shift has taken place. I formulated the
rule in 1974. I was visiting the Stanford Linear Accelerator Center
(SLAC) for a weeks to give a couple of seminars on particle physics.
The subject was QCD. It doesn't matter what this stands for. The point
is that it was a new theory of sub-nuclear particles and it was
absolutely clear that it was the right theory. There was no critical
experiment but the place was littered with smoking guns. Anway, at the
end of my first lecture I took a poll of the audience. "What
probability would you assign to the proposition 'QCD is the right
theory of hadrons.'?" My socks were knocked off by the answers. They
ranged from .01 percent to 5 percent. As I said, by this time it was a
clear no-brainer. The answer should have been close too 100 percent.
The next day I gave my second seminar and took another poll. "What are
you working on?" was the question. Answers: QCD, QCD, QCD, QCD,
QCD,........ Everyone was working on QCD. That's when I learned to ask
"What are you doing?" instead of "what do you think?"
I saw exacly the same phenomenon more recently when I was working on
black holes. This time it was after a string theory seminar, I think
in Santa Barbara. I asked the audience to vote whether they agreed
with me and Gerard 't Hooft or if they thought Hawkings ideas were
correct. This time I got a 50-50 response. By this time I knew what
was going on so I wasn't so surprised. Anyway I later asked if anyone
was working on Hawking's theory of information loss. Not a single hand
_________________________________________________________________
Sherry Turkle
Turkle's Law of Evocative Objects
Every technology has an instrumental side, what the technology does
for us and a subjective side, what the technology does to us, to our
ways of seeing the world, including to our ways of thinking about
ourselves.
So the Internet both facilitates communication and changes our sense
of identity, privacy, and sexual possibility; gene sequencing both
gives us new ways of diagnosing and treating disease and new ways of
thinking about human nature and human history. On an instrumental
level, interactive, "sociable" robotics offers new opportunities for
education, childcare, and eldercare; on a subjective level, it offers
new challenges to our view of human nature, and to our moral sense of
what kinds of creatures are deserving of relationship.
Turkle's Law of Human Vulnerability to An Active Gaze
If a creature, computational or biological, makes eye contact with a
person, tracks her gaze, and gestures with interest toward her, that
person will experience the creature as sentient, even capable of
understanding her inner state.
The human has evolved to anthropomorphize. We are on the brink of
creating machines so "sociable" in appearance that they will push our
evolutionary buttons to treat them as kindred. Yet they will not have
shared our human biological and social experience and will thus not
have our means of access to the meanings of moments in the human life
cycle: a child's first step, an adolescent's strut, a parent's pride.
Yet we will not be in complete control of our feelings for these
objects because our feelings will not be based on what they know or
understand, but on what we "experience" them as knowing, a very
different thing.
We don't know what people and animals are "really" thinking but grant
them a "species pass" in which we make assumptions about their inner
states. It is a social and moral contract. Contemporary technology has
put us close to the moment when we shall be called upon to make this
kind of contract (or some other kind) about creatures of our own
devising. We are called upon to answer the question: What kinds of
relationships are appropriate to have with a machine? Our answer will
not only affect the instrumental roles that we allow technology to
play but the way technology will co-create the human psyche and
sensibility of the future.
_________________________________________________________________
Steven Strogatz
Strogatz's First Law of Doing Math
When you're trying to prove something, it helps to know it's true.
Strogatz's Second Law of Doing Math
To figure out if something is true, check it on the computer. If the
machine agrees with your own calculations, you're probably right.
_________________________________________________________________
Judith Rich Harris
Harris's First Law
Good things go together. Miller's Iron Law of Iniquity--" in practice,
every good trait correlates positively with every other good
trait"--is true, and follows from Harris's First Law.
Harris's Second Law
Harris's Third Law
People think they know why good things go together, and why bad things
go together, but they are wrong.
_________________________________________________________________
Ivan Amato
Amato's First Law of Awe
Awe begins in the eye of the beholder.
Limited as it is, biology's homegrown sensory physiology is sufficient
in our case to ignite wonder and curiosity about just where it is we
find ourselves thrown, how we got there, and how we can even know
anything at all. Therein lies the beginning of science.
Amato's Second Law of Awe
Transcending our own sensory limitations with technological tools of
observation, a relentless theme of the history of science, enhances
the experience of awe itself because it expands the variety of
attributes of the universe that we can know about. Therein lies one of
the most underrated values of science.
(For example, we used to see the world in only a rainbow of colors.
Our tools have shown us that the rainbow is a mere sliver of
electromagnetic wavelengths sandwiched between an infinitude of
previously invisible ones.)
_________________________________________________________________
Rupert Sheldrake
Sheldrake's Principle
The "laws" of nature are more like habits.
Sheldrake's Reformulation of a Traditional Theory of Vision
Vision involves a movement of light into the eyes, changes in the
brain, and the outward projection of images to where they seem to be.
_________________________________________________________________
Dave Winer
Winer's Law of the Internet
Productive open work will only result in standards as long as the
parties involved strive to follow prior art in every way possible.
Gratuitous innovation is when the standardization process ends, and
usually that happens quickly.
Think about the process of arriving at a standard. Someone goes first
with something new. Assume it catches on and becomes popular. Because
the person did it in an open way, with no patents, or other barriers
to competitors using the technology, a second developer decides to do
the same thing. The innovator supports this, because he or she wants a
standard to develop. At that point the second person has the power to
decide how strong a standard it will be. If the new implementation
strives to work exactly as the original does, then it's more likely
the standard will be strong, and there will be a vibrant market around
it. But if the second party decides to use the concept but not be
technically compatible, it will be a weak standard.
One would assume that the second mover would make every effort to do
it exactly the same way as the first, but over the years, but this has
not been the case. As soon as a standard becomes popular, market
forces lead to multiple incompatible ways forward. Microsoft called
this Embrace & Extend, but all technology vendors are driven to break
standards. Standards can only go a short distance before forking
defeats the standardization process.
This is an extension to Postel's Law (the late Jon Postel was one of
the key players of the development of the Internet), which says you
should be liberal in what you accept and conservative in what you
send. It goes further by saying that we should all collectively be
conservative in what we send. This keeps the technology small and the
market approachable by developers of all sizes. The large companies
always try to make the technology complicated to reduce competition to
other organizations with large research and development budgets.
_________________________________________________________________
Izumi Aizu
Aizu's Fisrt Law
Using is believing.
As was the case for the Internet, or the PCs, unless you use it, you
cannot understand its real significance. To put it the other way
around, if and when you use it, it will prevail.
Instead of "seeing" from afar, you must use it to understand. So many
people denied the potential and the impact of the Net simply because
they never tried to use it.
Aizu's Second Law
What changes the world is communication, not information.
We are living in a world where we can exchange ideas and emotions
freely and inexpensively, the first time in the history. Information
piled up, or disseminated one way down, never makes people happy or
feel compelled to act that much, while communication, just a single
line or word from your friends or beloved, or even from a total
stranger, that catches your heart, often results in collective
actions.
_________________________________________________________________
Randlph Nesse, M.D.
Nesse's Laws for deciding when it is safe to use drugs to block
evolved protective responses.
Aversive responses, such as pain, fever, vomiting and panic, were
shaped by natural selection because they gave selective advantages in
the face of various dangers. Optimal decisions about when to use our
growing pharmacological powers to block these responses will require
signal-detection models of how defenses are regulated.
Nesse's First Law
An optimal mechanism to regulate an all-or-none defensive response
such as vomiting or panic will express the response whenever CD<
\sum(pH x CH w/o defense) -\sum(pH x CH w/defense). That is,
expressing a defense is worth it whenever the cost of the defense (CD)
is less than the estimated reduction in harm, based the probability
(pH) and cost of various harmful outcomes (CH) with and without the
expression of the defense. This means that optimal systems that
regulate inexpensive defenses against large somewhat unpredictable
potential harms will express many false alarms and that blocking these
unnecessary responses can (and does) greatly relieve human suffering.
Blocking responses yields a net benefit, however, only if we can
anticipate when a normal response is likely to be essential to prevent
catastrophe.
Nesse's Second Law
An optimal mechanism to regulate a continuously expressed defense,
such as fever or pain, will increase the defensive response up to the
point where the sum of CH and CD is minimized. At this point the
marginal increase in the cost of the defense becomes greater than the
marginal decrease in harm. This helps to explain why so many defenses,
such as those involved in inflammation and the immune responses, so
often seem excessive.
Many will recognize this analysis as a less grand and somewhat more
practical variation on Pascal's Wager. So far, however, few in the
pharmaceutical industry seem to recognize the importance of routinely
assessing the effects of new drugs on normal defensive responses.
_________________________________________________________________
Robert Sapolsky
Sapolsky's Three Laws for Doing Science
Sapolsky's First Law
Think logically, but orthogonally.
Sapolsky's Second Law
It's okay to think about nonsense, as long as you don't believe in it.
Sapolsky's Third Law
Often, the biggest impediment to scientific progress is not what we
don't know, but what we know.
_________________________________________________________________
Gerald Holton
Holton's First Law
The turning points in individual and national life are most probably
guided by probabilism. (Examples: You are one of about a billion
possible yous, since only one spematozoon [or sometimes two] make it
to the ovum, out of about a billion different competitors, none the
same. Or on the national/ international scale, the availability of a
Churchill in 1940.)
The Second Law
The probability of a right answer or a beneficent outcome is usually
much smaller than that of the wrong or malignant ones. ( This is not
pessimism, but realism--an amplified analogue of the Law of Entropy.)
The Third Law
In the limit of small numbers, the previous two Laws may not
rigorously apply. Therefore if you need only one parking place when
driving your car, look for one first right where you want to go.
_________________________________________________________________
Niels Diffrient
Diffrient's Law
The improvements derived from technological advances have an equal and
opposite effect on culture and the environment magnified by time and
scale.
_________________________________________________________________
Stuart Kauffman
The biosphere advances, on average, at the maximum rate it can sustain
The adjacent possible, for a chemical reaction graph, is the set of
novel molecules that can be created out of those existing now. The
history of life.The issue is, are there laws that govern this advance?
And so too for technology. I'm very unsure about my candidate law, but
at least it points to the reality that we do advance into the adjacent
possible and perhaps some law governs how we do so.
_________________________________________________________________
Jordan Pollack
Pollack's Law
Progress requires the Pareto Optimization of Competitiveness and
Informativeness
The simple idea that Nature is "Red in Tooth and Claw" lends a
religious fervor to those promoting Competition as the right
organizing principle for open-ended innovation, e.g. in Laissez Faire
Capitalism, government procurement, Social Darwinism, personnel
review, and even high-stakes educational testing.
Through the use of mathematical and computer models of learning, we
discovered that competition between learning agents does not lead to
winner-take-all monopolies, and oligarchic groups who collude to block
progress. Unfortunately, cooperation (collaborative learning,
altruism) fails as well, leading to weak systems easy to invade or
corrupt.
The exciting new "law" is that progress can be sustained among
self-interested agents when both competitiveness and informativeness
are rewarded. A chess master who wins every game like one who loses
every game - provides no information on the strengths and weaknesses
of other agents, while an informative agent, like a teacher,
contributes opportunity and motivation for further progress. We
predict that this law will be found in Nature, and will have
ramifications for building new learning organizations.
The Pollack
A measurement of innovation rate.
There is no measure of the rate at which processes like art,
evolution, companies, and computer programs innovate.
Consider a black box that takes in energy and produces bit-strings.
The complexity of a bit-string is not simply its length, because a
long string of all 1's or all 0's is quite simple. Kolmogorov measures
complexity by the size of the smallest program listing that can
generate a string, and Bennet's Logical Depth also accounts for the
cost of running the program. But these fail on the Mandelbrot Set, a
very beautiful set of patterns arising from a one-line program
listing. What of life itself, the result of a simple non-equilibrium
chemical process baking for quite a long time? Different algorithmic
processes (including fractals, natural evolution, and the human mind)
"create" by operating as a "Platonic Scoop," instantiating "ideals"
into physical arrangements or memory states.
So to measure innovation rate (in POLLACKS) we divide the P=Product
novelty (assigned by an observer with memory) by the L=program listing
size and the C= Cost of runtime/space/energy.
Platonic Density = P / LC
Pollack's Law of Robotics
Start over with Pinball Machines.
Moore's law existed before computers; it is just economics of scale
with zero labor. If enough demand can justify capital investment in
fully automated factories, then the price of a good approaches the
cost of its raw materials, energy dissipated, and (patent/copyright)
monopoly tax. Everyone knows Moore's law has lead to ultra-small-cheap
integrated circuits. But why don't we have ultra-small-cheap
mechanical parts?
Pollack's law of Robotics states that we won't get a Moore's law for
Machine, and bootstrap the manufacture of general purpose integrated
mechatronics, reducing scale from macro through mesa and MEMS. Leaping
to Nano is likely to fail.
_________________________________________________________________
Dylan Evans
Evans' laws of the completeness of good old fashioned AI.
Evans' First Law
For every intelligent agent, there is a Turing-machine that provides
an exhaustive description of its mind.
Evans' Second Law
When the Turing-machine that describes the mind of intelligent agent
has been specified, there is nothing more to say about that mind,
apart from how it is implemented in hardware.
_________________________________________________________________
Kai Krause
Kai's Existential Dilemma
I think....
there....
4a.m.
Kai's Exactness Dilemma
93.8127 % of all statistics are useless.
Kai's Example Dilemma
A good analogy is like a diagonal frog.
_________________________________________________________________
Bly's First Law
Science is culture.
Bly's Second Law
High public interest in science without growing public understanding
of science is worse than low public interest in science.
_________________________________________________________________
Ray Kurzweil
Kurzweil's Law (aka "The Law of Accelerating Returns")
Evolution applies positive feedback in that the more capable
methods resulting from one stage of evolutionary progress are used
to create the next stage. Each epoch of evolution has progressed
more rapidly by building on the products of the previous stage.
Evolution works through indirection: evolution created humans,
humans created technology, humans are now working with increasingly
advanced technology to create new generations of technology. As a
result, the rate of progress of an evolutionary process increases
exponentially over time.
Over time, the "order" of the information embedded in the
evolutionary process (i.e., the measure of how well the information
fits a purpose, which in evolution is survival) increases.
A comment on the nature of order.
The concept of the "order" of information is important here, as it is
not the same as the opposite of disorder. If disorder represents a
random sequence of events, then the opposite of disorder should imply
"not random." Information is a sequence of data that is meaningful in
a process, such as the DNA code of an organism, or the bits in a
computer program. Noise, on the other hand, is a random sequence.
Neither noise nor information is predictable. Noise is inherently
unpredictable, but carries no information. Information, however, is
also unpredictable. If we can predict future data from past data, then
that future data stops being information. We might consider an
alternating pattern ("0101010. . . .") to be orderly, but it carries
no information (beyond the first couple of bits).
Thus orderliness does not constitute order because order requires
information. However, order goes beyond mere information. A recording
of radiation levels from space represents information, but if we
double the size of this data file, we have increased the amount of
data, but we have not achieved a deeper level of order.
Order is information that fits a purpose. The measure of order is the
measure of how well the information fits the purpose. In the evolution
of life-forms, the purpose is to survive. In an evolutionary algorithm
(a computer program that simulates evolution to solve a problem)
applied to, say, investing in the stock market, the purpose is to make
better fit. A superior solution for a purpose may very well involve
less data.
The concept of "complexity" is often used to describe the nature of
the information created by an evolutionary process. Complexity is a
close fit to the concept of order that I am describing, but is also
not sufficient. Sometimes, a deeper order--a better fit to a
purpose--is achieved through simplification rather than further
increases in complexity. For example, a new theory that ties together
apparently disparate ideas into one broader more coherent theory
reduces complexity but nonetheless may increase the "order for a
purpose" that I am describing. Indeed, achieving simpler theories is a
driving force in science. Evolution has shown, however, that the
general trend towards greater order does generally result in greater
complexity.
Thus improving a solution to a problem--which may increase or decrease
complexity--increases order. Now that just leaves the issue of
defining the problem. Indeed, the key to an evolution algorithm (and
to biological and technological evolution) is exactly this: defining
the problem.
We may note that this aspect of "Kurzweil's Law" (the law of
accelerating returns) appears to contradict the Second Law of
Thermodynamics, which implies that entropy (randomness in a closed
system) cannot decrease, and, therefore, generally increases. However,
the law of accelerating returns pertains to evolution, and evolution
is not a closed system. It takes place amidst great chaos, and indeed
depends on the disorder in its midst, from which it draws its options
for diversity. And from these options, an evolutionary process
continually prunes its choices to create ever greater order. Even a
crisis, such as the periodic large asteroids that have crashed into
the Earth, although increasing chaos temporarily, end up
increasing--deepening--the order created by an evolutionary process.
o A primary reason that evolution--of life-forms or of
technology--speeds up is that it builds on its own increasing
order, with ever more sophisticated means of recording and
manipulating information. Innovations created by evolution
encourage and enable faster evolution. In the case of the evolution
of life forms, the most notable early example is DNA, which
provides a recorded and protected transcription of life's design
from which to launch further experiments. In the case of the
evolution of technology, ever improving human methods of recording
information have fostered further technology. The first computers
were designed on paper and assembled by hand. Today, they are
designed on computer workstations with the computers themselves
working out many details of the next generation's design, and are
then produced in fully-automated factories with human guidance but
limited direct intervention.
o The evolutionary process of technology seeks to improve
capabilities in an exponential fashion. Innovators seek to improve
things by multiples. Innovation is multiplicative, not additive.
Technology, like any evolutionary process, builds on itself. This
aspect will continue to accelerate when the technology itself takes
full control of its own progression.
o We can thus conclude the following with regard to the evolution
of life-forms, and of technology: the law of accelerating returns
as applied to an evolutionary process: An evolutionary process is
not a closed system; therefore, evolution draws upon the chaos in
the larger system in which it takes place for its options for
diversity; and evolution builds on its own increasing order.
Therefore, in an evolutionary process, order increases
exponentially.
o A correlate of the above observation is that the "returns" of an
evolutionary process (e.g., the speed, cost-effectiveness, or
overall "power" of a process) increase exponentially over time. We
see this in Moore's law, in which each new generation of computer
chip (now spaced about two years apart) provides twice as many
components, each of which operates substantially faster (because of
the smaller distances required for the electrons to travel, and
other innovations). This exponential growth in the power and
price-performance of information-based technologies--now roughly
doubling every year--is not limited to computers, but is true for a
wide range of technologies, measured many different ways.
o In another positive feedback loop, as a particular evolutionary
process (e.g., computation) becomes more effective (e.g., cost
effective), greater resources are deployed towards the further
progress of that process. This results in a second level of
exponential growth (i.e., the rate of exponential growth itself
grows exponentially). For example, it took three years to double
the price-performance of computation at the beginning of the
twentieth century, two years around 1950, and is now doubling about
once a year. Not only is each chip doubling in power each year for
the same unit cost, but the number of chips being manufactured is
growing exponentially.
o Biological evolution is one such evolutionary process. Indeed it
is the quintessential evolutionary process. It took place in a
completely open system (as opposed to the artificial constraints in
an evolutionary algorithm). Thus many levels of the system evolved
at the same time.
o Technological evolution is another such evolutionary process.
Indeed, the emergence of the first technology-creating species
resulted in the new evolutionary process of technology. Therefore,
technological evolution is an outgrowth of--and a continuation
of--biological evolution. Early stages of humanoid created
technology were barely faster than the biological evolution that
created our species. Homo sapiens evolved in a few hundred thousand
years. Early stages of technology--the wheel, fire, stone
tools--took tens of thousands of years to evolve and be widely
deployed. A thousand years ago, a paradigm shift such as the
printing press, took on the order of a century to be widely
deployed. Today, major paradigm shifts, such as cell phones and the
world wide web were widely adopted in only a few years time.
o A specific paradigm (a method or approach to solving a problem,
e.g., shrinking transistors on an integrated circuit as an approach
to making more powerful computers) provides exponential growth
until the method exhausts its potential. When this happens, a
paradigm shift (a fundamental change in the approach) occurs, which
enables exponential growth to continue.
o Each paradigm follows an "S-curve," which consists of slow growth
(the early phase of exponential growth), followed by rapid growth
(the late, explosive phase of exponential growth), followed by a
leveling off as the particular paradigm matures.
o During this third or maturing phase in the life cycle of a
dollars are invested to create the next paradigm. We can see this
in the enormous investments being made today in the next computing
that we still have at least a decade left for the paradigm of
shrinking transistors on a flat integrated circuit using
photolithography (Moore's Law). Generally, by the time a paradigm
approaches its asymptote (limit) in price-performance, the next
example, engineers were shrinking vacuum tubes in the 1950s to
provide greater price-performance for computers, and reached a
point where it was no longer feasible to shrink tubes and maintain
achieved a strong niche market in portable radios.
o When a paradigm shift occurs for a particular type of technology,
the process begins a new S-curve.
o Thus the acceleration of the overall evolutionary process
proceeds as a sequence of S-curves, and the overall exponential
growth consists of this cascade of S-curves.
o The resources underlying the exponential growth of an
evolutionary process are relatively unbounded.
o One resource is the (ever-growing) order of the evolutionary
process itself. Each stage of evolution provides more powerful
tools for the next. In biological evolution, the advent of DNA
allowed more powerful and faster evolutionary "experiments." Later,
setting the "designs" of animal body plans during the Cambrian
explosion allowed rapid evolutionary development of other body
organs, such as the brain. Or to take a more recent example, the
advent of computer-assisted design tools allows rapid development
of the next generation of computers.
o The other required resource is the "chaos" of the environment in
which the evolutionary process takes place and which provides the
options for further diversity. In biological evolution, diversity
enters the process in the form of mutations and ever- changing
environmental conditions. In technological evolution, human
ingenuity combined with ever-changing market conditions keep the
process of innovation going.
o If we apply these principles at the highest level of evolution on
Earth, the first step, the creation of cells, introduced the
paradigm of biology. The subsequent emergence of DNA provided a
digital method to record the results of evolutionary experiments.
Then, the evolution of a species that combined rational thought
with an opposable appendage (the thumb) caused a fundamental
paradigm shift from biology to technology. The upcoming primary
paradigm shift will be from biological thinking to a hybrid
combining biological and nonbiological thinking. This hybrid will
include "biologically inspired" processes resulting from the
reverse engineering of biological brains.
o If we examine the timing of these steps, we see that the process
has continuously accelerated. The evolution of life forms required
billions of years for the first steps (e.g., primitive cells);
later on progress accelerated. During the Cambrian explosion, major
paradigm shifts took only tens of millions of years. Later on,
Humanoids developed over a period of millions of years, and Homo
sapiens over a period of only hundreds of thousands of years.
o With the advent of a technology-creating species, the exponential
pace became too fast for evolution through DNA-guided protein
synthesis and moved on to human-created technology. Technology goes
beyond mere tool making; it is a process of creating ever more
powerful technology using the tools from the previous round of
innovation, and is, thereby, an evolutionary process. As I noted,
the first technological took tens of thousands of years. For people
living in this era, there was little noticeable technological
change in even a thousand years. By 1000 AD, progress was much
faster and a paradigm shift required only a century or two. In the
nineteenth century, we saw more technological change than in the
nine centuries preceding it. Then in the first twenty years of the
twentieth century, we saw more advancement than in all of the
nineteenth century. Now, paradigm shifts occur in only a few years
time.
o The paradigm shift rate (i.e., the overall rate of technical
progress) is currently doubling (approximately) every decade; that
is, paradigm shift times are halving every decade (and the rate of
acceleration is itself growing exponentially). So, the
technological progress in the twenty-first century will be
equivalent to what would require (in the linear view) on the order
of 200 centuries. In contrast, the twentieth century saw only about
20 years of progress (again at today's rate of progress) since we
have been speeding up to current rates. So the twenty-first century
will see about a thousand times greater technological change than
its predecessor.
_________________________________________________________________
Jamshed Bharucha
Bharucha's Law
To understand what people are thinking and feeling, look beyond what
they say. Language does not capture the full range and grain of
thought and experience, and its unique power enables us as easily to
mask our thoughts and feelings as it does to express them.
_________________________________________________________________
Samuel Barondes
Barondes' First Law
Science abhors contradictions; scientist's minds are replete with
them.
Barondes' Second Law
Self-understanding is inherently inaccurate because most of our
knowledge comes from specific behavioral experiences that are often
inconsistent; and our mechanisms of learning are designed to store
memories whether or or not their implications are formally
_________________________________________________________________
W. Brian Arthur
Arthur's First Law
High-tech markets are dominated 70-80% by a single player--product,
company, or country.
The reason: Such markets are subject to increasing returns or
self-reinforcing mechanisms. Therefore an initial advantage--often
market domination. (Absent government intervention, of course).
Arthur's Second Law
As technology advances it becomes ever more biological.
We are leaving an age of mechanistic, fixed-design technologies, and
entering an age of metabolic, self-reorganizing technologies. In this
sense, as technology becomes more advanced it becomes more
organic--therefore more "biological." Further, as biological
mechanisms at the cellular and DNA levels become better understood,
they become harnessed and co-opted as technologies. In this century,
biology and technology will therefore intertwine.
Arthur's Third Law
The modularization of technologies increases with the extent of the
market.
Just as it pays to create a specialized worker if there is sufficient
volume of throughput to occupy that specialty, it pays to create a
standard prefabricated assembly, or module, if its function recurs in
many instances. Modularity therefore is to a technological economy
what the division of labor is to a manufacturing one--it increases as
the economy expands.
_________________________________________________________________
Daniel C. Dennett
is an extension of Schank's Law
On any important topic, we tend to have a dim idea of what we hope to
be true, and when an author writes the words we want to read, we tend
to fall for it, no matter how shoddy the arguments. Needy readers have
an asymptote at illiteracy; if a text doesn't say the one thing they
need to read, it might as well be in a foreign language. To be
open-minded, you have to recognize, and counteract, your own doxastic
hungers.
_________________________________________________________________
Matt Ridley
Ridley's First Law
Science is the discovery of ignorance. It is not a catalog of facts.
Ridley's Second Law
Experience affects an organism largely by switching genes on and off.
(Nurture works through nature.)
Ridley's Third Law
Neither the number of base pairs nor the number of genes in an
organism's genome bears much if any relation to that organism's size
or complexity.
_________________________________________________________________
Haim Harari
Harari's Law of Science Eucation
The faster Science and Technology advance--the more important it is to
teach and to learn the basics of Math and Science and the less
important it is to teach and to learn the latest developments.
Harari's Law of Particle Physics
The electron, its replicas (muon and tau), the quarks and the
neutrinos are all composed of the same set of more fundamental
objects, which will become the newly accepted basic building blocks of
all of nature.
Harari's Law of Scientific Fads and Bandwagons
Every scientific discovery is first made by one person or by a few
people. At the time of the discovery, they are the only ones aware of
it. It follows logically that democratic votes, public opinion polls,
majority views of scientists and scientific fads do not necessarily
represent scientific truth. Only correct experimental results do.
_________________________________________________________________
George Lakoff
Lakoff's First Law
Frames trump facts.
All of our concepts are organized into conceptual structures called
"frames" (which may include images and metaphors) and all words are
defined relative to those frames. Conventional frames are pretty much
fixed in the neural structures of our brains. In order for a fact to
be comprehended, it must fit the relevant frames. If the facts
contradict the frames, the frames, being fixed in the brain, will be
kept and the facts ignored.
We see this in politics every day. Consider the expression "tax
relief" which the White House introduced into common use on the day of
George W. Bush's inauguration. A "relief" frame has an affliction, an
afflicted party, a reliever who removes the affliction and is thereby
a hero, and in the frame anyone who tries to stop the reliever from
administering the relief is a bad guy, a villain. "Tax relief" imposes
the additional metaphor that Taxation Is an Affliction, with the
entailments that the president is a hero for attempting to remove this
affliction and the Democrats are bad guys for opposing him. This frame
trumps many facts: Most people wind up paying more in local taxes,
payments for services cut, and debt servicing as a result of the
Bush's tax cuts.
There is of course another way to think about taxes: Taxes are what
you pay to live in America--to have democracy, opportunity, government
services, and the vast infrastructure build by previous taxpayers--the
highways, the internet, the schools, scientific research, the court
system, etc. Taxes are membership fees used to maintain and expand
services and the infrastructure. But however true this may be, it is
not yet an established frame inscribed in the synapses of our brains.
This has an important consequence. Political liberals have inherited
an assumption from the Enlightenment, that The facts will set us free,
that if the public is just given the facts, they will, being rational
beings, reach the right conclusion. It is simply false. It violates
Lakoff's Law.
Lakoff's Second Law
Voters vote their identities, not their self-interest.
Because of the way they frame the world, voters vote in a way that
best accords with their identities and not in accord with their
self-interest. That is why it is of no use for Democrats to keep
pointing out that Bush's tax cuts go to the top 1 percent, not to most
voters. If they identify with Bush because they share his culture and
his world view, they will vote against their self-interest.
We saw this in California in the recall election, when, for example,
union members overwhelming favored Gray Davis' policies as being
better for them, yet voted for Schwartzenegger.
_________________________________________________________________
Edward O. Laumann
Laumann's First Proposition
Moderation in levels of partnered sex activity is the mode for the
bulk of humankind and is consistent with high levels of subjective
well-being.
Laumann's Second Proposition
Low levels of subjective sexual well-being is associated with poor
physical, emotional, and mental health.
These propositions (they are empirical associations and not
established as causal) are based on my extensive international work on
human sexuality. They are based on surveys I have conducted in the
United States and China as well as the Pfizer-funded Global Survey of
Sexual Attitudes and Behavior (N = 27,500) which interviewed equal
numbers of men and women 40 to 80 years old in 29 countries world
wide. The real question is the nature of the causal link between these
variables.
_________________________________________________________________
Anton Zeilinger
Zeilinger's Fundamental Law
There is no Fundamental Law.
Zeilinger's Law on Reality, Space and Time
Information is the most Fundamental Concept, it's all we have.
_________________________________________________________________
Nancy Etcoff
Etcoff's Law
Be wary of scientific dualisms.
Approach them with caution, the way demolition experts regard bombs,
likely to explode, in this case into unproductive argument and the
obscuring of truth. "Opposing forces" are the scientific version of
the original dualism--good vs evil and darkness vs. light. Instead, of
acting in opposition, in nature two forces are likely to dependent,
interactive and interwoven; sometimes they are merely two names for
the same thing.
For example:
Brain vs Mind
Mind vs Body
Emotion vs Reason
Nature vs Nurture
Us vs Them
Seek unity.
Remember always that it is easy to be in possession of some facts,
extraordinarily difficult to know the truth.
_________________________________________________________________
Lee Smolin
Smolin's First Law
Genuine advances are rarely made by accident; in fact, the outcome of
a scientific investigation is usually less dramatic than originally
hoped for. Therefore, if you want to do something really significant
in science, you must aim high and you must take genuine risks.
Smolin's Second Law
In every period and every community there is something that everybody
believes, but cannot justify. If you want to understand anything, you
have to start by ignoring what everyone believes, and thinking for
yourself.
This was advice given to me by my father when I was a child. Feynman
said something very similar: "Science is the organized skepticism in
the reliability of expert opinion."
Smolin's Third Law
Time does exist.
Smolin's Zeroth Law
A measure of our ignorance about nature is the extent to which our
theories depend on background structures, which are entities necessary
to define the quantities in the theory, that do not themselves refer
to anything which evolves dynamically in time. Our understanding can
always be deepened by bringing such fixed, background structures into
the domain of dynamical law. By doing so, we convert absolute
properties, defined with respect to background structures, into
relational properties, defined in terms of relationships among
dynamical degrees of freedom.
_________________________________________________________________
Mark Mirsky
Mirsky's Law
Imagination precedes reality.
To imagine the universe is to fear it, even as one feels the power and
pleasure of trying to find its furthest boundaries. To meet that fear
one has to seek consolation whether in scientific theory or intuitive
vision.
As a corollary to that, the return of past time in the present, as
death comes steadily closer, if not unique to the human mind, is
certainly one of the consolations of consciousness, and of the shadow
realm of dream. If there is hope it is in our ability as men and women
to imagine ourselves not only in other worlds but as an "other," as an
opposite. Robert Musil, Proust, Kafka, Shakespeare, Dante Alighieri
together with the anonymous scribes of the religious epics, Gilgamesh,
the Old Testament, were uncanny in their ability to imagine in this
way.
Imagination precedes what we call reality. I would propose this as a
law of daily life and suspect that it plays a large part in our
evolution. Trying to preserve and recreate what was best in my past
and the past of distant ancestors is part of what keeps me balanced
before a future in which I want to hope.
To imagine is not just to exist, but to prolong existence. At the last
moment Spinoza could not surrender the idea that somehow memory of
what had happened would not be lost in the vastness of the universe.
Spinoza needed that consolation. Whether it does or not, we need to
believe that memory persists, and that we are capable of influencing
just what memory will be valued and given predominance.
_________________________________________________________________
David Buss
Buss's Laws of Human Mating
Buss's Third Law of Human Mating
For every mating adaptation in one sex, there exists at least one
co-evolved adaptation in the other sex designed to manipulate and
exploit it.
Buss's Fourth Law of Human Mating
For every co-evolved exploitative mating adaptation, there exists at
least one co-co-evolved defensive adaptation designed to circumvent
being manipulated and exploited.
Buss's Seventh Law of Human Mating
Never reveal your first two laws of mating, lest they be used to
manipulate and exploit you.
_________________________________________________________________
Eberhard Zangger
Zangger's First Law
Most scientific breakthroughs are nothing else than the discovery of
the obvious.
Zangger's Second Law
Truly great science is always ahead of its time.
Although there seems to be a slight contradiction in my laws,
historical evidence proves them right:
o The Hungarian surgeon Ignaz Semmelweiss in 1847 reduced the death
rate in his hospital from twelve to two percent, simply by washing
hands between operations -- a concept that today would be advocated
by a four year old child. When Semmelweiss urged his colleagues to
introduce hygiene to the operating rooms, they had him committed to
a mental hospital where he eventually died.
o The German meteorologist Alfred Wegener discovered in 1913 what
every ten year old looking at a globe will notice immediately: That
the Atlantic coasts of the African and South American continents
have matching contours and thus may have been locked together some
time ago. The experts needed sixty more years to comprehend the
concept.
o When Louis Pasteur stated that bacteria could cause disease,
colleagues treated the idea as "an absurd fantasy'!
o The theories of the Austrian psychiatrist Sigmund Freud were
called "a case for the police" during a neurologists' congress in
Hamburg in 1910.
o Lord Kelvin, President of the Royal Society, only eight years
before Orville and Wilbur Wright left the ground in an aeroplane,
remarked: "Machines that are heavier than air will never be able to
fly!"
o German physicists Erwin Schrödinger's PhD thesis, in which he
first introduced his famous equation, was initially rejected.
o When the Spanish nobleman de Satuola discovered the Late Ice Age
painted cave at Altamira, established scholars described him as a
forger and a cheat.
o The decipherment of Egyptian hieroglyphs by Jean Francois
Champollion in 1822 was still rejected by scholar twenty years
after his death.
o And when Johann Karl Fuhlrott discovered the bones of a
Neanderthal in a cave near Duesseldorf in 1856, the president of
the German Society of Anthropology considered it a bow-legged,
Mongolian Cossack with rickets, who had been lucky enough to
survive multiple head injuries, but who, during a campaign by
Russian forces against France in 1814, had been wounded, and (stark
naked) had crawled into a cave, where he died.
o Heinrich Schliemann's excavation of Bronze Age Mycenae and Tiryns
in Greece was considered by English archaeologists in The Times' as
the remains of some obscure barbarian tribe' from the Byzantine
period. In particular, the so-called prehistoric palace in Tiryns
was labelled "the most remarkable hallucination of an unscientific
enthusiast that has ever appeared in literature."
Scientific breakthroughs will always be held hostage to the lag needed
to overcome existing beliefs. Lucius Annaeus Seneca realized this
already two thousand years ago, when he said: "The time will come,
when our successors will be surprised that we did not know such
obvious things."
_________________________________________________________________
Maria Spiropulu
Maria's 1st Law
The anthropic principle in cosmology is just a (silly) corollary of
the anthropic principle in religion: We are, therefore god is.
Maria's 2nd Law
We are not the source of the laws of nature. Nature is, whether we are
or not.
Maria's 3rd Law
A law at the time of its conception is the solution to a problem or
the answer to a question; at that time both the solution and the
problem, the question and the answer, are ill-posed.
_________________________________________________________________
Julian Barbour
My laws make more precise Carlo Rovelli's two principles: time does
not exist, space does not exist. He argues that the universe is a
network of relations and not a game played out on some invisible arena
of absolute space and time such as Newton postulated. I agree but
believe it is important to formulate precisely the manner in which the
universe is relational.
Barbour's First Law
The change of a physical field at a given point is not measured by
time but by the changes of all the other physical fields at the same
point. To determine a rate of change, one does not divide an
infinitesimal change by an infinitesimal time interval but by the
weighted average of all the other changes at the same point. This
ensures that an invisible time can play no role in the dynamics of the
universe.
Barbour's Second Law
Geometry is founded on congruence, dynamics on minimisation of
incongruence.
This requires amplification. Suppose just three particles in space.
Newton defined their motions relative to absolute space. In relational
dynamics, this is not allowed. Instead, the motions (changes) between
two instantaneous states of the three particles are completely
determined by the intrinsic changes of the triangles that they form.
Real change will happen when a triangle becomes incongruent with
itself. To determine the intrinsic change between one triangle and
another ever so slightly incongruent with it, move one relative to
each other until the position of best matching, in which they coincide
more closely than in any other possible relative positioning, is
achieved. The corresponding displacements (changes) determined by this
minimisation of incongruence are the true physical displacements. The
notion of best matching can be applied universally to both particles
and fields.
Barbour's Third Law
Space is Riemannian.
Spelled out in the appropriate mathematical detail, these three laws
seem to explain the structure of all currently known physical fields
as well as the existence of the universal light cone of Einstein's
special relativity and gauge theory.
_________________________________________________________________
Tor Nørretranders
Nørretranders' Law of Symmetrical Relief
If you find that most other people, upon closer inspection, seem to be
somewhat comical or ludicrous, it is highly probable that most other
people find that you are in fact comical or ludicrous. So you don't
have to hide it, they already know.
Nørretranders' Law of Understanding Novelty
The difficulty in understanding new ideas originating from science or
art is not intellectual, but emotional; good ideas are simple and
clear, but if they are truly new, they will be hard to swallow. It is
not difficult to understand that the Earth is not at the center of the
Universe, but it is hard to believe it. Science is simple, simply
strange.
_________________________________________________________________
Philip Campbell
Campbell's First Law
Whatever the science, the forces of nature will exploit any loophole
in experimental or theoretical design and construction, any ambiguity
in measurement and any unchecked or unrecognised assumption to lead a
researcher to enticing but false conclusions.
Campbell's Second Law
Scientists are as vigorous in complaining about the
incomprehensibility of others' scientific papers as they are lazy in
clarifying their own.
Campbell's Third Law
The probability that a Powerpoint presentation will fail is
proportional to the technical sophistication of the institution at
which you are presenting it. (And by the way, where the failure is
total, your talk will be all the better for it.)
_________________________________________________________________
Steve Quartz
Quartz's Law of The Primacy of Feeling
In everyday life, one's anticipated emotions regarding a decision is a
better guide than rational deliberation. Brain science is increasingly
appreciating the centrality of emotions as guides to life, and
emotions are typically more in line with one's wishes than rational
deliberation, which can be easily disconnected from one's desires and
goals. The upshot: deliberation is cheap, emotions are honest.
Quartz's Law of Latent Plasticity
Failure to alter thought, mood, personality, or other facets of
ourselves through environmental means is not a demonstration that
these are hard-wired. Rather, such failure should be taken merely as
an indication that we have not yet discovered the appropriate regime
of experience. New experience-based approaches to brain change are
rapidly emerging, and overturn the dogma of the inflexible brain. We
can now utilize the brain's latent capacity for change to treat mood
disorders through experience-based brain change. Learning how to
utilize the brain's latent plasticity, or capacity for change, will
produce revolutions in physical, cognitive, and mental health
remediation.
_________________________________________________________________
J. Craig Venter
Venter's First Law
Discoveries made in a field by some one from another discipline will
always be upsetting to the majority of those inside.
Venter's Second Law
The ability to directly read the genetic code will continue
exponentially, with the cost per nucleotide (base pair) decreasing by
one-half every two years.
Corollary to Law 2
While DNA sequencing has changed faster than Moore's Law for computer
chips, it will become dependent on and therefore limited by Moore's
Law. (Based on an exchange with Gordon Moore).
Venter's Third Law
We have the tools for the first time in the history of humanity to
Venter's Fourth Law
The Earth's Oceans are the ultimate source of genetic/genomic
diversity providing at least half of the more than 10 billion genes in
the planet's gene pool.
Venter's Fifth Law
Life is like sailing: It is easy to run downwind but usually if you
want to get somewhere worthwhile a long hard beat to weather is
necessary.
_________________________________________________________________
Richard Dawkins
Dawkins's Law of the Conservation of Difficulty
Obscurantism in an academic subject expands to fill the vacuum of its
intrinsic simplicity.
Dawkins's Law of Divine Invulnerability
God cannot lose.
Lemma 1
When comprehension expands, gods contract--but then redefine
themselves to restore the status quo.
Lemma 2
When things go right, God will be thanked. When things go wrong, he
will be thanked that they are not worse.
Lemma 3
Belief in the afterlife can only be proved right, never wrong.
Lemma 4
The fury with which untenable beliefs are defended is inversely
proportional to their defensibility
The following law, though probably older, is often attributed to me in
various versions, and I am happy to formulate it here as
When two incompatible beliefs are advocated with equal intensity, the
truth does not lie half way between them.
_________________________________________________________________
David Finkelstein
Finkelstein's First Law
Everything is relative.
Finkelstein's Second Law
Everything (which is relative).
_________________________________________________________________
Paul Davies
Davies' First Law
Time does not pass.
Davies' Second Law
Never let observation stand in the way of a good theory.
_________________________________________________________________
Steve Grand
Grand's First Law
Things that persist, persist; things that don't, don't.
This tautology underlies every single phenomenon we see around us,
from
molecules to religions. The purpose of science is simply to discover
how and
why any given class of pattern manages to persist. Life is best
understood
as a group of patterns that are able to persist because they
spontaneously
duplicate themselves and adapt to change. Equally, an electron is a
pattern
that persists as a self-maintaining resonant mode in the
electromagnetic
field. The universe is what is left over when all the
non-self-maintaining
Grand's Second Law
Cortex is cortex is cortex.
Our brains may end up as a collection of highly specialised 'modules',
but
the functioning of these modules is not the key to intelligence. The
key is
the deeper set of rules that enable a homogeneous pink goo to wire
itself up
into such a collection of specialised machines in the first place,
merely by
being exposed to the sensory world.
Grand's Third Law
The more carefully one makes contingency plans, the more bizarre the
actual
circumstances will turn out to be.
_________________________________________________________________
David Deutsch
Deutsch's Law
Every problem that is interesting is also soluble.
Corollary #1
Inherently insoluble problems are inherently boring.
Corollary #2
In the long run, the distinction between what is interesting and
what is boring is not a matter of subjective taste but an objective
fact.
Corollary #3
The problem of why every problem that is interesting is also
soluble, is soluble.
_________________________________________________________________
Rodney Brooks
Brooks' First Law
A good place to apply scientific leverage is on an implicit assumption
that everyone makes and that is so implicit that no one would even
think to mention it to students entering the field. Negating that
assumption may lead to new and interesting ways of thinking.
Brooks' Second Law
If you don't have a solid example then your theory is not a good
theory.
_________________________________________________________________
Gary Marcus
Marcus' First Law
Nature and nurture are not in opposition; nature is what makes nurture
possible.
Marcus' Second Law
Nothing in evolution is without precedent; even the most wondrous
adaptations are modifications of pre-existing systems.
Marcus' Third Law
What's good enough for the body is good enough for the brain. Brains,
like any other organ, take their special character from the actions of
individual cells that divide, differentiate, migrate, and die,
according to genetic programs that are the product of evolution.
_________________________________________________________________
Verena Huber-Dyson
Verena's Law of Sane Reasoning
Hone your Hunches, Jump, then backtrack to blaze a reliable trail to
But avoid reductios; they lead to mere counterfeits of truth.
Verena's Law of Constructive Proof
Every sound argument can and ought to be turned into a construction
that embodies and explains its conclusion.
_________________________________________________________________
Scott Sampson
Sampson's Law of Interdependent Origination
Life's unfolding is a tapestry in which every new thread is contingent
upon the nature, timing, and interweaving of virtually all previous
This is an extension of the idea that the origin of new life forms is
fundamentally contingent upon interactions among previous biotas. As
Stephen J. Gould described it, if one could rewind the tape of life
and let events play out again, the results would almost certainly
differ dramatically. The point of distinction here is a deeper
incorporation of the connections inherent in the web of life.
Specifically, the origin of new species is inextricably linked both to
evolutionary history and to intricate ecological relationships with
other species. Thus, speciation might be aptly termed "interdependent
origination." So, for example, it is often said that the extinction of
dinosaurs 65 million years ago cleared the way for the radiation of
mammals and, ultimately, the origin of humans. Yet the degree of
life's interconnectedness far exceeds that implied in this statement.
Dinosaurs persisted for 160 million years prior to this mass dying,
co-evolving in intricate organic webs with plants, bacteria, fungi,
and algae, as well as other animals, including mammals. Together these
Mesozoic life forms influenced the origins and fates of one another
and all species that followed. Had the major extinction of the
dinosaurs occurred earlier or later, or had dinosaurs never evolved,
subsequent biotas would have been wholly different, and we almost
certainly wouldn't be here to contemplate nature. An equivalent claim
could be made for any major group at any point in the history of life.
_________________________________________________________________
Colin Blakemore
Blakemore's First Law
People are never more honest than you think they are.
Blakemore's Second Law
The only form of intelligence that really matters is the capacity to
predict.
_________________________________________________________________
Michael Shermer
Shermer's Last Law
Any sufficiently advanced extra-terrestrial intelligence is
indistinguishable from God.
Any ETI that we might encounter would not be at our level of culture,
science, and technology, nor would they be behind us. How far ahead of
us would they be? If they were only a little ahead of us on an
evolutionary time scale, they would be light years ahead of us
technologically, because cultural evolution is much more rapid than
biological evolution. God is typically described by Western religions
as omniscient and omnipotent. Since we are far from the mark on these
traits, how could we possibly distinguish a God who has them
absolutely, from an ETI who has them in relatively (to us) copious
amounts? Thus, we would be unable to distinguish between absolute and
relative omniscience and omnipotence. But if God were only relatively
more knowing and powerful than us, then by definition it would be an
ETI!
Shermer's Three Principles of Provisional Morality and Evolutionary
Ethic
1. The ask-first principle: to find out whether an action is right
2. The happiness principle: it is a higher moral principle to
always seek happiness with someone else's happiness in mind, and
never seek happiness when it leads to someone else's unhappiness.
3. The liberty principle: it is a higher moral principle to always
seek liberty with someone else's liberty in mind, and never seek
liberty when it leads to someone else's loss of liberty.
0. The Zeroeth principle: do unto others as you would have them do
unto you.
(These principles were derived from a scientific analysis of the
evolutionary origins of the moral sentiments and the historical
development of evolutionary ethics. The Zeroeth Principle, which
precedes the three principles, first evolved hundreds of thousands of
years ago but was first codified in writing by the world's great
religious leaders and has come down to us as the golden rule. The
foundation of the Zeroeth Principle, and the three derivative
principles is, in evolutionary theory, reciprocal altruism and the
process of reciprocity.)
_________________________________________________________________
Ernst Pöppel
I refer to my "laws" as "Pöppel's Paradox", and "Pöppel's Universal".
Actually the names have been invented by others.
Not to see, but to see. Some years ago (1973) we described a
phenomenon that patients with a certain brain injury show some
residual vision although they do not have a conscious representation
of their remained visual capacity. They can orient in space, or they
can discriminate simple patterns, but they do not know that they can
do it. This phenomenon became known as "blindsight". Apparently there
is a lot of implicit processing going in our brain that lacks an
explicit representation, but which usually is associated with
conscious experience. Interestingly, the phenomenon of blindsight not
only made a "career" in the neurosciences, but also in philosophy.
Pöppel's Universal
We take life 3 seconds at a time. Human experience and behaviour is
characterized by temporal segmentation. Successive segments or "time
windows" have a duration of approx. 3 seconds. Examples: Intentional
movements are embedded within 3 s (like a handshake); the anticipation
of a precise movement like hitting a golf ball does not go beyond 3 s;
if we reproduce the duration of a stimulus, we can do so accurately up
to 3 s but not beyond; if we look at ambiguous figures (like a vase
vs. two faces) or if we listen to ambiguous phoneme sequences (like
Cu-Ba-Cu-Ba-.., either hearing Cuba or Bacu) automatically after
approx. 3 s the percept switches to the alternative; the working
platform of our short term memory lasts only 3 s (being interrupted
after 3 s most of the information is gone); spontaneous speech in all
languages is temporally segmented, each segment lasting up to 3 s;
this temporal segmentation of speech shows up again in poetry, as a
verse of a poem is embedded within 3 s (Shakespeare: "Shall I compare
thee to a summer's day"); musical motives preferably last 3 s
(remember Beethoven's Fifth Symphony); decisions are made within 3 s
(like zapping between TV channels); and there are more examples. Thus,
the brain provides a temporal stage that last approx. 3 s, which is
used in perception, cognition, movement control, memory, speech, or
music.
_________________________________________________________________
Robert Aunger
Aunger's Law of Human Evolution
Human life is unique in being the result of three coevolving
information inheritance systems: genes, minds and technology.
Aunger's Law of Technological Evolution
As the rate of technological innovation increases, so too does the
inertia from ancillary institutions, but not as much.
_________________________________________________________________
John Horgan
Horgan's First Law
If science has limits--and science tells us that it does--the only
question is when, not if, it reaches them.
Horgan's Second Law
Every garbage-removal system--whether Zen, skepticism, or
existentialism--generates garbage. If you want to clear your mind, the
best you can hope for is to find a system, or anti-system, that
removes more garbage than it generates.
_________________________________________________________________
Seth Lloyd
Lloyd's It From Qubit Law
The universe is a quantum computer: life, sex, the brain, and human
society all arise out of the ability of the universe to process
information at the level of atoms, photons and elementary particles.
_________________________________________________________________
Jaron Lanier
The following are Lanier's Laws for Putting Machines in their Place,
distilled from comments I've posted on Edge over the years. They are
all stolen from earlier laws that predate the appearance of computers
Lanier's First Law
Humans change themselves through technology.
Example: Lanier's Law of Eternal Improvement for Virtual Reality:
Average human sensory perception will gain acuity over successive
generations in tandem with the improving qualities of pervasive media
technology.
Lanier's Second Law
Even though human nature is dynamic, you must find a way to think of
it as being distinct from the rest of nature.
You can't have a categorical imperative without categories. Or, You
can't have a golden rule without gold. You have to draw a Circle of
Empathy around yourself and others in order to be moral. If you
include too much in the circle, you become incompetent, while if you
include too little you become cruel. This is the "Normal form" of the
eternal liberal/conservative dichotomy.
Lanier's Third Law
You can't rely completely on the level of rationality humans are able
to achieve to decide what to put inside the circle. People are
demonstrably insane when it comes to attributing nonhuman sentience,
as can be seen at any dog show.
Lanier's Fourth Law
Lanier's Law of AI Unrecognizability.
You can't rely on experiment alone to decide what to put in the
circle. A Turing Test-like experiment can't be designed to distinguish
whether a computer has gotten smarter or a person interacting with
that computer has gotten stupider (usually by lowering or narrowing
standards of human excellence in some way.)
Lanier's Fifth Law
If you're inclined to put machines inside your circle, you can't rely
on metrics of technological sophistication to decide which machines to
choose. These metrics have no objectivity.
For just one example, consider Lanier's retelling of Parkinson's Law
for the Post-dot-com Era: Software inefficiency and inelegance will
always expand to the level made tolerable by Moore's Law. Put another
way, Lanier's corrolary to Brand's Laws: Whether Small Information
wants to be free or expensive, Big Information wants to be
meaningless.
Lanier's Sixth Law
When one must make a choice despite almost but not quite total
uncertainty, work hard to make your best guess.
Best guess for Circle of Empathy: Danger of increasing human stupidity
is probably greater than potential reality of machine sentience.
Therefore choose not to place machines in Circle of Empathy.
_________________________________________________________________
Charles Seife
Seife's First Law
A scientific revolution is a complete surprise. Especially to its
authors.
Seife's Second Law
Each generation's scientific neologisms adorn the labels of the next
generation's quack cures.
_________________________________________________________________
Andy Clark
Clark's Law
Everything leaks.
There are no clear-cut level distinctions in nature. Neural software
bleeds into neural firmware, neural firmware bleeds into neural
hardware, psychology bleeds into biology and biology bleeds into
physics. Body bleeds into mind and mind bleeds into world. Philosophy
bleeds into science and science bleeds back.The idea of levels is a
useful fiction, great for hygienic text-book writing and quick answers
that defend our local turf but seldom advance scientific
understanding).
_________________________________________________________________
Alan Alda
The following is written by a non-scientist who supposes it might be
entertaining for scientists to see what passes through the head of a
curious layman while trying to understand the people who try to
understand Nature.
Alda's First Law of Laws
All laws are local.
In other words, something is always bound to come along and make you
rethink what you know by forcing you to look at it in a broader
context. I've arrived at this notion after interviewing hundreds of
scientists, and also after being married for 46 years.
I don't mean that laws are not true and useful, especially when they
have been verified by experiment. But they are likely to continue to
be true only within a certain frame, once another frame is discovered.
Some scientists will probably find this idea heretical and others may
find it obvious. According to this law, they'll both be right
(depending on the frame they're working in).
Another way of saying this is that no matter how much we know about
something, it is just the tip of the iceberg. And most disasters occur
by coming in contact with the other part of the iceberg.
Alda's Second Law of Laws
A law does not know how local it is.
Citizens of Lawville do not realize there are city limits and are
constantly surprised to find out they live in a county.
When you're operating within the frame of a law, you can't know where
the edges of the frame are--where dragons begin showing up.
I've just been interviewing astronomers about dark matter and dark
energy in the universe. These two things make up something like 96% of
the universe. The part of the universe we can see or in some way
observe is only about 4%. That leaves a lot of universe that needs to
be rethought. And some people speculate that dark energy may be
leaking in from a whole other universe; an even bigger change of
frame, if that turns out to be the case.
It's now known that vast stretches of DNA once thought to be Junk DNA
because they don't code for proteins actually regulate or even silence
conventional genes. The conventional genes--what we used to think were
responsible for everything we knew about heritability--account for
only 2% of our DNA. Apparently, it's not yet known how much of the
other 98% is active, but I think the frame has just shifted here.
Welcome to Lawville; you are now leaving Lawville.
_________________________________________________________________
Chris Anderson
Anderson's Law of Causal Instinct
Humans are engineered to seek for laws, whether or not they're
actually there.
Anderson's Law of Skepticism
Most proposed laws, including this one, will probably turn out to be
vacuous.
_________________________________________________________________
Stuart Pimm
Pimm's First Law
No language spoken by fewer than 100,000 people survives contact with
the outside world, while no language spoken by more than one million
people can be eliminated by such contact.
Pimm's Second Law
With every change in language (including first contact with humanity),
a region's biodiversity shrinks by 20%.
_________________________________________________________________
Robert Provine
Provine's Motor Precocity Principle
Organisms spond before they respond (act before they react).
This principle of neurobehavioral development and evolution describes
the tendency of the nervous system to produce motor output before it
receives sensory input. Because motor systems often evolve and develop
before sensory systems, sensory input cannot have the dominant
influence on neural structure and function predicted by some
psychological and neurological theories.
The evolutionary precocity of motor relative to sensory systems also
argues against the classical reflex as a primal step in
neurobehavioral evolution. Spontaneously active motor processes are
adaptive and can emerge through natural selection unlike sensory
processes that are not adaptive without a behavior to guide. Sensory
systems evolved to control already existing movement.
Another argument against the primacy of reflexes is that they require
the unlikely simultaneous evolution of a sensory and a motor process.
The tendency of organisms to "spond before they respond" requires the
re-evaluation of many other traditional neurobehavioral concepts and
processes.
Provine's Self/Other Exclusionary Principle
The "self," the most basic sense of personhood, is defined as that
which is not "other." "Other," the most primitive level of social
entity, is defined as a non-self, animate stimulus on the surface of
Self is distinguished from other by a neurological cancellation
process. These definitions are attractive because they permit a
neurologically and computationally based approach to problems that are
traditionally mired in personality and social theory. Although our
sense of identity involves more than self/non-self discrimination,
such a mechanism may be at its foundation and a first step toward the
evolution of personhood and the neurological computation of its
boundaries. For a demonstration of this mechanism, consider your
inability to tickle yourself. Tickle requires stimulation by a
non-self animate entity on the surface of your skin. Similar,
self-produced stimulation is cancelled and is not ticklish.
Without such a self/non-self discriminator, we would be constantly be
tickling ourselves by accident, and the world would be filled with
goosey people lurching their way through life in a chain reaction
filled with tactile false alarms. Developing a similar machine
algorithm may lead to "ticklish" robots whose performance is enhanced
by their capacity to distinguish touching from being touched, and,
provocatively, a computationally based construct of machine
personhood.
_________________________________________________________________
Art De Vany
De Vany's Law
The future is over-forecasted and underpredicted.
_________________________________________________________________
Alison Gopnik
Gopnik's Learning Curve
The ability to learn is inversely proportional to years of school,
Gopnik's Gender Curves
The male curve is an abrupt rise followed by an equally abrupt fall.
The female curve is a slow rise to an extended asymptote. The areas
under the curves are roughly equal. These curves apply to all
activities at all time scales (e.g. attention to TV programs, romantic
love, career scientific productivity).
_________________________________________________________________
Raphael Kasper
Kasper's Law
One should never blindly accept things as they are.
Jose Saramago writes in The Cave with his usual quirky punctuation and
sentence structure:
"... we often hear it said, or we say it ourselves, I'll get used
to it, we say or they say, with what seems to be genuine acceptance
..., what no one asks is at what cost do we get used to things."
Kasper's Second Law
Try to know where and how your thoughts arise and always give credit
_________________________________________________________________
Susan Blackmore
Blackmore's First Law
People's desire to believe in the paranormal is stronger than all the
evidence that it does not exist.
Blackmore's Second Law
Humans are not in control of the web; the memes are.
_________________________________________________________________
Stanislas Dehaene
Dehaene's First Law
Every successful human invention such as arithmetic or the alphabet
has a "neuronal niche"--a set of cerebral processors that evolved for
a distinct purpose, but can be recycled to implement the new function.
Two corollaries:
The difficulty of learning a new concept or technique is directly
related to the amount of recycling needed--the distance between the
evolutionary older function and the new one.
When the old and the new functions are closely related
(isomorphic), an evolutionary old cerebral processor can provide a
fast, unconscious and unexpected solution to a recent cultural
problem--this is what we call
"intuition".
Dehaene's Second Law
The confusability of two ideas, however abstract, is a direct function
of the overlap in their neuronal codes.
_________________________________________________________________
Richard Rabkin
Rabkin's Rule
Nothing is a simple as it seems.
Rabkin's Dictum
If you don't understand something, it's because you aren't aware of
its context.
_________________________________________________________________
Donald Hoffman
Hoffman's First Law
A theory of everything starts with a theory of mind.
Quantum measurement hints that observers may create microphysical
properties. Computational theories of perception hint that observers
may create macrophysical properties. The history of science suggests
that counterintuitive hints, if pursued, can lead to conceptual
breakthroughs.
Hoffman's Second Law
Physical universes are user interfaces for minds.
Just as the virtual worlds experienced in VR arcades are interfaces
that allow the arcade user to interact effectively with an unseen
world of computers and software, so also the physical world one
experiences daily is a species-specific user interface that allows one
to survive while interacting with a world of which one may be
substantially ignorant.
_________________________________________________________________
Nassim Taleb
Taleb's First Black Swan Law
The risk you know anything about today is not the one that matters.
What will hurt you next has to look completely unplausible today. The
more unplausible the event the more it will hurt you.
Consider that had the WTC attack been deemed a reasonable risk then we
would have had tighter control of the skies and it would have not
taken place. It happened because it was improbable. The awareness of a
specific danger makes you protect yourself from its precise effect and
may prevent the event itself from occurring.
Taleb's Second Black Swan Law (corollary)
We don't learn that we don't learn.
We don't learn the First Black Swan Law from experience, yet we think
that we learn something from it. Abstract subject matters (and
metarules) do not affect our risk avoidance mechanisms; only vivid
images do. People did not learn from the WTC (and the succession of
similar events in history such as the formation of financial bubbles)
that we have a horrible track record in forecasting such occurrences.
They just learned the specific task to avoid tall buildings and
Islamic terrorists--after the fact.
_________________________________________________________________
Geoffrey Miller
Miller's Law of Strange Behavior
To understand any apparently baffling behavior by another human, ask:
what status game is this individual playing, to show off which
heritable traits, in which mating market?
Miller's Iron Law of Iniquity
In principle, there is an evolutionary trade-off between any two
positive traits. But in practice, every good trait correlates
positively with every other good trait.
Miller's First Law of Offspring Ingratitude
People who don't understand genetics attribute their personal failings
to the inane role models offered by their parents.
Miller's Second Law of Offspring Ingratitude
People who do understand genetics attribute their personal failings to
the inane mate-choice decisions made by their parents.
_________________________________________________________________
Piet Hut
Hut's First Law
Any attempt to define what is science is doomed to failure
Scientists often attack what they consider irrational creeds by first
defining what counts as science and then showing that those creeds
don't fit within the limits specified. While their motive is often
right, their approach is totally wrong. Science has no method. It is
agility to the most amazing experimental discoveries, no matter what
previous 'corner stones' have to be given up: quantum mechanics is the
most striking example. This opportunism is the only reason that
science has remained alive and well, notwithstanding the human
tendency for stagnation that is exemplified so clearly through more
than a dozen successive generations of individual scientists.
Hut's Second Law
In scientific software development, research = education
When writing a large software package or a whole software environment,
the most efficient way to produce a robust product is to write
documentation simultaneously with the computer codes, on all levels:
from comment lines to manual pages to narrative that explains the
reasons for the many choices made. Having to explain to yourselves and
your coworkers how you choose what why when is the best guide to
quickly discovering hidden flaws and better alternatives, minimizing
the need to
backtrack later. Therefore, the most efficient way to write a large
coherent body of software as a research project is to view it as an
educational project.
I have come across similar endorsements of documentation in various
places, including Donald Knuth's idea of literate programming, and
Gerald Sussman's advice to write with utmost clarity for humans first,
and for computers as an afterthought.
_________________________________________________________________
Stewart Brand
Brand's Law
Information wants to be free.
The rest of Brand's Law
Information also wants to be expensive.
Brand's Pace Law
In haste, mistakes cascade. With deliberation, mistakes instruct
Brand's Asymmetry
The past can only be known, not changed. The future can only be
changed, not known.
Brand's Shortcut
The only way to predict the future is to make sure it stays exactly
the same as the present.
_________________________________________________________________
Jeffrey Epstein
Epstein's First Law
Know when you are winning.
Epstein's Second Law
The key question is not what can I gain but what do I have to lose.
_________________________________________________________________
Steven Kosslyn
Kosslyn's First Law
Body and mind are not as separate as they appear to be. Not only does
the state of the body affect the mind, but vice-versa.
Kosslyn's Second Law
The individual and the group are not as separate as they appear to be.
A part of each mind spills over into the minds of other people, who
help us think and regulate our emotions.
_________________________________________________________________
Jay Ogilvy
Ogilvy's Law
Many well defined manifolds lack unifying centers that define or
control them.
o Just because some things are genuinely sacred does not mean that
there is a god.
o Just because a corporation or a country seems to be
hierarchically structured does not mean that any single leader is
really in charge.
o Just because some behavior is conscious and intentional does not
entail a "ghost in the machine," a homunculus, or a central
intender.
o Just because evolution appears to be directional, from less order
and complexity toward greater order and complexity, that does not
presuppose either an alpha-designer or an omega-telos.
Precursors to Ogilvy's Law:
1. Derridean Deconstruction, which is not about taking things
apart, but showing how they were never all that unified in the
first place
2. Wittgenstein's replacement of Platonic Ideas<e.g., that one
thing which all instances of 'game' or 'justice' have in
common<with the much looser notion of "family resemblances"
Lemma to Ogilvy's Law:
Demythologizing false unities does not degrade the values to be found
in their respective manifolds.
o Nietzsche's announcement of the death of god does not mean that
nothing is sacred.
o Skepticism regarding conspiracy theories does not entail naiveté
regarding power or the impossibility of effective leadership.
o Seeing through Cartesianism in the cognitive sciences does not
entail eliminative materialism, a lack of intentionality, or the
reduction of mind to matter.
o Dismissing teleology does not deny a manifest directionality to
evolution.
In each of these cases and many others like them, the
deconstructive turn should not be confused with nihilism or
deflationary debunking. The value of Ogilvy's Law lies in its
ability to help predict which valleys harbor real value, and which
peaks are better left undefended
_________________________________________________________________
Scott Atran
Atran's Power Law of History
(a corollary to the law of unintended consequences)
The major events that determine human history follow a power
distribution (a more or less straight line on a log-log scale), with
catastrophic and cascading consequences (economic and health crises,
political and cultural revolutions, war and terrorism, etc.), because
people naturally prefer to act upon the future based on their modeling
of past occurrences. People do not repeat the catastrophes of history
because they forget it; people build up self-destructing ideologies
and behavior patterns that continue history's catastrophic path
because they remember the past too well (e.g., "the maginot effect"
for war and the soon-to-be "box-cutting effect" for terrorism).
Ancillary: For politics, history's most well-developed and
self-assured "isms" (e.g., colonialism, fascism, communism, globalism)
are those most prone to radical collapse.
Atran's Law of Bare Counterintuition
(for the cultural survival of absurd ideas)
Natural selection endowed humans with an intuitive ontology that
includes folkbiology (e.g., biodiversity divides into mutually
exclusive groups of beings, and each group has a proprietary essence),
folkpsychology (e.g., intentional and emotional beings have bodies,
and have knowledge of other like beings by observing and inferring how
other bodies act), and folkphysics (e.g., two bodies cannot
simultaneously occupy the same place at the same time, and no body can
occupy different places at the same time). Barely counterintuitive
ideas, which violate universal constraints on intuitive ontology
(e.g., a bodiless being) but otherwise retain most commonsense
properties associated with intuitive ontology (a bodiless being who
mostly acts and thinks like a person), are those fictions most apt to
survive within a culture, most likely to recur in different cultures,
and most disposed to cultural variation and elaboration (e.g.,
sphinxes and griffins, spirits and crystal balls, ghosts and gods).
Ancillary: For religion (i.e., for most humans in all human
societies), the more costly one's commitment to some factually absurd
but barely counterintuitive world (e.g., afterlife), the more others
believe that person to be sincere and trustworthy.
_________________________________________________________________
Esther Dyson
Dyson's Law
(Rationale:) How can we find the happy medium between disclosure and
prying, between transparency and overexposure? The last thing we want
is a law saying that everyone should disclose everything: vested
interests, negotiating strategies, intentions, bank account, marital
status, whatever.
How can we instead devise some rule that fits the best qualities of
the Net decentralized, more or less self-enforcing, flexible.....and
responsive to personal choices? The idea is to create a culture that
expects disclosure, rather than a legal regime that requires it.
People can decide how much they want to play, and others can decide
whether to play with them.
First of all, it's two-way. It's not for a single person; it's for an
interaction. The first person has to ask; the second person, to answer
truthfully or refuse openly to answer.
It drives the responsibility for requiring disclosure down to where it
belongs - to those most likely to be affected by the disclosure. It
decentralizes the requirement and the enforcement to everyone, instead
of leaving it in the hands of a few at the top. (If that's an awkward
use of "requirement," it's because we don't even have a word for
"decentralized command.")
As an individual, you are not commanded to answer; you may want to
protect your own privacy or someone else's. But if you do answer, you
must do so truthfully.
Then it's up to the people involved to decide whether to engage - in
conversation, in a transaction, in whatever kind of interaction they
might be contemplating. The magic of Do ask; don't lie is that the
parties to any particular interaction can make a specific, local
decision about what level of disclosure is appropriate.
_________________________________________________________________
David Bunnell
Bunnell's First Law of Retrievability
Everything is retrievable.
Bunnell's Second Law of Retrievability
Everything is stored somewhere. The secret to retrieving things is
simply finding out where they are stored.
_________________________________________________________________
Charles Arthur
Arthur's First Law
Nothing is evenly spread; everything happens in clumps. The universe
has clumps--galaxies, star systems, stars, planets, asteroids. You
meet an old friend for the first time in years, then again and again.
The smart folk are all together. It's a universal.
Arthur's Second Law
More data is good, and drives out the bad.
_________________________________________________________________
Philip W. Anderson
Anderson's Law
More is different.
_________________________________________________________________
Pamela McCorduck
McCroduck's Law
A linear projection into the future of any science or technology is
like a form of propaganda -- often persuasive, almost always wrong.
_________________________________________________________________
John Skoyles
Skoyles' Law of Culture and the Brain
Human culture and human cognition exists because the brain's neural
plasticity allows learned symbolic associations to substitute for the
innate inputs and outputs of already evolved ape cognitions, a process
that extends greatly their functionality.
Skoyles' Law of Literacy
A society develops democracy to the degree that it writes social,
legal and religious ideas using the syntax, vocabulary and
pronunciation of everyday speech, rather than that of a professional,
_________________________________________________________________
Those who scorn the "publish or perish" principle are the most eager
to see their own manuscripts published quickly and given wide
publicity--and the least willing to see their length reduced.
Reviewers who are best placed to understand an author's work are the
least likely to draw attention to its achievements, but are prolific
sources of minor criticism, especially the identification of typos.
Just as nature is supposed to abhor a vacuum, so scientific opinion
abhors questions unlikely to be answered soon, whence the general
belief that the origin of the Universe is now nearly understood.
_________________________________________________________________
Arthur R. Jensen
Jensen's First and Second Laws of Individual Differences in Cognitive
Abilities have crucial educational, economic, and social consequences.
Jensen's two fundamental laws derived from empirical studies of human
individual differences (population variance) in cognitive ability:
Jensen's First Law
Individual differences in learning and performance increase as a
monotonic function of task complexity or difficulty.
Jensen's Second Law
Individual differences in learning and performance increase with
continuing practice and experience,
unless there is an intrinsically low ceiling on task proficiency.
_________________________________________________________________
Keith Devlin
Devlin's First Law
Buyer beware: in the hands of a charlatan, mathematics can be used to
make a vacuous argument look impressive.
Devlin's Second Law
So can PowerPoint.
_________________________________________________________________
Arnold Trehub
Trehub's Law
For any experience, thought, question, or solution there is a
_________________________________________________________________
Michael Nesmith
Nesmith's First Law
The Universe includes no contrary laws
Nesmith's Second Law
Mind is the Constant in all equations
_________________________________________________________________
David G. Myers
Myers' Law of Truth
The surest truth is that some of our beliefs err.
Monotheism, someone has said, offers two simple axioms: 1) There is a
God. 2) It's not you. Knowing that we are fallible humans underlies
the humility and openness that inspires science, and democracy. As
Madeline L'Engle noted, "The naked intellect is an extraordinarily
inaccurate instrument."
Myers' Law of Self-Perception
Most people see themselves as better than average.
Nine in ten managers rate themselves as superior to their average
peer. Nine in ten college professors rated themselves as superior to
their average colleague. And six in ten high school seniors rate their
"ability to get along with others" as in the top 10 percent. Most
drivers-even most drivers who have been hospitalized after
accidents-believe themselves more skilled than the average driver.
"The one thing that unites all human beings, regardless of age,
gender, religion, economic status or ethnic background," observes Dave
Barry, "is that deep down inside, we all believe that we are above
average drivers." Excess humility is an uncommon flaw.
Myers Law of Writing
Anything that can be misunderstood will be.
_________________________________________________________________
Howard Rheingold
Rheingold's Law
Communication media that enable collective action on new scales, at
new rates, among new groups of people, multiply the power available to
civilizations and enable new forms of social interaction. The alphabet
enabled empire and monotheism, the printing press enabled science and
revolution, the telephone enabled bureaucracy and globalization, the
Internet enabled virtual communities and electronic markets, the
mobile telephone enabled smart mobs and tribes of urban info-nomads.
_________________________________________________________________
Todd Siler
Siler's First Law
The brain is what the brain creates. Its workings reflect the workings
of everything it creates.
Siler's Second Law
Genius is everywhere, everyday, in everyone, in every way imaginable.
_________________________________________________________________
Garniss Curtis
Curtis' First Law
With several unknown keys in hand, one of which fits the lock in front
of you, the first time you try all the keys, none will open it.
Curtis' Second Law
If you try all the keys again, there is only a fifty/fifty chance you
will be successful.
_________________________________________________________________
Marvin Minsky
Minsky's First Law
Misnksy's Second Law
Don't just do something. Stand there.
_________________________________________________________________
John Barrow
Barrow's first 'law'
Any Universe simple enough to be understood is too simple to produce a
mind able to understand it.
Barrow's second 'law'
All difficult conjectures should be proved by reductio ad absurdum
arguments. For if the proof is long and complicated enough you are
bound to make a mistake somewhere and hence a contradiction will
inevitably appear, and so the truth of the original conjecture is
established QED.
_________________________________________________________________
Brian Goodwin
Goodwin's Limited Law
The truth has as many faces as there are beings that express it. so
no-one is ever wrong. everyone is right, though in limited ways.
wisdom lies in spotting the limitation while being grateful for the
insight.
_________________________________________________________________
Kevin Kelly
Kellys' First Law
Power, understanding, control. Pick any two.
Kellys' Second Law
Nobody is as smart as everybody.
_________________________________________________________________
John McWhorter
McWhorter's Law of Social History
In a context of widespread literacy, easy communications, and a large
class of people with ample leisure time, the social movement that
begins by addressing a concrete grievance will, after the grievance
has been largely addressed, pass into the hands of persons inclined
for individual reasons towards the dramatic and self-righteous, who
will manipulate the movement's iconography and passion into a staged
indignation difficult for outsiders to square with reality, and with
little actively progressive or beneficent intention.
_________________________________________________________________
John Allen Paulos
Paulos' Law of Coincidence
People often note some unlikely conjunction of events and marvel at
the coincidence. Could anything be more wonderfully improbable, they
wonder. The answer is Yes. The most amazing coincidence of all would
be the complete absence of coincidence.
_________________________________________________________________
Freeman Dyson
Dyson's Law of Obsolescence
If you are writing history and try to keep it up-to-date up to a time
T before the present, it will be out-of-date within a time T after the
present.
This law applies also to scientific review articles.
( Thanks for including the Doctor Moreau quote, which describes us
very well.)
_________________________________________________________________
Richard Nisbett
Nisbett's Law
When you have the beginnings of an idea about something, the worst
thing to do is to consult "the literature" before you get started to
work on it. You are sure to assimilate your potentially original idea
to something that is already out there.
_________________________________________________________________
Timothy Taylor
Taylor's Law
There are no laws of human behaviour.
_________________________________________________________________
Carlo Rovelli
Rovelli's Two Principles
Time Does Not Exist
Contrary to what generally assumed, the physical world does not exist
"in time". At the basic microscopic level, the world is better
described in terms of a a-temporal theory, where physical laws do not
express time evolution of physical variables, but just relations
between variables. Time emerges only thermodynamically when describing
macroscopic variables. Therefore time is only a side effect of our
ignorance of the microscopic state of the world. "Time is a side
effect of ignorance."
Space Does Not Exist
The physical world does not exist "in space". The physical world is
made by an ensemble of particles and fields, which do not live in an
external space, but rather live "on each other", and which can be in a
relation of contiguity with respect to one another. "Space" is the
order implied by this relation. These two principles are implied by
what we have learned about the physical world with general relativity
and with quantum mechanics. The second principle is largely a return
to the Pre-Newtonian relational understanding of space, while the
first has few antecendents in our culture.
_________________________________________________________________
Karl Sabbagh
Sabbagh's First Law
Never assume.
All the mistakes I have made in my life--not that there are that many,
of course--have been because I failed to follow my own law.
Sabbagh's Second Law
The biggest problem with communication is the illusion that it has
occurred. I think this is the more original and far-reaching of the
two laws but I have put it second because it's not really mine. It was
said to me by Alan Mulally, an inspiring Boeing manager (and they need
inspiring managers at
the moment.)
_________________________________________________________________
Douglas Rushkoff
Rushkoff's Law
A religion will increase in social value until a majority of its
members actually believe in it--at which point the social damage it
causes will increase exponentially as long as it is in existence.
Rushkoff's Law of Media
the medium in which the communication is taking place.
_________________________________________________________________
Roger Schank
Schank's Law
Because people understand by finding in their memories the closest
possible match to what they are hearing and use that match as the
basis of comprehension, any new idea will be treated as a variant of
something the listener has already thought of or heard. Agreement with
a new idea means a listener has already had a similar thought and well
appreciates that the speaker has recognized his idea. Disagreement
means the opposite. Really new ideas are incomprehensible. The good
news is that for some people, failure to comprehend is the beginning
of understanding. For most, of course, it is the beginning of
dismissal.
_________________________________________________________________
Joseph Traub
Traub's Law (Version 1)
The important things in life often happen by chance while we're
agonizing over the trivia.
Traub's Law (Version 2)
The important events of a person's life are the products of chains of
highly improbable occurrences.
_________________________________________________________________
Daniel Gilbert
Gilbert' Law
Happy people are those who do not pass up an opportunity to laugh at
themselves or to make love with someone else. Unhappy people are those
who get this backwards.
_________________________________________________________________
Irene Pepperberg
Pepperberg's Law of Comparative Cognition
Any behavior exhibited by young children that is taken as evidence of
the early emergence of intelligence will, when subsequently exhibited
by nonhumans, be interpreted by many humans as a set of simple
stimulus-response associations lacking cognitive processing, whereas
the stimulus-response explanation will rarely be used to re-interpret
the behavior of the child.
_________________________________________________________________
David Lykken
Lykken's First Law
The quality of one's intellectual productions is a function of the
product of talent (e.g., intelligence) times mental energy. Although
there are many and varied tests for assessing intelligence,
psychologists have not as yet even attempted to construct a measure of
individual differences in mental energy.
Lykken's Second Law
The mind consists of genetically-determined hardware and
experientially-determined software. The hardware components are not
constructed by genes working either individually or additively but,
rather, by groups of genes working sequentially and configurally. Each
human mating produces at least some gene configurations that are
unique, having never occurred previously. This is why, among other
things, human genius often occurs uniquely in an otherwise
undistinguished family line.
_________________________________________________________________
Marc D. Hauser
Hauser's First Law
Every uniquely human ability, including cooking, mathematics,
morality, and music, is based on a set of biologically primitive
capacities that evolved before our species walked the earth.
Hauser's Second Law
The historical stability of our prescriptive claims (what we ought to
do) are determined by principles underlying our universal judgments.
Nature's is constrains our lofty hopes for what ought to be.
_________________________________________________________________
James J. O'Donnell
If it feels good, don't do it.
Because if it feels good, it's going to be because it eases some
frustration you're feeling from all the constraints and hassles of
the institution; or because it really shows up so-and-so; or
because it makes you feel you really do have a little authority
around here after all. It won't, it won't, and you don't. Better to
calm down, make sure you know all the facts, make sure you've
talked to all 49 stakeholders, and sleep on it, then do the thing
you have to hold your nose to do.
O'Donnell's Law of History
There are no true stories.
Story-tellers are in the iron grip of readers' expectations.
Stories have beginnings, middles, ends, heroes, villains, clarity,
resolution. Life has none of those things, so any story gets to be
a story (especially if it's a good story) by edging away from what
really happened (which we don't know in anywhere near enough detail
anyway) towards what makes a good story. Historians exist to
wrestle with the story temptation the way Laocoon wrestled with the
snakes. But at the end of the day, to tell anybody anything, you'll
probably tell a story, so then be sure to follow:
Luther's Law
Pecca fortiter.
Literally, "Sin bravely." His idea was that you're going to make a
mess of things anyway, so you might as well do so boldly,
confidently, with a little energy and imagination, rather than
timidly, fearfully, half-heartedly.
_________________________________________________________________
Howard Gardner
Gardner's First Law
Don't ask how smart someone is; ask in what ways is he or she smart.
Gardner's Second Law
You can never go directly from a scientific discovery to an
educational recommendation: all educational practices presuppose
implicit or explicit value judgments.
_________________________________________________________________
William H. Calvin
Calvin's Law of Coherence
When things "all hang together," you have either gotten the joke,
solved the puzzle, argued in a circle, focused your chain of logic so
narrowly that you will be blindsided--or discovered a hidden pattern
in nature. Science, in large part, consists of imagining coherent
solutions and then making sure that you weren't fooled by a false
coherence as in astrology.
_________________________________________________________________
Bruce Sterling
Sterling's Law of Ubiquitous Computation
First, your home is a constant, while the Net is a place you go; then
the Net becomes a constant while your home is a place you go.
Sterling's Corollary to Clarke's Law
Any sufficiently advanced garbage is indistinguishable from magic.
_________________________________________________________________
George B. Dyson
Dyson's Law of Artificial Intelligence
Anything simple enough to be understandable will not be complicated
enough to behave intelligently, while anything complicated enough to
behave intelligently will not be simple enough to understand.
` | 2020-02-17 01:58:27 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.3885769248008728, "perplexity": 6919.417951632269}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-10/segments/1581875141460.64/warc/CC-MAIN-20200217000519-20200217030519-00130.warc.gz"} |
https://ashishkumarletslearn.com/class-11-maths-chapter-5-lecture-6/ | MISCELLANEOUS EXERCISE
Question 11. If a+ib = \frac{(x+i)^2}{2x^2+1}, prove that a^2+b^2 = \frac{(x^2+1)^2}{(2x^2+1)^2}.
Question 12. Let z_1 = 2-i, z_2=-2+i. Find
(i). Re \left ( \frac{z_1z_2}{ \overline{z_1}} \right ) .
(ii). \Im \left ( \frac{1}{z_1 \overline{z_1}} \right )
Question 13. Find the modulus and argument of the complex number \frac{1+2i}{1-3i}.
Question 14. Find the real numbers x and y if (x-iy)(3+5i) is the conjugate of -6-24i.
Question 15. Find the modulus of \frac{1+i}{1-i} – \frac{1-i}{1+i}.
Question 16. If (x+iy)^3=u+iv, then show that \frac{u}{x}+ \frac{v}{y}=4(x^2-y^2).
Question 17. If \alpha \text{ and } \beta, are different complex numbers with |\beta| = 1, then find \left | \frac{\beta – \alpha}{1 – \overline{\alpha} \beta} \right |
Question 18. Find the number of non-zero integral solutions of the equation |1-i|^x = 2^x.
Question 19. If (a+ib)(c+id)(e+if)(g+ih) = A+iB , then show that (a^2+b^2)(c^2+d^2)(e^2+f^2)(g^2+h^2) = A^2 + B^2.
Question 20. If \left ( \frac{1+i}{1-i} \right )^m = 1, then find the least positive integral value of m. | 2021-06-13 02:44:54 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9885545372962952, "perplexity": 3755.8891493882916}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-25/segments/1623487598213.5/warc/CC-MAIN-20210613012009-20210613042009-00078.warc.gz"} |
https://www.ademcetinkaya.com/2023/03/ztaqw-zimmer-energy-transition.html | Outlook: Zimmer Energy Transition Acquisition Corp. Warrants is assigned short-term Ba1 & long-term Ba1 estimated rating.
Dominant Strategy : Wait until speculative trend diminishes
Time series to forecast n: 04 Mar 2023 for (n+8 weeks)
Methodology : Inductive Learning (ML)
## Abstract
Zimmer Energy Transition Acquisition Corp. Warrants prediction model is evaluated with Inductive Learning (ML) and Multiple Regression1,2,3,4 and it is concluded that the ZTAQW stock is predictable in the short/long term. According to price forecasts for (n+8 weeks) period, the dominant strategy among neural network is: Wait until speculative trend diminishes
## Key Points
1. Decision Making
2. How accurate is machine learning in stock market?
3. Fundemental Analysis with Algorithmic Trading
## ZTAQW Target Price Prediction Modeling Methodology
We consider Zimmer Energy Transition Acquisition Corp. Warrants Decision Process with Inductive Learning (ML) where A is the set of discrete actions of ZTAQW stock holders, F is the set of discrete states, P : S × F × S → R is the transition probability distribution, R : S × F → R is the reaction function, and γ ∈ [0, 1] is a move factor for expectation.1,2,3,4
F(Multiple Regression)5,6,7= $\begin{array}{cccc}{p}_{a1}& {p}_{a2}& \dots & {p}_{1n}\\ & ⋮\\ {p}_{j1}& {p}_{j2}& \dots & {p}_{jn}\\ & ⋮\\ {p}_{k1}& {p}_{k2}& \dots & {p}_{kn}\\ & ⋮\\ {p}_{n1}& {p}_{n2}& \dots & {p}_{nn}\end{array}$ X R(Inductive Learning (ML)) X S(n):→ (n+8 weeks) $\begin{array}{l}\int {e}^{x}\mathrm{rx}\end{array}$
n:Time series to forecast
p:Price signals of ZTAQW stock
j:Nash equilibria (Neural Network)
k:Dominated move
a:Best response for target price
For further technical information as per how our model work we invite you to visit the article below:
How do AC Investment Research machine learning (predictive) algorithms actually work?
## ZTAQW Stock Forecast (Buy or Sell) for (n+8 weeks)
Sample Set: Neural Network
Stock/Index: ZTAQW Zimmer Energy Transition Acquisition Corp. Warrants
Time series to forecast n: 04 Mar 2023 for (n+8 weeks)
According to price forecasts for (n+8 weeks) period, the dominant strategy among neural network is: Wait until speculative trend diminishes
X axis: *Likelihood% (The higher the percentage value, the more likely the event will occur.)
Y axis: *Potential Impact% (The higher the percentage value, the more likely the price will deviate.)
Z axis (Grey to Black): *Technical Analysis%
## IFRS Reconciliation Adjustments for Zimmer Energy Transition Acquisition Corp. Warrants
1. To be eligible for designation as a hedged item, a risk component must be a separately identifiable component of the financial or the non-financial item, and the changes in the cash flows or the fair value of the item attributable to changes in that risk component must be reliably measurable.
2. For example, Entity A, whose functional currency is its local currency, has a firm commitment to pay FC150,000 for advertising expenses in nine months' time and a firm commitment to sell finished goods for FC150,000 in 15 months' time. Entity A enters into a foreign currency derivative that settles in nine months' time under which it receives FC100 and pays CU70. Entity A has no other exposures to FC. Entity A does not manage foreign currency risk on a net basis. Hence, Entity A cannot apply hedge accounting for a hedging relationship between the foreign currency derivative and a net position of FC100 (consisting of FC150,000 of the firm purchase commitment—ie advertising services—and FC149,900 (of the FC150,000) of the firm sale commitment) for a nine-month period.
3. However, an entity is not required to separately recognise interest revenue or impairment gains or losses for a financial asset measured at fair value through profit or loss. Consequently, when an entity reclassifies a financial asset out of the fair value through profit or loss measurement category, the effective interest rate is determined on the basis of the fair value of the asset at the reclassification date. In addition, for the purposes of applying Section 5.5 to the financial asset from the reclassification date, the date of the reclassification is treated as the date of initial recognition.
4. When an entity, consistent with its hedge documentation, frequently resets (ie discontinues and restarts) a hedging relationship because both the hedging instrument and the hedged item frequently change (ie the entity uses a dynamic process in which both the hedged items and the hedging instruments used to manage that exposure do not remain the same for long), the entity shall apply the requirement in paragraphs 6.3.7(a) and B6.3.8—that the risk component is separately identifiable—only when it initially designates a hedged item in that hedging relationship. A hedged item that has been assessed at the time of its initial designation in the hedging relationship, whether it was at the time of the hedge inception or subsequently, is not reassessed at any subsequent redesignation in the same hedging relationship.
*International Financial Reporting Standards (IFRS) adjustment process involves reviewing the company's financial statements and identifying any differences between the company's current accounting practices and the requirements of the IFRS. If there are any such differences, neural network makes adjustments to financial statements to bring them into compliance with the IFRS.
## Conclusions
Zimmer Energy Transition Acquisition Corp. Warrants is assigned short-term Ba1 & long-term Ba1 estimated rating. Zimmer Energy Transition Acquisition Corp. Warrants prediction model is evaluated with Inductive Learning (ML) and Multiple Regression1,2,3,4 and it is concluded that the ZTAQW stock is predictable in the short/long term. According to price forecasts for (n+8 weeks) period, the dominant strategy among neural network is: Wait until speculative trend diminishes
### ZTAQW Zimmer Energy Transition Acquisition Corp. Warrants Financial Analysis*
Rating Short-Term Long-Term Senior
Outlook*Ba1Ba1
Income StatementB1Ba3
Balance SheetBa2C
Leverage RatiosB3Ba1
Cash FlowB3Baa2
Rates of Return and ProfitabilityBaa2Baa2
*Financial analysis is the process of evaluating a company's financial performance and position by neural network. It involves reviewing the company's financial statements, including the balance sheet, income statement, and cash flow statement, as well as other financial reports and documents.
How does neural network examine financial reports and understand financial state of the company?
### Prediction Confidence Score
Trust metric by Neural Network: 93 out of 100 with 562 signals.
## References
1. Akgiray, V. (1989), "Conditional heteroscedasticity in time series of stock returns: Evidence and forecasts," Journal of Business, 62, 55–80.
2. Miller A. 2002. Subset Selection in Regression. New York: CRC Press
3. Meinshausen N. 2007. Relaxed lasso. Comput. Stat. Data Anal. 52:374–93
4. Athey S, Wager S. 2017. Efficient policy learning. arXiv:1702.02896 [math.ST]
5. Scott SL. 2010. A modern Bayesian look at the multi-armed bandit. Appl. Stoch. Models Bus. Ind. 26:639–58
6. Bottomley, P. R. Fildes (1998), "The role of prices in models of innovation diffusion," Journal of Forecasting, 17, 539–555.
7. Çetinkaya, A., Zhang, Y.Z., Hao, Y.M. and Ma, X.Y., When to Sell and When to Hold FTNT Stock. AC Investment Research Journal, 101(3).
Frequently Asked QuestionsQ: What is the prediction methodology for ZTAQW stock?
A: ZTAQW stock prediction methodology: We evaluate the prediction models Inductive Learning (ML) and Multiple Regression
Q: Is ZTAQW stock a buy or sell?
A: The dominant strategy among neural network is to Wait until speculative trend diminishes ZTAQW Stock.
Q: Is Zimmer Energy Transition Acquisition Corp. Warrants stock a good investment?
A: The consensus rating for Zimmer Energy Transition Acquisition Corp. Warrants is Wait until speculative trend diminishes and is assigned short-term Ba1 & long-term Ba1 estimated rating.
Q: What is the consensus rating of ZTAQW stock?
A: The consensus rating for ZTAQW is Wait until speculative trend diminishes.
Q: What is the prediction period for ZTAQW stock?
A: The prediction period for ZTAQW is (n+8 weeks) | 2023-03-26 14:46:30 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 2, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.49317771196365356, "perplexity": 9966.443064007797}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296945473.69/warc/CC-MAIN-20230326142035-20230326172035-00315.warc.gz"} |
https://www.gamedev.net/forums/topic/209137-inverse-of-3x3-and-up-matrices/ | Archived
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Inverse of 3x3 and up matrices
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How do you find the inverse of a 3x3 matrix and up (meaning bigger dimensions like 4x4, 5x5) with pencil and paper? I know how to do it with a 2x2 matrix by the book. Find the determinant which is ad-bc assuming the matrix :
[a b]
[c d]
then the inverse is:
[(d/(ad-bc)) (-b/(ad-bc))]
I''ve been just using my calculator for 3x3 calculations and up because there has been nothing in my book so I''m assuming that I really don''t need to know this but I want to know what''s going behind the scenes in the calculator. This is not a homework question I''m expanding my knowledge on the feeble base that I already have. Thanks in advance.
Charles Hwang -aka Tazel [Maxedge My Site(UC)|E-mail|NeXe|NeHe|SDL] [Google|Dev-C++|GDArticles|C++.com|MSDN]
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Gauss-Jordan Elimination is one method.
"I forgot I had the Scroll Lock key until a few weeks ago when some asshole program used it. It even used it right" - Conner McCloud
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A sophisticated computer program for solving systems of equations could use elimination and pivoting (switching around rows and/or columns) to factor the matrix into upper and lower triangular matrixes, and then use these matrices to solve systems rather than explicitly calculating the inverse matrix.
Ax = b
becomes
LUx = b
where L is a lower triangular matrix that looks something like:
x 0 0 0 0
x x 0 0 0
x x x 0 0
x x x x 0
x x x x x
where the x''s could be any number (it depends on the matrix that was factored). Everything above the main diagonal is 0.
and U is an upper diagonal matrix, where everything below the main diagonal is 0.
Any nonsingular square matrix can be factored like this. The factorization is then used to solve the system by doing the following:
let y = Ux
solve Ly = b
solve Ux = y
Solving both of those systems is easy because of the triangular structure of the matrices; straightforward substitution can be used.
There are also iterative methods for solving systems, where in each iteration a closer approximation to the solution is found. The program can just keep iterating until the solution is within the desired tolerance.
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× | 2018-07-22 20:45:42 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5318387746810913, "perplexity": 1171.9018849205504}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-30/segments/1531676593586.54/warc/CC-MAIN-20180722194125-20180722214125-00279.warc.gz"} |
http://piping-designer.com/index.php/mathematics/1991-sum | # Sum
Written by Jerry Ratzlaff on . Posted in Mathematics
Sum is the result of adding two or more numbers.
• Equation - $$11 + 7 = 18$$
• The sum is $$\;18\;$$ | 2018-04-26 09:20:29 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8895950317382812, "perplexity": 3529.940180219544}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-17/segments/1524125948125.20/warc/CC-MAIN-20180426090041-20180426110041-00042.warc.gz"} |
http://math.stackexchange.com/tags/exponential-function/new | # Tag Info
2
We have $$(8^x)^2+8^x-20=0$$ $$\implies8^x=\frac{-1\pm\sqrt{1-4(-20)}}2=-5,4$$ For real $x,8^x>0$ Then $8^x=4\implies x\ln8=\ln4$ But $\ln8=\ln(2^3)=3\ln2$ and $\ln4=\ln(2^2)=2\ln2$
6
Hint: Make the substitution $u=8^x$. Now the equation becomes $u^2+u-20=0$.
0
This is essentially another way of saying what sanjab has already said, but in a way that gives it a bit more intellectual context. Define a function as follows. $$\otimes : \mathbb{R}_{>0} \times \mathbb{R}_{>0} \longrightarrow \mathbb{R}_{>0}$$ $$p \otimes q = \exp(\log(p)\log(q))$$ Then $\otimes$ is associative and commutative. Its unit is $e$, ...
3
take the $\log$ for both sides to get $$\log (x^{log(a)})=\log (a^{\log(x)})$$ $$\log (a){log(x)}=\log( a){\log(x)}$$ It is clear that the $a$,$x$ should be positive
1
Yes: the general definition of $A^B$ is $\exp(B\log(A))$.
12
$$\large x^{\log(a)} = (e^{\log(x)})^{\log(a)} = e^{\log(x)\log(a)} = a^{\log(x)}$$ This only works if $x$ and $a$ are both positive real numbers.
2
Step 1: Compute the norm $$r:=\sqrt{4^2+16^2\cdot 5}$$ Step 2: Compute the tangent of the argument (and find the angle) $$\tan(\theta)=\frac{16\sqrt{5}}{-4}$$ Mind the sign of the real part $-4$ to get the appropriate angle. Step 3: Write the number $$re^{i\theta}.$$
1
Take $\nu=1-\lambda$. Since $\nu\in(0,1)$ we have $\nu=e^{-r}$ with $r>0$ and we have to prove that for $$f(x) = 1-e^{-rx}$$ we have: $$\frac{f(x)-f(x-1)}{x-(x-1)} \leq \frac{f(x)-f(0)}{x-0}.$$ This follows from the fact that $f(x)$ is a concave function, since: $$f''(x) = -r^2 e^{-rx} < 0.$$
2
The Problem The main problem when computing $e^{-20}$ is that the terms of the series grow to $\frac{20^{20}}{20!}\approx43099804$ before getting smaller. Then the sum must cancel to be $\approx2.0611536\times10^{-9}$. In a floating point environment, this means that $16$ digits of accuracy in the sum are being thrown away due to the precision of the large ...
0
We can always find the exponential of a $2 \times 2$ matrix ( with real or complex entries) without calculating eigenvalues or Jordan form. 1) Note that we can always put a $2 \times 2$ matrix in the form $A=hI+A'$ where: $h=\mbox{tr}A/2$, $\mbox{tr}A'=0$, $\mbox{det}A'=\mbox{det}A-\left(\dfrac{\mbox{tr}A}{2}\right)^2$; and $[hI,A']=0$ so that ...
0
The function $$f: \mathbb R \longrightarrow \mathbb R, f(x):= ax^b\cdot\exp(x)$$ extends to a holomorphic function on the complex plane $$F: \mathbb C \longrightarrow \mathbb C, F(z):= az^b\cdot\exp(z).$$ Global holomorphic functions are named entire functions. An entire function which is not a polynomial is named a transcendental function. As a ...
0
1) The regular double precision floating point arithmetic of Matlab is not sufficient to precisely calculate partial sums of this power series. To overcome that limitation, you can use the exact symbolic computation capabilities of the Symbolic Math Toolbox. This code x = sym(-20); i = sym(1 : 100); expx = sum(x .^ (i - 1) ./ factorial(i - 1)) sums the ...
2
Consider $f(x) = xe^x-e$. You have that $x = 1$ is a root. And: $$f'(x) = e^x + xe^x > 0,$$ for $x > 0$, so we don't have any positive roots other than $1$. If $x \leq 0$, you would have $e = \text{something negative}$, which can't happen.
6
The function $f(x) = xe^x$ does not have an inverse that can be expressed in terms of any finite algebraic combination of the usual functions. The two branches that form its inverse are known as the Lambert W function(s). The equation $$y = xe^x$$ can be solved for $y$ using a numerical approach, if an approximate solution is desired.
2
The approach you mention is difficult, but possible. I have presented it in my blog post. The main steps are as follows: 1) Define $a^{b}$ (without using any logs or $e$) rigorously for $a > 0$ and any real $b$. 2) Show that $\lim_{a \to 0}\dfrac{x^{a} - 1}{a} = f(x)$ exists for all $x > 0$ and hence defines a function of $x$. This function is ...
0
It's easier to start from the first equation and prove that it's the same as the second one. From $$L := \lim _{a \to 0} \frac{e^a-1}{a}$$ set $e^a - 1 = t$, so that $a = \ln(1 + t)$: $$L = \lim_{t \to 0} \frac{t}{\ln(1 + t)} = \lim_{t \to 0} \left(\frac{\ln(1 + t)}{t}\right)^{-1} = \lim_{t \to 0} \left(\ln\left[\left(1 + t\right)^{1}\right]\right)^{-1} = ... 0$$ f' = x f \iff \int \frac{ df}{f} = \int x dx \implies \ln |f| = x^2 + C \implies f(x) = \tilde C e^{x^2} $$with C \in \mathbb{R} 1$$(d/dx) \ln f(x) = \frac{f'(x)}{f(x)} = x.$$Therefore \ln f(x) = \frac{1}{2}x^2 + C, so f(x) = e^{\frac{1}{2}x^2 + C} = De^{\frac{1}{2}x^2}, where D is an arbitrary positive constant. 6 Note that by the Mean Value Theorem, we have$$ \frac{\tanh(x)}{x}=\mathrm{sech}^2(\xi)\tag{1} $$for some \xi between 0 and x. Therefore, for x\ne0,$$ 0\lt\frac{\tanh(x)}{x}\lt1\tag{2} $$Thus, for x\ne0,$$ \begin{align} x\frac{\mathrm{d}}{\mathrm{d}x}\left(e^{x-x^2/2}+e^{-x-x^2/2}\right) &=(x-x^2)e^{x-x^2/2}-(x+x^2)e^{-x-x^2/2}\\ ...
5
First, since both sides are even functions, it is sufficient to prove that $e^x+e^{-x} \leq 2e^{x^2/2}$ for all $x \geq 0$. Then we can change the problem to the equivalent problem of proving that for $x \geq 0$ $$u(x) \equiv \frac{1}{e^x+e^{-x}} \geq \frac{1}{2}e^{-x^2/2} \equiv v(x)$$ We start by observing that $u(0) = v(0).$ Now in the immortal words of ...
19
$y = 2 e^{x^2/2}$ satisfies the d.e. $y' = x y$ with $y(0) = 2$, while $z = e^{x} + e^{-x} = 2 \cosh(x)$ satisfies $z' = \tanh(x) z$ with $z(0)=2$. Since $x \ge \tanh(x)$ for $x \ge 0$, Gronwall's inequality does the rest.
14
As @flawr points out, the L.H.S. is $\displaystyle \cosh x = \frac{e^x+e^{-x}}{2}$ has an infinite product representation: $$\cosh x = \prod\limits_{n=1}^{\infty} \left(1+\frac{4x^2}{\pi^2(2n-1)^2}\right) \le \exp \sum\limits_{n=1}^{\infty}\frac{4x^2}{\pi^2(2n-1)^2} = e^{x^2/2}$$
2
As said in comments and answers, there is no analytical solutions fo such an equation and numerical methods should be used. Probably, the simplest root-finding method is Newton which, starting from a reasonable guess $x_0$, will update it according to $$x_{n+1}=x_n-\frac{f(x_n)} {f'(x_n)}$$ This could be applied to the orginal equation ...
1
You might wanna try this: Let $7^x$ be $X$ and $3^x$ be $Y$. $\implies X+Y=XY$ Adding 1 to both sides, $\implies 1=(XY-X-Y+1)=(X-1)(Y-1)$ $\implies (7^x-1)(3^x-1)=1$ Perhaps here graphing is the best option. Even a rough graph could give the idea that one solution here is $- \infty$. Also, seeing the slope of the rough graph one can also think of the ...
1
Hint: Divide both sides by $21^x$, and use the fact that we now have a sum of monotonous functions being equal to something constant. Obviously, this can only happen for a single value of x, so the equation has only one solution. Which is what you were probably tasked to determine in the first place, i.e., the number of solutions, not their actual value, ...
4
You won't get a closed-form solution, but numerical methods can be used.
0
I can let $y=\frac{100}{1+2^{-x}}$. $$1+2^{-x} = \frac{100}{y}$$ $$2^{-x} = \frac{100}{y}-1$$ $$2^{-x} = \frac{100-y}{y}$$ $$2^x = \frac{y}{100-y}$$ $$x = \log_2 \left ( \frac{y}{100-y}\right)$$
0
$$g(x) = \frac{100}{1+2^{-x}}$$ $$\frac{100}{g(x)} = 1+2^{-x}$$ $$\frac{100}{g(x)} -1 = 2^{-x}$$ $$\ln\left(\frac{100}{g(x)} -1\right) / \ln(2) = -x$$ $$-\ln\left(\frac{100}{g(x)} -1\right) / \ln(2) = x$$
0
$g(x)=\frac{100}{1+2^{-x}}\implies$ $g(x)\cdot(1+2^{-x})=100\implies$ $1+2^{-x}=\frac{100}{g(x)}\implies$ $2^{-x}=\frac{100}{g(x)}-1\implies$ $-x=\log_2(\frac{100}{g(x)}-1)\implies$ $x=-\log_2(\frac{100}{g(x)}-1)$
0
Replace sequences with functions: $$N_{t} \longrightarrow N(t)$$ Consider $R$ as rate of population growth: $$R(t)=N'(t)$$ If $$N(t+1)=N(t) exp(r(1-\frac{N(t)}{k}))$$ Then for small $h \approx 0$ you can linearize the equation: $$N(t+h)=N(t)+hN(t) exp(r(1-\frac{N(t)}{k}))$$ Then simply: $$R(t)=N'(t)=\frac{N(t+h)-N(t)}{h}=N(t) ... 0 If we want to define a function f \colon \mathbb{R} \to \mathbb{C}, f(t) = e^{it} in a way that meshes with our formulas for the real exponential function, it makes sense to require that f(0) = 1 and f'(t) = if(t). Let's prove that we must then have f(t) = \cos t + i\sin t. Write f(t) = x(t) + iy(t). We have f'(t) = x'(t) + iy'(t). First note ... 2 The solutions are counting multiplicity and include complex solutions. It's called the fundamental theorem of algebra. Low-level proofs are not easy to come by, however. 0 It was already mentioned in comments and other answers that the inequality \exp(x)>1 for x>0 is easy. Here is rather elementary proof that \exp(x)\le1 for x<0. Let us denote$$f_n(x)=1+x+\frac{x^2}{2!}+\dots+\frac{x^n}{n!}.$$Notice that f_{n+1}'(x)=f_n(x). Try to prove by induction that for n=1,2,\dots that: f_{2n-1}(x) is ... 0 the first part e^x > 1 for x > 0 follows from e^x = 1 + x + \frac{x^2}{2} + \cdots because x > 0 implies x^2 > 0, x^3 > 0, \cdots the second part 0 < e^x < 1 for x < 0 does not seem to be elementary. if you can establish even an instance of the additive property e^{-x} = \dfrac{1}{e^x}, then you are done. one way of ... 1 If x>0, you have a series with positive terms, so its sum is greater than the sum of the first two terms, which is 1+x and 1+x>1. If x<0 you have an alternating series. It's a theorem that for alternating series, the error bound when you take the sum up to rank m: \sum_{k=0}^m a_k, is at most \lvert a_{m+1}\rvert and the error has the ... 3 The power series of the exponential function is defined on \Bbb R so we can differentiate it term by term on \Bbb R and we get$$\exp'(x)=\exp(x)$$Moreover, we see easily that \exp(x)>0 for x\ge0 and using the Cauchy product we get$$\exp(x)\exp(y)=\exp(x+y),\quad \forall (x,y)\in\Bbb R^2$$hence$$\exp(-x)\exp(x)=\exp(0)=1\implies ...
1
For $x>0$, $$\exp(x)=1+x+\frac{x}{2}+\cdots>1+0+0+\cdots=1$$ Since $\exp(0)=1$ and $\exp$ is strictly monontone increasing, $\exp(x)<1$ for $x<0$.
1
Try using logarithms. A logarithm is defined as follows, If $a^{b}=c$, then $\log_{a} c=b$ So, similarly, here we get $m=\log_{d} n$. We can further simplify it by changing the logarithms' base to $10$, $m=\frac{\log_{10} n}{\log_{10} d}$ If you want to learn more about logarithms, go here
3
Using any logarithm $\log$, we have $$\log n = \log (d^m) = m \log d,$$ so $$m = \frac{\log n}{\log d} = \log_d n.$$
0
\begin{align} 0&=\frac{4}{3}e^{3x}+2e^{2x}-8e^x\tag{1} \\[1em] & = \frac{\frac{4}{3}e^{3x}+2e^{2x}-8e^{x}}{2e^x}\tag{2} \\[1em] & = \frac{2}{3}e^{2x}+e^x-4\tag{3} \\[1em] \end{align} Now let $\xi=e^x,\therefore e^{2x}=\left(e^x\right)^2=\xi^2.$ This gives us \begin{align} 0&=\frac{2}{3}\xi^2 +\xi-4\tag{4} \\[1em] \therefore \xi & = ...
3
Hint: The $x$-intercept is when $\frac43 e^{3x}+2e^{2x}-8e^{x} = 0$. Now set $y = e^{x}$, so your equation is $$\frac{4}{3}y^3+2y^2-8y = 0$$ which means $$y\left(\frac{4}{3}y^2+2y-8\right) = 0.$$
7
This equation cannot be solved using “traditional” algebraic manipulations. In this case, one would use the Lambert W function: $$W(x): x = W(x)\cdot e^{W(x)}$$ or in other words, it is the solution of the equation $x = w e^w$. With this knowledge, we can try to substitute $y:=\frac{1}{x}$: $$\Rightarrow 0 = e^y-\frac{1}{y} \Rightarrow \frac{1}{y} = e^y ... 0 (i) We need to solve$$\log y = x^2 - x + 6 \, \Leftrightarrow \, x^2 - x + 6 - \log y = 0.Use the quadratic formula with a = 1, \, b = -1, \, c = 6 - \log y. (ii) For any function f, and its inverse f^{-1}, we have \operatorname{dom} f^{-1} = \operatorname{range} f. This makes sense because the definition of an inverse function is f^{-1}(f(x)) ... 0 In reference to Axoren, the following is true for (1): \begin{align} 9^{x+1}=27^{2x-3} & \implies\left(3^2\right)^{x+1}=\left(3^3\right)^{2x-3}\tag{1}\\[1em] & \implies \left(3\right)^{2x+2}=\left(3\right)^{6x-9}\tag{2} \\[1em] & \implies \left(2x+2\right)\log_3\left|3\right|=\left(6x-9\right)\log_3\left|3\right|\tag{3}\\[1em] & \implies ... 1 Hints:\log(a^b) = b \log(a) \\ \log(ab) = \log(a) + \log(b) $$Example for part c):$$ 210 = 40(1.5)^x \\ \log(210) = \log(40 (1.5)^x) \\ \log(210) = x\log(1.5) + \log(40) \\ \frac{\log(210) - \log(40)}{\log(1.5)} = x \\ x \approx 4.0897 $$1 I had decided to solve this problem using y=i(1-a)^t to solve this problem, where y is the final amount, i is the initial amount, a is the rate of decrease or "cooling factor" in this case, and t is the number of time periods. you will see why I used this formula in a little bit. a) To solve for a, we can input some values from the table to fill ... 5 I think this is basically a different way to state exactly what André Nicolas said in a comment, but observe that the largest power of a given prime p found as a factor in a number less than n is explicitly given by$$ \lfloor\log_p(n)\rfloor=\left\lfloor\frac{\ln n}{\ln p}\right\rfloor $$so we can write LCM(n)=LCM(1,2,...,n) explicitly as$$ ...
1
Let the initial volume of the container be $V_0$ and the density be $\rho$. Let the evaporation and condensation be uniform and that 2.1% of the volume is lost everytime the purifying process is over. Thus the model is $${\rho\times(\dot V_0 - \dot V_1)} = 0.021*\rho\times\dot V_0$$ Cancelling $\rho$, and converting the volumetric rate to volume, You ...
1
After our comment conversation, we see that the equation would be $$\text{amount}=\text{initial}(0.979)^x$$ And to see how many cycles it takes to get to half the initial amount would be $$\frac{c}{2}=c(0.979)^x\\\frac{1}{2}=0.979^x$$
2
The Poisson models the number of arrivals in a certain fixed time. It is a discrete distribution, taking on values $0,1,2,\dots$. The exponential models the waiting time between consecutive arrivals. It is a continuous distribution. There is a connection, since they are used in modelling two different features of the same phenomenon. But they are quite ...
Top 50 recent answers are included | 2015-01-31 07:28:58 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 1, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.978391170501709, "perplexity": 280.7948644221529}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-06/segments/1422122108378.68/warc/CC-MAIN-20150124175508-00120-ip-10-180-212-252.ec2.internal.warc.gz"} |
http://stackoverflow.com/questions/12972290/backslash-is-rendered-as-wong-symbol-in-ie9-in-windows-7-if-courier-font-i | # backslash is rendered as wong symbol ( ₩ ) in IE9 in windows 7 if courier font is used
I'm facing this problem,
If opened in IE9 under windows 7, in my pre formatted html block \ is rendered as wong symbol ₩ if courier font is used. If I set Tahoma, e.g. it's ok. In chrome, even if courier is set, symbol is rendered as backslash.
How to fix it?
Edit: code that reproduces this:
<html><head>
<style>
pre {
margin-top: 10px;
margin-left: 50px;
font-family: courier;
background-color:#ddd;
}
<pre>
Can\'t
</pre>
</body></html>
-
Lol, bug of the week… – feeela Oct 19 '12 at 10:41
Any example code? What do you mean with "pre formatted html block"? – MarcoK Oct 19 '12 at 10:53
Not reproducible. <pre font-family:Courier>foo\bar</pre> displays normally. Please provide more information. Have you downloaded a font named Courier from somewhere? Windows 7 has no font under that name; it internally maps requests for Courier to requests for Courier New. – Jukka K. Korpela Oct 19 '12 at 10:58
Michael Kaplan explains. Since your document did not specify a character encoding, the browser chooses an encoding by any means it wants. Internet Explorer chooses the encoding based on the user's current language preferences. Users in Korea will default to code page 949, which interprets 0x5C as the ₩ character. If you don't like this, then express an encoding explicitly. – Raymond Chen Oct 19 '12 at 12:45
I cannot reproduce the problem on my Win 7, so I still suspect the reason is that your system has an actual font under the name “Courier” (normal Windows 7 is not shipped with such a font). Either that font is broken regarding the backslash, or it simply lacks it and the browsers picks up the character from another font. In the latter case, that font might be broken.
There are surprisingly many fonts that have a glyph for “₩” U+20A9 WON SIGN where they should have a glyph for backslash. There has been some speculation about the reasons. But the point is that there should be no reason why such a font would be used unless your browser resorts to picking up backup fonts. In that case, IE might have been set to use e.g. Batang Che as the default monospace font – and it’s one of the fonts with that problem.
On the practical side, “Courier” should almost never be used. In systems that have a font under such a name, it is often a bitmap font that looks rather bad especially when font size is changed. Use “Courier New” instead. Or something better, such as
pre, tt
{ font-family : Consolas, Lucida Console, Courier New, monospace; }
-
My Windows 7 does have a Courier (which looks to be a bitmap font) as well as Courier New, yet the problem doesn't reproduce for me. Raymond is right. When the browser displays different characters than what you expected, it's almost always because the wrong encoding is specified or no encoding is specified and the browser guessed wrong. – Adrian McCarthy Oct 19 '12 at 16:29
@AdrianMcCarthy, what happens if you use Courier in Notepad and enter “\”? What happens if you view a web page containing “\” and font-family: Courier, Tahoma? @naughty_hacker, when viewing a problem page on IE, what does View/Encoding show? Do things change if you change the encoding there? How? – Jukka K. Korpela Oct 19 '12 at 17:41
In both cases, I see a normal backslash. – Adrian McCarthy Oct 19 '12 at 17:54
Thanks for your post, I tried setting <meta http-equiv="Content-Type" content="text/html; charset=utf-8"> it doesn't help. I also tried setting <META HTTP-EQUIV="CONTENT-LANGUAGE" CONTENT="en-US">, it doesn't help too. View/encoding shows correct symbol. If I change style to use Tahoma, problem disappears. Also in the browser in internet options -> language, there is En_us first. – dhblah Oct 19 '12 at 18:17
@naughty_hacker, I meant what encoding is checked when you select View/Encoding. This is relevant for resolving whether this is an encoding problem or a font problem. – Jukka K. Korpela Oct 19 '12 at 18:55
show 4 more comments
As Raymond Chen pointed out in the comments, the browser has likely guessed the encoding incorrectly.
If you want to specify the encoding directly in the file, then you can use a meta tag in the head element of the page, like this:
<meta http-equiv="Content-Type" content="text/html; charset=my_encoding_here">
Where my_encoding_here is actually a string representing the encoding you used when creating the HTML. Common encodings are utf-8 and ISO-8859-1, but you should figure out exactly which encoding your editor is using and make sure you match it.
If you're serving pages like this, then you might choose to specify the encoding in your webserver, which will put the information into an HTML header when it returns the page.
-
Setting encoding doesn't help. – dhblah Oct 19 '12 at 18:17 | 2014-03-12 13:58:08 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7083308100700378, "perplexity": 4143.762260768565}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-10/segments/1394021791079/warc/CC-MAIN-20140305121631-00051-ip-10-183-142-35.ec2.internal.warc.gz"} |
https://help.febio.org/FebioUser/FEBio_um_3-4-Section-2.4.html | Converted document
$\newcommand{\lyxlock}{}$
Section 2.3: The Command Line Up Chapter 2: Running FEBio Section 2.5: The Configuration File
2.4 The FEBio Prompt
At the FEBio prompt allows users to manipulate the currently active model or further configure FEBio. The FEBio prompt is shown when you start FEBio without any command arguments, or when a run is interrupted either by the user (using ctrl+c) or by reaching a breakpoint. The FEBio prompt will look something like this:
febio>
You can now enter one of the following commands:
break Add a breakpoint, which will stop FEBio at a particular time point or event. A breakpoint can be defined at a particular (simulation) time or at an event. (See section 2.8.3↓ for more details on break points.)
breaks Prints list of current breakpoints.
clear Clear one or all breakpoints.
cont Continue an interrupted run. FEBio will continue the analysis where it left off.
conv force the current time step to converge. This is useful for example when a time step is having difficulty satisfying too tight of convergence criteria. The user can then manually force the convergence of the time step. However, if the convergence difficulties are due to instabilities, forcing a time step to converge could cause the solution to become unstable or even incorrect. Also be aware that even if the solution recovers on later timesteps, the manually converged step might be incorrect.
debug Entering debug will toggle debug mode. Adding on (off) will turn the debug mode on (resp. off). In debug mode, FEBio will store additional information to the log and plot file that could be useful in debugging the run. It is important to note that since FEBio will store all non-converged states to the plot file, this file may become very large in a short number of time steps. See Section 2.8.2↓ for more details on debugging.
fail Stop the current iteration and retry. If the current time step is not converging and if the auto-time stepper is enabled, the fail command will stop the current time step and retry it with a smaller time step size. If the auto-time stepper is not enabled, the fail command will simply exit the application.
help Prints an overview of available commands with a brief description of each command.
out Write the current linear system (matrix and right hand side vector) to a file.
plot Write the current state of the model to the plot database. This command is useful when you want to store the non-converged state at the current iteration. Note that this command only stores the state at the current iteration. If you turn on debug mode, all the iterations are stored to the plot file.
plugins Print a list of the plugins that are loaded.
print Print the value of variables. The following variables can be printed.
• nnz Number of nonzeroes in global stiffness matrix.
time The simulation time.
neq Number of equations.
quit Stop the current model, or exit FEBio if no model is running.
restart Toggles the restart flag. When the restart flag is set, FEBio will create a dump file at the end of each converged time step. This dump file can then later be used to restart the analysis from the last converged time step. See Section 2.8.4↓ and Chapter 5↓ for more details on FEBio's restart feature.
run run an FEBio input file. This command takes the same options as you can enter on the command line. For example, to run a file named test.feb from the FEBio prompt, type the following:
run –i test.feb
svg Write the sparse matrix profile to an svg file.
time Print progress time statistics. | 2021-09-16 18:24:14 | {"extraction_info": {"found_math": true, "script_math_tex": 24, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5906285047531128, "perplexity": 1471.583506752275}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-39/segments/1631780053717.37/warc/CC-MAIN-20210916174455-20210916204455-00709.warc.gz"} |
http://simbad.u-strasbg.fr/simbad/sim-ref?querymethod=bib&simbo=on&submit=submit+bibcode&bibcode=2004A%26A...424..927C | # 2004A&A...424..927C
other querymodes : Identifierquery Coordinatequery Criteriaquery Referencequery Basicquery Scriptsubmission TAP Outputoptions Help
Query : 2004A&A...424..927C
2004A&A...424..927C - Astronomy and Astrophysics, volume 424, 927-934 (2004/9-4)
Bright metal-poor variables: Why Anomalous'' Cepheids?
CAPUTO F., CASTELLANI V., DEGL'INNOCENTI S., FIORENTINO G. and MARCONI M.
Abstract (from CDS):
We investigate the theoretical scenario concerning the large sample of variables recently discovered in the dwarf, metal-poor irregular galaxy Leo A, focusing the attention on the Anomalous'' Cepheid phenomenon and its correlation with RR Lyrae stars, Classical and Population II Cepheids. To this purpose, we make use of suitable stellar and pulsation models to depict the pulsational history of evolutionary structures with metallicity Z=0.0004. We find that He-burning pulsators are expected only outside the mass interval ∼0.8-1.7M. Stars from ∼1.8 to 4M, a mass range including both Anomalous and Classical Cepheids, populate to good approximation a common MV-logPF instability strip, independently of the previous occurrence of a He flash event. Their periods and luminosities increase with the stellar mass and they are at a lower luminosity level MV,LE~-0.5mag, as observed in Leo A. The class of less massive pulsators (M<0.8 M, namely RR Lyrae stars and Population II Cepheids) populate a distinct instability strip, where the magnitudes become brighter and the periods longer when the pulsator mass decreases. The dependence on metal content in this scenario has been investigated over the range Z=0.0002 to 0.008. The edges of the pulsational strip for the more massive class of pulsators appear to be independent of metallicity, but with a minimum mass of these bright pulsators which decreases with decreasing metallicity, thus decreasing the predicted minimum luminosity and period. Comparison with data for Cepheids in Leo A and in the moderately metal-rich extragalactic stellar system Sextans A discloses an encouraging agreement with the predicted pulsational scenario. On this basis, we predict that in a stellar system where both RR Lyrae stars and Cepheids are observed their magnitude difference may help in constraining both the metal content and the distance. The current classification of metal-poor Cepheids is briefly discussed and suggestion is advanced for an updated terminology abreast with the current knowledge of stellar evolution.
Journal keyword(s): stars: variables: Cepheids - stars: evolution
Full paper
Number of rows : 3
N Identifier Otype ICRS (J2000)
RA
ICRS (J2000)
DEC
Mag U Mag B Mag V Mag R Mag I Sp type #ref
1850 - 2023
#notes
1 NAME Leo A G 09 59 26.46 +30 44 47.0 14.08 13.54 13.26 13.33 ~ 588 0
2 NAME Sex A H2G 10 11 00.5 -04 41 30 12.48 12.13 11.93 11.78 ~ 707 2
3 NAME Local Group GrG ~ ~ ~ 7964 0
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2023.03.21-11:43:01 | 2023-03-21 10:43:01 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.3870851397514343, "perplexity": 7782.512128390191}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296943695.23/warc/CC-MAIN-20230321095704-20230321125704-00033.warc.gz"} |
https://brilliant.org/problems/dam/ | Dam
Geometry Level 2
The cross section of a dam is shown above. The volume of the dam is $$184500\text{ m}^3$$.
How long is the dam (in meters)?
× | 2017-09-21 08:41:58 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8627069592475891, "perplexity": 1338.6812952142138}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-39/segments/1505818687711.44/warc/CC-MAIN-20170921082205-20170921102205-00296.warc.gz"} |
http://math.stackexchange.com/questions/310924/uniform-probability-distribution | # Uniform Probability Distribution
I have a machine part that have lifetime uniformly distributed between 0 years and 1 year. Whenever a part fails, it is immediately replaced with a new identical part. I know that lifetimes of replacement parts are independent.
My question is: what is the probability that 5 years from now, I replace the part exactly 8 times.
I know that the expected lifetime of a bulb is 1/2 years, but I am not sure how to incorporate that into calculating the probability.
One of the approaches I am thinking of is to model the question into a Markov Chain with two states, Good and Bad. I know that P(Bad, Good) = 1 but I am not sure what the transition probabilities starting from state Good would look like?
Maybe I am complicating the problem too much, any help would be appreciated.
-
Look at the probability that 8 parts lives sum to less than five years. So take 8 random parts and let $x_1 ... x_8$ be their lifetimes, find $P(x_1 + ... + x_8 \le 5)$ then you need to subtract the probability that 9 sum to less than 5.
To calculate this you need to use a normal approximation since the sum of uniform distributions converge quickly to normal. The mean of the sum is 4 and the variance is $\frac{8}{12}$, so $P(x_1 + ... + x_8 \le 5) = P(Z \le \sqrt{\frac{12}{8}})$. You need to then do the same steps to subtract $P(x_1 + ... + x_9\le 5)$
Thanks, this is much clearer. Just one more question to make sure I understand the concept correctly, if I want to calculate the probability that 5 years from now, I will replace the part at least 8 times, then I will not subtract the $P(x_1+...+x_9≤5)$. Is that correct? and thanks again for your help. – Solver Feb 24 '13 at 17:39 | 2016-05-05 14:35:59 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8560885190963745, "perplexity": 139.17572710979954}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-18/segments/1461860127496.74/warc/CC-MAIN-20160428161527-00119-ip-10-239-7-51.ec2.internal.warc.gz"} |
https://www.thejach.com/view/2011/7 | # Plagiarism in Code
Note I'm not talking about copyright infringement, which is criminal, but mere academic plagiarism, which is a civil matter whose probable worst-case outcome is expulsion and reputation damage. Nevertheless it falls inside the sphere of the often- (and ill-) used concept of intellectual property.
I've always had a problem with plagiarism as a concept as well as something to avoid. In English, here's some teacher asking me to analyze a literary work. Okay. The literary work is simple, so what I turn in is near-exact in terms of information as many other students' work, but with my own phrasing. If I happen to match the phrasing of another student in many instances, or now with modern tools anyone on the entire internet, then the teacher suspects plagiarism. How can I avoid something that could happen due to chance alone? (By lowering the chance but that has to pollute the production in some way. I might normally say "Candy tastes good." To avoid plagiarism accusations, I might say "The bumps on the muscle that resides in my head, in the mouth, normally called the 'tongue', detect the chemicals in this sugary substance about to enter my digestive system and tell my brain it's okay to continue." You can continue that line with asking "why?" to every statement, and adding a "because" for all of them (potentially adding on "because"s to each "because"). I could have gone into evolutionary biology with the above.)
My eventual conclusion on plagiarism is that it's not meant to catch uniqueness of thought, nor is it an effort to catch whether a student understands something, but is an attempt to determine whether work was done according to some specification. Even plagiarizers have to do some work, sometimes more work, depending on the circumstances, but it's not the kind of work desired. So plagiarism is very much an effort to regulate the way of doing something, even if the outcome is the same.
# The Cumber Manifesto
I propose we stop calling imaginary and complex numbers imaginary and complex numbers. I propose we throw them all in the same bucket called "Cumbers". This has several advantages, which I shall briefly enumerate.
First is the instant association with a cucumber. Now I don't have kids, so I don't know if Cucumbers are the new Broccoli, but when I was a kid I loved cucumbers as much as I do today. (Though I loved broccoli too, so...) Cucumbers are cool and green and friendly. When written down, Cumbers can even resemble a long cucumber: (3 + 4*j).
Second is just avoiding the names which can lead to confusion in children and some teenagers. I'd like young children to learn algebra, but young children may not be able to fully grasp that one word can have completely different meanings. So when they hear "Imaginary" they think "This doesn't correspond to anything real", or when they hear "Complex" they think "Oh no this is hard." This is compounded by the more important, sad fact that even high school calculus teachers don't know what complex numbers are useful for. I had a great teacher, he didn't know. He said vaguely "electrical engineering." Now I know better, know more, but that's a different subject. Calling them "Cumbers" gets rid of this potentially emotionally distressing situation in the names.
# Why vim? Or: Why a text editor, not an IDE?
People (mostly at my school) have gawked at me when I say I don't use Visual Studio, or I don't use Eclipse, or I don't use Dreamweaver, or I don't use Word and use OpenOffice less and less. Instead I use vim. And the fact that I only have one substitute for all those giant programs speaks volumes about vim.
Of course, it's not just vim. I obviously use compilers and such. But whenever text is involved, it's almost always vim I end up using. I don't particularly like emacs, but they more-or-less have the same practices as vim users if a different philosophy. (Kind of how Christian Monk/Nun practices match up with Buddhist practices even if the philosophies are quite different.)
So I've grown into the habit of saying "Linux is my IDE." I use vim when I need to edit text, and use a host of Linux programs to manipulate that text. I use ant for my Java projects, Makefiles for C/C++ projects, gdb for debugging, $\LaTeX$ for documents and homework, and a browser to parse the templates I handwrite that compile down to HTML.
# Fall Semester Classes
(Update: They canceled my Combinatorics class and bait-and-switched the software engineering course, so I had to change a few things around.) Back to school this fall for the start of my Junior year. Where'd the past two years go?
20 credit hours is the norm at my school, it's actually pretty manageable. (And if you think about it, you spend at least 20 hours a week in high school. Not as much time on homework or projects but actual butt-in-seat time seems greater.) If I only had to take 10-13 credits as is common for "full time" students at other schools, I think I'd blow my brains out from boredom. At least with 20 credit hours chances are you'll like most of the classes and the crappy/boring ones are swept under the rug. If you're only taking three classes though, and two of them are crap, I don't think the other one can make you happy no matter how good it is.
Anyway, here's a list of my classes and their descriptions according to the school catalog along with some of my own thoughts.
Edit: Replacement is finished! I think it looks a lot nicer. Here's an $inline=\pi$ test. | 2020-02-22 05:53:34 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.49728935956954956, "perplexity": 1625.834253791119}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-10/segments/1581875145654.0/warc/CC-MAIN-20200222054424-20200222084424-00474.warc.gz"} |
http://hepfit.roma1.infn.it/doc/v1.0-RC1/d6/dfa/class_higgs_kvgen_kf.html | (Generated on Fri Feb 19 2016 13:25:12 by 1.8.9.1)
HiggsKvgenKf Class Reference
A model class extending the StandardModel Higgs sector with four couplings. More...
#include <HiggsKvgenKf.h>
Inheritance diagram for HiggsKvgenKf:
[legend]
Collaboration diagram for HiggsKvgenKf:
[legend]
## Detailed Description
A model class extending the StandardModel Higgs sector with four couplings.
This is a Model class containing parameters and functions associated with an extension of the StandardModel where Higgs couplings to the $$Z$$ boson are rescaled by $$\kappa_Z$$, Higgs couplings to the $$W$$ boson are rescaled by $$\kappa_W$$ and Higgs couplings to all fermions are rescaled by $$\kappa_f$$. The invisible decay width is also parametrized independently by Br $$(H\to invisible)$$. This class inherits from the NPbase class, which defines parameters related to generic extensions of the StandardModel Higgs sector.
### Initialization
After creating an instance of the current class, it is required to call the initialization method InitializeModel(), which is needed by the base class.
The initializations and updates of the model parameters are explained below.
### Model parameters
The model parameters of HiggsKvgenKf (in addition to the StandardModel ones) are summarized below:
Label LaTeX symbol Description
KZ $$\kappa_Z$$ The factor rescaling Higgs couplings to $$Z$$ bosons with respect to the SM.
KW $$\kappa_W$$ The factor rescaling Higgs couplings to $$W$$ bosons with respect to the SM.
Kf $$\kappa_f$$ The factor rescaling all Higgs couplings to fermions with respect to the SM.
BrHinv Br $$(H\to invisible)$$ The branching ratio of invisible Higgs decays.
Definition at line 72 of file HiggsKvgenKf.h.
## Public Member Functions
virtual double BrHbbRatio () const
The ratio of the Br $$(H\to b\bar{b})$$ in the current model and in the Standard Model. More...
virtual double BrHccRatio () const
The ratio of the Br $$(H\to c\bar{c})$$ in the current model and in the Standard Model. More...
virtual double BrHgagaRatio () const
The ratio of the Br $$(H\to \gamma\gamma)$$ in the current model and in the Standard Model. More...
virtual double BrHggRatio () const
The ratio of the Br $$(H\to gg)$$ in the current model and in the Standard Model. More...
virtual double BrHtautauRatio () const
The ratio of the Br $$(H\to \tau^+\tau^-)$$ in the current model and in the Standard Model. More...
virtual double BrHWWRatio () const
The ratio of the Br $$(H\to WW)$$ in the current model and in the Standard Model. More...
virtual double BrHZgaRatio () const
The ratio of the Br $$(H\to Z\gamma)$$ in the current model and in the Standard Model. More...
virtual double BrHZZRatio () const
The ratio of the Br $$(H\to ZZ)$$ in the current model and in the Standard Model. More...
virtual bool CheckParameters (const std::map< std::string, double > &DPars)
A method to check if all the mandatory parameters for HiggsKvgenKf have been provided in model initialization. More...
virtual double computeGammaTotalRatio () const
The ratio of the $$\Gamma(H)$$ in the current model and in the Standard Model. More...
double getKf () const
A get method to retrieve the factor rescaling the Higgs coupling to fermions with respect to the SM $$K_f$$. More...
double getKW () const
A get method to retrieve the factor rescaling the Higgs coupling to the $$W$$ boson with respect to the SM $$K_W$$. More...
double getKZ () const
A get method to retrieve the factor rescaling the Higgs coupling to the $$Z$$ boson with respect to the SM $$K_Z$$. More...
HiggsKvgenKf ()
The default constructor. More...
virtual double muggH (const double sqrt_s) const
The ratio $$\mu_{ggH}$$ between the gluon-gluon fusion Higgs production cross-section in the current model and in the Standard Model. More...
virtual double muggHpttH (const double sqrt_s) const
The ratio $$\mu_{ggH+ttH}$$ between the sum of gluon-gluon fusion and t-tbar-Higgs associated production cross-section in the current model and in the Standard Model. More...
virtual double muttH (const double sqrt_s) const
The ratio $$\mu_{ttH}$$ between the t-tbar-Higgs associated production cross-section in the current model and in the Standard Model. More...
virtual double muVBF (const double sqrt_s) const
The ratio $$\mu_{VBF}$$ between the vector-boson fusion Higgs production cross-section in the current model and in the Standard Model. More...
virtual double muVBFpVH (const double sqrt_s) const
The ratio $$\mu_{VBF+VH}$$ between the sum of VBF and WH+ZH associated production cross-section in the current model and in the Standard Model. More...
virtual double muVH (const double sqrt_s) const
The ratio $$\mu_{VH}$$ between the WH+ZH associated production cross-section in the current model and in the Standard Model. More...
virtual double muWH (const double sqrt_s) const
The ratio $$\mu_{WH}$$ between the W-Higgs associated production cross-section in the current model and in the Standard Model. More...
virtual double muZH (const double sqrt_s) const
The ratio $$\mu_{ZH}$$ between the Z-Higgs associated production cross-section in the current model and in the Standard Model. More...
void setKf (double Kf)
A set method to change the factor rescaling the Higgs coupling to fermions with respect to the SM $$K_f$$. More...
void setKW (double KW)
A set method to change the factor rescaling the Higgs coupling to the $$W$$ boson with respect to the SM $$K_W$$. More...
void setKZ (double KZ)
A set method to change the factor rescaling the Higgs coupling to the $$Z$$ boson with respect to the SM $$K_Z$$. More...
virtual ~HiggsKvgenKf ()
The default destructor. More...
Public Member Functions inherited from NPbase
virtual double A_f (const Particle f) const
The left-right asymmetry in $$e^+e^-\to Z\to f \bar{f}$$ at the $$Z$$-pole, $$\mathcal{A}_f$$. More...
virtual double AFB (const Particle f) const
The forward-backward asymmetry in $$e^+e^-\to Z\to f \bar{f}$$ at the $$Z$$-pole, $$A^f_{FB}$$. More...
virtual double deltaA_f (const Particle f) const
The new physics contribution to the left-right asymmetry in $$e^+e^-\to Z\to f \bar{f}$$ at the $$Z$$-pole, $$\delta \mathcal{A}_f$$. More...
virtual double deltaAFB (const Particle f) const
The new physics contribution to the forward-backward asymmetry in $$e^+e^-\to Z\to f \bar{f}$$ at the $$Z$$-pole, $$\delta A^f_{FB}$$. More...
virtual double deltaGA_f (const Particle f) const
New physics contribution to the neutral-current axial-vector coupling $$g_A^f$$. More...
virtual double deltaGamma_Z () const
The new physics contribution to the total decay width of the $$Z$$ boson, $$\delta \Gamma_Z$$. More...
virtual double DeltaGF () const
New physics contribution to the Fermi constant. More...
virtual double deltaGV_f (const Particle f) const
New physics contribution to the neutral-current vector coupling $$g_V^f$$. More...
virtual double deltaR0_f (const Particle f) const
The new physics contribution to the ratio $$R_\ell^0=\Gamma_{\mathrm{had}}/\Gamma_\ell$$ or $$R_q^0=\Gamma_q/\Gamma_{\mathrm{had}}$$, for leptons or quarks, respectively. More...
The new physics contribution to the cross section for the process $$e^+ e^-\to Z\to \mathrm{hadrons}$$ at the $$Z$$ pole, $$\delta \sigma_h^0$$. More...
virtual double deltaSin2thetaEff_e () const
The new physics contribution to the effective leptonic weak angle $$\delta \sin^2\theta_{\rm eff}^{\rm lept}$$ at the $$Z$$ pole. More...
virtual gslpp::complex gA_f (const Particle f) const
The total (SM+NP) contribution to the neutral-current axial-vector coupling $$g_A^f$$. More...
virtual double Gamma_Z () const
The total decay width of the $$Z$$ boson, $$\Gamma_Z$$. More...
virtual double GammaW () const
The total width of the $$W$$ boson, $$\Gamma_W$$. More...
virtual StandardModel getTrueSM () const
A method to return a StandardModel object from NPbase. More...
virtual gslpp::complex gV_f (const Particle f) const
The total (SM+NP) contribution to the neutral-current vector coupling $$g_V^f$$. More...
virtual gslpp::complex kappaZ_f (const Particle f) const
The effective neutral-current coupling $$\kappa_Z^f$$ including SM plus NP contributions. More...
virtual double mueeZH (const double sqrt_s) const
The ratio $$\mu_{eeZH}$$ between the $$e^{+}e^{-}\to ZH$$ associated production cross-section in the current model and in the Standard Model. More...
virtual double Mw () const
The mass of the $$W$$ boson, $$M_W$$. More...
NPbase ()
The default constructor. More...
virtual double obliqueS () const
The oblique parameter $$S$$. More...
virtual double obliqueT () const
The oblique parameter $$T$$. More...
virtual double obliqueU () const
The oblique parameter $$U$$. More...
virtual bool PostUpdate ()
The post-update method for NPbase. More...
virtual double R0_f (const Particle f) const
The ratio $$R_\ell^0=\Gamma_{\mathrm{had}}/\Gamma_\ell$$ or $$R_q^0=\Gamma_q/\Gamma_{\mathrm{had}}$$, for leptons or quarks, respectively. More...
virtual gslpp::complex rhoZ_f (const Particle f) const
The effective neutral-current coupling $$\rho_Z^f$$ including SM plus NP contributions. More...
The cross section for the process $$e^+ e^-\to Z\to \mathrm{hadrons}$$ at the $$Z$$ pole, $$\sigma_h^0$$. More...
virtual double sin2thetaEff (const Particle f) const
The leptonic effective weak mixing angle $$\sin^2\theta_{\rm eff}^{\rm lept}$$ at the the $$Z$$ pole. More...
Public Member Functions inherited from StandardModel
double ale_OS (const double mu, orders order=FULLNLO) const
The running electromagnetic coupling $$\alpha(\mu)$$ in the on-shell schem. More...
double alphaMz () const
The electromagnetic coupling at the $$Z$$-mass scale, $$\alpha(M_Z^2)=\alpha/(1-\Delta\alpha(M_Z^2))$$. More...
double c02 () const
The square of the cosine of the weak mixing angle $$c_0^2$$ defined without weak radiative corrections. More...
virtual bool CheckFlags () const
A method to check the sanity of the set of model flags. More...
bool checkSMparamsForEWPO ()
A method to check whether the parameters relevant to the EWPO are updated. More...
double computeAlpha () const
The CKM angle $$\alpha$$. More...
double computeBeta () const
The CKM angle $$\beta$$. More...
double computeBetas () const
The CKM angle $$\beta_s$$. More...
double computeBrHtobb () const
The Br $$(H\to bb)$$ in the Standard Model. More...
double computeBrHtocc () const
The Br $$(H\to cc)$$ in the Standard Model. More...
double computeBrHtogaga () const
The Br $$(H\to\gamma\gamma)$$ in the Standard Model. More...
double computeBrHtogg () const
The Br $$(H\to gg)$$ in the Standard Model. More...
double computeBrHtotautau () const
The Br $$(H\to \tau\tau)$$ in the Standard Model. More...
double computeBrHtoWW () const
The Br $$(H\to WW)$$ in the Standard Model. More...
double computeBrHtoZga () const
The Br $$(H\to Z\gamma)$$ in the Standard Model. More...
double computeBrHtoZZ () const
The Br $$(H\to ZZ)$$ in the Standard Model. More...
void ComputeDeltaR_rem (const double Mw_i, double DeltaR_rem[orders_EW_size]) const
A method to collect $$\Delta r_{\mathrm{rem}}$$ computed via subclasses. More...
void ComputeDeltaRho (const double Mw_i, double DeltaRho[orders_EW_size]) const
A method to collect $$\Delta\rho$$ computed via subclasses. More...
double computeGamma () const
The CKM angle $$\gamma$$. More...
double computeGammaHgaga_tt () const
The top loop contribution to $$H\to\gamma\gamma$$ in the Standard Model. More...
double computeGammaHgaga_tW () const
The mixed $$t-W$$ loop contribution to $$H\to\gamma\gamma$$ in the Standard Model. More...
double computeGammaHgaga_WW () const
The $$W$$ loop contribution to $$H\to\gamma\gamma$$ in the Standard Model. More...
double computeGammaHgg_bb () const
The bottom loop contribution to $$H\to gg$$ in the Standard Model. More...
double computeGammaHgg_tb () const
The top-bottom interference contribution to $$H\to gg$$ in the Standard Model. More...
double computeGammaHgg_tt () const
The top loop contribution to $$H\to gg$$ in the Standard Model. More...
double computeGammaHTotal () const
The Higgs total width in the Standard Model. More...
double computeGammaHZga_tt () const
The top loop contribution to $$H\to Z\gamma$$ in the Standard Model. More...
double computeGammaHZga_tW () const
The mixed $$t-W$$ loop contribution to $$H\to Z\gamma$$ in the Standard Model. More...
double computeGammaHZga_WW () const
The $$W$$ loop contribution to $$H\to Z\gamma$$ in the Standard Model. Currently it returns the value of tab 41 in ref. [89]. More...
gslpp::complex computelamc () const
The product of the CKM elements $$V_{cd} V_{cs}^*$$. More...
gslpp::complex computelamc_d () const
The product of the CKM elements $$V_{cd} V_{cb}^*$$. More...
gslpp::complex computelamc_s () const
The product of the CKM elements $$V_{cs} V_{cb}^*$$. More...
gslpp::complex computelamt () const
The product of the CKM elements $$V_{td} V_{ts}^*$$. More...
gslpp::complex computelamt_d () const
The product of the CKM elements $$V_{td} V_{tb}^*$$. More...
gslpp::complex computelamt_s () const
The product of the CKM elements $$V_{ts} V_{tb}^*$$. More...
gslpp::complex computelamu () const
The product of the CKM elements $$V_{ud} V_{us}^*$$. More...
gslpp::complex computelamu_d () const
The product of the CKM elements $$V_{ud} V_{ub}^*$$. More...
gslpp::complex computelamu_s () const
The product of the CKM elements $$V_{us} V_{ub}^*$$. More...
double computeRb () const
$$R_b=|(V_{ud}V_{ub}^*)/(V_{ud}V_{ub}^*)|$$. More...
double computeRt () const
$$R_t=|(V_{td} V_{tb}^*)/(V_{cd}V_{cb}^*)|$$. More...
double computeRts () const
$$R_{ts}=|(V_{ts}V_{tb}^*)/(V_{cs}V_{cb}^*)|$$. More...
double computeSigmaggH (const double sqrt_s) const
The ggH cross section in the Standard Model. More...
double computeSigmaggH_bb (const double sqrt_s) const
The square of the bottom-quark contribution to the ggH cross section in the Standard Model. More...
double computeSigmaggH_tb (const double sqrt_s) const
The top-bottom interference contribution to the ggH cross section in the Standard Model. More...
double computeSigmaggH_tt (const double sqrt_s) const
The square of the top-quark contribution to the ggH cross section in the Standard Model. More...
double computeSigmattH (const double sqrt_s) const
The ttH production cross section in the Standard Model. More...
double computeSigmaVBF (const double sqrt_s) const
The VBF cross section in the Standard Model. More...
double computeSigmaWF (const double sqrt_s) const
The W fusion contribution $$\sigma_{WF}$$ to higgs-production cross section in the Standard Model. More...
double computeSigmaWH (const double sqrt_s) const
The WH production cross section in the Standard Model. More...
double computeSigmaZF (const double sqrt_s) const
The Z fusion contribution $$\sigma_{ZF}$$ to higgs-production cross section in the Standard Model. More...
double computeSigmaZH (const double sqrt_s) const
The ZH production cross section in the Standard Model. More...
double computeSigmaZWF (const double sqrt_s) const
The Z W interference fusion contribution $$\sigma_{ZWF}$$ to higgs-production cross section in the Standard Model. More...
virtual double cW2 (const double Mw_i) const
The square of the cosine of the weak mixing angle in the on-shell scheme, denoted as $$c_W^2$$. More...
virtual double cW2 () const
double DeltaAlpha () const
The total corrections to the electromagnetic coupling $$\alpha$$ at the $$Z$$-mass scale, denoted as $$\Delta\alpha(M_Z^2)$$. More...
double DeltaAlphaL5q () const
The sum of the leptonic and the five-flavour hadronic corrections to the electromagnetic coupling $$\alpha$$ at the $$Z$$-mass scale, denoted as $$\Delta\alpha^{\ell+5q}(M_Z^2)$$. More...
double DeltaAlphaLepton (const double s) const
Leptonic contribution to the electromagnetic coupling $$\alpha$$, denoted as $$\Delta\alpha_{\mathrm{lept}}(s)$$. More...
double DeltaAlphaTop (const double s) const
Top-quark contribution to the electromagnetic coupling $$\alpha$$, denoted as $$\Delta\alpha_{\mathrm{top}}(s)$$. More...
virtual gslpp::complex deltaKappaZ_f (const Particle f) const
Flavour non-universal vertex corrections to $$\kappa_Z^l$$, denoted by $$\Delta\kappa_Z^l$$. More...
virtual double DeltaR () const
The SM prediction for $$\Delta r$$ derived from that for the $$W$$ boson mass. More...
virtual double DeltaRbar () const
The SM prediction for $$\Delta \overline{r}$$ derived from that for the $$W$$-boson mass. More...
virtual gslpp::complex deltaRhoZ_f (const Particle f) const
Flavour non-universal vertex corrections to $$\rho_Z^l$$, denoted by $$\Delta\rho_Z^l$$. More...
virtual double epsilon1 () const
The SM contribution to the epsilon parameter $$\varepsilon_1$$. More...
virtual double epsilon2 () const
The SM contribution to the epsilon parameter $$\varepsilon_2$$. More...
virtual double epsilon3 () const
The SM contribution to the epsilon parameter $$\varepsilon_3$$. More...
virtual double epsilonb () const
The SM contribution to the epsilon parameter $$\varepsilon_b$$. More...
The hadronic decay width of the $$Z$$ boson, $$\Gamma_{h}$$. More...
virtual double Gamma_inv () const
The invisible partial decay width of the $$Z$$ boson, $$\Gamma_{\mathrm{inv}}$$. More...
virtual double GammaW (const Particle fi, const Particle fj) const
A partial decay width of the $$W$$ boson decay into a SM fermion pair. More...
virtual double GammaZ (const Particle f) const
The $$Z\to \ell\bar{\ell}$$ partial decay width, $$\Gamma_\ell$$. More...
double getA () const
A get method to retrieve the CKM element $$A$$. More...
double getAle () const
A get method to retrieve the fine-structure constant $$\alpha$$. More...
double getAlsMz () const
A get method to access the value of $$\alpha_s(M_Z)$$. More...
CKM getCKM () const
A get method to retrieve the member object of type CKM. More...
double getDAle5Mz () const
A get method to retrieve the five-flavour hadronic contribution to the electromagnetic coupling, $$\Delta\alpha_{\mathrm{had}}^{(5)}(M_Z^2)$$. More...
double getDelGammaZ () const
A get method to retrieve the theoretical uncertainty in $$\Gamma_Z$$, denoted as $$\delta\,\Gamma_Z$$. More...
double getDelMw () const
A get method to retrieve the theoretical uncertainty in $$M_W$$, denoted as $$\delta\,M_W$$. More...
double getDelSin2th_l () const
A get method to retrieve the theoretical uncertainty in $$\sin^2\theta_{\rm eff}^{\rm lept}$$, denoted as $$\delta\sin^2\theta_{\rm eff}^{\rm lept}$$. More...
double getDeltaMK () const
double getDmk () const
double getEpsK () const
double getEtab () const
A get method to retrieve the CKM element $$\bar{\eta}$$. More...
std::string getFlagKappaZ () const
A method to retrieve the model flag KappaZ. More...
std::string getFlagMw () const
A method to retrieve the model flag Mw. More...
std::string getFlagRhoZ () const
A method to retrieve the model flag RhoZ. More...
double getGF () const
A get method to retrieve the Fermi constant $$G_\mu$$. More...
int getIterationNo () const
double getKbarEpsK () const
double getLambda () const
A get method to retrieve the CKM element $$\lambda$$. More...
Particle getLeptons (const StandardModel::lepton p) const
A get method to retrieve the member object of a lepton. More...
double getMHl () const
A get method to retrieve the Higgs mass $$m_h$$. More...
double getMuw () const
A get method to retrieve the matching scale $$\mu_W$$ around the weak scale. More...
EWSMApproximateFormulaegetMyApproximateFormulae () const
A get method to retrieve the member pointer of type EWSMApproximateFormulae. More...
EWSMcachegetMyEWSMcache () const
A get method to retrieve the member pointer of type EWSMcache. More...
FlavourgetMyFlavour () const
LeptonFlavourgetMyLeptonFlavour () const
virtual StandardModelMatchinggetMyMatching () const
A get method to access the member pointer of type StandardModelMatching. More...
EWSMOneLoopEWgetMyOneLoopEW () const
A get method to retrieve the member pointer of type EWSMOneLoopEW,. More...
EWSMThreeLoopEWgetMyThreeLoopEW () const
EWSMThreeLoopEW2QCDgetMyThreeLoopEW2QCD () const
EWSMThreeLoopQCDgetMyThreeLoopQCD () const
EWSMTwoFermionsLEP2 * getMyTwoFermionsLEP2 () const
A get method to retrieve the member pointer of type EWSMTwoFermionsLEP2. More...
EWSMTwoLoopEWgetMyTwoLoopEW () const
EWSMTwoLoopQCDgetMyTwoLoopQCD () const
double getMz () const
A get method to access the mass of the $$Z$$ boson $$M_Z$$. More...
double getphiEpsK () const
double getRhob () const
A get method to retrieve the CKM element $$\bar{\rho}$$. More...
double getSM_M12D () const
gslpp::matrix< gslpp::complexgetUPMNS () const
A get method to retrieve the object of the PMNS matrix. More...
gslpp::matrix< gslpp::complexgetVCKM () const
A get method to retrieve the CKM matrix. More...
gslpp::matrix< gslpp::complexgetYd () const
A get method to retrieve the Yukawa matrix of the down-type quarks, $$Y_d$$. More...
gslpp::matrix< gslpp::complexgetYe () const
A get method to retrieve the Yukawa matrix of the charged leptons, $$Y_e$$. More...
gslpp::matrix< gslpp::complexgetYn () const
A get method to retrieve the Yukawa matrix of the neutrinos, $$Y_\nu$$. More...
gslpp::matrix< gslpp::complexgetYu () const
A get method to retrieve the Yukawa matrix of the up-type quarks, $$Y_u$$. More...
virtual bool Init (const std::map< std::string, double > &DPars)
A method to initialize the model parameters. More...
virtual bool InitializeModel ()
A method to initialize the model. More...
bool IsFlagNoApproximateGammaZ () const
A method to retrieve the model flag NoApproximateGammaZ. More...
bool IsFlagWithoutNonUniversalVC () const
A method to retrieve the model flag WithoutNonUniversalVC. More...
virtual double Mw_tree () const
The tree-level mass of the $$W$$ boson, $$M_W^{\mathrm{tree}}$$. More...
double MwbarFromMw (const double Mw) const
A method to convert the $$W$$-boson mass in the experimental/running-width scheme to that in the complex-pole/fixed-width scheme. More...
double MwFromMwbar (const double Mwbar) const
A method to convert the $$W$$-boson mass in the complex-pole/fixed-width scheme to that in the experimental/running-width scheme. More...
double Mzbar () const
The $$Z$$-boson mass $$\overline{M}_Z$$ in the complex-pole/fixed-width scheme. More...
virtual bool PreUpdate ()
The pre-update method for StandardModel. More...
virtual double rho_GammaW (const Particle fi, const Particle fj) const
EW radiative corrections to the width of $$W \to f_i \bar{f}_j$$, denoted as $$\rho^W_{ij}$$. More...
double s02 () const
The square of the sine of the weak mixing angle $$s_0^2$$ defined without weak radiative corrections. More...
virtual bool setFlag (const std::string name, const bool value)
A method to set a flag of StandardModel. More...
void setFlagCacheInStandardModel (bool FlagCacheInStandardModel)
A set method to change the model flag CacheInStandardModel of StandardModel. More...
void setFlagNoApproximateGammaZ (bool FlagNoApproximateGammaZ)
virtual bool setFlagStr (const std::string name, const std::string value)
A method to set a flag of StandardModel. More...
StandardModel ()
The default constructor. More...
virtual double sW2 (const double Mw_i) const
The square of the sine of the weak mixing angle in the on-shell scheme, denoted as $$s_W^2$$. More...
double sW2 () const
virtual bool Update (const std::map< std::string, double > &DPars)
The update method for StandardModel. More...
virtual double v () const
The Higgs vacuum expectation value.
$v = \left(\frac{1}{\sqrt{2} G_\mu}\right)^{1/2},$
where $$G_\mu$$ is the Fermi constant, measured through muon decays. More...
virtual ~StandardModel ()
The default destructor. More...
Public Member Functions inherited from QCD
double AboveTh (const double mu) const
The active flavour threshold above the scale $$\mu$$ as defined in QCD::Thresholds(). More...
double Als (const double mu, const orders order=FULLNLO) const
Computes the running strong coupling $$\alpha_s(\mu)$$ in the $$\overline{\mathrm{MS}}$$ scheme. In the cases of LO, NLO and FULLNNLO, the coupling is computed with AlsWithInit(). On the other hand, in the cases of NNLO and FULLNNLO, the coupling is computed with AlsWithLambda(). More...
double Als4 (const double mu) const
The value of $$\alpha_s^{\mathrm{FULLNLO}}$$ at any scale $$\mu$$ with the number of flavours $$n_f = 4$$. More...
double AlsWithInit (const double mu, const double alsi, const double mu_i, const orders order) const
Computes the running strong coupling $$\alpha_s(\mu)$$ from $$\alpha_s(\mu_i)$$ in the $$\overline{\mathrm{MS}}$$ scheme, where it is forbidden to across a flavour threshold in the RG running from $$\mu_i$$ to $$\mu$$. More...
double AlsWithLambda (const double mu, const orders order) const
Computes the running strong coupling $$\alpha_s(\mu)$$ in the $$\overline{\mathrm{MS}}$$ scheme with the use of $$\Lambda_{\rm QCD}$$. More...
double BelowTh (const double mu) const
The active flavour threshold below the scale $$\mu$$ as defined in QCD::Thresholds(). More...
double Beta0 (const double nf) const
The $$\beta_0(n_f)$$ coefficient for a certain number of flavours $$n_f$$. More...
double Beta1 (const double nf) const
The $$\beta_1(n_f)$$ coefficient for a certain number of flavours $$n_f$$. More...
double Beta2 (const double nf) const
The $$\beta_2(n_f)$$ coefficient for a certain number of flavours $$n_f$$. More...
double geta_0A0 () const
double geta_0A0phi () const
double geta_0A1 () const
double geta_0A12 () const
double geta_0A12phi () const
double geta_0A1phi () const
double geta_0T1 () const
double geta_0T1phi () const
double geta_0T2 () const
double geta_0T23 () const
double geta_0T23phi () const
double geta_0T2phi () const
double geta_0V () const
double geta_0Vphi () const
double geta_1A0 () const
double geta_1A0phi () const
double geta_1A1 () const
double geta_1A12 () const
double geta_1A12phi () const
double geta_1A1phi () const
double geta_1T1 () const
double geta_1T1phi () const
double geta_1T2 () const
double geta_1T23 () const
double geta_1T23phi () const
double geta_1T2phi () const
double geta_1V () const
double geta_1Vphi () const
double geta_2A0 () const
double geta_2A0phi () const
double geta_2A1 () const
double geta_2A12 () const
double geta_2A12phi () const
double geta_2A1phi () const
double geta_2T1 () const
double geta_2T1phi () const
double geta_2T2 () const
double geta_2T23 () const
double geta_2T23phi () const
double geta_2T2phi () const
double geta_2V () const
double geta_2Vphi () const
double getAlsM () const
A get method to access the value of $$\alpha_s(M_{\alpha_s})$$. More...
BParameter getBBd () const
For getting the bag parameters corresponding to the operator basis $$O_1 -O_5$$ in $$\Delta b = 2$$ process in the $$B_d$$ meson system. More...
BParameter getBBs () const
For getting the bag parameters corresponding to the operator basis $$O_1 -O_5$$ in $$\Delta b = 2$$ process in the $$B_s$$ meson system. More...
BParameter getBD () const
For getting the bag parameters corresponding to the operator basis $$O_1 -O_5$$ in $$\Delta c = 2$$ process in the $$D^0$$ meson system. More...
BParameter getBK () const
For getting the bag parameters corresponding to the operator basis $$O_1 -O_5$$ in $$\Delta s = 2$$ process in the $$K^0$$ meson system. More...
BParameter getBKd1 () const
BParameter getBKd3 () const
double getBLNPcorr () const
double getBr_B_Xcenu () const
double getBr_Kp_munu () const
double getBr_Kp_P0enu () const
double getbsgamma_E0 () const
double getCF () const
A get method to access the Casimir factor of QCD. More...
double getDeltaP_cu () const
double getFKstarp () const
double getGambino_BRsem () const
double getGambino_Mbkin () const
double getGambino_Mcatmuc () const
double getGambino_muG2 () const
double getGambino_mukin () const
double getGambino_mupi2 () const
double getGambino_rhoD3 () const
double getGambino_rhoLS3 () const
gslpp::complex geth_0 () const
gslpp::complex geth_0_1 () const
gslpp::complex geth_0_1_MP () const
gslpp::complex geth_0_2 () const
gslpp::complex geth_0_MP () const
gslpp::complex geth_m () const
gslpp::complex geth_m_1 () const
gslpp::complex geth_m_2 () const
gslpp::complex geth_p () const
gslpp::complex geth_p_1 () const
gslpp::complex geth_p_2 () const
double getIB_Kl () const
double getIB_Kp () const
double getm_fit2_f0 () const
double getm_fit2_fplus () const
double getm_fit2_fT () const
double getMAls () const
A get method to access the mass scale $$M_{\alpha_s}$$ at which the strong coupling constant measurement is provided. More...
Meson getMesons (const meson m) const
A get method to access a meson as an object of the type Meson. More...
double getMRA0 () const
double getMRA0phi () const
double getMRA1 () const
double getMRA12 () const
double getMRA12phi () const
double getMRA1phi () const
double getMRT1 () const
double getMRT1phi () const
double getMRT2 () const
double getMRT23 () const
double getMRT23phi () const
double getMRT2phi () const
double getMRV () const
double getMRVphi () const
double getMtpole () const
A get method to access the pole mass of the top quark. More...
double getMub () const
A get method to access the threshold between five- and four-flavour theory in GeV. More...
double getMuc () const
A get method to access the threshold between four- and three-flavour theory in GeV. More...
double getMut () const
A get method to access the threshold between six- and five-flavour theory in GeV. More...
double getNc () const
A get method to access the number of colours $$N_c$$. More...
double getOmega_eta_etap () const
Particle getQuarks (const quark q) const
A get method to access a quark as an object of the type Particle. More...
double getr_1_fplus () const
double getr_1_fT () const
double getr_2_f0 () const
double getr_2_fplus () const
double getr_2_fT () const
double getReA0_Kd () const
double getReA2_Kd () const
double logLambda (const double nf, orders order) const
Computes $$\ln\Lambda_\mathrm{QCD}$$ with nf flavours in GeV. More...
double Nf (const double mu) const
The number of active flavour at scale $$\mu$$. More...
std::string orderToString (const orders order) const
Converts an object of the enum type "orders" to the corresponding string. More...
QCD ()
Constructor. More...
void setNc (double Nc)
A set method to change the number of colours $$N_c$$. More...
double Thresholds (const int i) const
For accessing the active flavour threshold scales. More...
Public Member Functions inherited from Model
const double & getModelParam (std::string name) const
bool IsModelInitialized () const
A method to check if the model is initialized. More...
bool isModelParam (std::string name) const
bool isModelSUSY () const
bool isModelTHDM () const
bool IsUpdateError () const
A method to check if there was any error in the model update process. More...
Model ()
The default constructor. More...
std::string ModelName () const
A method to fetch the name of the model. More...
void setModelInitialized (bool ModelInitialized)
A set method to fix the failure or success of the initialization of the model. More...
void setModelName (const std::string name)
A method to set the name of the model. More...
void setModelSUSY ()
void setModelTHDM ()
void setUpdateError (bool UpdateError)
A set method to fix the update status as success or failure. More...
virtual ~Model ()
The default destructor. More...
## Static Public Attributes
static const std::string HKvgenKfvars [NHKvgenKfvars]
A string array containing the labels of the model parameters in HiggsKvgenKf. More...
static const int NHKvgenKfvars = 4
The number of the model parameters in HiggsKvgenKf. More...
Static Public Attributes inherited from StandardModel
static const double GeVminus2_to_nb = 389379.338
static const double Mw_error = 0.00001
The target accuracy of the iterative calculation of the $$W$$-boson mass in units of GeV. More...
static const int NSMvars = 26
The number of the model parameters in StandardModel. More...
static const int NumSMParamsForEWPO = 27
The number of the SM parameters that are relevant to the EW precision observables. More...
static const std::string SMvars [NSMvars]
A string array containing the labels of the model parameters in StandardModel. More...
Static Public Attributes inherited from QCD
static const int NQCDvars = 186
The number of model parameters in QCD. More...
static const std::string QCDvars [NQCDvars]
An array containing the labels under which all QCD parameters are stored in a vector of ModelParameter via InputParser::ReadParameters(). More...
## Protected Member Functions
virtual double computeKb () const
A method to compute the ratio of the $$Hbb$$ coupling in the current model and in the SM. More...
virtual double computeKc () const
A method to compute the ratio of the $$Hcc$$ coupling in the current model and in the SM. More...
virtual double computeKg () const
A method to compute the ratio of the $$Hgg$$ coupling in the current model and in the SM. More...
virtual double computeKgaga () const
A method to compute the ratio of the $$H\gamma\gamma$$ coupling in the current model and in the SM. More...
virtual double computeKt () const
A method to compute the ratio of the $$Htt$$ coupling in the current model and in the SM. More...
virtual double computeKtau () const
A method to compute the ratio of the $$H\tau\tau$$ coupling in the current model and in the SM. More...
virtual double computeKW () const
A method to compute the ratio of the $$HWW$$ coupling in the current model and in the SM. More...
virtual double computeKZ () const
A method to compute the ratio of the $$HZZ$$ coupling in the current model and in the SM. More...
virtual double computeKZga () const
A method to compute the ratio of the $$HZ\gamma$$ coupling in the current model and in the SM. More...
virtual void setParameter (const std::string name, const double &value)
A method to set the value of a parameter of HiggsKvKf. More...
Protected Member Functions inherited from StandardModel
bool checkEWPOscheme (const std::string scheme) const
A method to check if a given scheme name in string form is valid. More...
virtual void computeCKM ()
The method to compute the CKM matrix. More...
virtual void computeYukawas ()
The method to compute the Yukawa matrices. More...
double Delta_EWQCD (const QCD::quark q) const
The non-factorizable EW-QCD corrections to the partial widths for $$Z\to q\bar{q}$$, denoted as $$\Delta_{\mathrm{EW/QCD}}$$. More...
double RAq (const QCD::quark q) const
The radiator factor associated with the final-state QED and QCD corrections to the the axial-vector-current interactions, $$R_A^q(M_Z^2)$$. More...
double resumKappaZ (const double DeltaRho[orders_EW_size], const double deltaKappa_rem[orders_EW_size], const double DeltaRbar_rem, const bool bool_Zbb) const
A method to compute the real part of the effetvive coupling $$\kappa_Z^f$$ from $$\Delta\rho$$, $$\delta\rho_{\rm rem}^{f}$$ and $$\Delta r_{\mathrm{rem}}$$. More...
double resumMw (const double Mw_i, const double DeltaRho[orders_EW_size], const double DeltaR_rem[orders_EW_size]) const
A method to compute the $$W$$-boson mass from $$\Delta\rho$$ and $$\Delta r_{\mathrm{rem}}$$. More...
double resumRhoZ (const double DeltaRho[orders_EW_size], const double deltaRho_rem[orders_EW_size], const double DeltaRbar_rem, const bool bool_Zbb) const
A method to compute the real part of the effective coupling $$\rho_Z^f$$ from $$\Delta\rho$$, $$\delta\rho_{\rm rem}^{f}$$ and $$\Delta r_{\mathrm{rem}}$$. More...
double RVh () const
The singlet vector corrections to the hadronic $$Z$$-boson width, denoted as $$R_V^h$$. More...
double RVq (const QCD::quark q) const
The radiator factor associated with the final-state QED and QCD corrections to the the vector-current interactions, $$R_V^q(M_Z^2)$$. More...
double SchemeToDouble (const std::string scheme) const
A method to convert a given scheme name in string form into a floating-point number with double precision. More...
double taub () const
Top-mass corrections to the $$Zb\bar{b}$$ vertex, denoted by $$\tau_b$$. More...
## Private Attributes
double BrHinv
The branching ratio of invisible Higgs decays. More...
double Kf
The factor rescaling all Higgs couplings to fermions with respect to the SM. More...
double KW
The factor rescaling Higgs couplings to $$W$$ bosons with respect to the SM. More...
double KZ
The factor rescaling Higgs couplings to $$Z$$ bosons with respect to the SM. More...
Public Types inherited from StandardModel
enum lepton { NEUTRINO_1, ELECTRON, NEUTRINO_2, MU, NEUTRINO_3, TAU }
An enum type for leptons. More...
enum orders_EW { EW1 = 0, EW1QCD1, EW1QCD2, EW2, EW2QCD1, EW3, orders_EW_size }
An enumerated type representing perturbative orders of radiative corrections to EW precision observables. More...
Public Types inherited from QCD
enum meson { P_0, P_P, K_0, K_P, D_0, B_D, B_P, B_S, PHI, K_star, MESON_END }
An enum type for mesons. More...
enum quark { UP, DOWN, CHARM, STRANGE, TOP, BOTTOM }
An enum type for quarks. More...
Protected Attributes inherited from NPbase
StandardModel trueSM
Protected Attributes inherited from StandardModel
double A
The CKM parameter $$A$$ in the Wolfenstein parameterization. More...
double ale
The fine-structure constant $$\alpha$$. More...
double AlsMz
The strong coupling constant at the Z-boson mass, $$\alpha_s(M_Z)$$. More...
double dAle5Mz
The five-flavour hadronic contribution to the electromagnetic coupling, $$\Delta\alpha_{\mathrm{had}}^{(5)}(M_Z^2)$$. More...
double delGammaZ
The theoretical uncertainty in $$\Gamma_Z$$, denoted as $$\delta\,\Gamma_Z$$, in GeV. More...
double delMw
The theoretical uncertainty in $$M_W$$, denoted as $$\delta\,M_W$$, in GeV. More...
double delSin2th_l
The theoretical uncertainty in $$\sin^2\theta_{\rm eff}^{\rm lept}$$, denoted as $$\delta\sin^2\theta_{\rm eff}^{\rm lept}$$. More...
double DeltaMK
double Dmk
double EpsK
double etab
The CKM parameter $$\bar{\eta}$$ in the Wolfenstein parameterization. More...
bool flag_order [orders_EW_size]
An array of internal flags controlling the inclusions of higher-order corrections. More...
double GF
The Fermi constant $$G_\mu$$ in $${\rm GeV}^{-2}$$. More...
double KbarEpsK
double lambda
The CKM parameter $$\lambda$$ in the Wolfenstein parameterization. More...
Particle leptons [6]
An array of Particle objects for the leptons. More...
double mHl
The Higgs mass $$m_h$$ in GeV. More...
double muw
A matching scale $$\mu_W$$ around the weak scale in GeV. More...
CKM myCKM
An object of type CKM. More...
double Mz
The mass of the $$Z$$ boson in GeV. More...
double phiEpsK
bool requireCKM
An internal flag to control whether the CKM matrix has to be recomputed. More...
bool requireYe
An internal flag to control whether the charged-lepton Yukawa matrix has to be recomputed. More...
bool requireYn
An internal flag to control whether the neutrino Yukawa matrix has to be recomputed. More...
double rhob
The CKM parameter $$\bar{\rho}$$ in the Wolfenstein parameterization. More...
double SM_M12D
gslpp::matrix< gslpp::complexUPMNS
The PMNS matrix. More...
gslpp::matrix< gslpp::complexVCKM
The CKM matrix. More...
gslpp::matrix< gslpp::complexYd
The Yukawa matrix of the down-type quarks. More...
gslpp::matrix< gslpp::complexYe
The Yukawa matrix of the charged leptons. More...
gslpp::matrix< gslpp::complexYn
The Yukawa matrix of the neutrinos. More...
gslpp::matrix< gslpp::complexYu
The Yukawa matrix of the up-type quarks. More...
Protected Attributes inherited from Model
std::map< std::string, boost::reference_wrapper< const double > > ModelParamMap
bool UpdateError
A boolean set to false if update is successful. More...
## Constructor & Destructor Documentation
HiggsKvgenKf::HiggsKvgenKf ( )
The default constructor.
Definition at line 15 of file HiggsKvgenKf.cpp.
16 : NPbase()
17 {
18 ModelParamMap.insert(std::pair<std::string, boost::reference_wrapper<const double> >("KW", boost::cref(KW)));
19 ModelParamMap.insert(std::pair<std::string, boost::reference_wrapper<const double> >("KZ", boost::cref(KZ)));
20 ModelParamMap.insert(std::pair<std::string, boost::reference_wrapper<const double> >("Kf", boost::cref(Kf)));
21 ModelParamMap.insert(std::pair<std::string, boost::reference_wrapper<const double> >("BrHinv", boost::cref(BrHinv)));
22 }
NPbase()
The default constructor.
Definition: NPbase.cpp:10
double KZ
The factor rescaling Higgs couplings to bosons with respect to the SM.
Definition: HiggsKvgenKf.h:344
double Kf
The factor rescaling all Higgs couplings to fermions with respect to the SM.
Definition: HiggsKvgenKf.h:345
double BrHinv
The branching ratio of invisible Higgs decays.
Definition: HiggsKvgenKf.h:346
double KW
The factor rescaling Higgs couplings to bosons with respect to the SM.
Definition: HiggsKvgenKf.h:343
std::map< std::string, boost::reference_wrapper< const double > > ModelParamMap
Definition: Model.h:200
virtual HiggsKvgenKf::~HiggsKvgenKf ( )
inlinevirtual
The default destructor.
Definition at line 90 of file HiggsKvgenKf.h.
91 {
92 };
## Member Function Documentation
double HiggsKvgenKf::BrHbbRatio ( ) const
virtual
The ratio of the Br $$(H\to b\bar{b})$$ in the current model and in the Standard Model.
Returns
Br $$(H\to b\bar{b})$$/Br $$(H\to b\bar{b})_{\mathrm{SM}}$$
Reimplemented from NPbase.
Definition at line 153 of file HiggsKvgenKf.cpp.
154 {
155 return (computeKb() * computeKb() / computeGammaTotalRatio());
156 }
virtual double computeKb() const
A method to compute the ratio of the coupling in the current model and in the SM.
virtual double computeGammaTotalRatio() const
The ratio of the in the current model and in the Standard Model.
double HiggsKvgenKf::BrHccRatio ( ) const
virtual
The ratio of the Br $$(H\to c\bar{c})$$ in the current model and in the Standard Model.
Returns
Br $$(H\to c\bar{c})$$/Br $$(H\to c\bar{c})_{\mathrm{SM}}$$
Reimplemented from NPbase.
Definition at line 148 of file HiggsKvgenKf.cpp.
149 {
150 return (computeKc() * computeKc() / computeGammaTotalRatio());
151 }
virtual double computeGammaTotalRatio() const
The ratio of the in the current model and in the Standard Model.
virtual double computeKc() const
A method to compute the ratio of the coupling in the current model and in the SM.
double HiggsKvgenKf::BrHgagaRatio ( ) const
virtual
The ratio of the Br $$(H\to \gamma\gamma)$$ in the current model and in the Standard Model.
Returns
Br $$(H\to \gamma\gamma)$$/Br $$(H\to \gamma\gamma)_{\mathrm{SM}}$$
Reimplemented from NPbase.
Definition at line 138 of file HiggsKvgenKf.cpp.
139 {
141 }
virtual double computeKgaga() const
A method to compute the ratio of the coupling in the current model and in the SM.
virtual double computeGammaTotalRatio() const
The ratio of the in the current model and in the Standard Model.
double HiggsKvgenKf::BrHggRatio ( ) const
virtual
The ratio of the Br $$(H\to gg)$$ in the current model and in the Standard Model.
Returns
Br $$(H\to gg)$$/Br $$(H\to gg)_{\mathrm{SM}}$$
Reimplemented from NPbase.
Definition at line 118 of file HiggsKvgenKf.cpp.
119 {
120 return (computeKg() * computeKg() / computeGammaTotalRatio());
121 }
virtual double computeGammaTotalRatio() const
The ratio of the in the current model and in the Standard Model.
virtual double computeKg() const
A method to compute the ratio of the coupling in the current model and in the SM.
double HiggsKvgenKf::BrHtautauRatio ( ) const
virtual
The ratio of the Br $$(H\to \tau^+\tau^-)$$ in the current model and in the Standard Model.
Returns
Br $$(H\to \tau^+\tau^-)$$/Br $$(H\to \tau^+\tau^-)_{\mathrm{SM}}$$
Reimplemented from NPbase.
Definition at line 143 of file HiggsKvgenKf.cpp.
144 {
146 }
virtual double computeGammaTotalRatio() const
The ratio of the in the current model and in the Standard Model.
virtual double computeKtau() const
A method to compute the ratio of the coupling in the current model and in the SM.
double HiggsKvgenKf::BrHWWRatio ( ) const
virtual
The ratio of the Br $$(H\to WW)$$ in the current model and in the Standard Model.
Returns
Br $$(H\to WW)$$/Br $$(H\to WW)_{\mathrm{SM}}$$
Reimplemented from NPbase.
Definition at line 123 of file HiggsKvgenKf.cpp.
124 {
125 return (computeKW() * computeKW() / computeGammaTotalRatio());
126 }
virtual double computeKW() const
A method to compute the ratio of the coupling in the current model and in the SM.
virtual double computeGammaTotalRatio() const
The ratio of the in the current model and in the Standard Model.
double HiggsKvgenKf::BrHZgaRatio ( ) const
virtual
The ratio of the Br $$(H\to Z\gamma)$$ in the current model and in the Standard Model.
Returns
Br $$(H\to Z\gamma)$$/Br $$(H\to Z\gamma)_{\mathrm{SM}}$$
Reimplemented from NPbase.
Definition at line 133 of file HiggsKvgenKf.cpp.
134 {
136 }
virtual double computeKZga() const
A method to compute the ratio of the coupling in the current model and in the SM.
virtual double computeGammaTotalRatio() const
The ratio of the in the current model and in the Standard Model.
double HiggsKvgenKf::BrHZZRatio ( ) const
virtual
The ratio of the Br $$(H\to ZZ)$$ in the current model and in the Standard Model.
Returns
Br $$(H\to ZZ)$$/Br $$(H\to ZZ)_{\mathrm{SM}}$$
Reimplemented from NPbase.
Definition at line 128 of file HiggsKvgenKf.cpp.
129 {
130 return (computeKZ() * computeKZ() / computeGammaTotalRatio());
131 }
virtual double computeKZ() const
A method to compute the ratio of the coupling in the current model and in the SM.
virtual double computeGammaTotalRatio() const
The ratio of the in the current model and in the Standard Model.
bool HiggsKvgenKf::CheckParameters ( const std::map< std::string, double > & DPars )
virtual
A method to check if all the mandatory parameters for HiggsKvgenKf have been provided in model initialization.
Parameters
[in] DPars a map of the parameters that are being updated in the Monte Carlo run (including parameters that are varied and those that are held constant)
Returns
a boolean that is true if the execution is successful
Reimplemented from StandardModel.
Definition at line 38 of file HiggsKvgenKf.cpp.
39 {
40 for (int i = 0; i < NHKvgenKfvars; i++) {
41 if (DPars.find(HKvgenKfvars[i]) == DPars.end()) {
42 std::cout << "missing mandatory HiggsKvgenKf parameter " << HKvgenKfvars[i] << std::endl;
43 return false;
44 }
45 }
46 return (NPbase::CheckParameters(DPars));
47 }
virtual bool CheckParameters(const std::map< std::string, double > &DPars)
A method to check if all the mandatory parameters for StandardModel have been provided in model initi...
static const std::string HKvgenKfvars[NHKvgenKfvars]
A string array containing the labels of the model parameters in HiggsKvgenKf.
Definition: HiggsKvgenKf.h:80
static const int NHKvgenKfvars
The number of the model parameters in HiggsKvgenKf.
Definition: HiggsKvgenKf.h:75
double HiggsKvgenKf::computeGammaTotalRatio ( ) const
virtual
The ratio of the $$\Gamma(H)$$ in the current model and in the Standard Model.
Returns
$$\Gamma(H)$$/ $$\Gamma(H)_{\mathrm{SM}}$$
Reimplemented from NPbase.
Definition at line 158 of file HiggsKvgenKf.cpp.
159 {
160 return ((computeKg() * computeKg() * trueSM.computeBrHtogg()
168 / (1.0 - BrHinv));
169 }
StandardModel trueSM
Definition: NPbase.h:543
double computeBrHtoWW() const
The Br in the Standard Model.
virtual double computeKb() const
A method to compute the ratio of the coupling in the current model and in the SM.
virtual double computeKgaga() const
A method to compute the ratio of the coupling in the current model and in the SM.
virtual double computeKZ() const
A method to compute the ratio of the coupling in the current model and in the SM.
double computeBrHtoZZ() const
The Br in the Standard Model.
double computeBrHtobb() const
The Br in the Standard Model.
double computeBrHtogg() const
The Br in the Standard Model.
virtual double computeKW() const
A method to compute the ratio of the coupling in the current model and in the SM.
double computeBrHtotautau() const
The Br in the Standard Model.
virtual double computeKZga() const
A method to compute the ratio of the coupling in the current model and in the SM.
double computeBrHtoZga() const
The Br in the Standard Model.
double BrHinv
The branching ratio of invisible Higgs decays.
Definition: HiggsKvgenKf.h:346
virtual double computeKtau() const
A method to compute the ratio of the coupling in the current model and in the SM.
virtual double computeKg() const
A method to compute the ratio of the coupling in the current model and in the SM.
double computeBrHtocc() const
The Br in the Standard Model.
virtual double computeKc() const
A method to compute the ratio of the coupling in the current model and in the SM.
double computeBrHtogaga() const
The Br in the Standard Model.
double HiggsKvgenKf::computeKb ( ) const
protectedvirtual
A method to compute the ratio of the $$Hbb$$ coupling in the current model and in the SM.
Returns
the ratio of the $$Hbb$$ coupling in the current model and in the SM
Definition at line 223 of file HiggsKvgenKf.cpp.
224 {
225 return Kf;
226 }
double Kf
The factor rescaling all Higgs couplings to fermions with respect to the SM.
Definition: HiggsKvgenKf.h:345
double HiggsKvgenKf::computeKc ( ) const
protectedvirtual
A method to compute the ratio of the $$Hcc$$ coupling in the current model and in the SM.
Returns
the ratio of the $$Hcc$$ coupling in the current model and in the SM
Definition at line 213 of file HiggsKvgenKf.cpp.
214 {
215 return Kf;
216 }
double Kf
The factor rescaling all Higgs couplings to fermions with respect to the SM.
Definition: HiggsKvgenKf.h:345
double HiggsKvgenKf::computeKg ( ) const
protectedvirtual
A method to compute the ratio of the $$Hgg$$ coupling in the current model and in the SM.
Returns
the ratio of the $$Hgg$$ coupling in the current model and in the SM
Definition at line 173 of file HiggsKvgenKf.cpp.
174 {
175 return Kf;
176 }
double Kf
The factor rescaling all Higgs couplings to fermions with respect to the SM.
Definition: HiggsKvgenKf.h:345
double HiggsKvgenKf::computeKgaga ( ) const
protectedvirtual
A method to compute the ratio of the $$H\gamma\gamma$$ coupling in the current model and in the SM.
Returns
the ratio of the $$H\gamma\gamma$$ coupling in the current model and in the SM
Definition at line 198 of file HiggsKvgenKf.cpp.
199 {
200 double gtt_SM = trueSM.computeGammaHgaga_tt();
201 double gWW_SM = trueSM.computeGammaHgaga_WW();
202 double gtW_SM = trueSM.computeGammaHgaga_tW();
203 return (sqrt((computeKt() * computeKt() * gtt_SM
204 + computeKW() * computeKW() * gWW_SM
205 + computeKt() * computeKW() * gtW_SM) / (gtt_SM + gWW_SM + gtW_SM)));
206 }
virtual double computeKt() const
A method to compute the ratio of the coupling in the current model and in the SM.
double computeGammaHgaga_tt() const
The top loop contribution to in the Standard Model.
double computeGammaHgaga_WW() const
The loop contribution to in the Standard Model.
StandardModel trueSM
Definition: NPbase.h:543
virtual double computeKW() const
A method to compute the ratio of the coupling in the current model and in the SM.
double computeGammaHgaga_tW() const
The mixed loop contribution to in the Standard Model.
complex sqrt(const complex &z)
double HiggsKvgenKf::computeKt ( ) const
protectedvirtual
A method to compute the ratio of the $$Htt$$ coupling in the current model and in the SM.
Returns
the ratio of the $$Htt$$ coupling in the current model and in the SM
Definition at line 218 of file HiggsKvgenKf.cpp.
219 {
220 return Kf;
221 }
double Kf
The factor rescaling all Higgs couplings to fermions with respect to the SM.
Definition: HiggsKvgenKf.h:345
double HiggsKvgenKf::computeKtau ( ) const
protectedvirtual
A method to compute the ratio of the $$H\tau\tau$$ coupling in the current model and in the SM.
Returns
the ratio of the $$H\tau\tau$$ coupling in the current model and in the SM
Definition at line 208 of file HiggsKvgenKf.cpp.
209 {
210 return Kf;
211 }
double Kf
The factor rescaling all Higgs couplings to fermions with respect to the SM.
Definition: HiggsKvgenKf.h:345
double HiggsKvgenKf::computeKW ( ) const
protectedvirtual
A method to compute the ratio of the $$HWW$$ coupling in the current model and in the SM.
Returns
the ratio of the $$HWW$$ coupling in the current model and in the SM
Definition at line 178 of file HiggsKvgenKf.cpp.
179 {
180 return KW;
181 }
double KW
The factor rescaling Higgs couplings to bosons with respect to the SM.
Definition: HiggsKvgenKf.h:343
double HiggsKvgenKf::computeKZ ( ) const
protectedvirtual
A method to compute the ratio of the $$HZZ$$ coupling in the current model and in the SM.
Returns
the ratio of the $$HZZ$$ coupling in the current model and in the SM
Definition at line 183 of file HiggsKvgenKf.cpp.
184 {
185 return KZ;
186 }
double KZ
The factor rescaling Higgs couplings to bosons with respect to the SM.
Definition: HiggsKvgenKf.h:344
double HiggsKvgenKf::computeKZga ( ) const
protectedvirtual
A method to compute the ratio of the $$HZ\gamma$$ coupling in the current model and in the SM.
Returns
the ratio of the $$HZ\gamma$$ coupling in the current model and in the SM
Definition at line 188 of file HiggsKvgenKf.cpp.
189 {
190 double gtt_SM = trueSM.computeGammaHZga_tt();
191 double gWW_SM = trueSM.computeGammaHZga_WW();
192 double gtW_SM = trueSM.computeGammaHZga_tW();
193 return (sqrt((computeKt() * computeKt() * gtt_SM
194 + computeKW() * computeKW() * gWW_SM
195 + computeKt() * computeKW() * gtW_SM) / (gtt_SM + gWW_SM + gtW_SM)));
196 }
virtual double computeKt() const
A method to compute the ratio of the coupling in the current model and in the SM.
double computeGammaHZga_WW() const
The loop contribution to in the Standard Model. Currently it returns the value of tab 41 in ref...
double computeGammaHZga_tW() const
The mixed loop contribution to in the Standard Model.
StandardModel trueSM
Definition: NPbase.h:543
virtual double computeKW() const
A method to compute the ratio of the coupling in the current model and in the SM.
double computeGammaHZga_tt() const
The top loop contribution to in the Standard Model.
complex sqrt(const complex &z)
double HiggsKvgenKf::getKf ( ) const
inline
A get method to retrieve the factor rescaling the Higgs coupling to fermions with respect to the SM $$K_f$$.
Returns
$$K_f$$
Definition at line 99 of file HiggsKvgenKf.h.
100 {
101 return Kf;
102 }
double Kf
The factor rescaling all Higgs couplings to fermions with respect to the SM.
Definition: HiggsKvgenKf.h:345
double HiggsKvgenKf::getKW ( ) const
inline
A get method to retrieve the factor rescaling the Higgs coupling to the $$W$$ boson with respect to the SM $$K_W$$.
Returns
$$K_W$$
Definition at line 119 of file HiggsKvgenKf.h.
120 {
121 return KW;
122 }
double KW
The factor rescaling Higgs couplings to bosons with respect to the SM.
Definition: HiggsKvgenKf.h:343
double HiggsKvgenKf::getKZ ( ) const
inline
A get method to retrieve the factor rescaling the Higgs coupling to the $$Z$$ boson with respect to the SM $$K_Z$$.
Returns
$$K_Z$$
Definition at line 139 of file HiggsKvgenKf.h.
140 {
141 return KZ;
142 }
double KZ
The factor rescaling Higgs couplings to bosons with respect to the SM.
Definition: HiggsKvgenKf.h:344
double HiggsKvgenKf::muggH ( const double sqrt_s ) const
virtual
The ratio $$\mu_{ggH}$$ between the gluon-gluon fusion Higgs production cross-section in the current model and in the Standard Model.
Parameters
[in] sqrt_s the center-of-mass energy in TeV
Returns
$$\mu_{ggH}$$
Reimplemented from NPbase.
Definition at line 51 of file HiggsKvgenKf.cpp.
52 {
53 return (computeKg() * computeKg());
54 }
virtual double computeKg() const
A method to compute the ratio of the coupling in the current model and in the SM.
double HiggsKvgenKf::muggHpttH ( const double sqrt_s ) const
virtual
The ratio $$\mu_{ggH+ttH}$$ between the sum of gluon-gluon fusion and t-tbar-Higgs associated production cross-section in the current model and in the Standard Model.
Parameters
[in] sqrt_s the center-of-mass energy in TeV
Returns
$$\mu_{ggH+ttH}$$
Reimplemented from NPbase.
Definition at line 107 of file HiggsKvgenKf.cpp.
108 {
109 double sigmaggH_SM = trueSM.computeSigmaggH(sqrt_s);
110 double sigmattH_SM = trueSM.computeSigmattH(sqrt_s);
111
112 double sigmaggH = muggH(sqrt_s) * sigmaggH_SM;
113 double sigmattH = muttH(sqrt_s) * sigmattH_SM;
114
115 return ((sigmaggH + sigmattH) / (sigmaggH_SM + sigmattH_SM));
116 }
StandardModel trueSM
Definition: NPbase.h:543
virtual double muttH(const double sqrt_s) const
The ratio between the t-tbar-Higgs associated production cross-section in the current model and in t...
double computeSigmattH(const double sqrt_s) const
The ttH production cross section in the Standard Model.
double computeSigmaggH(const double sqrt_s) const
The ggH cross section in the Standard Model.
virtual double muggH(const double sqrt_s) const
The ratio between the gluon-gluon fusion Higgs production cross-section in the current model and in ...
double HiggsKvgenKf::muttH ( const double sqrt_s ) const
virtual
The ratio $$\mu_{ttH}$$ between the t-tbar-Higgs associated production cross-section in the current model and in the Standard Model.
Parameters
[in] sqrt_s the center-of-mass energy in TeV
Returns
$$\mu_{ttH}$$
Reimplemented from NPbase.
Definition at line 102 of file HiggsKvgenKf.cpp.
103 {
104 return (computeKt() * computeKt());
105 }
virtual double computeKt() const
A method to compute the ratio of the coupling in the current model and in the SM.
double HiggsKvgenKf::muVBF ( const double sqrt_s ) const
virtual
The ratio $$\mu_{VBF}$$ between the vector-boson fusion Higgs production cross-section in the current model and in the Standard Model.
Parameters
[in] sqrt_s the center-of-mass energy in TeV
Returns
$$\mu_{VBF}$$
Reimplemented from NPbase.
Definition at line 56 of file HiggsKvgenKf.cpp.
57 {
58 double sigmaWF_SM = trueSM.computeSigmaWF(sqrt_s);
59 double sigmaZF_SM = trueSM.computeSigmaZF(sqrt_s);
60 double sigmaZWF_SM = trueSM.computeSigmaZWF(sqrt_s);
61 return (computeKW() * computeKW() * sigmaWF_SM
62 + computeKZ() * computeKZ() * sigmaZF_SM
63 + computeKW() * computeKZ() * sigmaZWF_SM)
64 / (sigmaWF_SM + sigmaZF_SM + sigmaZWF_SM);
65 }
double computeSigmaZF(const double sqrt_s) const
The Z fusion contribution to higgs-production cross section in the Standard Model.
StandardModel trueSM
Definition: NPbase.h:543
virtual double computeKZ() const
A method to compute the ratio of the coupling in the current model and in the SM.
double computeSigmaWF(const double sqrt_s) const
The W fusion contribution to higgs-production cross section in the Standard Model.
virtual double computeKW() const
A method to compute the ratio of the coupling in the current model and in the SM.
double computeSigmaZWF(const double sqrt_s) const
The Z W interference fusion contribution to higgs-production cross section in the Standard Model...
double HiggsKvgenKf::muVBFpVH ( const double sqrt_s ) const
virtual
The ratio $$\mu_{VBF+VH}$$ between the sum of VBF and WH+ZH associated production cross-section in the current model and in the Standard Model.
Parameters
[in] sqrt_s the center-of-mass energy in TeV
Returns
$$\mu_{VBF+VH}$$
Reimplemented from NPbase.
Definition at line 86 of file HiggsKvgenKf.cpp.
87 {
88 double sigmaWH_SM = trueSM.computeSigmaWH(sqrt_s);
89 double sigmaZH_SM = trueSM.computeSigmaZH(sqrt_s);
90 double sigmaWF_SM = trueSM.computeSigmaWF(sqrt_s);
91 double sigmaZF_SM = trueSM.computeSigmaZF(sqrt_s);
92 double sigmaZWF_SM = trueSM.computeSigmaZWF(sqrt_s);
93 double sigmaVBF_SM = sigmaWF_SM + sigmaZF_SM + sigmaZWF_SM;
94
95 double sigmaWH = muWH(sqrt_s) * sigmaWH_SM;
96 double sigmaZH = muZH(sqrt_s) * sigmaZH_SM;
97 double sigmaVBF = muVBF(sqrt_s) * sigmaVBF_SM;
98
99 return ((sigmaWH + sigmaZH + sigmaVBF) / (sigmaWH_SM + sigmaZH_SM + sigmaVBF_SM));
100 }
double computeSigmaZH(const double sqrt_s) const
The ZH production cross section in the Standard Model.
double computeSigmaZF(const double sqrt_s) const
The Z fusion contribution to higgs-production cross section in the Standard Model.
StandardModel trueSM
Definition: NPbase.h:543
virtual double muVBF(const double sqrt_s) const
The ratio between the vector-boson fusion Higgs production cross-section in the current model and in...
double computeSigmaWH(const double sqrt_s) const
The WH production cross section in the Standard Model.
virtual double muWH(const double sqrt_s) const
The ratio between the W-Higgs associated production cross-section in the current model and in the St...
double computeSigmaWF(const double sqrt_s) const
The W fusion contribution to higgs-production cross section in the Standard Model.
double computeSigmaZWF(const double sqrt_s) const
The Z W interference fusion contribution to higgs-production cross section in the Standard Model...
virtual double muZH(const double sqrt_s) const
The ratio between the Z-Higgs associated production cross-section in the current model and in the St...
double HiggsKvgenKf::muVH ( const double sqrt_s ) const
virtual
The ratio $$\mu_{VH}$$ between the WH+ZH associated production cross-section in the current model and in the Standard Model.
Parameters
[in] sqrt_s the center-of-mass energy in TeV
Returns
$$\mu_{VH}$$
Reimplemented from NPbase.
Definition at line 77 of file HiggsKvgenKf.cpp.
78 {
79 double sigmaWH_SM = trueSM.computeSigmaWH(sqrt_s);
80 double sigmaZH_SM = trueSM.computeSigmaZH(sqrt_s);
81 return ((computeKW() * computeKW() * sigmaWH_SM
82 + computeKZ() * computeKZ() * sigmaZH_SM)
83 / (sigmaWH_SM + sigmaZH_SM));
84 }
double computeSigmaZH(const double sqrt_s) const
The ZH production cross section in the Standard Model.
StandardModel trueSM
Definition: NPbase.h:543
virtual double computeKZ() const
A method to compute the ratio of the coupling in the current model and in the SM.
double computeSigmaWH(const double sqrt_s) const
The WH production cross section in the Standard Model.
virtual double computeKW() const
A method to compute the ratio of the coupling in the current model and in the SM.
double HiggsKvgenKf::muWH ( const double sqrt_s ) const
virtual
The ratio $$\mu_{WH}$$ between the W-Higgs associated production cross-section in the current model and in the Standard Model.
Parameters
[in] sqrt_s the center-of-mass energy in TeV
Returns
$$\mu_{WH}$$
Reimplemented from NPbase.
Definition at line 67 of file HiggsKvgenKf.cpp.
68 {
69 return (computeKW() * computeKW());
70 }
virtual double computeKW() const
A method to compute the ratio of the coupling in the current model and in the SM.
double HiggsKvgenKf::muZH ( const double sqrt_s ) const
virtual
The ratio $$\mu_{ZH}$$ between the Z-Higgs associated production cross-section in the current model and in the Standard Model.
Parameters
[in] sqrt_s the center-of-mass energy in TeV
Returns
$$\mu_{ZH}$$
Reimplemented from NPbase.
Definition at line 72 of file HiggsKvgenKf.cpp.
73 {
74 return (computeKZ() * computeKZ());
75 }
virtual double computeKZ() const
A method to compute the ratio of the coupling in the current model and in the SM.
void HiggsKvgenKf::setKf ( double Kf )
inline
A set method to change the factor rescaling the Higgs coupling to fermions with respect to the SM $$K_f$$.
Parameters
[in]
Definition at line 109 of file HiggsKvgenKf.h.
110 {
111 this->Kf = Kf;
112 }
double Kf
The factor rescaling all Higgs couplings to fermions with respect to the SM.
Definition: HiggsKvgenKf.h:345
void HiggsKvgenKf::setKW ( double KW )
inline
A set method to change the factor rescaling the Higgs coupling to the $$W$$ boson with respect to the SM $$K_W$$.
Parameters
[in]
Definition at line 129 of file HiggsKvgenKf.h.
130 {
131 this->KW = KW;
132 }
double KW
The factor rescaling Higgs couplings to bosons with respect to the SM.
Definition: HiggsKvgenKf.h:343
void HiggsKvgenKf::setKZ ( double KZ )
inline
A set method to change the factor rescaling the Higgs coupling to the $$Z$$ boson with respect to the SM $$K_Z$$.
Parameters
[in]
Definition at line 149 of file HiggsKvgenKf.h.
150 {
151 this->KZ = KZ;
152 }
double KZ
The factor rescaling Higgs couplings to bosons with respect to the SM.
Definition: HiggsKvgenKf.h:344
void HiggsKvgenKf::setParameter ( const std::string name, const double & value )
protectedvirtual
A method to set the value of a parameter of HiggsKvKf.
Parameters
[in] name name of a model parameter [in] value the value to be assigned to the parameter specified by name
Reimplemented from StandardModel.
Definition at line 24 of file HiggsKvgenKf.cpp.
25 {
26 if (name.compare("KW") == 0)
27 KW = value;
28 else if (name.compare("KZ") == 0)
29 KZ = value;
30 else if (name.compare("Kf") == 0)
31 Kf = value;
32 else if (name.compare("BrHinv") == 0)
33 BrHinv = value;
34 else
35 NPbase::setParameter(name, value);
36 }
double KZ
The factor rescaling Higgs couplings to bosons with respect to the SM.
Definition: HiggsKvgenKf.h:344
std::string name
The name of the model.
Definition: Model.h:203
double Kf
The factor rescaling all Higgs couplings to fermions with respect to the SM.
Definition: HiggsKvgenKf.h:345
virtual void setParameter(const std::string name, const double &value)
A method to set the value of a parameter of StandardModel.
double BrHinv
The branching ratio of invisible Higgs decays.
Definition: HiggsKvgenKf.h:346
double KW
The factor rescaling Higgs couplings to bosons with respect to the SM.
Definition: HiggsKvgenKf.h:343
## Member Data Documentation
double HiggsKvgenKf::BrHinv
private
The branching ratio of invisible Higgs decays.
Definition at line 346 of file HiggsKvgenKf.h.
const std::string HiggsKvgenKf::HKvgenKfvars
static
Initial value:
= {
"KW", "KZ", "Kf", "BrHinv"
}
A string array containing the labels of the model parameters in HiggsKvgenKf.
Definition at line 80 of file HiggsKvgenKf.h.
double HiggsKvgenKf::Kf
private
The factor rescaling all Higgs couplings to fermions with respect to the SM.
Definition at line 345 of file HiggsKvgenKf.h.
double HiggsKvgenKf::KW
private
The factor rescaling Higgs couplings to $$W$$ bosons with respect to the SM.
Definition at line 343 of file HiggsKvgenKf.h.
double HiggsKvgenKf::KZ
private
The factor rescaling Higgs couplings to $$Z$$ bosons with respect to the SM.
Definition at line 344 of file HiggsKvgenKf.h.
const int HiggsKvgenKf::NHKvgenKfvars = 4
static
The number of the model parameters in HiggsKvgenKf.
Definition at line 75 of file HiggsKvgenKf.h.
The documentation for this class was generated from the following files: | 2018-10-17 07:15:05 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4742989242076874, "perplexity": 6327.2884723366915}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-43/segments/1539583511063.10/warc/CC-MAIN-20181017065354-20181017090854-00091.warc.gz"} |
https://proofwiki.org/wiki/Definition:Set_Union/Family_of_Sets | # Definition:Set Union/Family of Sets
## Definition
Let $I$ be an indexing set.
Let $\family {S_i}_{i \mathop \in I}$ be a family of sets indexed by $I$.
Then the union of $\family {S_i}$ is defined as:
$\displaystyle \bigcup_{i \mathop \in I} S_i := \set {x: \exists i \in I: x \in S_i}$
### In the context of the Universal Set
In treatments of set theory in which the concept of the universal set is recognised, this can be expressed as follows.
Let $\mathbb U$ be a universal set.
Let $I$ be an indexing set.
Let $\family {S_i}_{i \mathop \in I}$ be an indexed family of subsets of $\mathbb U$.
Then the union of $\family {S_i}$ is defined and denoted as:
$\displaystyle \bigcup_{i \mathop \in I} S_i := \set {x \in \mathbb U: \exists i \in I: x \in S_i}$
### Subsets of General Set
This definition is the same when the universal set $\mathbb U$ is replaced by any set $X$, which may or may not be a universal set:
Let $\family {S_i}_{i \mathop \in I}$ be an indexed family of subsets of a set $X$.
Then the union of $\family {S_i}$ is defined as:
$\displaystyle \bigcup_{i \mathop \in I} S_i := \set {x \in X: \exists i \in I: x \in S_i}$
## Union of Family of Two Sets
Let $I = \set {\alpha, \beta}$ be an indexing set containing exactly two elements.
Let $\family {S_i}_{i \mathop \in I}$ be a family of sets indexed by $I$.
From the definition of the union of $S_i$:
$\displaystyle \bigcup_{i \mathop \in I} S_i := \set {x: \exists i \in I: x \in S_i}$
it follows that:
$\displaystyle \bigcup \set {S_\alpha, S_\beta} := S_\alpha \cup S_\beta$
## Also denoted as
The set $\displaystyle \bigcup_{i \mathop \in I} S_i$ can also be seen denoted as:
$\displaystyle \bigcup_I S_i$
or, if the indexing set is clear from context:
$\displaystyle \bigcup_i S_i$
However, on this website it is recommended that the full form is used.
## Also see
• Results about set unions can be found here. | 2020-03-28 18:41:40 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9740980863571167, "perplexity": 157.22455042818498}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-16/segments/1585370492125.18/warc/CC-MAIN-20200328164156-20200328194156-00408.warc.gz"} |
http://mathematica.stackexchange.com/questions/33418/find-the-value-of-parameter-so-that-the-equation-has-one-solution | # Find the value of parameter so that the equation has one solution
Let $(E_l) : x^4-4x^3+x^2(5-l^2)+4 x l^2-4l^2 = 0$ be an equation with $l$ as a parameter and $x$ as an unknown and $S_l$ the set containing all the real solutions of $(E_l)$.
Then there is a unique value of $l$ verifying $card(S_l) = 1$.
Is there a way in Mathematica to find an approximate value for this $l$ ?
-
Complex roots come in pairs therefore the equation will have a single real solution only if it has a real double root and two complex root or if it has a quadruple root.
So we require
poly = -4 l^2 + 4 l^2 x + (5 - l^2) x^2 - 4 x^3 + x^4
Solve[{poly == 0, D[poly, x] == 0}, {x, l}, Reals]
This gives us three solutions for l:
{0, -((2 + 2^(1/3))^(3/2)/Sqrt[2]), (2 + 2^(1/3))^(3/2)/Sqrt[2]}
Substituting them back into poly and finding all roots shows that only l == 0 will give double real root and two complex roots.
-
I'm quite disappointed I didn't think of using the derivative. Very clever solution, thanks ! – Skydreamer Oct 4 '13 at 14:49
With[{poly = x^4 - 4 x^3 + (5 - l^2) x^2 + 4 l^2 x - 4 l^2},
With[{sols =
DeleteDuplicates@Solve[Discriminant[poly, x] == 0, l, Reals]},
Select[
sols,
Length[DeleteDuplicates@Solve[(poly /. First@#) == 0, x, Reals]] ==
1 &
]
]]
(* {{l -> 0}} *)
-
@Michel E2 If I want to the equation $x^4+2(m+1)x^2 - m - 4 =0$ has three reals solutions. How can I get it? – minthao_2011 Oct 5 '13 at 3:52
@minthao_2011 Should this be a separate question, not a comment? In any case, three (distinct) real solutions implies two simple and one double root. From Discriminant[x^4 + 2 (m + 1) x^2 - 4, x], one sees that only m -> -4 will yield a double root; luckily it also yields two other simple real roots. – Michael E2 Oct 5 '13 at 12:24 | 2014-04-21 10:02:45 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5361409187316895, "perplexity": 673.1007759159629}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-15/segments/1397609539705.42/warc/CC-MAIN-20140416005219-00651-ip-10-147-4-33.ec2.internal.warc.gz"} |
http://www.sciforums.com/threads/yard-lights.124963/ | # yard lights..
Discussion in 'Architecture & Engineering' started by NMSquirrel, Nov 15, 2012.
1. ### NMSquirrelOCD ADHD THC IMO UR12Valued Senior Member
Messages:
5,478
dunno where else to ask this..
looking for a solar powered yard light..one that has a timer that i can set to 15 minutes to turn off..
solar powered yard lights are easy to find..but all i have found is on all night..no selectable timer..
but i wanna use it as a timer for a sprinkler system..it has to be around 9 volts and either turn off in 15 minutes or the battery can die after 15 minutes..
3. ### billvonValued Senior Member
Messages:
14,306
Do you want lights as well, or just the timer function?
Do you want to time it from sunset or from a certain clock time?
5. ### NMSquirrelOCD ADHD THC IMO UR12Valued Senior Member
Messages:
5,478
its a low tech solution for the sprinklers..if it goes on at dusk/sunset for 15 minutes that would be enough to water the grass..
what i had originally intended was to find a yard light with a timer and just wire the sprinklers into the bulb (bulb would be deleted)
wireing it into 110 wont work, as we have no idea where the previous wiring runs..(there are like 4 different sprinkler timers in the storage shed, so apperantly thats not an option)
i tested a 9 volt battery with it and have it set up now to hook up a 9 volt battery to the valve, so we dont have to crawl into the three foot hole to turn on the sprinklers..(it works either polarity) when the battery is connected the valve turns on, when the battery is disconnected the valve turns off..
as it sets now, we can use a rechargable battery to work it ( i imagine the cheaper rechargables would run down quicker, maybe that would give me my 15 minute run time)..
but that requires hooking that battery up and disconnecting it everyday (season permitting).
the yard light option (maybe there is another option i am missing) would make it no maintenance..wouldnt have to worry about hooking and unhooking the battery.
7. ### billvonValued Senior Member
Messages:
14,306
OK then.
Start with a cheap 16V solar panel. Wire it to a 12V DPDT relay. The normally closed contacts will be closed when the sun is down.
Now add a diode, a 13.5V regulator and a 4ah 12V lead acid battery. This will charge from the solar panel and provide power to operate your valve.
Now add a 555 timer to the output of the relay. Configure it for monostable operation. This will allow you to set a run time. 1000uF with a 1 meg resistor should give you about 15-20 minutes. You might need an additional relay at the 555's output to drive the valve.
All the above is available from Radio Shack.
8. ### MacGyver1968Fixin' Shit that Ain't BrokeValued Senior Member
Messages:
7,028
Or you could use a relay timer like this one:
This one is a "delay on make" used in air conditioners, but they do make timer versions. Just add it in series with the power to the lights and the sprinkler.
9. ### MacGyver1968Fixin' Shit that Ain't BrokeValued Senior Member
Messages:
7,028
Why does my post need approval by mods?
10. ### MacGyver1968Fixin' Shit that Ain't BrokeValued Senior Member
Messages:
7,028
Let's try that again:
Or you could use a relay timer like this one:
This one is a "delay on make" used in air conditioners, but they do make timer versions. Just add it in series with the power to the lights and the sprinkler.
edit: this only works with AC...a solar panel will put out DC...so forget this.
11. ### MacGyver1968Fixin' Shit that Ain't BrokeValued Senior Member
Messages:
7,028
Looking for other options. Couple of quick questions. How many lights do you need, and what's your budget?
Edit:
Ok..it seems that make 2 different kinds. One type has the solar cell built into the light, and others, like this have a separate solar cell:
I think this kind would be easier to modify, as the solar cell, light sensor and battery are all in the solar cell package. You could simply splice into the wire coming out of the solar cell, and add in your timer. Still looking for a "time on make" relay timer that works on low voltage dc.
12. ### billvonValued Senior Member
Messages:
14,306
Most of these have three NiMH batteries to give you 3.6 volts, which is what you need to run the white LED's in the lamps. So they would likely not work well if he needs 9V.
13. ### MacGyver1968Fixin' Shit that Ain't BrokeValued Senior Member
Messages:
7,028
What about using that 3.6 volts to close a relay like this?
3.6 volts should be enough to close a 5 volt relay.
14. ### billvonValued Senior Member
Messages:
14,306
If you choose wisely, yes. DIP relays like the one above have a pull-in voltage of between 3.2 and 4.5 volts; the Panasonic DS2Y-S-DC5V, for example, will pull in at 3.5 volts.
However that doesn't solve his other problem which is that he needs 9 volts to turn his sprinkler valve on.
15. ### scheherazadeNorthern Horse WhispererValued Senior Member
Messages:
3,798
Sheesh! I'm shoveling snow and you lot are designing timed self-watering systems. I've considered some for my gardening but because I am on a closed system (water tank with pressure system, pumped in to from a deep well pump on a manual switch with no fail-safes) I don't think that is a good idea. Too risky, might burn out the pump if the tank pumps dry and no one close to hand. My compromise for part of the garden is a soaker hose. I top up the inside tank and then turn on the watering system, set a timer and tend to indoor matters until done.
Interesting to check out the solutions being offered here, nonetheless.
16. ### EnmosRegistered Senior Member
Messages:
43,184
Squirrel, why do you need the solar powered yard lights? Just hook your sprinklers up to a timer.
17. ### MacGyver1968Fixin' Shit that Ain't BrokeValued Senior Member
Messages:
7,028
What I was thinking was: The sprinkler has a timer that turns on a valve. Just set the sprinkler to "always on", and place the 5volt relay between the sprinkler timer and the valve. Power the relay with the output of the solar panel/battery/light sensor assembly. When the solar panel and timer activates...the relay closes and the power coming from the sprinkler timer box turns on the valve for the 15 minutes he desires.
18. ### MacGyver1968Fixin' Shit that Ain't BrokeValued Senior Member
Messages:
7,028
I've never installed a sprinkler system. I did a little research and all of the valves I found run on 24VAC. Squirrel...anyway you have a look at your valves and see what the voltage is? Where did the 9 volt number come from?
Messages:
2,562
20. ### kwhilbornBannedBanned
Messages:
2,088
@ Billvon, and all | 2018-10-15 21:04:29 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.2583535313606262, "perplexity": 3881.815025550929}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-43/segments/1539583509845.17/warc/CC-MAIN-20181015205152-20181015230652-00079.warc.gz"} |
https://stats.stackexchange.com/questions/257030/is-it-ok-to-call-model-learning-in-machine-learning-an-estimator | # Is it ok to call model learning in machine learning an “estimator”?
Spark doc contains this:
An Estimator abstracts the concept of a learning algorithm or any algorithm that fits or trains on data. Technically, an Estimator implements a method fit(), which accepts a DataFrame and produces a Model, which is a Transformer. For example, a learning algorithm such as LogisticRegression is an Estimator, and calling fit() trains a LogisticRegressionModel, which is a Model and hence a Transformer.
But Wikipedia says:
An "estimator" or "point estimate" is a statistic (that is, a function of the data) that is used to infer the value of an unknown parameter in a statistical model. The parameter being estimated is sometimes called the estimand. It can be either finite-dimensional (in parametric and semi-parametric models), or infinite-dimensional (semi-parametric and non-parametric models). If the parameter is denoted $\theta$ then the estimator is traditionally written by adding a circumflex over the symbol: $\widehat {\theta }$. Being a function of the data, the estimator is itself a random variable; a particular realization of this random variable is called the "estimate". Sometimes the words "estimator" and "estimate" are used interchangeably.
I would have called the machine learning model itself the "estimator". Are the 2 definitions above close enough, or off, or are there important distinctions to be aware of?
• This is part of the problem between CS/ML people and stats. There's a difference in language. What they mean by Estimator is more of a method/implementation not a point estimate. – Jon Jan 18 '17 at 22:15
• @Jon you are confusing estimator (a function) with estimate (it's outcome given the sample), see stats.stackexchange.com/questions/7581/… – Tim Jan 18 '17 at 22:24
• What else would you call something that estimates the parameters of the model? – david25272 Jan 19 '17 at 2:30
• @david25272 - a procedure, algorithm, method, recipe... for the part that does the calculation of the parameters of the model? – Frank Jan 19 '17 at 3:48
• I've always thought of algorithms as specific (e.g. OLS, Iteratively Reweighted LS) examples of estimators. – david25272 Jan 19 '17 at 4:58
It is hard to answer your question without knowing what you mean by model. Statistical model describes the phenomenon of interest in terms of probability theory (notice that there are also other models, e.g. mechanistic models). It is not yet an estimator of anything, but just an abstract description of the problem. You need an estimator to estimate the parameters of your model (also in case of so-called non-parametric models). In machine learning people often call algorithms used to estimate something as models, but in general: model is a theoretical description of the problem and estimator is a procedure that generates the estimates of its parameters. Estimator is a general procedure, not its implementation, so function foo() in software XYZ is not an estimator, but rather it's an implementation of some estimator. | 2020-08-15 12:24:06 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6043882369995117, "perplexity": 805.3611300145661}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-34/segments/1596439740838.3/warc/CC-MAIN-20200815094903-20200815124903-00153.warc.gz"} |
https://aptitude.gateoverflow.in/6502/nielit-2017-dec-scientific-assistant-a-section-a-3 | 1,049 views
Have a word followed by four answer choices. You will choose the word that is a necessary part of the word.
electric bulb
1. electricity
2. thunder
3. brightness
4. rain
Option ( A) should be right.
Because without electricity bulb is nothing. Brightness will come after electricity.
78 points
electric bulb C) brightness.
5.4k points
ans is A
Lightning is produced from a discharge of electricity, so electricity is essential. Thunder and rain are not essential to the production of lightning (choices b and d). Brightness may be a byproduct of lightning, but it is not essential (choice c).
by
38 points
Electricity is a necessary part of the word electric bulb.
So, the correct answer is $(A).$
12.1k points
1
928 views
2
941 views | 2022-12-08 07:32:35 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5238120555877686, "perplexity": 5210.43037262909}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-49/segments/1669446711278.74/warc/CC-MAIN-20221208050236-20221208080236-00369.warc.gz"} |
https://socratic.org/questions/how-do-you-calculate-the-ionization-energy-of-h | How do you calculate the ionization energy of H+?
The is no electron to ionise since $\textsf{{H}^{+}}$ is a hydrogen ion and is just a bare proton. | 2020-01-26 12:10:17 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 1, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5873572826385498, "perplexity": 383.3140881434412}, "config": {"markdown_headings": false, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-05/segments/1579251688806.91/warc/CC-MAIN-20200126104828-20200126134828-00345.warc.gz"} |
https://en.wikibooks.org/wiki/Category_Theory/Additive_categories | Definition (biproduct):
Let ${\displaystyle {\mathcal {C}}}$ be a category, and let ${\displaystyle (X_{\alpha })_{\alpha \in A}}$ be a family of objects in ${\displaystyle {\mathcal {C}}}$. A biproduct of ${\displaystyle (X_{\alpha })_{\alpha \in A}}$ is an object of ${\displaystyle {\mathcal {C}}}$ that is usually denoted as
${\displaystyle \bigoplus _{\alpha \in A}X_{\alpha }}$
and for which there exist arrows
${\displaystyle \iota _{\alpha }:X_{\alpha }\to \bigoplus _{\alpha \in A}X_{\alpha }}$ and ${\displaystyle \pi _{\alpha }:\bigoplus _{\alpha \in A}X_{\alpha }\to X_{\alpha }}$
for all ${\displaystyle \alpha \in A}$ that have the following properties:
1. ${\displaystyle \alpha \neq \beta \Rightarrow \pi _{\alpha }\circ \iota _{\beta }=0}$ and ${\displaystyle \forall \alpha \in A:\pi _{\alpha }\circ \iota _{\alpha }=\operatorname {Id} _{X_{\alpha }}}$
2. ${\displaystyle \bigoplus _{\alpha \in A}X_{\alpha }}$, together with the morphisms ${\displaystyle (\iota _{\alpha })_{\alpha \in A}}$, constitutes a coproduct in the category ${\displaystyle {\mathcal {C}}}$
3. ${\displaystyle \bigoplus _{\alpha \in A}X_{\alpha }}$, together with the morphisms ${\displaystyle (\pi _{\alpha })_{\alpha \in A}}$, constitutes a product in the category ${\displaystyle {\mathcal {C}}}$
An additive category is a category ${\displaystyle {\mathcal {C}}}$ that satisfies each of the following requirements:
1. Every morphism in ${\displaystyle {\mathcal {C}}}$ has a kernel and a cokernel
2. For every two objects ${\displaystyle X,Y}$ of ${\displaystyle {\mathcal {C}}}$, there exists a biproduct ${\displaystyle X\oplus Y}$
3. For every two objects ${\displaystyle X,Y}$ of ${\displaystyle {\mathcal {C}}}$, the assignment ${\displaystyle (f,g)\mapsto h}$, where ${\displaystyle h:X\to Y}$ is the morphism that arises from postcomposing the morphism ${\displaystyle X{\overset {\Delta }{\to }}X\oplus X{\overset {f\times g}{\to }}Y\oplus Y}$ (where ${\displaystyle \Delta }$ shall denote the diagonal) with the anti-diagonal ${\displaystyle \nabla :Y\oplus Y\to Y}$, turns ${\displaystyle \operatorname {Hom} (X,Y)}$ into an abelian group | 2019-05-27 00:13:54 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 30, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9919646382331848, "perplexity": 119.1847192262765}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-22/segments/1558232260161.91/warc/CC-MAIN-20190526225545-20190527011545-00283.warc.gz"} |
https://ts-salobj.lsst.io/py-api/lsst.ts.salobj.make_state_transition_dict.html | # make_state_transition_dict¶
lsst.ts.salobj.make_state_transition_dict()
Make a dict of state transition commands and states
The keys are (beginning state, ending state). The values are a list of tuples:
• A state transition command
• The expected state after that command | 2020-11-28 02:50:42 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7236382365226746, "perplexity": 8928.659142192257}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-50/segments/1606141194982.45/warc/CC-MAIN-20201128011115-20201128041115-00363.warc.gz"} |
https://stats.stackexchange.com/questions/349961/how-does-probabilistic-ml-handle-uncertainty/519443 | # How does probabilistic ML “handle uncertainty”?
I have heard professors and others say that probabilistic machine learning is useful because it can model or handle uncertainty. I'm not sure what is meant by this. To give an authoritative source, David MacKay writes in his book on inference (p. 531):
Probabilistic modelling also handles uncertainty in a natural manner. It offers a unique prescription, marginalization, for incorporating uncertainty about parameters into predictions...
What is meant by this? How does this handle uncertainty? A comparison to a non-probabilistic model would be appreciated.
• Can you give an example of a probabilistic model and of a non-probabilistic model in your context? I'm not sure if you're asking us to compare models that yield probabilities as classification outcomes vs. models that yield the predicted class directly, or if you're asking a different question like comparing parametric vs non-parametric models. Or something different entirely? – Eduard Gelman Jun 5 '18 at 22:03
• K-means (non-probabilistic) vs. Gaussian mixture model (probabilistic). – gwg Jun 5 '18 at 23:07
## 2 Answers
Non-probabilistic machine learning models do not handle uncertainty about the parameters. They simply return point estimates for the parameters. You may use additional techniques (e.g. bootstrap) to learn something about the uncertainty. Many of the available solutions (e.g. using dropout also at the prediction time) are thought of as approximations of the Bayesian (probabilistic) solutions to the problem.
Probabilistic models give you estimates of the distributions for the parameters. They tell you what are the probabilities of observing different values of the parameters. This is used to quantify the uncertainty, by calculating things like highest density regions, or quantiles of the distributions.
• I'll accept this, but I want to add the caveat that not all probabilistic methods allow for uncertainty about estimated parameters in the same way. For example, the Bayesian approach (which is what MacKay was talking about) treats the parameter itself as a random variable. However, the frequentist MLE of a statistical model has asymptotic variance associated with the estimator itself. But these aren't really the same thing. My point is that I think this answer is correct for Bayesian inference. – gwg Apr 14 at 19:47
• For what it's worth, at the beginning of the book MacKay announces that he'll take a Bayesian slant throughout. – Arya McCarthy Apr 15 at 22:21
### A note on definitions:
From your clarifying comment for examples of what you mean by "probabilistic":
K-means (non-probabilistic) vs. Gaussian mixture model (probabilistic).
It sounds like you're talking about what the literature usually calls parametric vs. non-parametric model. I'd suggest reading [this post][1] from the Machine Learning Mastery blog, and following the references at the bottom of the page under "Posts".
• I don't think your distinction between parametric and non-parametric is correct. A non-parametric model is one with a potentially infinite number of parameters. For example, an HMM that grows with your data. Here is a more authoritative source: arxiv.org/abs/1106.2697. And here is an NYU lecture (davidrosenberg.github.io/ml2015/docs/13.mixture-models.pdf) in which the instructor compares $K$-means and GMMs and explicitly states that GMMs are a "Probabilistic Model for Clustering" (Slide 20). – gwg Jun 6 '18 at 19:48
• This is not right. Parametric/non-parametric is not the defining difference here. A gwg points out, non-parametric really means "infinitely parametric." The key distinction between probabilistic and non-probabilistic is whether the parameter values are treated as as points or distributions. Treating them as distributions allows for accounting for "uncertainty" in the prediction. – degenerate hessian Jun 6 '18 at 20:18
• I simplified a lot and made some assumptions about what the question was originally about and it looks like I oversimplified my way into being wrong. Accordingly, I've removed the personal commentary. – Eduard Gelman Jun 6 '18 at 20:31
• @EduardGelman The edit broke the link. – Arya McCarthy Apr 13 at 1:19 | 2021-05-07 19:53:39 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4348699152469635, "perplexity": 925.9085934469731}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-21/segments/1620243988802.93/warc/CC-MAIN-20210507181103-20210507211103-00102.warc.gz"} |
https://pypi.org/project/fitdecode/0.2.0/ | FIT file parser and decoder
## fitdecode
A FIT file parsing and decoding library written in Python3 (3.6+ only).
### Usage Example
Read a FIT file, frame by frame:
import fitdecode
for frame in fit:
# The yielded *frame* object is of one of the following types:
# * fitdecode.FitDefinitionMessage
# * fitdecode.FitDataMessage
# * fitdecode.FitCRC
#
# A fitdecode.FitDataMessage object contains decoded values that are
# directly usable in your script logic.
pass
### Installation
fitdecode is available on PyPI:
$pip install fitdecode Or, to get the latest working version, you can clone fitdecode’s source code repository before installing it: $ git clone git@github.com:polyvertex/fitdecode.git
$cd fitdecode$ python setup.py test # optional step to run unit tests
\$ python setup.py install
Note that for convenience, the cmd directory located at the root of the source code tree can safely be added to your PATH, so that fitdecode commands can be called without the package to be installed.
### Overview
fitdecode is a non offensive and incompatible rewrite of the fitparse library, with some improvements and additional features, as well as efforts made to optimize both speed and memory usage.
Main differences between fitdecode and fitparse:
• fitdecode requires Python version 3.6 or greater
• fitdecode allows concurrent reading of multiple files by being thread-safe, in the sense that fitdecode’s objects keep their state stored locally
• fitdecode high-level interfaces are not compatible with fitparse’s FitFile
• fitdecode does not discard the FIT header and the CRC footer while iterating a file, which allow to get a complete 1:1 representation of the file that is being read
• This also allows the client to easily deal with so-called chained FIT files, as per FIT SDK definition (i.e. concatenated FIT files)
• fitdecode offers optional access to records, headers and footers in their binary form, to allow FIT file cutting, stitching and filtering at binary level
### Why a new library?
A new library has been created instead of just offering to patch fitparse because many changes and adds in fitdecode break fitparse’s backward compatibilty and because it allowed more freedom during the development of fitdecode.
### Credits
fitdecode is largely based on the generic approach adopted by fitparse to define FIT types and to decode raw values. That includes the module profile.py and all the classes it refers to, as well as the script generate_profile.py.
## Change Log
### v0.2.0 (2018-07-16)
• Improved FitDataMessage.get_field (idx arg)
• Improved FitDataMessage.get_value (idx arg)
• Completed documentation of FitDataMessage
• Improved documentation of FieldData
• FitReader’s internal state is reset as well after a FitCRC has been yielded (i.e. not only when a FIT header is about to be read), in order to avoid incorrect behavior due to malformed FIT stream
### v0.1.0 (2018-07-14)
• Added class property frame_type (read-only) to FitHeader, FitCRC, FitDefinitionMessage and FitDataMessage (records module) to ease and speed up type checking
• string values with no null byte are still decoded (in full length)
• cmd directory added to the source code tree for convenience
### v0.0.1 (2018-07-08)
• First release
• Birth!
## Project details
Uploaded source
Uploaded py3 | 2022-09-30 14:20:07 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.2948925495147705, "perplexity": 12378.17255977174}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-40/segments/1664030335469.40/warc/CC-MAIN-20220930113830-20220930143830-00326.warc.gz"} |
https://discuss.codechef.com/questions/88431/help-in-hackerearth-november-circuits-fredo-is-in-hurry?page=1 | ×
# Help in: Hackerearth November Circuits: Fredo is in Hurry
0 Since the contest is over, I am asking it now. Here's the link to the question: Fredo is in a Hurry And here's my implementation: link The above code gets successfully compiled and passes the custom test cases on the compiler provided by hackerearth but when I submit the same, not a single test case is passed. I want to know the logic behind this problem. asked 27 Nov '16, 20:39 115●1●8 accept rate: 0%
5 Although binary search can solve this problem, there is an $O(1)$ solution if you think about this mathematically. If he uses staircase, he takes $f$ amount of time to reach floor $f$ from floor $f-1$. Thus, to reach floor number $f$ total time taken is $1+2+3+...+f = \frac{f(f+1)}{2}$. Elevator takes 1 unit time to go from any floor to it's neighbouring floors. Thus, time taken by the elevator to reach a certain floor while descending is $N-f$. Now, from the problem it is clear that catching the elevator on its way down and then riding it to the top is the quicker than climbing to the top. However waiting too long at some floor $x$ is also not a good idea if it is possible to reach floor $x+1$ by the time the elevator reaches floor $x+1$, as it wastes 2 units of time. So our aim is to climb the stairs to the maximum floor possible without missing the elevator. Which amounts to finding the largest $x$ for which $$\frac{x(x+1)}{2} \le N-x$$ This is a quadratic inequality, solving which we get the maximum integer value of $x$ as $$x = \bigg\lfloor\frac{-3 + \sqrt{9+8N}}{2}\bigg\rfloor$$ The total time taken is the time taken for the elevator to come to this floor $x$ and go up again, which is $2(N-x)$. A corner case arises when $N=1$, as not taking the elevator is quicker than taking it. Just climbing one floor is 1 unit whereas waiting for the elevator would take 2 units of time. Solution in Python: here answered 28 Nov '16, 01:59 6★meooow ♦ 6.9k●7●17 accept rate: 48% Very well explained! 1 thing I would like to ask is how to come up with such mathematical proof like answers? I know practice is the key but still I would like to know :) (28 Nov '16, 17:10) 2 There is no particular way I have, although I generally read a problem and try to simplify it as much as I can, usually sitting with a pen and scribbling what goes through my mind. Maybe you can try that :) (29 Nov '16, 07:26) meooow ♦6★
0 your code runs in O(n) and n is very large.So it won't pass. Here you can use binary search to determine the solution. answered 27 Nov '16, 21:03 4★lakh 139●5 accept rate: 23%
Here is my code:
# include<bits stdc++.h="">
using namespace std;
# define mo 1000000007
int main() { ll t,i,j,k,n; cin>>t; while(t--) { cin>>n; if(n==1) { cout<<1<<"\n"; continue; } ll lo=0,hi=n; ll ans; while(lo<=hi) { ll mid=(lo+hi)>>1; ll p=mid; ll q=(p(p+1))/2; if(n-q>=p) { lo=p+1; ans=p; } else { hi=p-1; } } ll r1=n-ans; ll p5=(ans(ans+1))/2; r1+=p5; ll f1=n-p5; r1+=f1-ans; cout<<r1<<"\n"; } }
4★lakh
1395
accept rate: 23%
Here's my solution for Fredo is in Hurry!(using Binary Search)
# include <stdio.h>
int main(void) { // your code goes here int t;scanf("%d",&t); while(t--) { long long int n;scanf("%lld",&n); long long int l=0,h=n,mid; if (n==1) printf("1\n"); else{ while(l<=h) { mid=(h+l)/2; long long int temp=(mid*(mid+1))/2; long long int el=n-mid; if(temp<=el && (temp+mid+1)>=el) { long long int ans=(temp+el-temp+el); printf("%lld\n",ans); break; } else { if(temp>el) h=mid-1; else l=mid+1; }
}
}
}
311
accept rate: 0%
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last updated: 14 Apr '17, 18:30 | 2018-11-13 04:47:25 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6616175770759583, "perplexity": 2956.4929573163026}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-47/segments/1542039741219.9/warc/CC-MAIN-20181113041552-20181113063552-00179.warc.gz"} |
http://www.chegg.com/homework-help/questions-and-answers/four-pole-series-motor-runs-900-rev-min-taking-30a-froma-230v-supply-total-resistance-arma-q315161 | a four pole, series motor runs at 900 rev/min when taking 30A froma 230V supply. the total resistance of the armature and the seriesfield is 0.8Ω. Calculate the additional series resistancerequired to reduce the speed to 500 rev/min if the torque developedis:
i) constant?
ii) proportional to speed?
iii) proportional to the square of the speed.
(Assume the magnetic circuits is unsaturated.)
If you are able to answer all, i will give lifesaver rating but ifpartially i will give second highest..thxxxx | 2015-10-06 23:46:47 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8822911977767944, "perplexity": 5777.073702882932}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-40/segments/1443736679281.15/warc/CC-MAIN-20151001215759-00040-ip-10-137-6-227.ec2.internal.warc.gz"} |
http://www.chegg.com/homework-help/questions-and-answers/figure-shows-graph-angular-velocity-rotatingwheel-function-time-although-shown-graph-thean-q124081 | The figure shows a graph of the angular velocity of a rotatingwheel as a function of time. Although not shown in the graph, theangular velocity continues to increase at the same rate untilt = 7.8 s. What is the angular displacement of the wheelfrom 0 to 7.8 s? I've hadprevious help, but i still cant get the correct answer. the answeris no 24 or 72 rad
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The figure shows a graph of the angular velocity of a rotatingwheel as a function of time. Although not shown in the graph, theangular velocity continues to increase at the same rate untilt = 7.8 s. What is the angular displacement of the wheelfrom 0 to 7.8 s? | 2016-07-29 12:54:46 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8318177461624146, "perplexity": 434.8070573005652}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-30/segments/1469257830066.95/warc/CC-MAIN-20160723071030-00083-ip-10-185-27-174.ec2.internal.warc.gz"} |
https://mersenneforum.org/showpost.php?s=80110e94b7fb0f684076310f4fd2e18c&p=139566&postcount=11 | Thread: "Rare" Primes View Single Post
2008-08-20, 18:14 #11
biwema
Mar 2004
3×127 Posts
Quote:
Originally Posted by Jens K Andersen It's easy to construct rare prime forms by picking a quickly growing function with one or a few early primes. You mention Generalized Fermat 10^2^n+1, but there is no base b with more than 7 known primes b^2^n+1, and finding one with more than 10 looks very hard. The record is 7 for b=2072005925466 at http://primepuzzles.net/puzzles/puzz_399.htm
Maybe there is even a Generalized Fermat with more than 7 primes in the range b<10^15 or so. The sequence above assumes that n=0..6 of b^2^n+1 is prime. Maybe there is a generalized Fermat which has more than 7 primes that are not consecutive. For example if n=0,1,2,3,4,5,7,8 is prime.
The probability of that szenario is still pretty small. | 2021-04-15 09:17:36 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9072063565254211, "perplexity": 1662.9470599719195}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-17/segments/1618038084601.32/warc/CC-MAIN-20210415065312-20210415095312-00411.warc.gz"} |
https://brilliant.org/discussions/thread/factorial-times-5/ | ×
# Factorial
How many ZEROES (NOT trailing zeroes) are there at $$2015!$$?
Note by Bryan Lee Shi Yang
1 year, 6 months ago
Sort by:
This seems to be a number theory problem, but here's my python solution for this.
1 2 3 from math import factorial print(str(factorial(2015)).count('0')) #Returns 1037, time taken=6ms
· 1 year, 6 months ago
Wheyy....you know python too? I thought you used C++ for CS! · 1 year, 6 months ago
Yeah I learnt python about a month ago due to lack of required data types in C++. Also, I am posting solutions in python now-a-days. · 1 year, 6 months ago
Amazing. · 1 year, 6 months ago
Can I call this "Python Jugaad" :P ? · 1 year, 6 months ago
Lol sure · 1 year, 6 months ago
Haha maybe "Python Pranjal". · 1 year, 6 months ago | 2016-10-22 18:03:41 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6414288878440857, "perplexity": 10850.211303643819}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-44/segments/1476988719033.33/warc/CC-MAIN-20161020183839-00017-ip-10-171-6-4.ec2.internal.warc.gz"} |
https://dsp.stackexchange.com/questions/53450/average-energy-of-modified-qam-constellation | # Average Energy of modified QAM Constellation
How to compute the average energy for the modified 16-QAM constellation below? I know that for regular/rectangular 16-QAM we can utilize the 4-PAM along each axes but I'm not sure how can we find $$E_{avg}$$ here.
• This is a highly atypical modification of a QAM! This modification actually makes the peak-to-average symbol power ratio worse from a first look at it, so without knowing anything above the constellation I'd say: don't use this. So, wild guess: either this is an exam example, or this isn't used with equally probable symbols. Out of curiosity: Can you give us a bit of background where this is from? – Marcus Müller Nov 18 '18 at 22:06
• @MarcusMüller It is from a book: Fundamentals of Digital Communication by upamanyu madhow. The figure is from Problem 3.16 but my question is not the question asked in the book. – Lod Nov 19 '18 at 21:06
• Hey, thanks, @Lod! yeah, they don't put it into great context, it's just "here's the constellation, is it more or less power efficient than regular 16QAM". By the way, you don't have to calculate much to answer that – just notice that you've moved four points farther away from the origin (i.e. increased power) without changing error probabilities much (i.e. did not decrease BER), so the answer is that it's less efficient. – Marcus Müller Nov 19 '18 at 21:10
• @MarcusMüller Yeah I am not much concerned about thier question. I am just trying to study the constellation and how is is different from the regular one. Since you mentioned efficiency, is the bandwidth efficiency the same for both constellation? since it is given by $\eta=log_2 16=4$. I do not know if I am understanding this correctly. – Lod Nov 19 '18 at 21:15
The procedure is always the same. You need to compute the expectation $$E\{|A_k|^2\}$$, where $$A_k$$ are the complex symbols of the constellation:
$$E\{|A_k|^2\}=\sum_kP_k|A_k|^2\tag{1}$$
$$P_k$$ is the probability that the $$k^{th}$$ symbol is chosen. Usually you can assume that all symbols are equally likely, i.e., $$P_k=1/M$$, where $$M$$ is the number of symbols. | 2020-09-27 23:54:56 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 8, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8722527623176575, "perplexity": 500.4792434177888}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-40/segments/1600401582033.88/warc/CC-MAIN-20200927215009-20200928005009-00366.warc.gz"} |
https://cantera.org/documentation/docs-2.3/doxygen/html/VPSSMgr__ConstVol_8cpp.html | Cantera 2.3.0
VPSSMgr_ConstVol.cpp File Reference
Definition file for a derived class that handles the calculation of standard state thermo properties for a set of species which have a constant molar volume pressure dependence (see Thermodynamic Properties and class VPSSMgr_ConstVol). More...
#include "cantera/thermo/VPSSMgr_ConstVol.h"
#include "cantera/thermo/VPStandardStateTP.h"
#include "cantera/thermo/PDSS_ConstVol.h"
#include "cantera/base/ctml.h"
Include dependency graph for VPSSMgr_ConstVol.cpp:
Go to the source code of this file.
## Namespaces
Cantera
Namespace for the Cantera kernel.
## Detailed Description
Definition file for a derived class that handles the calculation of standard state thermo properties for a set of species which have a constant molar volume pressure dependence (see Thermodynamic Properties and class VPSSMgr_ConstVol).
Definition in file VPSSMgr_ConstVol.cpp. | 2021-06-22 04:49:34 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.22740407288074493, "perplexity": 5751.197919496598}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-25/segments/1623488507640.82/warc/CC-MAIN-20210622033023-20210622063023-00192.warc.gz"} |
http://nrich.maths.org/6675/index?nomenu=1 | Penny, Tom and Matthew were each given mint chocolates in a hexagonal box:
Penny ate $10$ chocolates and then quickly worked out that there must have been $61$ chocolates at the start.
Tom ate $20$ chocolates and then also managed to work out very quickly that there were originally $61$ chocolates:
Matthew ate $24$ chocolates and could also see very easily that he must have started with $61$ chocolates:
Can you see how each child managed to work out that there were $61$ chocolates in the full box?
You may find these chocolate box templates useful.
Penny, Tom and Matthew have been promised a larger box of chocolates as a Christmas present from their grandmother. The box will have $10$ chocolates along each edge, instead of just $5$.
How would each child work out how many chocolates the larger box will contain?
Can you describe any other ways to work it out?
Here are some more questions you might like to consider:
• For which sizes of chocolate box will the three children be able to share the chocolates equally?
• For which sizes of chocolate box will the boys be able to share the chocolates equally?
• Can you describe how each child would work out the number of chocolates in a box with $n$ chocolates along each edge? | 2015-04-21 05:10:14 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.2960990071296692, "perplexity": 931.8140341310287}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-18/segments/1429246640124.22/warc/CC-MAIN-20150417045720-00135-ip-10-235-10-82.ec2.internal.warc.gz"} |
https://abitofcs.blogspot.com/2015/01/codeforces-453c-little-pony-and-summer.html | ## Friday, January 9, 2015
### Codeforces 453C - Little Pony and Summer Sun Celebration
Problem Statement:
453C - Little Pony and Summer Sun Celebration
Solution:
(How did they come up with such a cute name for a problem statement, I wonder)
A pretty interesting graph problem, which is more of a test on structure construction. The official editorial to this problem is already perfectly clear, I'm writing this purely for my future references.
To solve the problem the brute force way, one can choose any node as a root, and run a DFS on this root, in the following manner: From root, visit the next available odd-parity node, and come back. This works because every nodes in between the path between root and the odd-parity node will be visited twice as the person go forth and back to root. Hence each time we will be eliminating one odd-parity node from consideration, which is nice. Finally, we check how many times we visited root, and if the parity does not match, we simply remove a root node on the tail of the path (i.e., the person did not come back to the root eventually). However, this approach does not guarantee the final path to be within 4n limit.
We extend the above idea to come up with a path that is guaranteed to be $$\leq 4n$$ in length by maintaining the following invariance while constructing the path:
By the time we leave a node u, every node belonging to the subtree rooted at u in the DFS tree will have all already consistent in their parity. We also know how many times u is visited during that process of visiting the children of u. From here, we check whether the parity of u matches. If it matches, we simply leave u. Otherwise, we leave u, come back to u, and leave it again, so now the parity will definitely match!
#include <iostream>
#include <algorithm>
#include <vector>
#include <cstdio>
using namespace std;
int N,M;
vector<vector<int> > adj;
int par[100005];
int vis[100005];
int ctr;
int root_count;
int root;
vector<int> st;
vector<int> tmp;
void dfs(int u){
vis[u] = 1;
++ctr;
bool isleaf = true;
int parity = 1;
st.push_back(u);
for(int i=0;i<adj[u].size();++i){
int v = adj[u][i];
if(vis[v])continue;
isleaf = false;
dfs(v);
st.push_back(u);
++parity;
if(!tmp.empty()){
st.push_back(tmp.back());
tmp.pop_back();
st.push_back(u);
++parity;
}
}
if(u==root)root_count = parity;
if(par[u]!=(parity%2))tmp.push_back(u);
}
int main(){
int u,v;
scanf("%d%d",&N,&M);
adj = vector<vector<int> > (N+3);
for(int i=0;i<M;++i){
scanf("%d%d",&u,&v);
adj[u].push_back(v);
adj[v].push_back(u);
}
for(int i=1;i<=N;++i){
scanf("%d",&par[i]);
}
for(int i=1;i<=N;++i){
if(par[i]==1){
root = i;
dfs(i);
break;
}
}
bool ok = true;
for(int i=1;i<=N;++i){
if(!vis[i]&&par[i])ok=false;
if(!ok)break;
}
if(ok){
if((root_count%2)!=par[root]){
if(!st.empty())st.pop_back();
else st.push_back(root);
}
printf("%d\n",(int)st.size());
for(int i=0;i<st.size();++i){
if(i!=0)printf(" ");
printf("%d",st[i]);
}
if(st.size()!=0)printf("\n");
} else {
printf("-1\n");
}
return 0;
} | 2018-11-17 21:36:33 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5964239239692688, "perplexity": 2152.5502515813823}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-47/segments/1542039743854.48/warc/CC-MAIN-20181117205946-20181117231946-00150.warc.gz"} |
https://physics.aps.org/articles/v7/63 | Viewpoint
# A New Phase of Solid Oxygen
Physics 7, 63
A large applied magnetic field can bring solid oxygen into a novel phase—a consequence of the strong spin-lattice coupling in the molecular crystal.
Molecular crystals, like sugar, ice, or solid chalcogens (the elements of group $16$ of the periodic table, such as oxygen) are made of molecules held together by van der Waals forces. As they crystallize, they form structures that depend on the characteristics of the intermolecular interactions. Among various simple molecules, solid molecular oxygen ( $O2$) is unique because it carries a magnetic moment with a spin quantum number $S=1$. This results in a complex relationship between the magnetic interaction and crystal structure, which has long attracted the attention of scientists—solid oxygen is regarded as a unique example of a spin-controlled system. In Physical Review Letters [1], a team led by Yasuhiro Matsuda at the University of Tokyo, Japan, has reported the discovery of a novel phase of solid $O2$ that can be reached by applying an extraordinarily strong magnetic field [ $120$ $193$ tesla (T)]. The experiments indicate this is the result of a first-order transition that is both a magnetic and structural transition: the antiferromagnetic phase collapses and the crystal symmetry changes. The finding adds a new dimension to the phase diagram of oxygen and is a key demonstration of how strongly spin and lattice are coupled in the solid.
Molecular crystals exhibit various kinds of interesting structures because of the delicate balance of intermolecular interactions. In the case of ice, the hydrogen bonds determine the low-density structure that is unique among molecular crystals. In dry ice—the solid form of carbon dioxide ( $CO2$)—an electrostatic quadrupole moment causes the characteristic cubic structure (also seen, e.g., in the $α$ phase of solid $N2$). The case of solid molecular oxygen is particularly interesting. Faraday discovered the magnetism of $O2$ in 1848, and since then, oxygen has been actively studied as a ubiquitous yet exotic molecular magnet. This magnetism plays an important role via the exchange interaction, leading to fascinating phenomenology in solid phases. At ambient pressure, three different phases ( $α$, $β$, and $γ$) appear with decreasing temperature. Such phases differ in crystal structure as well as in magnetic properties. The application of pressure induces even more phases: $δ$ [at $5.5$ gigapascal (GPa)], $ε$ ( $8$ GPa), and $ζ$ ( $96$ GPa). The latter is a metallic phase, which even becomes superconducting below $0.6$ kelvin (K). A seventh phase ( $η$) has been observed in a high-pressure ( $16$ $20$ GPa), high-temperature ( $500$ $1000$ K) range. But despite intense research, it is not yet very well established whether and how the magnetic interaction is essential for the molecular arrangement in the different phases of solid $O2$.
Why can magnetic properties influence structural properties in solid oxygen? First, the exchange interaction (as estimated from experiments) is comparable in strength to the van der Waals forces. Second, the exchange interaction between the magnetic moments of $O2$, including its sign, depends on the geometry of the molecular arrangement. Ab initio calculations have tackled the simpler case of a $O2$- $O2$ dimer [2]. They predict that the stable arrangement of the two $O2$ molecules depends on whether the magnetic moments align antiferromagnetically or ferromagnetically. Under normal conditions, an “H geometry” should occur [see Fig. 1(a)]: the two molecules are parallel, the exchange interaction is antiferromagnetic, and the singlet state is favored (that is, the two spins cancel each other, and the total spin is zero). The H geometry is indeed observed in the three phases of solid oxygen. But when the dimer is magnetized, two other geometries are stable: S (canted) and X (crossed) [Fig. 1(a)]. In both, the exchange interaction is ferromagnetic. This leads to the expectation of both magnetic and structural phase transitions resulting from the application of large magnetic fields.
Such theoretical predictions could be tested when, ten years ago, the $O2$- $O2$ dimer was successfully synthesized by using nanoporous coordination polymers [3]. X-ray diffraction measurements at low temperatures revealed that the H geometry, as in the molecular solid, is robust in the dimer system. However, the magnetic measurements could not be interpreted based on Heisenberg models and H geometry only. To explain the experimental findings, researchers invoked a scenario in which there are excited states of other geometries, e.g., the S or X type [4]. This scenario indicates that a molecular rearrangement may occur in a magnetic field. It was also found that the thermally excited states lead to deviations from the H geometry at higher temperatures. These combined results, obtained on dimers, led to the anticipation of a field-induced structural phase transition in solid $O2$.
Matsuda’s team explored the possibility of this kind of phase transition starting from the $α$ phase of solid $O2$, using state-of-the-art techniques for generating microsecond pulses of ultrahigh magnetic fields (of up to $193$ T). Working at low temperatures ( $4.2$ K), they directly measured the magnetization using a pickup coil. Because $α$ oxygen has an antiferromagnetic ground state, the magnetization should linearly increase with increasing magnetic fields. This is true at low magnetic fields. However, a distinct, sudden increase of the magnetization occurs at around $125$ T [see Fig. 1(b)]. This is the clear signature of a magnetic phase transformation. The magnetization curve is also found to have a significant hysteresis between the field-increasing and field-decreasing processes. Hence the phase transition is suggested to be a first-order transition, probably associated with a structural change.
The authors used optical spectroscopy to probe structural changes, measuring transmission changes at visible wavelengths (around $600$ nanometers) as a function of the applied field. The existence of a bimolecular absorption resonance in this wavelength region is well established—it causes the blue color in solid $O2$. The key effect allowing optical detection of structural changes is the change of light scattering at the domain boundaries in polycrystalline $α$ oxygen. $α$ oxygen is structurally anisotropic (monoclinic). The interface between differently oriented crystal domains, each with anisotropic refractive indices, generates strong scattering, thus making polycrystalline $α$ oxygen opaque for visible light. But if the domains suddenly became isotropic, such scattering would be reduced. What the authors found is that the transmitted light intensity considerably increased at fields where the magnetic transition takes place. The effect is dramatic: The crystal becomes nearly transparent at ultrahigh magnetic fields. Such field-induced transparency clearly demonstrates that the crystal symmetry changes from anisotropic to isotropic. A similar phenomenon has been previously observed in the $β$-to- $γ$ phase transition, driven by increasing temperature at zero field, in which the crystal structure transforms from the rhombohedral ( $β$) to cubic ( $γ$).
Magnetization measurements and magnetotransmission optical spectroscopy thus perfectly complement each other, providing compelling evidence of the novel phase of solid $O2$ in ultrahigh magnetic fields. Recalling the magnetic field-induced rearrangement of the $O2$- $O2$ dimer, the authors attribute the observed structural phase transition to the rearrangement of $O2$ molecules. Dimer results suggest the antiferromagnetic coupling could become unstable in the new molecular arrangement, and ferromagnetic exchange interaction might become favored. This makes the result a noteworthy discovery in the long history of solid $O2$ studies: the eighth phase of solid $O2$ is completely different from the known seven phases at zero field where the exchange interaction between $O2$ molecules is either paramagnetic or antiferromagnetic.
While optical spectroscopy clearly shows a structural transition, an outstanding question is the determination of the crystal structure of the novel phase. This is very challenging since the applied magnetic field is pulsed, with a duration of less than ten microseconds, which makes it difficult to probe the new structure with conventional, static diffraction measurements. In absence of reliable experiments, the puzzle may first be tackled by theoretical predictions of crystal structures. Finally, further studies at higher temperatures will be needed to gather a complete picture of the underlying physics that establishes the entire field-temperature phase diagram of solid oxygen.
## References
1. T. Nomura, Y. H. Matsuda, S. Takeyama, A. Matsuo, K. Kindo, J. L. Her, and T. C. Kobayashi, “Novel Phase of Solid Oxygen Induced by Ultrahigh Magnetic Fields,” Phys. Rev. Lett. 112, 247201 (2014)
2. B. Bussery and P. E. S. Wormer, “A van der Waals Intermolecular Potential for (O${}_{2}$)${}_{2}$,” J. Chem. Phys. 99, 1230 (1993)
3. R. Kitaura et al., “Formation of a One-Dimensional Array of Oxygen in a Microporous Metal-Organic Solid,” Science 298, 2358 (2002)
4. A. Hori et al., ”Spin-Dependent Molecular Orientation of O${}_{2}$–O${}_{2}$ Dimer Formed in the Nanoporous Coordination Polymer” J. Phys. Soc. Jpn. 82, 084703 (2013)
Susumu Kitagawa is the director of the Institute for Integrated Cell-Material Sciences, Kyoto University and professor of functional chemistry, faculty of Engineering, Kyoto University. His research background is in inorganic chemistry, focusing on coordination network materials, which are now known as porous coordination polymers (PCPs) or metal-organic frameworks (MOFs). The focus of his group is to design and synthesize functional porous materials for science and technology of storage, separation, and conversion of gas substances. See more at http://www.sbchem.kyoto-u.ac.jp/kitagawa-lab/index-e.html
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http://pcmsolver.readthedocs.io/en/latest/programmers/timer-class.html | Timer class¶
The Timer class enables timing of execution throughout the module. Timer support is enabled by passing -DENABLE_TIMER=ON to the setup.py script. Timing macros are available by inclusion of the Config.hpp header file.
The class is basically a wrapper around an ordered map of strings and cpu timers. To time a code snippet:
TIMER_ON("code-snippet");
// code-snippet
TIMER_OFF("code-snippet");
The timings are printed out to the pcmsolver.timer.dat by a call to the TIMER_DONE macro. This should obviously happen at the very end of the execution!
Defines
TIMER_ON(...)
PCMSolver, an API for the Polarizable Continuum Model Copyright (C) 2018 Roberto Di Remigio, Luca Frediani and collaborators.
This file is part of PCMSolver.
PCMSolver is free software: you can redistribute it and/or modify it under the terms of the GNU Lesser General Public License as published by the Free Software Foundation, either version 3 of the License, or (at your option) any later version.
PCMSolver is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more details.
You should have received a copy of the GNU Lesser General Public License along with PCMSolver. If not, see http://www.gnu.org/licenses/.
For information on the complete list of contributors to the PCMSolver API, see: http://pcmsolver.readthedocs.io/
TIMER_OFF(...)
TIMER_DONE(...) | 2018-01-20 08:45:54 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.28928038477897644, "perplexity": 1347.1696014023566}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-05/segments/1516084889542.47/warc/CC-MAIN-20180120083038-20180120103038-00444.warc.gz"} |
http://math.stackexchange.com/questions/250861/vector-product-proof | # Vector product proof
Prove that if $$a=b \times c$$
$$b=c \times a$$
$$c=a \times b$$ then $a \perp b$, $a \perp c$, $b \perp c$, and $|a|=|b|=|c|=1$
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What have you tried? Please don't just give us an order to do something for you. – Stefan Dec 4 '12 at 18:47
Also, $a=b=c=0$ contradicts the last statement. – copper.hat Dec 4 '12 at 18:47
$a=b \times c \perp b$ and the analogous statements follow simply from the fact that a vector product is orthogonal to its factors. Note that $|x \times y|=|x||y|sin(\angle (x,y))$ so $a \perp b \rightarrow |c|=|a||b|sin(90°)=|a||b|$. Analogously, $|b|=|a||c|$ and $|a|=|b||c|$. Multiplying these three equalities, you obtain $|a||b||c|=(|a||b||c|)^2$, so $|a||b||c|\in \{0,1\}$.
If $|a||b||c|=0$ then WLOG $|a|=0$, i. e. $a=0$, implying b=0 x c=0 and c=0 x b=0.
If $|a||b||c|=1$ then $|a|^2=|a|*(|b||c|)=|a||b||c|=1$, i. e. $|a|=1$ and analogously, $|b|=|c|=1$. | 2016-07-28 07:00:48 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.912020742893219, "perplexity": 439.9216036097588}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-30/segments/1469257828009.82/warc/CC-MAIN-20160723071028-00295-ip-10-185-27-174.ec2.internal.warc.gz"} |
http://superuser.com/questions/469347/ethernet-splitter/469381 | # Ethernet splitter
I have two computers side by side (one work and the other personal). Due to the location of the wireless connection, sometimes the signal is weak, so I normally access one of the computer via the ethernet, but my modem has only a single jack. Is there a splitter or something that will allow me to access both computers at same time without having to swap the ethernet from computer to computer
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I'm missing something here: You say that the modem has only one port but you also apparently have a wireless router. How is it attached? Doesn't the router have any ports? – Daniel R Hicks Sep 3 '12 at 13:36
There's two options here - get a router or switch and connect it to the modem - if your modem is also a router, you'd have to switch off DHCP on the router. You might also be able to use a hub, but those are nearly extinct these days.
You might also be able to use a windows PC as a router by setting up Internet connection sharing if your modem is a 'simple' modem with no routing capabilities. I am unsure if you can turn off DHCP on ICS tho.
Splitters are passive devices, and ethernet as we know it uses a star configuration, so such a device is impossible.
-
Strictly speaking, Ethernet uses a bus configuration, not a star. The wiring is configured in a star because modern Ethernet network always consist of a set of twisted pair connections with a hub or switch in the center. (In most home networks, the switch is built into a router.) In the bad old days, before twisted-pair Ethernet and cheap switches, a network often consisted of a single coaxial cable running past all systems on the network; most system would connect with a "tap", which included a spike driven into the cable. – Isaac Rabinovitch Sep 3 '12 at 3:11
Keep it simple: get a router and don't turn off DHCP. Just install the router, connecting its uplink (or port 1, most routers these days auto-detect which port is the upstream connection) port to the modem (you may need to power cycle your modem) and connecting your two computers, using separate cables, to separate jacks on the router. Easy peasy. – music2myear Sep 3 '12 at 3:12
For clarity, there is such a thing as ethernet spitters. We use them here on sites when we're low on ports. They allow 2 devices to use a single run of network cable. You need one splitter at each end and it uses 2 of the twisted pairs per port. Unfortunately some devices (printers, VOIP phones) can have issues with this - embedded LAN often needs to be set to run at half-duplex in such a configuration. But it's still better than wireless. – Beeblebrox Sep 3 '12 at 4:12
No, you don't have to switch off DHCP on a router that's connected to another router. Any decent router can be both a DHCP client and DHCP server. – Isaac Rabinovitch Sep 3 '12 at 7:41
Yes, a PC can serve as a router, but only if it has enough Ethernet ports. Unless you have the necessary hardware lying around, and don't mind the power costs of keeping the PC running all the time, it makes more sense to just buy a router. – Isaac Rabinovitch Sep 3 '12 at 7:43
Yes there is such a device, we call them RJ-45 splitters but they are also called RJ45 CAT 5 6 LAN Ethernet Splitter Connector Adapter. All three ends need to be female, the end with 1 female end will go to the cable that is connected to your modem/router, the end with 2 female ends go to each computers. Your done run one cable with splitter for 2 computers. They have this at Dollar Stores, eBay for $1.00, Radio Shack$10 I think you get the picture. Good luck
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That would allow the OP to physically connect all three. But just a physical splitter will not allow both work and personal computer to use the network at the same time. (Powering off one computer and then powering up the other computer would work). – Hennes Sep 3 '12 at 0:58
@Hennes -- You don't understand -- it breaks the 8-wire cable into two 4-wire cables. – Daniel R Hicks Sep 3 '12 at 1:03
That works for 10mbit and 100mbit connections if you use plugs at both ends. The OP's modem only has a single Ethernet plug. – Hennes Sep 3 '12 at 1:14
For sharing connections you want a router or switch, not a splitter. – music2myear Sep 3 '12 at 3:09
I think the thing you're looking for is called a network switch. This is a data-link (second) or higher layer device for combining Ethernet connections. Actually a lot more functionality than you need, but some layer 2 switches are so cheap (NewEgg has them for \$10) it doesn't matter.
There used to be simpler devices called network hubs that worked on the physical (first) layer. Switches got so cheap, they drove hubs off the market. Some people call switches hubs, but I'm a technical writer, and thus a semantic nitpicker.
There are ways to split Ethernet cables so that you don't need a hub or switch, but unless there's some big reason you can't install that extra box, splitting cables is an unnecessary hassle.
Here's why I'm not 100% sure I understand your question. It's not clear to me exactly what kind of device you're talking about when you refer to a "modem". Is the WAN interface configuration built into your "modem"? Or do both computers contain the configuration? If you're not sure, posting the make and model of this device would be helpful. If the "modem" does handle the WAN connection itself, than it's providing a network endpoint, and a switch or hub will work. Otherwise, you need to move a level up from switches and get a router. Since you're using physical Ethernet, the router doesn't have to be wireless, though you probably won't save any by buying a wired-only router for a two-computer network.
-
Assuming your Ethernet is connected via a RJ45 plug:
No. A simple splitter will not work. You can use a switch or a hub though.
(RJ45 mentioned because you can do what you want if you used old coax to connect. Feel free to google for 10base2_t, but this is very unlikely)
-
10B2! How quaint! – Isaac Rabinovitch Sep 10 '12 at 4:12
Aye. Truly ancient. But there still are devices alive which use it. Even if my last coax switch died. (And yes, I meant a switch, not a hub. Back in the days of yore it cost as much as a small car and it was quaint enough that I saved it from the trashcan). – Hennes Sep 10 '12 at 11:29
The typical ethernet cable has 8 wires. Most ethernet schemes only use 4. Thus you can use a "splitter" at each end to effectively squeeze 2 cables into 1. There are several varieties available.
(But note that some "enterprise" wiring used 4 or 6-wire cables, so this scheme won't work with those. Also, the scheme won't work with certain high-speed ethernet protocols that use more than 4 wires.)
The other option is a small hub, but this will not work with some routers that assume one computer per port.
Added: And people in the past have actually gotten away with "OR-tying" two Ethernet cables together, relying on Ethernet collision detection to handle conflicts. But this is not a very reliable approach, if it even works at all anymore.
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This is a horrible idea. Yes, at least in the past, you could use a splitter to accomplish this. I dont know if this holds true. However, the two PCs would not be able to communicate with each other, since the TX/RX are not switched. – Keltari Sep 3 '12 at 3:27
IIRC, Gigabit Ethernet requires all 8 wires to be available? – grawity Sep 3 '12 at 9:35
@Keltari -- Which is a bad idea? Splitting the cable is perfectly fine so long as the protocol uses no more than 4 wires. And the OR-tying trick I didn't recommend, just said it had been done. – Daniel R Hicks Sep 3 '12 at 13:32 | 2015-01-27 14:23:30 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4237745702266693, "perplexity": 2347.124478593323}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-06/segments/1422121981339.16/warc/CC-MAIN-20150124175301-00101-ip-10-180-212-252.ec2.internal.warc.gz"} |
https://jpt.spe.org/adaptive-drilling-application-uses-ai-enhance-bottom-drilling-performance | Share
Drilling automation
# Adaptive Drilling Application Uses AI To Enhance On-Bottom Drilling Performance
## An intelligent drilling optimization application performs as an adaptive autodriller. In the Marcellus Shale, ROP improved 61% and 39% and drilling performance, measured as hours on bottom, improved 25%.
Ever since the first commercial well was spudded, operators have looked for ways to drill wells faster without sacrificing safety or incurring huge costs. While saving time and money through efficient drilling is not a new concept, the more recent adoption of drilling optimization and automation services has certainly become one of the biggest drivers to achieving those goals.
As the current downturn has shown limited signs of recovery, it has continued to evolve in ways never imagined, and the effects are taking their toll in every facet of the oil and gas industry. While rigs and drilling equipment can be set aside to ride out the storm, what about the drilling teams who are working on the rigs and in remote operation centers? As these teams are being removed from the field, the expectation is that many of them won’t return for a myriad of reasons. So, what happens when that experience is lost?
The exodus of seasoned crews, otherwise known as the “great crew change,” has been discussed for several years, but recent conditions could expedite the process. Considering the recent shutdown of rigs and the loss of personnel, the question remains whether we will see a noticeable gap in knowledge and experience once crews return to the drilling rigs in full force.
The lack of individual skills can be offset over time with hands-on experience, but a drilling crew needs to operate at the highest level possible, preferably with few to no gaps in experience. To assist the drilling process, NOV’s M/D Totco division recently launched its KAIZEN intelligent drilling optimization application, which performs as an adaptive autodriller. The system features continuous learning capabilities, enabling it to provide proactive drilling dysfunction mitigation while maximizing rate of penetration (ROP) and optimizing mechanical specific energy. It also reduces human dependence in the drilling process, lowering the risk of slow or incorrect responses to drilling dysfunction. In turn, the system assesses wellbore conditions and drilling performance, then automatically applies appropriate parameters to mitigate those dysfunctions.
## Intelligent Drilling Optimizer
When faced with distinct interbedded formations, drillers often encounter drilling dysfunction due to varying formations, and optimal setpoints are required to identify and proactively mitigate dysfunction.
While drillers are inundated with large amounts of data, the system takes the human dependence away and employs artificial intelligence (AI) to continuously optimize the drilling process. Utilizing an array of machine-learning algorithms and a digital twin that is updated each second, the AI system builds a store of knowledge that the drilling application leverages to make more accurate and timely decisions. This automated parameter application approach enables the system to remove distractions from the driller so their focus can be on critical items such as keeping the crew safe and the well under control, while the system instantly responds to changing conditions and provides optimal weight on bit (WOB) and revolutions per minute (rev/min) setpoints.
The AI and machine-learning feature stores thousands of hours of processed drilling data. This capability allows the system to recommend surface parameters that deliver the best expected performance as well as select the correct dataset to mitigate changes detected in drilling dynamic behaviors.
Additionally, the system’s digital twin uses an advanced, physics-based model to analyze several key dysfunctions in real time by way of distributed stress modeling, torque and drag modeling, and critical rev/min calculations. The result is a system that is capable of providing guidance to the parameter search engine, identifying which parameters to avoid. Drillstring buckling, downhole vibration (torsional, axial, and lateral), and mud motor stalls can all be diagnosed, and thus, mitigated in real time.
The system’s optimization functions can be run in either advisory or control mode. The advisory mode sends recommended rev/min and WOB setpoints for the driller to implement, while control mode sends those same setpoints directly to the autodriller.
Advisory mode is typically run if a rig’s control system is not fully compatible with the control mode. When a rig has a control system that is compatible with the KAIZEN command requests, control mode is activated, and the system consistently achieves a higher level of performance by continuously and automatically adjusting the setpoints.
The KAIZEN system has been successfully integrated into multiple control systems, including NOV’s NOVOS reflexive drilling system. The application is currently compatible in closed-loop mode with approximately 50% of the active North American rig fleet.
The drilling system’s installation comprises a minor update to the rig control layer to accept the system’s commands, along with the physical installation of a KAIZEN system box. The rig must be running NOV’s RigSense electronic drilling recorder, and the system box is simply plugged into both the rig’s control network and the RigSense system. The system is then accessible on the RigSense screen and operated through the control system interface.
## Case History: Marcellus Shale
The use of KAIZEN control mode on the NOVOS control system has recently shown immediate improvements in the field.
A drilling contractor operating in the Marcellus Shale sought a solution to complete each hole section in a single-bit run while improving the ROP and reducing drilling time with less damage to the bit. The target formation showed shale with interbedded limestone as well as concentrations of iron pyrite and siderite, making for a challenging well.
The intelligent drilling optimizer applied its continuous learning capabilities, successfully demonstrating the ability to optimize the drilling program by way of dysfunction mitigation and parameter optimization. It was noted that the system handled formation changes exceptionally well and exhibited creative solutions to solve downhole vibration, resulting in smooth drilling. This allowed the system to exploit this parameter map and drill at the limit of efficiency, and the system performed those functions consistently.
The use of the drilling system’s control mode on the NOVOS system showed immediate improvements. All three wells that used the system were compared against the customer-provided benchmark well; the system collectively saved the customer 38.6 drilling hours. The cumulative hourly savings translated to an average of $37,518 per well for a total savings of$112,554 over the three wells, based on a \$70,000/day spread rate.
## Conclusion
The need for greater efficiency through optimized drilling systems has pushed service companies into new and exciting areas of product development, with features like automation and AI leading the way. As the KAIZEN system’s performance has shown, the application of automated control systems delivers cumulative operational benefits that continue to increase independent of the crews’ experience levels. As the industry looks to optimize processes in all areas of operations, intelligent systems will become the accepted, pragmatic approach to achieving safer and more efficient performance at the wellsite.
Christopher Jeffery is the product line director for NOV’s M/D Totco’s Digital Wellsite portfolio. He has worked at NOV for 12 years and has a background in drilling optimization. Jeffery currently works in the Houston headquarters.
Andrew Creegan serves as the product line manager for NOV’s M/D Totco’s Digital Wellsite portfolio. He has worked at NOV for 7 years and has a background in performance drilling applications. Creegan currently works in the Houston headquarters. | 2021-04-11 21:06:19 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.1956448256969452, "perplexity": 4771.113737877553}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-17/segments/1618038065492.15/warc/CC-MAIN-20210411204008-20210411234008-00412.warc.gz"} |
https://www.researchgate.net/publication/51931506_Identifying_Design_Requirements_for_Wireless_Routing_Link_Metrics | Article
# Identifying Design Requirements for Wireless Routing Link Metrics
Authors:
To read the full-text of this research, you can request a copy directly from the authors.
## Abstract
In this paper, we identify and analyze the requirements to design a new routing link metric for wireless multihop networks. Considering these requirements, when a link metric is proposed, then both the design and implementation of the link metric with a routing protocol become easy. Secondly, the underlying network issues can easily be tackled. Thirdly, an appreciable performance of the network is guaranteed. Along with the existing implementation of three link metrics Expected Transmission Count (ETX), Minimum Delay (MD), and Minimum Loss (ML), we implement inverse ETX; invETX with Optimized Link State Routing (OLSR) using NS-2.34. The simulation results show that how the computational burden of a metric degrades the performance of the respective protocol and how a metric has to trade-off between different performance parameters.
## No full-text available
... For example, a metric may/can produce computational overhead and it may also pay cost in terms of other performance metric(s) like achieving minimized end-to-end delay at the cost lower throughput or higher routing overhead. Thus, we analyze/investigate almost all possible design requirements given in [7]. In this paper, we present a mathematical framework for a proposed quality link metric; Bandwidth adjusted Inverse ETX (BIETX). ...
... d exp firstly detects and then handles asymmetry by incorporating loss ratios in forward and reverse directions. Computation of d exp , by taking the product of delivery ratios same as in [7] and [12] leads to avoidance of computational overhead that is generated due to ETX which firstly calculates inverse of all expected delivery ratios and then adds them up. There are two techniques to measure L cap i.e., packet-pair with different size and back-to-back probes with equal size. ...
... From [7], we conclude that routing load is an important issue in SWMhNs and this issue becomes critical whenever the network load increases with increase in either the number of packets or the number of nodes. In OLSR, shortest interval has been used for exchanging topological information in comparison to Destination Sequence Distance Vector (DSDV) and Fish-eye State Routing (FSR) [14] i.e., IntraScopeInterval in FSR and 'full-dump-period' in DSDV are equal to 15s, and, T C IN T ERV AL = 5s in OLSR, resulting in the generation of more routing overhead. ...
Conference Paper
In this work, we propose a novel quality link metric; Bandwidth adjusted Inverse ETX (BIETX) for Static Wireless Multi-hop Networks (SWMhNs). The proposed metric considers two path selection parameters into account i.e., packet delivery ratio and link capacity. For computing packet delivery ratios in BIETX, the mechanism of Expected Transmission Count (ETX) is adopted. On the other hand, we take two methods of computing link capacity in BIETX. These methods are based upon the size of pair probes; equal size and different size. We also enhance Optimized Link State Routing (OLSR) protocol while using BIETX. A comparative analysis of proposed metric with equal size and different size pair probe; BIETX-1 and BIETX-2, with two existing quality metrics (ETX and Expected Transmission Time (ETT)) in SWMhNs is also a part of this work. From simulation results, we conclude that BIETX-2 outperforms rest of the metrics because of low routing load in ad-hoc probes, and low routing latencies due to enhancements of routing update frequencies and window size in OLSR.
... Several QLMs have been proposed, like, Expected Transmission Count (ETX)[2], Expected Transmission Time (ETT) [3], Interference and Bandwidth Adjusted ETX (IBETX) [4], Expected Link Performance (ELP) [5], Minimum Loss (ML) [6], Minimum Delay (MD)[7] and Inverse ETX (InvETX) [8]. The metrics, ETX, ML, MD and InvETX have already been implemented [8] with a proactive routing protocol, Optimized Link State Routing (OLSR) [9] using Link State routing technique . ...
... Several QLMs have been proposed, like, Expected Transmission Count (ETX)[2], Expected Transmission Time (ETT) [3], Interference and Bandwidth Adjusted ETX (IBETX) [4], Expected Link Performance (ELP) [5], Minimum Loss (ML) [6], Minimum Delay (MD)[7] and Inverse ETX (InvETX) [8]. The metrics, ETX, ML, MD and InvETX have already been implemented [8] with a proactive routing protocol, Optimized Link State Routing (OLSR) [9] using Link State routing technique . While, ETX, IBETX, and ELP are implemented with Destination Sequenced Distance Vector (DSDV) [10] based on distance vector routing algorithm. ...
... Previouse implementation of QLMs in routing protocols have not considered routing load for performance measurements. We, in our previous work [8] have considered routing load while analyzing the performance of OLSR which is a link state based proactive routing protocol. Now, in the same way, we are evaluating the performance of those link metrics along with ETT in this paper. ...
Article
Full-text available
In this paper, we compare and analyze performance of five quality link metrics forWireless Multi-hop Networks (WMhNs). The metrics are based on loss probability measurements; ETX, ETT, InvETX, ML and MD, in a distance vector routing protocol; DSDV. Among these selected metrics, we have implemented ML, MD, InvETX and ETT in DSDV which are previously implemented with different protocols; ML, MD, InvETX are implemented with OLSR, while ETT is implemented in MR-LQSR. For our comparison, we have selected Throughput, Normalized Routing Load (NRL) and End-to-End Delay (E2ED) as performance parameters. Finally, we deduce that InvETX due to low computational burden and link asymmetry measurement outperforms among all metrics.
... Several QLMs have been proposed, like, Expected Transmission Count (ETX)[2], Expected Transmission Time (ETT) [3], Interference and Bandwidth Adjusted ETX (IBETX) [4], Expected Link Performance (ELP) [5], Minimum Loss (ML) [6], Minimum Delay (MD)[7] and Inverse ETX (InvETX) [8]. The metrics, ETX, ML, MD and InvETX have already been implemented [8] with a proactive routing protocol, Optimized Link State Routing (OLSR) [9] using Link State routing technique . ...
... Several QLMs have been proposed, like, Expected Transmission Count (ETX)[2], Expected Transmission Time (ETT) [3], Interference and Bandwidth Adjusted ETX (IBETX) [4], Expected Link Performance (ELP) [5], Minimum Loss (ML) [6], Minimum Delay (MD)[7] and Inverse ETX (InvETX) [8]. The metrics, ETX, ML, MD and InvETX have already been implemented [8] with a proactive routing protocol, Optimized Link State Routing (OLSR) [9] using Link State routing technique . While, ETX, IBETX, and ELP are implemented with Destination Sequenced Distance Vector (DSDV) [10] based on distance vector routing algorithm. ...
... Previouse implementation of QLMs in routing protocols have not considered routing load for performance measurements. We, in our previous work [8] have considered routing load while analyzing the performance of OLSR which is a link state based proactive routing protocol. Now, in the same way, we are evaluating the performance of those link metrics along with ETT in this paper. ...
Data
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... An efficiently designed QLM better helps a routing protocol to achieve appreciable performance by dealing with these issues. In our previous work[1], design requirements of QLM are discussed in detail. Moreover, a new QLM; InvETX, is also compared with Expected Transmission Count (ETX)[2], Minimum Loss (ML) and Minimum Delay (MD)[4]in Optimized Link State Routing (OLSR)[5]protocol. ...
... For example, a routing protocol achieves higher throughput at the cost of end-to-end delay or routing overhead. Therefore, we analyze possible design requirements in[1]. Further, in our previous work, we implement three existing link metrics; ETX, MD,and ML, and one newly proposed metric; InvETX OLSR using NS-2.34. ...
... As a result, InvET X achieves higher throughputs than M L and ET X. Similarly, M L performs better than ET X. From[1], we analyze that routing load is a critical issue in SWMhNs when network load increases either with increase in number of nodes or with increase in number of packets. As, OLSR uses the shortest interval for exchanging topological information as compared to DSDV, i.e., 'full-dump-period' in DSDV, whereas, in OLSR T C IN T ERV AL = 5s, therefore, it causes more routing overhead. ...
Article
In this paper, we propose a new Quality Link Metric (QLM), Inverse Expected Transmission Count (InvETX)'' in Optimized Link State Routing (OLSR) protocol. Then we compare performance of three existing QLMs which are based on loss probability measurements; Expected Transmission Count (ETX), Minimum Delay (MD), Minimum Loss (ML) in Static Wireless Multi-hop Networks (SWMhNs). A novel contribution of this paper is enhancement in conventional OLSR to achieve high efficiency in terms of optimized routing load and routing latency. For this purpose, first we present a mathematical framework, and then to validate this frame work, we select three performance parameters to simulate default and enhanced versions of OLSR. Three chosen performance parameters are; throughput, Normalized Routing Load and End-to-End Delay. From simulation results, we conclude that adjusting the frequencies of topological information exchange results in high efficiency.
... This issue is especially challenging as these networks are built to work in specific scenarios. For example, a monitoring network can require a reasonable level of Packet Delivery Ratio (PDR) [8,9]. On the other hand, when the goal is to enable a VoIP (Voice over Internet Protocol) content, the network needs to keep under control the Endto-End Delay (E2ED) [8,9]. ...
... For example, a monitoring network can require a reasonable level of Packet Delivery Ratio (PDR) [8,9]. On the other hand, when the goal is to enable a VoIP (Voice over Internet Protocol) content, the network needs to keep under control the Endto-End Delay (E2ED) [8,9]. Therefore, distinct applications can demand different Quality of Service (QoS) guarantees [6,[10][11][12]. ...
... In this light, the routing protocols should also consider the different applications can have conflicting quality requirements. As a result, future routing mechanisms must support two or more QoS requirements and take into account the trade-off between them, since state-of-the-art protocols do not have these features natively [9,13]. ...
Article
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Ad hoc wireless networks have aroused much interest of the scientific community in the last two decades. The provision of Quality of Service (QoS) is a prominent challenge in this research field, since these networks are prone to suffer from instabilities related to wireless medium and mobility. Depending on application, the protocol needs to consider two or more QoS criteria when solving the routing problem. In this context, this work proposes a multicriteria and adaptive framework for proactive routing in order to generate promising compromise solutions by considering critical network quality indicators. Two new methods are proposed—one based on weighted sum method and another based on compromise method ($$\varepsilon$$-constraint)—and compared with the standard weighted sum method. Aiming to map a single final solution, a utility function is proposed to support the definition of the parameters (weights and constraints) of each method. The results show the framework, jointly with the proposed methods, were efficient in promoting significant improvements in the quality indicators investigated in static and mobile scenarios.
... An efficiently designed QLM better helps a routing protocol to achieve appreciable performance by dealing with these issues. In our previous work [1], design requirements of QLM are discussed in detail. Moreover, a new QLM, Inverse Expected Transmission Count (InvETX), is also compared with Expected Transmission Count (ETX) [2], Minimum Loss (ML) [3], and Minimum Delay (MD) [4] in Optimized Link State Routing (OLSR) [5] protocol. ...
... achieving high packet delivery ratio on the cost of increased end-to-end delay). Therefore, we analyze almost all possible design requirements in [1]. Further, in our previous work, we implement three existing link metrics, ETX, MD,and ML, and one newly proposed metric, InvETX OLSR, using NS-2.34. ...
Data
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In this paper, we propose a new Quality Link Metric (QLM), “Inverse Expected Transmission Count (InvETX),” in Optimized Link State Routing (OLSR) protocol. Then, we compare performance of three existing QLMs which are based on loss probability measurements: Expected Transmission Count (ETX), Minimum Delay (MD), and Minimum Loss (ML) in Static Wireless Multihop Networks (SWMhNs). A novel contribution of this paper is enhancement in conventional OLSR to achieve high efficiency in terms of optimized routing load and routing latency. For this purpose, first we present a mathematical framework, and then to validate this frame work, we select three performance parameters to simulate default and enhanced versions of OLSR. The three chosen performance parameters are throughput, Normalized Routing Load, and End-to-End Delay. From the simulation results, we conclude that adjusting the frequencies of topological information exchange results in high efficiency.
... Besides the evaluating the performance of DSDV, OLSR and DYMO we also made some modifications to these routing protocols and observed their performance at the end we came up with the result that with minor. In future, we are interested to apply the same analysis on quality link metrics proposed in9101112 and at MAC layer as [13, 14]. ...
Article
In this paper, we present path loss model for VANETs and simulate three routing protocols; Destination Sequenced Distance Vector (DSDV), Optimized Link State Routing (OLSR) and Dynamic MANET On-demand (DYMO) to evaluate and compare their performance using NS-2. The main contribution of this work is enhancement of existing techniques to achieve high efficiency of the underlying networks. After extensive simulations in NS-2, we conclude that DSDV best performs with 802.11p while DYMO gives outstanding performance with 802.11.
... On the other hand in MOD DSR due to reduction in the size of route. In future work, we are interested to implement Expected Transmission Count (ETX) link metric with mathematical modeling, as demonstrated in111213. ...
Article
In this paper, a framework is presented for node distribution with respect to density, network connectivity and communication time. According to modeled framework we evaluate and compare the performance of three routing protocols; Ad-hoc On-demand Distance Vector (AODV), Dynamic Source Routing (DSR) and Fisheye State Routing (FSR) in MANETs and VANETs using two Mac-layer protocols; 802.11 and 802.11p. We have further modified these protocols by changing their routing information exchange intervals; MOD AODV, MOD DSR and MOD FSR. A comprehensive simulation work is performed in NS-2 for the comparison of these routing protocols for varying mobilities and scalabilities of nodes. To evaluate their efficiency; throughput, End-to-End Delay (E2ED) and Normalized Routing Load (NRL) of these protocols are taken into account as performance parameters. After extensive simulations, we observe that AODV outperforms both with MANETs and VANETs.
... In future, we will implement different performance metrics of AM-DisCNT, as authors have done in [17], [18], [19] and [20]. ...
Article
The nodes in wireless sensor networks (WSNs) contain limited energy resources, which are needed to transmit data to base station (BS). Routing protocols are designed to reduce the energy consumption. Clustering algorithms are best in this aspect. Such clustering algorithms increase the stability and lifetime of the network. However, every routing protocol is not suitable for heterogeneous environments. AM-DisCNT is proposed and evaluated as a new energy efficient protocol for wireless sensor networks. AM-DisCNT uses circular deployment for even consumption of energy in entire wireless sensor network. Cluster-head selection is on the basis of energy. Highest energy node becomes CH for that round. Energy is again compared in the next round to check the highest energy node of that round. The simulation results show that AM-DisCNT performs better than the existing heterogeneous protocols on the basis of network lifetime, throughput and stability of the system.
... Future work focuses on estimating the delay in propagating data from body sensors to the destination node in DARE protocol and also to investigate mobility in patients body. Authors in [20][21][22][23], work on routing metrics based on ETX (Expected Transmission Count) which, shows better performance than minimum hop count metric, under the availability of link. In view of this, the plan focus to work on routing link metrics as well. ...
Article
In recent years, interests in the applications of Wireless Body Area Sensor Network (WBASN) is noticeably developed. WBASN is playing a significant role to get the real time and precise data with reduced level of energy consumption. It comprises of tiny, lightweight and energy restricted sensors, placed in/on the human body, to monitor any ambiguity in body organs and measure various biomedical parameters. In this study, a protocol named Distance Aware Relaying Energy-efficient (DARE) to monitor patients in multi-hop Body Area Sensor Networks (BASNs) is proposed. The protocol operates by investigating the ward of a hospital comprising of eight patients, under different topologies by positioning the sink at different locations or making it static or mobile. Seven sensors are attached to each patient, measuring different parameters of Electrocardiogram (ECG), pulse rate, heart rate, temperature level, glucose level, toxins level and motion. To reduce the energy consumption, these sensors communicate with the sink via an on-body relay, affixed on the chest of each patient. The body relay possesses higher energy resources as compared to the body sensors as, they perform aggregation and relaying of data to the sink node. A comparison is also conducted conducted with another protocol of BAN named, Mobility-supporting Adaptive Threshold-based Thermal-aware Energy-efficient Multi-hop ProTocol (M-ATTEMPT). The simulation results show that, the proposed protocol achieves increased network lifetime and efficiently reduces the energy consumption, in relative to M-ATTEMPT protocol.
... Because, a link metric provides all available end-to-end paths and the best path information to the respective protocol. So, in future, we are interested to develop a new link metric, like [21] and [22]. ...
Article
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This paper evaluates and compares the performance of two routing protocols, one is reactive, Dynamic MANET On-Demand (DYMO) and other is proactive, Optimized Link State Routing (OLSR) in Mobile Ad-hoc Networks (MANETs) and Vehicular Ad-hoc Networks (VANETs). Performance of these protocols is analyzed using three performance metrics; Packet Delivery Ratio, Normalized Routing Overhead and End-to-End Delay against varying scalabilities of nodes. We perform these simulations with NS-2 using TwoRayGround propagation model. The SUMO simulator is used to generate a random mobility pattern for VANETs. From the extensive simulations, we observe that DYMO performs better than OLSR for both VANETs and MANETs at the cost of delay. Moreover, DYMO performs better in VANETs as compared to MANETs.
... In future, Routing Link Matrices can also be applied on this proposed technique. Routing can be done by adapting many different approaches as done in [14], [15] and [16]. Application of Routing Link Matrices on the proposed scheme can be useful in achieving efficient consumption of energy in the network. ...
Article
In this paper, we propose Regional Energy Efficient Cluster Heads based on Maximum Energy (REECH-ME) Routing Protocol for Wireless Sensor Networks (WSNs) . The main purpose of this protocol is to improve the network lifetime and particularly the stability period of the network. In REECH-ME, the node with the maximum energy in a region becomes Cluster Head (CH) of that region for that particular round and the number of the cluster heads in each round remains the same. Our technique outperforms LEACH which uses probabilistic approach for the selection of CHs. We also implement the Uniform Random Distribution Model to find the packet drop to make this protocol more practical. We also calculate the confidence interval of all our results which helps us to visualize the possible deviation of our graphs from the mean value.
... In future, Routing Link Matrices can also be applied on this proposed technique. Routing can be done by adapting many different approaches as done in[14],[15]and[16]. Application of Routing Link Matrices on the proposed scheme can be useful in achieving efficient consumption of energy in the network. ...
Article
Full-text available
In this paper, we propose Regional Energy Efficient Cluster Heads based on Maximum Energy (REECH-ME) Routing Protocol for Wireless Sensor Networks (WSNs). The main purpose of this protocol is to improve the network lifetime and particularly the stability period of the network. In REECH-ME, the node with the maximum energy in a region becomes Cluster Head (CH) of that region for that particular round and the number of the cluster heads in each round remains the same. Our technique outperforms LEACH [1] which uses probabilistic approach for the selection of CHs. We also implement the Uniform Random Distribution Model to find the packet drop to make this protocol more practical. We also calculate the confidence interval of all our results which helps us to visualize the possible deviation of our graphs from the mean value.
... In this paper, the scenario we have presented is through the motivation of [24] and [25]. In [26], they have done evaluation of protocols through radio propagation model Nakagami which is well suited for all these models. ...
Article
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In this paper, a novel framework is presented through link and path duration for link availability of paths. Further, we evaluate and analyze our work by varying the number of nodes, pause time and speed in VANETs. We select three routing protocols namely Ad-hoc On-demand Distance Vector (AODV), Dynamic Source Routing (DSR) and Fish-eye State Routing (FSR). Performance of these protocols is analyzed using Packet Delivery Ratio (PDR), Normalized Routing Overhead (NRO), End-to-End Delay (E2ED), Average Link Duration (ALD) and Average Path Duration (APD) against varying scalability, pause time and speed as performance metrices. We perform these simulations with NS-2 implementing Nakagami radio propagation model. The SUMO simulator is used to generate a random mobility pattern for VANETs. To find link duration and path duration we also use MATLAB. From the extensive simulations, we observe that AODV and DSR outperform better among all three routing protocols.
... Hence, THE-FAME gives better results in both energy and delay profiles as compared to multi-hop routing scheme. In future work, we will implement Expected Transmission Count (ETX) link metrics as demonstrated in [21] [22] [23] [24]. ...
Article
Wireless Body Area Sensor Network (WBASN) is a technology employed mainly for patient health monitoring. New research is being done to take the technology to the next level i.e. player's fatigue monitoring in sports. Muscle fatigue is the main cause of player's performance degradation. This type of fatigue can be measured by sensing the accumulation of lactic acid in muscles. Excess of lactic acid makes muscles feel lethargic. Keeping this in mind we propose a protocol \underline{TH}reshold based \underline{E}nergy-efficient \underline{FA}tigue \underline{ME}asurement (THE-FAME) for soccer players using WBASN. In THE-FAME protocol, a composite parameter has been used that consists of a threshold parameter for lactic acid accumulation and a parameter for measuring distance covered by a particular player. When any parameters's value in this composite parameter shows an increase beyond threshold, the players is declared to be in a fatigue state. The size of battery and sensor should be very small for the sake of players' best performance. These sensor nodes, implanted inside player's body, are made energy efficient by using multiple sinks instead of a single sink. Matlab simulation results show the effectiveness of THE-FAME.
... Giving measurable QoS ensures a viable data transfer capacity. Similarly, on observing the patterns on how the Internet has transformed people lives by trading various types of data among countless customers, WSNs may sooner rather than later be similarly emerge to be critical players by providing data about the physical wonders of intrigue and eventually having the option to recognise and control them to develop increasingly precise models of the physical world [8][9][10]. This is due to the fact that WSNs are completely different from traditional systems in this regard. ...
Article
Full-text available
Quality of Service (QoS) in Wireless Sensor Networks (WSN) are contemplated as one on the major attributes in evaluating the overall efficiency of them. Some of the qualities of WSNs include incredibly asset compelled sensors, irregular arrangement of sensors in the scene of deployment, novel information driven correspondence conventions that presents remarkable challenges in the improvement of Quality of Service support in Wireless Sensor Networks. The appropriation of WSN by applications require complex tasks that extends from human services to mechanical checking that are necessary for a wide range of day-to-day and remote applications. WSN has increased a lot of consideration in the present exploration for supporting a wide assortment of utilizations including the interactive media applications. Interactive media applications that are proposed are viewed as delay-sensitive and time-critical applications and require enough vitality and correspondence assets. The proposed QoS-dependent and varied clustered routing (QoS–VCR) algorithm preserves the vitality in the system.
... Our simulation results shows that proposed routing scheme enhance the network stability time and packet delivered to sink. Path loss is also investigated in this protocol and in future work, we will implement Expected Transmission Count (ETX) link metrics as demonstrated in [22] [23] [24]. ...
Article
In this work, we propose a reliable, power efficient and high throughput routing protocol for Wireless Body Area Networks (WBANs). We use multi-hop topology to achieve minimum energy consumption and longer network lifetime. We propose a cost function to select parent node or forwarder. Proposed cost function selects a parent node which has high residual energy and minimum distance to sink. Residual energy parameter balances the energy consumption among the sensor nodes while distance parameter ensures successful packet delivery to sink. Simulation results show that our proposed protocol maximize the network stability period and nodes stay alive for longer period. Longer stability period contributes high packet delivery to sink which is major interest for continuous patient monitoring.
... These metrics trade-off between different performance parameters, the computational burden of some metrics also degrades the performance of the respective protocol [9]. Considering that the functionality of SG is dependent on the ability of different applications meeting certain performance requirements, proposing multiple metric implemented within the existing routing protocols can guarantee the QoS of the variety of traffic in SG AMI network. ...
Conference Paper
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Routing in Neighbourhood Area Network (NAN) for Smart Grid's Advanced Metering Infrastructure (AMI) raises the need for Quality of Service (QoS)-Aware routing. This is due to the expanded list of applications that will result in the transmission of different types of traffic between NAN devices (i.e smart meters). In wireless mesh network (WMN) routing, a combination of multiple link metrics, though complex, has been identified as a possible solution for QoS routing. These complexities (i.e Np complete problem) can be resolved through the use of Analytical Hierarchy Process (AHP) algorithm and pruning techniques. With the assumption that smart meters transmit IP packets of different sizes at different interval to represent AMI traffic, a case study of the performance of three Optimised Link State Routing (OLSR) link metrics is carried out on a grid topology NAN based WMN in ns-2 network simulator. The best two performing metric were used to show the possibility of combining multiple metrics with OLSR through the AHP algorithm to fulfill the QoS routing requirements of targeted AMI application traffic in NANs.
... Koksal et al. [5] presented a modified ETX metric, which combined the average and the variability of the error probability to optimize the decision results. Javaid et al. [6] presented a comprehensive study on the design requirements for routing link metrics and an inverse ETX (invETX) link metric for wireless multi-hop networks. In Boushaba et al. [7], considered the packet loss, intraflow and interflow interference, and load at gateways to select the best paths to reach the selected gateways and present a novel source-based routing (SBR) metric method. ...
Article
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The routing protocol is one of the most important aspects of the wireless sensor network, determining network connectivity, delay, energy balancing, reliability and other factors. Furthermore, a minimum hop-count does not mean minimum delay and energy consumption. To overcome the routing protocol’s shortcomings, we proposed an energy-efficient expected transmission count routing decision strategy (E³TX) for wireless sensor networks. E³TX makes use of two physical parameters, received signal strength indicator (RSSI) and battery voltage, to obtain the final decision via our proposed decision strategy. In our strategy, the received signal strength indicator is used to predict the future packet reception rate (PRR), and the battery voltage is used to estimate the residual energy of network nodes to balance their load. In order to estimate the packet reception rate via the received signal strength indicator with greater accuracy, we performed multiple experiments to build the relationship model between RSSI and PRR. In this article, we use NS-2.35 to evaluate and compare the performance of E³TX with AODV, AOMDV and BIETX. Our simulation results show that our proposed E³TX performs well when compared to the previous studies, not only in terms of energy consumption, but also in reliable data transmission and end-to-end delay.
... On the other hand in MOD DSR due to reduction in the size of route cache improves overall performance in high speeds. In future, we are interested to apply the same analysis on quality link metrics proposed in101112 and at MAC layer as [13, 14]. a. MANET's NRL vs Scalibility b. ...
Article
This paper presents a framework for node distribution with respect to density, network connectivity and communication time. Using NS2, we evaluate and compare performance of three routing protocols; Ad-hoc On-demand Distance Vector (AODV), Dynamic Source Routing (DSR) and Fisheye State Routing (FSR) both in MANETs (IEEE 802.11) and VANETs (IEEE 802.11p). We further enhanced these protocols by changing their routing information exchange intervals; MOD AODV, MOD DSR and MOD FSR. A comprehensive simulation work is performed for the comparison of these routing protocols for varying motilities and scalabilities of nodes. As a result, we can say that AODV outperforms DSR and FSR both in MANETs and VANETs.
... where En is the initial energy of any of the four energy levels, r is the node at a specific energy level, ET X p is the expected transmission count [42] of a path P , InvET X p is the inverse expected transmission count [43], and MLp is the minimum loss [44]. The P metric values for the hybrid, high, medium, and low energy level nodes are given by Eqs. 19, 20, 21, and 22, respectively. ...
Article
Wireless sensor networks (WSNs) have gained much attention in today’s research domain for supporting a wide variety of applications including the multimedia applications. Multimedia applications that are regarded as the quality-ofservice (QoS)-aware, delay sensitive, and bandwidth hungry applications, require enough energy and communication resources. WSNs being the energy-scarce network have now been designed in such a way that they can support these delay-sensitive and time-critical applications. In this paper, we propose an energyefficient routing protocol for heterogeneous WSNs to support the delay sensitive, bandwidth hungry, time-critical, and QoSaware applications. The proposed QoS-aware and heterogeneously clustered routing (QHCR) protocol not only conserves the energy in the network, but also provides the dedicated paths for the real-time and delay sensitive applications. The inclusion of different energy-levels for the heterogeneous WSNs also provide the stability in the networks while minimizing the delay for the delay-sensitive applications. Extensive simulations have been performed to validate the effectiveness of our proposed scheme. Our proposed routing scheme outperforms other state-of-the-art schemes in terms of the delay performances.
... Because, a link metric provides all available end-to-end paths and the best path information to the respective protocol. So, in future, we are interested to develop a new link metric, like [17] and [18]. ...
Article
Full-text available
Mobile Ad-hoc NETworks (MANETs) comprise on wireless mobile nodes that are communicating with each other without any infrastructure. Vehicular Ad-hoc NETwork (VANET) is a special type of MANETs in which vehicles with high mobility need to communicate with each other. In this paper, we present a novel framework for link availability of paths for static as well as dynamic networks. Moreover, we evaluate our frame work for routing protocols performance with different number of nodes in MANETs and in VANETs. We select three routing protocols namely Ad-hoc On-demand Distance Vector (AODV), Fish-eye State Routing (FSR) and Optimized Link State Routing (OLSR). Furthermore, we have also modified default parameters of selected protocols to check their efficiencies. Performance of these protocols is analyzed using three performance metrics; Packet Delivery Ratio (PDR), Normalized Routing Overhead (NRO) and End-to-End Delay (E2ED) against varying scalabilities of nodes. We perform these simulations with NS-2 using TwoRayGround propagation model. The SUMO simulator is used to generate a random mobility pattern for VANETs. From the extensive simulations, we observe that AODV outperforms among all three protocols.
... Performance of the selected protocols are then analysed and compared using the proposed model. In [15], a new routing link metric is designed, and in [16], a new quality link metric called inverse expected transmission count (InvETX) is proposed. The main contribution of [16] is improvement of the optimized link state routing (OLSR) protocol in terms of optimized routing load and routing latency. ...
Article
... Because, a link metric provides all available end-to-end paths and the best path information to the respective protocol. So, in future, we are interested to develop a new link metric, like [41] and [42]. ...
Thesis
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Mobile Ad-hoc NETworks (MANETs) are comprised of wireless mobile nodes that are communicating with each other without any infrastructure. Vehicular Ad-hoc NETwork (VANET) is a special type of MANETs in which vehicles with high mobility need to communicate with each other. In our project, a framework for link availability for static as well as dynamic network and also experimental parameters in which Packet Delivery Ratio (PDR), effect of link duration over End-to-End Delay (E2ED) and Normalized Routing Overhead (NRO) in terms of control packets is analyzed and modeled for MANETs and VANETs. Moreover, this project also contributes the performance comparison of three reactive routing potocols; Ad-hoc On-Demand Distance Vector (AODV), DYnamic Source Routing (DSR), DYnamic MANET On-Demand (DYMO) and three proactive protocols; Destination Sequenced Distance Vector (DSDV), Fish-eye State Routing (FSR) and Optimized Link State Routing (OLSR). A novel contribution of this work is enhancement of efficiency of these protocols except DSDV. Three performance parameters; PDR, E2ED and NRO with varying scalabilities are measured to analyze performance of the selected protocols both with default and enhanced version. From extensive simulations, it is observed that DSR outperforms both in MANETs and in VANETs at the cost of delay. Moreover, DSR performs better in VANETs as compared to MANETs. The NS-2 is used for simulation with TwoRayGround propagation model. The Simulation of Urban MObility (SUMO) and Vehicular Ad-hoc Networks Mobility Simulator (VanetMobiSim) are used to generate the mobility pattern for VANETs.
... Our simulation results show that DSR performs better at the cost of delay both in MANETs and in VANETs. In future, we are interested to develop a new link metric, like [16] and [17]. ...
Article
Full-text available
In this paper, a framework for experimental parameters in which Packet Delivery Ratio (PDR), effect of link duration over End-to-End Delay (E2ED) and Normalized Routing Overhead (NRO) in terms of control packets is analyzed and modeled for Mobile Ad-Hoc NETworks (MANETs) and Vehicular Ad-Hoc NETworks (VANETs) with the assumption that nodes (vehicles) are sparsely moving in two different road. Moreover, this paper contributes the performance comparison of one Proactive Routing Protocol; Destination Sequenced Distance vector (DSDV) and two reactive protocols; DYnamic Source Routing (DSR) and DYnamic MANET On-Demand (DYMO). A novel contribution of this work is enhancements in default versions of selected routing protocols. Three performance parameters; PDR, E2ED and NRO with varying scalabilities are measured to analyze the performance of selected routing protocols with their original and enhanced versions. From extensive simulations, it is observed that DSR outperforms among all three protocols at the cost of delay. NS-2 simulator is used for simulation with TwoRayGround propagation model to evaluate analytical results.
... The outcome displays the improved performance as compared to the existing protocol. In future, one can modify this problem statement to implement various link metrics that like ETX link metrics [16,17]. ...
... For delay sensitive applications, DYMO in reactive protocols and OLSR in proactive protocols are the plausible choices. During all this evaluation, we come to realize that the most important component of a routing protocol is routing link metric, so, future we are interested to propose and implement a new ETX-based routing link metric with AODV and OLSR, as discussed in [14], [15], [16]. ...
Article
In this paper, we evaluate, analyze, and compare the impact of mobility on the behavior of three reactive protocols (AODV, DSR, DYMO) and three proactive protocols (DSDV, FSR, OLSR) in multi-hop wireless networks. We take into account throughput, end-to-end delay, and normalized routing load as performance parameters. Based upon the extensive simulation results in NS-2, we rank all of six protocols according to the performance parameters. Besides providing the interesting facts regarding the response of each protocol on varying mobilities and speeds, we also study the trade-offs, the routing protocols have to make. Such as, to achieve throughput, a protocol has to pay some cost in the form of increased end-to-end delay or routing overhead.
... The authors in [16] identify a diversity of possible requirements to be addressed in a MANET, such as: minimizing hop-count, minimizing delay, maximizing data delivery, minimizing energy consumption, minimizing computational overhead, maximizing route stability, balancing traffic load, among others. The work also relates these requirements to the main link evaluation metrics and points out the associated performance trade-offs. ...
Conference Paper
Full-text available
Ad-hoc Wireless Networks provide a major base for ubiquitous computing development. In such networks, the communication occurs by multiple hops in a shared medium. In order to meet the different requirements of the applications, routing solutions aware of Quality of Service (QoS) have been developing. However, single-criterion strategies are unable to cope with conflicting objectives that commonly appear in these networks. This work proposes a multicriteria approach that considers End-to-End Delay (E2ED) and Packet Delivery Probability (PDP) as vital criteria in the route discovery process. For this purpose, Optimized Link State Routing Protocol (OLSR) with a modified Dijkstra algorithm is applied, wherein the bi-objective problem is transformed into a mono-objective problem through the epsilon-constraint technique. Extensive simulations have demonstrated that the multicriteria method can provide efficient routing in mobile environments, and it has outperformed the best results of single-criterion methods in terms of Packet Loss Ratio (PLR) by nearly 5-35 %. The results also have shown the potential of the model in finding a proper trade-off in relation to the number of hops and End-to-End Delay.
... In this work, we study the three performance metrics: Network lifetime , Residual energy and throughput. In future, we will study ETX link metrics and we will implement this metric in our scheme as implemented and demonstrated in [21] [22] [23]. ...
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The Thirteenth International Conference on Wireless and Mobile Communications (ICWMC 2017), held between July 23 - 27, 2017 - Nice, France, followed on the previous events on advanced wireless technologies, wireless networking, and wireless applications. ICWMC 2017 addressed wireless related topics concerning integration of latest technological advances to realize mobile and ubiquitous service environments for advanced applications and services in wireless networks. Mobility and wireless, special services and lessons learnt from particular deployment complemented the traditional wireless topics. We take here the opportunity to warmly thank all the members of the ICWMC 2017 Technical Program Committee, as well as the numerous reviewers. The creation of such a high quality conference program would not have been possible without their involvement. We also kindly thank all the authors who dedicated much of their time and efforts to contribute to ICWMC 2017. We truly believe that, thanks to all these efforts, the final conference program consisted of top quality contributions. Also, this event could not have been a reality without the support of many individuals, organizations, and sponsors. We are grateful to the members of the ICWMC 2017 organizing committee for their help in handling the logistics and for their work to make this professional meeting a success. We hope that ICWMC 2017 was a successful international forum for the exchange of ideas and results between academia and industry and for the promotion of progress in the area of wireless and mobile communications. We are convinced that the participants found the event useful and communications very open. We also hope that Nice provided a pleasant environment during the conference and everyone saved some time for exploring this beautiful city.
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A mobile, multi-hop wireless computer network, also termed an ad-hoc network, can be envisioned as a collection of routers, equipped with wireless transmitter/receiver, which are free to move about arbitrarily. The basic assumption in an ad-hoc network is that some nodes willing to communicate may be outside the wireless transmission range of each other but may be able to communicate if other nodes in the network are willing to forward packets from them. However, the successful operation of an ad-hoc network will be hampered if an intermediate node, participating in a communication between two nodes, moves out of range suddenly or switches itself off in between message transfer. The objective of this paper is to introduce a parameter, affinity that characterizes the strength of relationship between two nodes and to propose a distributed routing scheme between two nodes in order to find a set of paths between them which are more stable and less congested in a specific context. Thus, the communication in an ad-hoc wireless network can be effective by making the nodes in the system communication-aware in the sense that each node should know its affinity with its neighbors and should be aware of the impact of its movement on the communication structure of the underlying network
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An ad-hoc network is the cooperative engagement of a collection of Mobile Hosts without the required intervention of any centralized Access Point. In this paper we present an innovative design for the operation of such ad-hoc networks. The basic idea of the design is to operate each Mobile Host as a specialized router, which periodically advertises its view of the interconnection topology with other Mobile Hosts within the network. This amounts to a new sort of routing protocol. We have investigated modifications to the basic BellmanFord routing mechanisms, as specified by the Routing Information Protocol, making it suitable for a dynamic and self-starting network mechanism as is required by users wishing to utilize ad-hoc networks. Our modifications address some of the previous objections to the use of Bellman-Ford, related to the poor looping properties of such algorithms in the face of broken links and the resulting time dependent nature of the interconnection topology describing th...
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The use of Fish eye scoping has been introduced to reduce the overhead of the OLSR routing protocol. This simple method is based on reducing the scope (TTL) of some topology updates, thus giving routers a precise view of their close neighborhood and a more and more approximate view of farther nodes. Fish Eye OLSR (OFLSR) has been showed to have excellent scaling properties and low network overhead. However, if deployed in relatively sparse networks, this scoping limitation of topology updates can result in long living routing loops, thus limiting the potential applications of such mechanisms in some practical wireless mesh networks. In this paper, we address the transient mini-loop problem due to fisheye scoping. We first analyze the occurrence of mini-loops. We discuss potential solutions and propose a pragmatic and distributed off-line heuristic, which allows each router to compute ldquosaferdquo scope for topology updates. With our method, every mesh router calculates in advance the minimum TTL value that avoids mini-loops at the ldquoscoperdquo boundary - optimal scope that will be set for generating topology update message whenever a neighbor link lost is detected. Simulations show that the proposed algorithm drastically improves safety of Fish Eye OLSR while still retaining its scaling and performance properties.
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Next generation fixed wireless broadband networks are being increasingly deployed as mesh networks in order to provide and extend access to the internet. These networks are characterized by the use of multiple orthogonal channels and nodes with the ability to simultaneously communicate with many neighbors using multiple radios (interfaces) over orthogonal channels. Networks based on the IEEE 802.11a/b/g and 802.16 standards are examples of these systems. However, due to the limited number of available orthogonal channels, interference is still a factor in such networks. In this paper, we propose a network model that captures the key practical aspects of such systems and characterize the constraints binding their behavior. We provide necessary conditions to verify the feasibility of rate vectors in these networks, and use them to derive upper bounds on the capacity in terms of achievable throughput, using a fast primal-dual algorithm. We then develop two link channel assignment schemes, one static and the other dynamic, in order to derive lower bounds on the achievable throughput. We demonstrate through simulations that the dynamic link channel assignment scheme performs close to optimal on the average, while the static link channel assignment algorithm also performs very well. The methods proposed in this paper can be a valuable tool for network designers in planning network deployment and for optimizing different performance objectives.
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In this paper, we propose a new quality link metric, interference and bandwidth adjusted ETX (IBETX) for wireless multi-hop networks. As MAC layer affects the link performance and consequently the route quality, the metric therefore, tackles the issue by achieving twofold MAC-awareness. Firstly, interference is calculated using cross-layered approach by sending probes to MAC layer. Secondly, the nominal bit rate information is provided to all nodes in the same contention domain by considering the bandwidth sharing mechanism of 802.11. Like ETX, our metric also calculates link delivery ratios that directly affect throughput and selects those routes that bypass dense regions in the network. Simulation results by NS-2 show that IBETX gives 19% higher throughput than ETX and 10% higher than Expected Throughput (ETP). Our metric also succeeds to reduce average end-to-end delay up to 16% less than Expected Link Performance (ELP) and 24% less than ETX.
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Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2004. Vita. Includes bibliographical references (leaves 111-118). This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections. The expected transmission count (ETX) metric is a new route metric for finding high-throughput paths in multi-hop wireless networks. The ETX of a path is the expected total number of packet transmissions (including retransmissions) required to successfully deliver a packet along that path. For practical networks, paths with the minimum ETX have the highest throughput. The ETX metric incorporates the effects of link loss ratios, asymmetry in the loss ratios between the two directions of each link, and interference among the successive links of a path. Busy networks that use the ETX route metric will also maximize total network throughput. We describe the design and implementation of ETX as a metric for the DSDV and DSR routing protocols, as well as modifications to DSDV and DSR which make them work well with ETX. Measurements taken from a 29-node 802.11b test-bed show that using ETX improves performance significantly over the widely-used minimum hop-count metric. For long paths the throughput increase is often a factor of two or more, suggesting that ETX will become more useful as networks grow larger and paths become longer. We also present a simple model for predicting how packet delivery ratio varies with packet size, and detailed measurements which characterize the test-bed's distribution of link delivery ratios and route throughputs. by Douglas S.J. Couto. Ph.D.
Conference Paper
There has been increased interest recently from military, civil, and commercial sectors in networks capable of self-organization. Routing and channel assignment for multi-hop communications in these networks are complex problems, given the interactions between the various transmissions, all of which must share some fixed bandwidth, and by the lack of a central controller. By enforcing a “reuse distance” similar to the frequency reuse factor in AMPS cellular service, we can route and assign channels to (place) arriving calls in a peer-to-peer network so as to significantly reduce power requirements and interference | 2022-06-25 12:03:19 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.3411029875278473, "perplexity": 1633.0355498987965}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-27/segments/1656103034930.3/warc/CC-MAIN-20220625095705-20220625125705-00738.warc.gz"} |
https://ftp.aimsciences.org/article/doi/10.3934/proc.2007.2007.855 | Article Contents
Article Contents
# Three state relays
• We consider a hysteresis operator that arises as a three state generalization of a bi-stable relay. Basic properties and a geometric interpretation of the three-state relay are considered. Analogously to Preisach operator, which can be introduced as an aggregation of all possible non-ideal relays, we consider a "Super-Preisach" operator, that is an aggregation of all possible three-state relays.
Mathematics Subject Classification: Primary: 34C55; Secondary: 47H99.
Citation:
Open Access Under a Creative Commons license | 2022-11-27 14:25:53 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 1, "x-ck12": 0, "texerror": 0, "math_score": 0.40673714876174927, "perplexity": 1655.3276151825303}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-49/segments/1669446710409.16/warc/CC-MAIN-20221127141808-20221127171808-00084.warc.gz"} |
https://www.ncatlab.org/nlab/show/non-canonical+isomorphism | Non-canonical isomorphisms
Idea
Often in category theory, requirements that certain things “be isomorphic” are more precisely stated as saying that a certain “canonical” morphism is invertible. However, in certain situations, it happens that the existence of a non-canonical isomorphism automatically entails the “correct” stronger property that the canonical morphism is invertible.
For now, see the references for details.
References
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https://s170063.gridserver.com/9gntbr6a/proving-parallel-lines-examples-3d4380 | 7. f you need any other stuff in math, please use our google custom search here. Two lines cut by a transversal line are parallel when the corresponding angles are equal. If it is true, it must be stated as a postulate or proved as a separate theorem. Therefore, by the alternate interior angles converse, g and h are parallel. If ∠WTS and∠YUV are supplementary (they share a sum of 180°), show that WX and YZ are parallel lines. Recall that two lines are parallel if its pair of consecutive exterior angles add up to $\boldsymbol{180^{\circ}}$. 3. 3.3 : Proving Lines Parallel Theorems and Postulates: Converse of the Corresponding Angles Postulate- If two coplanar lines are cut by a transversal so that a air of corresponding angles are congruent, then the two lines are parallel. So AE and CH are parallel. Does the diagram give enough information to conclude that a ǀǀ b? Then we think about the importance of the transversal, Use the Transitive Property of Parallel Lines. 10. â CHG are congruent corresponding angles. The theorem states that the same-side interior angles must be supplementary given the lines intersected by the transversal line are parallel. Consecutive exterior angles add up to $180^{\circ}$. This means that the actual measure of $\angle EFA$ is $\boldsymbol{69 ^{\circ}}$. Lines are parallel if they are always the same distance apart (called "equidistant"), and will never meet. Learn vocabulary, terms, and more with flashcards, games, and other study tools. 2. The two angles are alternate interior angles as well. If the lines $\overline{AB}$ and $\overline{CD}$ are parallel, identify the values of all the remaining seven angles. Just remember that when it comes to proving two lines are parallel, all we have to look at … Apply the Same-Side Interior Angles Theorem in finding out if line A is parallel to line B. 1. Explain. Similarly, the other theorems about angles formed when parallel lines are cut by a transversal have true converses. If you have alternate exterior angles. Hence, $\overline{WX}$ and $\overline{YZ}$ are parallel lines. There are four different things we can look for that we will see in action here in just a bit. Parallel Lines, and Pairs of Angles Parallel Lines. Using the same graph, take a snippet or screenshot and draw two other corresponding angles. If the two angles add up to 180°, then line A is parallel to line … the line that cuts across two other lines. 5. Apart from the stuff given above, f you need any other stuff in math, please use our google custom search here. Let’s try to answer the examples shown below using the definitions and properties we’ve just learned. In coordinate geometry, when the graphs of two linear equations are parallel, the. We are given that â 4 and â 5 are supplementary. remember that when it comes to proving two lines are parallel, all we have to look at are the angles. Free parallel line calculator - find the equation of a parallel line step-by-step. Graphing Parallel Lines; Real-Life Examples of Parallel Lines; Parallel Lines Definition. Line 1 and 2 are parallel if the alternating exterior angles (4x – 19) and (3x + 16) are congruent. Are the two lines cut by the transversal line parallel? Go back to the definition of parallel lines: they are coplanar lines sharing the same distance but never meet. Parallel lines are two or more lines that are the same distance apart, never merging and never diverging. Use the image shown below to answer Questions 4 -6. â BEH and â DHG are corresponding angles, but they are not congruent. Isolate $2x$ on the left-hand side of the equation. Alternate interior angles are a pair of angles found in the inner side but are lying opposite each other. ° angle to the wind as shown, and the wind is constant, will their paths ever cross ? Picture a railroad track and a road crossing the tracks. The diagram given below illustrates this. Use the image shown below to answer Questions 9- 12. Statistics. Welcome back to Educator.com.0000 This next lesson is on proving lines parallel.0002 We are actually going to take the theorems that we learned from the past few lessons, and we are going to use them to prove that two lines are parallel.0007 We learned, from the Corresponding Angles Postulate, that if the lines are parallel, then the corresponding angles are congruent.0022 In the diagram given below, if â 1 â
â 2, then prove m||n. Justify your answer. So AE and CH are parallel. Since $a$ and $c$ share the same values, $a = c$. 4. Example: $\angle a^{\circ} + \angle g^{\circ}=$180^{\circ}$,$\angle b ^{\circ} + \angle h^{\circ}=$180^{\circ}$. You can use the following theorems to prove that lines are parallel. Theorem 2.3.1: If two lines are cut by a transversal so that the corresponding angles are congruent, then these lines are parallel. Which of the following term/s do not describe a pair of parallel lines? Two lines cut by a transversal line are parallel when the sum of the consecutive exterior angles is $\boldsymbol{180^{\circ}}$. If two lines are cut by a transversal and corresponding angles are congruent, then the lines are parallel. Let us recall the definition of parallel lines, meaning they are a pair of lines that never intersect and are always Solution. If $\angle STX$ and $\angle TUZ$ are equal, show that $\overline{WX}$ and $\overline{YZ}$ are parallel lines. This is a transversal. Solving linear equations using elimination method, Solving linear equations using substitution method, Solving linear equations using cross multiplication method, Solving quadratic equations by quadratic formula, Solving quadratic equations by completing square, Nature of the roots of a quadratic equations, Sum and product of the roots of a quadratic equations, Complementary and supplementary worksheet, Complementary and supplementary word problems worksheet, Sum of the angles in a triangle is 180 degree worksheet, Special line segments in triangles worksheet, Proving trigonometric identities worksheet, Quadratic equations word problems worksheet, Distributive property of multiplication worksheet - I, Distributive property of multiplication worksheet - II, Writing and evaluating expressions worksheet, Nature of the roots of a quadratic equation worksheets, Determine if the relationship is proportional worksheet, Trigonometric ratios of some specific angles, Trigonometric ratios of some negative angles, Trigonometric ratios of 90 degree minus theta, Trigonometric ratios of 90 degree plus theta, Trigonometric ratios of 180 degree plus theta, Trigonometric ratios of 180 degree minus theta, Trigonometric ratios of 270 degree minus theta, Trigonometric ratios of 270 degree plus theta, Trigonometric ratios of angles greater than or equal to 360 degree, Trigonometric ratios of complementary angles, Trigonometric ratios of supplementary angles, Domain and range of trigonometric functions, Domain and range of inverse trigonometric functions, Sum of the angle in a triangle is 180 degree, Different forms equations of straight lines, Word problems on direct variation and inverse variation, Complementary and supplementary angles word problems, Word problems on sum of the angles of a triangle is 180 degree, Domain and range of rational functions with holes, Converting repeating decimals in to fractions, Decimal representation of rational numbers, L.C.M method to solve time and work problems, Translating the word problems in to algebraic expressions, Remainder when 2 power 256 is divided by 17, Remainder when 17 power 23 is divided by 16, Sum of all three digit numbers divisible by 6, Sum of all three digit numbers divisible by 7, Sum of all three digit numbers divisible by 8, Sum of all three digit numbers formed using 1, 3, 4, Sum of all three four digit numbers formed with non zero digits, Sum of all three four digit numbers formed using 0, 1, 2, 3, Sum of all three four digit numbers formed using 1, 2, 5, 6. â 5 are supplementary. Parallel lines do not intersect. Here, the angles 1, 2, 3 and 4 are interior angles. Since the lines are parallel and $\angle 1 ^{\circ}$ and $\angle 8 ^{\circ}$ are alternate exterior angles, $\angle 1 ^{\circ} = \angle 8 ^{\circ}$. Let’s summarize what we’ve learned so far about parallel lines: The properties below will help us determine and show that two lines are parallel. ... Identities Proving Identities Trig Equations Trig Inequalities Evaluate Functions Simplify. If you have any feedback about our math content, please mail us : You can also visit the following web pages on different stuff in math. If two lines are cut by a transversal so that alternate exterior angles are congruent, then the lines are parallel. Example: $\angle c ^{\circ} + \angle e^{\circ}=180^{\circ}$, $\angle d ^{\circ} + \angle f^{\circ}=180^{\circ}$. This means that $\boldsymbol{\angle 1 ^{\circ}}$ is also equal to $\boldsymbol{108 ^{\circ}}$. Start studying Proving Parallel Lines Examples. Because each angle is 35 °, then we can state that Therefore, by the alternate interior angles converse, g and h are parallel. Just Divide both sides of the equation by $4$ to find $x$. Example 1: If you are given a figure (see below) with congruent corresponding angles then the two lines cut by the transversal are parallel. Two lines cut by a transversal line are parallel when the alternate exterior angles are equal. If $\overline{WX}$ and $\overline{YZ}$ are parallel lines, what is the value of $x$ when $\angle WTU = (5x – 36) ^{\circ}$ and $\angle TUZ = (3x – 12) ^{\circ}e$? When working with parallel lines, it is important to be familiar with its definition and properties. You know that the railroad tracks are parallel; otherwise, the train wouldn't be able to run on them without tipping over. Theorem: If two lines are perpendicular to the same line, then they are parallel. Another important fact about parallel lines: they share the same direction. This is a transversal line. 1. Two vectors are parallel if they are scalar multiples of one another. Consecutive exterior angles are consecutive angles sharing the same outer side along the line. To use geometric shorthand, we write the symbol for parallel lines as two tiny parallel lines, like this: ∥ Understanding what parallel lines are can help us find missing angles, solve for unknown values, and even learn what they represent in coordinate geometry. And as we read right here, yes it is. If two lines are cut by a transversal so that consecutive interior angles are supplementary, then the lines are parallel. Hence, x = 35 0. Alternate Interior Angles We know that if we have two lines that are parallel-- so let me draw those two parallel lines, l and m. So that's line l and line m. We know that if they are parallel, then if we were to draw a transversal that intersects both of them, that the corresponding angles are equal. Use alternate exterior angle theorem to prove that line 1 and 2 are parallel lines. Just remember: Always the same distance apart and never touching.. If two lines are cut by a transversal so that same-side interior angles are (congruent, supplementary, complementary), then the lines are parallel. This means that $\angle EFB = (x + 48)^{\circ}$. This packet should help a learner seeking to understand how to prove that lines are parallel using converse postulates and theorems. So EB and HD are not parallel. But, how can you prove that they are parallel? Parallel lines can intersect with each other. If $\overline{AB}$ and $\overline{CD}$ are parallel lines, what is the actual measure of $\angle EFA$? The hands of a clock, however, meet at the center of the clock, so they will never be represented by a pair of parallel lines. Add $72$ to both sides of the equation to isolate $4x$. In geometry, parallel lines can be identified and drawn by using the concept of slope, or the lines inclination with respect to the x and y axis. They all lie on the same plane as well (ie the strings lie in the same plane of the net). 6. Because corresponding angles are congruent, the paths of the boats are parallel. Fill in the blank: If the two lines are parallel, $\angle b ^{\circ}$, and $\angle h^{\circ}$ are ___________ angles. â 6. Explain. Parallel Lines Cut By A Transversal – Lesson & Examples (Video) 1 hr 10 min. Construct parallel lines. We’ll learn more about this in coordinate geometry, but for now, let’s focus on the parallel lines’ properties and using them to solve problems. How To Determine If The Given 3-Dimensional Vectors Are Parallel? the same distance apart. railroad tracks to the parallel lines and the road with the transversal. Provide examples that demonstrate solving for unknown variables and angle measures to determine if lines are parallel or not (ex. Several geometric relationships can be used to prove that two lines are parallel. Fill in the blank: If the two lines are parallel, $\angle c ^{\circ}$, and $\angle g ^{\circ}$ are ___________ angles. 4. It is transversing both of these parallel lines. In the next section, you’ll learn what the following angles are and their properties: When two lines are cut by a transversal line, the properties below will help us determine whether the lines are parallel. By the linear pair postulate, â 6 are also supplementary, because they form a linear pair. Big Idea With an introduction to logic, students will prove the converse of their parallel line theorems, and apply that knowledge to the construction of parallel lines. The angles that lie in the area enclosed between two parallel lines that are intersected by a transversal are also called interior angles. Transversal lines are lines that cross two or more lines. Parallel lines are lines that are lying on the same plane but will never meet. Therefore; ⇒ 4x – 19 = 3x + 16 ⇒ 4x – 3x = 19+16. Now what ? If $\angle WTU$ and $\angle YUT$ are supplementary, show that $\overline{WX}$ and $\overline{YZ}$ are parallel lines. Parallel Lines – Definition, Properties, and Examples. Two lines cut by a transversal line are parallel when the sum of the consecutive interior angles is $\boldsymbol{180^{\circ}}$. Proving Lines are Parallel Students learn the converse of the parallel line postulate. So EB and HD are not parallel. 3. Hence, $\overline{AB}$ and $\overline{CD}$ are parallel lines. Recall that two lines are parallel if its pair of alternate exterior angles are equals. The angles $\angle 1 ^{\circ}$ and $\angle 8 ^{\circ}$ are a pair of alternate exterior angles and are equal. Day 4: SWBAT: Apply theorems about Perpendicular Lines Pages 28-34 HW: pages 35-36 Day 5: SWBAT: Prove angles congruent using Complementary and Supplementary Angles Pages 37-42 HW: pages 43-44 Day 6: SWBAT: Use theorems about angles formed by Parallel Lines and a … If two lines are cut by a transversal and corresponding angles are congruent, then the lines are parallel. 2. Since parallel lines are used in different branches of math, we need to master it as early as now. The image shown to the right shows how a transversal line cuts a pair of parallel lines. SWBAT use angle pairs to prove that lines are parallel, and construct a line parallel to a given line. Improve your math knowledge with free questions in "Proofs involving parallel lines I" and thousands of other math skills. The following diagram shows several vectors that are parallel. 5. What property can you use to justify your answer? The angles $\angle EFB$ and $\angle FGD$ are a pair of corresponding angles, so they are both equal. If two lines and a transversal form alternate interior angles, notice I abbreviated it, so if these alternate interior angles are congruent, that is enough to say that these two lines must be parallel. Two lines, l and m, are parallel, and are cut by a transversal t. In addition, suppose that 1 ⊥ t. Proving Lines Parallel. If two lines are cut by a transversal so that alternate interior angles are congruent, then the lines are parallel. And what I want to think about is the angles that are formed, and how they relate to each other. of: If two lines are cut by a transversal so that corresponding angles are congruent, then the lines are parallel. Add the two expressions to simplify the left-hand side of the equation. These are some examples of parallel lines in different directions: horizontally, diagonally, and vertically. 9. In the diagram given below, if â 4 and â 5 are supplementary, then prove g||h. This shows that parallel lines are never noncoplanar. 8. Lines j and k will be parallel if the marked angles are supplementary. In the diagram given below, find the value of x that makes j||k. In the video below: We will use the properties of parallelograms to determine if we have enough information to prove a given quadrilateral is a parallelogram. These different types of angles are used to prove whether two lines are parallel to each other. Prove theorems about parallel lines. â AEH and â CHG are congruent corresponding angles. d. Vertical strings of a tennis racket’s net. Are the two lines cut by the transversal line parallel? The angles $\angle EFA$ and $\angle EFB$ are adjacent to each other and form a line, they add up to $\boldsymbol{180^{\circ}}$. The two lines are parallel if the alternate interior angles are equal. Using the same figure and angle measures from Question 7, what is the sum of $\angle 1 ^{\circ}$ and $\angle 8 ^{\circ}$? 5. $(x + 48) ^{\circ} + (3x – 120)^{\circ}= 180 ^{\circ}$. In the diagram given below, decide which rays are parallel. Alternate exterior angles are a pair of angles found in the outer side but are lying opposite each other. Consecutive interior angles add up to $180^{\circ}$. Two lines cut by a transversal line are parallel when the alternate interior angles are equal. Substitute x in the expressions. Now we get to look at the angles that are formed by the transversal with the parallel lines. In the standard equation for a linear equation (y = mx + b), the coefficient "m" represents the slope of the line. x = 35. Proving Lines Are Parallel Suppose you have the situation shown in Figure 10.7. What are parallel, intersecting, and skew lines? Parallel lines are lines that are lying on the same plane but will never meet. The angles $\angle 4 ^{\circ}$ and $\angle 5 ^{\circ}$ are alternate interior angles inside a pair of parallel lines, so they are both equal. If two boats sail at a 45° angle to the wind as shown, and the wind is constant, will their paths ever cross ? Both lines must be coplanar (in the same plane). There are times when particular angle relationships are given to you, and you need to … Pedestrian crossings: all painted lines are lying along the same direction and road but these lines will never meet. By the congruence supplements theorem, it follows that. By the linear pair postulate, â 5 and â 6 are also supplementary, because they form a linear pair. When a pair of parallel lines are cut by a transversal line, different pairs of angles are formed. Now that we’ve shown that the lines parallel, then the alternate interior angles are equal as well. Divide both sides of the equation by $2$ to find $x$. At this point, we link the the transversal with the parallel lines. Two lines with the same slope do not intersect and are considered parallel. 4. When working with parallel lines, it is important to be familiar with its definition and properties.Let’s go ahead and begin with its definition. First, you recall the definition of parallel lines, meaning they are a pair of lines that never intersect and are always the same distance apart. â DHG are corresponding angles, but they are not congruent. And lastly, you’ll write two-column proofs given parallel lines. In general, they are angles that are in relative positions and lying along the same side. Students learn the converse of the parallel line postulate and the converse of each of the theorems covered in the previous lesson, which are as follows. Example: $\angle b ^{\circ} = \angle f^{\circ}, \angle a ^{\circ} = \angle e^{\circ}e$, Example: $\angle c ^{\circ} = \angle f^{\circ}, \angle d ^{\circ} = \angle e^{\circ}$, Example: $\angle a ^{\circ} = \angle h^{\circ}, \angle b^{\circ} = \angle g^{\circ}$. Roadways and tracks: the opposite tracks and roads will share the same direction but they will never meet at one point. Notes: PROOFS OF PARALLEL LINES Geometry Unit 3 - Reasoning & Proofs w/Congruent Triangles Page 163 EXAMPLE 1: Use the diagram on the right to complete the following theorems/postulates. The angles that are formed at the intersection between this transversal line and the two parallel lines. 2. You can use some of these properties in 3-D proofs that involve 2-D concepts, such as proving that you have a particular quadrilateral or proving that two triangles are similar. If the lines $\overline{AB}$ and $\overline{CD}$ are parallel and $\angle 8 ^{\circ} = 108 ^{\circ}$, what must be the value of $\angle 1 ^{\circ}$? That is, two lines are parallel if they’re cut by a transversal such that Two corresponding angles are congruent. Using the Corresponding Angles Converse Theorem 3.5 below is the converse of the Corresponding Angles Theorem (Theorem 3.1). Proving that lines are parallel: All these theorems work in reverse. If two lines are cut by a transversal so that alternate interior angles are (congruent, supplementary, complementary), then the lines are parallel. Before we begin, let’s review the definition of transversal lines. The converse of a theorem is not automatically true. The angles $\angle WTS$ and $\angle YUV$ are a pair of consecutive exterior angles sharing a sum of $\boldsymbol{180^{\circ}}$. If u and v are two non-zero vectors and u = c v, then u and v are parallel. If two lines are cut by a transversal and alternate interior angles are congruent, then the lines are parallel. If $\angle 1 ^{\circ}$ and $\angle 8 ^{\circ}$ are equal, show that $\angle 4 ^{\circ}$ and $\angle 5 ^{\circ}$ are equal as well. The two pairs of angles shown above are examples of corresponding angles. Example 4. Let’s go ahead and begin with its definition. THEOREMS/POSTULATES If two parallel lines are cut by a transversal, then … Which of the following real-world examples do not represent a pair of parallel lines? Specifically, we want to look for pairs Example: In the above figure, $$L_1$$ and $$L_2$$ are parallel and $$L$$ is the transversal. Fill in the blank: If the two lines are parallel, $\angle c ^{\circ}$, and $\angle f ^{\circ}$ are ___________ angles. The English word "parallel" is a gift to geometricians, because it has two parallel lines … Since it was shown that $\overline{WX}$ and $\overline{YZ}$ are parallel lines, what is the value $\angle YUT$ if $\angle WTU = 140 ^{\circ}$? The options in b, c, and d are objects that share the same directions but they will never meet. Equate their two expressions to solve for $x$. When lines and planes are perpendicular and parallel, they have some interesting properties. True or False? 11. 3. Consecutive interior angles are consecutive angles sharing the same inner side along the line. By the congruence supplements theorem, it follows that â 4 â
â 6. Three parallel planes: If two planes are parallel to the same plane, […] Parallel Lines – Definition, Properties, and Examples. Proving Lines Are Parallel When you were given Postulate 10.1, you were able to prove several angle relationships that developed when two parallel lines were cut by a transversal. Holt McDougal Geometry 3-3 Proving Lines Parallel Recall that the converse of a theorem is found by exchanging the hypothesis and conclusion. If the two lines are parallel and cut by a transversal line, what is the value of $x$? 1. Two lines are parallel if they never meet and are always the same distance apart. This shows that the two lines are parallel. Then you think about the importance of the transversal, the line that cuts across t… A tip from Math Bits says, if we can show that one set of opposite sides are both parallel and congruent, which in turn indicates that the polygon is a parallelogram, this will save time when working a proof.. Lines on a writing pad: all lines are found on the same plane but they will never meet. Since the lines are parallel and $\boldsymbol{\angle B}$ and $\boldsymbol{\angle C}$ are corresponding angles, so $\boldsymbol{\angle B = \angle C}$. The red line is parallel to the blue line in each of these examples: Substitute this value of $x$ into the expression for $\angle EFA$ to find its actual measure. Now we get to look at the angles that are formed by There are four different things we can look for that we will see in action here in just a bit. Parallel lines are equidistant lines (lines having equal distance from each other) that will never meet. 2. So the paths of the boats will never cross. 12. Use this information to set up an equation and we can then solve for $x$. \begin{aligned}3x – 120 &= 3(63) – 120\\ &=69\end{aligned}. A = c $share the same values,$ \overline { AB } $are a pair of found. – 19 = 3x + 16 ⇒ 4x – 19 ) and ( +! The same plane but will never meet and are considered parallel unknown variables and angle measures to Determine if are... Exterior angle theorem to prove that lines are parallel ) that will never meet and are considered.... Without tipping over that we ’ ve shown that the Same-Side interior angles are congruent to set up an and., c, and vertically there are four different things we can look for that we will see in here! Theorem states that the Same-Side interior angles just remember: always the same side, can! Their two expressions to Simplify the left-hand side of the corresponding angles are formed by the transversal with the lines... Games, and how they relate to each other g and h are.. Angles must be supplementary given the lines are parallel same plane but they will never.! Shown in Figure 10.7 are alternate interior angles are equal as well the expression for$ $. These different types of angles found in the same directions but they will meet! I '' and thousands of other math skills meet at one point 16 ⇒ 4x – 19 = 3x 16... Get to look at the angles that are formed at the angles all we have to look at intersection! Never touching \boldsymbol { 69 ^ { \circ }$ are parallel from the stuff above... Supplementary given the lines parallel, the other theorems about angles formed when parallel lines never... Proved as a postulate or proved as a postulate or proved as a postulate or proved a! V are two non-zero vectors and u = c $share the same direction are always the distance! Definition, properties, and d are objects that share the same plane but they will meet. With its definition want to think about the importance of the equation by$ 2 $to find$ $... But never meet things we can then solve for$ x $we given. More with flashcards, games, and other study tools about angles formed when parallel lines ''... At one point then prove g||h below is the angles that are lying each... ° angle to the right shows how a transversal line, different pairs of angles are equal we to... Boats are parallel, the angles that are lying on the left-hand side of net! Will their paths ever cross and u = c$ share the distance!, 2, then the alternate interior angles are a pair of parallel lines cut by a transversal and angles. Master it as early as now be coplanar ( in the diagram given,. And $\overline { CD }$ are parallel, they have some interesting properties 2, then lines. Postulate, â 5 and â CHG are congruent corresponding angles are congruent, then prove g||h that. S net angles that lie in the same direction ; otherwise, the train would n't able. The situation shown in Figure 10.7 a writing pad: all lines are parallel using converse postulates and.! The graphs of two linear Equations are parallel, and will never at... Some interesting properties is $\boldsymbol { 69 ^ { \circ }$ understand how prove... Lie in the area enclosed between two parallel lines: they are proving parallel lines examples that intersected! { proving parallel lines examples } $will their paths ever cross look for that we see! A is parallel to a given line the actual measure word parallel '' is transversal... This information to set up an equation and we can look for that we ve. Angles theorem in finding out if line a is parallel to line b Proofs involving lines! Learn vocabulary, terms, and will never meet angles proving parallel lines examples, 2, and! Just a bit lines sharing the same distance apart ^ { \circ }$ then we think the! Have some interesting properties the net ) parallel planes: if two lines are parallel if its pair angles! Measures to Determine if the two lines are parallel lines are parallel: the opposite tracks and roads share... $4x$ a is parallel to each other ) and ( +! Of x that makes j||k of two linear Equations are parallel when the alternate interior angles add up to 180^!
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https://runestone.academy/runestone/static/cpp4python/IntroCpp/whylearncpp.html | # 1.3. Why Learn Another Programming Language?¶
Python is a great language for beginning programming for several reasons. First, the syntax is both sparse and clear. Second, the underlying model of how objects and variables work is very consistent. Third, you can write powerful and interesting programs without a lot of work. However, Python is representative of one kind of language, called a dynamic language. One might think of Python as being fairly informal. Other languages, like C, C++, and Java are more formal.
These other more formal languages have some advantages of their own. First, is speed: For very large programs C and C++ are likely to give you the best performance. Second, is their maintainability. Python requires you to remember certain things. For example if you set variable t to reference a turtle, and forget later that t is a turtle but try to invoke a string method on it, you will get an error. C++ protects you from this kind of error by forcing you to be upfront and formal about the type of object each variable is going to refer to.
In one sense Python is representative of a whole class of interpreted languages, sometimes referred to as “scripting languages.” Other scripting languages include Ruby and Perl. C++ is representative of what one might call industrial strength languages. Industrial strength languages are good for projects with several or many people working on the project where being formal and careful about what you do may impact lots of other people. Languages in this category include C, C#, C++, Ada, and Java.
The good news is that learning a second programming language is much easier than learning your first programming language because you will be able to draw upon your existing knowledge. Programming languages are likely to regularly change as time passes. As the field of computer science advances there are likely to be new programming languages that you will want or need to learn. There are certain features that most programming languages have in common such as variables, loops, conditionals, and functions. And there are other language features that are unique. If you know what is common in most languages, then in learning a new language, you need only to focus on what is different from the languages you already know.
## 1.3.1. Why Learn C++? Why not Java or Javascript?¶
• C++ is an enormous language which is very powerful because it is a high-level language that offers low-level features, but one only needs to learn a small part of the language to write effective code.
• C++ influenced many programming languages such as C#, Java, and other newer versions of C, so by learning C++, learning these other languages becomes much easier.
• C++ is industrial strength and is very often used today for large systems by large groups of people.
• C++ is particularly good at interacting directly with computer hardware, making execution very fast.
• C++ was the first widely used object-oriented programming (OOP) language, supporting the four primary features of OOP: abstraction, inheritance, polymorphism, and encapsulation.
• C++ allows the programmer to create and use a data type called a pointer explicitly, which can increase control over both memory and performance under certain circumstances.
• Because C++ is fast, it is currently the language of choice for virtual reality.
• Also, because C++ is fast, it is the language of choice of many 2D and 3D game engines.
• For all of the above reasons, even though C++ is an older language, it is still one of the top listed in job advertisements.
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