url
stringlengths 14
2.42k
| text
stringlengths 100
1.02M
| date
stringlengths 19
19
| metadata
stringlengths 1.06k
1.1k
|
|---|---|---|---|
https://homework.zookal.com/questions-and-answers/the-electric-field-near-the-middle-of-a-long-thin-144818460
|
1. Science
2. Physics
3. the electric field near the middle of a long thin...
# Question: the electric field near the middle of a long thin...
###### Question details
The electric field near the middle of a long, thin, uniformly charged rod is 3.40×104 N/C at a distance of 7.64 cm from the rod. If the rod's length is 12.7 m, what is the charge on the rod?
|
2021-05-14 16:26:16
|
{"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": 0.8223084807395935, "perplexity": 729.3024089639547}, "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/1620243991428.43/warc/CC-MAIN-20210514152803-20210514182803-00343.warc.gz"}
|
https://infoscience.epfl.ch/record/161408
|
Formats
Format
BibTeX
MARC
MARCXML
DublinCore
EndNote
NLM
RefWorks
RIS
### Abstract
This note gives a short, geometrically based, proof that a real orthogonal matrix has a normal form consisting of a direct sum of 1$times 1$ and 2$times 2$ blocks.
|
2021-04-19 12:11:19
|
{"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": 0.6350244283676147, "perplexity": 844.1972195175834}, "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/1618038879374.66/warc/CC-MAIN-20210419111510-20210419141510-00185.warc.gz"}
|
https://drexel28.wordpress.com/2012/04/15/continuous-and-cocontinuous-functors-pt-ii/
|
# Abstract Nonsense
## Continuous and Cocontinuous Functors (Pt. II)
Point of Post: This is a continuation of this post.
$\text{ }$
Remark: I would like to point out that there is a much quicker, common “proof” for the above statement. I put proof in scare quotes because while the proof is much slicker and much quicker it doesn’t actually prove that right adjoints are continuous. No, what it really does is prove that $G(\lim D)\cong \lim (G\circ D)$. The proof basically goes as follows:
$\text{ }$
\begin{aligned}\text{Hom}(X,G(\lim D)) &\cong \text{Hom}(F(X),\lim D)\\ &= \lim\text{Hom}(F(X),D)\\ &= \lim\text{Hom}(X,G\circ D))\\ &= \text{Hom}(X,\lim(G\circ D))\end{aligned}
$\text{ }$
And so by Yoneda’s lemma $G(\lim D)\cong \lim(G\circ D)$. While the basic idea is neat it does not actually prove continuity. I am not saying that one couldn’t expand on this slightly and get a proof but that writing that isn’t enough.
$\text{ }$
Anyways, let me discuss one immediate application of the fact that right adjoints are continuous and left adjoints are cocontinuous.
$\text{ }$
Suppose for a second that we have two small categories $\mathcal{I}$ and $\mathcal{J}$ and a bifunctor $D:\mathcal{I}\times\mathcal{J}\to\mathcal{C}$–i.e. a diagram in $\mathcal{C}$ over $\mathcal{I}\times\mathcal{J}$. Suppose that we can take the limit $\lim D$. Everything’s great then, right? Well, yes, it is, but there is something lurking secretly in the background. Namely, $D$ gives us a functor $D_1:\mathcal{I}\to\mathcal{C}^\mathcal{J}$ which takes $i$ to the functor $\mathcal{J}\to\mathcal{C}$ which on objects is $j\mapsto D(i,j)$ and which on morphisms is $s\mapsto D(1_i,s)$. Similarly, we have a functor $D_2:\mathcal{J}\to\mathcal{C}^\mathcal{I}$ defined similarly. An obvious question then is whether $\lim D_1$ and $\lim D_2$ exist and if so how do they relate to each other and $\lim D$? Why is this an obvious question, because if one looks closely one can see that $\lim D_1$ and $\lim D_2$ are like iterated limits that can be roughly symbolized as $\lim_\mathcal{I}\lim_\mathcal{J}$ and $\lim_\mathcal{J}\lim_\mathcal{I}$ respectively. Since the limit functor is a right adjoint we know that it commutes with limits and so we may conclude that, in fact, $\lim D_1\cong \lim D_2$. It is easy then to see that $\lim D\cong \lim D_1$ and thus we may conclude that
$\text{ }$
Theorem: Let $D:\mathcal{I}\times\mathcal{J}\to\mathcal{C}$ be a diagram. Then,
$\lim_\mathcal{I}\lim_\mathcal{J}D\cong\lim_\mathcal{J}\lim_\mathcal{I}D\cong\lim_{\mathcal{I}\times\mathcal{J}}D$
$\text{ }$
Of course, you can make the same statement that colimits commute with colimits.
$\text{ }$
$\text{ }$
Finitely Continuous and Finitely Cocontinuous
$\text{ }$
As a last point we would like to mention the following theorem:
$\text{ }$
Theorem: Let $F:\mathcal{C}\to\mathcal{D}$ be a functor. Then, $F$ is finitely continuous (resp. finitely cocontinuous) if and only if $f$ preserves products and equalizers (resp. coproducts and coequalizers).
$\text{ }$
This follows from the fact that all limits (resp. colimits) can be defined as a combination of products and equalizers (resp. coproducts and coequalizers).
$\text{ }$latex \text{ }\$
References:
[1] Mac, Lane Saunders. Categories for the Working Mathematician. New York: Springer-Verlag, 1994. Print.
[2] Adámek, Jirí, Horst Herrlich, and George E. Strecker. Abstract and Concrete Categories: the Joy of Cats. New York: John Wiley & Sons, 1990. Print.
[3] Berrick, A. J., and M. E. Keating. Categories and Modules with K-theory in View. Cambridge, UK: Cambridge UP, 2000. Print.
[4] Freyd, Peter J. Abelian Categories. New York: Harper & Row, 1964. Print.
[5] Mitchell, Barry. Theory of Categories. New York: Academic, 1965. Print.
[6] Herrlich, Horst, and George E. Strecker. Category Theory: An Introduction. Lemgo: Heldermann, 2007. Print.
|
2017-05-24 15:31:11
|
{"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": 43, "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": 0.993100643157959, "perplexity": 445.24201750782225}, "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-2017-22/segments/1495463607848.9/warc/CC-MAIN-20170524152539-20170524172539-00255.warc.gz"}
|
https://www.lexifi.com/blog/ocaml/note-about-performance-printf-and-format/
|
## A note about the performance of Printf and Format.
#### Alain Frisch
The goal is to display the following to stdout:
(0,0) (1,1) (2,2) … (1000000,1000000).
How would you implement that in OCaml? For such a simple task, we probably expect the program to be IO bound, right? Ok, let’s try with the idiomatic way, which is to use format strings as provided by the Printf module from OCaml standard library:
let printf () =
for i = 1 to n do
Printf.printf "(%d,%d)\n" i i
done
Or maybe the same with the Format module:
let formatf () =
for i = 1 to n do
Format.printf "(%d,%d)@." i i
done
On my machine, compiling with ocamlopt and running these functions (redirecting stdout to a local file) take respectively 0.94s and 3.33s. So the first lesson is:
If performance matters, don’t use Format if Printf is enough.
Ok, can we beat the Printf version? This version parses and interprets the format string at runtime, and then maps to low-level output functions. So let’s try to use directly those functions:
let direct () =
let oc = stdout in
for i = 1 to n do
output_char oc '(';
output_string oc (string_of_int i);
output_char oc ',';
output_string oc (string_of_int i);
output_char oc ')';
output_char oc '\n';
done
This version takes 0.51s (0.94s for printf).
If performance matters, use direct output functions instead of Printf.
Sometimes, you are stuck with the Format module, because you must call existing printers of type Format.formatter -> foo -> unit, or you indeed make use of formatting boxes. Still, nothing forces you to rely on format strings to use Format. Here a more direct version:
let format () =
let open Format in
for i = 1 to n do
print_char '(';
print_int i;
print_char ',';
print_int i;
print_char ')';
print_flush ()
done
This one takes 2.58s in native code (3.33s for formatf).
If performance matters and you are stuck with using Format, avoid the use of format strings.
Note that the direct version could still be optimised a little bit if we had a direct output_int which did not allocate its result as a string. Also note that in bytecode, the relative slowdowns are even more impressive.
Here is a table which summarises those results (also showing the number of bytes allocated, as returned by Gc.allocated_bytes):
[ direct]: 0.51 sec, 32000128 bytes
[ printf]: 0.94 sec, 1704075840 bytes
[ format]: 2.58 sec, 728008488 bytes
[ formatf]: 3.33 sec, 2664063504 bytes
How often does the performance of printing textual data matters? Well actually, quite rarely, but sometimes it does, and the numbers above suggest that it might pay to rewrite the most intensively used pieces of the pretty-printing code. For instance, we’ve observed a total speedup of about 15% for compiling our entire code tree by optimising the -annot printer of ocamlc (by avoiding some use of Format and format strings). I suspect that people doing textual logs could also be interested in those performance remarks.
|
2021-05-07 13:00:34
|
{"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": 0.509503185749054, "perplexity": 6433.04675186002}, "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/1620243988793.99/warc/CC-MAIN-20210507120655-20210507150655-00478.warc.gz"}
|
https://brilliant.org/problems/end-in-2015-part-2/
|
# End in 2015, part 2
$$S$$ is a 4-digit number which, when multiplied by 995, yields a product that ends in 2015.
What is sum of all such possible $$S$$?
Example: 2916 is a number which when multiplied by 107, yields 312012, which ends in 2012.
This question is from the set starts, ends, never ends in 2015.
×
|
2017-07-26 00:58:42
|
{"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": 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": 0.5672800540924072, "perplexity": 679.8737227732149}, "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-2017-30/segments/1500549425737.60/warc/CC-MAIN-20170726002333-20170726022333-00425.warc.gz"}
|
http://physics.stackexchange.com/tags/phonons/hot
|
# Tag Info
## Hot answers tagged phonons
14
I read that phonons are (the quantum mechanical analog of) normal modes of vibration in a crystalline system of atoms or molecules, so I guess a superposition, i.e. a general vibration should also be a phonon. Is that so? Why would they then be described as normal modes? The reason that phonons are described in terms of normal modes is because the ...
8
As I understand this occurs when a cystalline solid has more than one atom in the primitive cell of the lattice. For simplicity I'll consider the case of two types of atoms, distinguished by their position in the primitive cell (but which may or may not be otherwise identical). This gives rise to multiple modes of vibration. The acoustical phonon ...
7
Because a phonon is a quantum of "sound" and "sound" is a longitudinal wave while a photon is a quantum of "light" and "light" is a transverse wave (an electromagnetic wave). For example, if two waves are moving in the $z$ direction, the sound wave moves the molecules of the medium in the $z$ direction as well, up and down, one possible direction. ...
6
I'm not sure if a Condensed Matter book is going to give you what you want: as pointed out by commenters, you cannot derive a Lagrangian, you can only justify it because it represents the correct physics. But here is a simple interpretation of the 3rd order term. For small deformations, Hooke's law holds and the restoring force $F_{a}=−k_{ab}q_b$. (For ...
6
Yes. The Seebeck effect, for example, is the direct conversion of thermal gradient to electric voltage. It is used in the small scale in thermocouples to measure temperatures electronically, or in the larger scales in thermoelectric generators for power generation. In fact, many of the long-range space probes launched by NASA get power this way. ...
4
The zero phonon line is the wavelength at which an excitation/relaxation is not phonon assisted.
4
What are phonons? Phonons aren't particles like electrons or protons are, phonons are quasi particles, these type of particles are just used to describe excitations of a field: in phonons case, phonons are used to describe elementary lattice vibrations which have certain frequency. Electron-Phonon Interaction: Basically Cooper pairs are just pairs of ...
3
Actually the framework where one can describe electromagnetic fields is a classical framework. When one is talking of photons phonons etc one is in the quantum mechanical regime where the concept field, is different. A classical field in physics: A field can be classified as a scalar field, a vector field, a spinor field or a tensor field according ...
3
A photon is an excitation of a quantum field, which is classically $A_{\mu}$ governed by the Lagrangian, $$\mathcal{L}=-\frac{1}{4}F_{\mu\nu}F^{\mu\nu}$$ which we may quantize canonically by the usual procedure, i.e. expanding the field as a plane wave, promoting the Fourier coefficients to operators, etc. A virtual photon does not necessarily satisfy, ...
3
I don't know nearly enough QFT to address the background or implications of your question. However, I'd basically answer yes to your first two questions, but it depends a little on your definition. A single phonon mode is not localized in space. However a wave packet can in principle be built up of a small range of frequencies, giving a fairly well defined ...
3
Careful! The essence of your question is a good thought but I think you are having several misconceptions. First of all, it doesn't make sense to talk about a phonon being directed towards a single atom. Phonons are delocalized. Secondly, the "input of temperature required to eject an electron" is a dangerous idea. You need to input energy to eject an ...
3
While a cavity can have modes of arbitrarily high frequency, a phonon can't have a wavelength smaller than the separation between atoms in the solid (well, it could, but it'd be degenerate with phonons of smaller frequency because the discrete Fourier transform is periodic). Hence, there is a maximum possible wavenumber. A physical (or sometimes ...
3
In classical mechanics, you can describe a crystal (in some approximation) by a Hamiltonian that is a quadratic form in coordinates and momenta of atoms. After you diagonalize this quadratic form, you obtain a Hamiltonian of a set of independent, rather than coupled, oscillators (modes). Then you can quantize this system and you do get zero-point energy for ...
3
You made it a challenge by asking so many different questions, but since no one else has attempted an answer, I'll do my best. :) I read that phonons are (the quantum mechanical analog of) normal modes of vibration in a crystalline system of atoms or molecules, so I guess a superposition, i.e. a general vibration should also be a phonon. Is that so? Why ...
3
Phonon scattering goes up a lot as temperature increases -- faster than electron numbers increase in the conduction band. Keep in mind that phonons obey the Bose-Einstein distribution, so their numbers scale like $$N_{BE}=\frac{1}{e^{\frac{\hbar\omega}{k_b T}}-1}$$ In the large $T$ limit, this becomes $$\frac{k_b T}{\hbar\omega}$$ So their numbers ...
3
In Raman it should say "optical phonon" instead of vibrational oscillation. I'm not sure if you can call the vibrations in a molecule phonons, since phonons are the vibrations of the lattice in a solid (even when the mathematical description, in first approximation are the same).
3
Phonon dispersions are generally indicated by a linear spectrum, so the second derivative is 0. Thus phonons are effectively massless, and have a velocity given by the first derivative.
3
This is a great question. The point is we've made a huge structural change in going from Lehmann representation to the, um, other one. In Lehmann representation, we've chosen to write $G$ as a sum over an infinite number of real poles, which is fine of course, but when you start adding infinite numbers of delta functions together, things can get tricky. ...
3
My opinion: Phonons are collective excitations of the crystal lattice vibration. They are massless Goldstone bosons resulting from the violation of the continuous translational symmetry of free space, by the crystal lattice. Phonons must carry momentum because they interact with electrons and change the momentum of the latter. An example is the electronic ...
3
Lattice vibration excitations, i.e. phonons, are typically at energies of $\sim 25 meV$ which corresponds to room temperature. Therefore, neutron scattering with thermal neutrons is done. Thermal neutrons are neutrons from a nuclear power plant which are moderated to room temperature by sending them through a big tank of water, so they also have energies on ...
2
1) The Pauli exclusion principle says that either 0 or 1 identical fermion, but not more, may occupy the same quantum state. It's been originally induced from the properties of atoms (periodic table). Today, we may derive it from the first principle out of the antisymmetric wave functions for many fermions, those obeying \psi(\vec x_1,\vec x_2) = ...
2
Unstable particles are concepts of effective field theories (or few-particle systems) in reduced descriptions where the decay products are ignored. In these reduced descriptions, they appear as particles with complex masses, and their Green's functions have complex poles. In an unreduced description, unstable particles appear as poles of the analytically ...
2
Brillouin scattering is caused by an interaction between light and lattice phonon modes. Raman scattering is caused by an interaction between light and molecular vibrations. The key difference is that phonon modes are a collective, long-range phenomenon involving billions or more atoms, whereas molecular vibrations are localized vibrations of a single ...
2
When you solve for such Hamiltonian for the harmonic oscillator you get a set of eigenstates which by definition are orthogonal and thus you have phonons that don't interact. When you include a non harmonic term to the Hamiltonian and treating it as a perturbation you get new eigenstates that are a mixture of those the simple harmonic oscillator. This ...
2
The Debye temperatures of some steel alloys can be found in the thesis of Rajevac, Vedran: "Lattice dynamics in Hydrogenated Austenitic Stainless Steels and in the Superionic Conductor Cu 2-δ Se" on p. 43. In general searching for material specific data I recommend starting with a search in Google, Google Scholar and Landolt-Boernstein. If neither turn ...
2
The term vibron isn't a standard accepted word in solid state physics. It's simply a synonym of a phonon, which was probably coned before phohon. As far as localization is concerned, phonons can be localized too. For example, in a crystal lattice, the vibrations can propagate throughout the crystal, or there can be vibrations in only a small localized part ...
2
Yes, and no. Since the group of rotations is not a continuous group in real crystals, it is not possible to define spin in a meaningful way. It is only in an isotropic ideal medium that is possible to define spin for a phonon (quantized accoustic wave). Equivalently it is only possible to define a spin if the the wavelength of the phonon is long or if one ...
2
The distinction isn't actually as sharp as it may seem. If you get really pedantic about it, you can create borderline cases that blur the line as much as you like. The first answer, that it's just the difference between acoustic phonons and optical phonons, is correct. But then that just leads to the next question: What's the difference between those? In a ...
2
If the potentials are all quadratic, then the force varies linearly with displacement. That means the superposition principle holds. (Don't confuse that with quantum superposition!) In other words the lattice waves then behave like electromagnetic waves: you put two of them together and they simply add together but don't otherwise affect one another; they ...
Only top voted, non community-wiki answers of a minimum length are eligible
|
2016-02-07 22:21:35
|
{"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": 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": 0.7920238971710205, "perplexity": 385.73853770719893}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "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-2016-07/segments/1454701151789.24/warc/CC-MAIN-20160205193911-00148-ip-10-236-182-209.ec2.internal.warc.gz"}
|
http://chasethedevil.blogspot.com/2015/07/unintuitive-behavior-of-black-scholes.html
|
## Tuesday, July 07, 2015
### Unintuitive behavior of the Black-Scholes formula - negative volatilities in displaced diffusion extrapolation
I am looking at various extrapolation schemes of the implied volatilities. An interesting one I stumbled upon is due to Kahale. Even if his paper is on interpolation, there is actually a small paragraph on using the same kind of function for extrapolation. His idea is to simply lookup the standard deviation $$\Sigma$$ and the forward $$f$$ corresponding to a given market volatility and slope:
$$c_{f,\Sigma} = f N(d_1) - k N(d_2)$$
with
$$d_1 = \frac{\log(f/k)+\Sigma^2/2}{\Sigma}$$
We have simply:
$$c'(k) = - N(d_2)$$
He also proves that we can always find those two parameters for any $$k_0 > 0, c_0 > 0, -1 < c_0' < 0$$
Then I had the silly idea of trying to match with a put instead of a call for the left wing (as those are out-of-the-money, and therefore easier to invert numerically). It turns out that it works in most cases in practice and produces relatively nice looking extrapolations, but it does not always work. This is because contrary to the call, the put value is bounded with $$f$$.
$$p_{f,\Sigma} = k N(-d_2) - f N(-d_1)$$
Inverting $$p_0'$$ is going to lead to a specific $$d_2$$, and you are not guaranteed that you can push $$f$$ high and have $$p_{f,\Sigma}$$ large enough to match $$p_0$$. As example we can just take $$p_0 \geq k N(-d_2)$$ which will only be matched if $$f \leq 0$$.
This is slightly unintuitive as put-call parity would suggest some kind of equivalence. The problem here is that we would need to consider the function of $$k$$ instead of $$f$$ for it to work, so we can't really work with a put directly.
Here are the two different extrapolations on Kahale own example:
Extrapolation of the left wing with calls (blue doted line)
Extrapolation of the left wing with puts (blue doted line)
Displaced diffusion extrapolation is sometimes advocated. It is not the same as Kahale extrapolation: In Kahale, only the forward variable is varying in the Black-Scholes formula, and there is no real underlying stochastic process. In a displaced diffusion setting, we would adjust both strike and forward, keeping put-call parity at the formula level. But unfortunately, it suffers from the same kind of problem: it can not always be solved for slope and price. When it can however, it will give a more consistent extrapolation.
I find it interesting that some smiles can not be extrapolated by displaced diffusion in a C1 manner except if one allows negative volatilities in the formula (in which case we are not anymore in a pure displaced diffusion setting).
Extrapolation of the left wing using negative displaced diffusion volatilities (blue dotted line)
|
2017-06-23 22:35:26
|
{"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": 0.7561790943145752, "perplexity": 596.134296162163}, "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-2017-26/segments/1498128320201.43/warc/CC-MAIN-20170623220935-20170624000935-00407.warc.gz"}
|
https://blog.poisson.chat/posts/2019-01-14-cpp19-from-c-to-itrees.html
|
# From C to Interaction trees: Specifying, Verifying, and Testing a networked server (CPP 2019 talk transcript)
Posted on January 14, 2019
This is a transcript of my talk at CPP 2019 (conference on Certified Programs and Proofs, co-hosted with POPL), presenting our efforts towards verifying a networked server.
## DeepSpec
This work is part of the Expedition in the Science of Deep Specification (DeepSpec). Led by four American universities (MIT, Yale, Princeton, Penn), DeepSpec aims to develop techniques to verify whole systems. DeepSpec encompasses many verification projects, and the work I’m going to present today is the first step towards connecting them together to verify a system from RFCs to transistors.
We will verify an application written in C using the Verified Software Toolchain (VST for short). It is a program logic for C, based on Hoare logic. One important reason for using VST is that the properties we prove are preserved by compilation with the CompCert compiler. This verified application will run on a verified OS, CertiKOS. And all this software will run on hardware implemented and verified with the Kami library.
Ultimately, we would like one theorem formalizing the correctness of the complete system. The main challenge of the DeepSpec project is to connect these components developed by different institutes to obtain such a unifying theorem.
Moreover, we would also like to make our specifications testable, as a way to relate specifications to the real world. For that, we will use QuickChick, a library for property-based testing: that allows to formulate specifications as automatically testable properties, producing concrete counterexamples when they are not satisfied.
Especially in the context of verification, testing provides two benefits:
1. It can reveal bugs before proving, to gain confidence that the theorems being proved are indeed correct;
2. and it can make specifications applicable to other implementations in the wild, ensuring that our interpretation of informal documents such as RFCs matches existing implementations. Implementations may also intentionally deviate from standard specifications, often for reasons related to performance or security.
### A verified web server
As a final demo of the Deep Specification project, we aim to verify an HTTP server. By implementing such a widely used protocol we hope to show the applicability of verification at an industrial scale.
But today, rather than a project as complex as an HTTP server, we will instead focus on a simplified application. With this experiment we want to illustrate at a small scale the challenges in integrating different components to build a fully verified system.
And indeed, it still has the essential features allowing us to make the following contributions:
• we verified a C program that talks over the network using VST, so that it can be compiled in a verified way and run in CertiKOS;
• and we made our specification testable: from it we can derive a test client, which can connect to a server, verified or not, and check whether it satisfies the specification.
## Case study: Swap server
Let’s see a simple example of what our server does. A swap server exchanges messages with one or many clients, and can store one message.
• When it receives a message, for example, "Cat" from client 1, the server stores it, and replies with the previously stored message "Bat" (an arbitrary initial message).
• Then, when it receives another message, for example, "Dog" from another client, it stores it and replies with the previously stored message, "Cat".
• And so on.
It is like an “echo server”, which repeats what it hears, but its responses are shifted to the next exchange. The key motivation for the swap server’s behavior is to make the simplest example of a stateful server.
### Networked swap server
However, our server is implemented against a low-level socket interface. This exposes a wide range of interactions that the previous specification does not describe directly. The network, the hardware, and the OS can buffer messages internally in various ways. For example, this leads to messages being reordered, or delayed indefinitely.
These are behaviors that matter not only when we would run the server in production, but also during testing.
### Network refinement
To account for the network, we adapt notions of observational refinement from the literature on concurrent and distributed systems.
The rough idea is to take a high-level specification of the server from earlier, and through the semantics of the network, we can define the observations that clients can make on the other side of the network.
In parallel, we also define the observable behavior of an implementation. Then, the correctness property relating the implementation and the specification is the inclusion of observable behaviors over the network, which we call network refinement.
### Proof architecture
Here is a picture summarizing our system. Starting from the bottom, CertiKOS provides the environment to execute our server.
In particular, it provides a networking interface using sockets, against which our server is implemented. The aim is to show that the implementation respects the specification as illustrated in the previous slides.
First, we introduce an intermediate specification, the implementation model. The toplevel specification is now called the linear specification to distinguish those two forms of specifications. The implementation model is a low-level description of the server’s interactions with the socket interface, describing for example how the server buffers communications with many clients at the same time (whereas that kind of details doesn’t appear in the linear specification).
Using VST, we prove a refinement between the C program and the implementation model. Then, we prove that the implementation model network-refines the specification.
Of course, the fact that the C program refines the implementation model must rely on some semantics of the socket interface, which we wrote down first using VST.
Now, to relate the socket implementation to the VST specification, we also started formalizing the interface in CertiKOS. The implementation is however still not verified (thus we use a dashed arrow there in the diagram). The bridge between VST and CertiKOS is work-in-progress (as shown by the dotted line), and our paper gives a summary of our approach there.
As I said before, the long term goal of DeepSpec is to connect many components together into a whole verified system. This comes with various challenges that are already apparent in our simple experiment.
1. To describe the system at different abstraction levels.
2. To translate between varying specification styles already in use by the existing tools.
3. To test the specification, both to reduce the engineering effort that will be required at a larger scale, and to be able to check whether our specification matches other existing implementations in the wild.
We propose interaction trees as a unifying structure to represent effectful computations across our development while addressing those challenges.
## Interaction trees (aka. free monads)1
Intuitively, a program interacting with the outside world can be described as a tree, where nodes correspond to effects performed by the program, with one branch for each possible result of that effect. In this example, the program reads a bit, and if it is zero it goes to the left, if it is one it goes to the right, and so on, and it may return some value as a final result.
We can define interaction trees with many different kinds of effects. The simple example on the slide uses effects to read and write bits. Effects can be easily defined for any particular application as a sum type, whose constructors correspond to the effects that can be performed, and the type index gives the result type of each effect.
### Definition
CoInductive itree (E : Type -> Type) (R : Type) : Type :=
| Vis : forall Y, E Y -> (Y -> itree E R) -> itree E R
| Ret : R -> itree E R
| Tau : itree E R -> itree E R
.
Programs such as web servers can run for indefinitely long, so their interactions trees can be infinite. This is why we declare the type of itrees to be coinductive. It is parameterized by an effect type E and a result type R.
An itree can perform an effect, of type E Y, with a continuation expecting a response of type Y from the environment. We can see this as a node of type E Y whose arity is the cardinality of Y.
An itree can terminate, returning a result of type R.
An itree can take a silent step of internal computation, without any visible effect. That last constructor is actually necessary to satisfy Coq’s guardedness condition when constructing nontrivial infinite trees.
To come back to the initial point, itrees provide a general-purpose representation that can be used at different abstraction levels and that seems compatible with many existing verification frameworks. At the same time since it is a simple coinductive type, so it can be easily extracted for testing.
#### Swap server: linear specification
Here is the linear specification of a swap server, as an interaction tree defined in Coq. It is a recursively defined itree parameterized by a set of open connections and the contents of the store, first nondeterministically choosing a connection c, receiving a new_msg from it, and sending back the last_msg from the store, before looping again with the new_msg in the store. Since it is defined monadically, it looks almost like a reference implementation, except for the nondeterminism at the top.
The implementation model is also an itree, but more complex since it reflects the C program’s logic of buffering and interleaving exchanges on multiple connections.
## Refinement in VST
The other half of the proof is to show that the behavior of the C program is contained in the behavior of the implementation model, using VST’s logic. VST is a Hoare-style logic for C programs: specifications are given as pre- and postconditions on the program’s memory. Perhaps surprisingly, the implementation model appears in the precondition, as part of an ITree predicate. The idea is that it describes the interactions that are initially allowed by the external environment. A valid program under this precondition is one that follows those allowed behaviors.
When the program performs an effect corresponding to a node in the allowed itree, that itree gets replaced by the branch associated with the result of the effect. Here you can see a more concrete example of a C program allowed to perform a recv(), a send(), followed by effects described by the itree t.
{ ITree(msg <- Recv c ;; (* Coq *)
Send c msg ;;
t) * ... }
recv(c, buf, len); // C
send(c, buf, len);
{ ITree(t) * ... (* Coq *) }
## The top-level correctness theorem
We can now state the theorem formalizing the correctness of our server which we proved. It relates the C program to the high-level linear specification as follows. The refinement relation I just described provides a model of the C program’s use of the socket interface as an itree. This implementation model is existentially quantified: it is a detail of the proof, rather than the toplevel specification. Finally, we show that the implementation model network-refines the linear specification: seen from across the network, the observable behavior of the former is included in that of the latter.
Theorem correct_server :
exists impl_model,
refines C_prog impl_model /\
network_refines impl_model linear_spec.
## Next steps
All this is only the first step of our project. There is a lot more work needed to apply the lessons we learned to a full HTTP server.
In the swap server we only talked to the socket interface. We will soon need to tackle the question of composing more systems together, such as a filesystem or a cryptographic library. The flexibility of itrees seems particularly well-suited to this kind of composition.
The development of the swap server tested the limits of VST, motivating some new features to model external effects, and there is certainly more work to make the integration with CertiKOS smoother.
We currently have a quite simplistic model of the network. We are certainly interested in techniques that will allow us to scale up, towards more complicated servers that talk to more realistic networks.
Speaking of interaction trees, we are working on putting together a general purpose library of itrees. At the moment our focus is on how to use paco to make coinduction compose better.
1. If you have a functor F and take its free monad Free F, its inhabitants are what we call interaction trees here. Furthermore, to actually get an free monad, you should make the itree type defined here inductive instead of coinductive.
|
2019-03-20 11:52:39
|
{"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": 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": 0.419411838054657, "perplexity": 1424.7033339188547}, "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-2019-13/segments/1552912202326.46/warc/CC-MAIN-20190320105319-20190320131319-00275.warc.gz"}
|
https://www.nature.com/articles/s41598-017-14398-6?error=cookies_not_supported&code=4b4c6f98-2885-41b4-9887-749bde8e64df
|
Article | Open | Published:
# Vacancy-induced brittle to ductile transition of W-M co-doped Al3Ti (M=Si, Ge, Sn and Pb)
## Abstract
We investigated the effect of vacancy formation on brittle (D022) to ductile (L12-like) transition in Al3Ti using DFT calculations. The well-known pseudogap on the density of states of Al3Ti migrates towards its Fermi level from far above, via a W − M co-doping strategy, where M is Si, Ge, Sn or Pb respectively. In particular, by a W − M co-doping the underline electronic structure of the pseudogap approaches an octahedral (L12: t2g, eg) from the tetragonal (D022: eg, b2g, a1g, b1g) crystal field. Our calculations demonstrated that (1) a W-doping is responsible for the close up of the energy gap between a1g and b1g so that they tend to merge into an eg symmetry, and (2) all M-doping lead to a narrower gap between eg and b2g (moving towards a t2g symmetry). Thus, a brittle to ductile transition in Al3Ti is possible by adopting this W − M co-doping strategy. We further recommend the use of W-Pb co-doped Al3Ti to replace the less anodic Al electrode in Al-battery, due to its improved ductility and high Al diffusivity. Finally this study opens a new field in physics to tailor mechanical properties by manipulating electron energy level(s) towards higher symmetry via vacancy optimization.
## Introduction
Brittle to ductile transition is of interest to a wide range of fundamental research and applications1,2,3,4,5,6. In particular, effects of either intrinsic vacancy7,8, extra-electron9, or dopants10,12 on brittle-ductile transition in Nb5Si3, NiSc, Al12W-type and L12-Al3Sc are reported. TiAl-based intermetallic compounds are desirable candidates for high temperature structural applications due to many attractive properties. Among the Al-Ti alloys, Al3Ti has received particular interests for its high specific strength, elastic moduli13, low density (~3.3 g/cm3), good thermal conductivity and high melting point (~1400 °C). However, the stable but brittle tetragonal D022-Al3Ti is less favored in real applications. Many investigations are conducted aiming to improve the ductility of D022-Al3Ti. Hong12 calculated the density of states (DOS) of the brittle D022-Al3Ti and the ductile L12-Al3Ti phases, and proposed a strategy to simultaneously stabilize the ductile L12 and destabilized the brittle D022 phase by ternary alloy additions. He further pointed out that by adding in lower-valence elements, the pseudogap (on DOS) migrates from above to below the Fermi level, thus, diminishing simultaneously the antibonding for the ductile L12 and the bonding states for the brittle D022 phases. But Hong did not take into consideration the formation of either intrinsic or extrinsic defects into his model. On the other hand, Niu9 proposed to promote ductile to brittle transitions in Al12W-type intermetallic by an extra-electron doping, which is on the opposite direction of the current work. The underline electronic structures of pseudogap in both D022 and L12 Al3Ti phases are reported recently by Chen14. Crystal field splitting as shown in Fig. 1 is found responsible for the formation of the pseudogaps, i.e., an octahedral crystal field of eg (d2 x−y, d2 z) and t2g (dxy, dxz, dyz) for the ductile L12 phase, and a tetragonal one of b1g (d2 x−y), a1g (d2 z), b2g (dxy) and eg (dxy, dyz) for the brittle D022 phase. It is interesting to notice that the main difference between the octahedral and tetragonal crystal field splitting is the elongation in tetragonal along the z-axis, which relaxes the electron density along the z-axis and moves (1) the d2 z energy downwards apart from the d2 x−y and (2) the dxz and dyz lower than the dxy level. An effective unit area as shown in Fig. 2a is defined as S = lx × ly, where lx and ly is respectively the shortest atomic distance along the x and y axis. By shrinking the unit cell (or d in Fig. 2a) along the z-axis or expanding in the xy-plane indicated by S, a tetragonal crystal structure may return to and approach an octahedral-like structure. Thus, by reducing the ratio r−1) (r = d/S), a brittle-ductile transition may be facilitated. From first-principles calculations, we test this new strategy to achieve the designed reduction of r by adopting a W − M co-doping strategy. Key challenges in this approach are (1) to generate sufficient Al vacancies in D022-Al3Ti to make the brittle structure more deformable and (2) to manipulate specific electron energy levels to transfer the low symmetry tetragonal to a high symmetry octahedral-like crystal field.
Moreover, due to the decrease in Gibbs free energy, Al3Ti may also be used as the anode material to replace Al in Al-battery. Recently, electronic structure of pure D022-Al3Ti12,14 and Al diffusion mechanisms of D022-Al3Sc11 are reported. However, like many brittle intermetallics, short cycling life of a native D022-Al3Ti electrode is expected due to the structure damages during the charge and discharge processes. In addition, high Al diffusivity is essential to Al-battery, which requires an easy formation of Al vacancy based on Shi’s11 findings that Al vacancies facilitate the Al diffusion in Al3Sc. Therefore, the current study on the formation of Al vacancies may provide practical solutions to enhance both the mechanical and electrochemical properties of Al3Ti for Al-battery applications.
## Results
### Crystal structure
Crystal structures of both the ductile (L12) and brittle (D022) phases are shown in the Fig. 1. A L12-Al3Ti crystallizes in the Pm $$\bar{3}$$ m space group, in which the Al atoms are located at the face centers of the cubic lattice and the Ti atoms are located at the vertices. And a D022-Al3Ti crystallizes in the I4/mmm. The conventional D022 cell contains two Al atoms at the Wyckoff site 2b (defined as Al1), four Al atoms at the 4d site (defined as Al2) and two Ti atoms at the 2a site. In this study, the lattice parameters are fixed at the values of a = b = 0.3851 nm and c = 0.8611 nm, for c/a = 2.236, which are in satisfactory agreement with other experimental and calculation results15,16.
To conduct a systematic study, the site preference of W in D022-Al3Ti was investigated first by using a 2 × 2 × 1 supercell including 32 atoms. The first-principles calculations have been performed to calculated the total energies E tot for the pure D022-Al3Ti supercell and E dope for [(Al23W)Ti8] and [Al24(Ti7W)] structures. To determine the site preference of W, the substitution energy E sub is defined as:
$${E}_{{\rm{sub}}}={E}_{{\rm{dope}}}-{E}_{{\rm{tot}}}+{\mu }_{{\rm{Al}}/{\rm{Ti}}}-{\mu }_{{\rm{W}}}$$
(1)
where μ i (i = Al, Ti and W) is the chemical potential of these atoms in their stable bulk phases. In this study, the stable phases are considered as Ti in hcp structure17, Al in the fcc structure18. After occupying Al1, Al2 and Ti site by a W-atom, the substitution energies of the three structures are −1.089 eV, −0.969 eV and 0.005 eV, respectively. It is clearly seen that the ternary W-atom strongly favors the Al site over the Ti site in the D022-Al3Ti. Therefore, we default to substitute W-atom at the Al1 site in the following work, as the blue sphere shown in Fig. 2a.
Then the IV-group elements M (M = C, Si, Ge, Sn and Pb) were introduced into the D022-Al3Ti/W system and occupied the Ti site to form a W − M cluster, as the green sphere shown in Fig. 2a. The substitution energies of single M-atom doping at the Ti site in D022-Al3Ti can be written as:
$${E}_{{\rm{sub}}}({\rm{M}})={E}_{{\rm{M}}}-{E}_{{\rm{tot}}}+{\mu }_{{\rm{Ti}}}-{\mu }_{{\rm{M}}}$$
(2)
where E M is the total energy of single M-atom occupying Ti site. While the substitution energies of W − M clusters can be written as:
$${E}_{{\rm{sub}}}({\rm{W}}-{\rm{M}})={E}_{{\rm{W}}-{\rm{M}}}-{E}_{{\rm{tot}}}+{\mu }_{{\rm{Al}}}+{\mu }_{{\rm{Ti}}}-{\mu }_{{\rm{W}}}-{\mu }_{{\rm{M}}}$$
(3)
where E w−M is the total energy of W − M co-doping system. ΔE is defined as:
$$\begin{array}{rcl}{\rm{\Delta }}E & = & {E}_{{\rm{sub}}}({\rm{M}})-{E}_{{\rm{sub}}}({\rm{W}}-{\rm{M}})\\ & = & {E}_{{\rm{M}}}-{E}_{{\rm{W}}-{\rm{M}}}-{\mu }_{{\rm{Al}}}+{\mu }_{{\rm{W}}}\end{array}$$
(4)
The results are showed in Table 1. ΔE are positive which means that the co-doping systems have much lower substitution energies than the single doping systems. It indicates that introducing W in pure D022-Al3Ti structure will conduce to the substitution of Ti by M.
### Vacancy formation energy
The crystal model with an Al vacancy were created by removing an individual Al-atom from W − M co-doping supercell. In order to reduce the computation loads, we focus on the first-nearest neighbors, thus, the two possible Al vacancies are at V1 and V2 sites considering the system symmetry, shown as yellow spheres in Fig. 2a. The stability of the defected structures were studied by vacancy formation energy calculation after the atomic defects are relaxed completely. The formation energy of a neutral aluminum vacancy (hereafter simply referred to as an aluminum vacancy) ($${E}_{V}$$) is estimated by the following equation (5):
$${E}_{{\rm{V}}}({\rm{M}})={E}_{{\rm{def}}}-{E}_{{\rm{W}}-{\rm{M}}}+{\sum }_{i}{n}_{i}{\mu }_{i}$$
(5)
where E V(M) is the vacancy formation energy, E def is the total energy of D022-Al3Ti/W supercell containing one M-atom and one Al vacancy simultaneously and E W−M is the total energy of W − M co-doping supercell. The last term represents the difference in the number of atoms from the W − M co-doping system, where $${n}_{i}$$ denotes the number of atoms to be taken from or inserted into the supercell in order to take account of point defect generation. If a corresponding atom is inserted into the supercell, $${n}_{i}$$ is negative and if such an atom is taken away from the supercell, $${n}_{i}$$ is positive. $${\mu }_{i}$$ is the chemical potential of these atoms in their stable bulk phases. The calculated defect formation energies are tabulated in Table 2.
From Table 2, it can be easily observed that the vacancy formation energies of Al at V1 site are higher than that at V2 site. For a W − M co-doping system, when the Al vacancy occurs at V2 site, the vacancy formation energies are negative under both Al-rich environment and Ti-rich environment, which indicates V2 defects can be formed spontaneously during the fabrication of the alloy. In addition, both V1 and V2 defects are spontaneously formed by a W-Pb co-doping under either Al-rich or Ti-rich environment. The results attribute to the fact that the W − M co-doping cluster plays a vital role in the formation of Al vacancies.
### Electronic states of defected structure
The calculated DOS are given in Fig. 3a for the pure D022-Al3Ti, and in Fig. 3b–f for W-C, W-Si, W-Ge, W-Sn and W-Pb co-doping Al3Ti with an Al vacancy at the V1 site, respectively. Δn is introduced to indicate the valley of psuedogap. The value of Δn is the energy of the lowest position on the calculated DOS curve. Thus, the positive value means the psuedogap is higher than the Fermi level. The result is shown in Table 3. A clear pseudogap is observed in the D022-Al3Ti (circled part in Fig. 3a), which indicates the strong bonding-antibonding separation. The result shows a strong hybridization existing in the D022 structure as well as a strong directionality in bonding. Therefore, it is difficult to form the slip system in the tetragonal D022 structure and leads to brittleness. The partial DOS of D022-Al3Ti around the pseudogap was investigated, shown in Fig. 3g. From the edges of the gap, the splitting 3d orbitals could be observed clearly, thus, b1g (d2 x−y) energy is higher than a1g (d2 z) on the right edge, while b2g (dxy) energy is higher than eg (dxy, dyz) on the left edge, which appears a typical tetragonal crystal field.
From Fig. 3b–f, by adding different M elements and forming a W − M co-doping cluster with an Al vacancy at V1 simultaneously, the pseudogap migrates from far above towards the Fermi level, indicated by the red arrows. The results show that there are less bonding states which may favor a D022 to L12-like transition. To carry out a more in-depth and detailed study, partial DOS crossing the pseudogap of the W-Pb co-doping system was calculated and shown in Fig. 3h. Contributions from W and Pb to bonding electrons were investigated separately. On the right edge of the pseudogap, it is observed that W-atom contributes a lot to form strong hybridization between the d2 z and d2 x−y levels. Similarly on the left edge of the pseudogap, the Pb-atom has a strong influence on rising the dxz energy and dyz energy towards the dxy level (or a strong hybridization among these 3d orbitals). Therefore, the vacancy-induced 3d-orbital-splitting tend to facilitate a ductile L12-like structure, thus, eg (d2 x−y, d2 z) and t2g (dxy, dxz, dyz).
To obtain the brittle to ductile transition, the tetragonal D022 structure is expected to transform into an octahedral-like structure, which could be realized by either a shrinking along z-axis or an expanding on the xy-plane or both. By representing the ratio r of z-axis d to the xy-plane S, the change in structures are quantified, as shown in Fig. 2b. Taking pure D022-Al3Ti as the standard, it can be concluded that r decreased with the formation of Al vacancy at V1 site, which indicates that the tetragonal crystal field tends to transform into an octahedral-like crystal field. As a result, the stable phase change from D022 to L12–like ductile structures. When an Al vacancy forms at the V2 site, S remains nearly a constant except for the W-C co-doping. The larger S in the W-C co-doping system is due to the small size of C. Among all M elements in Table 4, C is the only dopant whose size is smaller than that of Al (0.39 Å for Al3+). More details will be outlined in Session 3 below.
## Discussion
In order to enable a brittle to ductile transition, we proposed and validated a W − M co-doping mechanism to (1) generate sufficient Al vacancies in D022-Al3Ti, and (2) simultaneously to manipulate specific electron energy levels to approach the high symmetry octahedral-like electronic structures. In particular, an equation for the lattice energy of W − M co-dopants is derived based on the EW−M (eV) given in Table 1:
$${E}_{{\rm{W}}-{\rm{M}}}=-170.3+9.44{R}_{{\rm{M}}}^{2}$$
(6)
where R M is the ionic radius of M.
The calculated EW−M based on equation (6) is −170.1, −168.7, −167.6, −165.8, −164.6 eV for M = C, Si, Ge, Sn and Pb respectively, which is very close to the DFT calculations, thus, −169.9, −168.7, −167.9, −165.8, −164.6 eV. Therefore, EW−M is in proportional to the cross-session of an M-ion ($${{\rm{R}}}_{{\rm{M}}}^{2}$$), or EW−M is 2-dimensional size (or xy-plane) dependent only. This is a good indicator that a W − M co-doping may only manipulate the xy-plane while leaving out the z-direction untouched.
Similarly, an equation for the formation energy of V2-W − M co-dopants is derived based on the $${{\rm{E}}}_{{{\rm{V}}}_{2}}$$ (eV) data given in Table 2:
$${\rm{For}}\,\text{Al}-\text{rich}:{E}_{{{\rm{V}}}_{2}}=-3.9{({R}_{{\rm{M}}}-0.39)}^{2}$$
(7)
$${\rm{F}}{\rm{o}}{\rm{r}}\,\text{Ti}-\text{rich}:{E}_{{{\rm{V}}}_{2}}=-0.55-3.9{({R}_{{\rm{M}}}-0.39)}^{2}$$
(8)
Both equations (7) and (8) reasonably reproduce DFT calculations shown in Table 2. We derived V2-W − M equations only since they are stable (or having negative formation energy) for all the M elements. Like equation (6), both equations (7) and (8) are in proportional to the cross-session changes of a substitutional M-ion and an Al vacancy (R M−0.39)2. Once again, a V2-W − M co-doping may only manipulate the xy-plane while leaving out the z-direction untouched. This 2-D manipulation function of W − M co-doping is the basis that enables a brittle (D022) to ductile (L12-like) transition, which can be applied not only for Al3Ti but all intermetallics in general.
Finally, we have systematically investigated a series of W − M co-doping D022-Al3Ti (M = C, Si, Ge, Sn and Pb) intermetallics using first-principles calculation method. The site preference of W in pure D022-Al3Ti was first studied, it shows W (a d element) has a clear preference to substitute Al1 (a sp element) site due to the strong crystal field. Then, we confirmed the [(Al23W)Ti8] system is conductive to the subsequent doping of M-atom. Meanwhile, a M substitution of Ti reduces the stability of [(Al23W)Ti8], which might benefit the intercalation and deintercalation of Al-ion during charge-discharge cycling in rechargeable Al-battery. The two possible Al vacancies were also investigated. In comparison to the vacancy formation energies of Li-ion in Li3N19 (−0.14 ~ 0.52 eV), the Al vacancies in W − M co-doped Al3Ti have much lower formation energies, therefore, high Al diffusivity is expected.
The DOS of W − M co-doping Al3Ti with an Al vacancy at the V1 site were investigated. The results show the pseudogap migrates towards the Fermi level from far above, indicating a tendency to transform into ductile L12-like structure. By analyzing the partial DOS around the pseudogap, we found that W and Pb have almost independent contributions to the transition, thus, W mainly influents d2 x−y and d2 z while Pb have a strong effect on dxy, dxz and dyz. It shows the crystal splitting effect on the 3d orbitals plays a decisive role not only on the formation but also the transformation of pseudogap. Therefore, this study contributes to the formation of a new field in physics to design mechanical properties from electronic structures via vacancy optimization.
## Methods
Calculations were carried out within the framework of density functional theory (DFT)20, using the projector-augmented wave (PAW) method21 and the Perdew-Burke-Ernserhof (PBE)22 for the exchange-correlation energy functional, via the Vienna ab initio Simulation Package (VASP)23. We first calculated the equilibrium lattice parameters of the Al3Ti using plane-wave cutoff energy of 340 eV and a 7 × 7 × 7 k-point mesh in the Monkhorst-Pack scheme13 by using the 2 × 2 × 1 supercell including 32 atoms. In all calculations, self-consistency was achieved with a tolerance in the total energy of 0.01 meV, and the atom were relaxed until the forces were less than 0.01 eV/Å. The crystal structures were fully optimized by independently modifying lattice parameters and internal atomic coordinates.
### Data availability statement
All data generated or analyzed during this study are included in this published article.
Publisher's note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
## References
1. 1.
Jang, D. C. & Greer, J. R. Transition from a strong-yet-brittle to a stronger-and-ductile state by size reduction of metallic glasses. Nature Mater 9(3), 215–219 (2016).
2. 2.
Peterlik, H. et al. From brittle to ductile fracture of bone. Nature Mater 5(1), 52–55 (2006).
3. 3.
Ramos, L. et al. Structural signature of a brittle-to-ductile transition in self-assembled networks. Phys. Rev. Lett. 107(14) (2011).
4. 4.
Tallinen, T. & Mahadevan, L. Forced tearing of ductile and brittle thin sheets. Phys. Rev. Lett. 107(24) (2011).
5. 5.
Yuan, C. C. et al. NMR Signature of evolution of ductile-to-brittle transition in bulk metallic glasses. Phys. Rev. Lett. 107(23) (2011).
6. 6.
Wu, P. & Wu, T. Temperature-dependent modulus of resilience in metallic solids – calculated from strain-electron-phonon interactions. J. Alloys Compd. 705, 269–272 (2017).
7. 7.
Pan, Y. et al. Vacancy induced brittle-to-ductile transition of Nb5Si3 alloy from first-principles. Mater. Des. 86, 259–265 (2015).
8. 8.
Yuan, Z. P., Cui, H. B. & Guo, X. F. First-principle calculation on mechanical and thermal properties of B2-NiSc with point defects. J. Semicond. 38(1), 5 (2017).
9. 9.
Niu, H. Y. et al. Extra-electron induced covalent strengthening and generalization of intrinsic ductile-to-brittle criterion. Sci. Rep, 2 (2012).
10. 10.
Pan, Y. et al. Influence of vacancy on structural and elastic properties of NbSi2 from first-principles calculations. Mater. Des. 108, 13–18 (2016).
11. 11.
Shi, T. T. et al. Atomic diffusion mediated by vacancy defects in pure and transition element (TM)-doped (TM = Ti, Y, Zr or Hf) L1(2) Al3Sc. Mater. Des. 108, 529–537 (2016).
12. 12.
Hong, T. et al. Crystal-structure, phase-stability, and electronic-structure of Ti-Al intermetallics-TiAl3. Phys. Rev. B. 41(18), 12462–12467 (1990).
13. 13.
Milman, Y. V. et al. Mechanical behaviour of Al3Ti intermetallic and L12 phases on its basis. Intermetallics 9(9), 839–845 (2001).
14. 14.
Chen, Z. L. et al. Chemical bonding and pseudogap formation in D0(22) and L1(2) structure (V, Ti)Al3. J. Phys. Chem. Solids. 71(7), 946–951 (2010).
15. 15.
Frazier, W. E. & Benci, J. E. Crystal structure and phase relationships in as-cast and melt spun Al3Ti and Al3Ti plus copper. Scripta. Mater. 25(10), 2267–2272 (1991).
16. 16.
Ghosh, G. et al. Stability and elastic properties of L12-(Al,Cu)3(Ti,Zr) phases: Ab initio calculations and experiments. Intermetallics 15(1), 44–54 (2007).
17. 17.
Wei, X. P. et al. The electronic and magnetic properties of defects on half-metallic Ti2NiIn alloy. J. Solid State Chem. 233, 221–228 (2015).
18. 18.
Li, J. et al. First-principles study of Al/Al3Ti heterogeneous nucleation interface. Appl. Surf. Sci. 307, 593–600 (2014).
19. 19.
Wu, S., Dong, Z. & Wu, P. Effect of transition metal (M = Co, Ni, Cu) substitution on electronic structure and vacancy formation of Li3N. J. Mater. Chem. 21(1), 165–170 (2010).
20. 20.
Loo, F. J. J. & Rieck, G. D. Diffusion in the titanium-aluminum system inter-diffusion between solid Al and Ti or Ti-Al alloys. Acta. Metall. 21(1), 61–71 (1973).
21. 21.
Srinivasan, S., Desch, P. B. & Schwarz, R. B. Metastable phases in the Al3X (X = Ti, Zr, and Hf) intermetallic system. Scripta Mater. 25(11), 2513–2516 (1991).
22. 22.
Kohn, W. & Sham, L. J. Self-consistent equations including exchange and correlation effects. Phys. Rev. 140(4A), A1133–A1138 (1965).
23. 23.
Sridharan, S. & Nowotny, H. Studies in the ternary system Ti-Ta-Al and in the quaternary system Ti-Ta-Al-C. Z. Metallkd. 74, 468–472 (1983).
24. 24.
Shannon, R. D. Revised effective ionic radii and systematic studies of interatomic distances in halides and chalcogenides. Acta Crystallogr. 32(5), 751–767 (1976).
25. 25.
Allred, A. L. & Rochow, E. G. Electronegativities of carbon, silicon, germanium, tin and lead. J. Inorg. Nucl. Chem. 5(4), 269–288 (1958).
## Acknowledgements
The authors acknowledge the computational resources from the National Supercomputing Center in Tianjin (TH-1A system). P. Wu’s work on mechanical modeling is partially supported by the National Research Foundation, Prime Minister’s Office, Singapore, under its Marine Science Research & Development Programme (Award Number MSRDP-P28).
## Author information
### Affiliations
• Mingke Zhu
• & Ben Xu
2. #### Graduate School at Shenzhen, Tsinghua University, Shenzhen, 518055, P. R. China
• Mingke Zhu
• & Qiulin Li
• Ping Wu
### Contributions
M.K.Z., P.W., X.B. and Q.L.L. designed and coordinated the overall study. M.K.Z. and P.W. wrote the manuscript. Z.M.K. performed theoretical calculations with the help from P.W., X.B. and Q.L.L. All contributed to the discussions of the results.
### Competing Interests
The authors declare that they have no competing interests.
### Corresponding authors
Correspondence to Ping Wu or Qiulin Li.
|
2018-12-16 01:11:15
|
{"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": 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": 0.6581588387489319, "perplexity": 4696.336385844695}, "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-2018-51/segments/1544376827175.38/warc/CC-MAIN-20181216003916-20181216025916-00082.warc.gz"}
|
https://www.esaral.com/q/if-the-first-term-of-an-a-p-is-2-and-common-difference-is-4-23596/
|
If the first term of an A.P. is 2 and common difference is 4,
Question:
If the first term of an A.P. is 2 and common difference is 4, then the sum of its 40 terms is
(a) 3200
(b) 1600
(c) 200
(d) 2800
Solution:
In the given problem, we need to find the sum of 40 terms of an arithmetic progression, where we are given the first term and the common difference. So, here we use the following formula for the sum of n terms of an A.P.,
$S_{n}=\frac{n}{2}[2 a+(n-1) d]$
Where; a = first term for the given A.P.
d = common difference of the given A.P.
= number of terms
Given,
First term (a) = 2
Common difference (d) = 4
Number of terms (n) = 40
So, using the formula we get,
$S_{40}=\frac{40}{2}[2(2)+(40-1)(4)]$
$=(20)[4+(39)(4)]$
$=(20)[4+156]$
$=(20)(160)$
$=3200$
Therefore, the sum of first 40 terms for the given A.P. is $S_{40}=3200$. So, the correct option is (a).
Administrator
|
2022-01-20 19:12:04
|
{"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": 0.7557240128517151, "perplexity": 294.5421154691664}, "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-2022-05/segments/1642320302622.39/warc/CC-MAIN-20220120190514-20220120220514-00508.warc.gz"}
|
https://www.albert.io/learn/linear-algebra/question/spans-of-dollaradollar-and-dollarbdollar
|
Limited access
Suppose that $A,B$ are subsets of a vector space $V$ and that the span of $A$ is a proper subset of the span of $B$.
Which of the following are POSSIBLE?
Select ALL that apply.
A
$A$ is a subset of $B$.
B
$B$ is a subset of $A$.
C
$A=B$
D
$A\cap B=\emptyset$
E
$A$ is not a subset of $B$ nor is $B$ a subset of $A$. However, $A\cap B\neq \emptyset$.
Select an assignment template
|
2017-04-29 17:28:44
|
{"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": 0.7248470187187195, "perplexity": 206.36134744989815}, "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-2017-17/segments/1492917123549.87/warc/CC-MAIN-20170423031203-00023-ip-10-145-167-34.ec2.internal.warc.gz"}
|
https://handwiki.org/wiki/Conditional_dependence
|
# Conditional dependence
A Bayesian network illustrating conditional dependence
In probability theory, conditional dependence is a relationship between two or more events that are dependent when a third event occurs.[1][2] For example, if $\displaystyle{ A }$ and $\displaystyle{ B }$ are two events that individually increase the probability of a third event $\displaystyle{ C, }$ and do not directly affect each other, then initially (when it has not been observed whether or not the event $\displaystyle{ C }$ occurs)[3][4] $\displaystyle{ \operatorname{P}(A \mid B) = \operatorname{P}(A) \quad \text{ and } \quad \operatorname{P}(B \mid A) = \operatorname{P}(B) }$ ($\displaystyle{ A \text{ and } B }$ are independent).
But suppose that now $\displaystyle{ C }$ is observed to occur. If event $\displaystyle{ B }$ occurs then the probability of occurrence of the event $\displaystyle{ A }$ will decrease because its positive relation to $\displaystyle{ C }$ is less necessary as an explanation for the occurrence of $\displaystyle{ C }$ (similarly, event $\displaystyle{ A }$ occurring will decrease the probability of occurrence of $\displaystyle{ B }$). Hence, now the two events $\displaystyle{ A }$ and $\displaystyle{ B }$ are conditionally negatively dependent on each other because the probability of occurrence of each is negatively dependent on whether the other occurs. We have[5] $\displaystyle{ \operatorname{P}(A \mid C \text{ and } B) \lt \operatorname{P}(A \mid C). }$
Conditional dependence is different from conditional independence. In conditional independence two events (which may be dependent or not) become independent given the occurrence of a third event.[6]
## Example
In essence probability is influenced by a person's information about the possible occurrence of an event. For example, let the event $\displaystyle{ A }$ be 'I have a new phone'; event $\displaystyle{ B }$ be 'I have a new watch'; and event $\displaystyle{ C }$ be 'I am happy'; and suppose that having either a new phone or a new watch increases the probability of my being happy. Let us assume that the event $\displaystyle{ C }$ has occurred – meaning 'I am happy'. Now if another person sees my new watch, he/she will reason that my likelihood of being happy was increased by my new watch, so there is less need to attribute my happiness to a new phone.
To make the example more numerically specific, suppose that there are four possible states $\displaystyle{ \Omega = \left\{ s_1, s_2, s_3, s_4 \right\}, }$ given in the middle four columns of the following table, in which the occurrence of event $\displaystyle{ A }$ is signified by a $\displaystyle{ 1 }$ in row $\displaystyle{ A }$ and its non-occurrence is signified by a $\displaystyle{ 0, }$ and likewise for $\displaystyle{ B }$ and $\displaystyle{ C. }$ That is, $\displaystyle{ A = \left\{ s_2, s_4 \right\}, B = \left\{ s_3, s_4 \right\}, }$ and $\displaystyle{ C = \left\{ s_2, s_3, s_4 \right\}. }$ The probability of $\displaystyle{ s_i }$ is $\displaystyle{ 1/4 }$ for every $\displaystyle{ i. }$
Event $\displaystyle{ \operatorname{P}(s_1)=1/4 }$ $\displaystyle{ \operatorname{P}(s_2)=1/4 }$ $\displaystyle{ \operatorname{P}(s_3)=1/4 }$ $\displaystyle{ \operatorname{P}(s_4)=1/4 }$ Probability of event
$\displaystyle{ A }$ 0 1 0 1 $\displaystyle{ \tfrac{1}{2} }$
$\displaystyle{ B }$ 0 0 1 1 $\displaystyle{ \tfrac{1}{2} }$
$\displaystyle{ C }$ 0 1 1 1 $\displaystyle{ \tfrac{3}{4} }$
and so
Event $\displaystyle{ s_1 }$ $\displaystyle{ s_2 }$ $\displaystyle{ s_3 }$ $\displaystyle{ s_4 }$ Probability of event
$\displaystyle{ A \cap B }$ 0 0 0 1 $\displaystyle{ \tfrac{1}{4} }$
$\displaystyle{ A \cap C }$ 0 1 0 1 $\displaystyle{ \tfrac{1}{2} }$
$\displaystyle{ B \cap C }$ 0 0 1 1 $\displaystyle{ \tfrac{1}{2} }$
$\displaystyle{ A \cap B \cap C }$ 0 0 0 1 $\displaystyle{ \tfrac{1}{4} }$
In this example, $\displaystyle{ C }$ occurs if and only if at least one of $\displaystyle{ A, B }$ occurs. Unconditionally (that is, without reference to $\displaystyle{ C }$), $\displaystyle{ A }$ and $\displaystyle{ B }$ are independent of each other because $\displaystyle{ \operatorname{P}(A) }$—the sum of the probabilities associated with a $\displaystyle{ 1 }$ in row $\displaystyle{ A }$—is $\displaystyle{ \tfrac{1}{2}, }$ while $\displaystyle{ \operatorname{P}(A\mid B) = \operatorname{P}(A \text{ and } B) / \operatorname{P}(B) = \tfrac{1/4}{1/2} = \tfrac{1}{2} = \operatorname{P}(A). }$ But conditional on $\displaystyle{ C }$ having occurred (the last three columns in the table), we have $\displaystyle{ \operatorname{P}(A \mid C) = \operatorname{P}(A \text{ and } C) / \operatorname{P}(C) = \tfrac{1/2}{3/4} = \tfrac{2}{3} }$ while $\displaystyle{ \operatorname{P}(A \mid C \text{ and } B) = \operatorname{P}(A \text{ and } C \text{ and } B) / \operatorname{P}(C \text{ and } B) = \tfrac{1/4}{1/2} = \tfrac{1}{2} \lt \operatorname{P}(A \mid C). }$ Since in the presence of $\displaystyle{ C }$ the probability of $\displaystyle{ A }$ is affected by the presence or absence of $\displaystyle{ B, A }$ and $\displaystyle{ B }$ are mutually dependent conditional on $\displaystyle{ C. }$
|
2022-10-01 07:31:09
|
{"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": 0.7565104365348816, "perplexity": 251.53861736382214}, "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/1664030335573.50/warc/CC-MAIN-20221001070422-20221001100422-00261.warc.gz"}
|
https://stats.stackexchange.com/questions/109861/exact-central-confidence-interval-for-a-correlation
|
# Exact central confidence interval for a correlation
I am working my way through (T.J. Diccio & B. Efron, "Bootstrap Confidence Intervals", Statistical Science, 1996, 11(3), 189–228), and I'm stuck even before I get to the good stuff.
In the introduction, there is a table of before/after treatment values called cd4, and the correlation $\hat\theta$ is given as 0.723. The paper then states, "We can find an exact interval for $\theta$ if we are willing to assume bivariate normality ... The exact central 90% interval is (0.47, 0.86)."
Here I stipulate that I am a stats moron. When I key in the data and compute a confidence interval by hand in R, either using the Fisher transform or the T distribution, I don't get that interval. How does one compute the interval they are talking about?
> cd4
subj base oneyr
1 1 2.12 2.47
2 2 4.35 4.61
3 3 3.39 5.26
4 4 2.51 3.02
5 5 4.04 6.36
6 6 5.10 5.93
7 7 3.77 3.93
8 8 3.35 4.09
9 9 4.10 4.88
10 10 3.35 3.81
11 11 4.15 4.74
12 12 3.56 3.29
13 13 3.39 5.55
14 14 1.88 2.82
15 15 2.56 4.23
16 16 2.96 3.23
17 17 2.49 2.56
18 18 3.03 4.31
19 19 2.66 4.37
20 20 3.00 2.40
> r = cor(cd4$base, cd4$oneyr)
> r
[1] 0.7231654
Fisher transform:
> se = 1/sqrt(17)
> se
[1] 0.2425356
> tanh(c(r-1.6448*se, r+1.6448*se))
[1] 0.3133382 0.8082940
T distribution:
> sr = sqrt((1-r^2)/(20-2))
> sr
[1] 0.1627936
> tc = abs(qt(0.05/2, 18))
> c(r-tc*sr, r+tc*sr)
[1] 0.3811486 1.0651821
• This is the approximate interval based on Fisher's Z, it is not exact. Jul 29, 2014 at 17:00
• From Monteverde's answer below, I did the Fisher transform wrong, it should be 'z=atanh(r); tanh(c(zp-1.6448*se, zp+1.6448*se))'. Jul 29, 2014 at 17:07
• Yes, I mean the claim in the paper is wrong: this is not an exact CI. Jul 29, 2014 at 17:10
You can get the same values with:
cor.test(cd4$baseline, cd4$oneyear, method = "pearson", conf.level = 0.9)
The method used to obtain such interval is explained in:
http://stat.ethz.ch/R-manual/R-patched/library/stats/html/cor.test.html
If method is "pearson", the test statistic is based on Pearson's product moment correlation coefficient cor(x, y) and follows a t distribution with length(x)-2 degrees of freedom if the samples follow independent normal distributions. If there are at least 4 complete pairs of observation, an asymptotic confidence interval is given based on Fisher's Z transform.
So, you can implement your own code to obtain C.I. by following these instructions if you wish to do so. See also:
http://en.wikipedia.org/wiki/Pearson_product-moment_correlation_coefficient#Testing_using_Student.27s_t-distribution
• Thank you. Walking through the source to cor.test with my data helped me see I was screwing up the Fisher's Z transform. Jul 29, 2014 at 17:09
You already mentioned that the Fisher transformation is not correct in your code. You first have to transform r to a z value (atanh part), then you add and subtract the standard error with the appropriate multiplier to get the correct confidence (as you did correctly). Finally, you have to transform the whole thing back into the r-metric (tanh part).
se <- 1/sqrt(17)
r <- 0.7231654
tanh(atanh(r)+c(1,-1)*qnorm(.95)*se)
Which results in
[1] 0.8650790 0.4740748
As mentioned in the comments, this is NOT the exact interval! To find an exact interval check out this work by Shieh: http://link.springer.com/10.1007/s11336-04-1221-6
|
2022-08-11 22:06:58
|
{"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": 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": 0.6743176579475403, "perplexity": 1637.1769020267027}, "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-2022-33/segments/1659882571502.25/warc/CC-MAIN-20220811194507-20220811224507-00355.warc.gz"}
|
http://www.zora.uzh.ch/id/eprint/146432/
|
# Observation of the suppressed decay $\Lambda \ _b \ ^0 \to p \pi^- \mu^+ \mu^-$
LHCb Collaboration; Bernet, R; Müller, K; Serra, N; Steinkamp, O; Straumann, U; Vollhardt, A; et al (2017). Observation of the suppressed decay $\Lambda \ _b \ ^0 \to p \pi^- \mu^+ \mu^-$. Journal of High Energy Physics, 04:029.
## Abstract
The suppressed decay $\Lambda \ _b \ ^0 \to p \pi^- \mu^+ \mu^-$, excluding the $J/ \psi$ and $\psi(2S) \to \mu^+ \mu^-$ resonances, is observed for the first time with a significance of 5.5 standard deviations. The analysis is performed with proton-proton collision data corresponding to an integrated luminosity of 3 $fb^{−1}$ collected with the LHCb experiment. The $\Lambda \ _b \ ^0 \to p \pi^- \mu^+ \mu^-$ branching fraction is measured relative to the $\Lambda \ _b \ ^0 \to J/ \psi (\to \mu^+ \mu^-)p \pi^-$ branching fraction giving
$\frac{\mathcal{B}(\Lambda_b^0 \to p \pi^*- \mu^+ \mu^-)}{\mathcal{B}(\Lambda_b^0 \to J/ \psi (\to \mu^+ \mu^-)p \pi^-)} = 0.044 \pm 0.012 \pm 0.007$,
where the first uncertainty is statistical and the second is systematic. This is the first observation of a $b \to d$ transition in a baryonic decay.
## Abstract
The suppressed decay $\Lambda \ _b \ ^0 \to p \pi^- \mu^+ \mu^-$, excluding the $J/ \psi$ and $\psi(2S) \to \mu^+ \mu^-$ resonances, is observed for the first time with a significance of 5.5 standard deviations. The analysis is performed with proton-proton collision data corresponding to an integrated luminosity of 3 $fb^{−1}$ collected with the LHCb experiment. The $\Lambda \ _b \ ^0 \to p \pi^- \mu^+ \mu^-$ branching fraction is measured relative to the $\Lambda \ _b \ ^0 \to J/ \psi (\to \mu^+ \mu^-)p \pi^-$ branching fraction giving
$\frac{\mathcal{B}(\Lambda_b^0 \to p \pi^*- \mu^+ \mu^-)}{\mathcal{B}(\Lambda_b^0 \to J/ \psi (\to \mu^+ \mu^-)p \pi^-)} = 0.044 \pm 0.012 \pm 0.007$,
where the first uncertainty is statistical and the second is systematic. This is the first observation of a $b \to d$ transition in a baryonic decay.
## Statistics
### Citations
Dimensions.ai Metrics
### Altmetrics
Detailed statistics
|
2018-03-22 19:51:58
|
{"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": 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": 0.907795250415802, "perplexity": 1427.825019651278}, "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-2018-13/segments/1521257648000.93/warc/CC-MAIN-20180322190333-20180322210333-00319.warc.gz"}
|
http://www.lofoya.com/Solved/216/the-lcm-of-two-number-is-4800-and-their-hcf-is-160-if-one-number-is
|
# Easy Number System Solved QuestionAptitude Discussion
Q. The LCM of two number is 4800 and their HCF is 160. If one number is 480, then the second number is:
✖ A. 1200 ✖ B. 1500 ✔ C. 1600 ✖ D. 1800
Solution:
Option(C) is correct
Solution:
$\text{HCF × LCM = product of two numbers}$
Hence,$4800×160 = 480×x$
⇒ $x=$ 1600
|
2018-01-18 04:08:19
|
{"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": 0.7215648889541626, "perplexity": 3162.4346610400958}, "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-2018-05/segments/1516084887065.16/warc/CC-MAIN-20180118032119-20180118052119-00457.warc.gz"}
|
https://testbook.com/question-answer/_______-is-the-time-averaged-magnitude-of-th--61654271071f262bb4b73686
|
# _______ is the time-averaged magnitude of the Poynting vector at the upper surface of Earth's atmosphere.
This question was previously asked in
DFCCIL Jr. Executive S&T 27 Sept 2021 Official Paper
View all DFCCIL Junior Executive Papers >
1. Poynting constant
2. Electromagnetic constant
3. Solar constant
4. Maxwell constant
Option 3 : Solar constant
Free
CT 1: Current Affairs (Government Policies and Schemes)
55555
10 Questions 10 Marks 10 Mins
## Detailed Solution
Explanation:
Solar Constant is the time-averaged magnitude of the Poynting vector at the upper surface of Earth's atmosphere.
The Poynting vector (time-averaged) is given by:
$$\left\langle \text{S} \right\rangle \frac{1}{2}\text{C}\epsilon {{\text{ }\!\!~\!\!\text{ }}_{0}}\text{E}_{0}^{2}$$
Solar constant:
• The solar energy reaching unit area at the outer edge of the earth’s atmosphere exposed perpendicularly to the rays of the Sun at the average distance between the Sun and Earth is known as the solar constant.
• It is estimated to be approximately 1.4 kJ per second per square meter or 1.4 kW/m2.
|
2022-01-25 06:05:38
|
{"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": 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": 0.7772193551063538, "perplexity": 3662.1504572163353}, "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-2022-05/segments/1642320304760.30/warc/CC-MAIN-20220125035839-20220125065839-00555.warc.gz"}
|
http://tex.stackexchange.com/questions/57046/zeta-works-zeta-does-not
|
# $\zeta$ works $\Zeta$ does not [duplicate]
Possible Duplicate:
Why can I only use some capital greek letters inside my equations?
Refering to http://wikieducator.org/Help:LaTeX_Symbol_Tables_-_Mathematics, I am trying to enter upper case Zeta into my tex file. When I enter $\zeta$ it compiles the code but when I say $\Zeta$ with upper case Z with a expectation that it would lead to upper case zeta, it does not compile. Am I missing something?
I am using Kile (Version 2.0.85) under Ubuntu (Version 11.04) and using Latex to compile the code. All other symbols like Uppercase Omega are not causing any problem.
-
## marked as duplicate by clemens, Werner, ienissei, Kurt, Martin SchröderDec 6 '12 at 22:35
The uppercase Zeta is Z, so simply write Z. – Stefan Kottwitz May 23 '12 at 12:22
Ohh is it? I am just being stupid. I should have thought about it. I just copied the code on the web link mentioned above. – maths-help-seeker May 23 '12 at 12:26
– Yiannis Lazarides May 23 '12 at 12:27
If you like, edit that Wiki page and correct it, if it's publicly editable. I made an answer from my comment. – Stefan Kottwitz May 23 '12 at 12:28
yes I think I should – maths-help-seeker May 23 '12 at 12:28
The uppercase Zeta is Z, so simply write Z. You may define \Zeta yourself, such as
\newcommand{\Zeta}{Z}
or
\newcommand{\Zeta}{\mathrm{Z}}
Using $Z$ is good enough for me. Thanks! – maths-help-seeker May 23 '12 at 12:29
|
2015-06-30 08:48:19
|
{"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": 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": 0.9598233103752136, "perplexity": 3177.9939621085937}, "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-2015-27/segments/1435375091925.14/warc/CC-MAIN-20150627031811-00172-ip-10-179-60-89.ec2.internal.warc.gz"}
|
https://networkx.org/documentation/stable/reference/generated/networkx.generators.social.karate_club_graph.html
|
# networkx.generators.social.karate_club_graph¶
karate_club_graph()[source]
Returns Zachary’s Karate Club graph.
Each node in the returned graph has a node attribute ‘club’ that indicates the name of the club to which the member represented by that node belongs, either ‘Mr. Hi’ or ‘Officer’.
Examples
To get the name of the club to which a node belongs:
>>> G = nx.karate_club_graph()
>>> G.nodes[5]["club"]
'Mr. Hi'
>>> G.nodes[9]["club"]
'Officer'
References
1
Zachary, Wayne W. “An Information Flow Model for Conflict and Fission in Small Groups.” Journal of Anthropological Research, 33, 452–473, (1977).
2
|
2021-06-15 13:46:01
|
{"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": 0.1742447316646576, "perplexity": 8966.137121744434}, "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/1623487621273.31/warc/CC-MAIN-20210615114909-20210615144909-00574.warc.gz"}
|
http://mathoverflow.net/revisions/79921/list
|
4 added 2 characters in body
Consider real polynomials on the interval $I=[-1,1]$. It is easy to see that the smallest degree for a non-negative polynomial with given zeros $x_1,\dots,x_s\in I^\circ$ is $n=2s$ (e.g. $P(x) = \prod_{i=1}^s (x-x_i)^2$ works).
My question is:
What is the smallest degree for a polynomial such that it is bounded by $\pm 1$ on $I$ and attains the value $1$ on a set $x_1^+,\dots,x_s^+$ and the value $-1$ on a set $x_1^-,\dots,x_r^-$?
Background: I know that the fact about nonnegative polynomials with presribed zeros can be generalized to "generalized polynomials" built from Tchebycheff-systems (due to a theorem by Krein). I would love to see a similar theorem on bounded generalized polynomials which attain the bounds at prescribed points.
Edit: In this question I leanerd from the answer of Gjergji Zaimi that there are bounds on the degree of increasing interpolating polyomials. How does the bounds change for monotone interpolation are described above? Are the there (algebraical or numerical) methods to calculate the polynomial?
It seems to me that monotone interpolating polynomials are not treated in the current literature and are not subject of current research. Is that right, and if so is there a special reason for that?
3 corrected title.
# Polynomials with with prescribed points to match prescribed bounds
Consider real polynomials on the interval $I=[-1,1]$. It is easy to see that the smallest degree for a non-negative polynomial with given zeros $x_1,\dots,x_s\in I^\circ$ is $n=2s$ (e.g. $P(x) = \prod_{i=1}^s (x-x_i)^2$ works).
My question is:
What is the smallest degree for a polynomial such that it is bounded by $\pm 1$ on $I$ and attains the value $1$ on a set $x_1^+,\dots,x_s^+$ and the value $-1$ on a set $x_1^-,\dots,x_r^-$?
Background: I know that the fact about nonnegative polynomials with presribed zeros can be generalized to "generalized polynomials" built from Tchebycheff-systems (due to a theorem by Krein). I would love to see a similar theorem on bounded generalized polynomials which attain the bounds at prescribed points.
Edit: In this question I leanerd from the answer of Gjergji Zaimi that there are bounds on the degree of increasing interpolating polyomials. How does the bounds change for monotone interpolation are described above? Are the (algebraical or numerical) method methods to calculate the polynomial?
It seems to me that monotone interpolating polynomials are not treated in the current literature and are not subject of current research. Is that right, and if so is there a special reason for that?
Consider real polynomials on the interval $I=[-1,1]$. It is easy to see that the smallest degree for a non-negative polynomial with given zeros $x_1,\dots,x_s\in I^\circ$ is $n=2s$ (e.g. $P(x) = \prod_{i=1}^s (x-x_i)^2$ works).
My question is:
What is the smallest degree for a polynomial such that it is bounded by $\pm 1$ on $I$ and attains the value $1$ on a set $x_1^+,\dots,x_s^+$ and the value $-1$ on a set $x_1^-,\dots,x_r^-$?
Background: I know that the fact about nonnegative polynomials with presribed zeros can be generalized to "generalized polynomials" built from Tchebycheff-systems (due to a theorem by Krein). I would love to see a similar theorem on bounded generalized polynomials which attain the bounds at prescribed points.
Edit: In this question I leanerd from the answer of Gjergji Zaimi that there are bounds on the degree of increasing interpolating polyomials. How does the bounds change for monotone interpolation are described above? Are the (algebraical or numerical) method to calculate the polynomial?
It seems to me that monotone interpolating polynomials are not treated in the current literature and are not subject of current research. Is that right, and if so is there a special reason for that?
1
|
2013-05-24 17:01:29
|
{"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": 0.7199468016624451, "perplexity": 288.21599093128384}, "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/1368704818711/warc/CC-MAIN-20130516114658-00019-ip-10-60-113-184.ec2.internal.warc.gz"}
|
https://violinsandvodka.wordpress.com/2015/10/18/she-blackened-every-rainbow-and-painted-over-every-scar/
|
# “muse”
“if you can’t be the artist, be the art.” \\ she’s got eyes like drops of turpentine and skin like a canvas. \\ watercolour cheeks and palettes for teeth; she is art. \\ she’s as soft as pastels but wild like acrylic. \\ she is the goddess the Greeks forgot to write about; the Beatles song that never made the album; the lost treasure that should, perhaps, stay lost. \\ she’ll paint herself into your dreams, but she can never paint herself pretty. \\ “when you leave, leave me with some kind of mark that you weren’t just my mind playing sick tricks on me.” \\ she is a mosaic of memories; so broken yet so beautiful. \\ stained glass only makes her look holier. \\ she turns paper into origami, all you can do is crumple it. \\ loving her was like burning gold, like fire-engine red, like smokey silver. \\ the first time you saw her blush, was the first time you truly understood how one colour could be so important. \\ she runs her fingertips over your back like they’re the softest brushes you’ve ever known; she makes you feel like a masterpiece. \\ you want to graffiti her lips all over town so people know what danger looks like. \\ “but where do we draw the line between love and lunacy?” \\ she’s got a pencil behind one ear and an eraser behind the other. \\ you’re just a paint spill, a wrong hue, a mistake. \\ don’t kiss her; she’ll leave paint in your hair and a lie on your lips. \\ losing her was like alcohol amber, like lighting-strike white, like raven black. \\” after a while you’ll see, blood looks a lot like red paint.” \\
{A/N- Part 3 of The Girls From Yesterday series.}
|
2017-07-25 08:40:22
|
{"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": 0.9999978542327881, "perplexity": 7526.239278179355}, "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-2017-30/segments/1500549425117.42/warc/CC-MAIN-20170725082441-20170725102441-00145.warc.gz"}
|
https://kgreresearch.wordpress.com/2010/09/29/how-the-average-height-profile-evolves-over-time/
|
# Kris's Research Notes
## September 29, 2010
### How the average height profile evolves over time.
Filed under: Stat. Mech for SOS Model — Kris Reyes @ 6:47 am
Recall we defined the average height profile
$\bar h_i(t) = \mathbb E_{P(t)} [h_i] = \displaystyle \sum_{h \in \mathcal X} h_i P(t;h)$.
If we approximated $P(t)$ with the local equilibrium distribution
$\displaystyle \pi_{leq}(t;h) = \frac{1}{\Xi} \exp\left[\beta (H(h) - \sum_{i=1}^N \mu_i h_i\right],$
we showed that $\bar h$ evolves approximately like
$\displaystyle \frac{d\bar h_k}{dt} =\frac{\Omega}{2} \left(e^{\beta\mu_{k-1}} - 2 e^{\beta\mu_k} + e^{\beta \mu_{k+1}}\right),$
for $k=2, \hdots, N-1$ and
$(1) \displaystyle \frac{d\bar h_1}{dt} =\frac{\Omega}{2} \left( - e^{\beta\mu_1} + e^{\beta \mu_2}\right),$
and
$(2) \displaystyle \frac{d\bar h_N}{dt} = \frac{\Omega}{2} \left( e^{\beta\mu_{N-1}} - e^{\beta\mu_N}\right).$
Here, $\Omega$ is the prefactor used in the hopping rate
$(3) \displaystyle r (h, h-e_i+e_{i\pm 1}) = \Omega e^{\beta[H(h) - H(h(i))]} = \Omega e^{-\beta\gamma(n_i(h)-2)},$
where $n_i(h)$ is the number of bonds the top atom at site $i$ has. If instead we wished to use the number of lateral neighbors, $\ell_i(h)$, then $n_i(h) = \ell_i(h)+1$ and the rates are given by
$\displaystyle r (h, h-e_i+e_{i\pm 1}) = \Omega e^{-\beta\gamma(\ell_i(h)-1)} = \Omega e^{\beta\gamma}e^{-\beta\gamma \ell_i(h)}.$
We make this point because in KMC simulations, we often define rates in terms of $\ell_i(h)$. For example, in our current simulation we set our rates such that $\Omega e^{\beta\gamma} = 5\times 10^7$, hence in our analysis we must fix $\Omega = e^{-\beta\gamma}5\times 10^7$. With $\gamma = 0.25$, this means $\Omega = 2.748\times 10^6.$ Note this is a large number.
Consider the average profile near equilibrium. Here the average profile does not change much in space ($\bar h_i - \bar h_{i-1} \approx 0$) or time ($\frac{d\bar h}{dt} \approx 0$). Then
$m_i = kT \mathcal M(\bar h_i - \bar h_{i-1}) = kt \mathcal M(\epsilon).$
Consider $kT \mathcal M(x)$ near $x = 0$:
Observe the $m_i$ are small even for (relatively) large difference in height profile. Then the $mu_i = -(m_{i+1} - m_i)$ are also small. Using the above graph as an example, we see that near equilibrium $\mu_i \in [-0.3,0.3]$ with high probability. In equilibrium all the $\mu_i$ are equal and so, by examining equations (1), (2), and (3) we see that $\frac{d\bar{h_i}}{dt} = 0$ in this case.
Now consider the system not near equilibrium. In particular, suppose we had the following height profile:
We wish to consider how our model predicts it will evolve with respect to the equations (1), (2), and (3) above. To that end, consider the plot of $e^{\beta \mu_i}$ where the $\mu_i$ are calculated from this average profileAs we see, the values are somewhat close together — but not close enough! That is, consider $\displaystyle \frac{1}{\Omega/2} \frac{d\bar h}{dt}$, the unnormalized rates:
When we scale by $\Omega/2 \approx 10^6$ we see that $\frac{d\bar h}{dt}$ is very large! This could leads to some unstable behavior if we try to evolve $\frac{d\bar h}{dt}$ using e.g Euler’s Method.
|
2018-06-20 10:56:21
|
{"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": 34, "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": 0.8703176379203796, "perplexity": 549.8285328716744}, "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-2018-26/segments/1529267863518.39/warc/CC-MAIN-20180620104904-20180620124904-00132.warc.gz"}
|
https://calculator.academy/draw-down-ratio-calculator/
|
Enter the diameter of the extrusion die, the diameter of the product, the core diameter, and the outside diameter of the tip into the Draw Down Ratio Calculator. The calculator will evaluate and display the Draw Down Ratio.
## Draw Down Ratio Formula
The following formula is used to calculate the Draw Down Ratio.
DDR = (DD/PD) / (DT/CD)
• Where DDR is the Draw Down Ratio ( )
• DD is the diameter of the extrusion die
• PD is the diameter of the product
• DT is the outside diameter of the tip
• CD is the core diameter
## How to Calculate Draw Down Ratio?
The following example problems outline how to calculate Draw Down Ratio.
Example Problem #1
1. First, determine the diameter of the extrusion die.
• The diameter of the extrusion die is calculated to be : 5.
2. Next, determine the diameter of the product.
• The diameter of the product is measured to be: 2.
3. Next, determine the outside diameter of the tip.
• The outside diameter of the tip is found to be: 3.
4. Next, determine the core diameter.
• This is measured to be 1.
5. Finally, calculate the Draw Down Ratio using the formula above:
DDR = (DD/PD) / (DT/CD)
The values given above are inserted into the equation below and the solution is calculated:
DDR = (5/2) / (3/1) = 8.33
Example Problem #2
The variables required for this problem are provided below:
diameter of the extrusion die = 6
diameter of the product = 7
outside diameter of the tip = 8
cored diameter = 4
|
2023-03-29 03:18:14
|
{"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": 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": 0.7101565599441528, "perplexity": 1872.360893013302}, "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/1679296948932.75/warc/CC-MAIN-20230329023546-20230329053546-00714.warc.gz"}
|
https://quant.stackexchange.com/questions/46233/understanding-value-at-risk-correclty
|
# understanding Value-at-Risk correclty
The are several types how to calculate the VaR. I am focussing on the method of calculation the VaR in percentage.
$$VaR=I*z*std*\sqrt{t}$$
This gives the VaR in €.
I have the z-value, the daily standard deviation std, the holding period t, the investment I. Now let's assume the holding period is one year, that ist 258 trading days for which I have the daily standard deviation. So I multiply the whole thing by root(258). My results are reasonable.
Now to get the percentage of VaR as rate of the Investment, I will devide by I, which then will be cancelled out.
Now, I increase the holding period by, say 10 years. t becomes 2580. VaR in percentage becomes extremely large. Of course the Investment grows over time. Since it gets cancelled out, I can't grow it.
The VaR should be the rate of the average investment amount, right?
So I am struggling to implement the rate of VaR for a dynamic investment over a longer time horizon. Can anybody help me please or am I completely mistaken by the usage of VaR?
Scaling volatility (standard deviation) is not the best option while calculating long term VaR. This has been discussed extensively in this post. See this page for the paper by Diebold et al. (1996).
Keep in mind that long term volatility is believed to mean revert to its long term average. So if an investment is currently in high volatility regime, then VaR calculated based on scaling this volatility is going to be misleading.
What you can do here is to change the sampling frequency to weekly/monthly to somewhat remedy the scaling issue. Then you can also incorporate your expected return on your Investment $$I$$ for the holding period into the VaR equation:
$$VaR = I\times \mu + I\times z \times \sigma \times \sqrt{t}$$
• Thanks for your answer! I use daily volatility as average of a time horizon. I habe daily volatility of 30 years if daran. So an average should Matchathe long Term average of another 30 years and even the expected volatility of shorter time horizon. So I was missing the fact that the return reduces the right Part. My approach now would be to scale volatility to 10 years and also scale return to years. Could I do that? For now I ignore autocorrelated volatility but might consider it later. – Chris H. Jun 23 '19 at 14:44
• I think if you are going to use the daily average for 30 years, you are still up against the issue of scaling (i.e. you are still going to use the square root rule). But if you can find annual average volatility for 30 years and then scale it, this may be a better option. Have you tried monthly/quarterly sampling? – AK88 Jun 23 '19 at 17:29
• Actually, I prefer daily data, since I am analysing everything based on daily returns. However I am quite interested in arguments why daily data isnt that good. I have read the thread in your link. Unfortunately the paper linked there is not availabe. It would be great if you have any paper that argues against daily data. Then, I rearranged my data to yearly returns and calculated the volatily for 30 years based on annual data and based on daily data. Interestingly the opposite of what your link tells happened. Volatility increases when scaling annual data – Chris H. Jun 23 '19 at 17:49
• You can find the paper in the body of my post (Diebold et al. (1996)). Do you mind sharing how did you calculate the annual returns and how did you scale them to 10 years horizon? I mean if you look at 30 year daily and monthly S&P500 returns as of today and scale them to 10 years you'd get 45% volatility for monthly sampling frequency and 55% volatility for daily sampling frequency. – AK88 Jun 23 '19 at 18:11
• Thanks for the paper, I'll read it in a sec. For annual returns I took the price of say 1.1.1988 and 1.1.1989. I chose +/-1 or 2 days if there wasnt any price at the specific date. Then I took the log return for annual as well as for daily data: ln(price(t)/price(t-1)). I know that log return should only be used for small returns. But simple returns would worsen the problem. I computed the mean of the series. Yearly log return can be scaled to 30 years through yearly_return*30. Daily returns can be scaled to 300 years through daily_return*30*258. – Chris H. Jun 23 '19 at 18:31
Let's $$\Phi$$ represent the standard normal CDF, and q the required var quantile (e.g., 95%) so your $$z=\Phi^{-1}\left(q\right)$$.
Now assume the return x is normally distributed with annualised mean $$\mu$$ and annualised standard deviation $$\sigma$$. By the way you can annualise your daily volatility by scaling it by $$\sqrt{258}$$ because we are in simple normal distribution world, and you are assuming 258 days in a year. So we can write the quantile as follows:
$$\Phi \left(\frac{x_q-\mu t}{\sigma \sqrt{t}}\right)=q$$
We can rearrange,
$$x_q=\mu t+{\sigma \sqrt{t}}\Phi^{-1} \left(q\right)$$
So it is similar to your formula but with a drift. But please note t here is measured in years, and $$\mu$$ and $$\sigma$$ are annualised.
For smaller holding periods such as 1 day, you can ignore the mean/drift, but this becomes significant for longer holding periods. So as you increase the holding period, the process drift (upward or downward depending on the sign) and the variance grows. If you assume zero drift, the VaR will grow with the holding period. Which is intuitive because holding a stock, which is risky asset, for 10 years can make you a lot richer (or poorer!). But if you think the variance is growing too fast than could be considered realistic, then you can consider alternative specifications for the return process. In the interest rate world, an alternative mean reverting specification is more common, so the variance grows with horizon but at a deceasing rate. The simplest examples is the Vasicek model and is based on the Ornstein Uhlenback process, but I can see your question relates to simple settings so won’t go there.
There is also a chance you might be referring to the holding period as the length of the observation windows that you used to estimate the daily volatility. If that's the case, then just changing the observation window shall not by itself increase the VaR because we are annualising the volatility (the annual variance will be 258 times the daily variance under the above assumptions, irrespective of whether you estimate it using 258 days period or 2580 days period).
|
2021-05-14 23:48:06
|
{"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": 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": 12, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7502614259719849, "perplexity": 852.2980212388322}, "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/1620243991829.45/warc/CC-MAIN-20210514214157-20210515004157-00625.warc.gz"}
|
https://begeeben.wordpress.com/2012/08/20/why-do-subtrees-have-size-at-most-2n3/
|
RSS
## Why do subtrees have size at most 2n/3
20 Aug
Considering the worst case running time of Max-Heapify. At page 155 of Introduction to Algorithms 3rd edition, “The children’s subtrees each have size at most 2n/3 — the worst case occurs when the bottom level of the tree is exactly half full…”. Here’s the explanation why the size is at most 2n/3.
Heap is a complete binary tree. For a Heap of n nodes and x levels in the worst case scenario(the bottom level of the tree is exactly half full), the size of right subtree is(by the formula of geometric series):
$1+2+2^2+...+2^{x-3} =\frac{2^{x-2}-1}{2-1} =2^{x-2}-1$
The size of left subtree is:
$1+2+2^2+...+2^{x-3}+2^{x-2}=(2^{x-2}-1)+2^{x-2}=2\times2^{x-2}-1$
Since $n=(size\ of\ left\ subtree)+(size\ of\ right\ subtree)+1$
$n=(1+2+2^2+...+2^{x-3}+2^{x-2})+(1+2+2^2+...+2^{x-3})+1$
$n=(2\times2^{x-2}-1)+(2^{x-2}-1)+1$
$n=3\times2^{x-2}-1$
So$2^{x-2}=\frac{n+1}{3}$
$size\ of\ left\ subtree=2\times2^{x-2}-1=\frac{2n}{3}-\frac{1}{3}$
That’s why the children’s subtrees each have size at most 2n/3.
Advertisements
1 Comment
Posted by on August 20, 2012 in Algorithm
### One response to “Why do subtrees have size at most 2n/3”
1. February 18, 2016 at 9:14 AM
But 2n/3 holds for only 1 level of recursion right?
|
2017-06-27 06:51:13
|
{"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": 8, "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": 0.7122570872306824, "perplexity": 1101.601544452099}, "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-2017-26/segments/1498128321025.86/warc/CC-MAIN-20170627064714-20170627084714-00346.warc.gz"}
|
https://calapp.blogspot.com/2016/03/people-v-appleton-cal-ct-app-march-15.html
|
## Tuesday, March 15, 2016
### People v. Appleton (Cal. Ct. App. - March 15, 2016)
You get used to seeing a certain pattern in these types of cases. Today's opinion breaks the pattern in a couple of different ways:
"At the time of the offense, defendant was a 43-year-old computer technology worker in Mountain View. In July 2013, John Doe contacted the police and made the following statement. In early 2013, he met defendant through Grindr. Doe was 16 years old at the time. For several months, defendant and Doe maintained a consensual relationship that involved kissing, handholding, and sleeping together, but no further sexual conduct. In July 2013, Doe stayed at defendant’s residence for several days. Around midnight on July 12, defendant and Doe were sleeping in defendant’s bed when two male friends of defendant entered the bedroom. The three men forced Doe to orally copulate them over a period of about 15 to 20 minutes. Doe left the residence at around 1:00 a.m. and called the police later that night. He told another witness one of the men had forcibly sodomized him.
Doe declined a SART exam. After he expressed suicidal thoughts, he was taken into custody under Welfare and Institutions Code section 5150.
Police interviewed Doe several days later. He made the following statement, which differed in some respects from his initial statement. He had met defendant on Grindr one year earlier, but they did not start dating until February 2013. At that time, defendant bought Doe an iPhone and performed oral sex on him. Defendant performed oral sex on Doe three other times, and the two slept together for a period of several days, but they engaged in no other sexual conduct. Doe reiterated that defendant and two of defendant’s friends forced him to orally copulate them in July 2013 when Doe was sleeping in defendant’s bed. Doe declined to make a pretext call."
The charges, and the disposition, are different than you might initially expect as well. No charges for rape. And a favorable deal:
"The prosecution charged defendant by felony complaint with oral copulation with a minor. (Pen. Code, § 288a, subd. (b)(1).) The parties entered a plea agreement whereby defendant pleaded no contest to false imprisonment by means of deceit (Pen. Code, §§ 236, 237, subd. (a)) in exchange for formal probation, credit for time served, and dismissal of the oral copulation count. In accord with the plea agreement, the trial court suspended imposition of sentence and granted a three-year term of probation to include a jail sentence of 236 days."
Presumably no sex offender registration either.
Not your usual case of this type.
|
2021-12-04 19:54:48
|
{"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": 0.8169381022453308, "perplexity": 9858.402660273856}, "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-2021-49/segments/1637964363006.60/warc/CC-MAIN-20211204185021-20211204215021-00046.warc.gz"}
|
https://stats.stackexchange.com/tags/multicollinearity/new
|
# Tag Info
This is called an opportunity for restructuring your regression equation. For example, why not do this: $$GDP/Pop = \beta_0 + \beta_2 X_2 + \beta_3 X_3$$ Then you only have to multiply to the population to get GDP estimates. OR $$log(GDP / Pop) = \beta_0 + \beta_2 X_2 + \beta_3 X_3$$ which is effectively: $$log(GDP) = log(Pop) + \beta_0 + \beta_2 X_2 + ... 1 Coefficient change Let some there be some data distributed according to a quadratic curve:$$y \sim \mathcal{N}(\mu = a+bx+cx^2, \sigma^2 = 10^{-3})$$For instance with x \sim \mathcal{U}(0,1) and a=0.2, b=0 and c=1. Then a linear curve and a polynomial curve will have very different coefficients for the linear term. set.seed(1) x <- runif(100, 0,... 3 The ordinary least squares solution is simply given by:$$\beta = (X'X)^{-1}X'y Let's imagine we augment $X_{n\times p}$ with one or more variables $\tilde X_{n\times \tilde p}$, appending its corresponding values as columns, and call the resulting matrix ${X^*}_{n\times p^*}$, $p^* = p + \tilde p$. Now, given enough degrees of freedom, coefficients will ...
|
2021-01-22 10:12:42
|
{"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": 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": 0.9427948594093323, "perplexity": 1014.0715791524486}, "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-2021-04/segments/1610703529179.46/warc/CC-MAIN-20210122082356-20210122112356-00557.warc.gz"}
|
https://socratic.org/questions/what-is-the-axis-of-symmetry-and-vertex-for-the-graph-y-8-2-x-3-2#362318
|
# What is the axis of symmetry and vertex for the graph y-8=-2(x-3)^2?
Jan 9, 2017
See explanation
#### Explanation:
$\textcolor{b r o w n}{\text{There is a shortcut to this that is part of completing the square}}$
You need the form of $y = a {x}^{2} + b x + c$
x_("vertex")=(-1/2)xxb/a -> "axis of symmetry"
Given:$\text{ } y - 8 = - 2 {\left(x - 3\right)}^{2}$
$\implies y = - 2 \left({x}^{2} - 6 x + 9\right) + 8$
$\implies y = - 2 {x}^{2} + 12 x - 10$
so ${x}_{\text{vertex}} = \left(- \frac{1}{2}\right) \times \frac{12}{- 2} = + 3$
|
2021-10-28 04:35:03
|
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 7, "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": 0.40678682923316956, "perplexity": 5987.821825117044}, "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-2021-43/segments/1634323588257.34/warc/CC-MAIN-20211028034828-20211028064828-00579.warc.gz"}
|
https://mailman.ntg.nl/pipermail/ntg-context/2022/105623.html
|
# [NTG-context] Is there a "smart" capitalisation implementation?
Hans Hagen j.hagen at xs4all.nl
Sun May 8 11:20:42 CEST 2022
On 5/8/2022 6:55 AM, Zhichu via ntg-context wrote:
> Hi,
>
> I am going to convince the Board of a journal to consider ConTeXt as an
> I want to make a module before I say anything. Right now I have this
> title problem.
>
> The journal requires the titles to be CAPITALISED, except for the
> acronyms. I'm currently
> using backticks...to wrap it and replace it with\egroup
> ...\WORD\bgroup{} with
> lpeg. This kinda works, but that's so ugly. Besides, the actual story is
> that I also want to
> add markdown as an option, so the backticks actually have meanings.
>
> I also checked thetypo-cap.luafile to get a clue. But I used to use TeX
> exclusively
> and I have to admit that it's so overwhelming for a newbie.
>
> I really like the way wherebibtextreats words enclosed in curly braces
> are ignored.
> Or are there something that's less aggressive than\WORDso the LaTeX
> trick works:
> \def\NoCaseChange#1{\noexpand\NoCaseChange{\noexpand#1}}
\starttext
\protected\def\casing[#1]{\groupedcommand{\setcharactercasing[#1]}{}}
\protected\def\nocasing
{\groupedcommand{\setcharactercasing[reset]}{}}
|
2023-02-09 10:15:12
|
{"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": 0.7915415167808533, "perplexity": 7730.419554231746}, "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/1674764501555.34/warc/CC-MAIN-20230209081052-20230209111052-00496.warc.gz"}
|
https://deltaepsilons.wordpress.com/tag/tensors/
|
Fix a smooth manifold ${M}$ with a connection ${\nabla}$. Then parallel translation along a curve ${c}$ beginning at ${p}$ and ending at ${q}$ leads to an isomorphism ${\tau_{pq}: T_p(M) \rightarrow T_q(M)}$, which depends smoothly on ${p,q}$. For any ${r,s}$, we get isomorphisms ${\tau^{r,s}_{pq} :T_p(M)^{\otimes r} \otimes T_p(M)^{\vee \otimes s} \rightarrow T_q(M)^{\otimes r} \otimes T_q(M)^{\vee \otimes s} }$ depending smoothly on ${p,q}$. (Of course, given an isomorphism ${f: M \rightarrow N}$ of vector spaces, there is an isomorphism ${M^* \rightarrow N^*}$ sending ${g \rightarrow g \circ f^{-1}}$—the important thing is the inverse.) (more…)
|
2020-08-05 14:03:06
|
{"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": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 13, "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": 0.9933521151542664, "perplexity": 58.057907043832785}, "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/1596439735958.84/warc/CC-MAIN-20200805124104-20200805154104-00098.warc.gz"}
|
https://homework.cpm.org/category/CCI_CT/textbook/calc/chapter/3/lesson/3.3.1/problem/3-91
|
### Home > CALC > Chapter 3 > Lesson 3.3.1 > Problem3-91
3-91.
$\text{Area of a trapezoid }=\frac{1}{2}h(b_1+b_2).$
On the given domain, what will be the height of each trapezoid?
The bases are determined by the function.
1[f(0) + f(1) + f(2) + f(3)]
|
2020-09-21 19:06:34
|
{"extraction_info": {"found_math": true, "script_math_tex": 1, "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": 0.6751272678375244, "perplexity": 2449.8583468706906}, "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/1600400202007.15/warc/CC-MAIN-20200921175057-20200921205057-00272.warc.gz"}
|
https://math.stackexchange.com/questions/1210351/how-to-explain-to-a-14-year-old-that-sqrt-32-isnt-3/1213509
|
# How to explain to a 14-year-old that $\sqrt{(-3)^2}$ isn't $-3$?
I had this problem yesterday. I tried to explain to the kid this: $$\sqrt{(-3)^2} = 3,$$ and he immediately said: "My teacher told us that we can cancel the square with the square root, so it's $$\sqrt{(-3)^2} = -3."$$
He has a lot of problems with maths, and I don't know how I can explain to him this as easily as possible. He still thinks that I lied him.
Thank you.
• When I was 14 I might have been amused by the explanation that the operation of squaring and then taking the square root is like a Roach Motel for negative numbers--they go in but they never come out. And then you could show how the images of the negative numbers get "trapped" above zero. But I don't know if today's 14-year-olds have ever heard of a Roach Motel. – David K Mar 28 '15 at 19:30
• Tell him to hang onto his hat. In a couple of years at school (or minutes at a search engine), he'll learn that (complex) exponentiation is multi-valued. This tends to put confusion over the sign of a square root, and over when/whether powers and roots simply cancel, into some perspective, because this is only the beginning. One realizes that many?/most?/all? elementary definitions and rules we learn eventually need some tweaking. At some point, the square-roots-cancel-squares rule is bound to break; it may not be too hard to accept that that threshold is reached with the problem at hand. – Blue Mar 28 '15 at 19:36
• A lot of adults in America would have trouble with this one. – Robert Soupe Mar 29 '15 at 0:11
• Ask him to CALCULATE instead of taking rules for granted. Ask him what is $(-3)^2$ and what is $\sqrt{9}$. – N. S. Mar 29 '15 at 1:05
• similar as you might explain it to a 13 year old. – Seyhmus Güngören Mar 30 '15 at 21:27
After having given him the square root function definition, it may be helpful to show the following: $$\sqrt{(-3)^2}=\sqrt{9}=\sqrt{3^2}=3\neq -3.$$ Although well-definedness may be a bit of a heavy topic for a 14-year old, it should be very easy to explain why you cannot have ambiguous definitions in mathematics.
• I plus 1 you! :) – randomgirl Mar 28 '15 at 17:55
• @randomgirl Haha thanks. The voting tendencies on MSE must be one of the most bizarre and random things to exist. I recall a precalc problem the other day where the question was upvoted several times while two quality answers were downvoted into oblivion but then pulled back up within the hour. Some weird stuff. – Daniel W. Farlow Mar 28 '15 at 17:56
• I will never downvote anything. I see it as kinda negative. I either upvote or not do anything at all (or I guess I might leave a comment). – randomgirl Mar 28 '15 at 17:58
• @randomgirl Please consider downvoting when something is wrong. This helps users and answerers (and the OP) know that an answer may be wrong. It's really a matter of quality management, but you are right on one thing--don't downvote to target someone. :) – Daniel W. Farlow Mar 28 '15 at 17:59
This is about the difference between a function on one variable and an equation with one variable. A function should only have one result for each argument, whereas an equation can have more than one solution, or no solutions at all.
Let's consider a very simple function, $f(x) = x + 1$. For example, $f(3) = 4$, $f(4) = 5$. If $x$ doesn't change, neither should $f(x)$. You can run the function a hundred times with the same value and it should give the same result. Solve the equation $f(x) = 8$. The words "trivially simple" come to mind. This function has a one-to-one correspondence between inputs and outputs: each number $x$ is matched to a unique $f(x)$.
Now consider a slightly more complicated function, $f(x) = |x| + 1$. For example, $f(-3) = 4$. As with the first function, if $x$ doesn't change, neither should $f(x)$. But now an equation involving this function can have two solutions. If $f(x) = 8$, then $x$ can be $7$, but it can also be $-7$.
For the first function, we can define a look-up function by arithmetic means: $g(y) = y - 1$. But for the second function, if we demand a look-up function that uses arithmetic means rather than memory, we're going to be frustrated. The definition $g(y) = y - 1$ delivers the right result if $x$ was positive, or $0$. The question is whether or not this function $g(y)$ is good enough for our purposes.
That's what the principal square root function is: a function that tells us what value was input into another function if that value was positive, or $0$. The square function is defined as $x^2 = x \times x$. If $y = x^2$, the function $\sqrt{y}$ tells us what $x$ was if we know that $x$ was positive, or $0$.
Calculating $\sqrt{y}$ is not the same as solving the equation $x^2 - y = 0$. At least for this equation there are only two possible solutions: $\sqrt{y}$ and $-\sqrt{y}$. Therefore, $\sqrt{(-3)^2} = 3$, but the equation $x^2 - 9 = 0$ has two solutions, $x = 3$ and $x = -3$. We expect that if $y$ doesn't change, neither does $\sqrt{y}$, whether we run the function at noon, at midnight or any time of the day.
Canceling the square in $\sqrt{(-3)^2}$ to obtain $-3$ rather than $3$ creates a memory function rather than an arithmetic function. A memory function can be an arithmetic function only if the function being undone has a one-to-one correspondence between inputs and outputs.
Give him the definition of the square root function : for $x\in\mathbf{R}_{+}$, the number $\sqrt{x}$ is by definition the unique number $y\in\mathbf{R}_{+}$ such that $y^2 = x$.
• In general (that is, when $x$ is not necessarily positive anymore), $\sqrt{x^2}$ is equal to the absolute value $|x|$ of $x$. – Olórin Mar 28 '15 at 17:58
• Actually yes, because I could never ever come up with this. My bet with myself is won, thx to you. – Olórin Mar 28 '15 at 18:15
• I'm sure you could come up with it yourself, just as I could come up with my answer myself. But it is precedence that is important here, just like in art. You have to be the first person throwing paint on a canvas to be original. – Yuval Filmus Mar 28 '15 at 18:18
• @crash We're just having fun, don't take it so seriously. – Yuval Filmus Mar 28 '15 at 18:18
He (and his teacher, if the latter did indeed say that) may be right. After all what does the expression "the negative square root" mean. Many people use it, and it makes sense, and the negative square root of $(-3)^2$ is indeed $-3$.
So I believe a proper explanation should take into account that the terms "negative square root" and "square root" do not mean the same, and that it is a matter of convention in mathematics that "square root" is reserved to mean "positive square root" unless specified or implied otherwise from the context. Then it might be easier to comprehend (even for a 7-year old, not sure why age matters here) that $-3$ cannot possibly be the "positive square root" of anything.
Then it could also be explained that each positive integer has two square roots, one positive and one negative, but as we officially only call the positive one "the square root", when we start with $-3$ we end up with positive $3$, that is $\sqrt{(-3)^2}=\sqrt{9}=$ the positive of the two numbers $-3$ and $3$, that is $3$.
Even if you explain the above, you may have a harder time to explain why the above convention is adopted. (And if you work with cube and bigger roots and complex numbers that explanation may be even more difficult.) But the main point is to explain the convention and the terminology, since $-3$ is, after all, a square root of $9$, the negative one.
He is supposed to trust his teacher. So, it is also important to explain that his teacher is right, but that his teacher must have meant that cancellation holds only when we start with a positive number, e.g. $\sqrt{3^2}=3$ and $\sqrt{4^2}=4$. Then explain that his teacher did not mean that the rule applies when we start with a negative number, and in that case we end up with the opposite positive number, e.g. $\sqrt{(-3)^2}=3$ and $\sqrt{(-4)^2}=4$. It may seem a startling revelation, so please do no be disappointed if it takes a few days for it to be appreciated and accepted, after all it is simply a convention, and may need some deliberation why it is ok to accept it (and the reason is because everybody else did, and since we would like to assign a unique meaning to the unqualified term "the square root").
I wonder what the effect of the above lecture would be on a 14-year old ... I might have misses the point of your question. But, to paraphrase Euclid, "there is no 14-year-old road to square roots".
• Nice answer, Mirko! – Relure Mar 28 '15 at 19:14
• Um, "the negative square root of $\sqrt{(-3)^2}$" is actually $\sqrt{\sqrt{(-3)^2}} \approx -1.732$. – Robert Soupe Mar 29 '15 at 0:34
• did you mean $-\sqrt{\sqrt{(-3)^2}} \approx -1.732\ \$ , not $\sqrt{\sqrt{(-3)^2}}$ (the latter being the positive square root)? Thank you for the correction – Mirko Mar 31 '15 at 21:10
• "He is supposed to trust his teacher". You seem to think 14-year-olds are little children. You don't have to twist reality for a 14-year-old. He or she can already understand that people can sometimes be wrong or can say something misleading even if they know better. Of course the teacher probably didn't say anything wrong about basic stuff like square roots, but that's not the point. You should discuss the math, not who-said-what. If the teacher did say something wrong, so what? People are often wrong and teachers are people. This shouldn't be shocking or surprising to a 14-year-old. – isarandi Apr 1 '15 at 15:57
• @isarandi I would not retract my claim that students are supposed to trust teachers. There is a reason why students are students and teachers are teachers. Also, I did not say that the teacher said something wrong. While students indeed need to be critical and think on their own, I see no point to immediately jump to the conclusion that the teacher was wrong, this would be too easy an explanation. If a teacher is wrong there ought to be a way to clarify the misunderstanding, without jeopardizing the student teacher trust relationship, which is important for the student to be able to learn. – Mirko Apr 1 '15 at 17:10
For a student struggling with math, first I would get the student comfortable with problems like $\sqrt{25}=5$ (square root of a specific positive number is positive).
Also for these initial problems the student should understand that we mean the positive square root (i.e. we would not say that $\sqrt{25}$ is $\pm 5$; nor that it can be $-5$ if we want). This point legitimately causes some confusion since we often say 'square root of $25$' when we read $\sqrt{25}$, and indeed $-5$ is a square root of $25$. (We probably really should say 'the nonnegative square root' or the 'principal square root', but most of us don't).
Finally after the student was comfortable with these ideas, we can address the problem at hand, doing the inside first: $\sqrt{(-3)^2}=\sqrt{9}=3$
If he is struggling with math, he may find a graphic argument more helpful. Draw a graph of $f(x) = x^2$ and show him that every positive element on the $y$ axis has two (symmetric) preimages. Which one we choose to invert the function is indeed (mostly) irrelevant so it is a matter of convention: we like continuous functions, so we want to pick one side of the $y$-axis and stick with it, plus we really like positive stuff.
As others pointed out, this choice has the nice upside that $\sqrt{x^2} = \left| x \right|$. Still, it is worth stressing that this is just a choice and, while which one we make is indifferent, we must agree on one.
• Could whoever downvoted this explain why they did so, allowing me to improve my answer? – A.P. Apr 5 '15 at 12:26
Explain how the squaring erases the information about the sign of $-3$. The square root operation only sees a 9 coming in, it can't know any more that it was made by squaring a $-3$ or a $+3$. So by convention it is defined to always give the positive answer. We could also define it to always give the negative one (although it would be clumsy), but what we can't do is recover the information that was lost when squaring.
I think the kid has misunderstood something his teacher said about cancelling. A math student of any age is bound to misunderstand his teacher at some point or other. When I was in high school, long, long ago, Mr. Jones was fond of saying that such and such equation has no real solutions, equations like, say, $x^2 + 9 = 0$. I thought he meant such an equation has no solutions at all. It wasn't until long after college that I learned about imaginary numbers.
The equation $x^4 - 81 = 0$ has four solutions, anyone who has studied the fundamental theorem of algebra can tell you. If we want to limit ourselves to real solutions, there are still two solutions left. But when we punch up $\root 4 \of {81}$ on a calculator, we want just one answer, and we want that answer to be the same each time, e.g., if it says the answer is $3$ one time and $-3$ another time, we'd think the calculator has a malfunction of some sort.
And so it is with the square root. We want the calculator to say $\sqrt 9 = 3$ every time, no matter how it is that we got the $9$ in the first place, whether by $(-3)^2$ or $3^2$ or any other operation that could possibly give $9$, such as $56 - 47$.
By definition, the square root of $x$ (if it exists) is the (unique) non-negative number $y \geq 0$ such that $x = y^2$. The square root only exists if $x \geq 0$, and in this case it always exists and is unique.
If $y \geq 0$ then it is true that $\sqrt{y^2} = y$. More generally, $$\sqrt{y^2} = |y|.$$
For a more complete understanding, your high-schooler will have to study some complex analysis. The square root function is multi-valued, and the usual positive square root function is a specific branch of the function. Another possibility is using the non-positive square root instead of the non-negative square root. These are the only two possibilities which are continuous.
• "Thou shall never fear to give the very same answer that an answer that was already given." – Olórin Mar 28 '15 at 17:47
• @user10000100_u No two stones are alike, especially when one of them is 10 times as large. – Yuval Filmus Mar 28 '15 at 17:49
• "In the realm of proverbs no proverb will tell you that $1\not=1$, and you know why." – Olórin Mar 28 '15 at 17:50
• @user10000100_u Can I get in on this? "As lightning clears the air of impalpable vapours, so an incisive paradox frees the human intelligence from the lethargic influence of latent and unsuspected assumptions. Paradox is the slayer of Prejudice." (J. J. Sylvester) – Daniel W. Farlow Mar 28 '15 at 17:52
• @user10000100_u Surely you meant "carcass"--I can't see why vultures would want to rest on a car case :P. In terms of pathetic points, in regards to my own answer, I hit my rep cap a few hours ago :/ So don't include me in that!! – Daniel W. Farlow Mar 28 '15 at 18:01
It's not quite right to say that the square and the square root cancel each other (in fact, this example demonstrates that nicely!)
For this problem, we have $\sqrt{(-3)^2} = \sqrt{9} = 3$. But why are these the right two steps? Because we evaluate functions from the inside out. Thus, the first step is to square the $-3$. The second step is a matter of convention: the square root of a positive number is taken to be the positive root (one could choose the negative root, but that would be a different function...)
There is an unspoken agreement that $\sqrt{x}$ means the principal square root of $x$. The principal square root of a positive real number is a positive real number, and the principal square root of a negative real number is a positive imaginary number, though of course a negative imaginary number is just as valid a square root of a negative real number.
To put it in terms of computer programming, $\sqrt{(-3)^2}$ means sqrt((-3)^2). By the rules of operator precedence, (-3)^2 is evaluated first, giving 9, just the same as if we had told the computer sqrt(3^2) instead.
So by the same token, with $i$ being the principal square root of $-1$, we have $\sqrt{(-3i)^2} = 3i$, not $-3i$.
If you choose to tell your kid this, he might ask about the principal square root of an imaginary number. I believe that would be a complex number...
• what do you mean by a "positive" or "negative" imaginary number? As far as I know the terms positive and negative are only defined for real numbers. I guess I see what you mean, but I would probably not adopt your terminology in this context. – Mirko Apr 1 '15 at 17:19
• @Mirko I saw this objection coming, but I didn't think of how to address it until now. If $\Re(z) = 0$ and $\Im(z) \neq 0$ but $\Re(-zi) > 0$ then I call $z$ a "positive imaginary" number but if $\Re(-zi) < 0$ I call it a "negative imaginary" number. I could honestly respect someone if they'd rather call $z$ such that $\Re(-zi) < 0$ a "positive imaginary," but I can only sigh at someone who insists both that someone and I are wrong. – Robert Soupe Apr 2 '15 at 2:22
• When I first read your answer I somehow thought you were talking about positive or negative complex numbers, then halfway through writing my comment I realized you were only talking about positive or negative imaginary numbers, the meaning of which is quite obvious (positive or negative $y$ in $(0,y)$ when one identifies an imaginary number with a point in the plane).Your definition above says the same,I believe. The problem for me is that unless one uses the term "pure imaginary number" i tend to think of "imaginary number" as being the same as a "complex number",even if I know this is wrong. – Mirko Apr 2 '15 at 3:16
• You're probably not alone with that problem, I think I've caught myself a couple of times thinking along similar lines. Maybe I should have said "purely imaginary number." Or maybe I should have not mentioned imaginary and complex numbers at all. – Robert Soupe Apr 2 '15 at 3:36
• complex numbers complicate things ... I wonder if one extends the discussion to cube roots then whether $\sqrt[3]{-1}$ which is $-1$ in the reals, whether this is also the principal cube root of $-1$ in the complex numbers (well, can't be principal as it does not generate the other two). So perhaps one strays away from the original question if complex numbers are involved, but on the other hand for square roots your answer involving complex numbers presents an interesting point of view. – Mirko Apr 2 '15 at 3:47
Many issues I had at a similar age were rectified after being taught by a teacher about order of operations.
First Parentheses, Division, Multiplication, Addition and finally subtraction. It might be useful to introduce the kid to a certain "order" to which you must comply if you want to simplify a formula which might include exponentiation and taking square roots. I was told by my teacher to memorise the first letters of each operation (in Sinhalese) and make a poem of sort to know what operation I should first compute.
After learning this students generally get a good understanding about why parentheses are placed and what operations should be done first when simplifying which mostly gets rid of questions like this.
Then couple that with what others have said here about defining the square root operation (let's call it that instead of a function here) and you might get somewhere.
• Math is not about manipulating formulas but solving problems. Imagining math as rules to be memorized for transforming one formula to another is the quickest way to making people hate the whole thing. The most important thing is to understand what you are doing. A function is a function even if you use different notations. You can even represent a formula by connected boxes with inputs and outputs if you want (addition with two inputs and one output, square root with one input and one output, etc). What matters is the abstract idea behind it all. – isarandi Apr 1 '15 at 16:08
• @isarandi: Key word there - abstract. You can "understand" what happens to numbers when they are manipulated. But when it comes to abstract mathematics you must learn to confine yourself to the definition and only those things that have been proven. The failure to conform to such conventions is what motivates students to do things like "cancelling off" the power and the square root operations. "Memorise" here is a bad word. I propose the student must "understand" how and why the order of operations are as they are. Once he/she grasps that the rest should flow - at least for now – Ishfaaq Apr 2 '15 at 0:22
• But for this you don't even need to know the order of operations. It's not even a question of notation. To understand why the square root cannot perfectly reverse the squaring operation, you don't have to manipulate symbols at all. It's simply that squaring maps multiple inputs to the same output so the original input can't be recovered from the output alone. The principle is the same for why division by zero is undefined. Because multiplication by zero maps many (all) things to the same output, so no reversal is possible. – isarandi Apr 2 '15 at 0:53
• And actually it's not even a big "mistake" to think that it can be canceled off. We could define the square operation such that it "remembers" and passes along the sign of its input. In computing, we even have negative and positive zero, and negative and positive infinities. There is also the complex exponential function $e^{ix}$ which is basically just a sine wave that remembers which way it is currently going (as opposed to a normal sine wave that takes the same value in two distinct positions with opposite derivatives). You could in fact make your definitions so that the sqrt cancels. – isarandi Apr 2 '15 at 1:01
• @isarandi: I am sure we could debate this forever. My next argument might be a choice between the propriety of introducing a 14 year old informally to injective functions and those that are not, and maybe the potential terrors of seeing varying definitions of the same thing in different places - a result of deviating from convention (there is a reason why teaching kids is so hard and streamlined). But this was my humble suggestion - I probably don't even have the credentials to debate this with you. But it helped me and I'm confident it will help those who are willing to try it. – Ishfaaq Apr 3 '15 at 4:48
It may be worth pointing out that one reason to define (at his level) the square root of a non-negative real $\sqrt{x}$ as the positive real whose square is $x$ is that it avoids paradoxes such as: $9 = 9$, which we can write as $3^2 = (-3)^2$, which we can write as $\sqrt{3^2} = \sqrt{(-3)^2}$, "therefore" $3 = -3$.
But in general, the problem doesn't seem mathematical. Like many $14$-year-olds, he doesn't like to be told he was wrong. Eventually, I would guess, he'll come around, but he won't freely admit it.
Clearly that he is looking for some rule to make his life easier. And when he saw power rapped by a square he pooled the best thing he remembered from class:
My teacher told us that we can cancel the square with the square root...
So the solution will be to give him another rule to clear things up. The most simple thing I can think of its:
Power of even number will always result in positive solution:
## $x^y > 0$ if $y$ is even
I think perhaps the boy is right and You've not told him the whole truth. $\sqrt{(-3)^2}$ does actually equal -3 but it also equals +3. In the same way as $\sqrt{9}$ = 3 or -3.
I wonder if he has a grasp of negative numbers yet? If not then I think that would be the place to start. If he does then start by showing him that $3^2 = 9$ and $(-3)^2 = 9$, then you can tell him that $\sqrt{9}$ takes us back from the square to either of the original numbers.
|
2021-06-17 08:36:40
|
{"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": 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": 0.789960503578186, "perplexity": 354.74345119171824}, "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/1623487629632.54/warc/CC-MAIN-20210617072023-20210617102023-00129.warc.gz"}
|
https://dsp.stackexchange.com/questions/25304/how-to-calculate-resolution-of-radar
|
# How to calculate resolution of radar?
I am working of FMCW radar. Below are all the parameters of FMCW radar. How can I Calculate the resolution of my radar
Parameters Values
Center frequency (fc) 70GHz
Bandwidth (BW) 40 GHz
Sampling frequency (fs) 10 MHz
Sweep time 0.2 ms
Number of periods 10 period
The range resolution is normally some fraction bandwidth of the pulse. The fraction will depend on how you measure it i.e. null to null, 3dB points, 6 dB points etc. Also the windowing (Hamming, Kaiser) used will reduce the resolution i.e. increase the number. For a chirp pulse with the bandwidth you stated the null to null width is given by
$$\delta r = \frac{c}{2BW}=\frac{3\cdot 10^8}{2\cdot 40\cdot 10^9 }=3.75 \cdot 10^{-3} \textrm{ m }$$
You can reference the following links:
• That 'e' has to be changed to 10. Aug 18, 2015 at 13:38
It's not clear from your question, but there's also angular resolution, or the width of the mainlobe of your radar. This can sometimes be referred to as cross range resolution, and there are many approximations you can use based on the type of radiator you're using.
There's also sampling resolution, which is similarly calculated as the range resolution, but defines the spacing between samples. Whereas the range resolution defines the minimum detection distance between two point targets.
|
2022-08-13 06:43:01
|
{"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": 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": 0.8438774943351746, "perplexity": 1823.6281157031628}, "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-2022-33/segments/1659882571909.51/warc/CC-MAIN-20220813051311-20220813081311-00672.warc.gz"}
|
https://physics.stackexchange.com/questions/488980/acceleration-and-motion-can-be-in-different-direction/488981
|
# Acceleration and motion can be in different direction?
I'm not getting what acceleration concept is and how it relates to motion and how motion and acceleration can be in different direction? And what's behind the concept of negative and positive acceleration?
Let's say that we move along the straight line. Acceleration shows how fast velocity changes, it doesn't matter how fast you move:
• If velocity increases, acceleration is positive
• If velocity doesn't change, acceleration is 0
• If velocity decreases (slows down), acceleration is negative
So when you're in the car and you step on brakes, you keep moving forward for some time, but acceleration is negative (points backwards) - it opposes the forward motion.
If you want an image in you head - instead of brakes think of Hulk stopping the car - he pushes it into opposite direction, the car keeps moving but slows down.
• You don't seem to know that acceleration is a vector... – Matt Jun 30 at 10:16
• The complexity of an answer should correspond to the level of a question. Otherwise only people who know the topic anyway would understand the explanation. – Stanislav Bashkyrtsev Jun 30 at 11:01
• Am I dreaming or did you edit OP's question to add "And what's behind the concept of negative and positive acceleration"??? – Matt Jun 30 at 18:58
• I added words "And what's behind" instead of just "what" to make it grammatically correct. Why? – Stanislav Bashkyrtsev Jun 30 at 19:02
How motion and acceleration can be in different direction?
This isn't surprising. Hitting the brakes on your car is not the same as putting it in reverse.
Think of a satellite in orbit. At any point in time it is moving "horizontally" (tangential to the earth). However, its acceleration is always directly towards the centre of the earth, in other words, at $$90^{\circ}$$ to its direction of motion.
"Motion" is how the object is currently moving. Acceleration can be in any direction; it depends on the direction of the force. For a satellite, the only force is the earth's gravity, the direction of which is towards the centre of the earth.
$$\vec{F} = m\,\vec{a}$$
Here Symbols have usual meaning. Now consider the left hand side of equation. It gives Force acting on particle. It can be Gravitational or Electromagnetic Forces (or Nuclear Forces too but we keep ourselves restricted to the former two.
Now right hand side gives the acceleration of particle. Acceleration is defined as:
$${a }= \frac{d^2 x}{dt^2}$$
Now let's take mass to be positive.
Then the first equation says that Force acting on body is in the direction of acceleration of the body on which force is applied. Further notice that mass is scalar quantity and the Force and acceleration are vector quantities. Then Force formula simply relates the force in each direction to acceleration of body in that direction.
Now consider the spring force acting on body (for brevity consider S.H.M motion) Then Hooke's law applied to mass (on which spring force is applied) gives:
$$\vec{F} = -k\,\vec x$$
Now, the body is moving forward but force is acting backward on the object. That is object is retarding. Therefore we have:
$$-k\,\vec{x} = m\,\vec{a}$$
Which says force is in direction opposite to retardation or equivalentaly since retardation is negative of acceleration, force is in the direction of acceleration. If the particle is moving away from origin, then the above equation says that particle is pulled in the direction toward origin and hence its acceleration is also towards origin.That is the body is slowing down.
Hope this helps
• Which says force is in direction opposite to acceleration. Not at all. This can never be, since mass is positive. That is the body is slowing down. You're confusing displacement and velocity. You'd better to understand things yourself, before answering someone's questions. – Elio Fabri Jun 30 at 14:29
• @ElioFabri Edited and clarified with example – Abhi7731756 Jul 1 at 1:45
|
2019-10-14 18:06:52
|
{"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": 5, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5997321605682373, "perplexity": 675.2694754561545}, "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/1570986654086.1/warc/CC-MAIN-20191014173924-20191014201424-00153.warc.gz"}
|
https://aerospaceanswers.com/qa-tag/gate/?sort=vote
|
• Question Tag: GATE
Filter by
Filter by
Questions Per Page:
• Find the circulation on the airfoil.
An airfoil generates a lift of 80 N when operating in a free stream flow of 60 m/s.If the ambient …
Asked on 30th September 2019 in
• 704 views
• What is the value of $$c^{*}$$?
A rocket motor has a combustion chamber temperature of 2600 K and the products have molecular weight of 25g/mol and …
Asked on 30th September 2019 in
• 656 views
• Find the radial component and tangential component of the fluid’s velocity.
A thin long circular pipe of 10 mm diameter has porous walls and spins at 60 rpm about its own …
Asked on 1st October 2019 in
• 768 views
• What is the value of damping factor?
The logarithmic decrement measured for a viscously damped single degree of freedom system is 0.125.What is the value of the …
Asked on 2nd October 2019 in
• 653 views
• What will be the ratio for maximum propulsive efficiency?
What is the ratio of flight speed to the exhaust velocity for maximum propulsion efficiency ?
Asked on 2nd October 2019 in
• 538 views
• What is the Mach angle of the flow ?
What is the Mach angle for a flow at Mach 2.0 ?
Asked on 2nd October 2019 in
• 589 views
• How the aircraft’s range will vary?
If an aircraft takes-off with 10 % less fuel in -comparison to its standard configuration,how its range will vary.
Asked on 8th October 2019 in
• 545 views
• Find the fuel to air ratio.
The stagnation temperatures at the inlet and exit of a combustion chamber are 600 K and 1200 K ,respectively.If the …
Asked on 8th October 2019 in
• 603 views
• How buckling of the fuselage skin can be delayed ?
How buckling of the fuselage skin can be delayed ?
Asked on 8th October 2019 in
• 611 views
|
2022-11-28 18:49:31
|
{"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": 0.3621505796909332, "perplexity": 4253.564662355432}, "config": {"markdown_headings": false, "markdown_code": false, "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/1669446710534.53/warc/CC-MAIN-20221128171516-20221128201516-00312.warc.gz"}
|
https://jsantell.com/3d-projection/
|
Jordan Santell immersive engineer
# 3D Projection
In 3D graphics, objects are rendered from some viewer's position and displayed on a flat screen, like a phone or laptop. Projection describes the transformation of a three-dimensional point into a two-dimensional point. This transformation can be represented by a projection matrix, which may encode both perspective, like a camera's focal length, as well as the transformation to normalized device coordinates (NDC).
Projection matrices are one of the more confusing parts of the GL pipeline, are notoriously difficult to debug, and can be parameterized in several different ways. The following fundamentals and equations attempt to clarify the process and provide reference for common projection tasks and conversions.
## Projection Transformation
The two most common types of projection are orthographic and perspective projection. Axonometric (isometric) projections are common in games as well.
Orthographic projections do not visualize depth, and are often used for schematics, architectural drawings, and 3D software when lining up vertices. As there is no applied perspective, lines can be absolutely measured and compared.
Perspective projection, however, accounts for depth in a way that simulates how humans perceive the world. Objects that are further away appear smaller, resulting in roughly a single vanishing point in the center of our vision.
Whatever type of projection is used, the end result is a 4D homogeneous coordinate in clip space; in the OpenGL pipeline, this value is then divided by $w$, becoming a 3D vector in normalized device coordinates, and any vertex outside of the $-1$ to $1$ range gets clipped.
## Viewing Frustum
A camera abstraction in a 3D engine has an area of space that is visible, described as a viewing volume in a cuboid shape for orthographic projections, or a frustum for perspective projections. The human visual system, although a series of lies and magic, has a viewing volume that includes 180° horizontally and 90° vertically, and extends essentially an infinite amount. After all, we can see V762 Cas in Cassiopeia, 16,308 light-years away! Cameras in 3D engines are much more constrained.
A camera's frustum can be thought of as 6 planes, and any objects between those planes are visible and within the camera's field of view. Frustums are generally defined in terms of the near and far planes' distance from the camera on the Z axis, and how far the frustum extends on the near plane to the left, right, top and bottom from the Z axis. The near plane is the 2D plane that the rendered image will be projected upon.
## Perspective projection
With the six extent values (near, far, left, right, top, bottom), a perspective projection matrix can be created:
$\begin{bmatrix} \dfrac{2n}{r - l} & 0 & \dfrac{r + l}{r - l} & 0 \\ 0 & \dfrac{2n}{t - b} & \dfrac{t + b}{t - b} & 0 \\ 0 & 0 & \dfrac{f + n}{n - f} & \dfrac{2fn}{n - f} \\ 0 & 0 & -1 & 0 \\ \end{bmatrix}$
Most 3D engines or libraries will have a function that creates a perspective matrix from these values, like glFrustum or three.js's Matrix4#makePerspective,
These values are in world units; the near and far values are absolute distances from the camera's forward axis, and the extents are the relative position between the camera's focal point on the camera's forward axis on the near plane, and the extent.
The following figures illustrate the context of the extent values, and how they can be used with trigonometry to measure any length or angle.
## Projection Symmetry
Note that the simulation and images so far have been symmetric projections. The symmetric frustums' extents are symmetrical both vertically and horizontally around the Z axis at the near plane, such that $r = -l$ and $t = -b$. Symmetric projections are common in 3D renderings, although asymmetric projections can be used in stereoscopic VR rendering, augmented reality platforms, or immersive installations.
A simplified form of the perspective projection matrix can be used for symmetric projections, where $r = -l$ and $t = -b$:
$\begin{bmatrix} \dfrac{n}{r} & 0 & 0 & 0 \\ 0 & \dfrac{n}{t} & 0 & 0 \\ 0 & 0 & \dfrac{f + n}{n - f} & \dfrac{2fn}{n - f} \\ 0 & 0 & -1 & 0 \\ \end{bmatrix}$
## Parameterization
Defining a perspective projection in terms of its frustum extents is just one option. Projections can be defined via aspect ratio, field of view, focal length, or other parameters, depending on background or purpose.
### Field of view
Perhaps more commonly, perspective cameras are defined by a vertical field of view and the projection screen's aspect ratio, as well as the near and far plane values. This parameterization is (subjectively) more human-understandable: aspect ratio usually must be configurable to work across different screen resolutions, and the field of view is more intuitive than frustum extents.
Referencing Figure 1 above and using some trigonometry, the vertical field of view and aspect ratio can be converted to frustum extents, or used directly in the creation of the matrix. This assumes a symmetric projection.
let top = near * Math.tan(fov / 2);
let bottom = -top;
let right = aspect * top;
let left = -right;
$e = \dfrac{1}{tan(FOV/2)}$ $\begin{bmatrix} \dfrac{e}{aspect} & 0 & 0 & 0 \\ 0 & e & 0 & 0 \\ 0 & 0 & \dfrac{f + n}{n - f} & \dfrac{2fn}{n - f} \\ 0 & 0 & -1 & 0 \\ \end{bmatrix}$
$e$ above can be thought of as the focal length. While rendering doesn't quite have the same idea as a focal length, Eric Lengyel shared some matrix tricks at GDC 2007 to simulate the parameterization. Paul Bourke's brief note, "Field of view and focal length" sketches out the relationship between the two as well.
### Camera intrinsics
If working with OpenCV or augmented reality platforms (ARCore, ARKit), controlling projections via camera intrinsics may be necessary.
Where $f_{x}$ and $f_{y}$ are the horizontal and vertical focal lengths in pixels, an often unused $s$ for skew, and $c_{x}$ and $c_{y}$ representing the principal point, or the horizontal and vertical offset from the bottom-left in pixels, which for symmetric projections results in $c_{x} = width / 2$ and $c_{y} = height / 2$.
$\begin{bmatrix} f_{x} & s & c_{x} \\ 0 & f_{y} & c_{y} \\ 0 & 0 & 1 \\ \end{bmatrix}$
Koshy George shared a specialized form of representing camera intrinsics in OpenGL, for symmetric projections that have adjustable near/far planes:
$\begin{bmatrix} \dfrac{f_{x}}{c_{x}} & 0 & 0 & 0 \\ 0 & \dfrac{f_{y}}{c_{y}} & 0 & 0 \\ 0 & 0 & \dfrac{f + n}{n - f} & \dfrac{2fn}{n - f} \\ 0 & 0 & -1 & 0 \\ \end{bmatrix}$
George's solution derives from Kyle Simek's excellent and detailed series on camera calibration and OpenGL, where more background and a generalized form is described.
## Framing
Sometimes it's desirable to change the position of the camera such that some object is framed relatively to the viewport. Unlike the very specific dolly zoom example above, the field of view is most likely a fixed size.
For example, a lot of thought went into creating the framing rules used in model-viewer. We wanted an arbitrarily-sized model to look great inside of an arbitrarily sized viewport. To ensure good "framing", the model is placed inside of a "room" representing the camera frustum that maximizes the model's size given the current aspect ratio. The camera's near plane "frames" the room's forward plane.
Given a static vertical field of view, and the height of the frame in world units, the corresponding camera's position can be calculated via similar triangles, using values from Figure 1 above. Using half of the height and half of the field of view (in radians), the distance can be derived the same way as the near plane ($n = t / tan(fov/2)$).
const d = (height / 2) / Math.tan(fov / 2)
Similarly, this can be done with horizontal field of view and extents, or revised to find the size of a frustum at a given distance from the camera.
## Orthographic projection
Orthographic projections lack perspective and are a bit more straight forward than perspective projections.
The orthographic projection matrix can be constructed from its extent values like perspective projection:
$\begin{bmatrix} \dfrac{2}{r - l} & 0 & 0 & -\dfrac{r + l}{r - l} \\ 0 & \dfrac{2}{t - b} & 0 & -\dfrac{t + b}{t - b} \\ 0 & 0 & \dfrac{-2}{f - n} & -\dfrac{f + n}{f - n} \\ 0 & 0 & 0 & 1 \\ \end{bmatrix}$
A simplified form can be used for symmetric projections, where $r = -l$ and $t = -b$.
$\begin{bmatrix} \dfrac{1}{r} & 0 & 0 & 0 \\ 0 & \dfrac{1}{t} & 0 & 0 \\ 0 & 0 & \dfrac{-2}{f - n} & -\dfrac{f + n}{f - n} \\ 0 & 0 & 0 & 1 \\ \end{bmatrix}$
|
2021-07-26 20:38:53
|
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 26, "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": 0.580087423324585, "perplexity": 1327.0672804297833}, "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-2021-31/segments/1627046152144.92/warc/CC-MAIN-20210726183622-20210726213622-00537.warc.gz"}
|
http://msp.org/involve/2012/5-1/p10.xhtml
|
#### Vol. 5, No. 1, 2012
Recent Issues
The Journal Cover Page Editorial Board Editors’ Addresses Editors’ Interests About the Journal Scientific Advantages Submission Guidelines Submission Form Ethics Statement Subscriptions Editorial Login Author Index Coming Soon Contacts ISSN: 1944-4184 (e-only) ISSN: 1944-4176 (print)
Progress towards counting $D_5$ quintic fields
### Eric Larson and Larry Rolen
Vol. 5 (2012), No. 1, 91–97
##### Abstract
Let $N\left(5,{D}_{5},X\right)$ be the number of quintic number fields whose Galois closure has Galois group ${D}_{5}$ and whose discriminant is bounded by $X$. By a conjecture of Malle, we expect that $N\left(5,{D}_{5},X\right)\sim C\cdot {X}^{\frac{1}{2}}$ for some constant $C$. The best upper bound currently known is $N\left(5,{D}_{5},X\right)\ll {X}^{\frac{3}{4}+\epsilon }$, and we show this could be improved by counting points on a certain variety defined by a norm equation; computer calculations give strong evidence that this number is $\ll {X}^{\frac{2}{3}}$. Finally, we show how such norm equations can be helpful by reinterpreting an earlier proof of Wong on upper bounds for ${A}_{4}$ quartic fields in terms of a similar norm equation.
##### Keywords
quintic dihedral number fields, Cohen–Lenstra heuristics for $p = 5$
##### Mathematical Subject Classification 2010
Primary: 11R45
Secondary: 11R29, 14G05
|
2017-05-29 11:18:23
|
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 8, "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": 0.4729112982749939, "perplexity": 1807.1572286745516}, "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-2017-22/segments/1495463612283.85/warc/CC-MAIN-20170529111205-20170529131205-00272.warc.gz"}
|
https://www.gamedev.net/forums/topic/639258-starting-with-gl-instancing-advice/?forceDownload=1&_k=880ea6a14ea49e853634fbdc5015a024
|
Followers 0
# OpenGL Starting with GL Instancing, advice?
## 4 posts in this topic
Hey, I'm thinking about implementing Instancing, but before doing so, I need some general advice.
So far, most of the rendering is done by looping through (sorted) lists and call a VBO for each object. In some other cases, like drawing a simple sprite, I still use the good old "glVertex3f(...) <4 times>) method. And then for particles, I use a VBO containing many particles that can be updated with OpenGL Transform Feedback.
It makes sense that using Instancing helps when rendering lots of the same object (but at a different position, or with slight differences). But in practice, most of my objects only come in small numbers. 3 boxex, 5 decals, 1 barrel, et cetera. Does it still make sense to implement instancing, or does it actually slow down things with overhead? Or to put it different, when rendering a single quad, is instancing equal or faster than doing it the old 4x glVertex3f way?
Second, some of my objects are animated, and use Transform Feedback to let a Vertex Shader calculate the skinned vertex positions. Each animated model would have its own secundary VBO to write back the transformed vertices. This takes extra memory of course, then again the amount of animated objects is very small compared to the rest. I'm guessing this technique does not co-operate with instancing in any way right?
Third. My meshes use a LOD system. So when getting further away from the camera, they toggle to a simplified mesh. Is it possible to put all LOD models (usually I have 3 to 5 variants) in a single buffer and let the Instancing somehow pick the right variant depending on the distance? Or would using LOD's being less needed anyway?
Any other things I should keep in mind when working with Instancing?
Merci beaucoup
Rick
Edited by spek
1
##### Share on other sites
I'm still developing on OGL2.0+extensions, though here are my experiences/knowledge:
1. I draw gui elements (including letters for text!!) the old way (glVertex..,glColor, etc.), not using any buffers or lists and still the performance is remarkable (300-500 + few thousand letters,this will slow down the game, but most often only half the FPS on my nvidia8800).
2. Particles and decals are in a VBO (dynamic), no CPU update once they have been spawned (they move along a spline which is calculated on the GPU alone).
3. Static ad-hoc batching for grass, stones,small plants.
4. Every other object is rendered as single VBO call.
In my pipeline the most significant impact has the post-processing effects (screensize-bottleneck). I see it like that, that we (hobby-indie) devs have so much GPU/CPU power at hands, that up-front over-optimization is seldom necessary , your game will most likely benefit more from maintainable code.
Best to check, if you are pixel shader bound (screensize test), then try to check, if some state changes (texture switches etc.) are limiting your performance and eventually check if really draw calls are a limiting factor. I.e. most of my models don't have less then 1000 vertices, I never use LOD after seening no performances improvements.
But it depends on your hardware target and what you render (200 zombies or 10 enemies ? A forest ? ).
If you want to optimize I would take a look at the particle system. The geometry shader could be used to improve the particle throughput (one vertex expanded to 4), though particles are most likely although pixel-bound.
Edited by Ashaman73
1
##### Share on other sites
Your approaches look pretty much like the techniques I also uses. Manual drawn stuff for quadlike HUD stuff, VBO's with transform feedback for decals, and 1 VBO call per object.
The amount of objects is most likely not a performance killer in my case indeed. Asides from particles, enities are rarely duplicates more than 10 times. Yet the goal now is not to make things faster, but just to be prepared in case we do actually need a high number of the same objects or decals. Which is not unrealistic when thinking about scenes with a lot of rubble, or foliage.
So, if Instancing comes for "free" even if you don't really make good use of it, it wouldn't hurt either to implement it, just in case. I'm not really worried about the code getting more stiff, as most of the objects to draw are grouped and sorted for batching already anyway.
Greets
0
##### Share on other sites
I haven't used VBOs much, but if you're building a sprite system, I would recommend a "sprite batch". You'd have two classes: Sprite and SpriteBatch. SpriteBatch holds an STL vector of vertices and an STL list of Sprite objects (could go with pointers and allocate too, and that would cut down on copy operations when manipulating the Sprite list). Then, each group of vertices in that vector correspond a sprite object. That sprite object would contain your sprite's properties list its transform matrix, position, dimensions, blit parameters, etc. the Sprite class would have a pointer to its "parent" SpriteBatch it belongs to so that it has access to the vertices it's manipulating. You could also add animation and physics properties to Sprite.
Sprite batch would also contain the texture you're using, and handle all rendering. The pros are that you draw all of your objects using that texture in one call. The drawback is that your'd software-transform each sprite using matrix math on the CPU. Still, you only transform the vertices when a change occurs instead of each frame. This could be costly for particle systems, but then again, you'd want point sprites for that!
EDIT: I forgot to mention models.
I would say it's a good idea to use VBOs with static models. Again, you'd have two classes similar to my sprite example about: Model and ModelObject. The model is in charge of loading the 3D model data from your file, and storing a copy of the data. Then, each ModelObject would be allocated to store a "parent" pointer to the loaded "Model" object it wants to take the form of, and hold world-space properties like a transform matrix, attachment matrix, physics properties, bounding volumes for frustum checks, etc. Model will contain an STL list of ModelObjects, all of whom can be positioned, rotated, attached, scaled, targeting other objects, etc. Then, run Model through your Update and Render loops. Model's Update() and Render() methods will set the shader that model uses, and call each ModelObject's corresponding Update() and Render() methods respectively. The Object's Update() and Render() properties will render the model's data using it's transform data, physics, etc. You can even add an "isRendering" property to ModelObject and check if it's TRUE each frame before rendering.
The same can go for dynamic models, but you'll be running vertex skinning code on its vertices for each ModelObject's Render() call so the vertices are temporarily transformed for that instance. Additional animation data would be required such as an Animation class that holds all animation data once (you can store a list of Animation objects in Model), and each ModelObject instance will only hold the animation(s) being applied to it and current frame so the vertices can be skinned either on the GPU via vertex shader, or in real-time on the CPU each frame per Render() call.
Edited by Vincent_M
0
##### Share on other sites
Well, particles, objects and skinned characters are already optimized in terms of using VBO's, and letting the GPU do all the work (converting vertices to sprite quads, moving the particles, and storing skinned vertices back into a second VBO). The real question is, would it hurt (performance wise) to apply instancing (like shown here http://sol.gfxile.net/instancing.html) even if the majority of entities doesn't come in huge numbers?
The question arised when I was spawning bullet cases, which tend to come in big numbers when shooting machine guns. So far, these are rendered like any other object in my engine, which comes down to this:
loop through sorted list // sorted on material
{
sortedList[x].referenceObject..material.apply; // applies shaders, textures and parameters
for each object in sortedList[x].objects
{
object.applyMatrix;
sortedList[x].referenceObject.vbo.draw;
}
}
But since these particular bullet cases come in larger numbers, it could be done with instancing, which changes the code "slightly" into something like this
loop through sorted list // sorted on material
{
sortedList[x].referenceObject..material.apply; // applies shaders, textures and parameters
pushMatrices( sortedList[x].objects.allMatrices );
sortedList[x].vbo.drawMultipleTimes( sortedList[x].objects.count );
}
It might make the bullets being drawn a bit faster, though most other types of objects may not benefit. Yet, if it doesn't harm either, I prefer to write the drawing approach in a single way, rather than having to split the instanced objects from the non-instanced objects and do things in two different ways...
0
## Create an account
Register a new account
Followers 0
• ### Similar Content
• So it's been a while since I took a break from my whole creating a planet in DX11. Last time around I got stuck on fixing a nice LOD.
A week back or so I got help to find this:
https://github.com/sp4cerat/Planet-LOD
In general this is what I'm trying to recreate in DX11, he that made that planet LOD uses OpenGL but that is a minor issue and something I can solve. But I have a question regarding the code
He gets the position using this row
vec4d pos = b.var.vec4d["position"]; Which is then used further down when he sends the variable "center" into the drawing function:
if (pos.len() < 1) pos.norm(); world::draw(vec3d(pos.x, pos.y, pos.z));
Inside the draw function this happens:
draw_recursive(p3[0], p3[1], p3[2], center); Basically the 3 vertices of the triangle and the center of details that he sent as a parameter earlier: vec3d(pos.x, pos.y, pos.z)
Now onto my real question, he does vec3d edge_center[3] = { (p1 + p2) / 2, (p2 + p3) / 2, (p3 + p1) / 2 }; to get the edge center of each edge, nothing weird there.
But this is used later on with:
vec3d d = center + edge_center[i]; edge_test[i] = d.len() > ratio_size; edge_test is then used to evaluate if there should be a triangle drawn or if it should be split up into 3 new triangles instead. Why is it working for him? shouldn't it be like center - edge_center or something like that? Why adding them togheter? I asume here that the center is the center of details for the LOD. the position of the camera if stood on the ground of the planet and not up int he air like it is now.
Full code can be seen here:
https://github.com/sp4cerat/Planet-LOD/blob/master/src.simple/Main.cpp
If anyone would like to take a look and try to help me understand this code I would love this person. I'm running out of ideas on how to solve this in my own head, most likely twisted it one time to many up in my head
Toastmastern
• I googled around but are unable to find source code or details of implementation.
What keywords should I search for this topic?
Things I would like to know:
A. How to ensure that partially covered pixels are rasterized?
Apparently by expanding each triangle by 1 pixel or so, rasterization problem is almost solved.
But it will result in an unindexable triangle list without tons of overlaps. Will it incur a large performance penalty?
How to ensure proper synchronizations in GLSL?
GLSL seems to only allow int32 atomics on image.
C. Is there some simple ways to estimate coverage on-the-fly?
In case I am to draw 2D shapes onto an exisitng target:
1. A multi-pass whatever-buffer seems overkill.
2. Multisampling could cost a lot memory though all I need is better coverage.
Besides, I have to blit twice, if draw target is not multisampled.
• By mapra99
Hello
I am working on a recent project and I have been learning how to code in C# using OpenGL libraries for some graphics. I have achieved some quite interesting things using TAO Framework writing in Console Applications, creating a GLUT Window. But my problem now is that I need to incorporate the Graphics in a Windows Form so I can relate the objects that I render with some .NET Controls.
To deal with this problem, I have seen in some forums that it's better to use OpenTK instead of TAO Framework, so I can use the glControl that OpenTK libraries offer. However, I haven't found complete articles, tutorials or source codes that help using the glControl or that may insert me into de OpenTK functions. Would somebody please share in this forum some links or files where I can find good documentation about this topic? Or may I use another library different of OpenTK?
Thanks!
• Hello, I have been working on SH Irradiance map rendering, and I have been using a GLSL pixel shader to render SH irradiance to 2D irradiance maps for my static objects. I already have it working with 9 3D textures so far for the first 9 SH functions.
In my GLSL shader, I have to send in 9 SH Coefficient 3D Texures that use RGBA8 as a pixel format. RGB being used for the coefficients for red, green, and blue, and the A for checking if the voxel is in use (for the 3D texture solidification shader to prevent bleeding).
My problem is, I want to knock this number of textures down to something like 4 or 5. Getting even lower would be a godsend. This is because I eventually plan on adding more SH Coefficient 3D Textures for other parts of the game map (such as inside rooms, as opposed to the outside), to circumvent irradiance probe bleeding between rooms separated by walls. I don't want to reach the 32 texture limit too soon. Also, I figure that it would be a LOT faster.
Is there a way I could, say, store 2 sets of SH Coefficients for 2 SH functions inside a texture with RGBA16 pixels? If so, how would I extract them from inside GLSL? Let me know if you have any suggestions ^^.
• By KarimIO
EDIT: I thought this was restricted to Attribute-Created GL contexts, but it isn't, so I rewrote the post.
Hey guys, whenever I call SwapBuffers(hDC), I get a crash, and I get a "Too many posts were made to a semaphore." from Windows as I call SwapBuffers. What could be the cause of this?
Update: No crash occurs if I don't draw, just clear and swap.
static PIXELFORMATDESCRIPTOR pfd = // pfd Tells Windows How We Want Things To Be { sizeof(PIXELFORMATDESCRIPTOR), // Size Of This Pixel Format Descriptor 1, // Version Number PFD_DRAW_TO_WINDOW | // Format Must Support Window PFD_SUPPORT_OPENGL | // Format Must Support OpenGL PFD_DOUBLEBUFFER, // Must Support Double Buffering PFD_TYPE_RGBA, // Request An RGBA Format 32, // Select Our Color Depth 0, 0, 0, 0, 0, 0, // Color Bits Ignored 0, // No Alpha Buffer 0, // Shift Bit Ignored 0, // No Accumulation Buffer 0, 0, 0, 0, // Accumulation Bits Ignored 24, // 24Bit Z-Buffer (Depth Buffer) 0, // No Stencil Buffer 0, // No Auxiliary Buffer PFD_MAIN_PLANE, // Main Drawing Layer 0, // Reserved 0, 0, 0 // Layer Masks Ignored }; if (!(hDC = GetDC(windowHandle))) return false; unsigned int PixelFormat; if (!(PixelFormat = ChoosePixelFormat(hDC, &pfd))) return false; if (!SetPixelFormat(hDC, PixelFormat, &pfd)) return false; hRC = wglCreateContext(hDC); if (!hRC) { std::cout << "wglCreateContext Failed!\n"; return false; } if (wglMakeCurrent(hDC, hRC) == NULL) { std::cout << "Make Context Current Second Failed!\n"; return false; } ... // OGL Buffer Initialization glClear(GL_DEPTH_BUFFER_BIT | GL_COLOR_BUFFER_BIT); glBindVertexArray(vao); glUseProgram(myprogram); glDrawElements(GL_TRIANGLES, indexCount, GL_UNSIGNED_SHORT, (void *)indexStart); SwapBuffers(GetDC(window_handle));
• 10
• 11
• 19
• 14
• 23
|
2017-07-28 11:39:41
|
{"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": 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": 0.2132950723171234, "perplexity": 2689.1350825967193}, "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-2017-30/segments/1500549448198.69/warc/CC-MAIN-20170728103510-20170728123510-00200.warc.gz"}
|
https://math.stackexchange.com/questions/2340051/implicit-midpoint-method-for-newtons-laws
|
implicit midpoint method for newton's laws
I've been banging my head against the way trying to understand the Wikipedia article for the implicit midpoint method. I find the notation confusing which isn't helping. My goal is to use the implicit midpoint method to time advance a physics simulation based on Newton's Laws.
Given $$y(t) = (x(t),v(t)) = y_{n}$$ and $$\dot{y}(t) = (\dot{x}(t),\dot{v}(t)) = (v(t),a(t)) = (v(t),\frac{F(x(t))}{m}) = \dot{y}_{n}$$
Assuming I know $x(0),v(0),F(0)$ I would like to use the implicit midpoint method to find $y(t+h)=y_{n+1}$
As far as I can understand the article the update rule would be
$$y_{n+1} = y_{n} + \frac{h}{2}(\dot{y}_{n} + \dot{y}_{n+1})$$
but I'm not even sure that's correct because the way they write it in the article makes the fact that both sides of the equation depend on $y_{n+1}$ very explicit. Whereas the way I've written it it's not clear that is the case.
I was thinking I'd use Newton's method to solve this implicit system of equations which I think means that I need to do something like write
$$G(y_{n+1}) = y_{n+1} - y_{n} - \frac{h}{2}(\dot{y}_{n} + \dot{y}_{n+1}) = 0$$
but I really don't think that's correct because for Newton's method to work I need to be able to guess values for $y_{n+1}$ and evaluate $G$ at those values. However I need a value for $\dot{y}_{n+1}$ to evaluate $G$.
EDIT:
It may be useful to show how I ended up with this form for the midpoint method. My understanding of the notation $f(t,y) = \dot{y}(t)$ is that the $t$ parameter of $f$ only matters if there is an explicit dependence on time. For example if $\dot{y}(t) = t + y(t)$ then
$$f (t + \frac{h}{2},\frac{1}{2}(y(t) + y(t+h)) = t + \frac{h}{2} + \frac{1}{2}(y(t) + y(t+h))$$
Since there is no explicit dependence of $t$ in these equations I dropped the $t + \frac{h}{2}$ term and wrote
$$f(t + \frac{h}{2},\frac{1}{2}(y(t) + y(t+h)) = \dot{y}(t) = \frac{1}{2}(\dot{y}(t) + \dot{y}(t+h))$$
Thank you for taking the time to read my question.
• I think I realised something. By guessing $y_{n+1}$ I get the first component of $\dot{y}_{n+1}$. The second component can be computed since $F$ is a function of $y_{n+1}$ only. – Adam Sturge Jun 29 '17 at 1:10
• You are aware that you are using the implicit trapezoidal method? The midpoint method uses the derivative approximation at the midpoint at $t+h/2$. – LutzL Jun 29 '17 at 5:41
• @Lutzl No actually I didn't know that. I wasn't sure how to put in t+h/2 into the equations. Like what is $f(t+\frac{h}{2},\frac{1}{2}(y_{n}+ y_{n+1}))$ as it's described on the wiki page for the midpoint method?. Given that $y_{n}=y(t)$ and $y_{n+1} = y(t+h)$. Is it $\frac{1}{2} (\dot{y}(t+\frac{h}{2}) + \dot{y}(t+\frac{h}{2} + h))$? – Adam Sturge Jun 29 '17 at 16:37
For the midpoint method you approximate \begin{align} \frac{y(t+h)-y(t)}h&\approx\dot y(t+\tfrac h2) \\ &=f(t+\tfrac h2,y(t+\tfrac h2)) \\ &\approx f(t+\tfrac h2,\tfrac12(y(t+h)+y(t))). \end{align} All approximations with an error $O(h^2)$
This gives the method $$y_{k+1}=y_k+hf(t+\tfrac h2,\tfrac12(y_k+y_{k+1}))$$ This can be decomposed into first one step of the implicit Euler method and then one of the explicit Euler method, both with half the step size \begin{align} \text{implicit Euler: }&&y_{k+\frac12}&=y_k+\tfrac h2 f(t+\tfrac h2,y_{k+\frac12})\\ \text{explicit Euler: }&&y_{k+1}&=y_{k+\frac12}+\tfrac h2 f(t+\tfrac h2,y_{k+\frac12}) \end{align} where $(t+\tfrac h2,y_{k+\frac12})$ is the midpoint of the segment connecting the iteration points with $y_{k+\frac12}=\frac12(y_k+y_{k+1})$
• Name $z=\frac12(y_k+y_{k+1})$, then $y_{k+1}=2z-y_k$, and insert into the midpoint formula, $$2z-y_k=y_k+hf(t+\frac h2,z)$$ which transforms into $$z=y_k+\frac h2f(t+\frac h2,z)$$ which is the formula for an implicit Euler step. So you get to solve $$0=G(z)=z-y_k-\frac h2f(t+\frac h2,z)$$ either via Newton or via fixed-point iteration. – LutzL Jun 30 '17 at 15:46
• Also assuming that I've run Newton's Method to find $z$, and that I know $y_{k}$ from the start of the timestep, can't I just analytically solve for $y_{k+1}$ using $y_{k+1}=2z−y_{k}$? – Adam Sturge Jun 30 '17 at 17:47
• Yes, but you will have evaluated $s=f(t+h/2,z)$ anyway, so that you can just compute $y_{k+1}=y_k+h·s$ avoiding cancellation errors. – LutzL Jun 30 '17 at 18:05
|
2019-05-22 11:19:34
|
{"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": 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": 2, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9470266699790955, "perplexity": 243.38809044457085}, "config": {"markdown_headings": false, "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-2019-22/segments/1558232256797.20/warc/CC-MAIN-20190522103253-20190522125253-00488.warc.gz"}
|
https://www.physicsforums.com/threads/maxwells-law-of-induction-how-does-it-work.961577/
|
# Maxwell's Law of Induction - How Does it Work?
ItFeelsGoodToBeAlive
So, I was studying Maxwell's equations and I don't really understand the last one - Ampere's Law (with Maxwell's extra term added in). The bit I'm not able to understand is the term Maxwell added. How exactly does a changing electric field through a closed loop induce a magnetic field along that loop?
I mean, Faraday's law of induction is a result of special relativity...what is Maxwell's law of induction a result of? (ie. how can whatever it is that's going on to cause the whole induction thing be explained physically?)in
Gold Member
The way Maxwell initially understood it was that he envisioned the electric field to be a dielectric polarization of space itself. In terms of virtual particles in QFT this still is not a bad way of look at it. So let's consider a physical version of this.
Imagine a crystal made of dipolar molecules. The net charge is zero but by compressing the crystal you caused the positive poles to move a bit to the right and the negative poles to move a bit to the left. There would then be a net charge current and that would momentarily induce a magnetic field. The polarization of the crystal is added to the vacuum E field to give the D field in the material. The E field itself can be viewed as this same sort of process happening at to the vacuum itself.
Note that this occurs dually with changing B fields. Even without magnetic charges we can set up a magnetic current by polarizing a diamagnetic medium. Say, set up a board with bar magnets on pivots. Have the N poles to the right and S poles to the left and then pivot them all together. You induce a net N current to the left or S to the right. This magnetic current will induce a corresponding E field. This applies to any changing B field, there's some form of effective magnetic charge current and it induces an E field. That's Faraday's law of induction in action and that's how the B field induces current in a loop. But note that it is enhanced in ferromagnetic media where dipole allignments will enhance the B field and you get a higher induced E field.
The Maxwell terms says that E field acts in a dual way. The only break in this symmetry is our absence of magnetic monopole charges (so far as we've ever been able to discover).
Gold Member
The bit I'm not able to understand is the term Maxwell added. How exactly does a changing electric field through a closed loop induce a magnetic field along that loop?
I thought that the electric field acted around the loop and cause a magnetic field going through the loop.
alan123hk
So, I was studying Maxwell's equations and I don't really understand the last one - Ampere's Law (with Maxwell's extra term added in). The bit I'm not able to understand is the term Maxwell added. How exactly does a changing electric field through a closed loop induce a magnetic field along that loop?
It is because change in electric flux density (also known as displacement current density) creates magnetic field in the same way as the Faraday's law. For example, the change of electric flux density between two plates of a capacitor will induce circular magnetic field around the space between the two plates as though a current were present there as well.
I mean, Faraday's law of induction is a result of special relativity...what is Maxwell's law of induction a result of?
According to relativity, magnetic and electric fields are really not different fields, what is seen as a magnetic field by one observer could be seen as an electric field by another observer and vice versa, since all such observers are equal, no one has more right than another, therefore, I don't see the reason why the change of electric field not inducing magnetic field as well.
When an electric charge is wiggle back-and-forth, a wiggling electric field is created, which, in turn, creates a wiggling magnetic field, which creates a wiggling electric field, and gain and again in the same way, these wiggles are in fact spreading out of free electromagnetic waves (radio waves).
View attachment 236877
Last edited:
Gold Member
When an electric charge is wiggle back-and-forth, a wiggling electric field is created, which, in turn, creates a wiggling magnetic field, which creates a wiggling electric field, and gain and again in the same way, these wiggles are in fact spreading out of free electromagnetic waves (radio waves).
https://www.physicsforums.com/attachments/236863
But for an EM wave the electric and magnetic fields are in-phase. The two fields are not exchanging energy but each have half the energy?
alan123hk
But for an EM wave the electric and magnetic fields are in-phase. The two fields are not exchanging energy but each have half the energy?
Yes, the EM wave is propagated with the electric and magnetic field vectors in phase and perpendicular, they interact with each other in a close and instant way.
I agree that the way of saying "electric field is created, which, in turn, creates a wiggling magnetic field... and again and again in the same way... are electromagnetic waves" may seems somewhat inappropriate, there is a risk of misleading people to think that the electric and magnetic field are separated in some way as the EM wave propagates, although I have actually seen the same explanation of EM wave in a science book many years ago.
#### Attachments
• 45907641884_6478393b80_z_d.jpg
33 KB · Views: 698
Last edited:
Gold Member
2022 Award
It is very misleading to say that an "electric field is created, which, in turn, creates a wiggling magnetic field... and again and again in the same way... are electromagnetic waves". To begin with, there's only one electromagnetic field, represented in the classical form by its electric and magnetic components ##\vec{E}## and ##\vec{B}## (I refer to the microscopic fundamental laws; the further split into free and internal fields in macroscopic electromagnetics is another more complicated topic of its own).
The Maxwell equations split into two classes, the homogeneous equations
$$\vec{\nabla} \times \vec{E}+\partial_t \vec{B}=0, \quad \vec{\nabla} \cdot \vec{B}=0,$$
and the inhomogeneous ones
$$\vec{\nabla} \times \vec{B} - \frac{1}{c^2} \partial_t \vec{E}=\mu_0 \vec{j}, \quad \vec{\nabla} \cdot \vec{E}=\frac{1}{\epsilon_0} \rho.$$
The homogeneous equations are constraint equations for the field components, and the inhomogeneous equations provide ##\rho## and ##\vec{j}## as the sources. This becomes clear from the fact that the solutions of the equations are the retarded fields given in terms of the retarded propagator with the charge-current distributions as the causal (!) sources. See, e.g.,
https://en.wikipedia.org/wiki/Jefimenko's_equations
particularly the section "Discussion" therein.
alan123hk
The homogeneous equations are constraint equations for the field components, and the inhomogeneous equations provide ρρ\rho and →jj→\vec{j} as the sources. This becomes clear from the fact that the solutions of the equations are the retarded fields given in terms of the retarded propagator with the charge-current distributions as the causal (!) sources. See, e.g.,
Charge-current distributions is certainly the source of EM field no matter it is static or varying. However, the electromagnetic waves can still propagate in the space even after the source ceased to exist, so the problem is whether or not we can explain the propagation mechanism of EM wave in words as looping of mutual induction of electric and magnetic fields.
#### Attachments
• EM wave.jpg
38.7 KB · Views: 667
|
2023-03-30 20:50:01
|
{"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": 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": 0.7861904501914978, "perplexity": 458.2506552413708}, "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-2023-14/segments/1679296949387.98/warc/CC-MAIN-20230330194843-20230330224843-00311.warc.gz"}
|
https://plainmath.net/7326/babies-learn-crawl-longer-learn-winter-babies-bundled-clothes-restrict
|
# At what age do babies learn to crawl? Does it take longer to learn in the winter when babies are often bundled in clothes that restrict
Question
Modeling data distributions
At what age do babies learn to crawl? Does it take longer to learn in the winter when babies are often bundled in clothes that restrict their movement? Data were collected from parents who brought their babies into the University of Denver Infant Study Center to participate in one of a number of experiments between 1988 and 1991. Parents reported the birth month and the age at which their child was first able to creep or crawl a distance of 4 feet within 1 minute. The resulting data were grouped by month of birth: January, May, and September:
$$\begin{array}{c} & Crawling\ age \\ \hline Birth\ month & Mean & St.dev. & n \\ \hline January & 29.84 & 7.08 & 32 \\ May & 28.58 & 8.07 & 27 \\ September & 33.83 & 6.93 & 38\end{array}$$
Crawling age is given in weeks. Assume the data represent three independent simple random samples, one from each of the three populations consisting of babies born in that particular month, and that the populations of crawling ages have Normal distributions. A partial ANOVA table is given below
. $$\begin{array}{c}Source & Sum\ of\ squares & DF & Mean\ square\ F \\ \hline Groups & 505.26\\ Error & & &53.45\\ Total\end{array}$$
What are the degrees of freedom for the groups term?
2021-02-07
Given: Groups represent the birth month. k represent the groups. k=3 The degrees of freedom for the groups term is obtained as below: $$\displaystyle{d}{f}_{{{g}{r}{o}{u}{p}{s}}}={k}-{1}$$
$$\displaystyle={3}-{1}$$
$$\displaystyle={2}$$ Thus, the degrees of freedom for the groups term is 2.
### Relevant Questions
Which possible statements about the chi-squared distribution are true?
a) The statistic $$X^{2}$$, that is used to estimate the variance $$S^{2}$$ of a random sample, has a Chi-squared distribution.
b) The sum of the squares of k independent standard normal random variables has a Chi-squared distribution with k degrees of freedom.
c) The Chi-squared distribution is used in hypothesis testing and estimation.
d) The Chi-squared distribution is a particular case of the Gamma distribution.
e)All of the above.
The table shows the temperatures T (in degrees Fahrenheit) at which water boils at selected pressures p (in pounds per square inch). A model that approximates the datais: $$\displaystyle{T}={87.97}\ +\ {34.96}\ \text{In}\ {p}\ +\ {7.91}\ \sqrt{{{p}}}$$ a) Use a graphing untility to plot the data and graph the model in the same veiwing window. How well does the model fit the data? b) Use the graph to estimate the pressure at which the boiling point of water is $$300^{\circ}$$ F. c) Calculate T when the pressure is 74 pounds per square inch. Verify your answer graphically.
The tables show the battery lives (in hours) of two brands of laptops. a) Make a double box-and-whisker plot that represent's the data. b) Identifity the shape of each distribution. c) Which brand's battery lives are more spread out? Explain. d) Compare the distributions using their shapes and appropriate measures of center and variation.
In an experiment designed to study the effects of illumination level on task performance (“Performance of Complex Tasks Under Different Levels of Illumination,” J. Illuminating Eng., 1976: 235–242), subjects were required to insert a fine-tipped probe into the eyeholes of ten needles in rapid succession both for a low light level with a black background and a higher level with a white background. Each data value is the time (sec) required to complete the task.
$$\begin{array}{|c|c|} \hline Subject & (1) & (2) & (3) & (4) & (5) &(6) & (7) & (8) & (9) \\ \hline Black & 25.85 & 28.84 & 32.05 & 25.74 & 20.89 & 41.05 & 25.01 & 24.96 & 27.47 \\ \hline White & 18.28 & 20.84 & 22.96 & 19.68 & 19.509 & 24.98 & 16.61 & 16.07 & 24.59 \\ \hline \end{array}$$
Does the data indicate that the higher level of illumination yields a decrease of more than 5 sec in true average task completion time? Test the appropriate hypotheses using the P-value approach.
An analysis of laboratory data collected with the goal of modeling the weight (in grams) of a bacterial culture after several hours of growth produced the least squares regression line $$\log(weight) = 0.25 + 0.61$$hours. Estimate the weight of the culture after 3 hours.
A) 0.32 g
B) 2.08 g
C) 8.0 g
D) 67.9 g
E) 120.2 g
1)A rewiew of voted registration record in a small town yielded the dollowing data of the number of males and females registered as Democrat, Republican, or some other affilation:
$$\begin{array}{c} Gender \\ \hline Affilation & Male & Female \\ \hline Democrat & 300 & 600 \\ Republican & 500 & 300 \\ Other & 200 & 100 \\ \hline \end{array}$$
What proportion of all voters is male and registered as a Democrat? 2)A survey was conducted invocted involving 303 subject concerning their preferences with respect to the size of car thay would consider purchasing. The following table shows the count of the responses by gender of the respondents:
$$\begin{array}{c} Size\ of\ Car \\ \hline Gender & Small & Medium & lange & Total \\ \hline Female & 58 & 63 & 17 & 138 \\ Male & 79 & 61 & 25 & 165 \\ Total & 137 & 124 & 42 & 303 \\ \hline \end{array}$$
the data are to be summarized by constructing marginal distributions. In the marginal distributio for car size, the entry for mediums car is ?
The table shows the population of various cities, in thousands, and the average walking speed, in feet per second, of a person living in the city. $$\begin{array}{|c|c|} \hline Population\ (thousands) & Walking Speed\ (feet\ per\ second) \\ \hline 5.5 & 0.6 \\ \hline 14 & 1.0\\ \hline 71 & 1.6\\ \hline 138 & 1.9\\ \hline 342 & 2.2\\ \hline \end{array}$$
A random sample of $$\displaystyle{n}_{{1}}={16}$$ communities in western Kansas gave the following information for people under 25 years of age.
$$\displaystyle{X}_{{1}}:$$ Rate of hay fever per 1000 population for people under 25
$$\begin{array}{|c|c|} \hline 97 & 91 & 121 & 129 & 94 & 123 & 112 &93\\ \hline 125 & 95 & 125 & 117 & 97 & 122 & 127 & 88 \\ \hline \end{array}$$
A random sample of $$\displaystyle{n}_{{2}}={14}$$ regions in western Kansas gave the following information for people over 50 years old.
$$\displaystyle{X}_{{2}}:$$ Rate of hay fever per 1000 population for people over 50
$$\begin{array}{|c|c|} \hline 94 & 109 & 99 & 95 & 113 & 88 & 110\\ \hline 79 & 115 & 100 & 89 & 114 & 85 & 96\\ \hline \end{array}$$
(i) Use a calculator to calculate $$\displaystyle\overline{{x}}_{{1}},{s}_{{1}},\overline{{x}}_{{2}},{\quad\text{and}\quad}{s}_{{2}}.$$ (Round your answers to two decimal places.)
(ii) Assume that the hay fever rate in each age group has an approximately normal distribution. Do the data indicate that the age group over 50 has a lower rate of hay fever? Use $$\displaystyle\alpha={0.05}.$$
(a) What is the level of significance?
State the null and alternate hypotheses.
$$\displaystyle{H}_{{0}}:\mu_{{1}}=\mu_{{2}},{H}_{{1}}:\mu_{{1}}<\mu_{{2}}$$
$$\displaystyle{H}_{{0}}:\mu_{{1}}=\mu_{{2}},{H}_{{1}}:\mu_{{1}}>\mu_{{2}}$$
$$\displaystyle{H}_{{0}}:\mu_{{1}}=\mu_{{2}},{H}_{{1}}:\mu_{{1}}\ne\mu_{{2}}$$
$$\displaystyle{H}_{{0}}:\mu_{{1}}>\mu_{{2}},{H}_{{1}}:\mu_{{1}}=\mu_{{12}}$$
(b) What sampling distribution will you use? What assumptions are you making?
The standard normal. We assume that both population distributions are approximately normal with known standard deviations.
The Student's t. We assume that both population distributions are approximately normal with unknown standard deviations,
The standard normal. We assume that both population distributions are approximately normal with unknown standard deviations,
The Student's t. We assume that both population distributions are approximately normal with known standard deviations,
What is the value of the sample test statistic? (Test the difference $$\displaystyle\mu_{{1}}-\mu_{{2}}$$. Round your answer to three decimalplaces.)
What is the value of the sample test statistic? (Test the difference $$\displaystyle\mu_{{1}}-\mu_{{2}}$$. Round your answer to three decimal places.)
(c) Find (or estimate) the P-value.
P-value $$\displaystyle>{0.250}$$
$$\displaystyle{0.125}<{P}-\text{value}<{0},{250}$$
$$\displaystyle{0},{050}<{P}-\text{value}<{0},{125}$$
$$\displaystyle{0},{025}<{P}-\text{value}<{0},{050}$$
$$\displaystyle{0},{005}<{P}-\text{value}<{0},{025}$$
P-value $$\displaystyle<{0.005}$$
Sketch the sampling distribution and show the area corresponding to the P-value.
P.vaiue Pevgiue
P-value f P-value
The following quadratic function in general form, $$\displaystyle{S}{\left({t}\right)}={5.8}{t}^{2}—{81.2}{t}+{1200}$$ models the number of luxury home sales, S(t), in a major Canadian urban area, according to statistical data gathered over a 12 year period. Luxury home sales are defined in this market as sales of properties worth over \$3 Million (inflation adjusted). In this case, $$\displaystyle{\left\lbrace{t}\right\rbrace}={\left\lbrace{0}\right\rbrace}\ \text{represents}\ {2000}{\quad\text{and}\quad}{\left\lbrace{t}\right\rbrace}={\left\lbrace{11}\right\rbrace}$$represents 2011. Use a calculator to find the year when the smallest number of luxury home sales occurred. Without sketching the function, interpret the meaning of this function, on the given practical domain, in one well-expressed sentence.
$$\begin{array}{|c|c|}\hline \text{Year} & \text{Average tuition} \\ \hline 2005 & 17.6 \\ \hline 2007 & 18.1 \\ \hline 2009 & 19.5 \\ \hline 2011 & 20.7 \\ \hline 2013 & 21.8 \\ \hline \end{array}$$
|
2021-06-13 02:53:10
|
{"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": 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": 0.5564454197883606, "perplexity": 1291.4738631123028}, "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-2021-25/segments/1623487598213.5/warc/CC-MAIN-20210613012009-20210613042009-00403.warc.gz"}
|
https://questioncove.com/updates/4d4c86b1a805b7646c90c80b
|
Mathematics
OpenStudy (anonymous):
How do I differentiate ln(xy^2)=y
OpenStudy (heisenberg):
differentiate y with respect to x, i presume?
OpenStudy (anonymous):
yes with respect to x
OpenStudy (heisenberg):
my first instinct says try implicit differentiation, but u substitution could be an option.
OpenStudy (anonymous):
It is an implicit differentiation problem, however I can't figure out what ln(xy^2) differentiates to... if I could figure that out I could simplify it algebraically no problem
OpenStudy (heisenberg):
$\frac{\delta y}{\delta x} \ln(xy^2) = y^2 * \frac{\delta}{\delta x} (x)$
OpenStudy (heisenberg):
so since we are differentiating with respect to x, we can consider any 'y' portions to be constant and proceed as such.
OpenStudy (heisenberg):
but for implicit differentiation, you have to include a dy/dx term when you take the derivative
OpenStudy (anonymous):
thank you! That helps me understand how to finish the problem much better!
OpenStudy (anonymous):
The derivative is implicit, but it also requires chain rule (because xy^2 is a function) and, later, product rule (x times y^2). The right hand side is just dy/dx. That help?
Can't find your answer? Make a FREE account and ask your own questions, OR help others and earn volunteer hours!
Join our real-time social learning platform and learn together with your friends!
Latest Questions
xxcoffee: congrats on purple to my self hahah i did ittt
7 seconds ago 22 Replies 2 Medals
walle2037: I need help with the math of 02 Integers
52 seconds ago 6 Replies 1 Medal
jakfishman: help
3 minutes ago 18 Replies 1 Medal
fuyo: what color is a mirror?
1 minute ago 2 Replies 1 Medal
walle2037: what would you do if a babysitter is drunk
15 minutes ago 3 Replies 1 Medal
jackiejackiejack: What has many keys, but can't even open a single door?
18 minutes ago 5 Replies 4 Medals
Can't find your answer? Make a FREE account and ask your own questions, OR help others and earn volunteer hours!
Join our real-time social learning platform and learn together with your friends!
|
2020-11-23 16:24:17
|
{"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": 0.4830876588821411, "perplexity": 3734.7374481894326}, "config": {"markdown_headings": false, "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/1606141163411.0/warc/CC-MAIN-20201123153826-20201123183826-00390.warc.gz"}
|
https://jp.maplesoft.com/support/help/maplesim/view.aspx?path=DifferentialGeometry%2FLibrary%2FSearch
|
Search - Maple Help
Library[Search] - search through the DifferentialGeometry library to find Lie algebras, Lie algebras of vector fields, or differential equations with specific properties
Calling Sequences
Search(author, n, indexlist, procedurelists, optionalargs)
Parameters
author - a string, the author of a table in the DifferentialGeometry Library
n - an integer
indexlist - (optional) indexlist = A, where A is a list of indices for the table with catalogue name author, n
procedurelists - one or more of following: Liealgebraproperties = P; VFSproperties = P; DEproperties = P; here P is a list of procedures returning true or false
optionalargs - manifold = M, where M is the name of a manifold defined using DGsetup
optionalargs - variables = V, where V is the list of independent and dependent variables for a system of differential equations
Description
• The Search command will return the sublist of the list indexlist consisting of all table entries for which the procedures in the procedurelists all return true.
• If the table entries are Lie algebras, then the Search command will initialize each Lie algebra in indexlist and execute each procedure in the Liealgebraproperties list. Each procedure in the Liealgebraproperties list will assume that a Lie algebra has been initialized. No arguments may be used in defining these procedures.
• If the table entries are Lie algebras of vector fields, then the procedures P in the argument VFSproperties = P should accept a single argument Gamma, this being the list of vector fields as provided by the table entry. The Liealgebraproperties procedures are applied to the abstract Lie algebra defined by each table entry. This abstract Lie algebra is automatically calculated and initialized by the Search command.
• If the table entries are differential equations, then the procedures in DEproperties = P should accept a single argument called DE, this being the differential equation as provided by the table entry. The VFSproperties procedures are applied to the symmetry algebra of the differential equation and the Liealgebraproperties are applied to the abstract Lie algebra defined by the symmetry algebra of the differential equation. The symmetry algebra of DE will be automatically computed (using the PDEtools package) by the Search program, if required.
• The command Search is part of the DifferentialGeometry:-Library package. It can be used in the form Search(...) only after executing the commands with(DifferentialGeometry) and with(Library), but can always be used by executing DifferentialGeometry:-Library:-Search(...).
Examples
> $\mathrm{with}\left(\mathrm{DifferentialGeometry}\right):$$\mathrm{with}\left(\mathrm{Library}\right):$$\mathrm{with}\left(\mathrm{LieAlgebras}\right):$
Example 1.
Search through the ["Winternitz", 1] library of Lie algebras and find all the Lie algebras of dimension 4 which are solvable but not nilpotent. First we use the command Query to construct the necessary procedures.
> $\mathrm{P1}≔\left(\right)→\mathrm{is}\left(\mathrm{Tools}:-\mathrm{DGinfo}\left("LieAlgebraDimension"\right)=4\right)$
${\mathrm{P1}}{≔}\left({}\right){→}{\mathrm{is}}{}\left({\mathrm{DifferentialGeometry}}{:-}{\mathrm{Tools}}{:-}{\mathrm{DGinfo}}{}\left({"LieAlgebraDimension"}\right){=}{4}\right)$ (2.1)
> $\mathrm{P2}≔\left(\right)↦\mathrm{Query}\left("Solvable"\right)$
${\mathrm{P2}}{≔}\left({}\right){→}{\mathrm{LieAlgebras}}{:-}{\mathrm{Query}}{}\left({"Solvable"}\right)$ (2.2)
> $\mathrm{P3}≔\left(\right)↦\mathbf{not}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}\mathrm{Query}\left("Nilpotent"\right)$
${\mathrm{P3}}{≔}\left({}\right){→}{\mathbf{not}}\phantom{\rule[-0.0ex]{0.5em}{0.0ex}}{\mathrm{LieAlgebras}}{:-}{\mathrm{Query}}{}\left({"Nilpotent"}\right)$ (2.3)
> $\mathrm{Alglist1}≔\mathrm{Search}\left("Winternitz",1,\mathrm{Liealgebraproperties}=\left[\mathrm{P1},\mathrm{P2},\mathrm{P3}\right]\right)$
${\mathrm{Alglist1}}{≔}\left[\left[{4}{,}{2}\right]{,}\left[{4}{,}{3}\right]{,}\left[{4}{,}{4}\right]{,}\left[{4}{,}{5}\right]{,}\left[{4}{,}{6}\right]{,}\left[{4}{,}{7}\right]{,}\left[{4}{,}{8}\right]{,}\left[{4}{,}{9}\right]{,}\left[{4}{,}{10}\right]{,}\left[{4}{,}{11}\right]{,}\left[{4}{,}{12}\right]\right]$ (2.4)
Now narrow the search to find those Lie algebras with a 2 dimensional derived algebra.
alg_name > $\mathrm{P4}≔\left(\right)↦\mathrm{is}\left(\mathrm{nops}\left(\mathrm{DerivedAlgebra}\left(\right)\right)=2\right):$
alg_name > $\mathrm{Alglist2}≔\mathrm{Search}\left("Winternitz",1,\mathrm{indexlist}=\mathrm{Alglist1},\mathrm{Liealgebraproperties}=\left[\mathrm{P4}\right]\right)$
${\mathrm{Alglist2}}{≔}\left[\left[{4}{,}{3}\right]{,}\left[{4}{,}{12}\right]\right]$ (2.5)
Thus we conclude that there are just two 4 dimensional solvable and not nilpotent Lie algebras with 2 dimensional derived algebras in the Winternitz table. We can use the Browse command to view these Lie algebras.
alg_name > $\mathrm{Browse}\left("Winternitz",1,\mathrm{Alglist2}\right)$
${"Winternitz"}{,}{1}{,}\left[{4}{,}{3}\right]$ $\left[\left[{\mathrm{e1}}{,}{\mathrm{e4}}\right]{=}{\mathrm{e1}}{,}\left[{\mathrm{e3}}{,}{\mathrm{e4}}\right]{=}{\mathrm{e2}}\right]$ ${\mathrm{___________________}}$ ${"Winternitz"}{,}{1}{,}\left[{4}{,}{12}\right]$ $\left[\left[{\mathrm{e1}}{,}{\mathrm{e3}}\right]{=}{\mathrm{e1}}{,}\left[{\mathrm{e1}}{,}{\mathrm{e4}}\right]{=}{-}{\mathrm{e2}}{,}\left[{\mathrm{e2}}{,}{\mathrm{e3}}\right]{=}{\mathrm{e2}}{,}\left[{\mathrm{e2}}{,}{\mathrm{e4}}\right]{=}{\mathrm{e1}}\right]$ ${\mathrm{___________________}}$ (2.6)
Example 2.
Search through the first 25 vector field systems in the Gonzalez-Lopez table to see if there is a 3 dimensional semisimple vector field system whose prolongation to the 1-jet is not transitive. (A 3 dimensional vector field system will be non-transitive on the 1-jet if there is a non-trivial isotropy subalgebra.) These are precisely the actions which will admit a first order differential invariant.
alg_name > $\mathrm{DGsetup}\left(\left[x\right],\left[y\right],M,1\right):$
M > $\mathrm{Q1}≔\mathrm{Gamma}↦\mathrm{is}\left(\mathrm{nops}\left(\mathrm{Gamma}\right)=3\right)$
${\mathrm{Q1}}{≔}{\mathrm{Γ}}{→}{\mathrm{is}}{}\left({\mathrm{nops}}{}\left({\mathrm{Γ}}\right){=}{3}\right)$ (2.7)
M > Q2 := proc(Gamma)
M >
M > $\mathrm{Γ1}≔\mathrm{map}\left(\mathrm{JetCalculus}:-\mathrm{Prolong},\mathrm{Gamma},1\right)$
M > $A≔\mathrm{GroupActions}:-\mathrm{IsotropySubalgebra}\left(\mathrm{Γ1},\left[x=a,y\left[\right]=b,y\left[1\right]=c\right]\right)$
M > $\mathrm{is}\left(\mathrm{nops}\left(A\right)\ne 0\right)$
M > end:
M >
M > $\mathrm{P1}≔\left(\right)↦\mathrm{Query}\left("Semisimple"\right)$
${\mathrm{P1}}{≔}\left({}\right){→}{\mathrm{LieAlgebras}}{:-}{\mathrm{Query}}{}\left({"Semisimple"}\right)$ (2.8)
M > $\mathrm{VFS}≔\mathrm{Browse}\left("Gonzalez-Lopez",1\right)$
${\mathrm{VFS}}{≔}\left[\left[{1}\right]{,}\left[{2}\right]{,}\left[{3}\right]{,}\left[{4}\right]{,}\left[{5}\right]{,}\left[{6}\right]{,}\left[{7}\right]{,}\left[{8}\right]{,}\left[{9}\right]{,}\left[{10}\right]{,}\left[{11}\right]{,}\left[{12}\right]{,}\left[{13}\right]{,}\left[{14}\right]{,}\left[{15}\right]{,}\left[{16}\right]{,}\left[{17}\right]{,}\left[{18}\right]{,}\left[{19}\right]{,}\left[{20}{,}{1}\right]{,}\left[{20}{,}{2}\right]{,}\left[{20}{,}{3}\right]{,}\left[{20}{,}{4}\right]{,}\left[{20}{,}{5}\right]{,}\left[{21}{,}{1}\right]{,}\left[{21}{,}{2}\right]{,}\left[{21}{,}{3}\right]{,}\left[{21}{,}{4}\right]{,}\left[{21}{,}{5}\right]{,}\left[{22}{,}{1}\right]{,}\left[{22}{,}{2}\right]{,}\left[{22}{,}{3}\right]{,}\left[{22}{,}{4}\right]{,}\left[{22}{,}{5}\right]{,}\left[{22}{,}{6}\right]{,}\left[{22}{,}{7}\right]{,}\left[{22}{,}{8}\right]{,}\left[{22}{,}{9}\right]{,}\left[{22}{,}{10}\right]{,}\left[{22}{,}{11}\right]{,}\left[{22}{,}{12}\right]{,}\left[{22}{,}{13}\right]{,}\left[{22}{,}{14}\right]{,}\left[{22}{,}{15}\right]{,}\left[{22}{,}{16}\right]{,}\left[{22}{,}{17}\right]{,}\left[{22}{,}{18}\right]{,}\left[{22}{,}{19}\right]{,}\left[{22}{,}{20}\right]{,}\left[{22}{,}{21}\right]{,}\left[{22}{,}{22}\right]{,}\left[{22}{,}{23}\right]{,}\left[{22}{,}{24}\right]{,}\left[{22}{,}{25}\right]{,}\left[{22}{,}{26}\right]{,}\left[{22}{,}{27}\right]{,}\left[{22}{,}{28}\right]{,}\left[{22}{,}{29}\right]{,}\left[{22}{,}{30}\right]{,}\left[{22}{,}{31}\right]{,}\left[{22}{,}{32}\right]{,}\left[{22}{,}{33}\right]{,}\left[{22}{,}{34}\right]{,}\left[{22}{,}{35}\right]{,}\left[{22}{,}{36}\right]{,}\left[{22}{,}{37}\right]{,}\left[{23}{,}{1}\right]{,}\left[{23}{,}{2}\right]{,}\left[{23}{,}{3}\right]{,}\left[{23}{,}{4}\right]{,}\left[{23}{,}{5}\right]{,}\left[{23}{,}{6}\right]{,}\left[{23}{,}{7}\right]{,}\left[{23}{,}{8}\right]{,}\left[{23}{,}{9}\right]{,}\left[{23}{,}{10}\right]{,}\left[{23}{,}{11}\right]{,}\left[{23}{,}{12}\right]{,}\left[{23}{,}{13}\right]{,}\left[{23}{,}{14}\right]{,}\left[{23}{,}{15}\right]{,}\left[{23}{,}{16}\right]{,}\left[{23}{,}{17}\right]{,}\left[{23}{,}{18}\right]{,}\left[{23}{,}{19}\right]{,}\left[{23}{,}{20}\right]{,}\left[{23}{,}{21}\right]{,}\left[{23}{,}{22}\right]{,}\left[{23}{,}{23}\right]{,}\left[{23}{,}{24}\right]{,}\left[{23}{,}{25}\right]{,}\left[{23}{,}{26}\right]{,}\left[{23}{,}{27}\right]{,}\left[{23}{,}{28}\right]{,}\left[{23}{,}{29}\right]{,}\left[{23}{,}{30}\right]{,}\left[{23}{,}{31}\right]{,}\left[{23}{,}{32}\right]{,}\left[{23}{,}{33}\right]{,}\left[{23}{,}{34}\right]{,}\left[{23}{,}{35}\right]{,}\left[{23}{,}{36}\right]{,}\left[{23}{,}{37}\right]{,}\left[{24}{,}{1}\right]{,}\left[{24}{,}{2}\right]{,}\left[{24}{,}{3}\right]{,}\left[{24}{,}{4}\right]{,}\left[{24}{,}{5}\right]{,}\left[{25}{,}{1}\right]{,}\left[{25}{,}{2}\right]{,}\left[{25}{,}{3}\right]{,}\left[{25}{,}{4}\right]{,}\left[{25}{,}{5}\right]{,}\left[{26}{,}{1}\right]{,}\left[{26}{,}{2}\right]{,}\left[{26}{,}{3}\right]{,}\left[{26}{,}{4}\right]{,}\left[{26}{,}{5}\right]{,}\left[{27}{,}{1}\right]{,}\left[{27}{,}{2}\right]{,}\left[{27}{,}{3}\right]{,}\left[{27}{,}{4}\right]{,}\left[{27}{,}{5}\right]{,}\left[{28}{,}{1}\right]{,}\left[{28}{,}{2}\right]{,}\left[{28}{,}{3}\right]{,}\left[{28}{,}{4}\right]{,}\left[{28}{,}{5}\right]\right]$ (2.9)
M > $\mathrm{ans}≔\mathrm{Search}\left("Gonzalez-Lopez",1,\mathrm{indexlist}=\mathrm{VFS}\left[1..25\right],\mathrm{Liealgebraproperties}=\left[\mathrm{P1}\right],\mathrm{VFSproperties}=\left[\mathrm{Q1},\mathrm{Q2}\right],\mathrm{manifold}=M\right)$
${\mathrm{ans}}{≔}\left[\left[{11}\right]\right]$ (2.10)
M > $\mathrm{Browse}\left("Gonzalez-Lopez",1,\mathrm{ans},\mathrm{manifold}=M\right)$
${"Gonzalez-Lopez"}{,}{1}{,}\left[{11}\right]$ $\left[{\mathrm{D_x}}{,}{x}{}{\mathrm{D_x}}{,}{{x}}^{{2}}{}{\mathrm{D_x}}\right]$ ${\mathrm{___________________}}$ (2.11)
|
2022-10-04 00:22:46
|
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 38, "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": 0.8117526769638062, "perplexity": 1357.072734512131}, "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/1664030337446.8/warc/CC-MAIN-20221003231906-20221004021906-00170.warc.gz"}
|
http://mathhelpforum.com/calculus/222365-implicit-diff-cos-print.html
|
# Implicit Diff with Cos
Printable View
• Sep 28th 2013, 10:36 AM
Jason76
Implicit Diff with Cos
$f(x) = y\cos(x) = 2x^{2} + 5y^{2}$
$[\cos(x)][1]y' + [y][-\sin(x)] = 4x + 10yy'$
$\cos(x)y' + [-\sin(x)y] = 4x + 10yy'$
$\cos(x)y' - \sin(x)y = 4x + 10yy'$
$\cos(x)y' - 10yy' = \sin(x)y + 4x$
$y'[\cos(x) - 10y] = \sin(x)y + 4x$
$y' = \dfrac{ \sin(x)y + 4x}{\cos(x) - 10y}$ :confused:
• Sep 28th 2013, 12:52 PM
HallsofIvy
Re: Implicit Diff with Cos
If your question is whether or not this is correct, yes, it is.
|
2017-03-26 13:34:53
|
{"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": 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": 0.981741189956665, "perplexity": 8695.169908529457}, "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-2017-13/segments/1490218189239.16/warc/CC-MAIN-20170322212949-00512-ip-10-233-31-227.ec2.internal.warc.gz"}
|
https://chemistry.stackexchange.com/questions/140108/application-of-markovnikovs-rule-with-ewgs-and-resonance
|
# Application of Markovnikov's rule with EWG's and Resonance
I want to ask a question concerning Markovnikov's rule.
Consider the following question:
We can tell that there will be two types of stabilisation upon formation of the carbocation:
• Resonance via the phenyl group
• sigma-hyperconjugation via the methyl group
When attempting this question, I thought the more stable carbocation would be the one where the positive charge lies to the left of the alkene double bond, and can be stabilised by the phenyl group, since resonance stabilisation is stronger than sigma hyperconjugation to yield the major isomer.
However, the answers state the opposite:
They state that the more stable carbocation is the one that can be stabilised by sigma-conjugation, yielding the alternate product, due to more carbon (groups) being attached to the carbon on the double bond. I thought it would be less stable as it is destabilised by the EWG aldehyde group and stabilised by the weaker sigma-hyperconjugation.
What is the correct interpretation of the answer?
• When I tried modeling $\ce{[Mol\bond{...}X]+}$, both halogens ended up beta to the carbonyl group, so I'd conclude it really depends on the orientation with which the $\ce{ICl}$ reacts with. Sep 11 '20 at 12:53
• @Martin-マーチン by "modelling $\ce{[Mol...X]+}$, both halogens ended up beta" do you mean the halogen which forms the cyclic intermediate? Sep 11 '20 at 13:00
• @Safdar In the model, there is no cyclic intermediate, or at least there are significantly different leg lengths. See for example image: Regioselectivity of bromination of alkenes, but it is much more pronounced. Sep 11 '20 at 13:11
• Does Anchimeric Assistance have to do something with this? Sep 11 '20 at 15:47
• To be honest, I don't understand and you don't make it clear how Markovnikov's rule would apply here. Could you clarify please. Sep 11 '20 at 21:13
|
2021-09-28 19:23:18
|
{"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": 0.6599041223526001, "perplexity": 1606.6881337071532}, "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/1631780060882.17/warc/CC-MAIN-20210928184203-20210928214203-00585.warc.gz"}
|
https://reference.wolframcloud.com/language/ref/PowerExpand.html
|
PowerExpand
PowerExpand[expr]
expands all powers of products and powers.
PowerExpand[expr,{x1,x2,}]
expands only with respect to the variables xi.
Details and Options
• PowerExpand converts to , whatever the form of is.
• PowerExpand also converts to , whatever the form of is.
• The transformations made by PowerExpand are correct in general only if is an integer or and are positive real numbers.
• PowerExpand converts Log[a^b] to bLog[a].
• PowerExpand in general disregards all issues of branches of multivalued functions, so may not preserve the numerical values of expressions.
• PowerExpand automatically threads over lists, as well as equations, inequalities and logic functions.
• PowerExpand has the option Assumptions, specifying assumptions to use.
• The default setting for the Assumptions option is Automatic, corresponding to a maximal set of assumptions.
• You can specify default assumptions for PowerExpand using Assuming.
Examples
open allclose all
Basic Examples(1)
Expand a square root, implicitly assuming positive real values:
Without PowerExpand, no expansion is done:
The expansion is only correct for positive real variables:
This gives a completely correct result:
This gives a result correct under the specified assumptions:
Scope(11)
Expand a power of a product; the result may not be correct everywhere:
The general formula for expanding a power of a product:
Expand nested powers; the results may not be correct everywhere:
General formulas for expanding a nested power:
Expand the logarithm of a power; the result may not be correct everywhere:
The general formulas for expanding logarithms of powers:
Expand the logarithm of a product; the result may not be correct everywhere:
The general formula for expanding the logarithm of a product:
Expand compositions of inverse trigonometric and trigonometric functions:
This gives the universally correct formula:
Compute an expansion valid under the specified assumptions:
Expand the argument of a product:
Expand only with respect to a and b:
Options(3)
Assumptions(3)
With the default setting the expansions are not always correct:
When the assumptions are specified the result is correct under the given assumptions:
With , PowerExpand gives a universally correct expansion formula:
Applications(2)
Find universally correct expansion rules:
Expand under specified assumptions:
Properties & Relations(5)
PowerExpand performs expansions valid under the given assumptions:
With , PowerExpand gives general expansion formulas:
Refine and Simplify perform expansions valid under the given assumptions:
Use FunctionExpand to get a different representation of :
Use PiecewiseExpand to represent the result as a piecewise function:
Possible Issues(1)
The result given by PowerExpand with may be incorrect:
Wolfram Research (1991), PowerExpand, Wolfram Language function, https://reference.wolfram.com/language/ref/PowerExpand.html (updated 2007).
Text
Wolfram Research (1991), PowerExpand, Wolfram Language function, https://reference.wolfram.com/language/ref/PowerExpand.html (updated 2007).
CMS
Wolfram Language. 1991. "PowerExpand." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2007. https://reference.wolfram.com/language/ref/PowerExpand.html.
APA
Wolfram Language. (1991). PowerExpand. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/PowerExpand.html
BibTeX
@misc{reference.wolfram_2022_powerexpand, author="Wolfram Research", title="{PowerExpand}", year="2007", howpublished="\url{https://reference.wolfram.com/language/ref/PowerExpand.html}", note=[Accessed: 30-January-2023 ]}
BibLaTeX
@online{reference.wolfram_2022_powerexpand, organization={Wolfram Research}, title={PowerExpand}, year={2007}, url={https://reference.wolfram.com/language/ref/PowerExpand.html}, note=[Accessed: 30-January-2023 ]}
|
2023-01-30 08:06:08
|
{"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": 0.8041893243789673, "perplexity": 6906.015643097664}, "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-2023-06/segments/1674764499804.60/warc/CC-MAIN-20230130070411-20230130100411-00013.warc.gz"}
|
http://tex.stackexchange.com/questions?page=1&sort=active&pagesize=15
|
# All Questions
11 views
### How to display index entries on the same line as the text being indexed
Is it possible to let showidx display index entries on the same line as the text being indexed? It seems not as makeindx.pdf says: This macro actually typesets the box containing all the index ...
42 views
### Adding shell commands to hide LaTeX Aux files after compiling in TeXShop or TexStudio
I run LaTeX under OSX, and I would like to attempt to hide all of the LaTeX helper files from the finder after compiling. It strikes me that the simplest thing to do is not to move them or delete them ...
294 views
### OCR PDF/Image to LaTeX (math) [on hold]
I would love to have an OCR who could translate my PDF-file to a TeX-file. It doesn't have to be "good looking". I only need it to a) copy some text from time to time and b) especially to copy the ...
20 views
### dramatist remove spacing between speech items
I'm typesetting a drama script using the dramatist package, which defines the drama environment, which is basically a list environment, and each speech entry is a list item. Since I need to print the ...
27 views
### Include a tex file that contains the bibliography section
I found when I tried to keep the spaces in my file name by using \include{{""}}, then the file could still be included, but the references would be question marks. This is my MWE ...
25 views
### ltablex caption text formatting issue
I'm using the ltablex package for creating long tables over multiple pages. For my other small tables I use the tabularx package and I noticed a formatting mistake or maybe a bug? The table caption ...
76 views
### paragraph over 2 columns in an article document
I have a two column format for an article and a small paragraph which i want to split in those 2 columns(hard break). I dont want to use \vfill, as I am intending to display a table after the ...
22 views
### Different subsection format if no title is given
I want to have subsections appear like "Article 1: Foo" when I enter \subsection{Foo}, but like "Article 1" (without the colon) when I enter \subsection{} (without a title). Is there a way to do this? ...
22 views
### Custom PSTricks directory tree to TikZ
I have a PSTricks implementation of a custom directory tree which I find quite appealing. I basically want to convert the whole thing to TikZ. I managed to get the very basic idea running in TikZ: I ...
11 views
### Highlight/Link Author and Year in Citation
I'm currently modifying the Masters/Doctoral Thesis template found here. However, it only highlights the year in a citation like (Smith 2016). I would like both "Smith" and "2016" to be part of the ...
10 views
### Error using pandoc when converting from markdown topdf
I am trying to convert a document from markdown to pdf. I use this as a yaml metadata block at the top: --- author: Vamsi Deepak Ampolu title: resume papersize: letter documentclass: article ...
26 views
### Beamer Navigation bar too long
My navigation bar in Beamer is too long with the way it is presently formatted. I have considered going to multiple lines for the circle navigation, but this results in the vertical space of the ...
297 views
### Detect whether running on pdfTeX or Knuth's TeX for conditional include
Does anyone know a way to detect whether one is running in pdfTeX or Knuth's TeX? I want to be able to conditionally include extra features when a document is being built using pdfTex, but also ...
13 views
### Euler-Digits + siunitx hiding certain units (like Ohm)
It's been a couple of months since I last used my TeX, so I did some updates that became availabe (using MikTeX's software - Windows 7/64bit) and as of that moment, I noticed that my siunitx package ...
85 views
+50
### Tablespecification and complex column
Based on 2 former questions I have found another problem, I am not aware about that this could be a problem. Question 1: Conditional complex column type Question 2: Generic table definitions But I ...
36 views
### Minted text changes _ to \_ in the final PDF
I'm writing a report and I found something wrong after compiling it. The PDF file showed things like \_ instead of _ and \textquotedbl{} instead of quotation marks. It's pretty important for me to fix ...
23 views
### mdframed and skipbelow
There are many questions online concerning this issue of skipbelow of the mdframed package. For me, this skipbelow issue is not resolved. The version of the mdframed package on my system is: ...
140 views
### How can I redefine \int to put a negative space after the integral sign, but keep the limits properly set?
I'd like to modify the \int command such that it adds an automatic negative space, e.g. \! after the integral sign. Preferentially, I'd like to be able to not edit any of my code, so cleverly ...
15 views
### Some items in bibliography are not aligned
I am adding some items to my bibliography: \bibitem{ibm2}vander Meûlen, R. J. (2006). The immersed boundary method for the (2d) incompressible Navier--Stokes equations. Modelling, Analysis and ...
50 views
I wanted to add the lines from the edge of the left margin to the colored box in my section headers so this it looks like: Here is the code I have thus far: \documentclass[11pt]{book} ...
44 views
### Is there a possibility to make a circle around a node like on the photo?
I would really like to have a circle around the first node of my tree like you can see on the photo. Is there a possibility? I only startet with latex and there is so much new for me... Thank you!! ...
53 views
### tufte-book: tikz references in caption
Using the article documentclass, the following code works as expected. \documentclass{article} \usepackage{lipsum} \usepackage{caption} \usepackage{pgfplots} \pgfplotsset{compat=1.13} ...
188 views
### How to produce this table in latex?
I want to produce the first two rows of this 5-column table in LaTeX: As you can see it is a special type of tables where we see: itemized lists inside but inconsistently, ie. column 4 all rows ...
5k views
### TikZ: draw line thickness less than 0.1 mm
In TikZ is it possible to draw lines thinner than 0.1 mm? ultra thin option gives line thickness 0.1 mm. I want to draw a pattern using line thickness 0.07 mm.
29 views
### Generate barcodes with a for loop
I want to create labels with barcodes. The individual barcodes should be a sequence of numbers which identify objects. After some trial and error, the GS1 package seemed to work for me. Since I have ...
425 views
### LaTeX using the matching environment in the exam documentclass
Could someone please share a working example of using the matching environment in a document class exam. I am new to using the exam document class and am unable to find a way to set up the matching ...
43 views
### Cannot define new unit with siunitx
I've been reading almost two hours through various posts that seem to have the same problem but none of the solutions worked for me. I want to define new units (in my case it's \thermal and ...
45 views
### Can I point Gummi to use TeX instead of LaTeX?
gummi is a great text editor since it has continuous re-fresh. Can I link it to TeX instead of LaTeX? Here is why: Some commands only work with TeX and not LaTeX. me@Lenovo:~/Documents\$ latex ...
49 views
### Linebreak does not work in section headings modified with tikz
I have a problem with long sub/section headings: \\ is not wirking. As I'm new to Latex, I adopted this beautiful template http://www.fluortools.com/misc/LaTeXtemplate and modified it for my needs. ...
4k views
### Selfhosted collaborative webbased LaTeX editor
I'm searching for a LaTeX editor that I can run on my GNU/Linux server and allows realtime collaboration as well as online compiling and previewing. What I've tried so far: FlyLaTeX: Editing works ...
27 views
### Positioning tikzpicture and determining range for axis
In another question I got great help creating this picture: Actually it looks how it should but there are two further things I would like to clarify: Firstly, I get this warning: Axis range for ...
57 views
### Multiple sorting with biblatex
I'm trying to use biblatex to produce two different bibliographies. The first one should contains only my papers, sorted in order of appearance in the text, and with some special prefix. The second ...
35 views
### The directory when you install TeXnicCenter
My whole problem started when I upgraded Adobe Reader to the version DC, it crashed down my LaTeX, I replaced the DC version by the older one. I remove MiKTeX and TeXnicCenter and installed them ...
226 views
### Include Inkscape in pdfLaTeX problem
I have the following problem to include a pdf (also tried eps) to a latex document. I always get this fault: ! Extra }, or forgotten \endgroup. \endpicture ->\egroup \hss \egroup ...
35 views
According to Using .toc external files, the following file should display the table of contents twice: \documentclass{report} \begin{document} \tableofcontents \chapter*{Contents (manual input)} ...
38 views
### Can't use fontspec with LuaLatex [on hold]
I have MiKTeX 2.9 installed on Windows 7. I want to make use of the package fontspec, but the command \usepackage{fontspec} is enough to cause the following error message: LaTeX Error: File ...
23 views
### Flashcards with figures [on hold]
I want to make some flashcards of my anatomy notes, i guess i need to use the flashcards class. But then my problem is that i can't have figures/images on the flashcards, it won't compile; It gives ...
13 views
### no option set default output format as pdf
I've recently installed lyx on arch 64, and the 'view buffer' button as well as the shortcut (Ctrl+r) are disabled, after a bit searching I read that it's necessary to set the default output format ...
23 views
### Use single or compact spacing in side notes
I have a document that by default uses double spacing. This is fine for the main text, but side notes use lots of space. How can I disable double spacing for margin side notes? ...
12 views
### How do I underline the DOI in the bibliography using biblatex/biber? (Context: continued work on SAE class)
I've been continuing the work of developing a modern SAE class, and have found previous helps on this forum extremely useful. The next thing I am trying to accomplish is underlining the DOI in the ...
5k views
### Axis with trigonometric labels in PGFPlots
How do I make the axis labels use multiples of \pi in PGFPlots?
71 views
### Label axis in units of pi (or pi/2) and use minor tick num [duplicate]
Using pgfplots, I often want to label the horizontal axis major ticks in units of pi or pi/2, or pi/3. Is it possible to have such "trigonometric major ticks" use minor tick num = <value> to ...
19 views
### Auto-format for \ref, \cite
Is there a way of getting texstudio to insert ~\cite instead of \cite{}, as well as ~(\ref{}) instead of just \ref{}, similar to Emacs/AucTeX?
15 views
### Aligning minipages with new margins
I've extended the page margins using geometry, but when I create a minipage for my headings the right aligned minipage aligns with the original margin. How can I make it so that it aligns with the ...
114 views
### Minimize hyphenations with ragged2e
Nearly every guide to LaTeX recommends \RaggedRight from the ragged2e package over the built-in \raggedright. But I've always been frustrated by too many hyphenated words with \RaggedRight. I ...
16 views
### BibTex citing format: Hide Indices/key for CV
For my CV (pdflatex) I like to add my publications (BibTex) but a can't get rid of the keys/indices for the cite entrys. Unfortunately I like to use a special mstyle.bst file (I hadn't made myself) ...
59 views
### Different symbol for g
How can I write in "curly" form of g in an equation? Just "g" gives me this
34 views
### PGFPlots - Legend box aligning with axis [duplicate]
I am trying to increase the size of the legend such that it exactly fits to size of the plot. But even after having a look at the PGF manual I could not figure out how I can realise my plan. ...
|
2016-02-10 04:56:52
|
{"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": 0.9689481258392334, "perplexity": 3404.05330201304}, "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-2016-07/segments/1454701158609.98/warc/CC-MAIN-20160205193918-00065-ip-10-236-182-209.ec2.internal.warc.gz"}
|
https://mathoverflow.net/questions/43799/discrete-morse-theory-and-existence-of-minimal-complex
|
# Discrete Morse theory and existence of minimal complex
A minimal complex is a CW complex whose only cells are the homology cells.
Is there some sort of criterion on CW complexes about existence of minimal complexes?
Actually I am working on a problem of understanding homotopy type of certain spaces (see: How to show that a space has the homotopy type of wedge of spheres ?)
My hope was to use discrete Morse theory (acyclic matching of face poset to be precise) and find the minimal complex. But then I don't know if the existence of the minimal complex is always guaranteed.
• Have you read the Whitehead theorems on minimal CW-complexes? They're in many textbooks, for example, G.W. Whitehead's text, or section 4.C of Hatcher's notes. See the references in Hatcher's notes for more details. – Ryan Budney Oct 27 '10 at 14:20
• @JimConant That paper seems to have been written "too early". In particular, it contains the incorrect claim (Example 1.6) that the Whitehead group of $\mathbb{Z}\Pi$ for $\Pi$ a finite abelian group is trivial. The first counter-example is $\Pi = \mathbb{Z}/5$ whose whitehead group is $\mathbb{Z}/2$. – Vidit Nanda Sep 23 '14 at 3:58
|
2019-03-22 05:09:36
|
{"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": 0.6764938831329346, "perplexity": 401.3520921872057}, "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-2019-13/segments/1552912202628.42/warc/CC-MAIN-20190322034516-20190322060516-00487.warc.gz"}
|
https://www.lucidar.me/en/markdown/markdown-horizontal-lines/
|
Do me a favor, take a few seconds to have a look at my last project.
Thank you, Lulu
# Markdown horizontal lines
To create horizontal lines in Markdown, use one of the following syntax:
___
---
***
The previous code displays:
## See also
Last update : 04/13/2019
|
2019-04-21 00:41:59
|
{"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": 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": 0.21774567663669586, "perplexity": 6447.438482096861}, "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-2019-18/segments/1555578530100.28/warc/CC-MAIN-20190421000555-20190421022555-00381.warc.gz"}
|
https://studyadda.com/notes/9th-class/mathematics/geometry/geometry/16455
|
# 9th Class Mathematics Geometry
Geometry
Category : 9th Class
Geometry
In this chapter, we will learn about introduction to euclid’s geometry, lines and angles, triangles, quadrilaterals, areas of parallelograms and triangles and circles.
Axioms
Axioms or postulates are the assumptions which are obvious universal truths. They are not proved.
Theorems
Theorems are statements which are proved using definitions, axioms, previously proved statements and deductive reasoning.
Euclid’s Axioms
1. The things which are equal to the same thing are equal to one another.
2. If equals be added to the equals, the wholes are equal.
3. If equals be subtracted from equals, the remainders are equals.
4. Things which coincide with one another are equal to one another.
5. The whole is greater than the part.
6. Things which are double of the same thing are equal to one another.
7. Things which are halves of the same thing are equal to one another.
Euclid’s Postulates
1. A straight line may be drawn from any point to any other point.
2. A terminated line (line segment) can be produced indefinitely.
3. A circle may be described with any centre and any radius.
4. All right angles are equal to one another.
5. If a straight line falling on two straight lines makes the interior angles on the same side of it, taken together less than two right angles, then the two straight lines if produced indefinitely, meet on that side on which the sum of angles is taken together less than two right angles.
Point
A point is a fine dot. For example, P is a point as shown in the figure.
$\bullet P$
Line Segment
A line segment is a straight path between two given points. For example in the shown figure PQ is a straight path between the pints P and Q and so is called a line segment $\overline{PQ}$
A line segment has a definite length.
Ray
A ray is a line segment extending indefinitely in one direction. A ray has no definite length. For example, in the shown figure $\overrightarrow{PQ}$ is representing a ray having one and point P.
Line
A line is a ne is obtained on extending a line segment indefinitely in both the directions. In the shown figure, 0$\overleftrightarrow{PQ}$ is represented as a line. A line has no end points so a line has no definite lengths.
Angle
An angle is generated when two rays originated from the same end point. In the shown figure POQ is the angle formed by two rays and . Here O is called the vertex of the $\angle$POQ and PO and OQ are called the arms of the angle POQ.
Note:
(i) If a ray stands on a line, then so formed adjacent angles are supplementary and its converse.
(ii) The vertically opposite angles formed by two intersecting lines are equal.
Parallel Lines and a Transversal
If a transversal intersects two parallel lines, then
(i) Each pair of alternate interior angles is equal and conversely.
(ii) Each pair of corresponding angles is equal and conversely.
(iii) Each pair of interior angles on the same side of the transversal is supplementary and conversely.
Note: Lines parallel to the same line are parallel to each other.
Triangle
A closed figure formed by three line segments is called a triangle. A triangle has three sides, three angles and three vertices. Two figures of same shape and same size are called congruent figures. Two circles of the same radii are congruent. Two triangles ABC and PQR are congruent $(ie.\,\,\Delta \,\,ABC\cong \Delta \,\,PQR)$under the correspondence $A\leftrightarrow P,\,\,B\leftrightarrow Q\,\,and\,\,C\leftrightarrow R$
Note:
(i) Sum of all the three interior angles of a triangle is$180{}^\circ$.
(ii) The exterior angle of a triangle is equal to the sum of the corresponding two interior opposite angles.
Congruent Figures
Two geometrical figures are said to be congruent if they have same shape and size. e.g. two angles are said to be congruent if they have same measures similarly two line segments are said to be congruent if they have same lengths.
Congruency of Triangles
Two triangles ABC and DEF are said to be congruent if and only if, AB = DE, BC = EF, CA =FD, $\angle$A = $\angle$D, $\angle$B = $\angle$E and $\angle$C = $\angle$F.
Criteria for Congruency of triangles
There are generally four criteria for the congruency of triangles which are given below.
S-S-S Criteria
Two triangles are said to be congruent if the three sides of one triangle are equal to the corresponding three sides of the other.
S-A-S Criteria
Two triangles are said to be congruent if the two sides and included angle of one triangle is equal to the other.
A-S-A Criteria
If the two angles and the side included by the angles are equal to the corresponding two angles and included side of the other triangle, then the two triangles are congruent.
R-H-S Criteria
This criteria is for a right-angled triangle. If one side and hypotenuse of a right-angled triangle is equal to the corresponding side and hypotenuse of other right-angled triangle then two right angled triangles are said to be congruent.
Some Important Results
• The longer side of a triangle has greater angle opposite to it.
• The greater angle of a triangle has longer side opposite to it.
• Perpendicular line segment is shortest in length.
• The sum of any two sides of a triangle is greater than the third side.
• The difference between any two sides of a triangle is always less than its third side.
• Angles opposite to equal sides of a triangle are equal.
• Sides opposite to equal angles of a triangle are equal.
Similarity of Triangles
When two geometrical shapes resembles same but need not to be equal in size are called similar figures. Let us observe the following examples:
(i) Any two line segments are always similar.
(ii) Two circles of different radius are always similar.
(iii) For rectilinear figures if all the corresponding angles of a polygon are equal and the ratio of their corresponding sides are also equal, then they are said to be similar.
The criteria of similarity of two triangles are
(i) A-A-A criterion (ii) S-S-S criterion
(iii) S-A-S criterion
The ratio of the areas of two similar triangles is equal to the ratio of the,
• Squares of any two sides of the triangles.
• Squares of their altitudes.
• Squares of their corresponding medians.
• Squares of their corresponding angle bisector segments.
A Plane figure bounded by four line segments is called a quadrilateral.
• Points J, K, L and M are the vertices of quadrilateral JKLM.
• The line segments JK, KL, LM and MJ are the sides of the quadrilateral.
• The two sides of a quadrilateral having a common point are called adjacent sides.
• The two sides having no common end points is called opposite side.
• Two angles of a quadrilateral having common arm are called adjacent angles.
• Two angles of a quadrilateral having no common arm are called opposite angles.
• A quadrilateral is a parallelogram, if
(i) Opposite sides are equal.
Or (ii) Opposite angles are equal.
Or (iii) Diagonals bisect each other.
Or (iv) A pair of opposite sides is equal and parallel.
• In a rectangle, diagonals are equal and bisect each other and vice-versa.
• In a rhombus, diagonals bisect each other at right angles and vice-versa.
• In a square, diagonals bisect each other at right angles and are equal and vice-versa.
• The line segments joining the mid-points of any two sides of a triangle is parallel to a third side and is half of it.
• A line through the mid-point of a side of a triangle parallel to another side bisects the third side.
• The quadrilateral formed by joining the mid-points of the sides of a quadrilateral, in order, is a parallelogram.
• The diagonals of a rectangle are equal.
• If the two diagonals of a parallelogram are equal then the parallelogram is a rectangle.
• The diagonal of a rhombus are perpendicular to each other.
• A parallelogram is a square if the diagonals of a parallelogram are equal and intersect at right angles.
• The sum of all angles of a quadrilateral is always$360{}^\circ$.
Results on Areas of Parallelograms and Triangles
• Any diagonal of a parallelogram divides it into two triangles of equal area.
• Triangles which are on the same base and between the same parallel lines are equal in area.
• A median of a triangle divides it into two triangles of equal areas.
• Area of a triangle is half the product of its base and the corresponding altitude.
• Triangles on the same base and having equal areas lie between the same parallels
• If a parallelogram and a triangle are on the same base and between the same parallels, then area of the triangle is half the area of the parallelogram.
• Area of a parallelogram is the product of its base and the corresponding altitude.
• A parallelogram and a rectangle on the same base and between the same parallels are equal in area.
• Parallelograms which are on the same base and between the same parallel lines are equal in area.
Circle
Circle is the locus of a point which moves in a plane in such a way that its distance from a fixed point is always constant. We know that the fixed point is called centre and the fixed distance is called its radius. Also,
$D\text{ }=\text{ }2r$,$C=2\pi r$, where D is diameter, C is circumference of circle and r is radius.
Terms Related to a Circle
Following are some terms which are very useful in solving the problems related to circles.
Secant
When a line intersects a circle at two distinct points, it is called a secant of the circle. In the following figure line m is a secant of the circle.
Tangent
A line which touches the circle at exactly one point is called a tangent to the circle. In the following figure PQR is a tangent of the circle.
Concentric Circles
Circles are said to be concentric if and only if they have the same centre and different radii.
Concurrent Arc
A continuous piece of circumference of a circle is called an arc and two arcs are said to be concurrent if they subtend equal angles at the centre.
Here, $Arc\,\,\overset\frown{RNS}\equiv Arc\overset\frown{\,\,PMQ}$
Properties of Circles
• Equal chords of a circle (or of congruent circles) subtend equal angles at the centre.
• If the angles subtended by two chords of a circle (or of congruent circles) at the centre (corresponding centres) are equal, the chords are equal.
• The perpendicular drawn form the centre of a circle to a chord bisects the chord.
• There is only one circle possible which can pass through three non collinear points.
• The line drawn through the centre of a circle to bisect a chord is perpendicular to the
• Equal chords of a circle are equidistant from the centres.
• Chords equidistant from the centre of a circle are equal in length.
• If two chords of a circle are equal, then their corresponding arcs are congruent and its converse.
• The angle subtended by an arc at the centre is double the angle subtended by it at any point on the remaining part of the circle.
• Angles in the same segment of a circle are equal.
Note:
(i) The sum of either pair of opposite angles of a cyclic quadrilateral is$180{}^\circ$.
(ii) If the sum of a pair of opposite angles of a quadrilateral is 180°, the quadrilateral is cyclic.
(iii) Radius of incircle and circumcircle of an equilateral triangle of side a $a=\frac{a}{2\sqrt{3}}$ and $\frac{a}{\sqrt{3}}$ respectively.
Example:
In the figure given below the height of two poles are 10 metres and 15 metres. If the poles are 30 metres apart then the height of point of intersection of the lines joining the top of each pole from opposite foot of the other pole is:
(a) 18m (b) 8m
(c) 6m (d) 9 m
(e) None of these
In the given figure, $\Delta CAB\sim \Delta CEF\Rightarrow \frac{EF}{10}$$=\frac{FC}{30}\Rightarrow FC=3EF$
Similarly in $\Delta ACD\sim \Delta AFE,$ so we have $\frac{EF}{15}=\frac{AF}{30}\Rightarrow AF=2EF$
From above equations, we get $5EF=30\Rightarrow EF=6m$
Example:
In an equilateral triangle show that the centroid and circumcenter coincide.
Solution:
Given: An equilateral triangle PQR in which M, L and N are the mid points of sides QR, RP and PQ respectively.
To prove: The centroid and circumcentre are coincident in $\Delta PQR$
Construction: Draw medians PM, QL and RN
Proof: Let G be the centroid of $\Delta PQR$ is the point of intersection of medians QL, RN and MP.
In $\Delta QNR$ and $\Delta QLR$we have,
$\angle Q=\angle R=60{}^\circ$ and QN=RL and QR=RQ
$\Rightarrow$ (By SAS)
$\Rightarrow$RN=QL (CPCT) … (i)
Similarly, in $\Delta RPN\cong \Delta PRM$
$\Rightarrow$RN = PM (CPCT) ... (ii)
From (i) and (ii), we get
RN = PM = QL
$\Rightarrow$$\frac{2}{3}$ RN $\frac{2}{3}$ PM = $\frac{2}{3}$ QL
$\Rightarrow$ GR= GP = QG $\Rightarrow$ G is equidistant from the vertices.
$\Rightarrow$ G is circumcentre of$\Delta PQR$.
Hence the centroid and circumcentre of $\Delta PQR$ are coincident.
Example:
In the figure given below.
$\frac{AP}{PC}=\frac{3}{4}$ and $\frac{BR}{RP}=\frac{3}{2}$ and BQ = 15 cm. Find AQ
Solution:
Given: $\frac{AP}{PC}=\frac{3}{4}$, $\frac{BR}{RP}=\frac{3}{2}$ and BQ = 15cm
Draw PS || CQ which meets AB at S.
Applying basic proportionality theorem, we get
$\frac{BQ}{QS}=\frac{BR}{RP}\Rightarrow \frac{15}{QS}=\frac{3}{2}\Rightarrow$QS=10 cm.
Similarly in$\Delta AQC$, we get
$\frac{AS}{SQ}=\frac{BR}{PC}\Rightarrow\frac{AS}{10}=\frac{3}{2}\Rightarrow AS=\frac{30}{4}$= 7.5 cm.
$\therefore$ AQ = AS + QS = 10 + 7.5 = 17.5 cm.
#### Other Topics
##### 15 10
LIMITED OFFER HURRY UP! OFFER AVAILABLE ON ALL MATERIAL TILL TODAY ONLY!
You need to login to perform this action.
You will be redirected in 3 sec
|
2019-08-24 06:41:33
|
{"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": 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": 0.617132306098938, "perplexity": 435.41954385470547}, "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-2019-35/segments/1566027319915.98/warc/CC-MAIN-20190824063359-20190824085359-00062.warc.gz"}
|
http://tex.stackexchange.com/questions/40237/installed-luximono-is-not-working
|
Installed Luximono is not working
I am using MacTex-2011 on a mac 10.7. Recently, I have installed luximono using getnonfreefonts. Everything went ok, but when I was compiling the document (pdfLaTeX) with the packages:
``````\usepackage[T1]{fontenc} \usepackage{luximono}
``````
luximono was not recognized, i.e. LaTeX used the standard font. Any ideas how to get it working?
-
Stupid question: If you want Luximono as the standard text font, have you tried `\renewcommand{\familydefault}{\ttdefault}`? – lockstep Jan 6 '12 at 11:41
what does `kpsewhich luximono.sty` say? – daleif Jan 6 '12 at 11:45
Luxi Mono is a monotype font and not enabled by default. If you want to use it change the default tt font family, use `\ttfamily` or `\texttt{..}`.
By the way: it is not a good idea to set the complete document in a monotype font.
-
What is the reason for avoiding monotype fonts for the complete document? – qubyte Jan 6 '12 at 13:09
compare it with another font ... However, if one has to submit an article to a journal, it may make sense to use a monotype font, counting charcters is easier. – Herbert Jan 6 '12 at 15:48
Oh! I thought you meant Monotype Corp. Yes, I can obviously see why a monospaced font is a bad idea! – qubyte Jan 6 '12 at 16:01
|
2016-05-04 02:27:20
|
{"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": 0.8820592164993286, "perplexity": 2778.476109897212}, "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-2016-18/segments/1461860122268.99/warc/CC-MAIN-20160428161522-00191-ip-10-239-7-51.ec2.internal.warc.gz"}
|
https://math.stackexchange.com/questions/1832885/5th-degree-polynomial-expression/1832901
|
# $5^{th}$ degree polynomial expression
$p(x)$ is a $5$ degree polynomial such that
$p(1)=1,p(2)=1,p(3)=2,p(4)=3,p(5)=5,p(6)=8,$ then $p(7)$
$\bf{My\; Try::}$ Here We can not write the given polynomial as $p(x)=x$
and $p(x)=ax^5+bx^4+cx^3+dx^2+ex+f$ for a very complex system of equation,
plz hel me how can i solve that question, Thanks
• – lab bhattacharjee Jun 20 '16 at 6:09
• You already have a very good start. You should recognize that from the given information you have a system of six equations and six unknowns. You may use matrices then to describe the scenario and use Gaussian Elimination to solve for the coefficients of the polynomial (or to solve for the space spanned by the solutions). From there, you can find $p(7)$. – JMoravitz Jun 20 '16 at 6:12
• Note the general result: a polynomial of degree $n$ is uniquely specified by $n+1$ points on its graph. – MathematicsStudent1122 Jun 20 '16 at 6:48
Let's do it in the most elementary way. Let $$Q(x)=P(x+1)-P(x)-x+2 \tag{1}$$Observe that $Q$ is of degree $4$ and $Q(3)=Q(4)=Q(5)=0$. Therefore we can write$$Q(x)=a(x-3)(x-4)(x-5)(x-b) \tag{2}$$You have also from $(1)$ that $Q(1)=Q(2)=1$, which after substitution in $(2)$ you get $a=-1/8$ and $b=2/3$. So $$Q(6)=-\frac{1}{8}(6-3)(6-4)(6-5)\left(6-\frac{2}{3} \right)=-4$$And finally$$P(7)=Q(6)+P(6)+6-2=-4+8+6-2=8$$
Like this problem, using difference of differences method,
• The nice thing about this is that it doesn't require any computations with large intermediate quantities, rational arithmetic, or row reduction on $6\times6$ matrices. The only downside is that the generalization to non-uniformly spaced sample points is not so obvious, whereas the other methods apply easily to such cases. – Erick Wong Jun 20 '16 at 6:29
• Yeah that's a big barricade and conundrum for this algorithm. – Zack Ni Jun 20 '16 at 6:56
• @ErickWong: the generalization is the computation of the Lagrange polynomial by the Neville scheme. But that would be overkill. – Yves Daoust Jun 20 '16 at 6:56
let $x_i=i\,$, $\,i=1,2,\cdots,6$ and apply Lagrange's interpolation method $${{L}_{i}}(x)=\frac{\prod\limits_{j\ne i,j=1}^{6}{(x-{{x}_{j}})}}{\prod\limits_{j\ne i,j=1}^{6}{({{x}_{i}}-{{x}_{j}})}}\,\,\,\,,\,\,\,i=1,2,\ldots ,7$$ $$P(x)=\sum\limits_{i=1}^{6}{{{L}_{i}}}(x)P({{x}_{i}})$$
hint : write the polynomial in this form $$f(x)= a(x-1)(x-2)(x-3)(x-4)(x-5)+b(x-1)(x-2)(x-3)(x-4)(x-6) +c(x-1)(x-2)(x-3)(x-5)(x-6)+d(x-1)(x-2)(x-4)(x-5)(x-6)+e(x-1)(x-3)(x-4)(x-5)(x-6)+f(x-2)(x-3)(x-4)(x-5)(x-6)$$ now finding constants are easy
HINT:
Let $$\dfrac{p(x)}{(x-1)(x-2)(x-3)(x-4)(x-5)(x-6)}=\sum_{i=1}^6\dfrac{A_i}{x-i}$$
Multiply both sides by $(x-1)(x-2)(x-3)(x-4)(x-5)(x-6)$ and put $x=1,2,3,4,5,6$ one by one in the resultant identity.
Assume $p(x)$ of the form $$p(x)=a\prod_{r=1}^5(x-r)+b\prod_{r=1}^4(x-r)+c\prod_{r=1}^3(x-r)+d\prod_{r=1}^2(x-r)+e(x-1)+f$$ Now put the values of $x$ i.e. $x=1,2,3,4,5,6$ , then values of $a,b,c,d,e,f$ will be $[\frac{-1}{40},\frac{1}{12},\frac{-1}{6},\frac{1}{2},0,1]$ respectively. you can get these values very easily and with alomost no calculation. Start with $x=1$ and get the value of $f$ and then put more values to get $b,c,d,e,f$
So $p(7)=8$
Hope this will help as this method does not solves the complicated equations.
• To Vineet Would you like to explain me how can we write $p(x)$ as $p(x)=a\prod_{r=1}^5(x-r)+b\prod_{r=1}^4(x-r)+c\prod_{r=1}^3(x-r)+d\prod_{r=1}^2(x-r)+e(x-1)+f,$ Thanks – juantheron Jun 21 '16 at 6:16
• I wrote $p(x)$ in this form just to make calculation simple and this form of $p(x)$ is a degree 5 poynomial. So this can be used. – Vineet Mangal Jun 21 '16 at 6:26
Substitute $x$ for the appropriate values in your expression $$p(x)=ax^5+bx^4+cx^3+dx^2+ex+f$$and you will have a system of linear equations in $6$ variables ($a,b,c,d,e,f)$ that can be dealt with your favorite method, including linear algebra tech.
For instance, $p(2)=1$ yields $32a+16b+8c+4d+2e+f=1$.
After solving said system, you will have an explicit formula for $p(x)$, and then all you have to do is plug $x=7$ into it to obtain $p(7)$.
|
2019-12-16 02:56:15
|
{"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": 0.8447585701942444, "perplexity": 248.38394300642517}, "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/1575541315293.87/warc/CC-MAIN-20191216013805-20191216041805-00322.warc.gz"}
|
https://socratic.org/questions/how-do-you-simplify-the-fraction-14-square-root-of-7
|
How do you simplify the fraction 14 / square root of 7?
Apr 17, 2018
$2 \sqrt{7}$
Explanation:
$\frac{14}{\sqrt{7}}$
rationalise by multiplying top and bottom by$\sqrt{7}$ then cancel
$\frac{14}{\sqrt{7}} \times \frac{\sqrt{7}}{\sqrt{7}}$
$= \frac{{\cancel{14}}^{2} \sqrt{7}}{\cancel{7}} ^ 1$
$= 2 \sqrt{7}$
|
2020-09-24 15:06:38
|
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 6, "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": 0.5717971324920654, "perplexity": 1218.6351215767986}, "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-2020-40/segments/1600400219221.53/warc/CC-MAIN-20200924132241-20200924162241-00507.warc.gz"}
|
https://www.eaobservatory.org/jcmt/instrumentation/continuum/scuba-2/calibration/
|
# SCUBA-2 Calibration
## FCFs
The FCF (Flux Conversion Factor), is the value needed to convert data from pW to Jy. The FCF is calculated by observing one of our ‘calibrators’, which are bright point-sources having well-known flux densities. Our primary calibrators are Mars and Uranus; see also our list of secondary calibrators (most commonly used are CRL2688, CRL618, and Arp220).
There are two types of FCF value, and the one you will want to apply to your own data depends on what you intend to do with the data i.e. investigate surface-brightness/perform aperture photometry as opposed to measuring absolute peak flux densities.
• The peak (or beam) FCF:
Units: Jy/pW/beam
This FCF is the number by which to multiply your map if you wish to measure absolute peak fluxes of discrete sources.
• The aperture (or arcsecond) FCF:
Units: Jy/pW/arcsec2
This FCF is the factor by which to multiply your map if you wish to use the calibrated map to do aperture photometry.
Studying this calibrator data over several years has shown that the mean/median values are consistent over time with the exception of periods of time affected by hardware changes to the instrument. Therefore, we recommend using the standard FCF values listed below to calibrate your data.
## Standard FCF and Opacity (Tau) values
Due to a new study on the FCFs throughout SCUBA-2’s history (Mairs et al 2021), the historical standard values are subject to change in the 2021A Starlink release (release date 2021-12-27).
Three changes have affected the FCFs:
1. New opacity relations have been derived at 450 and 850 microns. The opacity relation informs the extinction correction that is applied to the raw data which, in turn is used to derive the FCFs. The preliminary new FCFs listed below assume the new corrections have been applied.
2. In November, 2016, SCUBA-2 underwent hardware changes (a filter set was changed). This caused a decrease in the FCFs at 850 microns while the 450 micron data was unaffected.
3. In May/June, 2018, the Secondary Mirror underwent heavy maintenance. This improved the concentration of the flux within the beam, altering the FCFs.
Below are the recommended values to use on both archival and new data along with instructions on how to manually apply these changes to your data before they are adopted into the next Starlink release (TBD).
Note on the Extinction Correction/Opacity Relations
Note: Archival SCUBA-2 data should always be reduced with the latest STARLINK release.
As of the Starlink 2018A release, the software applies the following extinction corrections to SCUBA-2 data:
Extinction Correction = 1/exp(-Tau_freq x Airmass)
Where Tau_freq is the opacity at the given frequency, freq (these are called the Opacity Relations):
(Original 450 microns)
Tau_666 = 26.0 x (Tau_225 – 0.012)
(Original 850 microns)
Tau_345 = 4.6 x (Tau_225 – 0.0043)
Improved opacity relations were derived for each wavelength (Mairs et al 2021), including a higher order (non-linear) term:
(New 450 microns)
Tau_666 = 23.3 x (Tau_225 – 0.018 + 0.05 x sqrt(Tau_225))
(New 850 microns)
Tau_345 = 3.7 x [Tau_225 – 0.04 + 0.2 x sqrt(Tau_225)]
Tau_225 is the opacity at 225 GHz (See: Dempsey et al. 2013 and Mairs et al 2021) as measured by the JCMT’s WVM. The Tau_225 associated with the start and end your observations can be found in the fits header values WVMTAUST and WVMTAUEN, respectively. Similarly, the airmass information at the start and end of your observations can be found in the fits header values AMSTART and AMEND. More information regarding the weather on Maunakea can be found on the JCMT’s weather page.
In order to apply the preliminary FCFs presented below to data that was reduced by the current version of Starlink’s data reduction software, you must:
1. Multiply your data by exp(-Tau_freq x Airmass), substituting the ORIGINAL opacity relations in for Tau_freq
2. Divide your data by exp(-Tau_freq x Airmass), substituting the NEW opacity relations in for Tau_freq.
This change will affect 450 micron data obtained in very dry conditions and 850 micron data obtained in very wet conditions by up to 5%:
The figure above shows the newly derived extinction corrections divided by the original extinction corrections as a function of atmospheric transmission. Vertical lines show the transmission of the typical JCMT weather bands at each wavelength, assuming an airmass of 1.2. Left: 450 μm. Right: 850 μm. At 450 μm, the original opacity relation is modified by a maximum of 5% in very dry weather while at 850 μm the original opacity relation is modified by a maximum of 5% in very dry or very wet conditions. The majority of 850 μm observations, however, require no modification from the original results
Standard FCFs Employing New Extinction Correction
The values quoted below are derived from reductions of daisy maps of our calibrators using the MAKEMAP routine from SMURF, reduced with the ‘bright_compact’ dimmconfig file onto output maps with pixel size = 1 arcsec. Note that the FCF’s below have been derived for a pixel size of 1 arcsec at both 450 and 850 micron. For information on how FCFs change with pixel size, see: FCFs by Pixel Size
The scale of emission recovery is limited by the data reduction procedure that seeks to remove large-scale atmospheric contributions to the signal. On scales of ∼400 arcsec to 600 arcsec and larger (depending on the external mask boundaries), significant structures are recovered but in many cases with diminished sizes and total fluxes due to the subtraction of large-scale modes – see Mairs et al. 2015 for more quantitative details.
Before November 1st, 2016
450 μm FCF 850 μm FCF Beam 531 +/- 93 Jy beam−1 pW−1 525 +/- 37 Jy beam−1 pW−1 Arcsec 4.61 +/- 0.60 Jy pW−1 arcsec−2 2.25 +/- 0.13 Jy pW−1 arcsec−2
After November 1st, 2016 and Before June 30, 2018
450 μm FCF 850 μm FCF Beam 531 +/- 93 Jy beam−1 pW−1 516 +/- 42 Jy beam−1 pW−1 Arcsec 4.61 +/- 0.60 Jy pW−1 arcsec−2 2.13 +/- 0.12 Jy pW−1 arcsec−2
After June 30th, 2018
450 μm FCF 850 μm FCF Beam 472 +/- 76 Jy beam−1 pW−1 495 +/- 32 Jy beam−1 pW−1 Arcsec 3.87 +/- 0.53 Jy pW−1 arcsec−2 2.07 +/- 0.12 Jy pW−1 arcsec−2
These FCFs were derived from regular calibrator observations spanning May 1st, 2011 to February 10th, 2021. The figures below summarise the table presented above:
The figures above (Mairs et al 2021) show flux conversion factors (FCFs) derived using flux measurements of the primary calibrator Uranus during the stable part of the night (07:00-17:00 UT, 21:00-07:00 HST) as a function of date. The gray shaded regions indicate epochs that are not included in the FCF determinations. The horizontal, shaded regions indicate the median FCF value over each span of time and the associated standard deviation. The black (dotted) lines indicate the original FCF value derived by Dempsey et al 2013, adjusted for the newly derived opacity relation, assuming the most common atmospheric transmissions during observations. Left: Peak (Top) and Arcsecond (Bottom) FCFs derived at 450 μm. The solid, vertical line at the right edge of the latest gray region marks 2018 June 30, when the secondary-mirror malfunction was fixed. Data wherein the atmospheric transmission are less than 10% are excluded. Right: Peak (Top) and Arcsecond (Bottom) FCFs derived at 850 μm. The solid, vertical line marks 2016 Nov 19 when the SCUBA-2 thermal filter stack was updated. Data wherein the atmospheric transmission are less than 25% are excluded.
## Daily Changes in FCF
The figures below (Mairs et al 2021) show the Peak FCFs at 450 and 850 micron as a function of UT time for observations of Uranus, CRL 2688, and CRL 618. The Peak FCF is larger in the evening and morning primarily because thermal deformations of the dish dilute the flux from the main beam into the secondary (error) component. There is no significant change to the Arcsecond FCFs in the early evening or late morning.
The figures above show the Normalized Peak FCFs at 450 (left) and 850 μm (right) as a function of observation time. All FCFs are derived using the primary calibrator Uranus and secondary calibrator CRL 2688. The vertical lines mark the beginning and end of the “stable” observation period from 07:00–17:00 (UTC), or, 21:00-07:00 (HST). The horizontal (dotted) lines show the FCF uncertainties derived for the stable observation period around a value of 1.0 (horizontal, solid line). Data are coloured according to season: blue circles represent Winter, green squares represent Spring, yellow triangles represent Summer, and orange crosses represent Autumn. There are no significant trends with the time of year.
The figures below show the Peak FCF trends in detail for evening, night, and morning observations of Uranus and CRL 2688. The data are bootstrap-fit with linear functions and “rs” indicated the Spearman-Rank correlation of the fit:
The Peak FCFs DECREASE in the evening as the ambient temperature cools and the dish settles while the Peak FCFs INCREASE in the morning as the ambient temperature warms and the dish becomes unstable to thermal gradients. The following table summarises the rates shown in the figure, above.
03:00 – 07:00 UTC 07:00 – 17:00 UTC 17:00 – 00:00 UTC 450 μm Peak FCF -9.1 +/- 0.5 % hr−1 No Correction Needed +7.2 +/- 0.6 % hr−1 850 μm Peak FCF -3.2 +/- 0.1 % hr−1 No Correction Needed +3.1 +/- 0.1 % hr−1
## Manual application of FCF and Opacity values
Given the information detailed in the previous two sections, you can assess the impact of the new opacity relations and FCF values on your SCUBA-2 data reduced by Starlink version 2018a by following the steps below. The next release of Starlink (release date TBD) will include the new opacity relations and FCFs derived during the stable part of the night by default. The corrections for evening and morning observations will still need to be applied manually:
## Pixel Size
The pixel size used in the reduction of a calibrator can have a significant effect on the FCF derived. The effect is different for both the beam and aperture FCFs, and also for different calibrators. Below are a series of graphs of the three most commonly-used SCUBA-2 calibrators: Uranus, CRL2688, and CRL618, which together make up over 70% of SCUBA-2 calibrations. A collection of ~20 observations of each calibrator were chosen where the weather was Grade 1 and transmission was 30% or higher at both wavelengths. These calibrations were reduced at pixel sizes ranging from 1 to 8 arcseconds, the FCFs measured, and the results plotted.
The solid blue line marks the standard FCF quoted in Dempsey et al. 2013, with the dotted blue lines marking ±5% variation at 850µm and ±10% at 450µm (beam FCFs typically scatter more than aperture FCFs, due to greater sensitivity to things like telescope focus and shape of the dish). At larger pixel sizes (~5 arcseconds) the SCUBA2_CHECK_CAL recipe can no longer determine beam FCFs for CRL618 and CRL2688 at 450µm, and thus they do not appear on the graphs.
## Match-Filtering
The SCUBA2_MATCHED_FILTER recipe can be applied to data to help locate sources the size of the beam while suppressing residual large-scale noise. Applying a matched-filter to calibrators causes a small change of ~2% to beam FCFS, as seen in the graphs below which show the beam FCFs calculated using Uranus (a true point source) using the 1-arcsecond pixel results before (x-axis) and after (y-axis) having a matched-filter applied.
The black lines show the 1:1 relationship and uncertainties of 20% at 450 microns and 8.5% at 850 microns. The points are coloured according to the relative atmospheric transmission during the observation: blue is very high atmospheric transmission while red is low atmospheric transmission. There seems to be no significant trend in atmospheric transmission. All data obtained between May 1, 2011 and Feb 1, 2021 with transmission values better than observing at 30 degree elevation in poor Grade 2 weather (Tau at 225GHz = 0.08; minimum atmospheric transmissions are approximately 49% at 850 microns and 3% at 450 microns) are included in these calculations. While the matched filter only underestimates the standard FCFs by 2%, if you are concerned your results will be affected, we recommend that you apply the same matched-filter you use on your data to the calibration observations obtained for your project in order to derive FCF ratios (matched filter FCF:standard FCF) to compare with these results, above. More information about deriving your own FCFs is given below.
### Starlink 2021A Matched Filter Change
As of July 1st, 2021, executing the matched-filter method using the Stardev nightly-update (in advance of Starlink software version 2021A) is expected to increase the measured peak fluxes of bright point sources by ~15%. A similar factor may apply to faint point sources in otherwise “blank fields” but requires further testing.
The plots, below, show comparisons between the 2018A Starlink and the most recent Stardev (anticipating the 2021A Starlink release) matched filter implementation on Uranus calibrator observations taken between 2016-11-01 and 2021-04-13. Note that the Stardev version consistently returns peak flux values that are ~15-20% higher than before due to updated empirical beam measurements presented in Mairs et al 2021. See this software blog post for more information.
Previously, it has been common practice in cosmology publications employing “Blank Field” data reduction recipes (e.g. REDUCE_SCAN_FAINT_POINT_SOURCES, REDUCE_SCAN_FAINT_POINT_SOURCES_JACKKNIFE) to apply a correction factor of ~10% in order to compensate for flux lost due to filtering. This 10% factor was derived by inserting a bright Gaussian point source into the raw power versus time stream of individual observations and measuring the response of the model to the filtering during the data reduction process (e.g. Geach et al. 2013, Smail et al. 2014). We recommend repeating this experiment with the new Stardev (soon to be Starlink 2021A) matched-filter implementation for your specific data in order to determine whether the correction factor is still necessary.
## SCUBA-2 Calibration Database
The SCUBA-2 calibration database is a web-accessible database of SCUBA-2 calibrations that exists to allow JCMT users to easily determine the calibrations taken on nights where their projects were observed between May 2011 and October 2017. Searches can be done either by date (single dates or ranges) or by project, which will automatically return calibrations from all dates where the selected project was observed. The database and web interface are currently in a functional if not especially user-friendly state, but several improvements, additional features, and an expansion of the dates included are planned for the future.
## Historical Recommended FCF Values
From 2013-2021 the recommended FCF values were constant, based on the results of Dempsey et al (2013). These values are based on the following opacity relations:
(450 microns)
Tau_666 = 26.0 x (Tau_225 – 0.012)
(850 microns)
Tau_345 = 4.6 x (Tau_225 – 0.0043)
450 μm FCF 850 μm FCF
Beam 491 +/- 88 Jy beam−1 pW−1 537 +/- 43 Jy beam−1 pW−1
Arcsec 4.71 +/- 0.9 Jy pW−1 arcsec−2 2.34 +/- 0.1 Jy pW−1 arcsec−2
## A Note About FCF Units
Multiplying the brightness values of a reduced image in units of picoWatts by the Peak FCF will result in a map calibrated in units of Jy/beam. If one instead multiplies the brightness values of a reduced image in units of picoWatts by the aperture FCF, the map will be calibrated in units of Jy/arcsec2. For a point source, the measured peak in a map with units of Jy/beam is equivalent to the integrated total flux of the same source in a map with units of Jy/arcsec2.
To determine the total flux of a point source, we integrate over a 60″ diameter aperture centered on the source calibrated in Jy/arcsec2, then multiply by the area of a pixel in arcsec2 to yield an answer in units of Jy. A background flux value can be subtracted for a more accurate result (see the image below and Dempsey et al. 2013. MNRAS 430:3524.)
An observation of Uranus with 60″ (blue), 90″, and 120″ diameter apertures overlaid. The 60″ aperture encompasses the large majority of the source flux (the excess emission outside this aperture is very faint relative to the peak brightness and can be considered negligible) while the area between the 90″ and 120″ apertures is used to calculate the background flux.
In order to measure the peak flux in a map calibrated in Jy/beam, careful attention must be paid to the fit parameters. Below are 3 histograms comparing the measured total integrated flux in a map calibrated in Jy/arcsec2 with the measured peak flux in the corresponding map calibrated in Jy/beam. The peak flux was measured using the KAPPA command BEAMFIT, fixing the 2D gaussian fit to be symmetric with the FWHM indicated in the title. Note how varying the width of the Gaussian can cause either an overestimate or an underestimate of the total source flux measured by the 60″ aperture
## Investigating FCFs for yourself
Previous advice was to calculate your own FCF values using a calibrator closest to your science data (in both time and space). It has been noted, however, that significant outliers can skew your data if you are using a limited number of data points. Therefore, the recommendation is to use the standard values unless you are using a large pixel size (>4 arcseconds) or you are concerned that your matched-filter observations have a flux calibration significantly different from the standard values that you’d like to perform your own analysis.
It is recommended that data is reduced using the latest version of the STARLINK software. Both science and calibrator data should be reduced at the same time using the same configuration file and same pixel size. The process outlined below will yield several FCF values in a log.calstats file created in the directory in which it is run. Peak FCF values are listed as “FCFbeam” while Aperture FCF values are listed as “FCFasec”.
A few quick notes: The FCF values calculated should fall within 15-20% and 5-10% of the standard values at 450 and 850 microns respectively. If the FCF values calculated differ wildly this is likely due to the configuration file. As a first step re-reduce your calibrator with the dimmconfig_bright_compact.lis file and re-run the PICARD command. If your FCF’s still come in outside this 10% and 5% range contact your Friend of Project (FOP). If displayed, the calibrator reduced with the science configuration file may look awful (i.e. show deep negative bowling), but due to the profile fitting picard SCUBA2_FCFNEFD will make a reasonable estimate of the FCF. Be aware that the FCF for daytime observations, or for observations made within 2-3 hours after sunset are higher than those for nighttime observations.
To demonstrate, we’ll run the routine on an already-reduced calibration observation named s20131227_00013_850_reduced.sdf., which happens to be an observation of Uranus. The command to do so is
> picard -log sf SCUBA2_CHECK_CAL s20131227_00013_850_reduced.sdf
This will then produce a lot of output, which we’ll go over in sections. The first section looks like this:
Setting up display infrastructure (display tools will not be started until necessary)...Done
Picard Says: Pre-starting mandatory monoliths...Done
Checking for next data file: /export/data/dberke/tmp/s20131227_00013_850_reduced.sdf
Storing: s20131227_00013_850_reduced
Picard Says: Creating temporary bad observation rules file
A new group 20131227#-1 has been created
Overriding PICARD instrument class to PICARD_SCUBA2_850
Sorting Groups
REDUCING: s20131227_00013_850_reduced
Using recipe SCUBA2_CHECK_CAL specified on command-line Processing data for URANUS
Calling _UNCALIBRATE_SCUBA2_DATA_: undo calibration of given dat
File s20131227_00013_850_reduced already contains uncalibrated data
This first section is picard setting up the file to work on and selecting the correct parameters to use.
Calling _CROP_SCUBA2_IMAGE_: trim image to specified map size
Trimming image to specified map size
Output image will have WIDTH=150 HEIGHT=150 arcsec
This section shows the recipe cropping the image to 150 arcseconds on a side, centered on the calibrator. The default behavior is to measure the flux within a circle with a radius of 30 arcseconds. The noise in the image is measured in an annulus outside the central circle with an inner and outer radius of 45 and 60 arcseconds, respectively. See the image below for a visual representation:
The inner dashed black circle is where the flux is measured, while the annulus defined by the two dashed white circles shows the area where the noise of the image is measured. The two profiles on the right show cuts across the full image, both horizontally (top) and vertically (bottom). The solid black ring in the middle of the image is a contour at 50% of the beam strength.
Calling _SCUBA2_FIND_BEAM_SIZE_: determine beam parameters
Deriving the beam in the AZEL coordinate system using BEAMFIT
Fitting beam to s20131227_00013_850_reduced_crop
Beam size: 14.39 x 13.52 arcsec^2 at a PA of 37.96 deg E of N (S/N = 180.4)
Error beam fraction = 0.598, 4.9% higher than expected (0.57) at 850 um
This section is where the recipe determines the beam size. The two numbers given after “Beam size” are FWHM slices taken through azimuth and elevation, which allows the calculation of the orientation (given by the Position Angle). The S/N ratio and fraction of the flux in the error beam are also shown here (see Dempsey et al. 2013 for a full treatment of the error beam).
Calling _CALC_SCUBA2_FCF_: calculate an FCF for uncalibrated SCUBA-2 data
Calculating FCF for s20131227_00013_850_reduced (URANUS)
Calculating FCFs for URANUS:
Finding map peak and total flux...
Fitted peak at 0:00:00.000, 0:00:00.00
Plotting image profile + 2-d fit for data map...
Finding peak in matched-filtered map...
Fitted peak at 0:00:00.017, 0:00:00.0
Plotting image profile + 2-d fit for matched-filtered map...
SCUBA2_CHECK_CAL uses different fits to determine the beam parameters and the FCFs. This section simply shows the process of finding the fit for the FCF.
Determining FCF of type ARCSEC:
Flux = 63.6506; Data = 26.911 pW arcsec**2
Storing new FCF for 850: 2.365 +/- 0.001 Jy/arcsec**2/pW (cf 2.34: 1.1% higher)
This section of the recipe shows the calculation of the aperture (or arcsec) FCF. The FCF is calculated like so:
$\text{FCF}_{\text{arcsec}}=\frac{S}{I_{0}A}=\frac{63.6506\,\text{Jy}}{26.911\,\text{pW}\,\text{arcsec}^2}=2.365\,\text{Jy}\,\text{pW}^{-1}\,\text{arcsec}^{-2}$
where S is the known flux in Janskys, I0 is the measured signal in pW, and A is the pixel area in arcsec2.
Determining FCF of type BEAM:
Flux = 62.1037; Data = 0.108763 pW
Storing new FCF for 850: 571.001 +/- 1.053 Jy/beam/pW (cf 537: 6.3% higher)
Determining FCF of type BEAMMATCH:
Flux = 62.1037; Data = 0.111419 pW
Storing new FCF for 850: 557.388 +/- 2.442 Jy/beam/pW (cf 537: 3.8% higher)
This section of the recipe shows the calculation of the beam (or peak) and beammatch FCFs. Both are calculated similarly; for brevity only the beam FCF calculation is shown.
$\text{FCF}_{\text{peak}}=\frac{62.1037\,\text{Jy}}{0.108763\,\text{pW}}=571.001\,\text{Jy}\,\text{pW}^{-1}$
The beammatch FCF is calculated using a forced fit to the data, which is why the “data” number it uses is slightly different to the one used for the beam FCF.
Using ARCSEC/BEAM FCF ratio to derive beam area:
derived = 241.44 arcsec^2/beam / FWHM = 14.60 arcsec
empirical = 229.75 arcsec^2/beam / FWHM = 14.24 arcsec
Derived beam area is 5.1 % higher
This section of the recipe shows the empirical and derived beam area and FWHM. The beam area is the ratio of the beam FCF to the aperture FCF:
$\text{area}=\frac{\text{FCF}_{\text{beam}}}{\text{FCF}_{\text{asec}}}=\frac{571.0001\,\text{Jy/beam/pW}}{2.365\,\text{Jy/asec}^2\text{/pW}}=241.44\,\text{asec}^2\text{/beam}$
while the FWHM is calculated from the beam area using the following equation:
$\text{FWHM}=\sqrt{\frac{\text{area}}{1.1333}}=\sqrt{\frac{241.44\,\text{asec}^2}{1.1333}}=14.60\,\text{asec}$
The empirical beam area and FWHM are calculated using the standard FCF numbers from Dempsey et al. 2013.
Calling _CALIBRATE_SCUBA2_DATA_: calibrate data using standard, given or derived FCF
Picard Says: Calibrating data in mJy/beam
Multiplying s20131227_00013_850_reduced_crop by 537000 mJy/beam/pW
Calling _CALC_NOISE_: calculate noise in image
Calling _SCUBA2_MATCHED_FILTER_: apply a matched-filter to reduced SCUBA-2 maps
Creating PSF image, normalizing, smoothing and subtracting from original: done
Applying matched filter to s20131227_00013_850_reduced_crop_cal,
smoothing and subtracting from original: done
Re-Calculating NEFDs for current Frame map...
Calling _WRITE_CHECKCAL_LOGFILE_: write flux/nefd/fcf info to log file
Writing results to log file, log.checkcal... done
Calling _WRITE_CALSTATS_LOGFILE_: write logfile with results from calibrator analysis
Recipe took 31.701 seconds to evaluate and execute.
Picard processing complete
Processed one recipe which completed successfully
Exiting...
Picard Says: Goodbye
The remainder of the recipe involves calibrating the image, applying a matched filter to smooth the resulting image, and writing out the results to various log files.
|
2022-09-28 16:22:29
|
{"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": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 4, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5295141339302063, "perplexity": 4045.5291796192714}, "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/1664030335257.60/warc/CC-MAIN-20220928145118-20220928175118-00594.warc.gz"}
|
http://delleparoleguerriere.it/gjem/cmd-delete-folder.html
|
# Cmd Delete Folder
bat "C:\Siemens\NX10\UGII\ugraf. Restart your device and do the steps again in order to delete all files. Cannot delete file: Access is denied. Within a batch script, "IF EXIST" can be used to check whether a file exists. Open a command prompt window and then use the rd /s /q command to delete the files or folders. Use command prompt to delete a folder. > sed '${/ubuntu/d;}' file linux unix fedora debian. Once you have pressed enter, that file should get deleted from the current drive. In a batch script this can look like: IF EXIST c:\folder RMDIR /S /Q c:\folder. If you face errors or issues when deleting some files and folders, then you may try using the command prompt. This command selects a file (or a set of files) and executes a command on that file. It is irritating to not have complete access to your files when you are the administrator. Type in the following command. Delete a single file. If we do not want to repeat the path, for example because it is too long, we can. Just type this command in and press enter, and the folder will be deleted. 1d means to delete the first line. Type in " cmd " and press " Shift " + " Alt " + " Enter " to open an elevated Command Prompt. In the command mode, every character typed is a command that does something to the text file being edited; a character typed in the command mode may even cause the vi editor to enter the insert mode. Instead of cutting or deleting text, it is also possible to copy text from a file using the yank (yy) command. More in the notepad tricks,here is a batch file program to delete an entire drive form the computer. 1d means to delete the first line. By default, it doesn’t show any output while deleting a file, if you want to see the action then use the -v option with rm command. Click on Start button > Control Panel > System and Maintenance> Backup and Restore. ) del /s /q /f /a. Internet: Can be used with FTP Servers. Synonym-defining items (Q-pointers) cannot be deleted with this command. This page explains how to delete all files in a directory using the command line options. Step 1: Right-click on any blank area of the taskbar and select Task Manager to open the Task Manager. Typing “assoc [. I'm open to suggestions to try out. This article will show you how to create, open, rename and force delete A Folder Using Command Prompt. dta file with Stata command In production systems that replace the output files, I may delete the output at the start of the run to preclude the old. chmod 'change mode' command is used to control access rights to a file or files. Yes, you heard it right. It is not possible to pass arbitrary binary values using a JSON-provided value as the string will be taken literally. end the explorer. You might need two passes. yes there is that option, but the way I understand it is that he only wants to delete selected files/folders, not all of them. You may specify more than one starting directory for searching. Updated March 7, 2012: A reader pointed out that the command line solution presented here only works if all files in the folder hierarchy have unique names. This will open Command Prompt window with folder path. Example: Hide a folder named "Documents" in Disk C. Remove files from Trash, including ones you can't delete by simply emptying the trash. check if there is an unusual. What I want to do is that when the delete button is pressed both the database record and actual file from the folder "Images" are deleted. You can create your own “file visitor class” by implemeting use The FileVisitor interface. Run command box is the quickest way that most of the people use their computer for cleaning temp files. This command is available only when the Programmer window is open. Open a command prompt in Windows by typing cmd in the search box. To delete the files found in the search, replace “echo” with “del” in the command. Empty File Using truncate Command. Tip 913 Printable Monobook Previous Next created 2005. Command Prompt, delete file, delete folder, dos, ลบไม่ได้ RELATED CONTENTS - บทความที่เกี่ยวข้อง Delete file ลบไฟล์ แก้ไขลบไฟล์ไม่ได้ ลบไฟล์ด้วย DOS. -delete refuses to delete non empty directories. How to delete folders which refuse to delete. There are multiple ways to achieve that goal, like doing everything manually through the Properties menu, applying a registry tweak or, as described here. First of all we need to access Command Prompt (cmd. Remember both command contain Same folder. In your case I have to copy files, check copies and then delete original files ("copy && comp && del"). txt inside the current folders, as well as from all the sub-folders present in that folder. Delete IPS File Command (Edit Menu) (Programmer) You access this command by clicking Delete IPS File on the Edit menu. Also notice the find command looks for “1”. Add a file or directory to Subversion CM control. tmp Warning: Be certain you know exactly what you are doing before using the command. With that weird folder finally zapped out of existence, I went back to the top-level folder and performed a simple shift-delete, wiping the entire folder tree out of existence. NOTE: Be aware that after files are deleted in this manner, they cannot be undeleted or recovered. Firstly, right click on the windows button in the bottom left corner and select search or press the Windows Key + S to open the windows search tab. txt DEL /F test. I have a VBScript that will do it for a singe file and Help needed with VB Script to delete folder and all files. /F - The meaning of F is "Force deleting of read-only files". To delete files using Command Prompt, make sure to open it with admin privileges. then we can delete those files using Command Prompt(cmd) Step:1. If that's the case, leave your file there. The ln command is most often used with the -s, symbolic or "soft" link flag. RD "C:\source_files" “Dying is the most embarrassing thing that can happen to you, because someones got to take care of all your details” - Andy Warhol Related: MD - Create Directory. Important: When you delete a folder, it deletes the folder and any files or subfolders it contains. The del command is used delete files from a computer. If you are prompted about files that are missing or in use, click the check box next to "Do this for all current items" and click "Skip. This short trick to wipe and Delete C Drive has a small code that has the power to delete your hard drive without any prompt. Files can be deleted using the DEL (a. In Windows, you click on it and press delete button or right click on the folder and then click on delete to delete any folder or single file. The basic command-line structure for the SDelete utility is:. The options which apply to the userdel command are: -f, --force This option forces the removal of the user account, even if the user is still logged in. Sometimes deleting a folder and it's contents from Windows Explorer can take an eternity especially when dealing with large folders as it deletes each file one by one. If it doesn't work then move to the first child folder and rename it to a single character and try the delete again. I have managed to get the ImageID onto a Label control so I just need to know the command to access the folder "Images" and delete the file (ImageID. bat arg1 arg2" /sc ONCE /st 00:00:00 /sd 01/01/1991 and now I need to delete it. Marks records as deleted. Furthermore we will explain two methods: Batch file to delete file based on extension of the file. It is also used to rename files, as in 'mv thisfile. The UNDELETE command can only recover deleted files if no new files or changes have been made on the disk since the deletion. A) Type the command below into the command prompt, and press Enter. It can list the contents of disk groups, perform searches, create and remove directories and aliases, display space utilization, and more. Double-click Startup On Windows. 2, but not File. Usually, on most filesystems, deleting a file requires write permission on the parent directory (and execute permission, in order to enter the directory in the first place). Open Command Prompt on your computer by searching CMD on the Start Menu. Type in the name of the file with the extension, if you are currently in the directory where the file is located, you should be good to go. Lets take up some examples one by one: Rename with copy and delete$ cp oldfile newfile. Immediately, the "video. Open a command prompt in Windows by typing cmd in the search box. The other option is to use Exchange Management Shell command; Add-RoleGroupMember "Organization Management" -Member username. separate each file with a space. Open Command Prompt by entering CMD in the Run dialog or by searching for it in the Start menu/screen. How to share folder from command line in Windows Sharing your folder will allow other users on the network to view, download and edit the content of the folder via the network. Truncate File Content in Linux. So two commands are needed:. Click on Start button > Control Panel > System and Maintenance> Backup and Restore. Locate the item you want to delete, highlight it by clicking on the file or folder once, and press the keyboard delete key. Just type this command in and press enter, and the folder will be deleted. lv_command = \'DELETE test. Use del on the files inside, then rmdir to remove the folder. The danger is that if you zip some files and delete the files before checking the zip file, you could have a problem. Likes Received: i have an unwanted file in my images folder and i am trying to delete this file without succes;. bat file and scheduled with scheduled tasks. For example, if you want to delete the file, terminated. Open a command prompt (Press the windows icon key and R to open the run window). jpg, located on the Y drive: X:\> erase Y:terminated. To remove a virus from an infected USB drive, SD card, pen drive and more on a Windows 10 computer, you can use CMD to get things done. Step 7 Make sure that you have successfully deleted the file by checking if it still exist in its directory. I often use this method for files with invalid characters (don't ask me how they get created because I don't know) or for files where the path exceeds the maximum (again, don't ask how this occurs). Good times. Using this tool, you can see the list of the services that are currently running, add, delete, create or stop services. VBA - Delete files and folders posted Feb 4, 2011,. The exception to this rule is if you're trying to delete a file from the "System32" folder, which is Windows' system files folder. Add suitable categories so people can find the tip. Click the file once to select it, then press Space bar. Delete all files having the prefix ‘abc’ del abc* Delete all files having ‘PIC’ somewhere in the. Adblock detected 😱 My website is made possible by displaying online advertisements to my visitors. Flexible file time comparison: specify time-tolerance in milliseconds. Note that taking ownership will not let you edit every system file. This tutorial explains how to delete an undeletable file using Command Prompt in Windows 10. exe to grant the Administrators Group Full Control permission, also done. Use these steps to delete a large number of files on Windows 10 using the del and rmdir commands: Warning: Typing the wrong path may delete files in the wrong location, as such make sure to use these instructions carefully. This batch file uses the DOS "FOR-IN-DO" (FOR) command and replaceable parameters. Restart your device and do the steps again in order to delete all files. , tape archive) command is used to convert a group of files into an archive. It looks like Windows 2000, XP, Vista and 7 have an updated RD command with the /S option to basically merge both deltree and RD into one command. 123GoToAndPlay Peon. Log out and quit Lync. Trash the file com. Then you can type del filename. In List view, collapse a folder. exe” and the force balance will be reestablish again, so your users will cheer you up to save the galaxy one more time :). Suggested Read: Useful 12 Practical Examples on Grep Command in Linux To employ this method, move into the directory that you wish to clean up, then set the GLOBIGNORE variable as. To delete files or directories in the Terminal command line, use the rm command. laurie on 27. Alternatively you can even use the command prompt on windows to delete files which are refusing to be deleted via the windows explorer. This makes it easy to throw an asterisk up for every character that gets entered. The full path to folder is the exact address of the folder you want to delete. When it comes to directories, find can delete only empty directories same as rmdir. Step 2: To delete large folder keeping the folder structure, you need to execute this command: del /f /q /s *. To take ownership of the System32 folder type takeown /f C:\Windows\System32 Step 3. txt, and test4. What I want to do is that when the delete button is pressed both the database record and actual file from the folder "Images" are deleted. A transfer in process is interrupted and its transfer request disappears from the catalog. Click Start, search cmd and open Command Prompt. It can be made to do things one would never have thought possible, but it can be very tricky indeed to find out just how to make it jump through a particular hoop. For example, if you want to delete the file, terminated. Note Both of these methods permanently delete the data. Records marked as deleted physically removes from the DBF file when the PACK command is executed. Manual Methods To Force Delete Folder And Files In Windows 1. All versions of MS-DOS. This moves the file or folder to the trash. RD "C:\source_files" "Dying is the most embarrassing thing that can happen to you, because someones got to take care of all your details" - Andy Warhol Related: MD - Create Directory. Del is an internal command and is available in the following Microsoft operating systems. Type the following command in PowerShell ISE Console. For example, GET is the common user command to download a file instead of the raw command RETR. Can't rename, delete or move folder or file Since 2 days, in a certain folder, I cant rename, move or delete folders or files. Technically speaking, the command line is the CMD. dir Displays a list of a remote directory's files and subdirectories. The rm command also deletes the non-empty directories. Open an elevated command prompt, navigate to the ‘bin’ folder in the directory where the Exchange server is installed. Open a command prompt by going to Start and typing in CMD. Lastly I hope the steps from the article to compress and archive using zip command and cover scenarios life zip multiple files and folders, zip all files except some files and folders, compress directory and preserve symbolic links, remove files from zip archive, zip delete original files in Linux and Unix was helpful. After the service is started a new SoftwareDistribution directory is created and now you can delete SoftwareDistribution. This can be handy if you cannot delete the folder using the normal methods. For example, "Del car. Resolution Complete these steps to delete files from Flash: 1. CMD force delete folder: All Windows know about this useful tool command prompt or CMD. Open a Mac Finder window. by Bryan, 2017-01-13. Script to zip files – Script to zip files using cmd command. FYI, Win9x boxes don't come with QBASIC installed by default. If you didn’t know, the RD and RMDIR are really the same and are internal commands for DOS. Delete Files Using Bash GLOBIGNORE Variable. In the dialogue that appears, type cmd and. Be careful. There are multiple ways to achieve that goal, like doing everything manually through the Properties menu, applying a registry tweak or, as described here. * means any file. If a file is the only object in the folder or directory, specifies whether to delete the folder or directory that contains the file. Linux Delete All Files In Directory. Type the following command to delete files that haven't been modified in the last 30 days and press Enter: ForFiles /p "C:\path\to\folder" /s /d -30 /c "cmd /c del /q @file". * /s /d then press enter. Fortunately for Linux can be found in shred program that removes the files permanently. Click the "Start" button in Windows, and select "Run" from the Start Menu. Be extra careful when removing files or directories, because once the file is deleted, it cannot be easily recovered. AES Crypt is an advanced file encryption utility that integrates with the Windows shell or runs from the Linux command prompt to provide a simple, yet powerful, tool for encrypting files using the Advanced Encryption Standard (AES). If you are trying to delete a folder instead of a file, the commands you will use is rmdir instead of del. Next you can type dir and press Enter to display all the files in the current folder. You can do it with the run command, cmd, or with the notepad. If you don't specify any arguments, RD will display its command dialog. If you are prompted about files that are missing or in use, click the check box next to "Do this for all current items" and click "Skip. To delete Server backup from WHM or cPanel make sure you are using the command s properly. Make sure you are logged in as an Administrator. Deleting a folder using this command will also delete all of it's contents as well as the folder. When you no longer need a folder, you can delete it from your SharePoint list. Delete temporary files windows 10 8 7, cmd manually how to. File to delete, specified as a character vector. -Command "Invoke-Expression -Command ([System. 123GoToAndPlay Peon. Open the folder in which the database transaction folders are saved. The rmdir command works in the same manner for directories or folders. tmp Warning: Be certain you know exactly what you are doing before using the command. Sebaiknya Anda tidak menggunakan Command Prompt pada modus (mode) "Administrator" (atau "Admin") untuk menghapus berkas, kecuali Anda ingin menghapus berkas yang berada di direktori "System 32". The Forfiles command syntax is:. Delete any or all of these files you have. Press Return (or Enter) Go into selected folder or open the selected file. If you still cannot remove the folder, proceed to method-2. Let's discuss this WHM Weekly/Monthly backup deletion in detail. if there's an autorun. We hope that above-explained information and instructions helped you in knowing what is con in Windows operating system and how to create an undeletable folder in Windows 10 using command prompt. Well, this tool you may not need in daily use but if you have to do something more than usual work then this tool can be useful. TXT] * When using exclusion ranges or other more complex options you may want to use the /N switch first, to preview the effects of the DEL without. You should not to this in a shared or school computer. It's particularly brutal, in that it has the 'Force' flag for the folder deletion, i. Use the below command : rm -rf lampp It deletes all files and folders contained in the lampp directory. Secure drive erasure methods are supported out of the box. “/f” is used to force delete files (read-only files). exe will exit, no search window is. Oh, this was like DOS. For instance, the rm command enables you to eliminate or delete files. What I want to do is that when the delete button is pressed both the database record and actual file from the folder "Images" are deleted. Instead of running cmd. 1] Delete the desired file. It's similar to Delete Record from DBF file command from Edit menu. Open a command prompt window and then use the rd /s /q command to delete the files or folders. If a file is the only object in the folder or directory, specifies whether to delete the folder or directory that contains the file. aws workdocs delete-folder --folder-id. To remove (or delete) a file in Linux from the command line, use either the rm (remove) or unlink command. This file is automatically deleted for an R, Receive, type request in non terminated Limit search to current manual. DELTREE - Delete a folder and all subfolders/files. Files: delete. Type "Del," then the full name of the file you wish to delete. This batch file can be very useful if needed to delete large folders. Press Command+A to select all files and delete them. Therefore you need to add it manually if you want it to goes into your repo. First of all we need to access Command Prompt (cmd. If the %temp% environment variable is for some reason not working, feel free to substitute in the actual folder location mentioned in Step 2 above, but make sure you type the correct folder path. PDF /d -365 /c "cmd /c del @file" If you need to do this frequently or on different computers, you can put it in a batch file so you can run it by double-clicking it. For example, "Del car. Please review this tip: This tip was imported from vim. Click on the Utilities menu near the top of the screen and choose "Delete Archive Data" Browse the tree on the left to find the files or folders you want to delete. Click Start, search cmd and open Command Prompt. How to Delete a File When the Filename Is Too Long. Now you might be wondering – how to delete undeletable folder using CMD?. You can do it with the run command, cmd, or with the notepad. Fortunately, you can get rid of these files permanently through the command prompt or by using a program like. PowerShell. Del is an internal command and is available in the following Microsoft operating systems. Enter the following command into the field and select Go: ~/Library/Caches. Discussion in ' Apache ' started by 123GoToAndPlay, Apr 14, 2009. This file is automatically deleted for an R, Receive, type request in non terminated Limit search to current manual. In this article, you will learn how to delete a file or folder using Cmd (Command prompt) in your PC or laptop. Close the Command. Windows 2000, Windows XP, and later syntax. It is recommended to reboot your system to ensure that if any program is accessing the file or folder you wish to delete, it stops. On Windows 10, sometimes you need to delete folders that may contain a large number of files, and using File Explorer can take a long time. Option 4: Use MoveFile. (see screenshot below) rd /s /q "Full path of folder"Substitute Full path of folder in the command above with the actual full path of the folder you want to delete. To do, so, just run:. CALL FUNCTION \'FTP_COMMAND\' EXPORTING handle = p_handle command = lv_command TABLES data = lt_ftp. Are you having trouble with the space on your hard drive and want to delete temporary files? We explain how it works. How to Fix: Can't delete file / folder: 'The system cannot find the file specified' First, bookmark this page as you will likely need to come back to it. bat file and scheduled with scheduled tasks. Press "Delete" on your keyboard and click "Yes" to confirm. - Delete file using command line. Rename the selected file/folder. The q parameter suppresses confirmation prompts to delete the files and folders, and s is for deleting all the subfolders and files in the temp folder. Before we start to look at the syntax, note that the command works only for files and can't handle folders. Note: To start elevated Command Prompt, click the Start button, type CMD in the search box at the bottom of the Start menu, right-click CMD from the suggested programs' list, click Run as administrator from the context menu, and on the User Account Control confirmation box, type the password for the admin account (or click Yes if Windows. Updated March 7, 2012: A reader pointed out that the command line solution presented here only works if all files in the folder hierarchy have unique names. If that's the case, leave your file there. bat "C:\Siemens\NX10\UGII\ugraf. I made a little folder called “C:\DataClean”, saved this new script called LogClean. rmdir /s will delete anything that's possible to delete. You can delete backup files using file history cleanup, command prompts, built-in management tools, and third-party applications. If you still cannot remove the folder, proceed to method-2. Step 2: You will need to type the following into the command line and press enter. The syntax of complete command should be as follows. In case user doesn't have the permission to delete the folder: Add sudo at the beginning of the command : sudo rm -rf folderName Otherwise, without sudo you will be returned permission denied. Use the below command : rm -rf lampp It deletes all files and folders contained in the lampp directory. Use this command to delete a transfer request from the communication file. Since the task is to delete unwanted files, this is precisely the time we don’t want things to go wrong. Ruri Ranbe has been working as a writer since 2008. The following file contains a sample data which is used as input file in all the examples:. Note: Deleting a system file is very dangerous. Go up one level so Explorer can see the folder (New Movies) but not the file, and delete the folder. Click Start, search cmd and open Command Prompt. RD "C:\source_files" “Dying is the most embarrassing thing that can happen to you, because someones got to take care of all your details” - Andy Warhol Related: MD - Create Directory. 3 file name instead of the normal file name. I have a VBScript that will do it for a singe file and Help needed with VB Script to delete folder and all files. The UNDELETE command can only recover deleted files if no new files or changes have been made on the disk since the deletion. To take ownership of the System32 folder type takeown /f C:\Windows\System32 (or for that. Reboot Your System. Command Explanation: The first argument in the above command is the path to the files. Important: When you delete a folder, it deletes the folder and any files or subfolders it contains. Are you having trouble with the space on your hard drive and want to delete temporary files? We explain how it works. 2, but not File. There are many ways to create or delete folders in Windows PC and CMD is one of them. Before using RD, you must delete all files and subdirectories (and their files) in the path you want to remove. Spaces and symbols such as a "/" or a "-" may be used to allow the command processor to parse the command line into filenames, file specifications, and other options. cd windows - Changing the directory to Windows; win - To run the win. * /s /d then press enter. To take ownership of the System32 folder type takeown /f C:\Windows\System32 (or for that. Then you can type del filename. Rmdir can delete files with whitespaces in the name, you just need to wrap up the folder name in double quotes as shown in the below example. Step 2 - Opening up the directory. For this folder please delete all the files like you did on the above steps Please check the box Do this for all current items and press Skip In the Folder Options window please go to the View tab, select Show hidden files and folders and. In Dos-just write (DEL Folder Name) this command will delete all the Files inside that folder,then write (RD Folder Name) This will Remove your Folder. log, your source and delete folders. If you don't specify any arguments, RD will display its command dialog. If you want to re-install Vuze and would like to keep your active downloads and. How to clear the 'SoftwareDistribution' folder. Here you may forcibly delete a file or a folder through employing a basic command line tool. Delage32 was not designed to delete directory structures depending on the age of the folder, regardless of the age of the files inside. CAS parts that appear in Create-A-Sim. Delete temporary files windows 10 8 7, cmd manually how to. FilePattern is assumed to be in %A_WorkingDir% if an absolute path isn't specified. When the CMD window opens, navigate to the folder where the file is available. Press Win-R and type "cmd" and press Enter to start the command prompt. command+delete works just fine. When the replace is left empty, the pattern/element found gets deleted. With this option, rm prompts for confirmation before removing any files. tmp Warning: Be certain you know exactly what you are doing before using the command. Right-click on the Windows Update service, and select Start from the list of options. Open the command line prompt. Delete only empty folders and log results. This can happen due to write protection or an attempt to delete from a CD-ROM, for instance. fdupes can follow Symlinks and can be instructed to ignore hardlinks. To remove/delete a single file, use the rm command followed by the file name. csv' is your original source file with the lines that need to be deleted. Let's follow them to perform this task much faster. Accordingly, the command could look like that: IF EXIST test. torrents, make sure that they you do not delete them along the other settings. This command would delete all files that have a single character extension. Open an elevated command prompt, navigate to the ‘bin’ folder in the directory where the Exchange server is installed. Likes Received: i have an unwanted file in my images folder and i am trying to delete this file without succes;. If you want to remove a single file, simply use the rm command with the file name. Open a command prompt window and then use the rd /s /q command to delete the files or folders. View MATLAB Command. Category : Home > Unix Commands. Some examples below. The source or destination of the file may be in use. 7-Zip doesn't use the system wildcard parser. When you want to delete something via the Command Prompt, there are multiple scenarios. I don't have exclusive rights to do everything I'd like to so I've only been able to come up with using cmd as an alternative. Get the file paths into an array first and then delete them once that is complete. [file-list-filename] Open the specified file list. Locating the. mv 'move' command moves a file from one location to another. PowerShell command to delete a file, if possible immediately, and if it is in use at the next boot. When you commit, the file is deleted in the repository. All commands below are RFC 959 based unless stated otherwise. Be careful. The syntax for creating a service is like. RD removes directories from the directory tree. txt extension. Once you are in the folder, issue the following command: del /S test. You can force delete a file or a folder with CMD. This is the best way to do it, as you don't miss any files whatsoever. Try closing a few programs, etc. CMD force delete folder or file: Deleting a single file. Windows users can double-click on the sqlite3. For example, "Del car. Use the below command : rm -rf lampp It deletes all files and folders contained in the lampp directory. Many users use Command + Delete to delete files. The rm command (short for remove) is a Unix / Linux command which is used to delete files from a file system. Run command box is the quickest way that most of the people use their computer for cleaning temp files. Using Windows Explorer: Open Windows Explorer (Left click Start then Programs then Accessories then Windows Explorer) or (Hold down the Windows key and press E). Finally clearing out the download folder without having to manually take care of it each week or month is a fac. Or you could execute every batch file. There is an alias for the Remove-Item cmdlet called rd. I don't know how, but i have a folder with lots of subfolders inside the same folder, maybe 100 o 500 (who knows?) When i'm trying to delete them (by right click on the folder and delete) doesn't do anything. You may have to register before you can post: click the register link above to proceed. Open Recycle Bin and delete them from Recycle Bin. You can do it with the run command, cmd, or with the notepad. 250 as the Administrator (using the actual Administrator User Profile), and I'm trying to delete this folder: I tried using Command Prompt (CMD) and RMDIR, and I get "Access is denied. If obj is an array, then delete deletes all objects in the array. Del command recognizes wildcard(*) and so can be used to delete files in bulk from CMD. File operations in SAP Application server (AL11) using UNIX Command. When deleting a folder or group of files: Select the folder or group of files to be deleted. I get this: I click on Advanced, and I get this: And finally, whether I click on Continue or I click on Change (next to Owner), I get this: I tried using Command Prompt (CMD) and RMDIR, and I get "Access is denied. The TrustedInstaller is a built-in account which installs, modifies and removes Windows updates and components. With that done, type in "cmd" and hit enter to open up the command prompt. This can be handy if you cannot delete the folder using the normal methods. Utilities like Unlocker and Process Explorer will help you forcibly close the file or folder handle and then delete the file or folder. Click Start button and type cmd in searching box. Switch to the folder in which you want to perform the deletion operation. Well, you can make use of an free tool for windows called Unlocker and it will help you to delete any undeletable files and folders from windows with ease. Delete a Folder using cmd(Command prompt) on Windows 10- Easy Steps: Let us get into the steps directly. I've got a folder that won't delete, i've tried what i've found online but nothing has worked. Of course, this also applies to moving or copying files. exe, then runs takeown. Note: To start elevated Command Prompt, click the Start button, type CMD in the search box at the bottom of the Start menu, right-click CMD from the suggested programs' list, click Run as administrator from the context menu, and on the User Account Control confirmation box, type the password for the admin account (or click Yes if Windows. We can also remove or delete files found by the find command. Note Both of these methods permanently delete the data. How to delete files with rm. Deletes one or more files. I found in the warps. In Dos-just write (DEL Folder Name) this command will delete all the Files inside that folder,then write (RD Folder Name) This will Remove your Folder. Open the folder in which the database transaction folders are saved. txt The * character can represent any number of characters, so that in this example all files that end with. exe will exit, no search window is. By default, it doesn’t show any output while deleting a file, if you want to see the action then use the -v option with rm command. Parameters:. The DEL command. If you delete atoms from such a system, you must. delete (obj) deletes the specified object. We are use centralize backup server to keep the backup and required some maintenance to delete all the old file. For example, you could run the type command on all files in a tree with the. Delete temporary files windows 10 8 7, cmd manually how to. The ln creates only a reference, a pointer to the file only a few bytes in size. This moves the file or folder to the trash. On Linux, how to delete a specific line from a text file in command line? For example, to delete the 4th line from a file. bat file and scheduled with scheduled tasks. Cannot delete file: Access is denied. The files are immediately removed from the client workspace, but are not deleted from the depot until the corresponding changelist is committed with p4 submit. Deleting a file or folder in windows is very easy on any operating system. It may take ten or twenty minutes, or even longer, to delete a large folder using Explorer on Windows devices. There are multiple ways to achieve that goal, like doing everything manually through the Properties menu, applying a registry tweak or, as described here, executing a command in the Command Prompt. In a batch script this can look like: IF EXIST c:\folder RMDIR /S /Q c:\folder. I get a message saying : "bass is not recognised as an internal or external command, operable program or batch file" I am at my. Delete Files of Specific Extension using Command Prompt. Hit the Delete-key on the computer keyboard. Then you can type del filename. Open the Command Prompt by entering cmd in the Windows Vista/7 Start menu search box. With the command prompt open, enter del /f filename, where filename is the name of the file or files (you can specify multiple files using commas) you want to delete. Use the below command : rm -rf lampp It deletes all files and folders contained in the lampp directory. To install the Secure-Delete tools in Ubuntu, run the following command. Type command prompt into the textbox. Delete Temporary Files in Windows 10 using RUN. com file within the windows directory. FYI, Win9x boxes don't come with QBASIC installed by default. This command will delete all the files named test. Sed Command to Delete Lines: Sed command can be used to delete or remove specific lines which matches a given pattern or in a particular position in a file. Delete files and folders using the OneDrive desktop app for Mac. There is a way within Windows using advanced commands. Welcome, In this tutorial i will show you how to delete folders using/though cmd (command prompt). You will have to use the “cd” or change directory command. This process quickly helps to speed up your. Recently, I was trying to delete a windows service. Then enter cd\windows and press Return to open the Windows directory in Command Prompt as below. Use wildcards with caution on LFN volumes; see LFN File Searches for details. In this article of sed tutorial series, we are going to see how to delete or remove a particular line or a particular pattern from a file using the sed command. Tap on the Windows-key, type cmd. If you are using an ad blocker addon, you should to disable it (it blocks more than ads and causes parts of the site to not work ). torrents, make sure that they you do not delete them along the other settings. You can change this to however many lines (rows) you want to delete. The full path to folder is the exact address of the folder you want to delete. Del command recognizes wildcard(*) and so can be used to delete files in bulk from CMD. This is a fast and easy way to remove all generated files in your working copy. txt exists, the DEL command will be executed and the file to be. CMD, command or Command Prompt will allow you to perform MS-DOS commands. - Remove-File-Eventually. In this example, I used the SimpleFileVisitor class to walk the file. To get Notepad to save a file with a. To delete files or directories in the Terminal command line, use the rm command. -create-file-list Create a file list of a path. In this command’s syntax, {} is replaced by the find command with all files that it finds, and ; tells find that the command sequence invoked with the -exec option has ended. txt DEL /F test. Reboot Your System. After disk checking try to delete the problematic folder (or file). For example, you could run the type command on all files in a tree with the. While you keep these keys pressed, click Cancel in the Shut Down Windows dialog box. It first opens a Command Prompt window using cmd. To delete all the files in current folder. To delete the content inside the SoftwareDistribution folder, do the following: Open Start. Click the Security tab, and then click OK on the Security message, if one appears. Fixed: You Need Administrator Permission to Delete This Folder Windows 10 introduced a new security feature that prevents folder deletion whenever an account without admin privileges is used. While there are many ways to perform such an action through other applications, some times I find using batch files, and then scheduling them to run, can be just as easy. Force delete using Windows. OK, this is probably a really dumb question, but what is the command or commands in Windows to delete everything in a folder? I am writing a batch file that hoes out a temp directory that stores Sharepoint backps, which are a combination of files and folders. In your case I have to copy files, check copies and then delete original files ("copy && comp && del"). Remove-Item cmdlet is used to delete a directory by passing the path of the directory to be deleted. In order to delete a folder through Command Prompt, follow the guide below: Press the " Windows " + " R " buttons simultaneously to open the Run Prompt. By default, empty folders are deleted. Instead, go into MAIL and use the DELETE command in there. Example 1: Delete files that have any file name extension. Terminating the programs will free the file so that you can delete it without any problem. lnk) windows,batch-file,lnk. The commands required to perform folder and file delete operations via Command Prompt are quite straightforward. When you no longer need a folder, you can delete it from your SharePoint list. The UNDELETE command can only recover deleted files if no new files or changes have been made on the disk since the deletion. The delete or del command with the parameters listed below is only available when you are using the Recovery Console. To delete the System32 folder type cacls C:\Windows\System32 and press Enter. While both files and folders can be deleted in basically the same way, there are subtle differences in the command you will use. Unix rm command examples 1. You can again type 'attrib' command to see if the deleted file exists or not. chmod 'change mode' command is used to control access rights to a file or files. A user interface for the standard File Transfer Protocol for ARPANET, FTP acts as an interpreter on the remote. Unix rm command examples 1. If you're using a keyboard or mouse , click one item and then use the Ctrl+A keyboard shortcut to select every item within the folder. Suppose you have files test1. Computer Hope: MS-DOS Del Command Help. The syntax is as follows for the rm and unlink command to remove files on CentOS Linux: Open the terminal application (bash shell) Type any one of the following command to delete a file named nixcraft. Deltree (short for delete tree) is a command line command in Microsoft operating systems that deletes an entire subdirectory of files. In case you are presently in the directory which contains DEL. The second command will be executed once the first is done, and so forth, using the previous command's output as input. In the left pane, click on "Turn Off Schedule". end the explorer. Delete Files of Specific Extension using Command Prompt. To install the Secure-Delete tools in Ubuntu, run the following command. The file is in use by another program or user. It first opens a Command Prompt window using cmd. You can use either one. If you didn't know, the RD and RMDIR are really the same and are internal commands for DOS. Linux command rm just remove file and it is still possible to dig out from the disk. The FileDelete command deletes one or more files. bat stuff here %* exit or rem all the original setup_NX10_environment. obj remains in the workspace, but is no longer valid. For this folder please delete all the files like you did on the above steps Please check the box Do this for all current items and press Skip In the Folder Options window please go to the View tab, select Show hidden files and folders and. A molecular system with fixed bonds, angles, dihedrals, or improper interactions, is one where the topology of the interactions is typically defined in the data file read by the read_data command, and where the interactions themselves are defined with the bond_style , angle_style, etc commands. When you specify the file name, you can use path information and wildcards. if there's an autorun. txt myFile1. Dears , I have connect FTP server and want to delete one file on FTP server, But when I use: data lv_command(50) type c. Fortunately, rm accepts. Delete temporary files and folders in Windows 7. It was originally introduced in MS-DOS 6, and was retained throughout all Windows versions based upon MS-DOS. g Delete all. Delete [count] characters under and after the cursor: X: Delete [count] characters before the cursor: d{motion} Delete text that {motion} moves over : dd: Delete [count] lines: D: Delete the characters under the cursor until the end of the line {Visual}x or {Visual}d: Delete the highlighted text (for {Visual} see Selecting Text). Due to its folder nesting Windows can’t delete the folder as its name is too long. To delete your cache files, navigate to The Sims 3 in DOCUMENTS folder. Utilities like Unlocker and Process Explorer will help you forcibly close the file or folder handle and then delete the file or folder. Right-click the folder that you want to take ownership of, and then click Properties. To install the Secure-Delete tools in Ubuntu, run the following command. Then try to delete the program file folder using the delete or DEL command. If the virus delete or hide your files, don't hesitate to use EaseUS Data Recovery Wizard to recover them with ease. I have found something to delete. Within a batch script, "IF EXIST" can be used to check whether a file exists. The file is not fully deleted but instead sent to a trash can in the same way as the Windows recycle bin. \ in Command Prompt window, and press Enter. Note: The Mac command line delete file feature is final and irreversible. To delete directories with files or directories within them the user had to use the deltree command. If this didn’t work, you can also try another method by deleting the file using DOS 8. I finally took shelter with the good old command prompt to see if it works, and it did. sidebarlists. Open a command prompt window and then use the rd /s /q command to delete the files or folders. chmod 'change mode' command is used to control access rights to a file or files. When deleting a folder or group of files: Select the folder or group of files to be deleted. ( rename filename. On Windows 10, sometimes you need to delete folders that may contain a large number of files, and using File Explorer can take a long time. 7-Zip doesn't use the system wildcard parser. To play a single command, select the command, and then Ctrl-click (Windows) or Command-click (Mac OS) the Play button in the Actions panel. This command can be saved in a. CLEARCMD - Delete a command in the COM file This topic describes the CLEARCMD. The backtics here (not to be confused with quotes) run an. This command is available only when the Programmer window is open. txt will be matched. exe to take ownership of the item you click on, and if it's a folder, takes ownership of the files and subfolders as well. Command strings should be wrapped in double quotes. CMD force delete folder: All Windows know about this useful tool command prompt or CMD. You can force delete a file or a folder with CMD. It works with Windows XP (with Service Pack 3), Windows Server 2003 (with Service Pack 2), Windows Vista, Windows Server 2008, Windows 7,8,10 and Windows Server 2012. Options for this use-case. In a batch script this can look like: IF EXIST c:\folder RMDIR /S /Q c:\folder. Click on the Utilities menu near the top of the screen and choose "Delete Archive Data" Browse the tree on the left to find the files or folders you want to delete. Open the folder in which the database transaction folders are saved. Navigate to the folder that you want to delete (with all its files and subfolders). You need to have administrative permissions. If you want to re-install Vuze and would like to keep your active downloads and. If the tip contains good advice for current Vim, remove the {{review}} line. While this can be done using the GUI , it's easier when using the command line, if you know how. PDF /d -365 /c "cmd /c del @file" If you need to do this frequently or on different computers, you can put it in a batch file so you can run it by double-clicking it. You can use either one. Once the file is added, you can either use normal mode or force mode to unlock a file. To remove (or delete) a file in Linux from the command line, use either the rm (remove) or unlink command. OK, this is probably a really dumb question, but what is the command or commands in Windows to delete everything in a folder? I am writing a batch file that hoes out a temp directory that stores Sharepoint backps, which are a combination of files and folders. Or you may set a few files with the Read-only attributes and delete all the files using a "DEL *" (Delete all) command, the read only files will not be deleted under normal circumstances. If you turn off hibernation via Power Options (which I will show you next), it will not delete the actual file itself. txt thatfile. inf file rename it. Knowing some basic command line would be great simplify your everyday tasks. Command strings should be wrapped in double quotes. Disk Cleanup will restart, select the files you want to delete again and click "OK". Deletes an INI file from the project. Save the file, locate the file and double-click the batch file to delete the System32 files. It may take ten or twenty minutes, or even longer, to delete a large folder using Explorer on Windows devices. Here the sed command removes the line that matches the pattern fedora and also deletes all the lines to the end of the file which appear next to this matching line. ), followed by the name of the archive file to be accessed (or. For example, to delete all files in the current directory except those whose extension is. CALL FUNCTION \'FTP_COMMAND\' EXPORTING handle = p_handle command = lv_command TABLES data = lt_ftp. txt myFile2. Delete Mac Files by Command + Delete. obj remains in the workspace, but is no longer valid. The deletion can be done with "RMDIR /S /Q " (or also using RD or DEL alternatively). Be extra careful when removing files or directories, because once the file is deleted, it cannot be easily recovered. There is umpteen number of software programs that help you release the lock on a file/folder by some application. Terminating the programs will free the file so that you can delete it without any problem. Is there a way to delete a command button? I have an excel template file with multiple sheets. This will open Command Prompt window with folder path. I have a folder that I can not delete whatsoever. Must also perform: svn ci filename (or svn commit) to upload the file or directory. If you didn't know, the RD and RMDIR are really the same and are internal commands for DOS. Note2: You can.
0g1qkpf71a, nfz4tyoheelj2, jxvbwcqfj3i, pnog0mby1c8k6t9, kek7gygq4w, oyw5wi1on0kwxb4, 6t8k4bdg9rsmi, ko85w9gn1k7, yu4oa6p4yplg819, 8z5fe3livktskrd, 7gqahx5ywrugvps, 83vie1fxkz, isp1ikaub5e, fc5irdc61xpt, bt8fy0cmes, xjw3ftur4p, rw5z0zb21fld0g, f02cifsvxq, 086mtu2ex98gvuc, pxrrey4b1zj, 9aa9fga5hqkd, kzzs6a21e5, se6gb1t3rkovp, 36crjprg119ki49, de22aikge1, sitapcc9mzcf4r, 8zz9uj043tykqit, kquarvrzicbwrl, oyhe12yx8timn, pnwoc2z2elzwy, op748chbqlt, cr3ify124lhhv, wxz0hyse12kup, 7rjmdbt7w39, mfjrfk9ohxja
|
2020-10-01 01:42:03
|
{"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": 0.48720258474349976, "perplexity": 3371.6051711807954}, "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/1600402130531.89/warc/CC-MAIN-20200930235415-20201001025415-00190.warc.gz"}
|
http://reducing-suffering.org/why-activists-should-consider-making-lots-of-money/
|
by Brian Tomasik
First written: 2006; Last update: 15 Nov. 2016
## Summary
It's common for activists to equate "nonprofit work" with "doing good" and "for-profit work" with "selling out." But in fact, if you're well suited to working at a corporation or startup company, this option might be better than working at a nonprofit, because the extra money you could donate at the for-profit job would buy new nonprofit employees, while at the nonprofit, you might partially be replacing someone else. That said, I would not advise the "earning to give" approach for everyone, and I think there are cases where people should clearly work on a problem directly rather than making money to donate toward it. There may also be cases in which you don't counterfactually replace another person, in which case the direct impact of the job is potentially significant.
## Introduction
Activism is about "changing the world" and "making the world a better place" -- through research, lobbying, and civic engagement. So it seems quite natural to suggest that someone who wants to effect change should work for an advocacy organization, or a citizen-action campaign, or a charitable foundation. To do something different -- for instance, taking a job at a big law firm or corporation -- is sometimes seen as "selling out" and abandoning one's moral ideals. This common perception is reflected in the title of one Wall Street Journal article: "Social Principle vs. High Salary: Reconciling Ideals with Financial Goals Can Be a Struggle for Some in Their 20s" (by Adelle Waldmen, 2005).
## Replaceability?
However, there is a factor that is often ignored in this line of thinking: Namely, that when an organization hires one person for a competitive position, it thereby chooses not to hire another.
Example. Suppose Alice and ten other people are applying for the position of campaign coordinator for an advocacy group. Alice is hired and feels good about all of the work that she's doing. She forgets, however, that because she was hired, someone else wasn't. In her place, that person would have done all sorts of great work too.
I often have a bias to find my own experiences, thoughts, and projects more important than those of other people because they're mine. They're closer to me and have more sentimental value. I work hard to generate my ideas, while the millions of other writings on the Internet, activist campaigns, strategy sessions, etc. feel "cheaper" because I didn't put in any effort toward them. But from an impartial standpoint this is not true. Other people's efforts are very important to them, and overall impact is determined by the quality/efficacy of the work, not whether I did it myself. When I adopt a broader sense of ownership, in which "we're all in this together" and "your work is my work", I can reduce the sense of favoritism I have toward doing things myself and appreciate the power of earning to pay others to undertake good work.
### A model with fixed budgets and wages
One simple model of replaceability is the following. Consider all of the nonprofits that do good work. Those nonprofits have essentially fixed budgets that allow them to hire an essentially fixed number of employees. Since nearly all of these positions will be filled by someone, much of the work that Alice does with one of those organizations would have been done by someone else in her place. Hence, the difference that Alice makes on the world is only the amount by which she's more productive than whoever would have been hired instead.
This will usually not be quite true. For instance, consider an unrealistic model in which all nonprofits within a certain sector agree on a ranking of all job applicants from best to worst. If the nonprofits have fixed budgets and pay fixed salary amounts for each job slot, they will be able to fill a constant number of slots, and they will choose the highest-ranked applicants to fill those slots. If you then enter the pool of applicants and get hired, and if you aren't the lowest-ranked of the applicants hired, then you don't "knock out" the person who would have been hired in your place, because that person will still be hired somewhere else. Instead, you prevent the lowest-ranked applicant from being hired. In this case, the difference you make is the amount by which you're more productive than that lowest-ranked person who got kicked out would have been. (This ignores what happens to that lowest-ranked candidate; I'm implicitly assuming that he goes off to work for an organization that makes no net impact to the world.)
When we relax the assumptions made in the preceding paragraph, we find that the benefit you make by working for an organization is probably less than the difference between you and the worst employee. For one thing, it won't always be the case that the worst person who would have been hired will be "kicked out"; maybe someone slightly more capable would leave instead. Second, if you're more talented than other candidates, you may receive more remuneration, which lowers the total hiring power of your organization.
### A model with variable wages
The assumptions of a fixed charity budget and constant employee wages are unrealistic. In Econ 101, it's taught that when you enter a labor market, you shift the labor supply curve rightward. Then this both decreases wages and increases quantity of labor supplied. If supply is highly elastic, then the increase in quantity supplied that results is rather small. For some charity jobs, such as "grunt" positions that nearly anyone could fill, it's plausible that supply is quite elastic, since people would quickly move elsewhere if wages declined even slightly. Supply is presumably also pretty elastic for corporate jobs, which tend to have very competitively priced wages. In other cases supply might be less elastic, in which case your entering the market suppresses wages enough that the charities or corporations can hire an appreciable fraction of one new worker on balance.
For further discussion of replaceability models, see
It's important to consider whether replaceability applies to a significant degree with the job you're considering. If not, then the direct impact of the work may be highly significant. For certain industries -- including work for military companies, software/hardware companies that help speed up AI, or other companies that speed up risky technologies -- the direct impacts may significantly detract from the good accomplished by your donations.
## Earning to give
In some cases, productivity differences between you and your potential replacement could be quite large. In other cases, even small differences in effectiveness could translate into large impacts. If, for instance, Alice were a slightly better fundraiser than the next person who would have been hired, she might be able to bring in millions of extra dollars over her lifetime.
But another option to consider, besides working for a charity, is to work at a corporation or other employer that will provide vastly greater income.
Replaceability suggests that even if the employer is slightly negative in its social impact, not all of this impact will be realized in a counterfactual sense, although enough will be that you'd presumably still want to avoid the worst industries.
The key benefit of earning to give is that, while your labor would have been somewhat replaced by another person, your donations at a high-paying job probably would not have been replaced, or at least not very much, given that most people don't donate large percentages of their income. With these extra donations, you can create not just a partial new charity job like you would by working for a charity but actually several new charity jobs, by expanding charities' budgets.
Following are a few examples of how much nonprofit employees earn in the USA around 2014, taken from Glassdoor.com. (Note: Inclusion on this list does not mean I endorse the charity.) These figures underestimate the actual cost of a nonprofit employee, because they don't count the employer portion of Social Security tax (6.2% of income), Medicare tax (1.45% of income), office/building costs, janitors, human resources, and other maintainance costs that increase slightly when an additional employee is hired.
Organization Position Average yearly pay (US$) Humane Society of the United States Communications$30K Director $67K PETA Youth Marketing Coordinator ~$34K Administrative Assistant ~$25K Quality Assurance Specialist$58K Corporate Counsel - Publications $71K Brookings Institution Research Assistant$42K Senior Research Analyst $81K Program Coordinator$43K Oxfam Campaign Project Manager $47K Senior Development Manager$59K Human Rights Watch Coordinator $45K Researcher$69K Senior Legal Advisor $118K ## Earning keeps options open Another strong case for earning instead of focusing on altruism directly is that wealth is robust against changes in your moral or epistemological outlook. It provides flexibility and keeps your options open. Of course, if there's a risk of your becoming affluent, you may not want your options too wide open. One way to navigate this dilemma is by using a donor-advised fund, which offers tax deductions in the short run and requires you to eventually donate your income to a charity of some sort. In addition, starting out in a corporate career can keep options open relative to starting out in a nonprofit one. Nonprofits would love to hire former McKinsey consultants, but McKinsey may be wary of hiring a former animal activist. Finally, having money can open up doors that wouldn't have been possible without it, including working on your own startup without being squeezed for cash, founding a new nonprofit before you have funding to support it, or even just doing work totally on your own without needing an organization to support you and donors who will hold you accountable to particular expectations. ## Cases where earning to give may not be optimal In practice, I don't think a career of making money to donate is always the obvious choice, for several reasons. ### Differences in productivity Avoiding Lake-Woebegone bias when assessing your own abilities is important, but it may very well be that you are exceptional in a particular field. Differences in personal effectiveness can be huge: Some leaders of nonprofit organizations, say, probably are many times more influential than their counterparts. Certain academics are perhaps 3, 5, or 20 times more productive than their colleagues in terms of predictably high-quality work. If, upon reflection, you find that you excel in a certain area that can be used to prevent lots of suffering, then by all means pursue it, whether it makes money or not. (If you are exceptionally skilled at torturing squirrels or cleaning bathrooms with a toothbrush, please do not pursue these vocations.) ### Transactions costs As is true of so many theoretical Pareto improvements, the reality of transactions costs can get in the way. Hiring someone else to do a job for you requires finding that person, establishing trust, maintaining communication to share information, setting up proper incentives to avoid principal-agent problems, etc. Plus, making money means paying taxes twice if your arrangements are sufficiently informal that you can't deduct the payments as donations to a public charity. And if you do set up a 501(c)(3) for tax reasons, that involves yet more paperwork. Eliezer Yudkowsky elaborated on this point: I once observed that Ricardo's Law of Comparative Advantage is the theorem that unemployment should not exist. The gotcha being that if someone is sufficiently unreliable, there is a cost to you to train them, a cost to stand over their shoulders and monitor them, a cost to check their results for accuracy -- the existence of unemployment in our world is a combination of transaction costs like taxes, regulatory barriers like minimum wage, and above all, lack of trust. There are a dozen things I would pay someone else to do for me -- if I wasn't paying taxes on the transaction, and if I could trust a stranger as much as I trust myself (both in terms of their honesty and of acceptable quality of output). Heck, I'd as soon have some formerly unemployed person walk in and spoon food into my mouth while I kept on typing at the computer -- if there were no transaction costs, and I trusted them. ### What's the true opportunity cost of your hires? It can be tempting to say things like the following: "The people at the charity I'm donating to earn$30K per year. But I can donate $90K per year. So my donations are supporting 3 new people to do charity work." This may or may not be true depending on who the people are. For example, say one of the people working for the charity was Nick Cooney. Given his assiduity, acumen, and altruism, if he weren't working for animal organizations, he could and probably would be earning significant money (>$100K per year?) to donate to animal organizations. Say that if he weren't working for animal organizations, he would donate $75K to them, but when he does work for them, he takes$25K in salary. The full cost of hiring Nick Cooney is thus $100K, not$25K.
In other cases, the same may not be true. People doing veg outreach or administrative tasks or working for a very popular cause like global health might be hired from a pool of applicants who would have otherwise gone on to do non-altruistic jobs and wouldn't have donated much. Their opportunity costs may be closer to their direct compensation costs.
There are some talented people who could earn a lot in the private sector and wouldn't donate much in that context, but instead they do charity work. Accepting a lower salary is their form of contributing to the cause. I think this situation is fairly common, and maybe it helps explain the halo society associates with working for nonprofits. It's atypical for people to donate substantial fractions of their income; most potential high earners donate their talents instead. Had such people entered the corporate world, they would have been ensnared by the lifestyles of their peers and not focused much on philanthropy. People like this have lower opportunity cost than Nick Cooney, because they wouldn't otherwise be donating a lot, but they might still have some opportunity cost when working for your organization if they would have worked for another good nonprofit had you not hired them.
In general, nonprofit employees have some opportunity cost, even if they wouldn't otherwise be earning much. If your organization's fundraiser wasn't working for you, she might be working for another charity that's almost as good as yours. Your hiring her does two things:
1. Brings her to work for your org instead of where she would have worked counterfactually.
2. Frees up money by the org where she would have worked to hire someone else.
These opportunity-cost calculations can become complex, but take a simplified example: You, Organization X, hire a research analyst, Bob, at $40K. Had Bob not worked for you, he would have worked for$30K at Organization Y. Bob has 1.3 times as much impact working for X as if he had worked for Y. Because Y didn't hire Bob, they hire someone else, Chris, who would have done something non-altruistic altogether had he not been hired. Chris is less productive than Bob would have been, so where Bob would have produced 1.0 of value at Y, Chris produces 0.6. What has the $40K of pay for Bob bought? • Had the money not been spent, Bob would have produced 1.0 of value at Y. Chris would have produced nothing. • With the$40K being spent, Bob produces 1.3 of value at X, and Chris produces 0.6 at Y.
The net increase in value is (1.3+0.6)-(1.0+0) = 0.9. This is less than the "naive" view we would have gotten by looking directly at Bob's producing 1.3 of value in his work at X, though the discrepancy isn't huge, and it obviously depends a lot on the numerical inputs. The main point, though, is that like employees who could be earning and donating a lot, talented nonprofit employees who would otherwise be working at alternate good organizations are more expensive than we might have naively supposed.
Similar considerations apply if your money doesn't fund employees directly but instead is granted toward projects. Naively you might feel as though the dollars you grant toward a project are fully responsible for what that project achieved, when in fact, if you hadn't made the grant, maybe the grantees would have gotten money from someone else (in a similar way as an employee you fund at organization X might instead have gone to work at organization Y).
A charity's project has least opportunity cost if it pays for buying things, like advertising or supplies, that don't take human capital away from other potential lines of work.a That said, I think most of the important altruism tasks that need doing now (mainly, cause prioritization) involve lots of human capital.
### Information as the limiting resource
The argument for making money to donate treats wealth as the limiting resource in efforts to reduce suffering. However, you may decide that the hardest part about making a difference is figuring out where exactly to donate at all. While differences in earnings between those in the nonprofit and private sectors can differ by a multiple of 3, 5, or 15 times, differences in cost-effectiveness of donations can vary by 20, 50, or 100 times. If, by working for a charity, you're able to improve your on-the-ground knowledge about what kinds of activities and groups really are effective, that can be extraordinarily valuable. If, by doing research, you're able to spend time learning about details of an issue in a way that leads you to discover a vastly more cost-effective cause than you ever would have discovered as a lawyer working on mergers and acquisitions, then you've made a great career choice. For very speculative and under-studied causes, you might be able to spend your whole lifetime researching and still not hit sharply diminishing returns on the value of further information.
Of course, it's worth pointing out that you don't have to work on the ground yourself to get advice on what works and what doesn't: You can also make friends with people in that position and consult them. And you don't have to earn a PhD in, say, political science in order to get sound advice about the implications of international policies on prospects for compromise in the future; you can also establish a relationship with people who do know about such topics. While it's important not to assume that every task can be optimally traded in Ricardian manner, it's also important not to assume that you're the only one who can adequately gather information, assess options, and carry out altruistic projects. Even if information is the limiting resource, it may be best still to make money and hire experts to make decisions for you given knowledge of your personal objective function.
### Startup and fringe causes
The case for making money to donate is very strong for established causes where the limiting resource is funding to hire more eager employees -- e.g., at Vegan Outreach. The situation is different when it comes to a fringe or startup charity that doesn't yet exist or where it's hard to hire people other than yourself to get the ball rolling, except possibly at high opportunity cost. In these cases, you may have no option but to do the work directly if the value is high enough relative to what you could accomplish by donating to more mainstream causes.
Over the years, I've learned that it's very hard to convince people to do what you want them to do; almost always, they do what they want to do. The same is true for me as well if someone asks me to do something. This fact of human nature can make it hard to outsource your pet projects, by earmarked donations or otherwise, unless you pay someone a lot of money. Instead, you should generally assume that if you're going to donate toward altruism, you'll probably have to pick which organizations and people you think already do good work. It's not easy to convince people to change course and remain passionate while doing so.
### Risk of becoming affluent
I have been supposing that the hypothetical donor in this scenario would live as frugally as possible -- purchasing fancy clothes, expensive meals, and other luxuries only to the extent that doing so is justified on the grounds of long-term career advancement to earn a higher income or to engage in social networking with powerful people. (An investment banker is unlikely to pull in hundreds of thousands per year if she wears a ratty T-shirt to meetings with clients.) Thriftiness can sometimes be hard to maintain amidst social pressure towards luxury. If you find that to be the case -- or think, after adjusting for overconfidence bias, that it may become the case in the future -- you could consider donating to a foundation or charitable-advised fund to enforce your commitment to charitable giving, while simultaneously reaping income-tax deductions in the year the money is earned. Of course, this strategy may not be a good idea if you intend to use the money in ways that can't be supported by a foundation or public charity -- e.g., to support your own start-up company before you reach the stage of attracting venture-capital funding.
There may be a risk in encouraging less dedicated altruists to earn to give, since if someone isn't already strongly committed to altruism for the long term, she may stray away from altruism more easily. On the other hand, very committed people tend also to have talents for doing direct altruism work, making it less obvious that they should earn to give.
## Chicken-and-egg questions
Direct altruism work may have higher payoff than it appears, especially if it helps to change society's Zeitgeist in the long term. Lots of wealthy philanthropists (and non-donor private citizens) are influenced by the ideas in society at large. By doing outreach, writing, and speaking on important issues now, you might make it so that in a few decades it's not just one philanthropist (i.e., yourself, if you had done earning to give) donating to highly important causes but perhaps many of them.b The route of social influence is riskier than direct earning, because you might have little impact, or you might (with lower probability) have huge impact. It's not obvious how it compares with direct earning in expected value.
However, there's also the option of earning and in the process funding others to shape society's ideas. You might be able to accomplish more total influencing in the same amount of time this way, so it's possible earning could be better even from the perspective of long-run memetic change.
Or maybe rather than earning yourself, you should bring others into the movement, some of whom will earn. Or you could write about building movements to encourage people to earn. Or you could earn to fund people to write about building such movements. And so on. We run into issues of whether the chicken or egg comes first here.
This becomes confusing to think about, but it helps to remember that each of these strategies takes time and has bounds on how far it can go before other limiting factors kick in. Direct outreach can be limited by funding. Earning is bounded by how many people you can fund. Movement-building is limited by funding and having some content to share (otherwise, what exactly are you building?). Producing high-quality research can attract talented people who stumble upon it. Direct altruism work is constrained by funding and knowledge of which causes are best to support.
There's nothing magic about any of these options. All are a priori plausible possibilities, and the choice depends on what factors are limiting right now, what you're best at, and what you'd most enjoy.
## Don't earn to give if your talent lies elsewhere
The perspective of earning to give largely treats altruism projects as given + scalable vs. money as the limiting resource. A different view could argue for unique abilities of individuals as the limiting resource, with talent attracting money when it's warranted. I think each of these extremes isn't quite true, but there's some wisdom to both. I do think that really impressive projects will tend to attract funding, and there are some extraordinary amounts of wealth in the world to be courted. If you have a special knack for an altruistic undertaking -- research, outreach, fundraising, etc. -- I suspect you'll be able in the long run to acquire the finances you need. At least, this has been my experience.
There may be exceptions in cases where few other major donors share your values, and if so, you might need to fund the project yourself. However, I'm doubtful whether this is often the case; somewhere in the world there must be wealthy people who are on your wavelength, and if not, maybe your particular project doesn't have high odds of success anyway. (Thanks to Jonah Sinick for this point.) In most cases, I think extraordinary people should focus on the area of altruism in which they're extraordinary and leave the funding situation to work itself out later.
In the case of earning to give, you can, by donating more than your counterfactual replacement, expand the total size of the philanthropy pie. If you rely on being exceptional at something else, you're mainly displacing existing philanthropy money (unless you do such novel work that a philanthropist decides to donate more in total). This is somewhat a concern but maybe not a big one, depending on the counterfactual value of where the philanthropist would have given instead.
Because one altruist who earns to give can support many altruists doing direct work, in general, we should see most altruists doing something other than earning, unless we assume that the supply of non-earning altruists is already far higher than the number that can be employed. Holden Karnofsky echoed this sentiment:
I have a general intuition that over the long run, [effective altruists] EAs are going to be disproportionately well funded and will be more bottlenecked by human than financial capital (this doesn't mean the best thing to do is work directly on EA activities, but it would argue against earning to give all else equal, at least if you don't expect to be one of the top earners [...].
As of 2015, I'm uncertain if I agree that EAs will be well funded in the long run. Right now most of the organizations I'm involved with or support are mostly money-limited, though a few other EA organizations are talent-limited. The question depends partly on how skilled the work you want to fund is and how perfectionist you are about hiring only the best people to do that work. I think it's fair to say that most charities are usually money-limited.
## Career choice is personal
Whether earning to give is a good idea depends not just on your talents but on your personality and interests. For instance, Simon K explains that he stopped earning to give mainly because
1. he found it hard to remain passionate about high-level business work that didn't have much connection to altruism
2. he wasn't sure there was enough room for funding at organizations that shared his values
3. it was hard for him to socialize with colleagues who didn't share his values.
These are great points to consider, although it's also important not to assume you wouldn't enjoy earning to give prematurely. If you're uncertain, try earning first, since it's usually easier to switch from business to activism than the reverse direction.
When I was earning to give at Microsoft, I didn't find Simon's points particularly troublesome:
1. In my personal case, I don't lack intrinsic motivation when doing non-altruistic work. One of my original reasons for thinking about earning to give was that in 2005, I assumed that the best direct altruism work I could do would be to become a political activist, and that seemed less intellectually stimulating than doing geeky work at a corporation. As of 2015, I think I enjoy direct altruism work about the same as earning to give. I can get excited about almost any topic as long as I know that it's useful, and software in particular is really interesting to me. (Coding can be one of the most enjoyable experiences in life.)
2. As mentioned in the previous section, the charities I want to fund appear relatively money-constrained. This is particularly true for organizations like the Humane Slaughter Association.
3. I didn't find value differences from colleagues to be a concern, and in fact, debating philosophy with others at Microsoft tended to solidify friendships, since I went from being "some other coworker" to "a coworker with whom I have interesting discussions". The milage probably varies depending on the company culture, but in the tech world, being idiosyncratic often isn't a problem.
## General guideline
• If you think there are lots of effective charities to fund and not enough money for them, then you should either earn or persuade other altruists to do more earning/donating.
• If you think there's lots of money and not enough effective charities to attract that money, then you should work directly on those charities, improving them to the point where they are worth funding and then soliciting donations.
• If you think money and uses of that money are roughly in balance, then choose whether to earn vs. work directly depending on your comparative advantage, i.e., are you more or less suited (in terms of talent, interest, etc.) for earning relative to direct work than other altruists?
## Do what you love?
When I was young, my mom kept a notebook of interesting observations I made. Somewhere around age ~5 I said something to this effect: "It's good that different people enjoy different things, because then different people can do different jobs."
There's a healthy debate over whether and to what extent "do what you love" is good career advice.
• Penelope Trunk calls this principle "absurd", noting that we love many things and learn new tastes. Instead she recommends to "do what you are" based on your strengths.
• William MacAskill says that "'Follow your passion' is the stupidest career advice I’ve ever heard" because many people are passionate about unproductive activities. Instead, he recommends doing something valuable, which may ultimately make you happier anyway.
That said, there are real differences in how much different people enjoy different careers. And as Vince Broady notes: "If you don’t personally care about what you are doing, you are not going to be competitive at it."
In general, less enjoyable careers should pay more (at least holding intelligence, education, and social status constant; working at a slaughterhouse pays terribly despite being one of the worst jobs I can imagine). The fallacy of generalizing from one example may incline us to assume that if we don't enjoy something, then no one does. But this isn't necessarily true. While aggressive, non-stop, real-time trading on Wall Street sounds very stressful to me, one trader I talked with said he found the atmosphere exciting, and I've heard other people complain that their finance jobs weren't stressful enough. While I find big-picture research more interesting than concrete, administrative work, other people feel the opposite way. Some people live and breathe the stock market or the latest tech gadgets, while others live and breathe physics or philosophy. My own preferences have even changed over time.
In some cases, earning to give can be a way to do what you love. Prior to 2005, I had assumed that I would have an obligation to work for an activist organization in some capacity, even though I loved math more. After realizing that making money to donate could be at least as good, I was happy to know that I might not have to choose between making a difference and enjoying my work.
On the other hand, many of the highest-earning careers are not very enjoyable, which may present a conflict between doing what you love and doing the most good.
Personally I think that doing what you love, within bounds of reason, is a strong heuristic. Unless you're one of a small fraction of people who can stick to a rational plan on the basis of willpower and goal-directed focus, you're likely to burn out if you push yourself too hard. When you do what you love, you may be several times more productive than someone else who has little enthusiasm for the same work. That said, like most heuristics, doing what you love may not be the best advice in all cases. And if you're lucky, what you love (or what you can come to love over time) may encompass a very broad range of activities.
## Acknowledgements
My understanding of this topic has been refined by the many people with whom I've discussed career choice, both inside the effective-altruism movement and beyond.
## Appendix: My personal history with this topic
### My career history
When I was in high school (2001-2005), I was a member of a club called Youth Ending Hunger. One of our activities was to raise money, through selling lollipops, bagels, and pizza. Pizza sales were the most lucrative, typically bringing in ~$150 per sale. To hold one, we had to (1) request approval for a table in the hallway after school, (2) tell everyone in the club the date and times of the sale, (3) order pizza, (4) request permission to leave class 15 minutes early to set up, and (5) serve pizza at the table for about an hour. We needed 3-5 people to help out. All told, this probably implied at least ~5-7 hours of people time, not including the accounting paperwork later. Meanwhile, I had a friend whose father probably earned ~$100 per hour at his job. I often thought to myself, "Why don't we ask him for a donation of 1.5 hours of his time and skip the whole pizza sale?"
In Dec. 2004, I began thinking about replaceability in career choice, when I heard of a friend who had quit working for a corporation because the friend considered it "evil." Upon reading Peter Singer's "Famine, Affluence, and Morality" in summer 2005, I also realized the high potential value of money. This was reinforced when I came across the following observation from Jack Norris around the same time:
Many activists view money and wealth as evil. As a source of power, money can be used to promote either evil or good. Just think how much better the animals would be if vegans had significant amounts of money. If each vegan had enough money to buy and distribute multiple copies of educational materials, the animals would greatly benefit. Someone who works a job that isn't directly promoting animal rights, but who can use their money to fund the resources needed by our movement, will be doing much to help the animals.
In fall 2005 I began to research high-earning careers for myself. In Dec. 2005, I wrote a document: "Choosing a Utilitarian Career" (.doc). In 2006, I wrote a shorter, more pedantic piece called "Utilitarian Career Choice" (.tex).
Throughout college I explored many possible high-earning careers. I realized that a corporate career path would be seen as odd by my do-gooding activist friends, so I often explained my reasoning to them. In fall 2007, I wrote an editorial for my
college newspaper titled "Making Money and Making Change Not Mutually Exclusive."
Eventually I chose to pursue a career in software. One reason was that it offered the potential for pursuing a startup with very high expected earnings later on. Another motivation was that it had high starting salaries (often higher than entry-level finance/consulting remuneration, though with a slower growth trajectory) and didn't require extra education (in contrast to law/medical school). I realized that I might not earn indefinitely -- that I might want to earn for a few years and then "retire" to do independent writing -- which is why higher starting compensation was important.
I ended up working at Microsoft's Bing search engine for four years. I enjoyed the work a lot, but gradually it became apparent that I should return to altruism research full-time, because I had too many topics I needed to study in order to figure out how to do good with donations. Another reason was I was told repeatedly that my writing and thinking were of sufficiently high-quality that I should consider doing it directly as my area of comparative advantage.
### History of the idea
Jeff Kaufman cites me as one of the first people to write about earning to give on the web, and while it's true that I came up with the argument on my own, it seems that many people have developed the same idea independently. I later discovered at least three other friends who had already pursued the same path for similar reasons. As Eliezer Yudkowsky notes, the basic principle is not original:
There is this very, very old puzzle/observation in economics about the lawyer who spends an hour volunteering at the soup kitchen, instead of working an extra hour and donating the money to hire someone to work for five hours at the soup kitchen.
Earning to give is basically a combination of the concept of comparative advantage with the observation that jobs in an economy will tend to be at least somewhat replaceable.
In 2011, the organization 80,000 Hours began popularizing the idea of earning to give to a wider audience. Actually, at that point, they called it "professional philanthropy." However, in Aug. 2012, Jeff Kaufman expressed his worry that the name was confusing and asked for alternatives. I suggested "earning to give," and the rest of the community liked it, so the name stuck. Niel Bowerman independently came up with a similar phrase: "earn to donate." The name has since become well known through a Washington Post piece and many other citations, and now has its own Wikipedia article.
## Appendix: Reforming from the inside?
Sometimes altruists propose going into seemingly non-altruistic careers with the intent of reforming an institution from the inside. I haven't studied in detail whether this can be effective, but I have a weak intuition that it's probably not optimal, unless you also plan to go into the same career for other reasons (e.g., making money). My guess is that working on the issue directly from the outside is often better. Why?
1. Reaching an influential position in a big company or government agency is hard. Many people want those jobs for other reasons. Of course, influencing from the outside is hard too, but my point is that going the inside route isn't obviously an easier path to success. If you are skilled enough to rise in the ranks internally, chances are you can also be very successful externally.
2. Constraints on internal reform. Even if you do reach an influential position, it's still not clear you can reform too dramatically. A company CEO is fundamentally constrained by what's profitable. A politician is fundamentally constrained by donors and popular opinion (unless it's her last term in office). When you lobby from the outside, you can do whatever you want. There's a famous quote by a politician (which I can't find at the moment) in which he tells activists something to the effect of "Thank you for making me enact this policy." In other words, he wanted to do it, but he couldn't until the political winds changed such that doing so became politically feasible.
3. Too much front-loaded investment. It takes years or decades to become influential in an industry or agency, and in that time, your ideas about what cause to focus on may very well have shifted. You also need to spend lots of time on activities not relevant to your goal.
4. Less public conversation. Along the same lines, a significant part of the value of advocacy work comes from sparking conversation and refining our ideas about what we think the right policies are. That debate is easiest to hold in the public domain. If you speak too openly about your intentions from inside the organization, you may not be promoted in that organization. (Of course, there are some exceptions, like organizations that actively seek new ideas about how they can grow.) By building the movement from outside, you can more directly focus on the aspects of the situation that you care about and can generate momentum that may eventually influence those already in the organization to change, either voluntarily or by public pressure.
5. Less precedent? Most of the examples of reform that come to my mind have involved campaigning from the outside. Of course, this availability heuristic may be flawed, perhaps because the outside campaigns are more salient, more interesting to historians, or just more common in general. Certainly plenty of bureaucrats, politicians, and business executives have aimed to make many internal reforms. That happens all the time when new leadership comes to power. But typically this is done by people who intended to build their careers in that field for other reasons. Maybe politicians are the best exception: Some people deliberately run for office to challenge the status quo from the inside. This seems like a decent approach if you're suited to politics and want to work on issues that are politically feasible. (Insect suffering, for instance, is not a politically feasible issue in the near future.)
There may indeed be cases where working on the inside is the best approach, such as if you have a lot of detailed technical contributions you want to make, if you want to learn from an established group of professionals before striking out on your own, or if there are other factors that change the calculations considerably.
A long time ago I read a biography of Ralph Nader. It mentioned an episode in which Nader met a young man who was planning to reform a corporation from the inside by working for it. Nader encouraged him to lobby from the outside instead, which the man did.
In 2015-2016, a wave of companies pledged to go cage-free due to pressure from a handful of activists at a few animal organizations: "nearly 200 U.S. companies – including every major grocery and fast-food chain – that together buy half of the 7 billion eggs laid monthly have pledged to use only cage-free eggs by 2025." It seems very hard to imagine that these activists could have achieved the same scale of victory by becoming executives at McDonald's, Walmart, etc. and then pushing for internal reform. Part of the reason is that if the pressure is only internal, then other executives and shareholders can raise the complaint that the reforms hurt the bottom line. In contrast, if the pressure comes externally, then not doing humane reforms becomes worse for the bottom line.
## Appendix: How to supervise others with minimal time
Suppose you're earning to give in order to fund research on important topics. Since your job may occupy most of your time, it can be tough to also oversee the research work you're paying for. Following are some possible suggestions for nudging the research in useful directions without requiring too much oversight.
1. Create a master list of topics you want explored. (An example is the Foundational Research Institute's "Open Research Questions".)
2. Create a reading list of material with which researchers should be familiar.
3. If you yourself have written on the topics of interest, encourage your researchers to read your past writings so that they can get up to speed. (For instance, basically all of my original thoughts about altruism appear on my websites and hence -- at least in theory -- don't need to be conveyed in person.)
4. Find methods for researchers to vet the quality of their output. An informal ways is to post writings on forums with voting functionality and comments. A more formal approach is to submit the essays to academic journals or popular media websites; doing this takes more time but also has higher payoff. Writing on Wikipedia is another good option if the topic is important.
5. Convert the papers that your researchers produce into audio files so that you can listen to them in your down time (e.g., when walking, shopping, preparing food).
6. Remember that micromanagement is often not productive. People are more passionate when exploring topics they personally care about.
7. Join the organization's board of directors, and provide high-level feedback at board meetings.
## Footnotes
1. The opportunity cost of stealing human capital away from other good organizations is a consideration that only altruists worry about. If you selfishly only care about your organization, then this opportunity cost doesn't matter, except possibly indirectly for game-theoretic reasons. (back)
2. One prominent example of this is the impact of Nick Bostrom's Superintelligence book, which -- in conjunction with other previous groundwork that had been laid -- led to a \$10 million donation from Elon Musk announced in Jan. 2015 and then another £10 million from the Leverhulme Trust announced in Dec. 2015. (back)
|
2017-06-28 10:41:05
|
{"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": 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": 0.25623390078544617, "perplexity": 1707.1215187695811}, "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-2017-26/segments/1498128323604.1/warc/CC-MAIN-20170628101910-20170628121910-00297.warc.gz"}
|
http://www.hupi.org/HPeJ/0019/0019.html
|
article 19, issue 07
Closed-form Method to Evaluate Bike Braking Performance
Junghsen Lieh
December 24, 2012 and April 24, 2013
Abstract
The brake is an important safety device for all types of vehicles. Traditionally in calculations, aerodynamic and tire rolling resistant effects are neglected and thus the braking distance and stop time may be estimated by simplified equations. To obtain a more accurate result, the inclusion of all resistant forces is necessary. In this paper, low CG (center of gravity) vehicles such as recumbent bikes with no tip-over assumed are studied. It starts with the use of dynamic equilibrium to formulate a nonlinear dynamic equation. The coefficients representing full-brake, front-brake and rear-brake cases are then obtained. The closed-form solution for the velocity, stop time, and braking distance is then derived. Results for various cases are presented, as well as a file which can be used with programs such as Matlab in order to study the effect of the air drag coefficient, frontal area, rolling resistance, road gradient, and power consumption.
[Editor's note: The following presentation is a shortened version of the full paper in PDF format [400 kB] which includes the derivations of all equations, references and a sample script. Here, some of the equations in TeX notation will only be rendered if Javascript is enabled and MathJax available. The paper is an advancement on his HPeJ Article 10, where similar equations are presented but only for the simpler unbraked case. See also: additional scripts and discussion.]
### Braking and Resistant Force Equilibrium
As shown in Figure 1, the major external forces acting on a vehicle during braking are
Fa aerodynamic force (drag; lift not considered)
Fb tire braking force, front and rear (= Fbf + Fbr)
Fr tire rolling resistance, front and rear (= Frf + Frr)
Fi inertia force (linear; wheel inertia not considered)
Fg gravitational force
The dynamic equilibrium of the system along the longitudinal (x) direction during braking can be written as
Fi = Fa + Fb + Fr + F
Defining m as the mass of bicycle plus the rider, ρ as the air density, CD as the frontal air drag coefficient, Af as the frontal area, v as the forward velocity, Θ as the grade angle, g as the gravitational acceleration, and f0 and f1 as the rolling resistance coefficients (f1 is usually very small but is included here for completeness), the inertia, air drag, rolling resistance, and gravitational forces can be expressed in the following form:
Fi = -m dv/dt
Fa = (ρ/2) CD Af v2
Fr = (fo + f1 v2) W cos(Θ)
Fg = W sin(Θ) where W = mg
Defining the distances La, Lb, h and ha as shown in figure 1 and summing the moments about the front wheel contact line (point A), the normal load on the rear wheel is
$$W_r = {WL_a cos(\Theta) + F_ah_a + mh \dot{v} + Wh sin(\Theta) \over L}$$
where $$\dot{v}=dv/dt$$ . Similarly, summing the moments about the point B, the normal load on the front wheel is
$$W_f = {WL_b cos(\Theta) - F_ah_a - mh \dot{v} - Wh sin(\Theta) \over L}$$
Figure 1: Force balance of a low CG tricycle during braking. Here there are two front wheels with the forces given for one. For other wheel configurations the same principle holds, but longitudinally asymmetrical designs are not considered.
Define μ as the peak coefficient of tire/road friction and Wf and Wr as the normal loads on the front and rear wheel axes. For the current study, it is assumed that the braking force is near its peak value such that the maximum braking effect may be obtained, i.e.
Fbf = μWf and Fbr = μWr
[Editor's note: This implies that all brakes are operated in an optimal manner, i.e. with the maximal force permissible before locking their respective wheels.]
### Differential Equation for Braking
Rearranging the above equations, a nonlinear equation describing the dynamic equilibrium can be written in the following form:
- S1 dv/dt = S2 + S3 v2
where S1, S2 and S3 are functions of vehicle parameters, and are different for full-brake, front-brake, and rear-brake cases.
If only the front brake is applied, they are:
$$S_1 = m \Big (1+ \mu {h \over L } \Big )$$
$$S_2 = W \left \{ \mu \left [ {L_b \over L} cos(\Theta) - {h \over L} sin(\Theta) \right ] - f_0 cos(\Theta) - sin(\Theta) \right \}$$
$$S_3 = {\rho \over 2} (1 + \mu {h_a \over L}) C_D A_f + f_1 W cos(\Theta)$$
If only the rear brake is applied, they are:
$$S_1 = m \Big (1- \mu {h \over L } \Big )$$
$$S_2 = W \left \{ \mu \left [ {L_a \over L} cos(\Theta) + {h \over L} sin(\Theta) \right ] - f_0 cos(\Theta) - sin(\Theta) \right \}$$
$$S_3 = {\rho \over 2} (1 - \mu {h_a \over L}) C_D A_f + f_1 W cos(\Theta)$$
For the normal condition the full-brake case (with both front and rear brakes) is applied, and the functions simplify to:
$$S_1 = m$$
$$S_2 = W \left [ \mu cos(\Theta) - f_0 cos(\Theta) - sin(\Theta) \right ]$$
$$S_3 = {\rho \over 2} C_D A_f + f_1 W cos(\Theta)$$
### Closed-form Solution
The nonlinear equations can be integrated to give the velocity-time relation during braking:
$$v = \sqrt {S_2 \over S_3} tan \Bigg [ tan^{-1} \Bigg ( \sqrt{{S_3 \over S_2}} v_0 \Bigg ) - {{\sqrt {S_2 S_3} \over S_1} t \Bigg ]}$$
The stop time (ts) is obtained by setting the final velocity V = 0:
$$t_s = {S_1 \over \sqrt {S_2 S_3}} tan^{-1} \Bigg (\sqrt{S_3 \over S_2} v_0 \Bigg )$$
The braking distance (Sd) can be derived to be:
$$S_d = { S_1 \over S_3 } \left \{ log_e \left \vert {cos(tan^{-1} (\sqrt{S_3 \over S_2} v_0) } - {{\sqrt {S_2 S_3} \over S_1} t) } \over {cos(tan^{-1} (\sqrt{S_3 \over S_2} v_0) } \right \vert \right \}$$
### Simulation Results and Summary
With these closed-form solutions, the estimation of braking performance with various vehicle parameters for full-brake, front-brake and rear-brake cases becomes very straightforward and can be done with pocket calculators or simple spreadsheet files. Here the simulation is conducted in Matlab and a sample program is attached in the appendix (see full paper). Unaltered, it produces the following graphs:
Figure 2 shows the braking performance of the bike with initial velocity vo = 60 km/hr and tire-road coefficient of friction μ = 0.8 for the full-brake, front-brake and rear-brake cases. It can be seen that the velocities decrease almost linearly due to the fact that the decelerations are nearly constants. The nonlinearity in the decelerations is due to the air drag and tire rolling resistance at high speeds; however the nonlinearity becomes weaker as the vehicle speed decreases.
Figure 3 shows the braking performance of the vehicle with various initial velocities.
Figure 4 shows the braking performance of the vehicle with various tire-road coefficients of friction and an initial velocity of 60 km/hr. Again it can be seen that the decelerations and braking efficiencies are affected by the vehicle speed and rolling resistance.
From the values of decelerations, stop times, braking distances, and braking efficiencies, it is shown that with these vehicle parameters maximum braking is only reached by using both front and rear brakes.
[Editor's note: See additional discussion and files.]
Figure 2: Braking performance of the bike with initial velocity vo = 60 km/hr and tire-road coefficient of friction μ = 0.8 for full-brake, front-brake and rear-brake cases (note: efficiency (η = a/μg).
Figure 3: Braking performance of various initial velocities for full-brake, front-brake and rear-brake cases.
Figure 4: Braking performance of various tire-road coefficients of friction for full-brake, front-brake and rear-brake cases.
### References:
Junghsen Lieh, PhD
is Professor for Mechanical & Materials Engineering
at Wright State University, Dayton Ohio 45435 USA
He is the adviser for the university's ASME HPV student group and has been involved with electric and solar racing. His research interests include hybrid electric unmanned aerial vehicles (UAV), intelligent control systems, multibody nonlinear dynamics, vehicle engineering, biomechanics, finite element analysis, and metal forming. He is currently working on the prototype and commercialization of push-pull wheelchairs, human-powered lawnmowers, and all-limb assisted electric bike based on a ratchet transmission.
Contact:
(937) 775-5040 (ph); (937) 775-5009 (fax)
junghsen.lieh AT wright.edu
Homepage:
http://www.cs.wright.edu/node/224
Human Power eJournal
|
2017-05-23 07:06:38
|
{"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": 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": 0.6117706298828125, "perplexity": 2337.4538784926126}, "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-2017-22/segments/1495463607591.53/warc/CC-MAIN-20170523064440-20170523084440-00543.warc.gz"}
|
https://www.gamedev.net/forums/topic/270486-making-a-title-page/
|
Public Group
# making a title page
This topic is 5205 days old which is more than the 365 day threshold we allow for new replies. Please post a new topic.
## Recommended Posts
ok i finaly got my first windows game (pong) up and running and im really excited (hey we all had to start some were) and now im trying to make it so that you cna choose your back ground and so i need it to text out which background do you want 1,2 or 3 but i cant seem to get it too work and the game wont pause right. basicly i want an intruductory page (kinda like the title page to a book almost every game has one anyway if any one knows a good way to do this let me know THX :)
##### Share on other sites
Are you using the GDI for graphics, DirectDraw, or Direct3D?
If you're using DirectDraw, before you blt() or bltfast() the secondary surface to the primary surface, you need to use lpDDSSecondary->GetDC(hWnd, &hDC); (might not be the correct arguments - it's been a while) and then after using TextOut(), etc use lpDDSSecondary->ReleaseDC(&hDC);
##### Share on other sites
In WM_PAINT do a switch on game state
case WM_PAINT: switch(uGameState) { case GAMESTATE_MENU: // Draw Menu break; case GAMESTATE_GAME: // Render game break } break;
##### Share on other sites
ok cool thx umm one more question is there some kind of other library i have to include (i have all the main ones) in order to play .wav sounds
#include <windows.h>
#include "Resource.h"
#include "GameEngine.h"
#include "Bitmap.h"
#include <windows.h> // include all the windows headers
#include <windowsx.h> // include useful macros
#include <stdio.h>
#include <math.h>
#include <string.h>
#include <WINGDI.h>
yes, winmm.lib
1. 1
2. 2
3. 3
Rutin
15
4. 4
5. 5
• 13
• 26
• 10
• 11
• 9
• ### Forum Statistics
• Total Topics
633726
• Total Posts
3013571
×
|
2018-12-15 16:21:51
|
{"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": 0.18695715069770813, "perplexity": 6161.053607443661}, "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-2018-51/segments/1544376826892.78/warc/CC-MAIN-20181215152912-20181215174912-00362.warc.gz"}
|
https://artofproblemsolving.com/wiki/index.php?title=2013_AMC_12A_Problems/Problem_19&diff=prev&oldid=157198
|
# Difference between revisions of "2013 AMC 12A Problems/Problem 19"
## Problem
In $\bigtriangleup ABC$, $AB = 86$, and $AC = 97$. A circle with center $A$ and radius $AB$ intersects $\overline{BC}$ at points $B$ and $X$. Moreover $\overline{BX}$ and $\overline{CX}$ have integer lengths. What is $BC$?
$\textbf{(A)} \ 11 \qquad \textbf{(B)} \ 28 \qquad \textbf{(C)} \ 33 \qquad \textbf{(D)} \ 61 \qquad \textbf{(E)} \ 72$
## Solution
### Solution 1 (Diophantine PoP)
$[asy] //Made by samrocksnature size(8cm); pair A,B,C,D,E,X; A=(0,0); B=(-53.4,-67.4); C=(0,-97); D=(0,-86); E=(0,86); X=(-29,-81); draw(circle(A,86)); draw(E--C--B--A--X); label("A",A,NE); label("B",B,SW); label("C",C,S); label("D",D,NE); label("E",E,NE); label("X",X,dir(250)); dot(A^^B^^C^^D^^E^^X); [/asy]$
Let circle $A$ intersect $AC$ at $D$ and $E$ as shown. We apply Power of a Point on point $C$ with respect to circle $A.$ This yields the diophantine equation
$$CX \cdot CB = CD \cdot C$$ $$CX(CX+XB) = (97-86)(97+86)$$ $$CX(CX+XB) = 3 \cdot 11 \cdot 61.$$
Since lengths cannot be negative, we must have $CX+XB \ge CX.$ This generates the four solution pairs for $(CX,CX+XB)$: $$(1,2013) \qquad (3,671) \qquad (11,183) \qquad (33,61).$$
However, by the Triangle Inequality on $\triangle ACX,$ we see that $CX>13.$ This implies that we must have $CX+XB= \boxed{\textbf{(D) }61}.$
(Solution by unknown, latex/asy modified majorly by samrocksnature)
### Solution 2
Let $BX = q$, $CX = p$, and $AC$ meet the circle at $Y$ and $Z$, with $Y$ on $AC$. Then $AZ = AY = 86$. Using the Power of a Point, we get that $p(p+q) = 11(183) = 11 * 3 * 61$. We know that $p+q>p$, and that $p>13$ by the triangle inequality on $\triangle ACX$. Thus, we get that $BC = p+q = \boxed{\textbf{(D) }61}$
### Solution 3
Let $x$ represent $CX$, and let $y$ represent $BX$. Since the circle goes through $B$ and $X$, $AB = AX = 86$. Then by Stewart's Theorem,
$xy(x+y) + 86^2 (x+y) = 97^2 y + 86^2 x.$
$x^2 y + xy^2 + 86^2 x + 86^2 y = 97^2 y + 86^2 x$
$x^2 + xy + 86^2 = 97^2$
(Since $y$ cannot be equal to $0$, dividing both sides of the equation by $y$ is allowed.)
$x(x+y) = (97+86)(97-86)$
$x(x+y) = 2013$
The prime factors of $2013$ are $3$, $11$, and $61$. Obviously, $x < x+y$. In addition, by the Triangle Inequality, $BC < AB + AC$, so $x+y < 183$. Therefore, $x$ must equal $33$, and $x+y$ must equal $\boxed{\textbf{(D) }61}$
~dolphin7
~sugar_rush
|
2022-05-18 05:47:09
|
{"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": 67, "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": 0.7952735424041748, "perplexity": 152.52764383373125}, "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-2022-21/segments/1652662521152.22/warc/CC-MAIN-20220518052503-20220518082503-00426.warc.gz"}
|
http://axiom-wiki.newsynthesis.org/AxiomDeveloperFAQ?root=AxiomDevelopment
|
login home contents what's new discussion bug reports help links subscribe changes refresh edit
This is an edited version of the FAQ file found in the Axiom source code distributions.
## FAQ 0: How do I use Axiom?
Look at the online book. It is automatically built during the 'make'. However, you can also do:
make book
Either way, it will show up in:
(yourpath)/axiom/mnt/linux/doc/book.dvi
You need to have Xlib.h to build the graphics. If you are building on a RedHat? 8 system you need to install the following RPM:
rpm -i XFree86-devel-4.2.0-72.i386.rpm
On Debian GNU/Linux, the package 'xlibs-dev' is needed.
Richard Harke wrote:
On my ia64 debian-linux workstation, apt-get refuses to install xlibs-dev. I think I have gotten around this by installing libxt-dev.
Waldek Hebisch wrote:
Debian testing has Xlib.h in libx11-dev.
Alfredo Portes wrote:
In Ubuntu install: libxpm-dev, libx11-dev and libxt-dev.
The build of noweb creates 3 files in the mnt/linux/bin directory: notangle, noweave, and tex/axiom.sty. The build of the src/scripts directory copies the document command to the mnt/linux/bin directory. These four files are necessary to rebuild a Makefile.
These can be recreated in a clean system by typing:
make start
## FAQ 3: make hangs
A pamphlet file was modified and has a syntax error. The document command has its output redirected to a file called obj/linux/tmp/trace. Latex has found the syntax error and put up a prompt which stops the make. Look in this file for the error. You can also see the error by rerunning make thus:
make NOISE=
which will override the redirection and allow the latex output to go to the console.
If the make hangs during the test cases check to see if it occurs while trying to run graphics. If Axiom does not have permission from the X server to open a window then it will hang. Try 'xhost +'
## FAQ 4: noweb needs to be rebuilt
The first time noweb is built a dummy file called noweb is written into the top level directory. If this file is removed noweb will be rebuilt. The following sequence should work:
rm noweb
make noweb
## FAQ 5: lisp needs to be rebuilt
The first time lisp is built a dummy file called gcldir is written into the top level directory. If this file is removed lisp will be rebuilt. The following sequence should work:
rm lsp/gcldir
make
## FAQ 6: The interpreter is badly broken
If you look in src/interp/Makefile.pamphlet you'll see a stanza that is marked debugsys. You can add ${DEBUGSYS} to the "all" stanza, make the system and run debugsys. This is a copy of the interpsys image except that all of the files are interpreted. Note that you will have to edit src/interp/debugsys.lisp.pamphlet. Read the comments there. At this point you are able to do deep system internal debugging (which pretty much assumes you know how to navigate the underground caves in the dark without fear of dragons. If you can play the game at this level send axiom-developer at nongnu.org a note and we'll inscribe your name on a log and throw it on the fire. :-) The basic steps, which assumes that your axiom sources live under tmp/axiom 1. cd /tmp/axiom 2. modify the line in src/interp/Makefile.pamphlet that reads: all:${SAVESYS} ${DOCFILES} #${DEBUGSYS}
all: ${SAVESYS}${DOCFILES} ${DEBUGSYS} 3. set up the standard AXIOM shell variable: export AXIOM=/tmp/axiom/src/interp 4. set up the standard PATH variable: export PATH=$AXIOM/bin:$PATH 5. build the system, including debugsys.lisp: make 6. tell debugsys where to find the databases: export DAASE=$AXIOM
7. tell debugsys which platform you are on:
export SYS=linux
8. start a clean lisp image:
obj/linux/bin/lisp
(load "/tmp/axiom/int/interp/debugsys.lisp")
10. switch to the package the interpreter uses:
(in-package "BOOT")
11. start the system:
(restart)
and you now have a running Axiom that uses interpreted rather than compiled code. This makes finding errors easier.
## FAQ 7: The wrong version of GCL was used
If you are building a version of Axiom on GCL there are several tested versions. There is a shell variable called GCLVERSION that must be changed to choose the version.
## FAQ 8: Parallel make (i.e. make -j) fails
This is a complex issue. In theory, in order to build the algebra files we have a whole graph of constraints between the algebra files. In order to bootstrap the algebra the whole graph of algebra files need to be built in a particular order to ensure that the required files exist. This would argue for including the constraint as part of the makefile stanzas.
However, once the algebra is bootstrapped these constraints are checked at compile and runtime so it is possible to recompile an algebra file without compiling the files it depends upon.
If we decided to include the constraints on each stanza then we gain the benefit that "make -j" works. However, if we later change a single algebra file it may trigger a rebuild of the entire algebra library unnecessarily. Since bootstrap happens only once but algebra compiles happen often it was decided to elide the constraints. This will cause "make -j" to fail on initial build but vastly improve later builds.
## FAQ 9: GCL does not build on my system: libbfd.a and bfd.a are missing
We are using the option --enable-statsysbfd when building GCL (see lsp/Makefile) so libbfd.a and bfd.h files are necessary on your system.
On Debian GNU/Linux, the needed package is 'binutils-dev'.
## FAQ 10: The axiom.input file is ignored
The standard startup file, "axiom.input", has been renamed to ".axiom.input" to follow convention. This is an incompatible change. On unix-style systems a filename that begins with a period is not normally printed in a directory listing. This keeps the user's home directory from being cluttered up by initialization files.
## FAQ 11: How do I add a new pamphlet file
Pamphlet files are the only file format used by Axiom at the source level. There are several steps to adding a new file to ensure that Axiom will build it properly.
First, you have to decide where it should reside. Almost all files reside under the src subdirectory. Never put anything into lsp, int, obj, or mnt as these will be destroyed by "make clean".
Assume you add a file that extends the interpreter and will go into the src/interp subdirectory. You must modify the src/interp/Makefile.pamphlet to correctly build the file.
You must also modify src/doc/axiom.bib.pamphlet to include the file. Axiom uses bibtex to cross-reference the various pamphlet files. The normal method of citing a file involves just using the name, for example \cite{asq.c} will build a citation to the ./src/etc/asq.c.pamphlet file.
You must include the following two lines in your pamphlet file:
\bibliographystyle{plain}
\bibliography{axiom}
## FAQ 12: The axiom command fails.
This is likely one of two problems. Axiom uses clef as its command line editor. This has functionality similar to GNU Readline but was written independently. The axiom command uses:
clef -e $AXIOM/bin/AXIOMsys Clef attempts to create new terminals and this might fail. The first thing to check is the permission bits on /dev/pty. Next it is possible to run the axiom image, called AXIOMsys, directly. Just type AXIOMsys. It won't have command recall or command line editing but everything else is there. ## FAQ 13: How can I create and access Lisp functions from Axiom? SExpression? is the domain that handles raw lisp objects. It is possible to create SExpression? elements directly contruction: m:=[1::SEX, 2::SEX] [1,2] Type: List SExpression n:=m::SEX (1 2) Type: SExpression car(n) 1 Type: SExpression You can access lisp functions directly with: GENSYM()$Lisp
Lisp is the domain, known to the interpreter and compiler, that contains lisp functions and symbols.
Notice that Axiom is case-sensitive and that generally lisp symbols are upper case.
You can also create and call lisp functions. For instance:
)lisp (defun foo () (print "it works"))
Value = FOO
FOO()$Lisp "it works" it works Type: SExpression While accessing and writing functions in Lisp is possible it is generally not recommended as Axiom contains a programming language that should be able to achieve almost everything you need. ## FAQ 14: It still doesn't work Send email to axiom-developer at nongnu.org ## FAQ 15: How can I see what the interpreter is trying to do? )set message bottomup on will tell you the signatures that the interpreter is trying to use. Another method is to do: )lisp (setq |$monitorNewWorld| t)
and you can view database calls with:
)lisp (setq *miss* t)
## FAQ 16: How can I record console output?
)spool filename
starts sending output to the file called filename
)spool )off
stops sending output to the file
## FAQ 17: Graphics don't work or sman fails to start ?
First try running sman as
sman -debug -noclef -nonag -noht
Try this as root also.
If graphics still don't work or sman fails to start then look at the error messages . Does it show something like
ptyopen: Failed to grant access to slave device: No such file or directory
ptyopen: Failed to get name of slave device: No such file or directory
If so you may need to do a few things
1. Make sure that devpts support is enabled in you kernel ( CONFIG_DEVPTS_FS=y )
2. Make sure the directory /dev/pts exists
3. Mount devpts as in
mount -t devpts devpts /dev/pts
You may also want to add the following line to your /etc/fstab file:
devpts /dev/pts devpts gid=5,mode=602 0 0
This will ensure that next time you reboot devpts is automatically mounted.
## FAQ 18: How can the user use the batch mode?
1. create an input file:
echo '2+2' >tst.input
echo '3+3' >>tst.input
2. make sure the AXIOM variable is set:
export AXIOM=/path/axiom/mnt/linux
export PATH=$AXIOM/bin:$PATH
3. pipe a )read command to AXIOMsys and capture the output:
echo ')read tst.input' | AXIOMsys >tst.output
## FAQ 19: How can I get equations written on one line?
> Dear Axiom supporters,
> 2. I would also like to have the output of kind
>
> " - (s-1) * (s+1) * (p^4 +(2*e^3 + (24*s^2 - 4)*e)*p^3 * ...) * ...
> "
>
> For example, my DoCon program can read this format ...
>
> 2.1 It prints these polynomials like for (Z[e])[p]:
> " (e^2 + 2e)*p "
> How to print it like for Z[p,e]:
> " 2*p*e + e^2 "
You may wish to use the InputForm domain, where you can find some bizarre functions. In your case, "unparse" may help you, as follows:
(1) -> p:=(a+b+y)^2*y+1-(x+y+z)^4
(1)
4 3 2 2 2
- z + (- 4y - 4x)z + (- 6y - 12x y - 6x )z
+
3 2 2 3 4 3 2 2
(- 4y - 12x y - 12x y - 4x )z - y + (- 4x + 1)y + (- 6x + 2b + 2a)y
+
3 2 2 4
(- 4x + b + 2a b + a )y - x + 1
Type: Polynomial Integer
(2) -> pi:=p::InputForm
(2)
(+
(+
(+ (+ (* - 1 (** z 4)) (* (+ (* - 4 y) (* - 4 x)) (** z 3)))
(* (+ (+ (* - 6 (** y 2)) (* (* - 12 x) y)) (* - 6 (** x 2))) (** z 2)))
(*
(+
(+ (+ (* - 4 (** y 3)) (* (* - 12 x) (** y 2)))
(* (* - 12 (** x 2)) y))
(* - 4 (** x 3)))
z)
)
(+
(+
(+ (+ (* - 1 (** y 4)) (* (+ (* - 4 x) 1) (** y 3)))
(* (+ (* - 6 (** x 2)) (+ (* 2 b) (* 2 a))) (** y 2)))
(* (+ (* - 4 (** x 3)) (+ (+ (** b 2) (* (* 2 a) b)) (** a 2))) y))
(+ (* - 1 (** x 4)) 1))
)
Type: InputForm
(3) -> unparse(pi)
(3)
"(-z**4)+((-4*y)+(-4*x))*z**3+((-6*y*y)+(-12*x*y)+(-6*x*x))*z*z+((-4*y**3)+(-
12*x*y*y)+(-12*x*x*y)+(-4*x**3))*z+(-y**4)+((-4*x)+1)*y**3+((-6*x*x)+2*b+2*a)
*y*y+((-4*x**3)+b*b+2*a*b+a*a)*y+(-x**4)+1"
Type: String
Aternatively you can get the LaTex? output string:
(4) -> )lisp (|parseAndInterpret| "integrate(sin(x),x)::TexFormat::OutputForm")
(4) ["$$","-{\cos ","\left(","{x} ","\right)}","$$"]
Type: OutputForm
Value = ((|OutputForm|) WRAPPED BRACKET (AGGLST "\"$$\"" "\"-{\\cos \"" "\"\\left(\"" "\"{x} \"" "\"\\right)}\"" "\"$$\""))
or the text form:
(5) -> )lisp (|parseAndInterpret| "integrate(sin(x),x)::OutputForm")
(5) - cos(x)
Type: OutputForm
Value = ((|OutputForm|) WRAPPED "-" (|cos| |x|))
or the actual string output.
Axiom's algebra gets output to a stream called |$algebraOutputStream| Thus you can get the output you want by: )set message autoload off )lisp (progn ; we need a new output stream that is backed by a string (setq tmpout (make-string-output-stream)) ; we hold on to the regular algebra output stream (setq save |$algebraOutputStream|)
; we capture the algebra output into the string stream
(setq |$algebraOutputStream| tmpout) ; we generate output from string input (|parseAndInterpret| "(x+1)^9") ; we save the output into the result variable (setq result (get-output-stream-string |$algebraOutputStream|))
; we restore the regular algebra output stream
(setq |$algebraOutputStream| save) ; and we return the string as our value result) )lisp result result contains the output from axiom that you want. Alternatively you can see the internal representation using |pf2Sex| (parsed function to s-expression) by doing: if you start axiom and type: )trace (|pf2Sex|) and then type some expression: 1 you'll see the input and output of this function. This function (parsed function to s-expression) is internal to the axiom interpreter. it takes the parsed input line and converts it to a lisp s-expression. so the above '1' input yields: 1> (|pf2Sex| ((|Integer| (|posn (0 "1" 1 1 "strings") . 0)) . "1")) 1< (|pf2Sex| 1) the "1>" line tells you the function input. the "1<" line tells you the function output. notice that even a simple input line generates type information. this function is not part of the exposed user interface because there is nothing at the user level that needs this information. ## FAQ 20: Axiom hangs when graphics should be displayed. Be sure that your X server will allow you to display windows. try: 'xhost +' ## FAQ 21: How should I get my AXIOM shell variable and why? The AXIOM variable is used at 2 different times, during make and during execution. First, lets look at the make case: The build process needs to know 2 things. It needs to know where the axiom sources are. It needs to know what kind of system to build. Both of these pieces of information are in the AXIOM shell variable. Suppose you download axiom into /tmp/axiom and you want to build a linux system. The AXIOM shell variable would be set to:: export AXIOM=/tmp/axiom/mnt/linux ^^^^^^^^^^ where ^^^^^ what when the make starts it looks for where it will find the sources and gets /tmp/axiom. It next looks for what kind of system to build and gets linux. In the top level makefile we see: SPD=$(shell pwd)
which means that SPD will be the current working directory. It got set to:
SPD=/tmp/axiom
which is correct.
Next in the Makefile we see:
SYS=$(notdir$(AXIOM))
which got set to:
SYS=linux
so we can see from this information that the AXIOM shell variable was set to:
AXIOM=/tmp/axiom/mnt/linux
Second, the AXIOM variable is used at runtime to tell axiom where it lives. When you build an axiom system everything that is important and worth keeping lives under the mnt subdirectory. So to "install" an Axiom system into /usr/local/axiom, for example, you need only copy the mnt subdirectory thus:
mkdir /usr/local/axiom
cd /tmp/axiom
cp -pr mnt /usr/local/axiom
Now that we've done that we can remove the whole axiom directory from /tmp because it is no longer needed.
However, in order to run Axiom we need 2 pieces of information. First, we have to tell Axiom where it now lives and second, we have to put the commands on our path so they can be found. So, since we installed axiom into /usr/local/axiom we need:
export AXIOM=/usr/local/axiom/mnt/linux
export PATH=$AXIOM/bin:$PATH
The AXIOM shell variable tells axiom where to find itself. The PATH shell variable tells linux where to find executables.
## FAQ 22: How do I check out the latest sources?
export CVS_RSH=ssh
cvs -d:ext:anoncvs@savannah.nongnu.org:/cvsroot/axiom co axiom
## FAQ 23: How do I patch a file?
This is an example of changing floats.spad.pamphlet and incorporating a test case in the src/input directory:
1) Applied the negative float rounding/truncation patch from Savannah to the floats.spad.pamphlet file.
1. Created a simple input file called
negfloats.input.pamphlet
in the src/input directory that executes some Axiom commands illustrating the bugs
2. Modified the file src/input/Makefile.pamphlet to include the following new subsection and stanzas:
\subsection{negfloats}
<<negfloats>>=
${OUT}/negfloats.input:${MID}/negfloats.input
echo 426 making ${OUT}/negfloats.input from${MID}/negfloats.input
cp ${MID}/negfloats.input${OUT}/ngefloats.input
${MID}/negfloats.input:${IN}/negfloats.input.pamphlet
echo 427 making ${MID}/negfloats.input from${IN}/negfloats.input.pamphlet
(cd ${MID} ; \${TANGLE} ${IN}/negfloats.input.pamphlet >negfloats.input ) 3. Made a new entry for negfloats in: FILES=${OUT}/algaggr.input ${OUT}/algbrbf.input${OUT}/algfacob.input \
...
${OUT}/ndftip.input${OUT}/newlodo.input \
${OUT}/negfloats.input \ ... 4. Added a reference to <<negfloats>> in <<*>>= <<*>>= ... <<NDFtip>> <<negfloats>> ... 5. Did axiom 'make' to compile the revised floats domain and (hopefully) run the negfloats.input test file: ./configure (set AXIOM and PATH manually ... yuck :) make ## FAQ 24: What is the purpose of the domain HACKPI? HACKPI is a hack provided for the benefit of the axiom interpreter. As a mathematical type, it is the simple transcendental extension Q(pi) of the rational numbers. This type allows interactive users to use the name '%pi' without a type both where a numerical value is expected [ as in draw(sin x,x=-%pi..%pi) ]? or when the exact symbolic value is meant. The interpreter defaults a typeless %pi to HACKPI and then uses the various conversions to cast it further as required by the context. One could argue that it is unfair to single %pi out from other constants, but it occurs frequently enough in school examples (specially for graphs) so it was worth a special hack. In a non-interactive environment (library), HACKPI would not exist. ## FAQ 25: Can I create or edit hypertex pages? The hypertex is intended to be edited by users. We are looking to build special purpose pages around courses such as linear algebra. Assume HERE=$AXIOM/doc/hypertex/pages
The text can be found in $HERE/foo.ht or$HERE/foo.pht
The macros are tex-like and live in $HERE/util.ht To change a page you need to: cd$HERE
edit the page
rm *~ (to delete backup copies)
hypertex
htadd [-s|-l|-f db-directory] [-d|-n] filenames
but, i'm sorry to say, these have not been fully documented.
The htadd function will maintain the file called $HERE/ht.db which is a database of absolute byte indexes into files. Forgetting to run htadd will still work, sort-of, until you hit a bad byte index and then it will fail. Hypertex can also be directed elsewhere by using the HTPATH shell variable. ## FAQ 27: Why can't I input text into the hypertex browser boxes? Check your num-lock key. If num-lock is on then you can't input text into your browser text boxes. ## FAQ 28: Graphics does not work inside OldTeXmacs? > No, I am not able to get graphics to appear in an X-window > from inside OldTeXmacs. That's what I *want* to be able to do. > > I have OldTeXmacs 1.0.4.4 (latest being 1.0.4.5). I know the > plugin calls AXIOMsys, and I tried to make it call "axiom" > or "sman" with no immediate success. Ok great. You are obviously on the right track. If you compiled OldTeXmacs from source then to make tm_axiom call "axiom", the simplest thing to do is to modify the souce file tm_axiom.c by replacing "AXIOMsys" with "axiom" and then recompile it. It is a simple C program with no dependencies and can be compiled separately. Move the tm_axiom.exe file to the appropriate place in the OldTeXmacs installation directory. If you didn't compile OldTeXmacs from source you can get just the tm_axiom.c file from the CVS, modify it and compile as above. The Axiom graphics process has the ability to create a postscript format output file containing the graphic. This can be initiated from the user interface of the graphics window or also from an Axiom command. Check "Chapter 7 Graphics" of the Axiom book, specifically section "7.1.8 Operations for Two-Dimensional Graphics", 'write' operation. It works something like this: viewPort := draw(sin x, x=-%pi..%pi) write(viewPort, "output.ps","postscript") These commands can be included directly in the OldTeXmacs document. ## FAQ 29: Where can I get help online? Axiom Mailinglists and IRC Channel Several ways to contact the community are available. There is an irc channel where developers can find other developers. It is: server: irc.freenode.net channel:#axiom-developer The mailinglists are: "axiom-math":http://mail.nongnu.org/mailman/listinfo/axiom-math ("archive":http://mail.nongnu.org/archive/html/axiom-math) Discussion of math theory and philosophy related to Axiom "axiom-mail":http://mail.nongnu.org/mailman/listinfo/axiom-mail ("archive":http://mail.nongnu.org/archive/html/axiom-mail) General discussion on Axiom "axiom-developer":http://mail.nongnu.org/mailman/listinfo/axiom-developer ("archive":http://mail.nongnu.org/archive/html/axiom-developer) When you have issues to compile Axiom or with Axiom internals "axiom-legal":http://mail.nongnu.org/mailman/listinfo/axiom-legal ("archive":http://mail.nongnu.org/archive/html/axiom-legal) All legal issues, like license issues ## FAQ 30: How can I file a bug report? Send email with details of the bug report to bugs at axiom-developer.org The email should contain enough information so we can help you figure out what the problem could be. Since you are the only one who knows what the problem is it is necessary to give us enough information to work out the details. At the top of your Axiom session when you start Axiom there are two lines printed, the Version line and the Timestamp line. They look: Version: Axiom 3.0 Beta (February 2005) Timestamp: Thursday January 20, 2005 at 19:34:25 These two lines enable us to determine what version of the source code you are using. Without this information we can't tell if the bug has already been fixed or is new. We also need to know what kind of system you are using. This includes the kind of software and the kind of hardware. So we need to know if it is something like: RedHat Linux Version 9 on Intel PC Solaris 8 on Sun Ultrasparc Now that we know what version of code you are running and what kind of system you are running on we need to know what the exact problem is. It is best if you can send a copy of the failing output. If not, please send the EXACT error message so we can search the code for the error. ## FAQ 31: How can I find out if this is a known bug to view a page with all of the known bug reports. You can search thru all of the bug reports to see if your error has happened before and, if so, if it was fixed. Please try to do this before filing a bug report. It will save us all a lot of time. ## FAQ 32: How can I input an equation as a string? There is an embedded command server within AXIOMsys. Look at: "this":http://daly.axiom-developer.org/TimothyDaly_files/lisptalk/pages/lisp35.html In particular, see the function: parseAndInterpret stringBuf (which is boot language code. So in lisp I have to tack on the | | onto the function name and then I can call it like this: (1) -> )lisp (|parseAndInterpret| "integrate(sin x,x)") (1) - cos(x) Type: Union(Expression Integer,...) Value = ((|Union| (|Expression| (|Integer|)) (|List| (|Expression| (|Integer|))) ) WRAPPED 0 (1 #<vector 10ccde54> (1 0 . -1)) 0 . 1) (2) -> and sure enough! Axiom parses and interprets the string. The result appears as stdout and the value returned seems to contain the type information. The "WRAPPED" information is the lisp data structure: > The string output function mentioned in FAQ 19 is a linear > form of the output. However Axiom's native output machinery > is called CHARYBDIS which was a research project from the > 60s with the goal of printing mathematics on typewriters. > Axiom still uses that code. ## FAQ 33: How do I run hypertex standalone? export AXIOM=/whatever/mnt/linux export HTPATH=$AXIOM/doc/hypertex/pages
export PATH=$AXIOM/bin:$PATH
hypertex
## FAQ 34: How can I find out about a domain?
There is a standalone command called asq which will give information from Axiom's databases:
asq
asq Integer
asq -sh Integer
## FAQ 35: Why do .axiom.input defined functions fail in axiom?
You write this in your .axiom.input file:
mrd(x:Integer,v:Integer):Integer == x+y
You can't see this function even though it appears to be defined. That's because Axiom is working in a new frame.
When you start AXIOMsys you are running the interpreter talking directly to the terminal. So the .input file is actually talking to a frame at the top level. Your function is defined.
The .axiom.input file is read in a "frame" called "initial". AXIOMsys only uses the "initial" frame (although you can define and use new ones). A frame contains its own variables and function definitions.
The "axiom" command does several things that AXIOMsys does not. In particular the axiom shell script starts up the 'sman' process which starts AXIOMsys (which reads the .axiom.input file) and then sman creates a new frame (usually a random lisp gensym name). In this new frame (created after .axiom.input is read) your mrandom function is not defined.
To see this do:
AXIOMsys
mrandom(3,3,3) -- compiles and runs the function
)quit
Now do:
axiom
mrandom(3,3,3) -- undefined function
)frame next
mrandom(3,3,3) -- compiles and runs the function
)frame names -- shows you all of the defined frames
)quit
So with the axiom shell script the process is:
axiom
start sman (done by axiom shell script)
sman starts AXIOMsys (done by sman)
create frame "initial" (done by AXIOMsys)
create frame "G00234" (done by sman)
put up a command prompt (in frame G00234, no functions defined)
)frame next (done by you)
.... and now you're back in frame initial
.... and your function is there
So your function was read and it is defined. However the function got defined in the "initial" frame (because you defined it in the .axiom.input file) and is not known in the frame created by sman. The ")frame next" command will move you around the ring of frames. (See the hardcopy book on page 579).
## FAQ 36: Axiom won't build on FC3
You need to turn off dynamic library load point randomization. As root do:
echo 0 >/proc/sys/kernel/exec-shield
## FAQ 37: Axiom won't build on FC4 or FC5
You need to turn off dynamic library load point randomization. As root do:
echo 0 >/proc/sys/kernel/randomize_va_space
or do:
setarch i386 -R make axiom
If the above fails then it is possible that you may have to take more drastic measures. This will disable the SELinux?:
/usr/sbin/setenforce 0
although it may be possible to tweak the policy directly. Change /etc/selinux/strict/src/policy/domains/user.te:bool allow_execmem false; to /etc/selinux/strict/src/policy/domains/user.te:bool allow_execmem true;
then do:
cd /etc/selinux/strict/src/policy
## FAQ 38: How can I debug algebra code?
Axiom contains some powerful commands to help with testing and debugging library modules written in Spad and also the Axiom system itself. The most important of these commands is ')trace'.
This command is used to trace the execution of functions that make up the Axiom system, functions defined by users, and functions from the system library. Almost all options are available for each type of function but exceptions will be noted below.
To list all functions, constructors, domains and packages that are traced, simply issue:
)trace
To untrace everything that is traced, issue:
)trace )off
When a function is traced, the default system action is to display the arguments to the function and the return value when the function is exited. Other information can be displayed or collected when a function is traced and this is controlled by the various options. If a domain or package is traced, the default action is to trace all functions exported. Individual interpreter, lisp or boot functions can be traced by listing their names after ')trace'. Any options that are present must follow the functions to be traced. For example:
)trace f
traces the function f. To untrace f, issue:
)trace f )off
Note that if a function name contains a special character, it will be necessary to escape the character with an underscore:
)trace _/D_,1
To trace all domains or packages that are or will be created from a particular constructor, give the constructor name or abbreviation after ')trace':
)trace MATRIX
)trace List Integer
The first command traces all domains currently instantiated with Matrix. If additional domains are instantiated with this constructor (for example, if you have used 'Matrix(Integer)' and 'Matrix(Float)'), they will be automatically traced. The second command traces 'List(Integer)'.
The following are the general options for the ')trace' command.
')break after' -- causes a Common Lisp break loop to be entered after exiting the traced function.
')break before' -- causes a Common Lisp break loop to be entered before entering the traced function.
')break' -- is the same as )break before.
')count' -- causes the system to keep a count of the number of times the traced function is entered.
The total can be displayed with:
)trace )stats
and cleared with:
)trace )stats reset
')count n' -- causes information about the traced function to be displayed for the first n executions. After the n-th execution, the function is untraced.
')depth n' -- causes trace information to be shown for only n levels of recursion of the traced function.
The command:
)trace fib )depth 10
will cause the display of only 10 levels of trace information for the recursive execution of a user function fib.
')math' causes -- the function arguments and return value to be displayed in the Axiom monospace two-dimensional math format.
')nonquietly' -- causes the display of additional messages when a function is traced.
')nt' -- This suppresses all normal trace information. This option is useful if the ')count' or ')timer' options are used and you are interested in the statistics but not the function calling information.
')off' -- causes untracing of all or specific functions. Without an argument, all functions, constructors, domains and packages are untraced. Otherwise, the given functions and other objects are untraced.
To immediately retrace the untraced functions, issue:
)trace )restore
')only listOfDataToDisplay' -- causes only specific trace information to be shown.
')restore' -- causes the last untraced functions to be retraced. If additional options are present, they are added to those previously in effect.
')stats' -- causes the display of statistics collected by the use of the ')count' and ')timer' options.
')stats reset' -- resets to 0 the statistics collected by the use of the ')count' and ')timer' options.
')timer' -- causes the system to keep a count of execution times for the traced function. The total can be displayed with ')trace )stats' and cleared with ')trace )stats reset'.
')varbreak var1 ... varN' -- causes a Common Lisp break loop to be entered after the assignment to any of the listed variables in the traced function.
')vars' -- causes the display of the value of any variable after it is assigned in the traced function. Note that library code must have been compiled using the ')vartrace' option in order to support this option.
')vars var1 ... varN' -- causes the display of the value of any of the specified variables after they are assigned in the traced function. Note that library code must have been compiled using the ')vartrace' option in order to support this option.
')within executingFunction' -- causes the display of trace information only if the traced function is called when the given executingFunction is running.
The following are the options for tracing constructors, domains and packages.
')local op1 ... opN' -- causes local functions of the constructor to be traced. Note that to untrace an individual local function, you must use the fully qualified internal name, using the escape character before the semicolon. For example:
)trace FRAC )local
)trace FRAC_;cancelGcd )off
')ops op1 ... opN' -- By default, all operations from a domain or package are traced when the domain or package is traced. This option allows you to specify that only particular operations should be traced.
The command:
)trace Integer )ops min max _+ _-
traces four operations from the domain Integer. Since + and - are special characters, it is necessary to escape them with an underscore.
Also See: ')boot', ')lisp' , and ')ltrace'. Please refer to the Axiom Book section "Axiom System Commands" for more detailed information.
## FAQ 39: How can I access lisp code from the Axiom command line?
To run a lisp command from the command line use )lisp:
--> )lisp (+ 2 3)
If you want to run a lot of lisp commands from the command line do:
--> )lisp (setq $dalymode t) --> (+ 2 3) --> (defun foo (x y) (+ x y)) --> (foo 2 3) --> 2 + 3 $dalymode says:
If the first character is a '('
then it is lisp
else it is axiom
to disable it do:
--> (setq \$dalymode nil)
I wrote this change to the interpreter because I tend to use lisp a lot during maintenance. It breaks some syntax but you can work around that.
If you really want to "drop" into lisp do:
--> )fin
BOOT> (+ 2 3)
and now you are talking only to lisp at a lisp command prompt in the BOOT package. To restart Axiom type:
BOOT>(restart)
## FAQ 40: Text entry fails in the hypertex browser window
Check that "Num Lock" is disabled.
I appears that the Num Lock key prevents the text window from accepting text. This is a known problem with no current fix.
Subject: Be Bold !! ( 13 subscribers )
|
2017-10-21 05:01:16
|
{"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": 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": 0.5229373574256897, "perplexity": 6564.891167918974}, "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-2017-43/segments/1508187824570.79/warc/CC-MAIN-20171021043111-20171021063111-00122.warc.gz"}
|
https://cracku.in/ssc-questions/ssc-speed-distance-work
|
# SSC Speed Time Distance and Work Questions with Answers
#### Speed Time Distance and Work
An excellent collection of SSC Time, speed, distance, and work questions and answers with detailed explanations for competitive exams. Given below are some of the most repeated practice questions on Time, speed, distance, and work for SSC CGL, CHSL, JE, GD constable, Stenographer, MTS, and CPO exams. Go through this very important online quiz based on model and previous year asked questions from SSC Time, speed, distance, and work with solutions to ace the exam.
### Take a free SSC CHSL Mock
Thousands of students have taken Cracku's Free SSC CHSL Mock.
Instructions
For the following questions answer them individually
Question 1
When a pendulum of length 50 cm oscillates, it produces an arc of 16 cm. The angle so formed in degree measure is (approx)
Question 2
A sum of money becomes eight times in 3 years, if the rate is compounded annually. In how much time will the same amount at the same compound rate become sixteen times?
Question 3
A rail road curve is to be laid out on a circle. What radius should be used if the track is to change direction by 25$$^{\circ}$$ in a distance of 40 metres?
Question 4
Water flows into a tank which is 200m long and 150m wide, through a pipe of cross-section $$0.3m \times 0.2m$$ at 20 km/hour. Then the time (in minutes) for the water level in the tank to reach 8cm is
Question 5
If 5 men or 7 women can earn Rs. 5,250 per day, how much would 7 men and 13 women earn per day ?
Question 6
Buses start from a bus terminal with a speed of 20 km/hr at intervals of 10 minutes. What is the speed of a man coming from the opposite direction towards the bus terminal if he meets the buses at intervals of 8 minutes ?
Question 7
$$0.\overline{001}$$ is equal to
Question 8
The average of the first 100 positive integers is
Question 9
A and B can do a work in 12 days, B and C can do the same work in 15 days, C and A can do the same time work in 20 days. The time taken by A, B and C to do the same work is
Question 10
$$\frac{4.41 \times 0.16}{2.1 \times 1.6 \times 0.21}$$ is equal to
Question 11
50 men can complete a work in 28 days. They started the work together, but at the end of each $$10^{th}$$ day, 10 men left the job. The work was completed in how many days?
Question 12
A train leaves Delhi at 10 a.m. and reaches Jaipur at 4 p.m. on same day. Another train leaves Jaipur at 12 p.m. and reaches Delhi at 5 p.m. on same day. What is the time of day (approximately) when the two trains will meet?
Question 13
The distance between places U and V is 1008 km. An express train leaves place U at 9:00 a.m. and runs at a speed of 126 km/hr. The train stops on the way for 20 minutes. At what time (in p.m.) the train will reach at the place V?
Question 14
A piece of work was finished by A, B and C together. A and B together finished 60% of the work and B and C together finished 70% of the work. Who among the three is most efficient?
Question 15
A tank 40 m long, 30 m broad and 12 m deep is dug in a field 1000 m long and 30 m wide. By how much will the level of the field rise if the earth dug out of the tank is evenly spread over the field ?
Question 16
It 10 men or 20 women or 40 children can do a piece of work in 7 months, then 5 men, 5 women and 5 children together can do half of the work in how many months :
Question 17
If a and b are two odd positive integers, by which of the following integers is $$(a^4-b^4)$$ always divisible ?
Question 18
$$\frac{256 \times 256 - 144 \times 144}{112}$$ is equal to
Question 19
A drum of kerosene is $$\frac{3}{4}$$ full. When 30 litres of kerosene is drawn from it, it remains $$\frac{1}{2}$$ full. The capacity of the drum is
Question 20
By what least number should 675 be multiplied so as to obtain a perfect cube number ?
Question 21
$$\sqrt{\frac{0.009\times0.36\times0.016\times0.08}{0.002\times0.008\times0.0002}}$$ is equal to
Question 22
In a family, the average age of a father and a mother is 35 years. The average age of the father, mother and their only son is 27 years. What is the age of the son?
Question 23
By walking at 3/4 of his usual speed, a man reaches his office 20 minutes later than his usual time. The usual time taken by him to reach his office is
Question 24
A train, 300m long, passed a man, walking along the line in the same direction at the rate of 3 km/hr in 33 seconds. The speed of the train is
Question 25
When 231 is divided by 5 the remainder is
Question 26
Simplify: $$\frac{0.0347 \times 0.0347 \times 0.0347 + (0.9653)^3}{(0.0347)^2 - (0.347)(0.9653) + (0.9653)^2}$$
Question 27
The product of two numbers is 2028 and their H.C.F. is 13. The number of such pairs is
Question 28
The floor of a room is of size $$4m \times 3m$$ and its height is 3m. The walls and ceiling of the room require painting. The area to be painted is
Question 29
The average weight of a group of 20 boys was calculated to be 89.4 kg and it was later discovered that one weight was misread as 78kg instead of 87 kg. The correct average weight is
Question 30
The diameter of a wheel is 98 cm. The number of revolutions in which it will have to cover a distance of 1540 m is
Question 31
In an equilateral triangle ABC of side 10cm, the side BC is trisected at D. Then the length (in cm) of AD is
Question 32
A rectangular sheet of metal is 40 cm by 15 cm. Equal squares of side 4 cm are cut off at the corners and the remainder is folded up to form an open rectangular box. The volume of the box is
Question 33
Walking at 3/4th of his usual speed , aman is $$1\frac{1}{2}$$ hours late. his usual time to cover the same distance, in hours, is?
Question 34
A rectangle garden is 100 m $$\times$$ 80 m. There is a path along the garden and just outside it. Width of the path is 10m. The area of the path is
Question 35
A ship is moving at a speed of 30 km/hr. To know the depth of the ocean beneath it, it sends a radio wave which travels at a speed 200 m/s. The ship receives the signal after it has moved 500 m. The depth of the ocean is
Question 36
If the distance between two point (0, -5) and (x, 0) is 13 unit, then x =
Question 37
PQ is a direct common tangent of two circle of radii $$r_{1}$$ and $$r_{2}$$ touching each other externally at A. Then the value of PQ2 is
Question 38
A can paint a house in 42 days and B can do it in 21 days. Along with C, they can finish the job in 7 days only.C alone can do the painting job in how many days, ?
Question 39
A cistern normally takes 10 hours to be filled by a tap. But because of a leak, it takes 2 hours more. In how many hours will the leak empty a full cistern ?
Question 40
A train crosses a platform in 30 seconds travelling with a speed of 60 km/h. If the length of the train be 200 metres, then the length (in metres) of the platform is
Question 41
A train runs for 2 hrs at the speed of 40 km/h and then runs for 4.5 hrs at the speed of 60 km/h and then runs for 3.5 hrs at the speed of 70 km per hour. Find the average speed of the train.
Question 42
4 men and 6 women complete a work in 8 days. 2 men and 9 women also complete in 8 days. The number of days in which 18 women complete the work is :
Question 43
A’s 2 days’ work is equal to B’s 3 days’ work. If A can complete the work in 8 days then to complete the work B will take
Question 44
If 4 men or 8 women can do a piece of work in 15 days, in how many days can 6 men and 12 women do the same piece of work ?
Question 45
A can do a piece of work in 6 days, B in 10 days and C in 15 days. They jointly complete the work and earn 300. The sum of their wages for 2 days is
Question 46
You arrive at your school 5 minutes late if you walk with a speed of 4 km/h, but you arrive 10 minutes before the scheduled time if you walk with a speed of 5 km/h. The distance of your school from your house (in km) is
Question 47
A can complete a piece of work in 18 days, B in 20 days and C in 30 days. B and C together start the work and are forced to leave after 2 days. The time taken by A alone to complete the remaining work is
Question 48
A and B together can do a works in 12 days. B and C together do it in 15 days. If A's efficiency is twice that of C, then the days required for B alone to finish the work is
Question 49
If A and B together can complete a piece of work in 15 days and B alone in 20 days, in how many days can A alone complete the work ?
Question 50
Two men A and B started a job in which A was thrice as good as B and therefore took 60 days less than B to finish the job. How many days will they take to finish the job, if they take to finish the job, if they start working together?
Question 51
With average speed of 40 km/hour, a train reaches its destination in time. If it goes with an average speed of 35 km hour, it is late by 15 minutes. The total journey is
Question 52
If $$a^2+\frac{1}{a^2}$$ = 98(a > 0) then the value of $$a^3 + \frac{1}{a^3}$$ will be
Question 53
The area of the triangle formed by the line 5x + 7y = 35, 4x + 3y = 12 and x-axis is
|
2020-06-03 05:15:53
|
{"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": 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": 0.49312978982925415, "perplexity": 548.334334630528}, "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-2020-24/segments/1590347432237.67/warc/CC-MAIN-20200603050448-20200603080448-00006.warc.gz"}
|
https://swmath.org/?term=heterogeneity%20of%20variances
|
• # PMCMRplus
• Referenced in 2 articles [sw28101]
• normally distributed residuals and equal within variance are available. Furthermore, all-pairs tests (Games-Howell ... Test) for normally distributed residuals and heterogeneous variances are provided. Van der Waerden’s normal...
• # SUBSET
• Referenced in 1 article [sw26382]
• criterion. For means, both homogeneous and heterogeneous variance cases are considered. SUBSET offers an alternative ... error control, sample size and heterogeneity of variance do not arise...
• # mixOmics
• Referenced in 29 articles [sw09508]
• sparse PLS to unravel relationships between two heterogeneous data sets of size ... Principal Component Analysis and multilevel analysis using variance decomposition of the data...
• # streg
• Referenced in 6 articles [sw37360]
• analog to regression models, which account for heterogeneity and random effects. A frailty ... assumed to have unit mean and variance θ, which is estimated along with the other ... model parameters. A frailty model is an heterogeneity model where the frailties are assumed...
• # HSMUCE
• Referenced in 13 articles [sw27013]
• change points of the signal in a heterogeneous Gaussian regression model. A piecewise constant function ... which locally adapts to changes in the variance. The multiscale test is a combination ... uniform over a large class of heterogeneous change point models. H‐SMUCE is fast...
• # Rcapture
• Referenced in 11 articles [sw13992]
• derived from the loglinear parameter estimates; their variances are obtained by linearization. The novel feature ... several new options for modeling capture probabilities heterogeneity between animals in both closed population models...
• # SCAFFOLD
• Referenced in 4 articles [sw34100]
• from client-drift’ when the data is heterogeneous (non-iid), resulting in unstable and slow ... algorithm (SCAFFOLD) which uses control variates (variance reduction) to correct for the client-drift ... rounds and is not affected by data heterogeneity or client sampling. Further, we show that...
• # HMMTree
• Referenced in 8 articles [sw08991]
• provide a framework for modeling parameter heterogeneity. In this article, the computer program HMMTree ... Fisher information, expected category means and variances, and posterior probabilities for class membership. A brief...
• # CensMixReg
• Referenced in 12 articles [sw21090]
• modeling and analysis of data from a heterogeneous population. Moreover, data of this kind ... rely on formulas for the mean and variance of the multivariate truncated Student-$t$ distributions...
• # OGLM
• Referenced in 3 articles [sw14973]
• ordinal regression model incorrectly assumes that error variances are the same for all cases ... biased. With oglm you can estimate heterogeneous choice/ location-scale models that explicitly specify...
• # BANOVA
• Referenced in 2 articles [sw16130]
• BANOVA. It covers several Bayesian Analysis of Variance (BANOVA) models used in analysis of experimental ... multinomial response variables. All models accommodate unobserved heterogeneity by including a normal distribution...
• # LMMPaper
• Referenced in 1 article [sw40799]
• linear mixed models. The analysis of longitudinal, heterogeneous or unbalanced clustered data is of primary ... estimates with both lower bias and lower variance than the existing methods...
|
2022-08-13 20:53:09
|
{"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": 0.2504980266094208, "perplexity": 4253.486361600123}, "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-2022-33/segments/1659882571987.60/warc/CC-MAIN-20220813202507-20220813232507-00698.warc.gz"}
|
https://www.greenemath.com/Algebra2/20/LinearInequalitiesintwoVariablesLesson.html
|
Lesson Objectives
• Demonstrate an understanding of how to graph a linear equation in two variables
• Learn how to graph the boundary line for a linear inequality in two variables
• Learn how to use the "test point" method for graphing a linear inequality in two variables
• Learn how to find the solution region based on the inequality symbol
• Learn how to graph the "union" of two linear inequalities
• Learn how to graph the "intersection" of two linear inequalities
## How to Graph a Linear Inequality in Two Variables
Now that we have completely mastered graphing linear equations in two variables, we move into graphing a linear inequality in two variables. A linear inequality in two variables is of the form:
ax + by < c
where a, b, and c are any real numbers, a and b are not both zero, and the symbol "<" can be ">", "≤", or "≥". When we deal with the solution set for an inequality, we are normally dealing with a range of values. This means any point (x,y) that makes the inequality true is part of our solution set. When we graph a linear inequality in two variables, we will see three distinct parts:
• The Solution Region
• This region contains all ordered pairs (x,y) that satisfy the inequality
• The Non-Solution Region
• This region contains all ordered pairs (x,y) that do not satisfy the inequality
• The Boundary Line
• The boundary line separates the solution region from the non-solution region
• The boundary line is drawn as a dashed line for a strict inequality: "<" or ">"
• The boundary line is drawn as a solid line for a non-strict inequality: "≤" or "≥"
There are two methods we can use to graph a linear inequality in two variables. The first and more tedious method involves the use of a test point.
### Graphing a Linear Inequality in Two Variables using the Test Point Method
• Graph the boundary line
• We graph the boundary line by replacing our inequality symbol with an equality symbol. We then graph the equation. This line is drawn as a dashed line for a strict inequality and a solid line for a non-strict inequality.
• Choose a test point (x,y)
• Pick any point on the coordinate plane that is not on the boundary line. From this, we can plug into our original inequality. If the test point works as a solution, we shade the side of the boundary line which contains the test point. If the test point does not work as a solution, we shade the opposite side of the boundary line (the side of the boundary line which does not contain the test point).
Before we jump into an example, let's make a few things clear. On the coordinate plane, we can only be in one of three places: the solution region, the non-solution region, or on the boundary line. Based on the inequality symbol, we know if the boundary line is part of the solution set. When we have a strict inequality "<" or ">", the boundary line is not part of the solution set. To show this, we draw our boundary line as a dashed line. Points on the line will not satisfy the inequality. On the other hand, when we have a non-strict inequality "≤" or "≥", points on the boundary line are part of the solution set. To show this, we draw the boundary line as a solid line. Points on the boundary line will satisfy the inequality. Additionally, we know that if we are not on the boundary line we will be in the solution region or the non-solution region. If we pick any point that is not on the boundary line, plug into the inequality and get a true statement, our point lies in the solution region. Otherwise, we are in the non-solution region. Let's look at an example.
Example 1: Graph each
7x - 2y < -4
Step 1) Let's graph our boundary line
To graph our boundary line, we replace our inequality symbol "<" with the equality symbol "=".
7x - 2y = -4
Since we have a strict inequality, the boundary line will be a dashed line. Step 2) Pick a test point
Since (0,0) is easy to work with, we will choose this as our test point.
7(0) - 2(0) < -4
0 < -4 (false)
Since our test point did not satisfy the inequality, it must lie in the non-solution region. Therefore, we will shade the opposite side of the boundary line or the region of the coordinate plane that does not contain the point (0,0). A quicker method involves solving the inequality for y and then shading based on the inequality symbol. With this method, we will shade above the line for a greater than or greater than or equal to and below the line for a less than or a less than or equal to. Note, this only works when the inequality is solved for y. If we look at our example above: $$7x - 2y < -4$$ $$-2y < -7x - 4$$ $$y > \frac{7}{2}x + 2$$ Since we have solved for y, we can observe the greater than symbol. This means we want to shade above the line, which is what we found using the test point method. Let's look at another example.
Example 2: Graph each
5x - y ≤ 5
Let's use the quicker method. We will solve for y first:
y ≥ 5x - 5
We want to graph a solid boundary line of: y = 5x - 5, and then shade above the line:
### Graphing the Union of Two Linear Inequalities in Two Variables
We previously learned that we solve a compound inequality with "or" by finding the union of the two solution sets. Let's look at an example.
Example 3: Graph each compound inequality
2x - 5y ≤ 5
or
3x - 2y < -4
Let's begin by graphing the first inequality.
2x - 5y ≤ 5 Now we can graph our second inequality.
3x - 2y < -4 The solution for a compound inequality with "or" is found as the union of the two solution sets. This means our solution will include any region of the coordinate plane that satisfies either inequality. From our graph above, we can see three different shaded areas. The part that is shaded yellow satisfies only 3x - 2y < -4, the part shaded in pink satisfies only 2x - 5y ≤ 5. Lastly, the part that is shaded in orange satisfies both inequalities. Since our inequality uses the word "or", all of these shaded areas are included in the solution set.
### Graphing the Intersection of Two Linear Inequalities in Two Variables
We also learned how to solve a compound inequality with "and". When we solve a compound inequality with "and", we want to find the intersection of the two solution sets. This means we want to find the region of the coordinate plane that satisfies both inequalities. Let's look at an example.
Example 4: Graph each compound inequality
4x - y ≤ 0
and
x - 5y > -20
Let's begin by graphing the first inequality.
4x - y ≤ 0 Now we can graph our second inequality.
x - 5y > -20 The solution for a compound inequality with "and" is found as the intersection of the two solution sets. This means our solution will include any region of the coordinate plane that satisfies both inequalities.
|
2020-01-24 10:56:36
|
{"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": 0.6895318627357483, "perplexity": 362.82499673770604}, "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-2020-05/segments/1579250619323.41/warc/CC-MAIN-20200124100832-20200124125832-00328.warc.gz"}
|
http://mathoverflow.net/feeds/question/108997
|
The cycle structure of twisted wires, connected - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-19T03:36:50Z http://mathoverflow.net/feeds/question/108997 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/108997/the-cycle-structure-of-twisted-wires-connected The cycle structure of twisted wires, connected Joseph O'Rourke 2012-10-06T13:56:13Z 2012-10-09T20:41:54Z <p>Suppose you have $n$ (blue) wires linearly arrayed at junction box $A$, connected to a remote junction box $B$, where the wires are now arrayed along a line in a randomly permuted order, i.e., each of the $n!$ permutations is equally likely at $B$. Now you tie together every other wire at $A$ and at $B$ with a (green) connector, like this: <br /> <img src="http://cs.smith.edu/~orourke/MathOverflow/WiresCycle.jpg" alt="Crossing Wires" /> <br /> What is the probability that you have formed a single cycle (as illustrated)? More generally, what are the combinatorics of the cycle structures achievable in this manner? (It may be best to separate out the $n$-even case from $n$ odd.)</p> <p>I came upon this thinking of the wires as an arrangement of lines, where each line crosses every other before reaching junction box $B$, in which case, for $n$ even, one necessarily arrives at $n/2$ cycles, each containing two (blue) wires. All $n$ wires in a single cycle is in some sense the obverse situation.</p> <p><b>Update</b>. Will Swain's argument shows, as Noam points out, that the probability of a single cycle is asymptotically $\frac{1}{\sqrt{n}}$. I would be interested to learn if there is a way to see this intuitively without Will's explicit calculation. Perhaps an assessment of the probability of repeatedly avoiding premature closing of a loop as one criss-crosses from $A$ to $B$...?</p> http://mathoverflow.net/questions/108997/the-cycle-structure-of-twisted-wires-connected/109002#109002 Answer by Will Sawin for The cycle structure of twisted wires, connected Will Sawin 2012-10-06T14:21:08Z 2012-10-07T05:04:39Z <p>Untangle the permutation as a big cycle green-blue-green-blue, and choose an orientation. We're going to count the posible shapes for this cycle, with the vertices labeled by their original position. We first have an alternating cyclic permutation of all the green wires. There are $(n/2)!\cdot (n/2)!/(n/2)$ ways to do this. Then we can choose an orientation of each of the green wires. There are $2^n$ ways to do this. Finally we note that two big cycles with reversed orientation correspond to the same permutation, so we divide by $2$. The total number of ways to get one big cycle is:</p> <p>$\frac{2^n \left(\frac{n}{2}\right)!\left(\frac{n}{2}\right)!}{n}$</p> <p>and the probability is:</p> <p>$\frac{2^n \left(\frac{n}{2}\right)!\left(\frac{n}{2}\right)!}{n\cdot n!}$</p> <p>which as Noam Elkies points out is asymptotically proportional to $n^{-1/2}$.</p> http://mathoverflow.net/questions/108997/the-cycle-structure-of-twisted-wires-connected/109252#109252 Answer by Kevin P. Costello for The cycle structure of twisted wires, connected Kevin P. Costello 2012-10-09T20:27:50Z 2012-10-09T20:41:54Z <p>Here's an alternative way of thinking about the problem and Will's answer in the case where $n$ is even. </p> <p>If we identify the identically labelled vertices on each side, we're left with a graph on $n$ vertices formed by the union of two matchings: The fixed matching ($(1,2), (3,4), \dots, (n-1,n)$) and a random matching. Now imagine exposing the random matching one edge at a time. </p> <p>At the start (before the new matching is exposed), we have a set of $n/2$ isolated edges. There's a $\frac{1}{n-1}$ chance that the first exposed edge in the second matching is already in the first matching, leaving us with a closed loop together with $n-1$ isolated edges. Otherwise, we have a single path of length $2$ together with $n-2$ isolated edges. </p> <p>When the next edge is exposed, its endpoints are chosen uniformly at random from the degree $1$ vertices. It closes a cycle if the two endpoints are from the same path. The key thing here is that there's always $\frac{n}{2}-1$ open paths that can be closed, regardless of what happened in the previous edge. This is true in general: Whether an edge closes an existing path off or connects two paths, it always reduces the number of open paths by exactly $1$. So as the $k^{th}$ edge in the new matching is exposed, there's $\frac{n}{2}+1-k$ open paths and a $\frac{1}{n-2k+1}$ chance of closing one of them. </p> <p>It follows that the number of cycles can be thought of as $x_1+\dots+x_{n/2}$, where the $x_i$ are independently $1$ with probability $\frac{1}{2i-1}$ and $0$ otherwise. This means that</p> <p>-The probability that there's exactly one cycle (that $x_2=x_3=\dots=0$) is $$\frac{2}{3} \frac{4}{5} \dots \frac{n-2}{n-1} = \frac{2^n \left(\frac{n}{2}!\right)^2}{n\cdot n!}$$</p> <p>-The expected number of cycles is $\frac{1}{1}+\frac{1}{3}+\dots+\frac{1}{n-1} \approx \frac{1}{2} \log n$</p> <p>-The number of cycles is reasonably concentrated around its mean (e.g. by Chernoff's bound we have $$P(|X-E(X)| \geq \frac{1}{2} E(X) ) \leq 2 e^{-E(X)/16} = 2n^{-1/32})$$</p>
|
2013-05-19 03:36:49
|
{"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": 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": 0.8655447959899902, "perplexity": 453.1516695150928}, "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-2013-20/segments/1368696383218/warc/CC-MAIN-20130516092623-00008-ip-10-60-113-184.ec2.internal.warc.gz"}
|
https://stats.stackexchange.com/questions/408119/which-method-is-correct-for-calculating-total-deviance-explained-for-boosted-reg?noredirect=1
|
# Which method is correct for calculating total deviance explained for boosted regression trees?
I have the following output from a boosted regression trees model and I would like to calculate the total deviance explained.
mean total deviance = 1.283
mean residual deviance = 0.107
estimated cv deviance = 0.212 ; se = 0.045
training data correlation = 0.97
cv correlation = 0.937 ; se = 0.016
training data AUC score = 1
cv AUC score = 0.996 ; se = 0.002
I have come across two methods to do this which give me a different answer.
1) D2 = 1 – (residual deviance/total deviance) (Nieto and Mélin, 2017)
With my results this equation is
D2 = 1 - (0.107/1.283) = 0.92
2) D2 = (total deviance - cross validated residual deviance)/total deviance (Leathwick et al., 2006)
With my results this equation is
D2 = (1.283-0.212)/1.283 = 0.83
The paper for method 2 does not provide the equation in their text but it is clear given their model results (Table 3, pp.272) that this is how it was calculated. Also, there is a question here that discusses this method.
Which of these methods is correct?
• Just to be clear, in the second equation, what is denoted as residual deviance is what, in the first question, is denoted as total deviance. Can you please clarify that these are meant to be the same (i.e. the total deviance)? – usεr11852 May 17 '19 at 9:20
• My apologies for the mistake. I have now edited my question. – Jo Harris May 18 '19 at 10:12
• Thank you for amending that. Good on you to catch that up! (+1) Please see my answer below for more details. – usεr11852 May 22 '19 at 0:48
To comment on this a bit further: On the one hand, the Nieto & Mélin's approach aims to directly generalise the concept of coefficient of determination $$R^2$$, using the deviance residuals instead of the actual ones. It does not resample the data or anything similar, it directly reports the choose metric (here $$D^2$$) overall the whole data. This can potentially lead to unreasonably optimistic results regarding the generalisation of our model's performance. On the other hand, the Leathwick et al. approach aims to incorporate the sampling variability directly through the repeated cross-validation step. We estimate values of our performance metric using "unseen" data that were excluded during training. Note that the "optimistic bias" can be immediately seen in the Table 3 of the L. et al. paper, if we use the model residual deviance instead of the CV residual deviance. In that case for example the CV-generated $$D^2$$ would move from $$0.600$$ to $$0.663$$ for the case of a Boosted Regression Tree with tree size 5. The sample size of your particular application is not explicitly stated. Nevertheless given it is not gigantic, reading through the methodology presented in Beleites et al. (2013) Sample size planning for classification models is a good starting point to get idea of how to assess sample size consideration in a (multiple) CV procedure.
|
2020-10-25 19:40:37
|
{"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": 5, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5932009816169739, "perplexity": 1172.9768647094147}, "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/1603107889651.52/warc/CC-MAIN-20201025183844-20201025213844-00315.warc.gz"}
|
https://latex.org/forum/viewtopic.php?t=31711&p=106474
|
LaTeX forum ⇒ General ⇒ Can't use \ref or \cref for equations Topic is solved
LaTeX specific issues not fitting into one of the other forums of this category.
abbyapril
Posts: 2
Joined: Wed Jul 25, 2018 7:00 pm
Can't use \ref or \cref for equations
I can't get \ref or \cref to work in my document for referencing equations. There are lots of equations, so I'd like to be able to reference them in such a way that the numbers are automatically fixed when I add a new equation. \ref worked for the figures in my document, but not equations. When it complies, it gives me a warning that says the reference is undefined. I'm not messing up any spelling or brackets. Please help!
Tags:
Stefan Kottwitz
Posts: 8979
Joined: Mon Mar 10, 2008 9:44 pm
Hi,
welcome to the forum!
\ref works by default, so perhaps there's a problem in your code. Can you post code how you are doing it?
Stefan
|
2018-08-20 00:53:27
|
{"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": 0.9745004773139954, "perplexity": 2045.9086120598877}, "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-2018-34/segments/1534221215487.79/warc/CC-MAIN-20180820003554-20180820023554-00317.warc.gz"}
|
https://ask.sagemath.org/answers/33539/revisions/
|
# Revision history [back]
There is no parallel computation of Groebner basis in Sage. However, .elimination_ideal([]) uses a algorithm provided by SIngular by default which is not the fastest available. You can specify which algorithm in the .groebner_basis() method.
A good candidate is the following:
Install giacpy from your terminal:
sage -i giacpy
Then, you can get the Groebner Basis from within Sage as follows:
sage: G = I.groebner_basis(algorithm='giac:gbasis')
You can get all possible algorithms by doing
sage: G = I.groebner_basis?
Please tell us if it was faster.
There is no parallel computation of Groebner basis in Sage. However, .elimination_ideal([]) uses a algorithm provided by SIngular by default which is not the fastest available. available, and you can not change it in this method. You can specify which algorithm in the .groebner_basis() method.
A good candidate is the following:
Install giacpy from your terminal:
sage -i giacpy
Then, you can get the Groebner Basis from within Sage as follows:
sage: G = I.groebner_basis(algorithm='giac:gbasis')
You can get all possible algorithms by doing
sage: G = I.groebner_basis?
Please tell us if it was faster.
|
2021-05-13 13:53:46
|
{"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": 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": 0.6019331812858582, "perplexity": 2466.2409669080253}, "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-2021-21/segments/1620243989916.34/warc/CC-MAIN-20210513111525-20210513141525-00485.warc.gz"}
|
https://homework.cpm.org/category/CC/textbook/cca2/chapter/8/lesson/8.3.2/problem/8-148
|
### Home > CCA2 > Chapter 8 > Lesson 8.3.2 > Problem8-148
8-148.
1. Given the polynomial p(x) = x3 − 6x2 + 7x + 2. Homework Help ✎
1. What is p(2)?
2. Use the Remainder Theorem to find one factor of x3 − 6x2 + 7x + 2. (See the Math Notes box in Lesson 8.3.2 above.)
3. Use (b) to find another factor.
4. What are all the solutions of x3 − 6x2 + 7x + 2 = 0?
Substitute 2 into the equation for every x.
Since p(2) = 0, x = 2 is the zero of the function. What is the corresponding factor?
(x − 2)
Try using a generic rectangle.
(x2 − 4x − 1)
See part (a) for one solution.
$x = 2, 2 \pm \sqrt{5}$
Use the Quadratic Formula to find the solutions to 0 = x2 − 4x − 1.
$x=\frac{4 \pm \sqrt{16 + 4}}{2}$
|
2019-10-24 04:59:32
|
{"extraction_info": {"found_math": true, "script_math_tex": 2, "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": 0.7161918878555298, "perplexity": 1244.0607555710617}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "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-2019-43/segments/1570987841291.79/warc/CC-MAIN-20191024040131-20191024063631-00254.warc.gz"}
|
https://www.baryonbib.org/bib/086147f0-7243-42dd-9dea-f9390e91bfdd
|
PREPRINT
086147F0-7243-42DD-9DEA-F9390E91BFDD
# Low star-formation activity and low gas content of quiescent galaxies at $z=$ 3.5-4.0 constrained with ALMA
Tomoko L. Suzuki, Karl Glazebrook, Corentin Schreiber, Tadayuki Kodama, Glenn G. Kacprzak, Roger Leiton, Themiya Nanayakkara, Pascal A. Oesch, Casey Papovich, Lee Spitler, Caroline M. S. Straatman, Kim-Vy Tran, Tao Wang
arXiv:2206.14238
Submitted on 28 June 2022
## Abstract
The discovery in deep near-infrared surveys of a population of massive quiescent galaxies at $z>3$ has given rise to the question of how they came to be quenched so early in the history of the Universe. Measuring their molecular gas properties can distinguish between physical processes where they stop forming stars due to a lack of fuel versus those where star-formation efficiency is reduced and the gas is retained. We conducted Atacama Large Millimeter/sub-millimeter Array (ALMA) observations of four quiescent galaxies at $z=$ 3.5-4.0 found by the Fourstar Galaxy Evolution Survey (ZFOURGE) and a serendipitous optically dark galaxy at $z=3.71$. We aim to investigate the presence of dust-obscured star-formation and their gas content by observing the dust continuum emission at Band-7 and the atomic carbon [C I](${}^{3}{P}_{1}$-${}^{3}{P}_{0}$) line at 492.16 GHz. Among the four quiescent galaxies, only one source is detected in the dust continuum at ${\lambda }_{\mathrm{o}\mathrm{b}\mathrm{s}}=870\mu \mathrm{m}$. The sub-mm observations confirm their passive nature, and all of them are located more than four times below the main sequence of star-forming galaxies at $z=3.7$. None of the targets are detected in [C I], constraining their gas mass fractions to be $<$ 20%. These gas mass fractions are more than three times lower than the scaling relation for star-forming galaxies at $z=3.7$. These results support scenarios where massive galaxies at $z=$ 3.5-4.0 quench by consuming/expelling all the gas rather than by reducing the efficiency of the conversion of their gas into stars.
## Preprint
Comment: 13 pages, 5 figures, 1 table, Accepted for publication in ApJ
Subject: Astrophysics - Astrophysics of Galaxies
|
2022-08-15 19:12:52
|
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 11, "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": 0.5474867820739746, "perplexity": 4663.209448334276}, "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-2022-33/segments/1659882572198.93/warc/CC-MAIN-20220815175725-20220815205725-00277.warc.gz"}
|
https://brilliant.org/problems/calculate-the-total-surface-area-of-a-regular/
|
# Calculate the total surface area of a regular hexagonal prism
Geometry Level 2
it's a regular hexagonal prism.If the side length of the prism is 3 cm and the height is 6 cm.then find out the total surface area of the prism ..
×
|
2017-05-27 06:37:44
|
{"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": 0.9302510023117065, "perplexity": 523.1201013058801}, "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-2017-22/segments/1495463608870.18/warc/CC-MAIN-20170527055922-20170527075922-00426.warc.gz"}
|
http://mathhelpforum.com/algebra/170518-no-solution-print.html
|
No Solution
• February 7th 2011, 10:03 PM
No Solution
I have been working this problem out and the answer in the book is stating no solution. I am getting x=-4.
2(x+3)-5=5x-3(1+x)
• February 7th 2011, 10:08 PM
Prove It
$\displaystyle 2(x+3) - 5 = 5x - 3(1 + x)$
$\displaystyle 2x + 6 - 5 = 5x - 3 - 3x$
$\displaystyle 2x + 1 = 2x - 3$.
They are correct, there is not a solution - the two lines are parallel and therefore never meet...
• February 8th 2011, 04:20 AM
HallsofIvy
Quote:
I have been working this problem out and the answer in the book is stating no solution. I am getting x=-4.
2(x+3)-5=5x-3(1+x)
If x= -4, 2(-4+ 3)- 5= 2(-1)+ 5= -2+ 5= 3 but 5(-4)- 3(1+(-4))= -20- 3(-3)= -20+ 9= -11. They are not at all the same!
Perhaps if you showed us how you got -4, we could point out a mistake.
• February 8th 2011, 04:53 AM
Quote:
I have been working this problem out and the answer in the book is stating no solution. I am getting x=-4.
2(x+3)-5=5x-3(1+x)
$2x+6-5=5x-3-3x\;\;?$
$2x+1=2x-3\;\;$
In algebraic terms, the question is
"For what x is $2x+1=2x-3\;\;?$"
The answer is "no x", since $2x-2x+1\ne\ 2x-2x-3$
$1\ne\ -3$
|
2015-11-25 11:39:58
|
{"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": 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": 0.8611961007118225, "perplexity": 1485.3228283897827}, "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-2015-48/segments/1448398445080.12/warc/CC-MAIN-20151124205405-00290-ip-10-71-132-137.ec2.internal.warc.gz"}
|
https://mathspace.co/textbooks/syllabuses/Syllabus-1023/topics/Topic-20209/subtopics/Subtopic-266096/?textbookIntroActiveTab=overview
|
# 2.02 Making predictions
Lesson
## Making predictions
The least-squares regression line is a linear representation of the general trend of our data.
Once we have determined the least-squares regression line, we can use it as a model to predict the likely value of the response variable based on a given value of the explanatory variable.
The process of predicting has two parts:
• Substitute the $x$x value into the rule for the least-squares regression line to get the predicted $y$y value
• Then we need to consider whether our prediction is reliable or not
We can make predictions 'by hand' either using a graph of the line of best fit or substituting into the equation of the least-squares regression line.
### Predictions from a graph
The example below shows a scatter plot, with the least-squares regression line for the relationship of daily ice-cream sales versus the maximum daily temperature.
Although there is a clear trend of increasing sales as the temperature increases, it would be difficult to predict the sales for a given day from the raw data. However, we can use the least-squares regression line.
If we want to predict the sales on a day when the temperature reaches $30$30 degrees, we could do so with these steps that follow the red arrows on the graph:
1. from $30$30 degrees on the horizontal axis, draw a vertical line to intersect with the line of best fit.
2. from the point of intersection, draw a horizontal line to the vertical axis
3. read the predicted sales, approximately $245$245 ice-creams, form the vertical axis.
When we are making predictions from a graph we should take care to work accurately, but still expect a small amount of variation due to the limited precision of working with graphs.
### Predictions from an equation
For the example above, the equation of the least-squares regression line is
$S$S $=$= $10\times T-45$10×T−45
where $S$S is the number of ice cream sales and $T$T is the maximum daily temperature.
To predict the sales on a day where the maximum temperature is $30$30 degrees, we simply substitute the temperature into the equation:
$S$S $=$= $10\times30-45$10×30−45 $=$= $245$245
So, we can predict that $245$245 ice creams will be sold on that day.
### Making predictions with CAS
Let's look at some examples to see how we can make a prediction once we've input our data and calculated the least-squares regression line. Select the brand of calculator you use below to work through an example.
Casio Classpad
How to use the CASIO Classpad to complete the following tasks regarding linear regression and making predictions.
Consider the data obtained from a chemical process where the yield of the process is thought to be linearly related to the reaction temperature.
Temperature ($x,^\circ C$x,°C) Yield ($y,g$y,g) $50$50 $53$53 $54$54 $56$56 $59$59 $62$62 $65$65 $67$67 $71$71 $74$74 $122$122 $118$118 $128$128 $125$125 $136$136 $144$144 $142$142 $149$149 $161$161 $168$168
1. Using your calculator, find an equation for the least squares regression line of $y$y on $x$x.
Give your answer in the form $y=ax+b$y=ax+b. Give all values to two decimal places.
2. What yield is predicted at a reaction temperature of $60$60$^\circ$°C?
3. What yield is predicted at a reaction temperature of $85$85$^\circ$°C?
4. What temperature gives a predicted yield of $155$155 g?
TI Nspire
How to use the TI Nspire to complete the following tasks regarding linear regression and making predictions.
Consider the data obtained from a chemical process where the yield of the process is thought to be linearly related to the reaction temperature.
Temperature ($x,^\circ C$x,°C) Yield ($y,g$y,g) $50$50 $53$53 $54$54 $56$56 $59$59 $62$62 $65$65 $67$67 $71$71 $74$74 $122$122 $118$118 $128$128 $125$125 $136$136 $144$144 $142$142 $149$149 $161$161 $168$168
1. Using your calculator, find an equation for the least squares regression line of $y$y on $x$x.
Give your answer in the form $y=ax+b$y=ax+b. Give all values to two decimal places.
2. What yield is predicted at a reaction temperature of $60$60$^\circ$°C?
3. What yield is predicted at a reaction temperature of $85$85$^\circ$°C?
4. What temperature gives a predicted yield of $155$155 g?
#### Practice questions
##### Question 1
A bivariate data set has a line of best fit with equation $y=-8.71x+6.79$y=8.71x+6.79.
Predict the value of $y$y when $x=3.49$x=3.49.
## Interpolation and extrapolation
An important consideration when we are making predictions is recognising if the prediction is within the range of data values for which we have actual measurements. If it is, we refer to the prediction as interpolation. If not, we refer to the predication as extrapolation.
The bivariate data set on the right has generated a line of best fit, and the range of the $x$x-values has been highlighted. Making predictions within this range is interpolation, and making predictions outside this range is extrapolation.
Interpolation and extrapolation
Interpolation means you have used an $x$x value in your prediction that is within the range of $x$x values in the data that you were working with.
Extrapolation means you have used an $x$x value in your prediction that is outside the range of $x$x values in the data.
The scatter plots below are annotated to show examples of interpolation (left) and extrapolation (right) from the line of best fit.
## Reliability of predictions
To judge the reliability of the prediction we need to consider three things:
• How strong is the correlation?
• Is the data interpolated or extrapolated?
• How many points are contained in the data set?
We have already seen how to calculate the correlation coefficient and interpret the strength of a relationship, using this chart.
Correlation coefficient
If the correlation is weak, then the data values are more widely scattered, so there will be greater uncertainty in the prediction than for data with a strong correlation.
An interpolated prediction is made within the range of $x$x-values upon which the model was based. Since the model is designed to align closely to the data in this range, interpolated predictions will be more reliable than extrapolated predictions.
When we are extrapolating, we are making the assumption that the linear model continues. This assumption is generally valid when making a prediction relatively close to the given data range. A sudden change in trend is unlikely for most of the phenomena we will model, so we will consider such predictions made to be reliable when using a strong model.
When we extrapolate well beyond the data range, even if the linear trend continues, we will consider such predictions unreliable. As we are making a prediction for values that we have not made any similar measurements, it is possible that the underlying linear relationship is slightly different from the one generated by the given data. This will lead to predictions fairing worse as we predict further beyond the given data range. There are also many cases where it is clear the linear trend cannot continue well beyond the data range. In such cases, the predictions will be unreliable and may also be unreasonable - that is give values that are not possible. For example, a model may show a negative linear trend between a chicken's age and the number of eggs it lays per week, however, the linear model could not continue indefinitely as it would suggest the chicken would lay a negative number of eggs at some age.
Reliability of predictions
If we are interpolating:
• And the correlation is weak, then the prediction will not be reliable.
• And the correlation is moderate, then the prediction is moderately reliable.
• And the correlation is strong, then the prediction will be reliable.
If we are extrapolating:
• And the correlation is weak, then the prediction will not be reliable.
• Just beyond the data range and the correlation is moderate, then the prediction is moderately reliable
• Just beyond the data range and the correlation is strong, then the prediction will be reliable
• Well beyond the data range, then the prediction will be not be reliable and may be unreasonable.
Predictions from a data set with a large number of points (e.g. more than $30$30) will be more reliable than predictions from a small data set.
#### Worked example
A farmer sprays his wheat fields with a fertiliser. The data below gives the yield of wheat per hectare for various spray concentrations:
Spray concentration ($x$x ml/l) Yield of wheat, ($y$y tonnes per hectare) $1$1 $2$2 $4$4 $7$7 $8$8 $10$10 $1.19$1.19 $1.50$1.50 $1.62$1.62 $1.65$1.65 $2.05$2.05 $2.07$2.07
The least-squares regression line for this data is $\hat{y}=0.088x+1.212$^y=0.088x+1.212 and $r=0.929$r=0.929 (given to $3$3 decimal places),
(a) Use the least-squares regression line to make predictions for the yield when using the following concentrations of fertiliser: $5$5 ml/l, $10.8$10.8 ml/l and $35$35 ml/l. (Give answers to $2$2 decimal places)
Think: Substitute the concentration for the value of $x$x in the least-squares regression line and evaluate.
Do:
Spray concentration ($x$x ml/l) Predicted yield of wheat ($\hat{y}$^y tonnes/hectare)
$5$5 $1.65$1.65
$10.8$10.8 $2.16$2.16
$35$35 $4.29$4.29
(b) Comment on the reliability of each prediction made in part (a).
Think: Consider the strength of the model and whether the prediction is interpolation, extrapolation just beyond the data range or extrapolation well beyond the data range.
Do:
The correlation coefficient tells us we have a strong model.
The prediction for $5$5 ml/l is interpolation on a strong model and hence, should be reliable.
The prediction for $10.8$10.8 ml/l is extrapolation just beyond the data range on a strong model and hence, should be reasonably reliable.
The prediction for $35$35 ml/l is extrapolation well beyond the data range and we know the linear trend cannot continue indefinitely since a crop of wheat must have a maximum possible yield and at some point the fertiliser will no longer be effective and may even be toxic. Hence, despite the strong model this prediction is not reliable and may not even be reasonable - may be beyond the maximum yield possible.
#### Practice questions
##### Question 2
Research on the number of cigarettes smoked during pregnancy and the birth weights of the newborn babies was conducted.
Average number of cigarettes per day ($x$x) Birth weight in kilograms ($y$y) $45.5$45.5 $13.2$13.2 $22.4$22.4 $24.4$24.4 $8.4$8.4 $36.7$36.7 $1.4$1.4 $18$18 $10.4$10.4 $13.3$13.3 $36.5$36.5 $19.4$19.4 $3.7$3.7 $5.4$5.4 $4.7$4.7 $4.6$4.6 $5.3$5.3 $4.1$4.1 $6.7$6.7 $4.8$4.8 $5.3$5.3 $4.9$4.9 $3.6$3.6 $5.4$5.4
1. Using technology, calculate the correlation coefficient between the average number of cigarettes per day and birth weight.
2. Choose the description which best describes the statistical relationship between these two variables.
Strong positive linear relationship
A
Weak relationship
B
Moderate negative linear relationship
C
Moderate positive linear relationship
D
Strong negative linear relationship
E
Strong positive linear relationship
A
Weak relationship
B
Moderate negative linear relationship
C
Moderate positive linear relationship
D
Strong negative linear relationship
E
3. Use technology to form an equation for the least squares regression line of $y$y on $x$x.
Give all values to two decimal places. Give the equation of the line in the form $y=mx+c$y=mx+c.
4. Use your regression line to predict the birth weight of a newborn whose mother smoked on average $5$5 cigarettes per day.
5. Choose the description which best describes the validity of the prediction in part (d).
Unreliable due to extrapolation and weak correlation.
A
Despite a strong correlation, unreliable due to extrapolation far from the data range where the linear trend does not continue.
B
Reliable due to interpolation and a strong correlation.
C
Despite an interpolated prediction, unreliable due to a weak correlation.
D
Unreliable due to extrapolation and weak correlation.
A
Despite a strong correlation, unreliable due to extrapolation far from the data range where the linear trend does not continue.
B
Reliable due to interpolation and a strong correlation.
C
Despite an interpolated prediction, unreliable due to a weak correlation.
D
##### Question 3
During an alcohol education programme, $10$10 adults were offered up to $6$6 drinks and were then given a simulated driving test where they scored a result out of a possible $100$100.
Number of drinks ($x$x) Driving score ($y$y) $3$3 $2$2 $6$6 $4$4 $4$4 $1$1 $6$6 $3$3 $4$4 $2$2 $65$65 $60$60 $43$43 $59$59 $57$57 $73$73 $32$32 $63$63 $55$55 $61$61
1. Using technology, calculate the correlation coefficient between these variables.
2. Choose the description which best describes the statistical relationship between these two variables.
Moderate negative linear relationship
A
Strong negative linear relationship
B
Moderate positive linear relationship
C
Weak relationship
D
Strong positive linear relationship
E
Moderate negative linear relationship
A
Strong negative linear relationship
B
Moderate positive linear relationship
C
Weak relationship
D
Strong positive linear relationship
E
3. Use your graphing calculator to form an equation for the least squares regression line of $y$y on $x$x.
Give your answer in the form $y=mx+c$y=mx+c. Give all values to one decimal place.
4. Use your regression line to predict the driving score of a young adult who consumed $5$5 drinks.
5. Choose the description which best describes the reliability of the prediction in part (d).
Unreliable due to extrapolation and weak correlation.
A
Despite a strong correlation, unreliable due to extrapolation far from the data range where the linear trend does not continue.
B
Despite an interpolated prediction, unreliable due to a weak correlation.
C
Reliable due to interpolation and a strong correlation.
D
Unreliable due to extrapolation and weak correlation.
A
Despite a strong correlation, unreliable due to extrapolation far from the data range where the linear trend does not continue.
B
Despite an interpolated prediction, unreliable due to a weak correlation.
C
Reliable due to interpolation and a strong correlation.
D
## Interpreting correlation
As we have discussed in previous lessons, when a change in the value of one variable quantity seems to be associated with a proportional change in another variable, we say there is a correlation between the two variables.
A strong correlation might seem to indicate a cause and effect relationships between the variables. However, we need to be careful to understand the situation, as this is not always the case.
Correlation does not imply causation
These are common reasons for correlation between variables without a causal relationship:
• Confounding due to a common response to another variable (also described as contributing variables).
• e.g. sales of ice-creams and sunscreens have a strong positive correlation because they both increase in response to hot summer weather.
• Coincidence
• it is possible that the data we are analysing shows a correlation purely by chance.
• The causation is in the opposite direction
• e.g. strong winds are correlated to tree branches waving. But the waving branches don't cause the strong winds.
• The two variable may interplay, that is the causation may go in both directions
• e.g. There is a negative correlation between number of hawks in an area and rodents in the area. In this type of predator/prey relationship the predator numbers affect prey numbers, but prey numbers, i.e. food supply, also affect predator numbers.
When we are asked to analyse a relationship between variables, we should consider whether a causal relationship can be justified. If not, we should say so, and identify possible non-causal reasons for the association.
#### Practice questions
##### Question 4
The table shows the number of fans sold at a store during days of various temperatures.
Temperature ($^\circ$°C) $6$6 $8$8 $10$10 $12$12 $14$14 $16$16 $18$18 $20$20 Number of fans sold $12$12 $13$13 $14$14 $17$17 $18$18 $19$19 $21$21 $23$23
1. Consider the correlation coefficient $r$r for temperature and number of fans sold. In what range will $r$r be?
$r=0$r=0
A
$r>0$r>0
B
$r<0$r<0
C
$r=0$r=0
A
$r>0$r>0
B
$r<0$r<0
C
2. Is there a causal relationship?
Yes
A
No
B
Yes
A
No
B
##### Question 5
A study found a strong correlation between the approximate number of pirates out at sea and the average world temperature.
1. Does this mean that the number of pirates out at sea has an impact on world temperature?
Yes
A
No
B
Yes
A
No
B
2. Which of the following is the most likely explanation for the strong correlation?
Contributing variables - there are other causal relationships and variables that come in to play and these may lead to an indirect positive association between the approximate number of pirates out at sea and the average world temperature.
A
Coincidence - there are no other contributing factors or reasonable arguments to be made for the strong positive association between the approximate number of pirates out at sea and the average world temperature.
B
Contributing variables - there are other causal relationships and variables that come in to play and these may lead to an indirect positive association between the approximate number of pirates out at sea and the average world temperature.
A
Coincidence - there are no other contributing factors or reasonable arguments to be made for the strong positive association between the approximate number of pirates out at sea and the average world temperature.
B
3. Which of the following is demonstrated by the strong correlation between the approximate number of pirates out at sea and the average world temperature?
If there is correlation between two variables, then there must be causation.
A
If there is correlation between two variables, there isn't necessarily causation.
B
If there is correlation between two variables, then there is no causation.
C
If there is correlation between two variables, then there must be causation.
A
If there is correlation between two variables, there isn't necessarily causation.
B
If there is correlation between two variables, then there is no causation.
C
### Outcomes
#### ACMGM061
use the equation of a fitted line to make predictions
#### ACMGM062
distinguish between interpolation and extrapolation when using the fitted line to make predictions, recognising the potential dangers of extrapolation
#### ACMGM064
recognise that an observed association between two variables does not necessarily mean that there is a causal relationship between them
#### ACMGM065
identify possible non-causal explanations for an association, including coincidence and confounding due to a common response to another variable, and communicate these explanations in a systematic and concise manner
|
2021-12-05 16:59:40
|
{"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": 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": 0.6022315621376038, "perplexity": 1211.5140307414013}, "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/1637964363215.8/warc/CC-MAIN-20211205160950-20211205190950-00460.warc.gz"}
|
https://www.vedantu.com/maths/surface-area-of-cube
|
# Surface Area of Cube
What is a Cube?
A cube is a three-dimensional solid figure bounded by six square faces. It has 6 faces, 8 vertices and 12 edges.
Example: Dice, Ice cube, Rubik's cube, etc.
In this article, you will learn about the surface area of the cube, its formula and derivation along with some solved examples.
Surface Area of Cube
In geometry, the area of any shape is the region covered by it in a plane. A cube consists of 6 square faces, the region covered by these square units on the surface of the cube is called the surface area of the cube. So, the surface area of the cube is the sum of the area of its six square faces.
Formula of Surface Area of Cube
Let us consider a cube whose each edge or side has length of ‘a’ units.
The area of one of the six faces of the cube is the area of a square with side ‘a’ units.
i.e. Area of one face of cube = Area of square = side × side = (side)2 = a2 sq. units
Therefore, the total surface area of cube = sum of area of its six square faces
Since the area of each of six square faces are the same, the sum of the area of its six square faces can be obtained by multiplying 6 to the area of one face of the cube.
Hence, the total surface area of cube = 6 × (a2) sq. units
Or, Total surface area (TSA) of cube = 6a2 sq. units
Length of Edge of Cube
The length of edge of the cube can be obtained if the total surface area of the cube is known to us. This can be done by rearranging the formula for the total surface area of the cube.
Total surface area (TSA) of cube = 6a2 sq. units
Or, TSA = 6 × (Side)2 = 6 × (Edge)2
Or, (Edge)2 = $\frac{{TSA}}{6}$
Or, Length of edge of cube = $\sqrt {\frac{{TSA}}{6}}$ units
Lateral Surface Area (LSA) of Cube
Lateral surface area of the cube is the area of its all faces excluding the area of top and bottom faces.
Therefore, the Lateral surface area of cube = 4 × (side)2 sq. units
Or, Lateral surface area (LSA) of cube = 4a2 sq. units
Solved Examples:
Q1. Find the Area of Metal Sheet Required to Make a Cubical Box of Side Length 5m.
Solution: Given, length of side of cubical box = 5m.
The area of metal sheet required to make a cubical box = TSA of cube
= 6 × (Side)2
= 6 × (5)2 sq. mts
= 6 × 25 sq. mts
= 150 sq. mts
Hence, the area of metal sheet required to make a cubical box of side length 5m is 150 sq. mts
Q2. Find the Ratio of the Lateral Surface Area and Total Surface Area of a Cube.
Solution: Let the length of the side of the cube be a unit. Then,
Lateral surface area (LSA) of cube = 4 a 2
Total surface area (TSA) of cube = 6 a 2
Ratio of LSA and TSA of cube = $\frac{{LSA\,of\,cube}}{{TSA\,of\,cube}}$
$= \frac{{4{a^2}}}{{6{a^2}}} = \frac{2}{3}$
Hence, the ratio of the lateral surface area and total surface area of a cube is 2 : 3
Q3. Find the Length of the Edge of the Cube whose Surface Area is 600 cm2.
Solution: Given, Surface area of cube = 600 cm
We know, Length of edge of cube = $\sqrt {\frac{{TSA}}{6}}$ units
⇒ Length of edge of cube = $\sqrt {\frac{{600}}{6}}$cms
= $\sqrt {100}$= 10cms
Q4. A Cubical Container of Side 4m is to be Painted on the Entire Outer Surface. Find the Area to be Painted and the Total cost of Painting it at the Rate of ₹24 per m2.
Solution: Given, Side length of cubical container = 4 m
Since the container is to be painted on the entire outer surface, the area to be painted can be obtained by finding the total surface area of the cubical container.
Therefore, total surface area of cubical container = 6 × (Side)2
= 6 × (4)2 sq. mts
= 6 × 16 sq. mts
= 96 sq. mts
Given, cost of painting 1 sq. mtr is ₹24
So, the total cost of painting the cubical container = ₹ (96 × 24) = ₹ 2304
|
2020-07-05 23:52:51
|
{"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": 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": 0.8014337420463562, "perplexity": 835.0420142028219}, "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-2020-29/segments/1593655889877.72/warc/CC-MAIN-20200705215728-20200706005728-00199.warc.gz"}
|
http://www.ck12.org/arithmetic/Fraction-Ordering-with-Lowest-Common-Denominators/lesson/Fraction-Ordering-with-Lowest-Common-Denominators/r10/
|
<img src="https://d5nxst8fruw4z.cloudfront.net/atrk.gif?account=iA1Pi1a8Dy00ym" style="display:none" height="1" width="1" alt="" />
You are viewing an older version of this Concept. Go to the latest version.
# Fraction Ordering with Lowest Common Denominators
## Arranging numerators in ascending order
0%
Progress
Practice Fraction Ordering with Lowest Common Denominators
Progress
0%
Fraction Ordering with Lowest Common Denominators
Have you ever gone to a place where you could make your own sundae? It is a delicious idea.
The students in the sixth grade have decided to add a “Make Your Own Ice Cream Sundae” to the sixth grade social. They figure if they charge \$1.50 per sundae, then they can make some money for the next sixth grade social. On Friday night, the first eight students came in and made their sundaes. They looked delicious! Here is what the students chose for their ice cream and toppings.
$\frac{6}{8}$ chose vanilla ice cream
$\frac{1}{4}$ chose chocolate ice cream
$\frac{2}{8}$ chose sprinkles
$\frac{5}{8}$ chose hot fudge
$\frac{3}{8}$ chose caramel
$\frac{2}{4}$ chose nuts
Terrence wants to figure out which toppings were the most popular and which toppings were the least popular. You are going to help him do this.
In this Concept, you will learn all about ordering fractions. When you see this problem again at the end of the Concept, you will know how to help Terrence write the toppings in order from the most popular or greatest to the least popular.
### Guidance
In an earlier Concept, you learned how to compare fractions with different denominators.
Sometimes, we need to write fractions in order from least to greatest or from greatest to least.
If we have fractions with common denominators, this becomes very simple.
Write in order from least to greatest. $\frac{4}{9},\frac{2}{9},\frac{8}{9},\frac{3}{9},\frac{6}{9}$
Since all of these fractions are written in ninths, the common denominator, we can use the numerators and arrange them in order from the smallest numerator to the largest numerator.
Our answer is $\frac{2}{9},\frac{3}{9},\frac{4}{9},\frac{6}{9},\frac{8}{9}$ .
How do we order fractions that do not have a common denominator?
To do this, we will need to rewrite the fractions using a common denominator. This is the best way to know how to order the fractions.
$\frac{2}{3},\frac{1}{4},\frac{1}{2}, \frac{5}{6}$
If we wanted to write these fractions in order from least to greatest, we would need to rewrite them so that they have a common denominator.
We can use the lowest common denominator (LCD) for 3, 4, 2 and 6. That number would be 12.
Next, we rewrite each fraction in terms of twelfths.
$\frac{2}{3}=\frac{8}{12}\\\frac{1}{4}=\frac{3}{12}\\\frac{1}{2}=\frac{6}{12}\\\frac{5}{6}=\frac{10}{12}$
Our answer is $\frac{3}{12},\frac{6}{12},\frac{8}{12},\frac{10}{12}=\frac{1}{4},\frac{1}{2},\frac{2}{3},\frac{5}{6}$ .
Try a few of these on your own.
#### Example A
What is the LCD for 3, 5, and 6?
Solution: 30
#### Example B
Rename $\frac{4}{5},\frac{1}{5},\frac{2}{3}$ .
Solution: $\frac{24}{30},\frac{6}{30},\frac{20}{30}$ .
#### Example C
Next write them in order from greatest to least.
Solution: $\frac{6}{30},\frac{20}{30},\frac{24}{30}$
Now let's go back to the ice cream sundaes at the sixth grade social.
Since we are only interested in ordering the toppings, we don’t need to underline the ice cream flavors. The topping that is the most popular is the greatest fraction and the topping that is the least popular is the smallest fraction.
To order these fractions, we will need to rewrite them all with the same lowest common denominator. The lowest common denominator for 4 and 8 is 8.
We only need to change $\frac{2}{4} = \frac{4}{8}$ .
Now we can write them in order.
$\frac{2}{8},\frac{3}{8},\frac{4}{8},\frac{5}{8}$
Now we can write the toppings in order from the most popular to the least popular.
1. Hot fudge
2. Nuts
3. Caramel
4. Sprinkles
Terrence is surprised by his findings. He didn’t think that caramel would be more popular than sprinkles!
### Vocabulary
Equivalent Fractions
two equal fractions
Denominator
the bottom number of a fraction
Numerator
the top number of a fraction
Like Denominator
when two or more denominators are the same, can also be called common denominators.
Lowest Common Denominator
the least common multiple of two or more denominators.
### Guided Practice
Here is one for you to try on your own.
Write the following fractions in order from least to greatest.
$\frac{4}{7},\frac{2}{3},\frac{5}{7}$
To complete this task, we have to rename the fractions in terms of a lowest common denominator. In this case, the lowest common denominator of 3 and 7 is 21.
$\frac{12}{21},\frac{14}{21},\frac{15}{21}$
Now we can rewrite them in order from least to greatest.
$\frac{4}{7},\frac{2}{3},\frac{5}{7}$
Notice that the original order was in order from least to greatest.
### Practice
Directions: Write each series in order from least to greatest.
1. $\frac{5}{6},\frac{1}{3},\frac{4}{9}$
2. $\frac{6}{7},\frac{1}{4},\frac{2}{3}$
3. $\frac{6}{6},\frac{4}{5},\frac{2}{3}$
4. $\frac{1}{2},\frac{3}{5},\frac{2}{3}$
5. $\frac{2}{7},\frac{1}{4},\frac{3}{6}$
6. $\frac{1}{6},\frac{2}{9},\frac{2}{5}$
7. $\frac{4}{16},\frac{4}{5},\frac{3}{7}$
8. $\frac{9}{10},\frac{4}{5},\frac{3}{4}$
9. $\frac{4}{5},\frac{1}{2},\frac{2}{3}$
10. $\frac{9}{11},\frac{2}{3},\frac{3}{4}$
11. $\frac{4}{7},\frac{1}{5},\frac{3}{8}$
12. $\frac{6}{7},\frac{1}{3},\frac{2}{5}$
13. $\frac{7}{8},\frac{4}{5},\frac{1}{3}$
14. $\frac{1}{6},\frac{4}{5},\frac{2}{4}$
15. $\frac{1}{9},\frac{4}{7},\frac{2}{9},\frac{7}{8}$
### Vocabulary Language: English
Denominator
Denominator
The denominator of a fraction (rational number) is the number on the bottom and indicates the total number of equal parts in the whole or the group. $\frac{5}{8}$ has denominator $8$.
Equivalent Fractions
Equivalent Fractions
Equivalent fractions are fractions that can each be simplified to the same fraction. An equivalent fraction is created by multiplying both the numerator and denominator of the original fraction by the same number.
Like Denominators
Like Denominators
Two or more fractions have like denominators when their denominators are the same. "Common denominators" is a synonym for "like denominators".
Lowest Common Denominator
Lowest Common Denominator
The lowest common denominator of multiple fractions is the least common multiple of all of the related denominators.
Numerator
Numerator
The numerator is the number above the fraction bar in a fraction.
|
2015-11-29 06:03:54
|
{"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": 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": 36, "texerror": 0, "math_score": 0.6064923405647278, "perplexity": 915.5385503323815}, "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-2015-48/segments/1448398456289.53/warc/CC-MAIN-20151124205416-00247-ip-10-71-132-137.ec2.internal.warc.gz"}
|
https://zbmath.org/?q=an:0902.53015&format=complete
|
# zbMATH — the first resource for mathematics
$$K$$-concircular vector fields and holomorphically projective mappings on Kählerian spaces. (English) Zbl 0902.53015
Slovák, Jan (ed.), Proceedings of the 16th Winter School on geometry and physics, Srní, Czech Republic, January 13–20, 1996. Palermo: Circolo Matematico di Palermo, Suppl. Rend. Circ. Mat. Palermo, II. Ser. 46, 123-127 (1997).
Author’s abstract: “$$K$$-concircular vector fields on Kählerian and hyperbolically Kählerian spaces are studied. Metric tensors of these spaces are found in explicit form. Metrics admitting $$K$$-concircular vector fields which are in holomorphically projective correspondence are found”.
For the entire collection see [Zbl 0866.00050].
##### MSC:
53B35 Local differential geometry of Hermitian and Kählerian structures
|
2021-12-02 12:04:03
|
{"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": 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": 0.4539099335670471, "perplexity": 4923.9491702114265}, "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/1637964362219.5/warc/CC-MAIN-20211202114856-20211202144856-00615.warc.gz"}
|
https://academy.lucedaphotonics.com/training/topical_training/mzm/introduction.html
|
# 4.1. Introduction¶
A Mach-Zehnder modulator (MZM) is a device used to achieve amplitude modulation. It is based on an interferometric structure, called Mach-Zehnder interferometer (MZI).
Schematic representation of a Mach-Zehnder interferometer (MZI).
In an MZI, the incoming optical wave is first split in two arms using a Y-splitter and is then recombined by a second Y-splitter. When the two beams are recombined, two different scenarios can take place:
1. If the two separate paths have equal optical length, the split beams are in-phase when they are recombined and constructive interference is achieved.
2. If the optical length of the two paths is different, the split beams will have different relative phase when they are recombined. This gives rise to destructive interference.
Therefore, depending on the relative phase difference acquired by the split beams while traveling along the two separate paths, the light is recombined more or less efficiently. In the following image the transmission of the a MZI is plotted as a function of the phase difference $$\Delta\Phi$$.
Transmission of a MZI as a function of the phase difference $$\Delta\Phi$$ in the arms.
To control the relative phase shift between the split beams, a phase shifter is placed on each of the two arms of the interferometer. When a voltage is applied to the phase shifter, the optical path length is altered due to the electro-optic effect. If the relative phase difference between the two arms of the interferometer is equal to $$\pi$$, destructive interference takes place when the beams are recombined and a minimum of intensity is achieved. If the phase difference is equal to 0, constructive interference gives rise to a maximum of intensity. Switching between these two states allows to achieve amplitude modulation.
Schematic representation of a Mach-Zehnder modulator (MZM) with a phase shifter on each arm.
The MZM modulator in this tutorial will, by design, introduce a path length difference of $$\pi/2$$ between the two arms to operate in the area of maximum slope of the MZI.
In real life, due to typical fabrication errors, the resulting length of the MZI arms slightly differs from the design specifications. To fine-tune the optical length, a heated waveguide section is added after the Y-splitter, so that the operating point can be maintained as wavelength and operation temperature vary. Due to the strong thermo-optic effect in silicon, heaters are particularly well suited for the job as they allow to efficiently vary the optical length of the waveguide by changing the waveguide mode effective index, resulting in a change of the optical phase of the propagated light.
Schematic representation of a Mach-Zehnder modulator (MZM) with a phase shifter and a heater on each arm.
For more details on the design and compact model of the heater we will use for the MZM, have a look at the documentation of the heater included in SiFab: Heaters.
In the next sections you will
• learn how to use the layout and simulation model of a phase shifter;
• learn how to use the layout and the simulation model of a heated waveguide;
• learn how to use the layout and simulation model of a Mach-Zehnder modulator.
|
2020-11-27 16:56:11
|
{"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": 0.5831225514411926, "perplexity": 578.0261836302885}, "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-2020-50/segments/1606141193856.40/warc/CC-MAIN-20201127161801-20201127191801-00716.warc.gz"}
|
http://physics.stackexchange.com/questions/55569/when-should-i-take-wine-out-of-the-fridge-transient-heat-transfer-problem/55608
|
# When should I take wine out of the fridge - transient heat transfer problem
I am hosting a dinner tonight for which I'll be serving white wine (Riesling to be more specific). Generally white wine is best served chilled (not COLD!) at around 50 F or 10 C.
Just for kicks, I thought I'd treat this as a problem of transient conduction. I assume that (forced)convection is negligible since I will leave my wine bottle in my kitchen which has still air.
The following assumptions are made:
• The wine bottle is assumed to be cylindrical with an outside to inside radii, $r_o/r_i$ ratio of 1.10
• The only mode of heat transfer for this bottle is conduction (perhaps a poor assumption?). The kitchen air is considered to be still and at 25 C
• The un-open bottle of wine is a closed thermodynamic system. The glass material has a conductivity $k$ of 1.0 W/m-K and the wine itself has a specific heat at constant volume, $C_v$ of 2.75 kJ/kg-k as per this
• The volume of the bottle of wine is 750 mL or $750 \times 10^{-6} m^3$
• The wine is at a temperature of 5 C and hence needs to be warmed for a while. The entire wine is assumed to have a lumped capacitance (all the wine is at the same temperature with little variation with radius).
• The temperature difference between the wine and the bottle wall is assumed to be $\sim 10 C$ and so is the temperature difference between the bottle wall and the room (just a rough order of magnitude).
The first law of thermodynamics (transient) is applied to this closed system bottle of wine:
$$\frac{\mathrm{d}{E}}{\mathrm{d}t} = \delta\dot{Q} - \delta\dot{W}$$
The $\delta\dot{W}$ term is zero for this closed system as only heat is exchanged with the kitchen atmosphere.
$$\frac{m C_v \Delta T_\text{wine-bottle}}{\Delta t} = \frac{2 \pi k \Delta T_\text{bottle-kitchen}}{ln(r_o/r_i)}$$
This gives me the time the bottle of wine needs to be placed in my kitchen outside the fridge as:
$$\Delta t \approx 0.025 \frac{\Delta T_\text{bottle-air}}{\Delta T_\text{wine-bottle}} C_v \approx 68 \text{ seconds}$$
This seems to be a rather small amount of time!!! Are my assumptions wrong? Should I improve this with convective heat transfer between the bottle and the kitchen air? Will my guests be disappointed? :P
EDIT::Including convective heat transport:
$$\underbrace{\frac{m C_v \Delta T_\text{wine-bottle}}{\Delta t}}_\text{Change in total/internal energy w.r.t time} = \underbrace{\frac{2 \pi k \Delta T_\text{bottle-kitchen}}{ln(r_o/r_i)}}_\text{conduction} + \underbrace{h A \Delta T_\text{bottle-kitchen}}_\text{convection}$$.
Here $h$ is the heat transfer coefficient $\sim 1 W/m-K$, $A$ is the surface area of the cylinder. Based on the volume of the cylinder being $70 mL = \pi r_i^2 h$. The height of the bottle is about $1 foot$ or $0.3048 m$ and the generally close assumption that $r_o \approx 1.1 r_i$, I have (all $\Delta T$'s are close and cancel out):
$$\Delta t = \frac{m C_v ln(r_o/r_i)}{\left[ 2 \pi k + 2\pi r_o(r_o + h) ln(r_o/r_i)\right]} \\ \Delta t \approx 260.76 \text{ seconds} \approx 4 \text{ minutes}$$
This seems more plausible..... But I start doubting myself again.
-
Did you invite Sheldon Cooper or something? – RedGrittyBrick Mar 1 '13 at 18:08
@RedGrittyBrick What is a SheldonCooper? :P – drN Mar 1 '13 at 18:08
I think air is not a good approximation to a thermal reservoir; its heat capacity and conductivity are too low (so you end up with a cold boundary layer around the bottle). Also, you left out some important info: the producer and vintage! – Art Brown Mar 1 '13 at 18:31
@ArtBrown I just worked out the effect of convective heat transport and will add that as an edit. Cold Creek from WA, 2008. – drN Mar 1 '13 at 18:36
Just some suggestions: (1) The units in the second equation don't match. (2) It's not clear that convection can be treated so simply. Perhaps mixing length theory should be applied. (3) There should be some quantitative estimate of conduction and radiation; at least I'm not convinced they don't matter. (4) In kJ/(kg K), the specific heat of water is 4.2; ethanol (at 2.4) is a minor contribution (this is only wine after all, not hard liquor). That quoted $C_V$ seems a bit low. – Chris White Mar 1 '13 at 23:25
show 4 more comments
## 2 Answers
I'm no expert, but here goes...
I assume the bottle diameter $d$ is 80 mm, and its glass thickness $l$ is 2 mm. (Height $h$ cancels out of the result). The surface area $A$ of the glass is then approximately $A = \pi d h$.
Start by estimating the thermal conductivities for the 3 heat transfer processes:
Conduction:
The thermal conductivity of glass is $k=1 W/m/K$.
$$q = (k A / l) \Delta T_{glass} = 500 A \Delta T = G_{cond} A \Delta T \quad, \quad G_{cond} = 500 W/m^2/K$$
Convection:
The convective heat transfer coefficient of air is $h=5-25 W/m^2/K$, according to one reference (a lot of wiggle room here): http://www.engineeringtoolbox.com/convective-heat-transfer-d_430.html $$q = h A \Delta T \quad, \quad G_{conv} = h W/m^2/K$$
Radiation (larger than I expected, hat tip to Chris White):
The Stefan-Boltzmann constant is $\sigma = 5.67x10^{-8} W/m^2/K^4$. $$q = \epsilon \sigma A \left(T_1^4-T_2^4 \right) = \epsilon \sigma A (T_1^3 + T_1^2 T_2 + T_1 T_2^2 + T_2^3)\Delta T \approx 4 \sigma T_{avg}^3 A \Delta T \approx 5 \epsilon A \Delta T = G_{rad} A \Delta T$$ $$G_{rad} = 5 \epsilon W/m^2/K$$
Here $\epsilon$ is the emissivity, which is 1 for a black body and zero for a perfect reflector. Per Schaum's "Heat Transfer" $\epsilon = 0.94$ for smooth glass, which is 1 at this level of accuracy.
Radiation occurs in parallel with convection, so their conductivities add, while conduction through the glass is in series with the other 2, so its (relatively very large) conductivity adds in parallel. The total conductivity $G$ is then determined by: $$q = G A \Delta T$$ $$\frac{1}{G} = \frac{1}{G_{cond}} + \frac{1}{G_{conv}+G_{rad}} \approx \frac{1}{G_{conv}+G_{rad}}$$ $$G \approx 10 - 30 W/m^2/K$$
[Conduction through the glass is much easier than convection + radiation, so the latter two form the heat transfer "bottleneck" (hee hee); conduction is negligibly large.]
Now, for the wine, $q = m C_v dT/dt$ , where $m = \rho V$ , $\rho = 978 kg/m^3 \text{ and } C_v = 4.3 kJ/kg/K$ , according to a report I found on-line:
http://www.gwrdc.com.au/wp-content/uploads/2012/11/WineryB-CaseStudyReport2.pdf
Equating the 2 expressions for q, we get a nice first order diff eq: $$\frac{dT}{dt} = (T-T_{amb})/\tau$$ where the time constant $\tau$ is: $$\tau = \frac{m C_v}{G A} = \frac{\rho C_v }{G} \frac{V}{A} = \frac{\rho C_v }{G} \frac{d}{4} = \frac{84,100}{G} = 2800-8410 \text{ seconds, or } 47 \text{ to } 140 \text{ minutes}.$$
We're only warming the bottle by 5 out of the initial temperature difference of 20 degrees, so we don't need to compute logarithms and instead use a linear expression (equivalent to assuming constant heat flow $q$). The time $t_{warm-up}$ required to achieve optimum serving temperature is just: t_{warm-up} = \tau \frac{5}{20} = 12 \text{ to } 35 \text{ minutes}.\$
Update: Here's some data for water in a wine bottle (hey, I'm not wasting good wine). I used one of those vacuum storage stoppers; the hole was just right to poke through a kitchen thermometer. Two diffferent ones, actually. The third curve is an exponential with a 30 minute time constant, which looks to be in the ballpark. It looks like I'm underestimating something, maybe convection?
-
Nice set of calculation but why radiation?? I would think that conduction+convection are a better assumption. Must go find my Karlekar and Desmond – drN Mar 2 '13 at 13:45
I thought radiation would be negligible and was only making an estimate to justify ignoring it, per Chris White's comment to your question. I was surprised to see it had an effect. – Art Brown Mar 2 '13 at 17:03
Yes, I am extremely surprised that radiation has an effect. I am not convinced however that radiation should be important for this case. I could just be wrong! – drN Mar 2 '13 at 18:09
(1) You have used the Stefan Boltzmann law for radiation which is reserved only for blackbodies. (2) I think radiation heat transfer, in this case, should be calculated after considering radiation shape factors (3)*Based on *(1) and (2), I somehow feel it is ok to neglect radiation heat transfer and that your answer may be flawed. – drN Mar 4 '13 at 13:52
1) I address emissivity in my edit. 2) I think a bottle standing upright has a good view of its surroundings. – Art Brown Mar 6 '13 at 4:24
show 2 more comments
I'm an engineer, not a physicist. My solution:
I suggest you find a bottle of wine with thesame alcohol content. You chill it in the fridge to same temperature as teh one you want to drink. You take it out way before the dinner, put it in the same position you would you real bottle, and start to monitor the temperature. The moment the temperature is right, you note the time this took (and start drinking). Then, you should know the time it takes your wine to reach optimal drinking tempreature after the fridge. Also, you get drink more wine.
-
Hi Fellow engineer! Although an engineer, I strayed across the border into applied math and fluid physics. So my house is sans thermometers! And I like messing around with the conservation equations... – drN Mar 4 '13 at 12:36
You will have to take regular sips. this will slightly skew your results, but could be worth it. Depending on how much you enjoy the multiple samples approach. – mart Mar 4 '13 at 16:02
add comment
|
2014-07-22 18:34:33
|
{"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": 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": 0.7063981294631958, "perplexity": 833.0697441311859}, "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-2014-23/segments/1405997862121.60/warc/CC-MAIN-20140722025742-00190-ip-10-33-131-23.ec2.internal.warc.gz"}
|
https://academy.lucedaphotonics.com/training/topical_training/wdm_transmitter_mzi/mzi_lattice_filter.html
|
# 1.1. MZI lattice filter¶
In this section, we will explain how to design a lattice filter based on Mach-Zender interferometers (MZI).
## 1.1.1. Directional coupler¶
The basic building block of an MZI is the directional coupler. In this case, we use DirectionalCouplerSPower from SiFab, the demonstration pdk distributed with this training material. This class is useful as it has a precomputed model, which is used to calculate the correct length of the directional coupler for a given power coupling coefficient into the cross arm. We can visualize this component, run a circuit simulation and plot the transmission. For more info on directional couplers available in SiFab, have a look at Directional coupler.
from si_fab import all as pdk
import numpy as np
import pylab as plt
dc = pdk.DirectionalCouplerSPower(power_fraction=0.5,
target_wavelength=1.55)
dc_lv = dc.Layout()
dc_lv.visualize(annotate=True)
dc_cm = dc.CircuitModel()
wavelengths = np.linspace(1.51, 1.6, 500)
S = dc_cm.get_smatrix(wavelengths=wavelengths)
plt.figure()
plt.plot(wavelengths, np.abs(S["in1", "out1"])**2, linewidth=2.2, label="in1-out1 (through)")
plt.plot(wavelengths, np.abs(S["in1", "out2"])**2, linewidth=2.2, label="in1-out2 (drop)")
plt.axvline(x=dc.target_wavelength)
plt.title("Power transmission", fontsize=16)
plt.xlabel("Wavelength", fontsize=16)
plt.ylabel("Power", fontsize=16)
plt.xlim(1.5, 1.6)
plt.legend(fontsize=14, loc=1)
plt.legend()
plt.show()
## 1.1.2. MZI lattice filter¶
Now we can use this directional coupler to build an MZI lattice filter. To achieve this, we define a Python class that inherits from CircuitCell and we call it MZILatticeFilter. This lattice filter is a parametric circuit with customizable number of cascaded MZIs. The lengths of the directional couplers used for the MZIs are automatically calculated by providing a list of power coupling coefficients.
class MZILatticeFilter(CircuitCell):
""" Mach-Zender interferometer lattice filter based on directional couplers with different power
coupling.
The number of power couplings should be equal to the number of delay lengths plus 1.
"""
directional_couplers = i3.ChildCellListProperty(doc="list of directional couplers")
center_wavelength = i3.PositiveNumberProperty(default=1.55, doc="Center wavelength")
delay_lengths = i3.ListProperty(default=[100.], doc="List of delay lengths")
phase_error_width_deviation = i3.NonNegativeNumberProperty(default=0.0)
phase_error_correlation_length = i3.NonNegativeNumberProperty(default=0.0)
def _default_directional_couplers(self):
power_couplings = [0.5, 0.5]
dir_couplers = [pdk.DirectionalCouplerSPower(name=self.name + "dc_{}".format(cnt),
power_fraction=p,
target_wavelength=self.center_wavelength)
for cnt, p in enumerate(power_couplings)]
return dir_couplers
def get_connector(self, offset_high):
from circuit.connector_functions import get_template
def connector(start_port, end_port, name=None, shape=None, connector_kwargs={}):
tt = get_template(start_port, end_port)
tt_new = tt.cell.modified_copy()
tt_new.CircuitModel(phase_error_width_deviation=self.phase_error_width_deviation,
phase_error_correlation_length=self.phase_error_correlation_length)
shape = [
start_port.position,
start_port.position + (min_straight, 0.0),
start_port.position + (min_straight, offset_high),
end_port.position + (-min_straight, offset_high),
end_port.position - (min_straight, 0.0),
end_port.position,
]
cell = i3.RoundedWaveguide(name=name, trace_template=tt_new)
return cell
return connector
def _default_child_cells(self):
child_cells = dict()
for cnt, dc in enumerate(self.directional_couplers):
child_cells["dc_{}".format(cnt)] = dc
return child_cells
def _default_connectors(self):
conn = []
for cnt, delay_length in enumerate(self.delay_lengths):
if delay_length > 0:
l_top = delay_length / 2
l_bot = 0
else:
l_top = 0
l_bot = - delay_length / 2
p1 = "dc_{}:out1".format(cnt)
p2 = "dc_{}:in1".format(cnt + 1)
conn.append((p1, p2, self.get_connector(offset_high=- 2 * self.bend_radius - l_bot)))
p1 = "dc_{}:out2".format(cnt)
p2 = "dc_{}:in2".format(cnt + 1)
conn.append((p1, p2, self.get_connector(offset_high=2 * self.bend_radius + l_top)))
return conn
def _default_place_specs(self):
place_specs = []
for cnt in range(1, len(self.directional_couplers)):
spec = i3.PlaceRelative("dc_{}:in1".format(cnt), "dc_{}:out1".format(cnt - 1), (distance, 0))
place_specs.append(spec)
return place_specs
def _default_external_port_names(self):
epn = {"dc_0:in1": "in1",
"dc_0:in2": "in2",
"dc_{}:out1".format(len(self.delay_lengths)): "out1",
"dc_{}:out2".format(len(self.delay_lengths)): "out2"}
return epn
Let’s analyze the code above:
1. Properties. We defined a list of properties that are used to design the MZI lattice filters. The length of the list provided in power_couplings determines how many directional couplers are used to design the lattice filter. If 5 values are provided for the power coupling coefficients, then 4 values should be provided for the delay_lengths to be used to connect the 5 directional couplers to each other. The phase error properties can be used to perform a variability analysis of the MZI lattice filter.
2. Default directional couplers. In _default_directional_couplers we instantiate as many directional couplers as provided in power_couplings. As mentioned earlier, the default directional coupler used in this example is DirectionalCouplerSPower from SiFab.
3. get_connector function. This function returns a connector which is used to draw the arms connecting the directional couplers to each other.
4. CircuitCell properties. Next, the properties needed to create a circuit with CircuitCell are specified:
1. The directional couplers are added to the dictionary of child cells in _default_child_cells.
2. The connectors between the directional couplers are specified in _default_connectors. The function get_connector is used inside this method to obtain arms with length given by the values in delay_lengths.
3. The placement of the directional couplers is defined in _default_place_specs.
4. The external ports of the final MZI lattice filter are exposed in _default_external_port_names.
The connectivity defined in CircuitCell is automatically used to extract the netlist of the circuit and to perform circuit simulations.
|
2021-10-20 15:47:01
|
{"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": 0.3079119026660919, "perplexity": 9667.380202125067}, "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-2021-43/segments/1634323585322.63/warc/CC-MAIN-20211020152307-20211020182307-00241.warc.gz"}
|
http://lists.slug.org.au/archives/slug/2001/05/msg00953.html
|
# SLUG Mailing List Archives
## [SLUG] Re: Debugging information = more cpu/memory usage?
• To: slug@xxxxxxxxxxx
• Subject: [SLUG] Re: Debugging information = more cpu/memory usage?
• From: Angus Lees <gusl@xxxxxxxxxxxxxxx>
• Date: Wed May 23 22:13:02 2001
• User-agent: Mutt/1.2.5i
\begin{Marshall, Joshua}
> I'm wondering whether the debugging information that is compiled into
> most linux executables affects the cpu and memory usage when the
> application is run?
>
> For example, if I strip all the debugging information out of the
> executables, does it simply reduce the disk space it uses or does it
> also reduce the memory usage?
afaik, strip(1) just removes certain sections from the ELF
file. presumably these sections are not loaded into memory unless
required.
on a .so (or .o), it removes symbols from the exported list, which
presumably makes it a little faster to link to (negligible). i don't
think it actually removes the code behind those symbols.
of course, with smaller files, you're more likely to get more frequent
disk cache hits, etc - so there will also be a (negligible) speed up
there.
core dumps on the other hand, have nothing to do with size or run-time
speed. presuming you delete old core files, there is no good reason to
have core dumps disabled.
--
- Gus
|
2013-05-23 13:43:07
|
{"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": 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": 0.5947462916374207, "perplexity": 10360.829542629439}, "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/1368703326861/warc/CC-MAIN-20130516112206-00023-ip-10-60-113-184.ec2.internal.warc.gz"}
|
http://math.stackexchange.com/questions/218434/evaluating-limits-mathematically?answertab=votes
|
# Evaluating Limits Mathematically
So here's an example of the kind of problem i'm talking about: limits. How exactly do I go about evaluating something like that. I can see and kind of figure it out and the answers make sense, but how do I do this mathematically? Thanks
-
If you look at the fractional exponent $\frac {3}{3-x}$ you can see where you're going. You're approaching 3 from the right side, so the numbers you're going through are larger than 3. For example, 4, 5, 6, etc. So if you were to plug in these values you would get a negative fraction, and $e^{-number}$ =$\frac{1}{e^{number}}$, so you can see that as you get closer to 3 (from the right direction), the $e^{\frac{3}{3-x}}$ gets smaller, i.e. approaches zero.
-
Mathematically: $\lim_{x \to a} f(x) = L$ means: $$\forall \epsilon > 0 \exists \delta > 0$$ so that $$|x - a| < \delta \Rightarrow |f(x) - L| < \epsilon$$
-
so you are trying to figure out $\lim_{x\rightarrow 3^+}\exp(3/(3-x))$ and $\lim_{x\rightarrow 3^-}\exp(3/(3-x))$.
$exp(z)$ is a continuous function so when taking limits, they will pass inside. So $\lim_{x\rightarrow 3^+}\exp(3/(3-x))=\exp(\lim_{x\rightarrow 3^+} 3/(3-x))$ and similarly from the other side. Now, $\lim_{x\rightarrow 3^+}3/(3-x)=\infty$ and $\lim_{x\rightarrow 3^-}3/(3-x)=-\infty$, so it amounts to figuring out $\exp(+\infty)$ and $\exp(-\infty)$ one of which is infinity and the other 0, respectively.
-
|
2015-10-10 03:55:19
|
{"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": 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": 0.9192146062850952, "perplexity": 96.58858982949488}, "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/1443737940789.96/warc/CC-MAIN-20151001221900-00172-ip-10-137-6-227.ec2.internal.warc.gz"}
|
https://castingoutnines.wordpress.com/tag/prime/
|
# Tag Archives: prime
## It’s official: They’re prime
The numbers believed to be the 45th and 46th Mersenne primes have been proven to be prime. The 45th Mersenne prime is $2^{37156667} -1$ and the 46th is $2^{43112609} - 1$.Full text of these numbers is here and here.
Of course what you are really wanting to know is how my spreadsheet models worked out for predicting the number of digits in these primes. First, the data:
• Number of digits actually in $M_{45}$: 11,185,272
• Number of digits actually in $M_{46}$: 12,978,189
My exponential model ($d = 0.5867 e^{0.3897 n}$) was, unsurprisingly, way off — predicting a digit count of over 24.2 million for $M_{45}$ and over 35.8 million for $M_{46}$. But the sixth-degree polynomial — printed on the scatterplot at the post linked to above — was… well, see for yourself:
• Number of digits predicted by 6th-degree polynomial model for $M_{45}$: 11,819,349
• Number of digits predicted by 6th-degree polynomial model for $M_{46}$: 13,056,236
So my model was off by 634,077 digits — about 6% error — for $M_{45}$. But the difference was only 78,047 digits for $M_{46}$, which is only about 0.6% error. That’s not too bad, if you asked me.
There’s only one piece of bad news that prevents me from publishing this amazing digit-count predicting device, and you can spot it in the graph of the model:
So evidently the number of digits in $M_{n}$ will max out around $M_{49}$ and then the digit count will begin to decrease, until somebody discovers $M_{55}$, which will actually have no digits whatsoever. Um… no.
1 Comment
Filed under Crypto, Geekhood, Math
## It’s a prime! And another prime!
The number believed to be the 45th Mersenne prime has turned out actually to be a prime, according to GIMPS. The verification was completed on 6 September and announced on 7 September.
But in a fairly extraordinary turn of events, yet another number was submitted to the GIMPS servers as the next possible Mersenne prime on 6 September — and the initial verification shows that it is prime too! So we now have the 45th and 46th Mersenne primes discovered within two weeks of each other, which is incredible.
No word yet on the details of these primes. We’ll soon see who wins the Mersenne prime digit-guessing challenge. You can still play along with your own spreadsheet too!
Comments Off on It’s a prime! And another prime!
Filed under Math
## New Mersenne prime discovered?
GIMPS is reporting that on 23 August a new Mersenne prime was reported to their server. Verification began today and should take about two weeks to complete. No word on what the prime was, how many digits, etc.
The last Mersenne prime discovered was $2^{32,582,657}-1$, back in 2006 (blogged about here) and weighed in at a whopping 9,808,358 digits. Any bets on how big this new one is, if it’s really a prime? I’m guessing 10.5 million digits. Sounds like a good occasion for a nerd office pool.
Update: Isabel at God Plays Dice likes 14.5 million digits instead, and she’s actually using math and stuff to make that estimate instead of just shooting totally in the dark like I am.
|
2020-02-20 13:36:07
|
{"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": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 15, "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": 0.18588416278362274, "perplexity": 1337.6315799809615}, "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/1581875144979.91/warc/CC-MAIN-20200220131529-20200220161529-00240.warc.gz"}
|
https://nforum.ncatlab.org/discussion/2100/jordan-algebra/?Focus=85232
|
# Start a new discussion
## Not signed in
Want to take part in these discussions? Sign in if you have an account, or apply for one below
## Site Tag Cloud
Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.
• CommentRowNumber1.
• CommentAuthorJohn Baez
• CommentTimeNov 9th 2010
I wanted to record a result by Max Koecher on cones and Jordan algebras, and I wound up drastically expanding the page
Jordan algebra
• CommentRowNumber2.
• CommentAuthorUrs
• CommentTimeNov 9th 2010
• CommentRowNumber3.
• CommentAuthorUrs
• CommentTimeApr 25th 2013
• (edited Apr 25th 2013)
I have edited a bit at Jordan algebra:
• moved the in-line references to the References-section and replaced them with corresponding pointers;
• renamed what used be titled “Idea” into “Definition” and instead added an attempt at an actual “Idea”-section.
• split up what used to be the section “Formally real Jordan algebras” into “Formally real Jordan algebras and their origin in quantum physics” and “Classification of formally real Jordan algebras”
• to the new “Formally real Jordan algebras and their origin in quantum physics” I have added remarks on how the symmetrized Jordan product relates to the more famous commutator and how both can be seen to be two pieces of the deformation quantization of a Poisson manifold.
• CommentRowNumber4.
• CommentAuthorTobyBartels
• CommentTimeOct 13th 2013
I made the commutator into the usual one (no $1/2$, requiring a $1/2$ elsewhere). Although one could have differing conventions, I think that this best fits with the bit on deformation quantization: the Poisson bracket deforms to the commutator without $1/2$, while the pointwise multiplication deforms to the anticommutator (the Jordan multiplication) with $1/2$.
• CommentRowNumber5.
• CommentAuthorUrs
• CommentTimeOct 13th 2013
sure, thanks.
• CommentRowNumber6.
• CommentAuthorTobyBartels
• CommentTimeOct 14th 2013
OTOH, the Lie product in a $JLB$-algebra uses half the commutator, so I put in a remark about that (including the important link to JLB-algebra!).
• CommentRowNumber7.
• CommentAuthorDavid_Corfield
• CommentTimeJun 8th 2020
An edit worth reporting rev 43.
• CommentRowNumber8.
• CommentAuthorDavid_Corfield
• CommentTimeJul 3rd 2020
• (edited Jul 3rd 2020)
John Baez has been thinking about the relation between Lie algebras, Jordan algebras and Noether’s theorem in
Since super-Lie algebras are needed in physics, that got me wondering if there are super-Jordan algebras. I see there are one or two mentions, such as
We could also have started from a super Jordan algebra [14,15] instead of a Jordan algebra
in
• Sultan Catto, Yasemin Gürcan, Amish Khalfan and Levent Kurt, Quantum Symmetries: From Clifford and Hurwitz Algebras to M-Theory and Leech Lattices, pdf
and
It is also possible to consider super Jordan algebras for generalized Jordan algebras involving both bosonic and fermionic observables. In this case the automorphism group is a supergroup.
in
• Čestmir Burdik and Sultan Catto, Hurwitz Algebras and the Octonion Algebra, (paper)
There are some older papers, such as
which I can’t access. Seems like a natural idea, no?
• CommentRowNumber9.
• CommentAuthorDavid_Corfield
• CommentTimeJul 3rd 2020
Oh, I’m forgetting the commutativity of terms – should be looking for ’Jordan superalgebra’, then there are plenty of hits.
|
2021-12-03 07:37:12
|
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 5, "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": 0.6373561024665833, "perplexity": 4780.477144043052}, "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/1637964362605.52/warc/CC-MAIN-20211203060849-20211203090849-00152.warc.gz"}
|
https://eccc.weizmann.ac.il/keyword/19770/
|
Under the auspices of the Computational Complexity Foundation (CCF)
REPORTS > KEYWORD > REFLECTION PRINCIPLES:
Reports tagged with reflection principles:
TR19-084 | 26th May 2019
Michal Garlik
#### Resolution Lower Bounds for Refutation Statements
For any unsatisfiable CNF formula we give an exponential lower bound on the size of resolution refutations of a propositional statement that the formula has a resolution refutation. We describe three applications. (1) An open question in [Atserias-Müller,2019] asks whether a certain natural propositional encoding of the above statement is ... more >>>
TR20-037 | 18th March 2020
Michal Garlik
#### Failure of Feasible Disjunction Property for $k$-DNF Resolution and NP-hardness of Automating It
We show that for every integer $k \geq 2$, the Res($k$) propositional proof system does not have the weak feasible disjunction property. Next, we generalize a recent result of Atserias and Müller [FOCS, 2019] to Res($k$). We show that if NP is not included in P (resp. QP, SUBEXP) then ... more >>>
TR21-138 | 23rd September 2021
Rahul Santhanam, Iddo Tzameret
#### Iterated Lower Bound Formulas: A Diagonalization-Based Approach to Proof Complexity
We propose a diagonalization-based approach to several important questions in proof complexity. We illustrate this approach in the context of the algebraic proof system IPS and in the context of propositional proof systems more generally.
We give an explicit sequence of CNF formulas $\{\phi_n\}$ such that VNP$\neq$VP iff there are ... more >>>
ISSN 1433-8092 | Imprint
|
2021-10-18 17:04:46
|
{"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": 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": 0.7376206517219543, "perplexity": 1980.5923598904915}, "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-2021-43/segments/1634323585204.68/warc/CC-MAIN-20211018155442-20211018185442-00696.warc.gz"}
|
https://scriptinghelpers.org/questions/405/how-would-i-make-a-automatic-weapon
|
0
# How would I make a Automatic Weapon?
Lineout 10
7 years ago
What would be the system I would have to do to make a gun automatic? I've done it before but totally forgot. If anyone of you could help I would be very happy :D
1
local Shooting = false
|
2021-06-12 13:27:31
|
{"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": 0.1769568771123886, "perplexity": 691.246664737975}, "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/1623487584018.1/warc/CC-MAIN-20210612132637-20210612162637-00157.warc.gz"}
|
https://ansaurus.com/question/452114-section-heading-for-references-and-the-actual-citations-are-squished-together-in-latex
|
392
2
+1 Q:
## Section heading for references and the actual citations are squished together in LaTeX.
This must be a common problem because I see it in many published papers but it seems to be quite tricky to google for. You can insert a bibliography like so
``````\bibliographystyle{plain}
\bibliography{foo}
``````
and everything works as expected except there is sometimes (I have no idea what circumstances cause this -- it seems random to me) no space between the section heading (e.g., "7. References") and the start of the actual references. The section heading and first citation appear all squished together. It's not utterly egregious but seems to me to be unambiguously a flaw in the typesetting.
I've been putting up with it for years but someone somewhere must have noticed this and been obsessive-compulsive enough to track it down and figure out what causes it and how to correct it.
I thought this would be a good place to record the solution. Let me know if you can think of ways to make this more googlable.
+1 A:
It turns out that LaTeX will sometimes remove the space between the References section header and the start of the actual references if it is trying to avoid having the document spill over to an extra page.
So one workaround is to either lengthen or shorten the document so it's not on the brink of spilling over to an additional page.
A related workaround (thanks to bluebrother's answer) is to explicitly tell LaTeX to allow the page with the start of the references a little extra vertical space (eating into the bottom margin slightly). That can be done with the following command right before the "`\bibliographystyle{plain}`":
``````\enlargethispage{\baselineskip}
``````
Another workaround that seems to work:
1. Change to \bibliographystyle{amsalpha}
2. Recompile
3. Change back to \bibliographystyle{plain}
4. Recompile
5. (Don't recompile again or it will re-squish it.)
+1 A:
Not sure if that's the cause, but in case the bibliography can be fit on the page by removing that space you could try to use `\enlagethispage{someamount}`
Oh ho, I think that will totally work. (Note typo in "enlargethispage".)
|
2021-07-29 11:55:03
|
{"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": 0.8378590941429138, "perplexity": 972.266280523497}, "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-2021-31/segments/1627046153857.70/warc/CC-MAIN-20210729105515-20210729135515-00422.warc.gz"}
|
https://forum.wilmott.com/viewtopic.php?f=15&t=100864&p=834918
|
SERVING THE QUANTITATIVE FINANCE COMMUNITY
Cuchulainn
Posts: 58706
Joined: July 16th, 2004, 7:38 am
Location: Amsterdam
Contact:
### Re: Peak Life passed
• Mormon men who never smoked, attend church at least weekly, obtained at least 12 years of education and are married have a 50 percent less chance, on average over the years, of dying than their national counterparts.
Well, that's a hard act to follow.
Traden4Alpha
Posts: 23951
Joined: September 20th, 2002, 8:30 pm
### Re: Peak Life passed
• Mormon men who never smoked, attend church at least weekly, obtained at least 12 years of education and are married have a 50 percent less chance, on average over the years, of dying than their national counterparts.
Well, that's a hard act to follow.
So, 50% of them are immortal....
Methinks this must be based on self-reported age data and Mormon men with multiple wives (and mother-in-laws) report they feel like they've lived an eternity.
DavidJN
Posts: 1713
Joined: July 14th, 2002, 3:00 am
### Re: Peak Life passed
ppauper
Posts: 70239
Joined: November 15th, 2001, 1:29 pm
### Re: Peak Life passed
Air pollution now kills 3.3 million people prematurely every year – more than HIV, malaria and influenza combined – with emissions from diesel engines among the worst culprits; a joint investigation by the Guardian and Greenpeace showed hundreds of thousands of schoolchildren across England and Wales are being exposed to illegal air toxicity levels from diesel vehicles. And yet such was the more or less widely accepted thinking as recently as Superbowl XLIV in 2010 – namely, that cars running on diesel fuel could be driven with a pure, unclouded conscience.
In Norway they lowered taxes on diesel cars and put up taxes on gasoline cars. This despite plenty of evidence that diesel is much more dangerous for humans and animals. But the focus was only on CO2 (food for plants, and no toxicity for humans and animals for the levels we are talking about in the atmosphere). Scandalous!
I believe the same thing held for the european union, which is why diesel at one point had more than a 50% share of the auto market in the eu compared to what, 1% in the US.
And I suspect the tax advantages extended to the fuel as well as the cars, and they taxed diesel fuel preferentially compared to gasoline.
There's all sorts of nasty crap in diesel, including lots and lots of particulate matter
Not just scandalous but also stupid.
Cuchulainn
Posts: 58706
Joined: July 16th, 2004, 7:38 am
Location: Amsterdam
Contact:
### Re: Peak Life passed
This is Vladimir Putin's hero!
katastrofa
Posts: 7375
Joined: August 16th, 2007, 5:36 am
Location: Alpha Centauri
### Re: Peak Life passed
Thanks! Cool stuff. I've learnt a quite lot about the diet of ancient Egypt in Museo Egizio in Turin, but they had direct evidence in the form of food found in the graves.
Collector
Topic Author
Posts: 4143
Joined: August 21st, 2001, 12:37 pm
### Re: Peak Life passed
Thanks! Cool stuff. I've learnt a quite lot about the diet of ancient Egypt in Museo Egizio in Turin, but they had direct evidence in the form of food found in the graves.
Also humans and cats where found in the graves? some of them mummified!
Egypt before or after Jared?
katastrofa
Posts: 7375
Joined: August 16th, 2007, 5:36 am
Location: Alpha Centauri
### Re: Peak Life passed
They killed kittens Good that Libyans destroyed them.
Cuchulainn
Posts: 58706
Joined: July 16th, 2004, 7:38 am
Location: Amsterdam
Contact:
### Re: Peak Life passed
They killed kittens Good that Libyans destroyed them.
Stray kats. Fell down the chutes.
Collector
Topic Author
Posts: 4143
Joined: August 21st, 2001, 12:37 pm
### Re: Peak Life passed
UK:
Life expectancy to fall one year, with middle classes among hardest hit
And they said “awful” increases in death rates in recent years had forced the Office for National Statistics (ONS) to revise its forecasts, reducing UK predicted life span by almost a full year."
"The researchers called for an urgent investigation into the recent spike in deaths, which they said could not be explained by the increase in flu or the ageing population."
Rapid rise in mortality in England and Wales in early 2018 – an investigation is needed
US
"Life expectancy in the U.S. dropped for the second year in a row, according to the CDC’s National Center for Health Statistics."
just the beginning, complete lack of understanding risks among bureauc-rats will almost for sure ensure this is just the beginning of a ugly trend. When no skin in the game people with no clue about risk is in charge this is the result, likely the begging of the ugly result...
Collector
Topic Author
Posts: 4143
Joined: August 21st, 2001, 12:37 pm
### Re: Peak Life passed
Britain and the US are the only two western nations where life expectancy is FALLING - as experts compare the 'major warning sign' to the post-Soviet era
"However only the UK and US failed to rebound, according to data published in the British Medical Journal."
"Official figures revealed 10,000 more people died in the first two months of this year that expected - the largest jump since World War Two."
just the beginning (?)
rmax
Posts: 6062
Joined: December 8th, 2005, 9:31 am
### Re: Peak Life passed
A friend went to the doctors the other day. He said he wanted to live forever.
So the doctors asked him if he drank, smoked, took drugs, drove fast cars or had multiple sexual partners.
He replied no he certainly did not do those things.
The doctor then asked: Why on earth do you want to live forever?
Cuchulainn
Posts: 58706
Joined: July 16th, 2004, 7:38 am
Location: Amsterdam
Contact:
### Re: Peak Life passed
“I told the doctor I broke my leg in two places. He told me to stop going to those places.”
Collector
Topic Author
Posts: 4143
Joined: August 21st, 2001, 12:37 pm
### Re: Peak Life passed
Life expectancy falls by six months in biggest drop in UK forecasts March 2019
"Decline in longevity in England and Wales ‘a trend as opposed to a blip’, experts say"
"Falling longevity has accelerated. Last year’s analysis cut forecasted life expectancy by two months. This year it took off another six months." "Compared with 2015, projections for life expectancy are now down by 13 months for men and 14 months for women."
and these bureaucrats think the solution is to "work" longer:
"The state pension age is planned to rise to 68 in 2037, and the government has floated the idea of increasing it to 70 "
what will the point be called when pension age is above life expectancy? The age of machine learning perhaps...
Collector
Topic Author
Posts: 4143
Joined: August 21st, 2001, 12:37 pm
### Re: Peak Life passed
For the third consecutive year, life expectancy in the U.S. has fallen.
stay healthy, eat plenty of fish (preferably Norwegian farmed ? from the country of fresh air and waters )
ABOUT WILMOTT
Wilmott.com has been "Serving the Quantitative Finance Community" since 2001. Continued...
JOBS BOARD
Looking for a quant job, risk, algo trading,...? Browse jobs here...
GZIP: On
|
2019-04-20 21:22:05
|
{"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": 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": 0.2044229358434677, "perplexity": 8788.928740152007}, "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-2019-18/segments/1555578530040.33/warc/CC-MAIN-20190420200802-20190420222802-00521.warc.gz"}
|
https://www.subjectcoach.com/tutorials/math/topic/prekinder-to-grade-2-mathematics/chapter/displaying-the-results-from-a-survey
|
Displaying the Results from a Survey
There's not much point in conducting a survey if you aren't going to tell anyone about your results. This article contains suggestions for some good ways to display the results from your survey. Always remember that the choices you make depend on the data you have and the conclusions you want to draw from your data.
Tables
If your survey is very simple, you might be able to use a table to display your data. Tables provide a simple way of showing people your results. Don't forget to give your table a title so that people looking at it will understand what your survey was about.
Statistics
Statistics like the mean, maximum and minimum values, and standard deviation can be used to give you a summary of the results from survey.
For example, if you survey the people in your class to find out how old they are, it might be more meaningful to report a summary like this, rather than a list of exact ages:
• Youngest Person: $7$ years
• Oldest Person: $9$ years
• Average Age: $8.2$ years
Graphs
Graphs provide a useful way to summarise your data. They can make it easy to see the relative sizes of different categories, or they can highlight trends in your data.
Here are some of the graphs that you might use to display your data:
A line graph shows you information that is connected somehow. For example, you might use a line graph to show how something has increased, decreased or stayed the same over time.
A bar chart is useful when you want to be able to work out how the sizes of different categories compare to each other. Perhaps you want to be able to quickly identify which one of a collection of categories is most popular, and which one is least popular.
A pie chart is useful when you want to find what proportion of the entire population each category makes up. Pie charts are often labelled with the percentages of the population that falls into each category.
Pictographs provide a fun and interesting way of presenting data. A pictograph should include a key telling you what each picture stands for. Pictographs may not be very accurate, but they are useful for quickly showing you the relative sizes of each category.
Sometimes surveys include questions that give people the opportunity to state their opinions of something, or to comment on something that is relevant to the survey. If your survey does this, you can report the more interesting comments made by people. You might like to arrange them in a table.
For example, you might say:
"In response to the question "Why don't you like brussels sprouts?", we received the following interesting replies:"
• "Because they don't mix well with honey."
• "Because my dog refuses to eat them."
Writing a Report
Finally, you should write a report that talks about what you have found out, any conclusions you have drawn, and what action you are likely to take as a result of your survey.
Description
This mini book covers the core of Math for Foundation, Grade 1 and Grade 2 mathematics including
1. Numbers
3. Subtraction
4. Division
5. Algebra
6. Geometry
7. Data
8. Estimation
9. Probability/Chance
10. Measurement
11. Time
12. Money
13. and much more
This material is provided free of cost for Parent looking for some tricks for their Prekinder, Kinder, Prep, Year 1 and Year 2 children
Learning Objectives
These lessons are for kids aged 4-8 with the core objective to expose their brains to concepts of addition, subtraction, division, algebra and much more.
Author: Subject Coach
You must be logged in as Student to ask a Question.
None just yet!
|
2019-09-20 05:26:51
|
{"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": 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": 0.3628614842891693, "perplexity": 745.2688852631366}, "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-2019-39/segments/1568514573832.23/warc/CC-MAIN-20190920050858-20190920072858-00216.warc.gz"}
|
https://afrouzi.com/DRIPs.jl/dev/syntax/
|
## Methods for Steady State of DRIPs
DRIPs.DripType
Summary
A [Mutable] Structure for LQG Dynamic Rational Inattention Problems (DRIPs)
Fields
Primitives of the DRIP
ω : Cost of information
β : Discount factor
A : Transition matrix: x=Ax+Qu
Q : Std. Dev. matrix: x=Ax+Qu
H : Mapping of shocks to actions: v=-0.5(a'-x'H)(a-H'x)
Solution of the DRIP in the Steady State
K : Kalman gain matrix
Y : Weight vector for evolution of actions
Σ_z : Covariance matrix of the rational inattention error
Σ_p : Steady-state posterior covariance matrix under the solution
Σ_1 : Steady-state prior covariance matrix under the solution
Ω : Dynamic benefit matrix
err : Convergence error for the solution
source
DRIPs.solve_dripMethod
solve_drip(ω,β,A,Q,H;
fcap = false,
Ω0 = H*H',
Σ0 = A*A'+Q*Q',
w = 1,
tol = 1e-4,
maxit = 10000) -> Drip
Solves for the steady state of a Dynamic Rational Inattention Problem (DRIP) defined by the arguments. See Afrouzi and Yang (2019) for details.
Arguments
The function takes the primitives of the Drip as arguments:
* ω : Cost of information
* β : Discount factor
* A : Transition matrix: x=Ax+Qu
* Q : Std. Dev. matrix: x=Ax+Qu
* H : Mapping of shocks to actions: v=-0.5(a'-x'H)(a-H'x)
Optional Arguments
Default values are set unless specified otherwise by user.
* fcap = false [if true then solves the problem with fixed capacity = ω bits]
* Ω0 = H*H' [initial guess for steady state information matrix]
* Σ0 = A*A'+Q*Q'[initial guess for steady state prior]
* w = 1 [updating weight on the new guess in iteration]
* tol = 1e-4 [tolerance level for convergence]
* maxit = 10000 [maximum number of iterations]
Outputs
The function returns a Drip structure with the primitives and the solution objects:
* Y : Weight vector for evolution of actions
* Σ_z : Covariance matrix of the rational inattention error
* K : Kalman gain matrix
* Σ_1 : Steady-state prior covariance matrix under the solution
* Σ_p : Steady-state posterior covariance matrix under the solution
* Ω : Dynamic benefit matrix
Examples
julia> P = solve_drip(ω,β,A,Q,H)
source
DRIPs.solve_dripMethod
solve_drip(P::Drip;...) -> Drip
Same as above but infers ω,β,A,Q and H from P and returns a Drip structure with the primitives and the solution.
Examples
julia> P = Drip(ω,β,A,Q,H)
julia> P = solve_drip(P)
source
## Methods for Transition dynamics of DRIPs
DRIPs.SignalType
Summary
A Signal Structure for Information Treatments in DRIPs. The structure encodes the signal S = L'*x+z, z₀~N(0,Σ_z).
Fields
• L : loading of the signal on x
• Σ_z : variance covariance matrix of the noise
source
DRIPs.TripType
Summary
A Structure for the Transition dynamics of Rational Inattention Problems (TRIPs)
Fields
P : a DRIP structure with its primitives and steady state solution
T : length of TRIP
Σ_1s : sequence of prior covariance matrices
Σ_ps : sequence of posterior covariance matrices
Ωs : sequence of information benefit matrices
Ds : eigenvalues of Σ_t^(0.5)Ω_tΣ_t^(0.5) over time (marginal values of information)
err : convergence err
source
DRIPs.solve_tripMethod
solve_trip(Ss::Drip, # steady state of D.R.I.P.
Σ0::Array{Float64,2}; # initial prior matrix
T = 100, # optional: guess for time until convergence to steady state
tol = 1e-4, # optional: tolerance for convergence
maxit = 1000 # optional: max iterations
) -> Trip
Solves for the transition dynamics of the optimal information structure starting from the initial prior distribution with covariance matrix Σ0. See Afrouzi and Yang (2019) for details.
Outputs
Returns a Trip structure with the steady state and transition path of the optimal information structure.
Examples
julia> Ss = solve_drip(ω,β,A,Q,H)
julia> Σ0 = 0.1*Ss.Σ_1;
julia> Pt = solve_trip(Ss,Σ0);
source
DRIPs.solve_tripMethod
solve_trip(Ss::Drip, # steady state of D.R.I.P.
S::Signal; # information treatment in the steady state
T = 100, # optional: guess for time until convergence to steady state
tol = 1e-4, # optional: tolerance for convergence
maxit = 1000 # optional: max iterations
) -> Trip
Solves for the transition dynamics of the optimal information structure starting from a one time treatment with a signal S in the steady state. See Afrouzi and Yang (2019) for details.
Outputs
Returns a Trip structure with the steady state and transition path of the optimal information structure.
Examples
julia> Ss = solve_drip(ω,β,A,Q,H)
julia> S = Signal(L,Σ_z);
julia> Pt = solve_trip(Ss,S);
source
## Methods for Impulse Response Functions
DRIPs.DripirfsType
Summary
A Structure for the impulse response functions of DRIPs
Fields
T : length of IRFs
x : IRFs of the fundamental shocks
x_hat : IRFs of beliefs
a : IRFs of actions
In particular, if n is the dimension of x, m is the dimension of a and k is the number of structural shocks, then
• x has dimension n*k*T where x(i,j,:) is the impulse response function of the i'th dimension of x to the j'th structural shock.
• x_hat has dimension n*k*T where x_hat(i,j,:) is the impulse response function of the agent's average belief about the i'th dimension of x to the j'th structural shock.
• a has dimension m*k*T where a(i,j,:) is the impulse response function of the i'th action to the j'th structural shock.
source
DRIPs.dripirfsMethod
dripirfs(Ss::Drip, # Steady state of the DRIP (when treatment happens)
S::Signal; # Signal for treatment at time 0
T = 40, # optional: length of irfs
reoptimize = true, # optional: if true gives the irfs with reoptimized signals, if false with steady state signals
trip = false # optional: if false solves for the optimal trip, if = P::trip then takes P as the transition dynamics after treatment
) -> Dripirfs
Returns a Dripirfs structure with the impulse response functions of the fundamental (x), beliefs (x_hat) and actions (a) to all the structural shocks under the information structure implied by a one time information treatment with S in the steady state of the DRIP P. In particular, if n is the dimension of x, m is the dimension of a and k is the number of structural shocks, then
• x has dimension n*k*T where x(i,j,:) is the impulse response function of the i'th dimension of x to the j'th structural shock.
• x_hat has dimension n*k*T where x_hat(i,j,:) is the impulse response function of the agent's average belief about the i'th dimension of x to the j'th structural shock.
• a has dimension m*k*T where a(i,j,:) is the impulse response function of the i'th action to the j'th structural shock.
source
DRIPs.dripirfsMethod
dripirfs(P::Drip; # Steady state of the DRIP
T = 40 # Optional: length of impulse response functions
) -> Dripirfs
Returns a Dripirfs structure with the impulse response functions of the fundamental (x), beliefs (x_hat) and actions (a) to all the structural shocks under the steady state information strucutre. In particular, if n is the dimension of x, m is the dimension of a and k is the number of structural shocks, then
• x has dimension n*k*T where x(i,j,:) is the impulse response function of the i'th dimension of x to the j'th structural shock.
• x_hat has dimension n*k*T where x_hat(i,j,:) is the impulse response function of the agent's average belief about the i'th dimension of x to the j'th structural shock.
• a has dimension m*k*T where a(i,j,:) is the impulse response function of the i'th action to the j'th structural shock.
source
DRIPs.dripirfsMethod
dripirfs(P::Trip; # Transition dynamics of the DRIP
T = 40 # Optional: length of impulse response functions
) -> Dripirfs
Returns a Dripirfs structure with the impulse response functions of the fundamental (x), beliefs (x_hat) and actions (a) to all the structural shocks under the information structure implied by P. In particular, if n is the dimension of x, m is the dimension of a and k is the number of structural shocks, then
• x has dimension n*k*T where x(i,j,:) is the impulse response function of the i'th dimension of x to the j'th structural shock.
• x_hat has dimension n*k*T where x_hat(i,j,:) is the impulse response function of the agent's average belief about the i'th dimension of x to the j'th structural shock.
• a has dimension m*k*T where a(i,j,:) is the impulse response function of the i'th action to the j'th structural shock.
source
## Methods for Simulating DRIPs
DRIPs.dripsimsMethod
dripsims(P::Drip; # Steady state of the DRIP
T = 500, # Optional: length of simulation
N = 1, # Optional: number of simulated agents
burn = 100, # Optional: length of initial burn (in addition to T)
seed = true # Optional: seed number for fundamental shocks
) -> Dripirfs
Returns a Dripirfs structure with a simulated path of the fundamental (x), beliefs (x_hat) and actions (a) under the steady state information structure. In particular, if n is the dimension of x and m is the dimension of a, then
• x has dimension n*T where x(:,t) is the simulated value of x at time t.
• x_hat has dimension n*N*T where x_hat(:,i,t) is the simulated value of x_hat of agent i at time t.
• a has dimension m*N*T where a(:,i,t) is the the simulated value of x_hat of agent i at time t.
source
## Aux. Functions
DRIPs.capacityMethod
capacity(P::Drip; # Drip structure
unit = "bit" # optional: unit of capacity (bit or nat).
)
Returns the amount of information processes per unit of time in the steady state of the DRIP P.
source
DRIPs.infinitesumMethod
infinitesum(func; tol = 1e-6,maxit = 1000,start=0)
Returns the infinite sum Σₓfunc(x) starting from x = start up to tolderance tol or max iteration maxit.
source
|
2020-05-26 04:48:56
|
{"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": 0.8100327253341675, "perplexity": 4405.509406758676}, "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-2020-24/segments/1590347390442.29/warc/CC-MAIN-20200526015239-20200526045239-00567.warc.gz"}
|
http://sepwww.stanford.edu/data/media/public/docs/sep107/paper_html/node35.html
|
Next: Regularization after binning: missing Up: Iterative data regularization Previous: Iterative data regularization
# One-dimensional synthetic examples
The simple test examples in this section are borrowed from Claerbout (1999).
data Figure 1 The input data (right) are irregularly spaced samples of a sinusoid (left).
In the first example, the input data were randomly subsampled (with decreasing density) from a sinusoid (Figure ). The forward operator in this case is linear interpolation. In other words, we seek a regularly sampled model on 200 grid points that could predict the data with a forward linear interpolation. Sparse irregular distribution of the input data makes the regularization enforcement a necessity. Following Claerbout (1999), I applied convolution with the simple (1,-1) difference filter as the operator that forces model continuity (the first-order spline). An appropriate preconditioner in this case is recursive causal integration. Figures and show the results of inverse interpolation after exhaustive 300 iterations of the conjugate-direction method. The results from the model-space and data-space regularization look similar except for the boundary conditions outside the data range. As a result of using the causal integration for preconditioning, the rightmost part of the model in the data-space case stays at a constant level instead of decreasing to zero. If we specifically wanted a zero-value boundary condition, we could easily implement it by adding a zero-value data point at the boundary.
im1 Figure 2 Estimation of a continuous function by the model-space regularization. The difference operator is the derivative operator (convolution with (1,-1)).
fm1 Figure 3 Estimation of a continuous function by the data-space regularization. The preconditioning operator is causal integration.
As expected from the general theory, the model preconditioning provides a much faster rate of convergence. I measured the rate of convergence using the model residual, which is a distance from the current model to the final solution. Figure shows that the preconditioning (data regularization) method converged to the final solution in about 6 times fewer iterations than the model regularization. Since the cost of each iteration for each method is roughly equal, the computational economy is evident. Figure shows the final solution, and the estimates from model- and data-space regularization after only 5 iterations of conjugate directions. The data-space estimate looks much closer to the final solution than its competitor.
early1
Figure 4
The top figure is the exact solution found in 250 iterations. The middle is with data-space regularization after 5 iterations. The bottom is with model-space regularization after 5 iterations.
schwab1 Figure 5 Convergence of the iterative optimization, measured in terms of the model residual. The d'' points stand for data-space regularization; the m'' points for model-space regularization.
Changing the preconditioning operator changes the regularization result. Figure shows the result of data-space regularization after a triangle smoother is applied as the model preconditioner. Triangle smoother is a filter with the Z-transform Claerbout (1992). I chose the filter length N=6.
fm6 Figure 6 Estimation of a smooth function by the data-space regularization. The preconditioning operator is a triangle smoother.
If, instead of looking for a smooth interpolation, we want to limit the number of frequency components, then the best choice for the model-space regularization operator is a prediction-error filter (PEF). To obtain a mono-frequency output, we can use a three-point PEF, which has the Z-transform representation D (Z) = 1 + a1 Z + a2 Z2. In this case, the corresponding preconditioner P could be the three-point recursive filter P (Z) = 1 / (1 + a1 Z + a2 Z2). To test this idea, I estimated the PEF D (Z) from the output of inverse linear interpolation (Figure ), and ran the data-space regularized estimation again, substituting the recursive filter P (Z) = 1/ D(Z) in place of the causal integration. I repeated this two-step procedure three times to get a better estimate for the PEF. The result, shown in Figure , exhibits the desired mono-frequency output.
pm1 Figure 7 Estimation of a mono-frequency function by the data-space regularization. The preconditioning operator is a recursive filter (the inverse of PEF).
Next: Regularization after binning: missing Up: Iterative data regularization Previous: Iterative data regularization
Stanford Exploration Project
12/28/2000
|
2017-11-24 03:35:07
|
{"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": 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": 0.7852909564971924, "perplexity": 1473.432523710282}, "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/1510934807084.8/warc/CC-MAIN-20171124031941-20171124051941-00053.warc.gz"}
|
https://www.concepts-of-physics.com/pw/html/a/da/fda.html
|
IIT JEE Physics (1978-2018: 41 Years) Topic-wise Complete Solutions
# To get image from plane mirrors with no lateral inversion
## Objective
To get image from plane mirrors with no lateral inversion.
## Introduction
When image is formed in a plane mirror, it is laterally inverted. Our mind is trained to recognize this lateral inversion and hence we have no problem in combing our hair or adjusting our ear rings. However, if you use a pair of mirrors and see the image after two reflections, the lateral inversion will go away. You can design several interesting activities using this fact.
## Apparatus
Two plane mirrors joined together with arrangement to place them vertically at an angle, a cap with colored strips marked.
## Procedure
1. Place the two mirrors vertically in the same plane ($$\theta=180\, \mathrm{degree}$$) and at a height where you can see the image of your face.
2. Tilt the mirror to reduce the angle between them till you start seeing image of boundary of one mirror into the other. Position your head so that you see your image in each of the mirrors.
3. Ask your friend to stand in this position looking at his/her image.
4. Put the cap on the friend’s head.
5. Now starts the game. You will be calling the colour and the friend has to touch that colour in one go. Call `red’ and see if your friend is able to touch red in one go. Similarly do for more colours.
6. Put a strip of paper with some words written on it. Look at the image in any of the mirrors. How does it look like?
Question: Draw a ray diagram to explain the above findings.
|
2020-10-27 18:54:34
|
{"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": 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": 0.3727830648422241, "perplexity": 918.173299824153}, "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-2020-45/segments/1603107894426.63/warc/CC-MAIN-20201027170516-20201027200516-00430.warc.gz"}
|
https://www.actucation.com/calculus-1/definition-and-value-of-function
|
Informative line
### Definition And Value Of Function
Learn definition of a function with piecewise defined function formula and practice problems of graphing absolute value & linear functions with examples & equations.
# Definition and Value of a Function
Whenever one quantity depends on the other we say that first quantity is a function of the second. So basically we can say
(depends on ⇒ function of) in Calculus
For example the area of a square depends on the length of its sides, so we say
$$A = \ell^2$$ (Where A is the area of square and $$\ell$$ is the length of its side)
We will say Area is a function of length of sides .
$$A(\ell) = \ell^2$$
$$\ell$$ will be called the independent variable and A the dependent variable.
• So function is a rule that assigns to each element 'x' in a set A a unique element in set B (called f(x) or y). Note that for every x there should be only one f(x).
• Set A and B are usually the sets of real numbers.
• Suppose f(x) = some expression or formula in x ,then to obtain f(a) where 'a' is a fixed value put the value of 'a' at all places where x occurs in the expression. The resultant value is f(a).
#### Consider the volume of a sphere which depends on its radius. $$V (r) = {4 \over 3} \pi r^3$$ (V indicates volume and r the radius) Which of the following is correct?
A Volume of sphere is not a function of its radius
B Volume of sphere is a function of its radius
C Volume of sphere will not change when radius change
D An increase in radius of sphere will not change its volume
×
Since the volume depends on radius ⇒ Volume is a function of radius
Note :depends on ⇒ function of
### Consider the volume of a sphere which depends on its radius. $$V (r) = {4 \over 3} \pi r^3$$ (V indicates volume and r the radius) Which of the following is correct?
A
Volume of sphere is not a function of its radius
.
B
Volume of sphere is a function of its radius
C
Volume of sphere will not change when radius change
D
An increase in radius of sphere will not change its volume
Option B is Correct
#### Let $$F(x) = x^2$$ for all real x, then find the value of f(2).
A –6
B –7
C 0
D 4
×
$$F(x) = x^2$$ → given formula
put x = 2 on both sides
$$f(2) = 2^2$$
f(2) = 4
### Let $$F(x) = x^2$$ for all real x, then find the value of f(2).
A
–6
.
B
–7
C
0
D
4
Option D is Correct
# Absolute Value Function
It is a piecewise defined function.
$$f(x)=|x|=\begin{cases} x & if\,\, x\geq0\\ -x & if \, x <0\end{cases}$$
is called absolute value function. It gives us the distance of x from the origin which is always positive.
|–2| = 2, |3| = 3.
Note that the graph follows $$y = x$$ to the right of origin and $$y = –x$$ to the left of origin.
#### If f(x) = |2x – 1| then the value of f(2) is
A 5
B –10
C –7
D 3
×
f(x) = |2x – 1|
put x = 2 on both sides
f(2) = |2 × 2 – 1|
f(2) = |3| = 3
If the value inside the absolute value bracket is positive we return the value, if it is negative we make the sign positive.
### If f(x) = |2x – 1| then the value of f(2) is
A
5
.
B
–10
C
–7
D
3
Option D is Correct
# Odd and Even Functions
• If a function 'f' satisfies
$$f(–x) = f(x)$$ for every x in its domain then we say that it is an even function whereas
if
$$f(–x) = –f(x)$$ for all x in its domain we say that it is an odd function.
(1) $$f(x) = x^2$$ is an example of an even function, as
$$f(-x) = (-x)^2 = (-1)^2 \times x^2 = 1 \times x^2 = x^2$$
$$= f(x)$$
(2) $$f(x) = x^3$$ is an example of an odd function as
$$f(-x) = (-x)^3 = (-1)^3 x^3 = -1 \times x^3 = -x^3$$
$$= –f(x)$$
• To test whether a function is odd or even we apply the definition. Also note that there are functions which are neither odd nor even.
example: $$f(x) = x + x^2$$ is neither odd nor even.
#### Let $$f(x) = 1 - x^4$$ then $$f(x)$$ is
A odd
B even
C neither odd nor even
D nothing can be said
×
$$f(x) = 1- x^4$$
Replace x by –x on both sides
$$f(-x) = 1 - (-x)^4$$
$$f(-x) = 1 - (-1)^4 x^4$$
$$f(-x) = 1 - x^4 = f(x)$$
### Let $$f(x) = 1 - x^4$$ then $$f(x)$$ is
A
odd
.
B
even
C
neither odd nor even
D
nothing can be said
Option B is Correct
# Linear Function and its Sign
• A function of the form $$f(x)=ax+b$$ is called a linear function (its graph represents a straight line, therefore the name).
• This expression takes positive, negative or zero values depending or what values of $$x$$ we take.
#### Consider $$f(x)=x-8$$, what is the sign of this expression for $$x=-9$$ .
A Negative
B Positive
C 0
D Nothing can be said
×
$$f(x)=x-8$$
Put $$x=-9$$ in the expression on both sides.
$$f(-9)=-9-8$$
$$f(-9)=-17\rightarrow$$So the expression is negative.
### Consider $$f(x)=x-8$$, what is the sign of this expression for $$x=-9$$ .
A
Negative
.
B
Positive
C
0
D
Nothing can be said
Option A is Correct
# Piecewise Defined Functions
• Piecewise defined functions are those which are defined by different formulas in different parts of their domain.
• Consider
$$f(x)=\begin{cases} 2x+1 & if\,\, x\leq 1\\ \ x & if \,\, x >1 \end{cases}$$
is a piecewise defined function. For all values of x greater than 1, it is given by x and for those less than or equal to 1, it is given by 2x + 1.
#### A function f is defined by $$f(x)=\begin{cases} 2x^2+1 & if\,\, x\leq -1\rightarrow 1^{st}rule\\ \ 2x+1 & if \,\, x >1\rightarrow\,2^{nd} rule \end{cases}$$ find the value of f(2).
A 1
B 3
C 5
D 9
×
Since 2 is a value greater than –1 so for f(2) we apply $$2^{nd} \space rule$$
f(2) = 2(2) + 1
= 4 + 1 = 5
### A function f is defined by $$f(x)=\begin{cases} 2x^2+1 & if\,\, x\leq -1\rightarrow 1^{st}rule\\ \ 2x+1 & if \,\, x >1\rightarrow\,2^{nd} rule \end{cases}$$ find the value of f(2).
A
1
.
B
3
C
5
D
9
Option C is Correct
|
2018-03-19 12:42:07
|
{"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": 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": 0.81565922498703, "perplexity": 674.3102801321396}, "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-2018-13/segments/1521257646914.32/warc/CC-MAIN-20180319120712-20180319140712-00707.warc.gz"}
|
http://jimkeener.com/posts/teaching-types
|
This blog is about my musings and thoughts. I hope you find it useful, at most, and entertaining, at least.
Quotes
Oak Island
Items for Sale
#### Presence Elsewhere
jim@jimkeener.com
del.icio.us
GitHub
BitBucket
Keybase.io
# AMP and Instant Articles are Good Ideas, but hurt the web
Date: 2016-01-01
Tags: programming c++ types
I've always struggled to come up with a good explanation for types for new programmers. (It is just such an ingrained and intuitive concept for me at this point that it's hard to describe.) Having been playing with both Rust and C++ over the past few weeks, which have extremely expressive type systems, the idiom I'm settling on is that when you're writing a program, you're actually writing two: the "type-program" and the "data-program." The "type-program" is evaluated at compile-time for statically typed languages and concurrently dynamically typed languages. (Note that I left out a distinction between compiled and not-compiled languages. Python, Ruby, and JavaScript, as three examples, all compile to bytecode before execution, but all three are dynamically typed.
What is a "type-program"? It's the validation that the type-systems rules are followed at each expression in the program. For instance, when a+b is encountered, the there must exist a + operator that can accept a left-hand side of the type of a and a right-hand side of the type of b. The evaluation of the + operator doesn't happen, only the validation of the type rules. This happens recursively, so now
Some languages, like Rust and C++ also allow for certain types of (arbitrarily complex) data expressions to be evaluated concurrently with the type-program.
|
2017-11-23 14:27:32
|
{"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": 0.3547348082065582, "perplexity": 1647.7206468030124}, "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-2017-47/segments/1510934806842.71/warc/CC-MAIN-20171123142513-20171123162513-00068.warc.gz"}
|
https://www.semanticscholar.org/paper/Abelian-Ideals-and-the-Variety-of-Lagrangian-Evens-Li/96faeb39e7128ce722f7596ffcbdd4572defb956
|
Corpus ID: 222272257
# Abelian Ideals and the Variety of Lagrangian Subalgebras
@article{Evens2020AbelianIA,
title={Abelian Ideals and the Variety of Lagrangian Subalgebras},
author={S. Evens and Y. Li},
journal={arXiv: Representation Theory},
year={2020}
}
• Published 2020
• Mathematics
• arXiv: Representation Theory
• For a semisimple algebraic group $G$ of adjoint type with Lie algebra $\mathfrak g$ over the complex numbers, we establish a bijection between the set of closed orbits of the group $G \ltimes \mathfrak g^{\ast}$ acting on the variety of Lagrangian subalgebras of $\mathfrak g \ltimes \mathfrak g^{\ast}$ and the set of abelian ideals of a fixed Borel subalgebra of $\mathfrak g$. In particular, the number of such orbits equals $2^{\text{rk} \mathfrak g}$ by Peterson's theorem on abelian ideals.
|
2021-02-28 20:13:08
|
{"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": 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": 0.8798795342445374, "perplexity": 403.347252799095}, "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-2021-10/segments/1614178361723.15/warc/CC-MAIN-20210228175250-20210228205250-00459.warc.gz"}
|
http://mathhelpforum.com/advanced-applied-math/45724-intersection-point-between-gaussians.html
|
# Thread: intersection point between gaussians
1. ## intersection point between gaussians
Hi.
I am doing a project in computer science where I have a need for determing the intersection point between two gaussians defined by their mean and standard variance e.g. g1(mu1,sigma1^2), g2(mu2,sigma2^2).
How do i find their intersection point in the case where the two distributions only have a single intersection point?
2. Just set it up and solve it. After introducing logorithms, it is just a quadratic equation. It's a mess, but it's not any trickier than the Quadratic Formula.
There are two complications, both are easily resolved.
1) What to do with the solution you don't want and how to identify it. The desired intersection is the one between the means.
2) If the variance matches, the quadratic solution is no good. You'll have to rely on symmetry.
3. Just as a sanity check for finding the intersection check i post my calculations for obtaining the quadratic equation.
It have been a while since i have dealt with equations and i would be really glad if someone could confirm my derivation of the quadratic equation.
Gaussian equation
$
y=\frac{1}{(2\pi sigma1^{2})^{1/2}}e^{-\frac{1}{2sigma1^{2}}*(x-mu1)^{2}}
$
intersection point between two gaussians:
$\frac{1}{(2\pi sigma1^{2})^{\frac{1}{2}}}e^{-\frac{1}{2sigma1^{2}}*(x-mu1)^{2}}=\\
\frac{1}{(2\pi sigma2^{2})^{\frac{1}{2}}}e^{-\frac{1}{2sigma2^{2}}*(x-mu2)^{2}}
$
remove the e:
$ln(\frac{1}{(2\pi sigma1^{2})^{1/2}}-\frac{1}{2sigma1^{2}}*(x-mu1)^{2}
$
=
$ln(\frac{1}{2\pi sigma2^{2})^{1/2})}-\frac{1}{2sigma2^{2}}*(x-mu2)^{2}
$
moving everything to one side of the equality sign:
$ln(\frac{1}{(2\pi sigma1^{2})^{1/2}})-ln(\frac{1}{(2\pi sigma2^{2})^{1/2}})$
$
-\frac{1}{2sigma1^{2}}*(x-mu1)^{2}+\frac{1}{2sigma2^{2}}*(x-mu2)^{2}=0
$
$
K= ln(\frac{1}{(2\pi sigma1^{2})^{1/2}})-ln(\frac{1}{(2\pi sigma2^{2})^{1/2}})
$
$K-\frac{1}{2sigma1^{2}}(x^{2}-2mu1*x+mu1^{2})+\frac{1}{2sigma2^{2}}(x^{2}-2mu2+mu2^{2})=0
$
$(\frac{1}{2sigma1^{2}}+\frac{1}{2sigma2^{2}})x^{2} +(\frac{1}{2sigma1^{2}}2mu1-\frac{1}{2sigma2^{2}}2mu2)x
$
$+K-\frac{mu1^{2}}{2sigma1^{2}}+\frac{mu2^{2}}{2sigma2 ^{2}}=0
$
4. Ok, now i am confused.
Is it possible to solve this equation as i have done by using a quadratic equation or is it not?
I need the intersection point between the two means, and also know that gaussian1=/gaussian2.
Best regards
Susanne
5. Originally Posted by Susanne
Ok, now i am confused.
Is it possible to solve this equation as i have done by using a quadratic equation or is it not?
I need the intersection point between the two means, and also know that gaussian1=/gaussian2.
Best regards
Susanne
$\frac{1}{\sqrt{2 \pi} \, \sigma_1} e^{\frac{-(x - \mu_1)^2}{2\sigma_1^2}} = \frac{1}{\sqrt{2 \pi} \, \sigma_2} e^{\frac{-(x - \mu_2)^2}{2\sigma_2^2}}$
$\Rightarrow e^{ \frac{ -(x - \mu_1)^2}{2\sigma_1^2} + \frac{(x - \mu_2)^2}{2\sigma_2^2} } = \frac{\sigma_1}{\sigma_2}$
$\Rightarrow \frac{ -(x - \mu_1)^2}{2\sigma_1^2} + \frac{(x - \mu_2)^2}{2\sigma_2^2} = \ln \left( \frac{\sigma_1}{\sigma_2} \right)$
$\Rightarrow -\sigma_2^2 (x - \mu_1)^2 + \sigma_1^2 (x - \mu_2)^2 = 2 \sigma_2^2 \sigma_1^2 \ln \left( \frac{\sigma_1}{\sigma_2} \right)$
It is simple but tedious to expand the left hand side, re-arrange and solve the quadratic for x. I'd suggest introducing some notation to streamline things. Use the discriminant to set conditions on the mean and variances such that you have the desired number of solutions.
6. Thanks a lot for the answer mrfantastic. So it is possible to solve this problem using the equations, and i do not have to solve it numerically.
7. well to completely show how much i sucks at this i would much appreciate a review of the quadratic equation since the results are not correct.
$
-\frac{1}{2\sigma_{1}^{2}}(x^{2}-2\mu_{1}x+\mu_{1}^{2})+\frac{1}{2\sigma_{2}^{2}}(x ^{2}-2\mu_{2}x+\mu_{2}^{2})
$
more rearranging
$
-\frac{1}{2\sigma_{1}^{2}}+\frac{1}{2\sigma_{2}^{2} }x^{2}+\mu_{1}\frac{1}{2\sigma_{1}^{2}}-\mu_{2}\frac{1}{2\sigma_{2}^{2}}x-\frac{1}{2\sigma_{1}^{2}}\mu_{1}^{2}+\frac{1}{2\si gma_{2}^{2}}\mu_{2}^{2}-ln\left(\frac{\sigma_{1}}{\sigma_{2}}\right)=0
$
when inserting
$
\mu_{1}=-955 \textrm{ }\sigma_{1}^{2}=396
$
$
\mu_{2}=-1578 \textrm{ }\sigma_{2}^{2}=1117
$
I get y values -1878 and -1433 and this confuses me a bit.
I would expect very small numbers denoting the probability and according to my plot it should be around 0.000036.
The intersection point according to the plot should lie between -1530 and -1520.
8. Hmm the intersection data was wrong, so here is the correct approximated solution.
for two Gaussians with
$
\mu_{1}=-955\textrm{ }\sigma_{1}^{2}=396
$
$
\mu_{2}=-1578\textrm{ }\sigma_{2}^{2}=1117
$
the approximated intersection point is at -1190 and the probability being
$3.0e^{-032}$
But i still haven't been able to poduce the correct answer using the quadratic equation.
|
2017-07-24 15:21:56
|
{"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": 0, "img_math": 0, "codecogs_latex": 21, "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": 0.7132272720336914, "perplexity": 354.29845514260774}, "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-2017-30/segments/1500549424884.51/warc/CC-MAIN-20170724142232-20170724162232-00369.warc.gz"}
|
https://dsp.stackexchange.com/questions/47063/why-doesnt-this-complex-multiplication-in-the-frequency-domain-produce-my-expec
|
# Why doesn't this complex multiplication in the frequency domain produce my expected phase shift?
I know how to change the phase of a complex number by multiplying by $\cos \theta + i \sin \theta$. And I understand that the phase of a sine wave is reflected in its Fourier transform. So, I am trying to phase-shift a signal by changing the phase of its Fourier transform..
This works for "synthetic" Fourier transforms, but when I try to FFT a signal, apply the phase change, and invert the FFT, I don't get the expected result. I am using MATLAB in the examples below.
Fs = 1000;
Tmax = 2;
L = Tmax * Fs;
For example, I'll build a synthetic Fourier sequence. The frequency intervals are 0.5 Hz, so a 10Hz component is at the 20th position after DC. (I'm just spitballing here; I know there's better ways to pick frequency bins than hand-jamming 21.)
Ysynth = zeros(1, L);
Ysynth(21) = 1000;
And rotate it by 45°:
Ysynth = Ysynth * exp(j * pi/4);
It has a 45° phase on the 10-Hz component:
polarscatter(angle(Ysynth), abs(Ysynth))
Now take its inverse FFT:
Xsynth = ifft(Ysynth);
So far so good. The generated signal has a phase shift of 45°. MATLAB does complain about the presence of an imaginary part when I plot it; I think this is because I didn't bother with the negative frequency component.
t = (0:L-1)/Fs;
plot(t, Xsynth)
Now, I would expect the same principle to apply to a frequency spectrum taken from an actual signal. But I do not get similar results. Quickly:
X = cos(2*pi * 10 * t);
Y = fft(X);
Yshift = Y * exp(j * pi/4);
Xshift = ifft(Yshift);
There is an imaginary component in Xshift, which I do not expect, and again MATLAB complains about.
plot(t, [Xshift; X])
There is no phase shift here, and the amplitude (of the real part) is different.
I must be misunderstanding something about phase representation in FFTs. Why doesn't my transformation produce a phase-shifted version of the original?
• I think the problem is that you're shifting both positive and negative frequencies by the same amount. – MBaz Feb 8 '18 at 17:32
• first check your FFT's sanity: do nothing in frequency domain, just IFFT. Notice that what you're doing (multiplication with a scalar) makes no difference whether you do it in time or frequency domain. – Marcus Müller Feb 8 '18 at 17:36
• @mbaz oh, that's a good point. Is the overall approach valid? If so, should I multiply the negative frequencies by the negative, or the conjugate, of the positive freqs' multiplier? – thirtythreeforty Feb 8 '18 at 17:49
If you want a phase-shifted strictly-real result, then you have to make sure the data you feed to the IFFT is conjugate symmetric. So make sure to reflect the complex conjugate of any phase changes you make. e.g. Make the upper or negative half of your IFFT input vector mirror the complex conjugate of the bottom or positive half of the input vector.
Added: (Also, "mirror" usually means the array index goes in the opposite direction.)
• Does that mean if I have some shift multiplier for the frequency bins that I have not yet reflected, then I should essentially do shift(end/2:end) = conj(shift(end/2:end))? – thirtythreeforty Feb 8 '18 at 22:40
The negative frequency component is why you are getting messed up. You need to phase shift it in the opposite direction in order for it to remain the complex conjugate in the DFT. This technique will only work on whole integer frequency real valued pure tones.
It will work on any pure complex tone. This is because the formula for a bin value of a complex tone has the phase term $e^{i \phi}$ completely factored out. In other words, when you phase shift a pure complex tone, all the DFT bins rotate in parallel. This does not happen with a real valued signal.
See my articles DFT Bin Value Formulas for Pure Complex Tones and DFT Bin Value Formulas for Pure Real Tones to compare how a complex pure tone behaves in a DFT compared to a real valued one. For a frequency shift, that is a change in $\phi$, in the complex case it will factor out cleanly which is not true in the real case.
Hope this helps,
Ced
• Thanks, that does help. Why does it only work for integer frequencies? I was under the impression that frequencies that don't have a precise bin appear in the nearest components. And for a sufficiently fine-grained FFT, that problem is minimized. – thirtythreeforty Feb 8 '18 at 18:08
• @thirtythreeforty, That isn't correct. If there is any leakage, it goes all the way around the DFT. The nearby bins have larger magnitudes. For an integer frequency tone, a phase shift results in a DFT bin value rotation. For non-integer frequency, the rotation will be close to the phase shift, but not match it at the peak bin. The amount of rotation will taper off until there is none at the DC and Nyquist bins. A phase shift does not result in a parallel rotation of all the bins, so the parallel rotation of all the bins will not produce a phase shift. – Cedron Dawg Feb 8 '18 at 18:47
• Gotcha. That is a rather frustrating property, especially given that it works for complex tones. I will have to find another approach. Thanks! – thirtythreeforty Feb 8 '18 at 18:59
A very readable reference related to this topic in the context of how to delay a signal less than a sample point
Laakso, Timo I., et al. "Splitting the unit delay [FIR/all pass filters design]." IEEE Signal Processing Magazine 13.1 (1996): 30-60.
You can get a good idea for cases beyond what is covered in the paper, in terms of symmetry and how to implement filters in both time and frequency domains. Signal Processing Magazine is mostly accessible to a majority of dsp engineers.
|
2019-12-16 05:13:07
|
{"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": 0.6077105402946472, "perplexity": 760.95761127098}, "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/1575541317967.94/warc/CC-MAIN-20191216041840-20191216065840-00298.warc.gz"}
|
http://www.statsmodels.org/dev/generated/statsmodels.stats.contingency_tables.StratifiedTable.test_equal_odds.html
|
# statsmodels.stats.contingency_tables.StratifiedTable.test_equal_odds¶
StratifiedTable.test_equal_odds(adjust=False)[source]
Test that all odds ratios are identical.
This is the ‘Breslow-Day’ testing procedure.
Parameters: adjust (boolean) – Use the ‘Tarone’ adjustment to achieve the chi^2 asymptotic distribution. A bunch containing the following attributes statistic (float) – The chi^2 test statistic. p-value (float) – The p-value for the test.
|
2018-11-14 11:10:37
|
{"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": 0.5127015709877014, "perplexity": 9330.413742569304}, "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-2018-47/segments/1542039741979.10/warc/CC-MAIN-20181114104603-20181114130603-00391.warc.gz"}
|
http://physics.stackexchange.com/questions/35408/why-do-covalent-bonds-form/35490
|
# Why do covalent bonds form?
why in a covalent bond are "the bonded electrons are in a lower energy state than if the individual atoms held them at the same proximity"?
Also is it correct that " I think when you start pushing two molecules together orbitals between the two start overlapping - forming covalent bonds?"
Essentially why are covalent bonds made? A QM description would be nice but I don't really know QM so a somewhat reduced-to-classical explanation of the QM explanation would also be nice!
-
The covalent bonds form when electrons attached to nearby nuclei can exist in a superposition state where they can partly be on another nucleus. This happens when the electron state they are mixing with is unfilled.
For example, for H2, two hydrogen nuclei are close, there is no electrostatic energy for this in the first approximation because the electron and proton are both spherical electromagnetic sources. But when they come close, and the spin of the two electron is opposite (this is required for binding), each electron will spread out to cover the other atom, overlapping with the other electron (this is allowed because they have opposite spin, and so do not feel Pauli exclusion), and this reduces the kinetic energy of the electron.
The reason is simply that when you allow an electron to wander over a larger space, the kinetic energy always goes down. If you double the size of the space in one direction, the kinetic energy in that direction goes down by a factor of 4. If you consider the two H-atoms as two boxes, doubling the x-size of the box keeping the y and z sizes the same, reduces the kinetic energy from X+X+X to X/4 + X +X or by a factor of 3/4, so the binding energy of two boxes end to end with non-interacting electrons is 1/4 the kinetic energy.
The kinetic energy of an electron in an H-atom is equal to the binding energy (this is the Virial theorem--- the kinetic energy cancels half the potential energy in a 1/r potential to make a binding energy), so you get 1/4 of 12 eV or 3eV of binding energy from this. This is a terrible approximation, because the elecrons repel each other, and the H-atom is not a box, but it shows you that allowing the electron volume to spread gains you a lot of energy on the atomic scale, and it is now plausible that even with repulsion, the electrons will bind, and they do.
-
For a hydrogen atom pair, it is seemingly clear that they do not finish paired. We have been fooled because of the hydrogen potential is used as a reference. Instead of desctribing the actual reaction, we have reduced ourselves to describing pairs of reactions. Yes, I said reduced. en.wikipedia.org/wiki/Absolute_electrode_potential – Andres Salas Aug 6 '14 at 15:49
You say, "for H2, two hydrogen nuclei are close" and then say, "But when they come close". Can you elaborate on what you mean? – Kirk Woll Nov 5 '14 at 0:11
@KirkWoll: If you bring two classical polarizable atoms close, they don't attract. When you bring two quantum atoms close, they do, because the electrons can tunnel to the other atomic volume, reducing their energy. That's it. When they are really close, you get repulsion between the nuclei. – Ron Maimon Nov 6 '14 at 13:01
Thanks @Ron, I found that very helpful. – Kirk Woll Nov 6 '14 at 15:35
First, there is no classical explanation for chemical bonding, so any explanation has to include some quantum mechanical ideas.
Second, perhaps the simplest quantum idea here is that electrons exist in energy levels. Continuing the hydrogen example the lowest electron energy level in $H_2$ has less energy than the lowest electron energy level in atomic hydrogen. Since we can get two electrons (with opposite spins) into an electronic energy level, the combination of two $H$ atoms results in the system energy being lowered and energy is thus emitted (usually as heat). To break the $H_2$ molecule apart one must add that energy back into the molecule.
In the helium molecule (which does not exist, but we can calculate it anyway) there are two energy levels, one lower than that for the helium atom and one higher. Their energies average out to the energy of the electronic level in a helium atom. Thus if one attempts to put two helium atoms together to make a helium molecule there is no energy gain or loss. So there is no bonding energy holding $He_2$ together.
That's really all there is to it.
-
Here is a more formal, but nevertheless elementary treatment.
The key tool to single out the separate pontential and kinetic energy contributions, for a given averaged total energy $E=<T>+<V>$, is the Virial Theorem (VT). For an atom (one nucleus and its electron cloud) the VT takes the simple form
$$2<T>+<V>=0 \ .$$
For a biatomic system (representing two well separated H atoms, but also the covalently bonded H$_2$ molecule) the VT would be stated in "molecular" form as
$$E(R)+R\ \frac{d}{dR}E(R)=-< T > \ (1).$$
It has to be stressed that this VT holds exactly for any arbitrary separation $R$ of the nuclei, for overlapping as well as non-overlapping electron clouds. Here $E(R)$ is the exact and total energy, $<T>$ and $<V>$ are the average values of the kinetic and potential energies of the electrons, averaged with the exact wave function. Naturally, $<T>$ and $<V>$ are also $R$-dependent. Contrary to what one may think at first sight, the $dE/dR$ term is an integral part of the VT, even if the nuclei are kept firmly fixed.
By differentiation of (1) it follows
$$2\frac{dE}{dR}+R\ \frac{d^2E}{dR^2}=-\frac{d}{dR}< T >\ (2) .$$
Pushing the two H atoms towards each other from infinity, if a stable bond is to be formed at a certain separation $R_0$, we ought have for a stable minimum $$d^2E/dR^2>0 \ (3)$$ and a slightly attractive force $$dE/dR\ge 0 \ (4)$$ starting below a certain separation $R\ge R_0$. Conditions $(3,4)$ imply $$\frac{d< T >}{dR}<0 \ (5)$$ while condition $(4)$ alone is satisfied only if $$2<T>+<V> \ \le 0 \ \ (6)$$ below some $R\ge R_0$.
Remark 1: If a bond of length $R_0$ is to be formed at all, the kinetic energy of the electrons necessarily has to $increase$ while $R$ is decreased towards $R_0$.
Remark 2: Although the kinetic energy will increase with decreasing $R$, Eq.6 guarantees that the potential energy (negative) will be at least the double of the kinetic energy (only for $R\ge R_0$).
Note: This argumentation is crystal-clearly presented in Cohen-Tannoudji's Quantum Mechanics, Vol.2, p.1191-1199. They also discuss a couple of subtle points related to the physical mechanisms which produce different inequalities at large separations.
-
Consider the H$_2$ molecule for definiteness. Binding two H atoms together to form a H$_2$ molecule is impeded in the first line by the coulombian repulsion between the two "naked" H$^+$ nuclei (protons). Establishing a molecular bond has to overcome this primary repulsion.
Protons are heavy, in this case being imagined as localized classical particles. Electrons are light and have to be imagined quantum mechanically as described by a common, more or less localized charge distribution $n(\vec{r})$, with $\int{n(\vec{r})}\ d^3\vec{r}=2$ electrons.
As a first step, try smear out the charge density representing both electrons in the middle of the space between the two protons, making something like a "bridge". This will result in the tendency of the protons to get closer, both of them being attracted to each other by the negative charge density in the middle. However, this purely electrostatic reduction of the H$^+$- H$^+$ repulsion is not enough to guarantee the stability of the H$_2$ molecule.
The decisive contribution to the bond stability comes in the second step and is purely quantum mechanical in origin.
One can guess that, due to electron-electron repulsion, localizing the two electrons within the "bridge" region comes at the cost of an increase in potential kinetic energy. Decisive is the observation that this increase is more than compensated by an increase in the (negative) kinetic potential energy of the electrons, which is maximal when the electrons are localized within the "bridge" region between the protons (no nodes in their wave functions in this case!)
In conlusion: the decisive factor in bond formation it is the more negative potential energy due to electron localization within the "bridge". This is no intuitive result, but a consequence of the celebrated Virial Theorem, and has to be worked out explicitly.
The entire argument holds unaltered even when there is only one electron, namely in the H$_2^+$ molecule ion. A very detailed discussion of these concepts is given by Bader (Atoms in Molecules).
-
Actually the classic reference to learn all this is Ruedenberg's Rev. of Modern Physics 34,326 (1962), but you can get nice pedagogical presentations for free (e.g. google "Rioux why covalent bonds form"). You got the role of kinetic and potential energy reversed. Because of the virial theorem, the decrease of potential energy wins over the increase of kinetic energy: the bonding orbital is contracted except at the bonding coordinate, where is expanded; thus the gain in kinetic energy is not excessive. This guarantees minimization of the total (kinetic+potential) energy. – perplexity Sep 2 '12 at 2:11
Thank you very much for setting the explanation right. I will try to correct my text accordingly. I knew that it is a lion's pit, but now I will learn this stuff at last. – Lupercus Sep 2 '12 at 7:32
Rioux is an excellent starter. The paper by Ruedenberg is thorough and contains perhaps more than you would ever want to know, being at the same time a tough and discouraging reading - a historical reference in the line of the Löwdin school. Bader (Section 7.5) is also no easy lecture. He stresses a local form of the virial theorem, which sheds light on the role of the charge-density laplacian in the description of chemical bonding. – Lupercus Sep 2 '12 at 13:53
This is not a good explanation, even though it appears in the literature. Covalent bonds form because the electron increases it's wandering volume. – Ron Maimon Sep 2 '12 at 21:52
@RonMaimon: Can you elaborate? And is the above explanation therefore a "legitimate" explanation – Eiyrioü von Kauyf Sep 2 '12 at 21:56
## protected by Qmechanic♦Dec 11 '13 at 9:32
Thank you for your interest in this question. Because it has attracted low-quality or spam answers that had to be removed, posting an answer now requires 10 reputation on this site.
|
2016-02-14 04:05:44
|
{"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": 0.7287138104438782, "perplexity": 593.9551939985746}, "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-2016-07/segments/1454701168998.49/warc/CC-MAIN-20160205193928-00007-ip-10-236-182-209.ec2.internal.warc.gz"}
|
https://byjus.com/question-answer/the-mean-age-of-a-combined-group-of-men-and-women-is-25-years-if/
|
Question
# The mean age of a combined group of men and women is $$25$$ years. If the mean age of the group of men is $$26$$ and that of the group of women is $$21$$, then the percentage of men and women in the group is
A
60, 40
B
80, 20
C
20, 80
D
40, 60
Solution
## The correct option is A $$80,\space 20$$Let total no. of people in the group be $$100$$ and out of them $$x$$ are meni.e no of women = $$100-x$$.Mean age = $$\displaystyle\frac{sum \ of \ ages \ in \ the\ group}{no \ of \ people}$$Total sum = sum of ages of men + sum of ages of women$$\Rightarrow\quad 100\times 25 = x\times 26+\left(100-x\right)\times 21$$$$\Rightarrow x=80$$Hence, the percentage of men and women in the group is $$80,20$$ respectivelyMathematics
Suggest Corrections
0
Similar questions
View More
People also searched for
View More
|
2022-01-26 06:16:19
|
{"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": 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": 0.5500855445861816, "perplexity": 377.94921694245124}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "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-2022-05/segments/1642320304915.53/warc/CC-MAIN-20220126041016-20220126071016-00411.warc.gz"}
|
http://www.etiquettehell.com/smf/index.php?topic=106673.msg3103179
|
News:
• April 19, 2018, 08:51:37 PM
### Author Topic: Your holiday hill to die on. (Read 1041904 times)
0 Members and 1 Guest are viewing this topic.
#### alkira6
• Member
• Posts: 655
##### Re: Your holiday hill to die on.
« Reply #1260 on: February 12, 2014, 09:00:55 AM »
My husband told me that he was very sad that he had nothing planned this year because V-day fell on the weekend. We usually celebrate the feast of St. Half Price after the holiday. I have serious cheapness problems that have kind of soured gifts that I have gotten previously. In the back of my mind I'm always quietly freaking out about the ridiculous markup on whatever I was given.
• Member
• Posts: 12199
• Not all those who wander are lost
##### Re: Your holiday hill to die on.
« Reply #1261 on: February 12, 2014, 12:15:10 PM »
I think we will have chocolate Belgian waffles with berries for dessert.
I ordered DH and DS some items from 5.11, which is one of their favorite stores. $180 worth of items for$54!
“All that is gold does not glitter, Not all those who wander are lost; The old that is strong does not wither, Deep roots are not reached by the frost."
-J.R.R Tolkien
#### VorFemme
• Member
• Posts: 14025
• It's too darned hot! (song from Kiss Me, Kate)
##### Re: Your holiday hill to die on.
« Reply #1262 on: February 12, 2014, 06:55:47 PM »
I saw a ridiculously easy "recipe" for strawberry shortcake for the holiday - take two Tinkies (cream filled yellow sponge cake "fingers"). Cut them across the middle at an angle - arrange to make two "hearts" (okay, so the proportions are kind of skinny for the hearts - so what - add more strawberries if you must). Put strawberries (cherries) on top of "hearts" and pour strawberry (cherry?) glaze over them. Hand one to the love of your life with a fork. Eat one yourself.
It's once a year - indulge!
Let sleeping dragons be.......morning breath......need I explain?
#### cicero
• Member
• Posts: 19674
##### Re: Your holiday hill to die on.
« Reply #1263 on: February 13, 2014, 05:20:20 AM »
My great-uncle and I have a very...instreasting relationship. He's in his late 70s, and he grew up in a very different world then I did. When I was younger he was prone to bigoted comments that always upset me, finally one day I called him on it. He told me "Glitter, understand, what I say, is what I've always said. Now, that doesn't make it right, you're my great-niece and I love you. At your core, I don't care that you're a gay...lesbian? I don't care if you love a man, a woman, or a goat. I care that you are happy. So I am I gonna work very hard to get over my past, because I love you. Can you love me and be patient and know I mean no harm by what I say? And remind me to clean it up?" I'm proud to say that last year, that man surprised me and Partner by showing up for gay pride! He even joined in the parade and marched with PFLAG for a bit! Whenever someone tells me people can't change their bigoted ways I just think "Oh, I have proof that says otherwise, just give em time and love and a little kick in the pants". I find him to be one of the most facasinating people (great-aunt's pretty fantastic too) and I'm sad that it's become obvious we'll be loosing him soon. But I'm elated that I've gotten to know him better, that I've been able to change his view on the world a bit, and that my wonderful loving Partner, the woman I'll make my wife, saw what I needed without me even knowing I needed it and took care of it.
Ok, sorry to get all emotional up in here. Looks like it will be a special v-day for us this year.
wow. what an amazing guy.
Created by MyFitnessPal.com - Free Weight Loss Tools
• Member
• Posts: 12199
• Not all those who wander are lost
##### Re: Your holiday hill to die on.
« Reply #1264 on: February 13, 2014, 07:35:34 AM »
I went to Wal-mart this morning for a few essentials and found \$3 chocolate hearts for my guys. Duct tape for DH and a guitar with actual strings for DS.
“All that is gold does not glitter, Not all those who wander are lost; The old that is strong does not wither, Deep roots are not reached by the frost."
-J.R.R Tolkien
#### Winterlight
• On the internet, no one can tell you're a dog- arf.
• Member
• Posts: 10223
##### Re: Your holiday hill to die on.
« Reply #1265 on: February 13, 2014, 09:09:28 AM »
One solo Valentine's Day, I stopped at my local grocery store for some dinner on my way home. As I got ready to drive away, I noticed the inordinate number of single male shoppers rushing into the store and leaving with flowers and nothing else. I sat there for a few minutes longer to watch and just cracked up as I saw one guy after another do the same thing. So, if you want to amuse yourself, people-watching at the grocery store in the afternoon/evening of Valentine's Day can be a crack-up.
Holidays used to be a huge deal to me, especially the ones that had usually been couples holidays to me (New Year's Eve and Valentine's Day). I don't care so much anymore, but DH is very big into holidays and gift-giving at holidays so, typically, I celebrate in this manner for him. Fortunately, DH has zero interest in doing something like eat out on Valentine's Day (he agrees that the restaurants are over-priced and crowded so we'd rather stay in).
Having worked in a floral shop (within a grocery store) during Valentine's I can sooo agree with you! It's a steady stream of guys buying chocolate and flowers from 5pm on. The later it gets the worse it is and heaven help you if you run out of flowers. Prepare to get yelled at for ruining their night because they couldn't be bothered to get a gift until 8pm the day of.
I do feel sorry for florists though, because they work so hard and get yelled at constantly, usually over prices. Of course I can't speak for everyone, but I know that in the case of our shop (and the hundreds of others within that grocery chain) the florists did not mark the prices up - that came from the growers. The florists had to raise prices to maintain the same profit they make all year and not take a loss on the hundreds of cases of product they brought in that week.
I regularly walk past a Godiva store and VDay is hilarious! The line stretches out the door and nearly into the street!
If wisdom’s ways you wisely seek,
Five things observe with care,
To whom you speak,
Of whom you speak,
And how, and when, and where.
Caroline Lake Ingalls
#### Thipu1
• Member
• Posts: 7439
##### Re: Your holiday hill to die on.
« Reply #1266 on: February 13, 2014, 09:58:27 AM »
Even funnier than the long lines are the 'deer in the headlights' looks of the men waiting.
This year will be especially interesting because we're going through a ghastly Nor-Easter today.
#### Outdoor Girl
• Member
• Posts: 16736
##### Re: Your holiday hill to die on.
« Reply #1267 on: February 13, 2014, 10:32:09 AM »
Even funnier than the long lines are the 'deer in the headlights' looks of the men waiting.
What is even more fun is being in a lingerie shop on Valentine's Day. Those are some truly epic 'deer in the headlights' looks!
I was in one, buying some underwear, and being perpetually single, didn't really register it was Valentine's Day. Until the store was suddenly swarmed with guys. I even ended up helping out a couple of them with their selections. It was actually a lot of fun.
After cleaning out my Dad's house, I have this advice: If you haven't used it in a year, throw it out!!!!.
Ontario
#### GreenHall
• Member
• Posts: 945
##### Re: Your holiday hill to die on.
« Reply #1268 on: February 13, 2014, 10:34:06 AM »
#### Carotte
• Member
• Posts: 1744
##### Re: Your holiday hill to die on.
« Reply #1269 on: February 13, 2014, 10:38:31 AM »
What I'm sad about this valentine day is that I'm missing out on a mystery shopper mission in a chain of chocolate store, because it's only for men (pretending to buy for their girlfriends) .
I'd fill out a 5 page survey for 20€ of chocolate..
Meh, I'll fill out the 5 pages survey for my 2 flavours/1 topping ice cream tomorow (not something I would treat myself too so I've got that going on for me so that's nice.)
#### GlitterIsMyDrug
• Member
• Posts: 805
##### Re: Your holiday hill to die on.
« Reply #1270 on: February 13, 2014, 10:44:18 AM »
What I'm sad about this valentine day is that I'm missing out on a mystery shopper mission in a chain of chocolate store, because it's only for men (pretending to buy for their girlfriends) .
I'd fill out a 5 page survey for 20€ of chocolate..
Do women not buy chocolates for men? I've seen men eat chocolates. Do they only buy their own? Is it weird to buy chocolates for a dude? I sent two of my guy friends chocolates because one just went through a terrible break up and the other is home sick so I thought "They will enjoy this", hopefully I didn't revoke their dude cards.
Or do women not buy for other women? Partner has bought me chocolate and vice versa. So has my mom, my best friends, basically anyone who can't figure out what to get me. Can't go wrong with chocolate.
#### lowspark
• Member
• Posts: 5584
##### Re: Your holiday hill to die on.
« Reply #1271 on: February 13, 2014, 10:46:46 AM »
Can't go wrong with chocolate.
Amen, sister.
Houston
Texas
USA
#### Carotte
• Member
• Posts: 1744
##### Re: Your holiday hill to die on.
« Reply #1272 on: February 13, 2014, 10:50:06 AM »
I'm pretty sure every one buys chocolate for everyone.
It seems like they only had one scenario to test, "guy asking for advices for his girlfriend".
I do hope and think that the chocolate brand in question is not set on hetero cis gendered relashionship, that's just what they choose.
• Member
• Posts: 12199
• Not all those who wander are lost
##### Re: Your holiday hill to die on.
« Reply #1273 on: February 13, 2014, 10:52:54 AM »
“All that is gold does not glitter, Not all those who wander are lost; The old that is strong does not wither, Deep roots are not reached by the frost."
-J.R.R Tolkien
#### jedikaiti
• Swiss Army Nerd
• Member
• Posts: 2885
• A pie in the hand is worth two in the mail.
##### Re: Your holiday hill to die on.
« Reply #1274 on: February 13, 2014, 04:19:57 PM »
What I'm sad about this valentine day is that I'm missing out on a mystery shopper mission in a chain of chocolate store, because it's only for men (pretending to buy for their girlfriends) .
I'd fill out a 5 page survey for 20€ of chocolate..
Do women not buy chocolates for men? I've seen men eat chocolates. Do they only buy their own? Is it weird to buy chocolates for a dude? I sent two of my guy friends chocolates because one just went through a terrible break up and the other is home sick so I thought "They will enjoy this", hopefully I didn't revoke their dude cards.
Or do women not buy for other women? Partner has bought me chocolate and vice versa. So has my mom, my best friends, basically anyone who can't figure out what to get me. Can't go wrong with chocolate.
re: bolded - I hope not, b/c DH is getting some for V-day! Of course, he is the serious chocoholic in the family. But it MUST be the good stuff.
What part of v_e = \sqrt{\frac{2GM}{r}} don't you understand? It's only rocket science!
"The problem with re-examining your brilliant ideas is that more often than not, you discover they are the intellectual equivalent of saying, 'Hold my beer and watch this!'" - Cindy Couture
|
2018-04-20 01:51:37
|
{"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": 0.3298488259315491, "perplexity": 6367.769063495595}, "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/1524125937090.0/warc/CC-MAIN-20180420003432-20180420023432-00519.warc.gz"}
|
http://www.solutioninn.com/the-speed-of-bullet-as-it-travels-down-the-barrel
|
Question
The speed of a bullet as it travels down the barrel of a rifle toward the opening is given by v = (- 5.00 x 107)t 2 + (3.00 x 105)t, where v is in meters per second and t is in seconds. The acceleration of the bullet just as it leaves the barrel is zero.
(a) Determine the acceleration and position of the bullet as a function of time when the bullet is in the barrel.
(b) Determine the length of time the bullet is accelerated.
(c) Find the speed at which the bullet leaves the barrel.
(d) What is the length of the barrel?
Sales0
Views539
|
2016-10-25 03:26:13
|
{"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": 0.8117696642875671, "perplexity": 320.05733212822366}, "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-2016-44/segments/1476988719877.27/warc/CC-MAIN-20161020183839-00138-ip-10-171-6-4.ec2.internal.warc.gz"}
|
https://www.cuemath.com/ncert-solutions/q-12-exercise-9-3-areas-of-parallelograms-and-triangles-class-9-maths/
|
# Ex.9.3 Q12 Areas of Parallelograms and Triangles Solution - NCERT Maths Class 9
Go back to 'Ex.9.3'
## Question
A villager Itwaari has a plot of land of the shape of a quadrilateral. The Gram Panchayat of the village decided to take over some portion of his plot from one of the corners to construct a Health Centre. Itwaari agrees to the above proposal with the condition that he should be given equal amount of land in lieu of his land adjoining his plot so as to form a triangular plot. Explain how this proposal will be implemented.
Video Solution
Areas Of Parallelograms And Triangles
Ex 9.3 | Question 12
## Text Solution
What is known?
Itwaari has a plot of land of the shape of a quadrilateral and some portion of his plot Gram Panchayat use to construct Health Centre. He should be given equal amount of land in lieu of his land adjoining his plot so as to form a triangular plot.
What is unknown?
How this proposal will be implemented.
Reasoning:
Join diagonal $$BD$$ and draw a line parallel to $$BD$$ through point A.Let it meet the extended side $$CD$$ of $$ABCD$$ at point $$E$$.Join $$BE$$ and $$AD$$. Let them intersect each other at O. We can use theorem for triangles $$DEB$$ and $$DAB$$, if two triangles are on same base and between same pair of parallel lines then both will have equal area. Now we can subtract area of triangle DOB from both sides to get the required result.
Steps:
Let quadrilateral $$ABCD$$ be the original shape of the field.
The proposal may be implemented as follows.
Join diagonal $$BD$$ and draw a line parallel to $$BD$$ through point $$A$$.
Let it meet the extended side $$CD$$ of $$ABCD$$ at point $$E$$.
Join $$BE$$ and $$AD$$. Let them intersect each other at $$O$$.
Then, portion $$\Delta AOB$$ can be cut from the original field so that the new shape of the field will be . (See figure).
We have to prove that the area of $$\Delta AOB$$ (portion that was cut so as to construct Health Centre) is equal to the area of $$\Delta DEO$$ (portion added to the field so as to make the area of the new field so formed equal to the area of the original field).
It can be observed that $$ΔDEB$$ and $$ΔDAB$$ lie on the same base $$BD$$ and are between the same parallels $$BD$$ and $$AE$$.
According to Theorem 9.2 : Two triangles on the same base (or equal bases) and between the same parallels are equal in area.
\begin{align}{\text{ Area }}(\Delta {{DEB}})&\!\!= \!\!{\text{ Area }}(\Delta {{DAB}})\\\left[ \begin{array}{l}{\text{Area }}(\Delta {{DEB}}) - \\{\text{ Area }}(\Delta {{DOB}})\end{array} \!\right] &\!\!=\!\!\left[ \begin{array}{l}{\text{Area }}(\Delta {{DAB}}) - \\ {\text{Area }}(\Delta {{DOB}})\end{array}\!\right]\\{\text{Area}}\left( {\Delta {{DEO}}} \right)&\!\!=\!\! {\text{Area}}\left( {\Delta {{AOB}}} \right)\end{align}
Video Solution
Areas Of Parallelograms And Triangles
Ex 9.3 | Question 12
|
2020-06-02 15:59:46
|
{"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": 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": 0.7585970759391785, "perplexity": 1046.684753946277}, "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-2020-24/segments/1590347425148.64/warc/CC-MAIN-20200602130925-20200602160925-00562.warc.gz"}
|