url stringlengths 14 2.42k | text stringlengths 100 1.02M | date stringlengths 19 19 | metadata stringlengths 1.06k 1.1k |
|---|---|---|---|
https://wiki.hotmapsdev.hevs.ch/en/CM-Biomass-potential | ## In a glance
This module calculates the energy potential from different biomass sources (forest and agricultural residues) within a NUTS3 region.
To Top
## Introduction
This module assess the biomass energy that might be generated from a biomass source. The CM use the default dataset for the whole EU that are at NUTS3 level. The CM do not consider which is the biomass that can be sustainable used for the energy production.
To Top
## Inputs and outputs
Input layers and parameters are:
• Percentage of solid waste collected (default value: 90%)
• Efficiency in transforming solid waste in thermal energy (default value: 50%)
• Efficiency in transforming solid waste in electrical energy (default value: 20%)
• Percentage of agriculture residues collected (default value: 60%)
• Efficiency in transforming agriculture residues in thermal energy (default value: 50%)
• Efficiency in transforming agriculture residues in electrical energy (default value: 20%)
• Percentage of livestock effluents collected (default value: 50%)
• Efficiency in transforming livestock effluents in thermal energy (default value: 50%)
• Efficiency in transforming livestock effluents in electrical energy (default value: 20%)
• Percentage of forest residues collected (default value: 50%)
• Efficiency in transforming forest residues in thermal energy (default value: 50%)
• Efficiency in transforming forest residues in electrical energy (default value: 20%)
Output layers and parameters are:
• Total biomass heat energy potential
• Total biomass electric energy potential
• Graph with the energy produced per biomass source
To Top
## Method
The module for each biomass resource available apply a first percentage to reduce the total amount of biomass that can be effectively and realistically collected. For instance for the forestry biomass can have different percentage of biomass collection rate depending on the forestry ground conditions (e.g. slope, terrain roughness) and the mechanization of the process (e.g. use of cable crane, harvester and forwarder, etc.). While for each source the user can select the efficiency in transforming the biomass energy into thermal and electricity energy. The user can select different efficiency per biomass sources, because different source might require different treatment and process.
To Top
## GitHub repository of this calculation module
Here you get the bleeding-edge development for this calculation module.
To Top
## Sample run
To Top
## How to cite
Pietro Zambelli, in Hotmaps-Wiki, CM-Heatsource-potential (September 2020)
To Top
## Authors and reviewers
Institute of Renewable Energy
viale Druso 1
39100 Bolzano
To Top
To Top
To Top | 2020-09-19 00:04:01 | {"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": 0.5885050892829895, "perplexity": 11118.649283645214}, "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/1600400189264.5/warc/CC-MAIN-20200918221856-20200919011856-00427.warc.gz"} |
https://physics.stackexchange.com/questions/427363/where-will-the-charge-of-a-mass-will-go-having-some-net-charge-when-completely | # Where will the charge of a mass will go (having some net charge) when completely converted to energy?
All my confusion began while thinking of can charge be related to energy. Now Coulomb's law state that two body having some charges apply forces on each other which is true. And according to Newton $F=ma$ means force can be exerted on a body having some mass. Since charges apply forces so it should not possible that they exist without mass! Either it is negligible, but there should some mass if charge exists but that shouldn't be zero.
Now $F=k\frac{q_1q_2}{r^2}=ma$ where $F$ is force on $q_2$ of mass $m$ due to $q_1$. Now if we start converting mass $m$ into energy keeping $q_1$ fixed at it's position and $q_1$ constant, the acceleration of the mass will increases and charge $q_2$ will be there on the mass till traces of $m$ exists and making force due to charges constant, by this concept I concluded that any amount of charge can exist on any amount of mass means $1\,\text{C}$ of charge can exist on a body of mass of order $10\,\text{kg}$ or $10\,\text{mg}$ or $10\,\text{ng}$.
Now coming to point that if I take a mass and given it some net charge $q$ and started converting that mass into energy (somehow) till that mass completely gets converted into energy so that no mass exist for the charge to gather on, then where should that charge $q$ will go, will it get destroyed or it also gets converted into energy? If it gets converted into energy then there shouldn't some more energy released rather than $mc^2$
This is my approach to prove $E=mc^2$ hope someone will tell me what I am missing or may be I am right!
• "as charges can not exist without mass because..." I got lost at that point; looks like you have a few sentence stubs and it's pretty confusing. Could you revisit the punctuation and expand that rationale behind $E=mc²+ kq$? That doesn't make much sense to me. – user191954 Sep 7 '18 at 16:52
First thing to note is that only certain interactions can result in annihilation, and thus to energy given out via $E=mc^2$. This can only happen between a particle and its anti-particle (to my knowledge). However, even were annihilation between two particles which were not mutual anti-particles possible, it still wouldn't occur in the scenario you describe, because of conservation of charge, which states that charge can't be lost or gained in an interaction.
There would be some energy implicit within the collision, because the particles, as they got closer, would accelerate faster and faster due to their increased proximity, and the effects of the inverse square law. All of their potential energy caused by their mutual interactions would be converted to kinetic energy - that's about as close as I can get to a $+kq$, I'm afraid. | 2019-12-14 02:47:47 | {"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": 0.67621910572052, "perplexity": 342.62907891702736}, "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/1575540579703.26/warc/CC-MAIN-20191214014220-20191214042220-00424.warc.gz"} |
http://www.maths.manchester.ac.uk/our-research/events/seminars/algebra/previous-seminars/spherical-objects-and-simple-curves.htm | ## Spherical objects and simple curves
#### Sebastian Opper (Cologne)
A theorem by Burban and Drozd (2011) states that the category Perf En of perfect complexes over a cycle of projective lines $$E_n$$ $$(n\in N)$$ can be modeled by a subcategory of $$D^b(\Gamma_n)$$, the bounded derived category of finitely generated modules over a certain gentle algebra $$\Gamma_n$$. In particular, questions about spherical objects in $$Perf(E_n)$$ and their associated spherical twists can be studied by means of the gentle algebra. Inspired by the Homological Mirror Symmetry Conjecture, I will establish a connection between homotopy bands of $$\Gamma_n$$ in the sense of Bekkert and Merklen (2003) and certain curves on the torus with $$n$$ punctures. I will explain how the combinatorics of morphisms, mapping cones and spherical twists in $$D^b(\Gamma_n)$$ are connected to intersection points, surgeries and Dehn twists by simple curves. Finally, I will talk about applications to spherical objects in $$Perf(E_n)$$. | 2018-09-23 08:03:29 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.682285487651825, "perplexity": 374.35872878511015}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-39/segments/1537267159165.63/warc/CC-MAIN-20180923075529-20180923095929-00087.warc.gz"} |
http://www.openproblemgarden.org/op/shuffle_exchange_conjecture | # Shuffle-Exchange Conjecture
Importance: High ✭✭✭
Author(s): Beneš, Václav E. Folklore Stone, Harold S.
Subject: Combinatorics
Keywords:
Posted by: Vadim Lioubimov on: November 27th, 2009
Given integers $k,n\ge2$, let $d(k,n)$ be the smallest integer $d\ge2$ such that the symmetric group $\frak S$ on the set of all words of length $n$ over a $k$-letter alphabet can be generated as $\frak S = (\sigma \frak G)^d$, where $\sigma\in \frak S$ is the \emph{shuffle permutation} defined by $\sigma(x_1 x_2 \dots x_{n}) = x_2 \dots x_{n} x_1$, and $\frak G$ is the \emph{exchange group} consisting of all permutations in $\frak S$ preserving the first $n-1$ letters in the words.
\begin{problem}[SE] Find $d(k,n)$. \end{problem}
\begin{conjecture}[SE] $d(k,n)=2n-1$. \end{conjecture}
This beautiful and difficult problem arises in switching networks theory and has important applications in parallel processing, sorting networks, card shuffling, etc. In this area it is perhaps the most famous open question which is at the center of the quest to understand the phenonemon of network rearrangeability. Both the problem and conjecture are referred to as \emph{Shuffle-Exchange} (\emph{SE}) ones. The case $k=2$ of SE problem (but not the conjecture) can be traced back to the work of Stone [S71], where he showed that $d(2,n)\le n^2$. The upper bound $d(k,n)\le 2n-1$ is the central case of \OPrefnum[Beneš conjecture]{37181} [B75], while the lower bound $d(k,n)\ge 2n-1$ can be easily seen (it is also a special case of the \OPrefnum[stronger version]{37181} [B75] of Beneš conjecture, which turned out to be generally false). Over more than three decades SE conjecture, especially its case $k=2$, has received a lot of attention, mostly in the context of switching networks, with rather modest results. %and generated huge literature, Note that $d(k,n)\le m$ is equivalent to $\frak S = (\sigma \frak G)^m$, for any integer $m\ge2$. Furthermore, it is easy to see that the latter decomposition is equivalent to $\frak S = \frak G_1 \frak G_2\dots \frak G_{m}$, where $\frak G_i:=\sigma^{i} \frak G \sigma^{-i}$ is the subgroup of $\frak S$ consisting of all permutations which may only change the letters on the position $i-1\ (\text{mod } n) + 1$ in the words.
Also, the case $n=2$ of SE conjecture can be reformulated as the following
\begin{theorem}[$\star$] Every permutation of entries of a square matrix can be obtained in 3 steps as follows: first by permuting entries in the columns, then - in the rows, and then - in the columns again. Moreover, some permutations cannot be obtained in less than 3 of such steps. \end{theorem}
(The parameter $k$ in the case $n=2$ of SE conjecture corresponds to the size $k\times k$ of a matrix in the theorem.) Moreover, the general case of SE conjecture can be reformulated as a straightforward generalization of Theorem ($\star$) to the $n$-dimensional cubic matrices (of size $k\times\dots\times k$) stating that every permutation of entries of such a matrix can be obtained in $2n-1$ steps in a similar way, and this number is generally a precise lower bound.
Theorem ($\star$) holds as being easily equivalent to the special case of the following classical result when each part of the multigraph has size $k$:
\begin{theorem}[König] A $k$-regular bipartite multigraph is $k$-edge-colorable. \end{theorem}
The function $d(k,n)$ admits 3 main interpretations (that are not immediately equivalent), "group-theoretic" (presented in the beginning), "combinatorial" (below), and \OPrefnum["graph-theoretic"]{37089}, each of which provides its own framework for SE problem and suggests its own interesting natural generalizations and extensions. Accordingly, there are 3 equivalent forms of SE problem/conjecture. Although the group-theoretic interpretation of $d(k,n)$ is the shortest and most elegant among the three, it seems the least natural when it comes to proving the known results and studying SE problem more deeply. I believe that SE problem is very deep and combinatorial by nature. I also strongly believe in the validity of SE conjecture.
\section{2. Combinatorial form of SE problem/conjecture} Given a pure abstract simplicial complex $\Delta$ of rank $n\ge2$ and a positive integer $\ell$, an \emph{$\ell$-transition} is a map that assigns to evey pair of ordered facets, $x_1,\dots,x_{n}$ and $y_1,\dots,y_{n}$, a sequence of vertices $z_1,\dots,z_{\ell}$ such that every $n$-segment of the sequence $x_1,\dots,x_{n},z_1,\dots,z_{\ell}, y_1,\dots,y_{n}$ forms a facet. Let $\text{tr}(\Delta)$ be the smallest $\ell$, or $\infty$ if none exists, for which there exists an $\ell$-transition. Note that $\text{tr}(\Delta)\le \ell$ is equivalent to the existence of $\ell$-transition for $\Delta$, for any $\ell\ge 1$.
Given integers $k,n\ge2$, let $\Delta_{k,n}$ be the pure abstract simplicial complex of rank $n$ whose vertex set is the set $V_{k,n}$ of all uniform $k$-partitions (i.e., ones consisting of $k$ equal-sized blocks) of a $k^n$-set, and whose facets are all $n$-subsets of $V_{k,n}$ with zero infinum. Using normal reasoning, it is not hard to show [L04] the following
\begin{theorem} $d(k,n) = \text{tr}(\Delta_{k,n})+n$. \end{theorem}
Thus, the combinatorial forms of SE problem and conjecture can be formulated as to find $\text{tr}(\Delta_{k,n})$ and that $\text{tr}(\Delta_{k,n})=n-1$, respectively.
The \emph{infinum} (or \emph{meet}) of two partitions $\mathbf{a}$ and $\mathbf{b}$ of a set $E$ is the partition of $E$ defined by $$\mathbf{a\wedge b} := \big\{\, a\cap b\ne\varnothing \ | \ a\in\mathbf{a} \ \&\ b\in\mathbf{b} \,\big\}.$$ Note that together with the operation $\wedge$, the collection of all partitions of $E$ forms a semilattice %n algebraic (i.e., a commutative and idempotent semigroup) with the identity and zero being the partitions $\mathbf{1}_E:=\{E\}$ and $\mathbf{0}_E:=\big\{\{x\} \ | \ x\in E \big\}$, respectively.
Observe that the complex $\Delta_{k,n}$ is non-matroidal for all $(k,n)\ne (2,2)$.
\section{3. Constructive version of SE problem/conjecture}
Application-wise it is important not only to establish a certain decomposition $\frak S = (\sigma \frak G)^m$ or, equivalently, \OPrefnum[rearrangeability]{37089} of the \OPrefnum[graph $(\text{SE}(k,n))^{m-1}$]{37089} or, equivalently, the existence of an $(m-n)$-transition for the complex $\Delta_{k,n}$, but also to find a corresponding efficient factorization/routing/transition algorithm.
Given an identity $A = A_1A_2\dots A_\m$, where all $A_i$ are subsets of a multiplicative group, a \emph{factorization algorithm} finds for every $a\in A$ an $m$-tuple $(a_1,\dots,a_m)\in A_1\times \dots \times A_m$ such that $a = a_1a_2\dots a_m$. Given a rearrangeable graph $(\text{SE}(k,n))^{m-1}$, a \emph{routing algorithm} takes a \OPrefnum[mask]{37089} of the graph as input and returns a corresponding \OPrefnum[routing]{37089}. Given a pure simplicial complex $\Delta$ with $\text{tr}(\Delta)\le r$, an \emph{$r$-transition algorithm} realizes an $r$-transition for $\Delta$. It is not hard to prove
\begin{theorem} Any factorization algorithm for $\frak S = (\sigma \frak G)^m$ translates into a routing algorithm for $(\text{SE}(k,n))^{m-1}$ and into an $(m-n)$-transition algorithm for $\Delta_{k,n}$ of the same complexity, and vise versa. Consequently, $D^{*}(k,n) = R^{*}(k,n) = T^{*}(k,n)$. \end{theorem} Here $D^*(k,n)$, $R^*(k,n)$, and $T^{*}(k,n)$ are the sets of all $m\ge 2$, respectively, for which there exists an efficient polynomial-time (in $k^n$) factorization/routing/transition algorithm mentioned in the above theorem (we will also write $A \buildrel{*}\over= A_1A_2\dots A_m$ to indicate the existence of such a factorization algorithm for $A = A_1A_2\dots A_m$, where each $A_i\subseteq \frak S$). Clearly, $$d^*(k,n)\ge d(k,n)= r(k,n)=\text{tr}(\Delta_{k,n})+n,$$ where $d^*(k,n):= \min D^*(k,n)$ with the usual convention $\min\varnothing :=\infty$, and $r(k,n)$ is defined \OPrefnum[here]{37089}.
It is easy to see that $d\in D^*(k,n)$ implies $[d,\infty)\subseteq D^*(k,n)$ (equivalently, the same is true for $R^*(k,n)$ and $T^{*}(k,n)$). Consequently, $d^*(k,n)\le m$ is equivalent to $\frak S \buildrel{*}\over= (\sigma \frak G)^m$. \begin{problem}[CSE] Find (or estimate) $d^*(k,n)$ and specify the corresponding factorization/routing/transition algorithm for the upper bound. \end{problem} \begin{conjecture}[CSE] $d^*(k,n)=2n-1$. \end{conjecture} Both the problem and conjecture are referred here to as \emph{Constructive Shuffle-Exchange} (\emph{CSE}) ones. The conjecture was proposed in [L04]. Clearly, CSE conjecture implies SE one as $2n-1\le d(k,n)\le d^*(k,n)$.
\section{4. Main results}
So far SE/CSE conjecture has been only settled in the following 3 cases: $n=2$, $(k,n)=(2,3)$, and $(k,n)=(2,4)$. That is, the following 3 identities holds: $$(1)\ d(k,2) = d^*(k,2) = 3,\ \ (2)\ d(2,3) = d^*(2,3) = 5,\ \ (3)\ d(2,4) = d^*(2,4) = 7.$$ Also, there are 2 the following major results on SE/CSE problem: \begin{itemize} \item (4) $d(k,n)\ge 2n-1$. \item (5) $d^{(*)}(k,n)\le d^{(*)}(k,r)+3(n-r)$, if $n > r$. \end{itemize}
The lower bound (4) follows immediately from the obvious observation that $\text{tr}(\Delta) \ge \dim(\Delta)$, for any pure complex $\Delta$.
Note that (4) reduces SE (CSE) conjecture to $d^{(*)}(k,n)\le 2n-1$ which is equivalent to $\frak S \buildrel{(*)}\over= (\sigma \frak G)^{2n-1}$. In fact, the main reason why SE/CSE conjecture is widely believable, apart from results (1-4), is a close similarity between the latter decomposition and the following well known result [B65, L04] (that is not hard to derive from the constructive version of the König's theorem): \begin{theorem}[Beneš] $\frak S \buildrel{*}\over= (\frak G\sigma^{-1})^{n-1}\frak G(\sigma \frak G)^{n-1}$. \end{theorem}
Combining (1) and (3) with (5) yields respectively the following 2 best known upper bounds (in addition to (2)) for both $d(k,n)$ and $d^*(k,n)$: \begin{itemize} \item $d(k,n)\le d^*(k,n)\le 3n-3$. \item $d(2,n)\le d^*(2,n)\le 3n-5$, if $n\ge4$. \end{itemize}
As it was mentioned earlier, the case $n=2$ of SE conjecture is easily equivalent to the following case of the Konig's theorem: a $k$-regular bipartite multigraph $B$ with $k$-vertex parts is $k$-edge-colorable. Moreover, any $k$-edge-coloring algorithm for the graph $B$ easily translates into a factorization/routing/1-transition algorithm of the same complexity for $\frak S = (\sigma \frak G)^3$ (at $n=2$) or the graph $(\text{SE}(k,2))^{2}$ or the complex $\Delta_{k,2}$, respectively, and vise versa. Consequently, as there are many efficient polynomial-time (in $k^2$) $k$-edge-coloring algorithms well known for the graph $B$, the case $n=2$ of CSE conjecture also holds.
There are at least 6 alternative proofs proposed for the case $(k,n)=(2,3)$ of CSE conjecture. Although they may look quite different, each proof is essentially based on either of 3 similar short and elegant algorithms which we refer to as A1 [RV87, LT89, L04], A2 [ND00, L04] and A3 [KR91]. Each algorithm is based on a 2-edge-coloring algorithm for a 2-regular bipartite multigraph with 4-vertex parts. Namely, A1 uses 2, A2 uses at most 2, and A3 uses 1 application(s) of such an algorithm. Each algorithm A\emph{i} deals with 2 cases in which the procedure is especially simple. The algorithms A1 and A2 are very efficient (with A2 being slightly faster than A1), while A3 is not so (contrary to what is claimed in [KR91]) as it relies on an exhausting search to determine the case for each input permutation. However, A3 has some theoretical advantage over A1 and A2 as its 2 cases partition the symmetric group $S_8$ into 2 classes that do not depend on a realization of the algorithm. In [L04], both algorithms A1 and A2 are explicitly described as 2-transition algorithms for the complex $\Delta_{2,3}$, and the corresponding 2 proofs for the statement $\text{\rm tr}(\Delta_{2,3})=2$ are particularly transparent. Moreover, the latter statement, the algorithms and the proofs are straightforwardly generalized [L05] to a wide class of 2-dimensional pure abstract simplicial complexes.
A brute force verification for the case $(k,n)=(2,4)$ of SE conjecture was first reported in [R95]. The first theoretical proof for such case of CSE conjecture was proposed (in graph-theoretic terms) in [ND00]. Although the ideas behind the underlying algorithm for this proof are simple, the algorithm deals with a huge and intricate tree of cases and is substantially more complicated (and not so elegant) than that of the case $(k,n)=(2,3)$. As a result, the proof is very tedious, hard to verify, and leaves little hope for using a similar approach to prove the next case $(k,n)=(2,5)$ of CSE conjecture. An essentially similar but slightly better organized algorithm and proof for (3) were proposed in [DS08] (with no reference to [ND00]).
The upper bound (5) was first obtained in [VR88] for the case $k=2$ and (i) $d^{(*)}(k,r)=2r-1$. In other words, it was shown that (i) at $k=2$ implies $d^{(*)}(2,n)\le 3n-r-1$, if $n > r$. A much simpler proof of (5) for the case $r=2,3$ and (i) appeared in [LT89]. The latter proof was easily extended [ND00] to an arbitrary $r\ge2$. A transparent combinatorial proof in terms of the complex $\Delta_{k,n}$ for the general case of (5) was proposed in [L04]. This proof (together with its underlying transition algorithm) was generalized [L05] to a wide class of pure abstract simplicial complexes of arbitrary dimensions. Namely, it was shown that, given a complex $\Delta$ in this class and an integer $1\le m<\dim(\Delta)$, $$\text{tr}(\Delta) \le 2m + \max \big\{ \text{tr}(\Delta/F) \mid F\in\Delta,\ |F|=m \big\}$$ and, moreover, that any $\ell$-transition algorithm for the complexes $\Delta/F$ can be efficiently used to make a $(2m+\ell)$-transition algorithm for $\Delta$. Note that (5) can be easily obtained as an instance of the latter result. Here $\Delta/ F$ is the \emph{link} of a face $F$ in $\Delta$, i.e., a subcomplex of $\Delta$ defined by $$\Delta/ F := \{ A\in \Delta \ | \ A\cap F = \varnothing \ \&\ A\cup F\in\Delta \big\}.$$ It is worth noting that there are many flawed proofs for SE conjecture in the literature. Most notably, in [Ba01] (the general case) and [C03] (the case $k=2$). The latter proof was first refuted in [BHL06], while the former remains unrefuted in the literature.
## Bibliography
[B65] V.E. Benes, \emph {Mathematical theory of connecting networks and telephone traffic}, Academic Press, New York, 1965.
*[S71] H.S. Stone, \emph {Parallel processing with the perfect shuffle}, IEEE Trans. on Computers \textbf{C-20} (1971), 153-161.
*[B75] V.E. Beneš, \emph {Proving the rearrangeability of connecting networks by group calculation}, Bell Syst. Tech. J. \textbf{54} (1975), 421-434.
[RV87] C.S. Raghavendra, A. Varma, \emph {Rearrangeability of 5-stage shuffle/exchange network for N=8}, IEEE Trans. on Commun. \textbf{COM-35} (1987), 808-812.
[VR88] A. Varma, C.S. Raghavendra, \emph {Rearrangeability of multistage shuffle/exchange networks}, IEEE Trans. on Commun. \textbf{36} (1988), 1138-1147.
[LT89] N. Linial, M. Tarsi, \emph {Interpolation between bases and the shuffle-exchange networks}, European J. of Combinatorics, \textbf{10(1)} (1989), 29-39.
[KR91] K. Kim, C.S. Raghavendra, \emph {A Simple Algorithm to Route Arbitrary Permutations on 8-input 5-stage Shuffle/Exchange Network}, Proc. 5th International Parallel Processing Symposium (1991), 398-403.
[R95] C.S. Raghavendra, \emph {On the rearrangeability conjecture of $(2\log_2 N -1)$-stage shuffle/exchange network}, IEEE Computer Society, Tech. Committee on Comp. Arch. Newsletter, Position paper (Winter 1995), 10-12.
[ND00] H.Q. Ngo, D.Z. Du, \href[\emph{On the rearrangeability of shuffle-exchange networks}]{http://www.cs.umn.edu/research/technical_reports.php?page=report&report_id=00-045}, Tech. Report TR00-045, Dept. of Computer Science, Univ. of Minnesota (2000)
[Ba01] R.E. Bashirov, \emph {On the rearrangeability of 2s-1 stage networks employing uniform interconnection pattern} Calcolo, Springer Verlag, \textbf{38(2)} (2001), 85-97.
[C03] H. Cam, \emph {Rearrangeability of (2n-1)-stage shuffle-exchange networks}, SIAM J. on Computing \textbf{32(3)} (2003), 557-585.
[L04] V. Lioubimov, \emph {Decomposition of symmetric group into product of stabilizers and Shuffle-Exchange problem}, manuscript (2004).
[L05] V. Lioubimov, \emph {Facet transitions in abstract simplicial complexes}, manuscript (2005).
[BHL06] X. Bao, F.K. Hwang, Q. Li, \emph {Rearrangeability of bit permutation networks}, Theoretical Computer Science, \textbf{352(1)} (2006), 197-214.
[DS08] H. Dai, X. Shen, \emph {Rearrangeability of 7-stage 16x16 shuffle-exchange networks}, Frontiers of Electrical and Electronic Engineering in China, \textbf{3(4)} (2008), 440-458.
* indicates original appearance(s) of problem. | 2018-02-25 23:52:20 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 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": 0.9448519349098206, "perplexity": 777.8709378299321}, "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-2018-09/segments/1518891817523.0/warc/CC-MAIN-20180225225657-20180226005657-00153.warc.gz"} |
https://johncarlosbaez.wordpress.com/2020/02/27/topos-theory-part-8/ | ## Topos Theory (Part 8)
Let’s look at an example of a presheaf topos, to see what various things I’ve been talking about actually look like—especially the subobject classifier.
Our example will illustrate the connection between topos theory and intuitionistic logic: that is, logic where the law of excluded middle, “p or not p”, fails. Intuitionistic logic goes back to Brouwer, who happens to have been born this very day in 1881. Topos theory formalizes intuitionistic logic in a way he might not have liked. But it does roughly capture some of his thoughts about how mathematics is an activity that happens in time.
The subobject classifier in the category of sets is the 2-element set
$\{\mathrm{true}, \mathrm{false}\}$
and it’s a Boolean algebra with the usual operations of logic. But the subobject classifier in a topos is usually more complicated. It can have more than 2 elements. Of course, it’s not just a set, it’s an object in a topos—but remember, an object of a topos still has a set of ‘elements’. The subobject classifier is usually not a Boolean algebra: it’s something more general called an internal Heyting algebra, where the law of excluded middle may not hold. When that happens, logic inside the topos is intuitionistic.
We’re not really ready to talk about internal Heyting algebras, but we are ready to see a topos with an interesting subobject classifier.
### Time-dependent sets
Let’s imagine a world where sets are ‘time-dependent’, but in the following special way. As time passes, a set can get new elements as we learn more about it. We can also learn new equations between elements, so elements that were previously distinct can merge. But we never think an element is in a set and then discover it’s not, and we never think two elements are equal and then discover they’re not.
You can think of this as a naive model of an infallible mathematician proving more and more as time goes by.
To keep things simple, let’s suppose that time starts at zero and proceeds in steps. So, our set of times will be the natural numbers. Let’s think of the the natural numbers with their usual ordering as a category. We get a category $\mathsf{N}$ where the objects are natural numbers and there’s one morphism from $n$ to $m$ if $n \le m,$ and none otherwise. We’ll write
$i_{n,m} \colon n \to m$
for the unique morphism from $n$ to $m$ when $n \le m.$ Note that all these morphisms are composites of those of the form $i_{n,n+1}.$
Our topos will consist of presheaves on $\mathsf{N}^{\mathrm{op}}.$ Of course the definition of presheaf also also involves an ‘op’, so the two ops cancel and our topos is
$\mathsf{Set}^{\mathsf{N}}$
The double ‘op’ is somewhat annoying when you’re first trying to find your footing, but such is life.
What’s an object of $\mathsf{Set}^{\mathsf{N}}$ like? It consists of a set $X(n)$ and a map
$X(i_{n,n+1}) \colon X(n) \to X(n+1)$
for each natural number $n.$ As time passes, new elements can appear. That is, $X(n+1)$ can have elements that aren’t in the image of $f_n.$ Elements can merge. That is, $X(i_{n,n+1})$ can map two elements of $X(n)$ to the same element of $X_{n+1}.$ But elements can’t ‘disappear’ or ‘split’.
You should draw such a thing. In class I drew it as something like an ‘infinitely deep tree’ where we move down the tree as time passes. Newly appearing elements are leaves, and branches can merge as we move down the tree. It doesn’t have a root—it keeps going down forever! Also, it’s not necessarily connected. So, we could call it an ‘infinitely deep forest’: a disjoint union of infinitely deep trees. You can imagine a surreal sort of rainforest that keeps going down forever.
### Representables
What’s a representable object of $\mathsf{Set}^{\mathsf{N}}$ like? Thanks to the annoying ‘op’ business, a representable object is a functor of the form
$\mathrm{hom}(n, -) \colon \mathsf{N} \to\ \mathsf{Set}$
So, $\mathrm{hom}(n, m)$ is empty for $m < n$ and it has one element for $m \ge n.$ We can say it's a time-dependent set with a single element, `discovered at time $n$’. In terms of our rainforest imagery, it looks like a very skinny infinitely deep tree with no branches—sort of like a telephone pole.
The Yoneda lemma, or one of its offshoots, says that every object in $\mathsf{Set}^{\mathsf{N}}$ is a colimit of representables. See Proposition 1 in Section I.5 for details. In terms of our pictures, this means that any rainforest can be built from telephone poles.
How does that work, exactly? The colimit of any diagram can be built by first taking the coproduct of every object in the diagram and then taking a coequalizer that forces all the necessary triangles to commute. So, we should think about first taking a coproduct of representables, and then a coequalizer.
A coproduct acts like a 'disjoint union'. So, a coproduct of representables can be visualized as a disjoint union of telephone poles of various heights. Note that in this sort of time-dependent set elements can appear but never merge.
Puzzle. Show that $X \in \mathsf{Set}^{\mathsf{N}}$ is a coproduct of representables if and only if all the maps
$X(i_{n,n+1}) \colon X(n) \to X(n+1)$
are injections.
We can take a coequalizer to ‘glue together’ telephone poles and get more interesting infinitely deep trees… or indeed, infinitely deep forests.
Puzzle. Let $X \in \mathsf{Set}^{\mathsf{N}}$ be a time-dependent set with 2 elements at time 0 and 1 element at all later times. Show how to build $X$ by taking a coproduct of two representables and then taking a coequalizer.
In terms of pictures, we are taking two telephone poles and gluing them together except at the very top, getting an infinitely deep tree that branches at the top.
### Subobjects
What’s a subobject of an object $X \in \mathsf{Set}^{\mathsf{N}}$ like? By definition it’s an equivalence class of monomorphisms into $X.$ I explained the equivalence relation last time. But we can work out what all this amounts to:
Puzzle. Show that a subobject of $X \in \mathsf{Set}^{\mathsf{N}}$ is the same as a subset $S(n) \subseteq X(n)$ for each natural number $n$ such that $S(n)$ is mapped into $S(n+1)$ by the map
$X(i_{n,n+1}) \colon X(n) \to X(n+1).$
Puzzle. Draw an object of $\mathsf{Set}^{\mathsf{N}}$ together with a subobject.
I would draw an ‘infinitely deep forest’ in green and then draw a ‘subforest’, maybe shading it in brown. As we follow any branch down, it can enter the subforest and change from green to brown. It can then never turn green again as you go further down.
In other words: at any time you can learn that an element of your time-dependent set $\mathsf{S}$ is in some time-dependent subset $\mathsf{T}.$ But once you learn it’s in, you know this for the rest of time!
This suggests that in this topos, the truth values are not merely ‘true’ and ‘false’. For each $n$ there should be a truth value ‘becomes true at time $n$‘. And there should be a truth value ‘never becomes true’—or in other words, ‘false’.
### The subobject classifier
Now let’s systematically study the subobject classifier of $\mathsf{Set}^{\mathsf{N}}.$ We saw last time how to determine the subobject classifier in any presheaf category, though I didn’t explain why this procedure actually works. Let’s apply the procedure in our example here to get some intuition for it.
Last time I claimed that the subobject classifier in a presheaf topos $\mathsf{Set}^{\mathsf{C}^{\textrm{op}}}$ is a presheaf
$\Omega \colon \mathsf{C}^{\textrm{op}} \to \mathsf{Set}$
that sends any object $c$ to the set of all sieves on $c.$ Remember, a sieve on $c$ is a collection of morphisms with target $c$ that’s closed under precomposition.
So, let’s start by seeing what this means in our example. The annoying ‘op’ comes in now, because our category $\mathsf{Set}^{\mathsf{N}}$ is the category of presheaves on $\mathsf{N}^{\mathrm{op}}.$ By definition, a sieve on $n$ is a collection of morphisms in $\mathsf{N}^{\mathrm{op}}$ with target $n$ that is closed under precomposition. So, in terms of the category$\mathsf{N},$ a sieve is a collection of morphisms with source $n$ that’s closed under postcomposition.
For each natural number $i$ there’s a sieve on $n$ consisting of all the morphisms from $n$ to the objects $n+i, n+i+1,$ $n+i+2, \dots.$ Clearly this is closed under postcomposition. Let’s call this sieve $t_i.$
There’s also another sieve on $n,$ namely the empty sieve: the sieve with no morphisms at all. Let’s call this sieve $t_\infty.$
Puzzle. Show that all the sieves on $n$ are those of the form $t_0, t_1, t_2, \dots$ together with $t_\infty.$
Thus, we know this about the subobject classifier:
$\Omega(n) = \{t_0, t_1, t_2, \dots, t_\infty\}$
We’ll see that $t_0$ means ‘true now’, $t_1$ means ‘true tomorrow’, $t_2$ means ‘true the next day’, and so on… while $t_\infty$ means ‘never true’— or in other words, false. Mac Lane and Moerdijk call the subscript $i$ in $t_i$ the ‘time to truth’. It’s how long you have to wait for something to become true.
So we’ve seen what $\Omega$ does to objects of $\mathsf{N}.$ But what does it do to morphisms?
We can guess: if something is true in $i$ days now, tomorrow it will be true in $i - 1$ days, or in 0 days if $i - 1 = -1.$ And of course if it’s never true now, it will never be true tomorrow.
Let’s check this.
Suppose $S$ is any sieve on $n.$ Then $\Omega(i_{n,m})S$ is a sieve on $m,$ and a morphism is in this sieve iff its composite with $i_{n,m}$ is in $S.$ This follows from the general description I gave last time.
Puzzle. Show that
$\Omega(i_{n,n+1}) \colon \Omega(n) \to \Omega(n+1)$
maps $t_i$ to $t_{i-1}$ if $i - 1 \ge 0$, and to $t_0$ otherwise. (Here we say that infinity minus any natural number is still infinity.)
So, our idea is working!
Now you know enough to draw the subobject classifier. If you draw it as an infinitely deep forest, it has infinitely many leaves on top, where $n = 0.$ These are $t_0, t_1, t_2, \dots, t_\infty.$ As we follow these down to $n = 1,$ the $t_1$ branch merges with the $t_0$ branch, while the other branches get renamed: $t_2$ gets renamed $t_1,$ $t_3$ gets renamed $t_2,$ and so on. But not all the branches get renamed! The $t_\infty$ branch is still called $t_\infty.$
As we continue to go down, the same thing keeps happening forever.
Puzzle. How many connected components does this infinitely deep forest have?
Next: a subobject classifier $\Omega$ in a topos needs to be equipped with an element
$\mathrm{true} \colon 1 \to \Omega$
What is this in our example? We can guess. ‘True’ should mean true now. The terminal time-dependent set $1$ has one element for each time $n.$ So, $\mathrm{true}$ should map this one element to $t_0 \in \Omega(n).$
Now you can check this guess:
Puzzle. Show that for any time-dependent set $X,$ morphisms
$\chi \colon X \to \Omega$
correspond in a one-to-one way with subobjects of $X.$
One nice way to start tackling this problem is to draw a time-dependent set $X$ and a subobject of it, say $S.$ Next to these draw $\Omega.$ Then figure out which choice of $\chi \colon X \to \Omega$ sends precisely the elements of $S$ to $t_0.$
That will help you see how subobjects determine morphisms to $\Omega.$ But morphisms to $\Omega$ should also determine subobjects! For this, draw a time-dependent set and a morphism from it to $\Omega.$ Show that the elements that get mapped to $t_0$ form a subobject of $X.$
Once you’ve done this, you’ll be ready to give a more formal argument:
Puzzle. Show that for any $X \in \mathsf{Set}^{\mathsf{N}}$ there is a bijection between morphisms
$\chi \colon X \to \Omega$
and subobjects of $X,$ given as follows: for any such morphism $\chi$, we pull back $\mathrm{true}$ along $\chi$ obtaining a mono
$i \colon S \rightarrowtail X$
and then take the subobject of $X$ corresponding to this.
When you do this, it means you understand the subobject classifier in the topos of time-dependent sets! You may understand it now… but if not, maybe you’ll understand it tomorrow, or the next day.
The series so far:
Part 1: sheaves, elementary topoi, Grothendieck topoi and geometric morphisms.
Part 2: turning presheaves into bundles and vice versa; turning sheaves into etale spaces and vice versa.
Part 3: sheafification; the adjunction between presheaves and bundles.
Part 4: direct and inverse images of sheaves.
Part 5: why presheaf categories are elementary topoi: colimits and limits in presheaf categories.
Part 6: why presheaf categories are elementary topoi: cartesian closed categories and why presheaf categories are cartesian closed.
Part 7: why presheaf categories are elementary topoi: subobjects and subobject classifiers, and why presheaf categories have a subobject classifier.
Part 8: an example: the topos of time-dependent sets, and its subobject classifier.
This site uses Akismet to reduce spam. Learn how your comment data is processed. | 2020-03-30 20:28:43 | {"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": 132, "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": 0.8343265652656555, "perplexity": 431.20434664423334}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-16/segments/1585370497301.29/warc/CC-MAIN-20200330181842-20200330211842-00215.warc.gz"} |
https://www.physicsforums.com/threads/linear-de.787102/ | # Linear DE
1. Dec 11, 2014
### basty
1. The problem statement, all variables and given/known data
This problem appears as one of exercise, of a linear differential equations chapter in my DE book.
$y \ dx - 4(x + y^6) \ dy = 0$
How to change above equation in a standard form of a linear differential equation?
The standard form of a linear differential equation is:
$\frac{dy}{dx} + P(x) y = f(x)$
It appears that the above equation is not linear because the power of $y$ is not 1 instead of 6.
Also, what is its integrating factor $(e^{\int P(x) \ dx})$?
2. Relevant equations
3. The attempt at a solution
$y \ dx - 4(x + y^6) \ dy = 0$
$y - 4(x + y^6) \frac{dy}{dx} = 0$
$4(x + y^6) \frac{dy}{dx} - y = 0$
$\frac{dy}{dx} - \frac{1}{4(x + y^6) }y = 0$
2. Dec 11, 2014
### LCKurtz
You are correct. It is not linear.
That's the wrong question to ask. Your equation is in the form $Pdx + Qdy=f(x)$. Look in your text about exact DE's and what condition on $P$ and $Q$ makes the equation exact.
[Edit, added] And if the equation isn't exact is it possible to find an integrating factor that makes it exact?
Last edited: Dec 11, 2014 | 2017-08-17 11:09:50 | {"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": 0.8121646642684937, "perplexity": 523.1608006788584}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-34/segments/1502886103167.97/warc/CC-MAIN-20170817092444-20170817112444-00637.warc.gz"} |
https://math.answers.com/algebra/If_the_circumference_is_8_feet_what_is_the_diameter_of_the_circle | 0
# If the circumference is 8 feet what is the diameter of the circle?
Wiki User
2010-05-11 14:18:28
If the circumference is 8 feet, the diameter of the circle is: 2.55 feet.
Wiki User
2010-05-11 14:18:28
Study guides
20 cards
## A number a power of a variable or a product of the two is a monomial while a polynomial is the of monomials
➡️
See all cards
3.8
2254 Reviews
Earn +20 pts
Q: If the circumference is 8 feet what is the diameter of the circle?
Submit
Still have questions? | 2023-03-26 13:19:56 | {"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": 0.8767890334129333, "perplexity": 1781.4184709280737}, "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/1679296945472.93/warc/CC-MAIN-20230326111045-20230326141045-00173.warc.gz"} |
https://sgmathsacad.com/resources/ri-2021-jc2-prelim-p2-q09/ | RI/2021/JC2/Prelim/P2/Q09
A bag initially contains 3 red balls and 3 black balls. Whenever a red ball is drawn from the bag, it is put back into the bag together with an extra red ball. Whenever a black ball is drawn from the bag, it is not put back into the bag and no extra balls are added.
Isaac draws $$n$$ balls from the bag, one after another, where $$n \in Z ^{*}$$, and $$R$$ denotes the number of red balls out of the $$n$$ balls drawn.
(a) Give two reasons why $$R$$ cannot be modelled using a Binomial distribution.
[2]
(b) For $$n=3$$, find
(i) $$P (R \geq 1)$$,
[2]
(ii) the probability that the first ball drawn is black given that at least 1 of the 3 balls drawn is red.
[3]
(c) For $$n=31$$, show that $$P (R=31)=\frac{1}{714}$$.
[2]
(d) Isaac wins 100 dollars for each red ball he draws if all the balls he draws from the bag are red, and does not win any money otherwise. What is the maximum amount of money Isaac would win if the probability of all the balls he draws are red exceeds $$0.0001$$ ?
[3] | 2023-03-28 03:16:53 | {"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": 0.8758358955383301, "perplexity": 170.407169476653}, "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/1679296948756.99/warc/CC-MAIN-20230328011555-20230328041555-00616.warc.gz"} |
https://mathspace.co/textbooks/syllabuses/Syllabus-952/topics/Topic-19850/subtopics/Subtopic-263382/?textbookIntroActiveTab=overview | # Investigation: Modeling tsunami movement
Lesson
## Objectives
• To work with a radical function.
• Paper
• Pen
• Internet
• Calculator
## Procedure
Tsunamis are series of large ocean waves that can be caused by an underwater volcanic eruption, earthquake or landslide. Tsunamis are dangerous because they can reach up to 500 miles per hour. Due to the enormous threat a tsunami poses, it is important for scientists to track any possible tsunamis that may be occurring. Several tsunami research facilities exist that constantly monitor the movement of the waves in the oceans to ensure that they can give warning to the areas that are in danger. There are two equations that are important for monitoring tsunamis:
1. $s$s=$\sqrt{g\times d}$g×d where s=speed in meters per second, $g$g=acceleration due to gravity ($9.8$9.8 meters per second$^2$2 ) and $d$d= depth of the ocean in meters
2. $t$t=$\frac{d}{s}$ds where t= the tsunami’s travel time to shore in seconds, $d$d= the distance to shore in meters, and $s$s=the speed at which the tsunami is traveling in meters per second
In this investigation we will be investigating how fast tsunamis move and how long it takes them to reach varying locations using these equations.
## Questions
1. What would be the speed of a tsunami that was located in a part of the ocean that is $1200$1200 meters deep?
• Is the speed a rational or irrational number?
2. What would be the speed of a tsunami that was located in a part of the ocean that is $2400$2400 meters deep?
• Is the speed a rational or irrational number?
3. Is the speed of the tsunami at a depth of $2400$2400 meters double the speed of the tsunami located at a depth of $1200$1200 meters? Why or why not?
4. Work with a friend to answer the last questions:
5. Suppose that an earthquake hits at the coordinates $40N$40N, $140W$140W . Assume that the depth of the water at the epicenter of the tsunami is $4500$4500 meters. How long will it take for the tsunami to reach Santa Barbara, California? How long will it take to reach San Francisco, California?
To find the distance from the epicenter to the city you can look up the latitude and longitude of the city and then create a right triangle using the difference in latitudes as one leg and difference in longitudes as the other leg. Then solve for the hypotenuse and use the map scale to turn this into kilometers. Or, you can use a map application online to measure the distance.
2. Would the tsunami take longer to reach Santa Barbara or San Francisco?
3. Why is it important to be able to determine the amount of time it will take a tsunami to reach different locations?
### Outcomes
#### F.IF.B.4'''
For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. '''Include rational, square root and cube root; emphasize selection of appropriate models. | 2021-12-06 14:49:17 | {"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": 0.5350436568260193, "perplexity": 1033.3349969720446}, "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/1637964363301.3/warc/CC-MAIN-20211206133552-20211206163552-00079.warc.gz"} |
https://zims-en.kiwix.campusafrica.gos.orange.com/wikipedia_en_all_nopic/A/Identifiability | Identifiability
In statistics, identifiability is a property which a model must satisfy in order for precise inference to be possible. A model is identifiable if it is theoretically possible to learn the true values of this model's underlying parameters after obtaining an infinite number of observations from it. Mathematically, this is equivalent to saying that different values of the parameters must generate different probability distributions of the observable variables. Usually the model is identifiable only under certain technical restrictions, in which case the set of these requirements is called the identification conditions.
For a less technical treatment, see Parameter identification problem.
A model that fails to be identifiable is said to be non-identifiable or unidentifiable: two or more parametrizations are observationally equivalent. In some cases, even though a model is non-identifiable, it is still possible to learn the true values of a certain subset of the model parameters. In this case we say that the model is partially identifiable. In other cases it may be possible to learn the location of the true parameter up to a certain finite region of the parameter space, in which case the model is set identifiable.
Aside from strictly theoretical exploration of the model properties, identifiability can be referred to in a wider scope when a model is tested with experimental data sets, using identifiability analysis.[1]
Definition
Let ${\displaystyle {\mathcal {P}}=\{P_{\theta }:\theta \in \Theta \}}$ be a statistical model where the parameter space ${\displaystyle \Theta }$ is either finite- or infinite-dimensional. We say that ${\displaystyle {\mathcal {P}}}$ is identifiable if the mapping ${\displaystyle \theta \mapsto P_{\theta }}$ is one-to-one:[2]
${\displaystyle P_{\theta _{1}}=P_{\theta _{2}}\quad \Rightarrow \quad \theta _{1}=\theta _{2}\quad \ {\text{for all }}\theta _{1},\theta _{2}\in \Theta .}$
This definition means that distinct values of θ should correspond to distinct probability distributions: if θ1θ2, then also Pθ1Pθ2.[3] If the distributions are defined in terms of the probability density functions (pdfs), then two pdfs should be considered distinct only if they differ on a set of non-zero measure (for example two functions ƒ1(x) = 10 x < 1 and ƒ2(x) = 10 x 1 differ only at a single point x = 1 — a set of measure zero — and thus cannot be considered as distinct pdfs).
Identifiability of the model in the sense of invertibility of the map ${\displaystyle \theta \mapsto P_{\theta }}$ is equivalent to being able to learn the model's true parameter if the model can be observed indefinitely long. Indeed, if {Xt} S is the sequence of observations from the model, then by the strong law of large numbers,
${\displaystyle {\frac {1}{T}}\sum _{t=1}^{T}\mathbf {1} _{\{X_{t}\in A\}}\ {\xrightarrow {\text{a.s.}}}\ \Pr[X_{t}\in A],}$
for every measurable set A S (here 1{...} is the indicator function). Thus, with an infinite number of observations we will be able to find the true probability distribution P0 in the model, and since the identifiability condition above requires that the map ${\displaystyle \theta \mapsto P_{\theta }}$ be invertible, we will also be able to find the true value of the parameter which generated given distribution P0.
Examples
Example 1
Let ${\displaystyle {\mathcal {P}}}$ be the normal location-scale family:
${\displaystyle {\mathcal {P}}={\Big \{}\ f_{\theta }(x)={\tfrac {1}{{\sqrt {2\pi }}\sigma }}e^{-{\frac {1}{2\sigma ^{2}}}(x-\mu )^{2}}\ {\Big |}\ \theta =(\mu ,\sigma ):\mu \in \mathbb {R} ,\,\sigma \!>0\ {\Big \}}.}$
Then
{\displaystyle {\begin{aligned}&f_{\theta _{1}}=f_{\theta _{2}}\\[6pt]\Longleftrightarrow {}&{\frac {1}{{\sqrt {2\pi }}\sigma _{1}}}\exp \left(-{\frac {1}{2\sigma _{1}^{2}}}(x-\mu _{1})^{2}\right)={\frac {1}{{\sqrt {2\pi }}\sigma _{2}}}\exp \left(-{\frac {1}{2\sigma _{2}^{2}}}(x-\mu _{2})^{2}\right)\\[6pt]\Longleftrightarrow {}&{\frac {1}{\sigma _{1}^{2}}}(x-\mu _{1})^{2}+\ln \sigma _{1}={\frac {1}{\sigma _{2}^{2}}}(x-\mu _{2})^{2}+\ln \sigma _{2}\\[6pt]\Longleftrightarrow {}&x^{2}\left({\frac {1}{\sigma _{1}^{2}}}-{\frac {1}{\sigma _{2}^{2}}}\right)-2x\left({\frac {\mu _{1}}{\sigma _{1}^{2}}}-{\frac {\mu _{2}}{\sigma _{2}^{2}}}\right)+\left({\frac {\mu _{1}^{2}}{\sigma _{1}^{2}}}-{\frac {\mu _{2}^{2}}{\sigma _{2}^{2}}}+\ln \sigma _{1}-\ln \sigma _{2}\right)=0\end{aligned}}}
This expression is equal to zero for almost all x only when all its coefficients are equal to zero, which is only possible when |σ1| = |σ2| and μ1 = μ2. Since in the scale parameter σ is restricted to be greater than zero, we conclude that the model is identifiable: ƒθ1 = ƒθ2θ1 = θ2.
Example 2
Let ${\displaystyle {\mathcal {P}}}$ be the standard linear regression model:
${\displaystyle y=\beta 'x+\varepsilon ,\quad \mathrm {E} [\,\varepsilon \mid x\,]=0}$
(where ′ denotes matrix transpose). Then the parameter β is identifiable if and only if the matrix ${\displaystyle \mathrm {E} [xx']}$ is invertible. Thus, this is the identification condition in the model.
Example 3
Suppose ${\displaystyle {\mathcal {P}}}$ is the classical errors-in-variables linear model:
${\displaystyle {\begin{cases}y=\beta x^{*}+\varepsilon ,\\x=x^{*}+\eta ,\end{cases}}}$
where (ε,η,x*) are jointly normal independent random variables with zero expected value and unknown variances, and only the variables (x,y) are observed. Then this model is not identifiable,[4] only the product βσ² is (where σ² is the variance of the latent regressor x*). This is also an example of a set identifiable model: although the exact value of β cannot be learned, we can guarantee that it must lie somewhere in the interval (βyx, 1÷βxy), where βyx is the coefficient in OLS regression of y on x, and βxy is the coefficient in OLS regression of x on y.[5]
If we abandon the normality assumption and require that x* were not normally distributed, retaining only the independence condition ε η x*, then the model becomes identifiable.[4]
Software
In the case of parameter estimation in partially observed dynamical systems, the profile likelihood can be also used for structural and practical identifiability analysis.[6] An implementation of the is available in the MATLAB Toolbox PottersWheel.
References
Citations
1. Raue, A.; Kreutz, C.; Maiwald, T.; Bachmann, J.; Schilling, M.; Klingmuller, U.; Timmer, J. (2009-08-01). "Structural and practical identifiability analysis of partially observed dynamical models by exploiting the profile likelihood". Bioinformatics. 25 (15): 1923–1929. doi:10.1093/bioinformatics/btp358. PMID 19505944.
2. Lehmann & Casella 1998, Definition 1.5.2
3. van der Vaart 1998, p. 62
4. Reiersøl 1950
5. Casella & Berger 2001, p. 583
6. Raue, A; Kreutz, C; Maiwald, T; Bachmann, J; Schilling, M; Klingmüller, U; Timmer, J (2009), "Structural and practical identifiability analysis of partially observed dynamical models by exploiting the profile likelihood", Bioinformatics, 25 (15): 1923–9, doi:10.1093/bioinformatics/btp358, PMID 19505944, archived from the original on 2013-01-13.
Sources
• Walter, É.; Pronzato, L. (1997), Identification of Parametric Models from Experimental Data, Springer | 2021-10-20 03:16:08 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 16, "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": 0.915557324886322, "perplexity": 1019.361187777218}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-43/segments/1634323585302.56/warc/CC-MAIN-20211020024111-20211020054111-00551.warc.gz"} |
https://therbootcamp.github.io/BaselRBootcamp_2018April/_sessions/D2S3_CaseStudies/Financial_Data_Case_Study.html | ## Overview
In this case study, you will jointly analyse historic data of three major stock indices, the Dow Jones, the DAX, and the Nikkei, and the exchange rates between the US dollar, the Euro, and the Yen. Using this data, you will address several questions. How large was the impact of the recent financial crisis on the respective stock markets? How correlated is the development between the stock markets? What is the relationship between stock market returns and exchange rates? To address these questions, you will import several data files, while tuning import parameters to match the idiosyncracies of the data. You will merge the data files into a single data frame, and mutate the data to reflect changes in index price and exchange rate. You will analyze correlations of stock indices among themselves and to exchange rates. You create illustrative plots for each of the analyses. Below you will find several tasks that will guide you through these steps. For the most part these tasks require you to make use of what you have learned in the sessions Data I/O, Data Wrangling, and Statistics. However, they will also go beyond what you have learned, in particular when it comes to plotting. In those cases, the tasks will provide the necessary code and guidance.
Variables of data sets “^DJI.csv”, “^GDAXI.csv”, “^N225.csv”
Variable Description
Date Current day
Open Day’s price when the stock exchange opened
High Day’s highest price
Low Day’s lowest price
Close Day’s closing price
Adj Close Adjusted closing price that has been amended to include any distributions and corporate actions that occurred at any time prior to the next day’s open
Variables of data sets “euro-dollar.txt”, “yen-dollar.txt”
Variable Description
Date (currently unnamed) Current day
Rate (currently unnamed) Day’s exchange rate in terms of 1 US Dollar. E.g., a value of .75 means that the respective currenty is worth a fraction of .75 of 1 US Dollar
## Data I/O
1. Open a new R script and save it as a new file called finance_case_study.R. At the top of the script, using comments, write your name and the date. Then, load the tidyversepackage. Here’s how the top of your script should look:
## NAME
## DATE
## Sales Data - Case Study
library(tidyverse)
1. Load in the stock index data sets, “^DJI.csv”, “^GDAXI.csv”, and “^N225.csv”, from the data folder, using the read_csv()-function. In so doing, set an explicit na-argument to account for the fact that “^GDAXI.csv” “^N225.csv” use a specific character string to represent missings in the data. To identify the NA-character string in the data open one of them (in a standard text viewer, e.g., textedit).
2. Load in the exchange rate data sets, “euro-dollar.txt” and “yen-dollar.txt”, from the data folder, using the read_delim()-function and \t as the delim-argument (separates by tabulator). Observe the inferred data types and the variables names. There’s something wrong. First, we want the columns to be called Date and Rate (and not be taken from the first row). To achieve this, include the col_names-argument and assign to it a vector that contains the variable names. Second, we want the Date-variable to be of type date. To achieve this, use the parse_date function with format = '%d %b %Y', which specifies the exact format the dates are formatted in, and overwrite the existing Date-variable.
3. Get a first impression of the datasets using print(), typeof() and str(). What type are the data objects, what variables do they contain?
## Data Wrangling
1. Create a single data frame from all five datasets that includes only the variables containing the dates, the stock index (unadjusted) closing prices, and the exchange rates. Do this by piping (i.e., using %>%) together several inner_join()-functions, joining the data sets one-by-one using the Date variable. At the end, rename the variables appropriately using the rename()-function. Note, in joining two data sets you can control the naming of overlapping variable names using the suffix-argument of the inner_join()-function. Observe that inner_join() takes care of the fact that different dates are available in each of the data sets by only retaining dates for which all data sets provide data on.
2. Create new variables containing the change in index price and exchange rate for each variable using the mutate-function(). To compute the change, use the diff()-function. Since diff() will return n - 1 change values, add an NA at the first position of the change variable à la c(NA, diff(my_variable)).
3. Create a variable containing merely the year of the date variable using mutate() and year() from the lubridate-package (should have been installed with the tidyverse). First, load the lubridate-package.
4. Create a long version of data frame, in which variables occupy different rows rather than columns, using the gather()-function from the tidyr-package (also part of the tidyverse). To do this use the command below. You may have to (or want to) change the object/variable names. The first two arguments (given we used pipes) to the gather-function specify the names of the new variables, the third and fourth specify the names of the variable containing the dates and years with a leading hyphen. Check out the example in the ?gather-help file. When done, inspect the object and compare it (visually) to the original, wide version.
# create long version of data frame
long_data = data %>% gather(variable, value, -Date, -year)
## Statistics (& Plotting)
1. Plot the price development of the three stock indices using the following command (using the long data object). The code uses a modern and very powerful plotting package called ggplot2, which you will be introduced to on the second weekend of the course. For the code to work, you may have to adjust the object and variable names to match the ones in your data frame. Inspecting the plot, do you see a significant drop anywhere?
# create long version of data frame
temp_data <- long_data %>% filter(variable %in% c("Close_dow","Close_dax","Close_nik"))
ggplot(data = temp_data, mapping = aes(x = Date, y = value)) +
geom_line() +
facet_grid(~variable)
1. Calculate the overall stock index price change per year. Use group_by(), summarize(), and sum() on the stock index change variables. Remember there were NA’s in two of the stock index price variables. When was the biggest drop in stock index prices?
2. Now that you know when the biggest drop occured, do you not wonder which stock index suffered the biggest loss? Compare the overall losses to the index price on the first trading day of that year. To do this, first identify the first date available for that year and then filter() the data based on the respective character string to retrieve that day’s closing prices. Then divide the overall stock price change by that years first closing price. Which stock index suffered the greatest relative loss?
3. One driver behind the results observed for the last two tasks is that modern financial markets are closely intertwined, to the extend that a change in one market can bring about a change in the markets. Evaluate this aspect of financial markets by correlating the stock index change variables among each other using cor(). Note that cor() can take a data frame as an argument to produce the full correlation matrix among all variables. Also, don’t forget about the NAs - there is an argument for cor() to deal with them. How closely are the stock indices related and which ones are most closely related?
4. Evaluate the stability of the relationships between financial markets by analyzing the correlations for each year. Note that here have to specify each pairwise correlation separately in order to summarize() the correlation for each year (rather than computing the entire correlation matrix).
5. Another important index of the financial markets is the exchange rate to other currencies. Generally, it is assumed that a strong economcy translates in both a strong stock index and a strong currency relative to other currencies. First, evaluate whether changes in exchange rates correlate with each other the same way that stock indices do.
6. Now evaluate whether exchange rates vary as a function of the difference between stock indices. I.e., does, for instance, a large difference between Dow Jones and DAX translate into a strong Dollar relative to the EURO? Based on the above intuition this should be the case. However, economic theory has also produced an alternative hypothesis. That is, foreign investors who benefit from a rise in stock index price may be motivated to sell their holdings and exhange them for their own currency to mantain a neutral position. This would, in effect, depreciate the currency at the same time as the stock index is outperforming, thus producing a negative relationship. What do you think? Ask the data.
7. Now, evaluate the stability of the above relationship for each year separately? Can you make out a stable pattern? No? I guess it depends. | 2021-06-16 00:36:58 | {"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": 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": 0.34168896079063416, "perplexity": 1710.1227143759868}, "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/1623487621699.22/warc/CC-MAIN-20210616001810-20210616031810-00059.warc.gz"} |
https://www.thestudentroom.co.uk/showthread.php?t=5860006 | Trig Equation
Watch
Announcements
#1
. Solve for x.
0
1 year ago
#2
(Original post by esrever)
. Solve for x.
double angle formula?
0
1 year ago
#3
cos^2(x)-2cos(x)sin(x)+0.6=0
sin^2(x)=0.6
1
#4
(Original post by mqb2766)
double angle formula?
Do you mean rewriting 2sin(x)cos(x) as sin(2x)?
0
#5
(Original post by 8013)
cos^2(x)-2cos(x)sin(x)+0.6=0
sin^2(x)=0.6
Can you please provide some more steps?
0
1 year ago
#6
(Original post by esrever)
Do you mean rewriting 2sin(x)cos(x) as sin(2x)?
yes and similar for cos^2(x)
0
#7
(Original post by mqb2766)
yes and similar for cos^2(x)
I tried it but got . I don't know where to proceed from here.
Last edited by esrever; 1 year ago
0
1 year ago
#8
Good point :-). Give me a sec.
(Original post by esrever)
I tried it but got . I don't know where to proceed from here.
0
1 year ago
#9
(Original post by mqb2766)
Good point :-). Give me a sec.
Convert the cos and sin into a single
Rsin(2x + alpha)
then solve.
1
1 year ago
#10
(Original post by 8013)
cos^2(x)-2cos(x)sin(x)+0.6=0
sin^2(x)=0.6
{cos(2x) + 1}/2 -sin(2x) + 0.6 = 0
cos(2x) - 2sin(2x) = -2,2
now apply the wave form method.... Rcos(2x + α) = -2.2
1
#11
Thank you so much . But my textbook quotes an alternative method (which I found quite counter-intuitive):
Rewrite as it as and then use .
Isn't there a easier way similar to this?
0
1 year ago
#12
(Original post by esrever)
Thank you so much . But my textbook quotes an alternative method (which I found quite counter-intuitive):
Rewrite as it as and then use .
Isn't there a easier way similar to this?
When you have a quadratic like this, the usual ways are to 1) convert into a double angle (as above) or 2) solve as a quadratic (as textbook). It looked like a double angle because of the cos^2 and cos*sin terms, but there are usually a few different ways to solve and as long as you spot the sub, the textbook answer is ok.
Last edited by mqb2766; 1 year ago
0
#13
(Original post by mqb2766)
When you have a quadratic like this, the usual ways are to 1) convert into a double angle (as above) or 2) solve as a quadratic (as textbook). It looked like a double angle because of the cos^2 and cos*sin terms, but there are usually a few different ways to solve and as long as you spot the sub, the textbook answer is ok.
Thank you so much
0
1 year ago
#14
(Original post by esrever)
Thank you so much . But my textbook quotes an alternative method (which I found quite counter-intuitive):
Rewrite as it as and then use .
Isn't there a easier way similar to this?
that method works. in the exam they would give you a hint... they would not expect you to spot that right away.
0
#15
(Original post by the bear)
that method works. in the exam they would give you a hint... they would not expect you to spot that right away.
That's likely but recent further maths questions have been very tricky though
0
X
new posts
Back
to top
Latest
My Feed
Oops, nobody has postedin the last few hours.
Why not re-start the conversation?
see more
See more of what you like onThe Student Room
You can personalise what you see on TSR. Tell us a little about yourself to get started.
Poll
Join the discussion
Current uni students - are you thinking of dropping out of university?
Yes, I'm seriously considering dropping out (49)
16.33%
I'm not sure (8)
2.67%
No, I'm going to stick it out for now (103)
34.33%
I have already dropped out (4)
1.33%
I'm not a current university student (136)
45.33% | 2020-10-22 04:22:31 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8102817535400391, "perplexity": 3012.8443939846607}, "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-2020-45/segments/1603107878879.33/warc/CC-MAIN-20201022024236-20201022054236-00475.warc.gz"} |
https://socratic.org/questions/how-do-you-graph-y-sin-x-2-1#316707 | # How do you graph y=sin x/2?
Oct 1, 2016
graph{y= sin(x/2) [-10, 10, -5, 5]}
#### Explanation:
Standard Form of a Sine Function: y=a sin (b(x-h))+k
a:
- Amplitude, half the distance from the highest to lowest point on the graph or the farthest distance from the mid line
- Vertical stretch (a>1) or vertical compression ( 1>a>0)
- Reflection across the x-axis (-a)
b:
- Period ( $\frac{2 \pi}{\left\mid b \right\mid}$) : The length of one cycle of the function
- Horizontal stretch (1>b>0) or horizontal compression (b>1)
- Reflection across the y-axis (-b)
h:
- Phase shift: If (x-h), the graph is shifted right, if (x+h), the graph is shifted left.
k:
- Mid line (y=k) : the horixantal line in the middle of the highest and lowest points on the graph
- Vertical shift by moving the mid line
y= sin (x/2)
Key Features:
Amplitude: 1
Period: 4$\pi$ ( $\frac{2 \pi}{\frac{1}{2}}$)
Phase shift: None
Midline: y=0 | 2021-10-26 01:59:02 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 3, "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": 0.6242561340332031, "perplexity": 5861.3240695909335}, "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-2021-43/segments/1634323587794.19/warc/CC-MAIN-20211026011138-20211026041138-00640.warc.gz"} |
http://wwww.thermalfluidscentral.org/encyclopedia/index.php/One-dimensional_transient_heat_conduction_in_sphere | # One-dimensional transient heat conduction in sphere
One-dimensional heat conduction in a spherical coordinate system can be solved by introducing a new dependent variable. Let us consider a sphere with radius of ro and a uniform initial temperature of Ti. It is exposed to a fluid with a temperature of ${T_\infty }$ (${T_\infty } < {T_i}$) and the convective heat transfer coefficient between the fluid and finite slab is h. Assuming that there is no internal heat generation and constant thermophysical properties, the governing equation is
$\frac{1}{r}\frac{{{\partial ^2}(rT)}}{{\partial {r^2}}} = \frac{1}{\alpha }\frac{{\partial T}}{{\partial t}},{\rm{ }}0 < x < {r_o},{\rm{ }}t > 0 \qquad \qquad(1)$
subject to the following boundary and initial conditions
$\frac{{\partial T}}{{\partial r}} = 0,{\rm{ }}r = 0{\rm{ (axisymmetric)}} \qquad \qquad(2)$
$- k\frac{{\partial T}}{{\partial r}} = h(T - {T_\infty }),{\rm{ }}r = {r_o} \qquad \qquad(3)$
$T = {T_i},{\rm{ }}0 < r < {r_o},{\rm{ }}t = 0 \qquad \qquad(4)$
By using the following dimensionless variables $\theta = \frac{{T - {T_\infty }}}{{{T_i} - {T_\infty }}},{\rm{ }}R = \frac{r}{{{r_o}}},{\rm{ Fo}} = \frac{{\alpha t}}{{r_o^2}},{\rm{ Bi}} = \frac{{h{r_o}}}{k}$
eqs. (1) – (4) can be nondimensionalized as
$\frac{1}{R}\frac{{{\partial ^2}(R\theta )}}{{\partial {R^2}}} = \frac{{\partial \theta }}{{\partial {\rm{Fo}}}},{\rm{ }}0 < R < 1,{\rm{ Fo}} > 0 \qquad \qquad(5)$
$\frac{{\partial \theta }}{{\partial R}} = 0,{\rm{ }}R = 0 \qquad \qquad(6)$
$- \frac{{\partial \theta }}{{\partial R}} = {\rm{Bi}}\theta ,{\rm{ R}} = 1 \qquad \qquad(7)$
$\theta = 1,{\rm{ }}0 < R < 1,{\rm{ Fo}} = 0 \qquad \qquad(8)$
Defining a new dependent variable
$U = R\theta \qquad \qquad(9)$
eqs. (5) – (8) become
$\frac{{{\partial ^2}U}}{{\partial {R^2}}} = \frac{{\partial U}}{{\partial {\rm{Fo}}}},{\rm{ }}0 < R < 1,{\rm{ Fo}} > 0 \qquad \qquad(10)$
$\frac{{\partial \theta }}{{\partial R}} = 0,{\rm{ }}R = 0 \qquad \qquad(11)$
$- \frac{{\partial U}}{{\partial R}} = ({\rm{Bi - 1)}}\theta ,{\rm{ R}} = 1 \qquad \qquad(12)$
$U = R,{\rm{ }}0 < R < 1,{\rm{ Fo}} = 0 \qquad \qquad(13)$
It can be seen that eqs. (10) – (13) are identical to the case of heat conduction in a finite slab with a non-uniform initial temperature. This problem can be readily solved by using the method of separation of variables (see Problem 3.28). After the solution is obtained, one can change the dependent variable back to θ and the result is
$\theta = \frac{1}{R}\sum\limits_{n = 1}^\infty {\frac{{4[\sin ({\lambda _n}) - {\lambda _n}\cos ({\lambda _n})]}}{{{\lambda _n}[2{\lambda _n} - \sin (2{\lambda _n})]}}} \sin ({\lambda _n}R){e^{ - \lambda _n^2{\rm{Fo}}}} \qquad \qquad(14)$
where the eigenvalue is the positive root of the following equation
$1 - {\lambda _n}\cot {\lambda _n} = {\rm{Bi}} \qquad \qquad(15)$
## References
Faghri, A., Zhang, Y., and Howell, J. R., 2010, Advanced Heat and Mass Transfer, Global Digital Press, Columbia, MO. | 2022-12-08 03:02:38 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 18, "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": 0.8866787552833557, "perplexity": 411.3561997645363}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-49/segments/1669446711232.54/warc/CC-MAIN-20221208014204-20221208044204-00326.warc.gz"} |
https://rojefferson.blog/2020/12/29/qft-in-curved-space-part-1-green-functions/?like_comment=469&_wpnonce=3efefe88d4 | QFT in curved space, part 1: Green functions
I was recently** asked to give a lecture on black hole thermodynamics and the associated quantum puzzles, which provided a perfect excuse to spend some time reviewing one of my favourite subjects: quantum field theory (QFT) in curved spacetime. I’ll mostly follow the canonical reference by Birrell and Davies [1], and will use this series of posts to highlight a number of important and/or interesting aspects along the way. I spent many a happy hour with this book as a graduate student, and warmly recommend it to anyone desiring a more complete treatment.
**(That is, “recently” when I started this back in February. I had intended to finish the series before posting the individual parts, to avoid retroactive edits as my understanding and plans for future segments evolves, but alas the constant pressure to publish (or, perhaps more charitably, the fact that I don’t get paid to teach a course on this stuff) means that studies of this sort are frequently pushed down my priority list (and that was before an international move in the midst of a global pandemic, for those wondering why I haven’t posted in so long). Since such time constraints are likely to continue — on top of which, I have no fixed end-point in mind for this vast subject — I’ve decided to release the first few parts I’ve been sitting on, lest they never see the light of day. I hope to add more installments as time permits.)
I’m going to start by discussing Green functions (commonly but improperly called “Green’s functions”), which manifest one of the deepest relationships between gravity, quantum field theory, and thermodynamics, namely the thermodynamic character of the vacuum state. Specifically, the fact that Green functions are periodic in imaginary time — also known as the KMS or Kubo-Martin-Schwinger condition — hints at an intimate relationship between Euclidean field theory and statistical mechanics, and underlies the thermal nature of horizons (including, but not limited to, those of black holes).
For simplicity, I’ll stick to Green functions of free scalar fields ${\phi(x)}$, where the ${D}$-vector ${x=(t,\mathbf{x})}$. As a notational aside, I will depart from [1] in favour of the modern convention in which the spacetime dimension is denoted ${D=d\!+\!1}$, with Greek indices running over the full ${D}$-dimensional spacetime, and Latin indices restricted to the ${d}$-dimensional spatial component. While I’m at it, I should also warn you that [1] uses the exceedingly unpalatable mostly-minus convention ${\eta_{\mu\nu}=(+,-,-,-)}$, whereas I’m going to use mostly-plus ${\eta_{\mu\nu}=(-,+,+,+)}$. The former seems to be preferred by particle physicists, because they share with small children a preference for timelike 4-vectors to have positive magnitude. But the latter is generally preferred by relativists and most workers in high-energy theory and quantum gravity, because 3-vectors have no minus signs (i.e., it’s consistent with the non-relativistic case, whereas mostly-plus yields a negative-definite metric), raising and lowering indices involves flipping only a single sign (arguably the most important for our purposes, since we’ll be Wick rotating between Lorentzian and Euclidean signature; mostly-plus would again lead to a negative-definite Euclidean metric), and the extension to general dimensions contains only a single ${-1}$ in the determinant (as opposed to a factor of ${(-1)^D}$ in mostly-minus).
Notational disclaimers dispensed with, the Lagrangian density is
$\displaystyle \mathcal{L}(x)=-\frac{1}{2}\left(\eta^{\mu\nu}\partial_\mu\phi\partial_\nu\phi+m^2\phi^2\right)~, \ \ \ \ \ (1)$
where ${\eta^{\mu\nu}}$ is the Minkowski metric (no curved space just yet). By applying the variational principle ${\delta S=0}$ to the action
$\displaystyle S=\int\!\mathrm{d}^Dx\mathcal{L}~, \ \ \ \ \ (2)$
we obtain the familiar Klein-Gordon equation
$\displaystyle \left(\square-m^2\right)\phi=0~, \ \ \ \ \ (3)$
where ${\square\equiv\eta^{\mu\nu}\partial_\mu\partial_\nu}$. The general solution, upon imposing that ${\phi}$ be real-valued, is
$\displaystyle \phi(x)=\int\!\frac{\mathrm{d}^dk}{2\omega(2\pi)^d}\left[a_k e^{i\mathbf{k}\mathbf{x}-i\omega t}+a_k^\dagger e^{-i\mathbf{k}\mathbf{x}+i\omega t}\right]~, \ \ \ \ \ (4)$
where ${k=(\omega,\mathbf{k})}$ (note that [1] restricts to the case of a discrete spectrum, as though the system were in a box; useful for imposing an IR regulator, but unnecessary for our purposes, and potentially problematic if we want to consider Lorentz boosts or Euclidean continuations). Here ${a_k}$ is the annihilation operator that kills the vacuum state, i.e., ${a_k|0\rangle=0}$ (so ${\phi}$, by extension, is a real-valued field operator).
One last (lengthy, but important) notational aside: different authors make different choices for the integration measure ${\int\!\frac{\mathrm{d}^dk}{f(k)}}$, which affects a number of later formulas, and can cause confusion when comparing different sources. The convention I’m using is physically well-motivated in that it makes the measure Lorentz invariant while encoding the on-shell condition ${k^2\!=\!-m^2}$. That is, the Lorentz invariant measure in the full ${D}$-dimensional spacetime is ${\int\!\mathrm{d}^Dk}$. If we then impose the on-shell condition along with ${\omega>0}$ (in the form of the Heaviside function ${\Theta(\omega)}$), we have
$\displaystyle \int\!\mathrm{d}^Dk\,\delta(k^2+m^2)\Theta(\omega) =\int\!\mathrm{d}\omega\int\!\mathrm{d}^dk\,\delta(\mathbf{k}^2-\omega^2+m^2)\Theta(\omega)~. \ \ \ \ \ (5)$
We now use the following trick: if a smooth function ${g(x)}$ has a root at ${x_0}$, then we may write
$\displaystyle \int\!\mathrm{d} x\,\delta(g(x))=\int\!\mathrm{d} x\,\frac{\delta(x-x_0)}{|g'(x)|} =\frac{1}{|g'(x_0)|} \ \ \ \ \ (6)$
where the prime denotes the derivative with respect to ${x}$. In the present case, ${{g(\omega)=\mathbf{k}^2-\omega^2+m^2}}$, and ${x_0^2=\mathbf{k}^2+m^2}$ (note that the Heaviside function will select the positive root). Thus
$\displaystyle \int\!\mathrm{d}\omega\!\int\!\mathrm{d}^dk\,\delta(\mathbf{k}^2-\omega^2+m^2)\Theta(\omega) =\int\!\frac{\mathrm{d}^dk}{2\sqrt{\mathbf{k}^2+m^2}}~. \ \ \ \ \ (7)$
Finally, since ${k}$ and ${x}$ are related by a Fourier transform, we must adopt a convention for the associated factor of ${(2\pi)^d}$. Mathematicians seem to prefer splitting this so that both ${\mathrm{d}^dk}$ and ${\mathrm{d}^d x}$ get a factor of ${(2\pi)^{d/2}}$, but physicists favour simply attaching it all to the momentum, so that
$\displaystyle \hat\phi(k)=\int\!\mathrm{d}^dx\,e^{-ikx}\phi(x) \qquad\mathrm{and}\qquad \phi(x)=\int\!\frac{\mathrm{d}^dk}{(2\pi)^d}\,e^{ikx}\hat\phi(k)~. \ \ \ \ \ (8)$
which further implies the convention
$\displaystyle (2\pi)^d\delta^d(k-p)=\int\!\mathrm{d}^dx\,e^{-i(k-p)x} \qquad \mathrm{and} \qquad \delta^d(x-y)=\int\!\frac{\mathrm{d}^dk}{(2\pi)^d}\,e^{ik(x-y)}~, \ \ \ \ \ (9)$
as one can readily verify by substituting ${\phi(x)}$ into ${\hat\phi(k)}$ (or vice versa):
\displaystyle \begin{aligned} \hat\phi(k)&=\int\!\mathrm{d}^dx\,e^{-ikx}\!\int\!\frac{\mathrm{d}^dp}{(2\pi)^d}\,e^{ipx}\hat\phi(p) =\int\!\frac{\mathrm{d}^dp}{(2\pi)^d}\int\!\mathrm{d}^dx\,e^{-i(k-p)x}\hat\phi(p)\\ &=\int\!\mathrm{d}^dp\,\delta^d(k-p)\hat\phi(p) =\hat\phi(k)~. \end{aligned} \ \ \ \ \ (10)
Thus our choice for the measure in (4):
$\displaystyle \int\!\frac{\mathrm{d}^dk}{f(k)}\equiv\int\!\frac{\mathrm{d}^dk}{2\sqrt{\mathbf{k}^2+m^2}(2\pi)^d} =\int\!\frac{\mathrm{d}^dk}{2\omega(2\pi)^d}~. \ \ \ \ \ (11)$
(I realize that was a bit tedious, but setting one’s conventions straight will pay dividends later. Trust me: I’ve lost hours trying to sort out factors of ${2\pi}$ and the like for failure to invest this time at the start).
We can now consider vacuum expectation values of products of field operators ${\phi}$. For free scalar fields, these can always be decomposed into two-point functions, which therefore play a defining role. In particular, we can construct various Green functions of the wave operator ${(\square-m^2)}$ from the two-point correlator ${\langle\phi(x)\phi(x')\rangle}$, including the familiar Feynman propagator. Following [1], we’ll denote the expectation values of the commutator and anticommutator as follows:
\displaystyle \begin{aligned} iG(x,x')&=\langle\left[\phi(x),\phi(x')\right]\rangle=G^+\!(x,x')-G^-\!(x,x')~,\\ G^{(1)}(x,x')&=\langle\left\{\phi(x),\phi(x')\right\}\rangle=G^+\!(x,x')+G^-\!(x,x')~, \end{aligned} \ \ \ \ \ (12)
where ${G^{\pm}}$ on the far right-hand sides are the so-called positive/negative frequency Wightman functions,
\displaystyle \begin{aligned} G^+\!(x,x')&=\langle\phi(x)\phi(x')\rangle~,\\ G^-\!(x,x')&=\langle\phi(x')\phi(x)\rangle~. \end{aligned} \ \ \ \ \ (13)
Note that while physicists call all of these Green functions, they’re technically kernels, i.e.,
$\displaystyle \left(\square_x-m^2\right)\mathcal{G}(x,x')=0~,\qquad\qquad\mathcal{G}\in\{G,\,G^{(1)}\!,G^{\pm}\}~. \ \ \ \ \ (14)$
One can immediately verify this by observing that since ${\square_x}$ acts only on ${\phi(x)}$ (that is, ${\square_x\phi(x')=0}$), it reduces to the Klein-Gordon equation above for the Wightman functions, from which the others follow.
Using these building blocks, we can consider the true Green functions
$\displaystyle iG_F(x,x')=\langle\mathcal{T}\phi(x)\phi(x')\rangle=\Theta(t-t')G^+\!(x,x')+\Theta(t'-t)G^-\!(x,x')~, \ \ \ \ \ (15)$
which is the familiar (time-ordered, ${\mathcal{T}}$) Feynman propagator, and
\displaystyle \begin{aligned} G_R(x,x')&=-\Theta(t-t')G(x,x')~,\\ G_A(x,x')&=\Theta(t'-t)G(x,x')~, \end{aligned} \ \ \ \ \ (16)
which are the retarded (R) and advanced (A) propagators. All three of these are Green functions of the wave operator, i.e.,
$\displaystyle \left(\square_x-m^2\right)\mathcal{G}(x,x')=\delta^D(x-x')~,\qquad\qquad\mathcal{G}\in\{G_F,G_R,G_A\}~. \ \ \ \ \ (17)$
Let’s verify this for the Feynman propagator; the others are similar. Using the fact that ${\eta^{\mu\nu}\partial_\nu\Theta(t-t')=\eta^{\mu0}\partial_0\Theta(t-t')=\eta^{\mu0}\delta(t-t')}$, we have
\displaystyle \begin{aligned} \square_x G_F=&-i\eta^{\mu0}\partial_\mu\left[\delta(t-t')G^+\!(x,x')-\delta(t'-t)G^-\!(x,x')\right]\\ &-i\eta^{\mu\nu}\partial_\mu\left[\Theta(t-t')\partial_\nu G^+\!(x,x')+\Theta(t'-t)\partial_\nu G^-\!(x,x')\right]~. \end{aligned} \ \ \ \ \ (18)
Now observe that by virtue of the delta function, the equal-time commutator ${{[\phi(t,\mathbf{x}),\phi(t,\mathbf{x}')]=0}}$ means that in the first line, ${G^+=G^-}$. And since the delta function itself is even, this implies that the first two terms cancel, so we continue with just the second line:
\displaystyle \begin{aligned} \square_x G_F=&-i\eta^{00}\left[\delta(t-t')\partial_0 G^+\!(x,x')-\delta(t'-t)\partial_0 G^-\!(x,x')\right]\\ &-i\eta^{\mu\nu}\left[\Theta(t-t')\partial_\mu\partial_\nu G^+\!(x,x')+\Theta(t'-t)\partial_\mu\partial_\nu G^-\!(x,x')\right]\\ =&\,\,i\delta(t-t')\left[\pi(x)\phi(x')-\phi(x')\pi(x)\right]\\ &-i\left[\Theta(t-t')\square_x G^+\!(x,x')+\Theta(t'-t)\square_x G^-\!(x,x')\right]~, \end{aligned} \ \ \ \ \ (19)
where in the second step, we have used the fact that the delta function is even, and identified the conjugate momentum ${\pi(x)=\partial_0\phi(x)}$. Then by (14), the second line will vanish for all values of ${t\!-\!t'}$ when we add in the ${-m^2}$ term of the wave operator, and the first line is just (minus) the equal-time commutator ${[\phi(t,\mathbf{x}),\pi(t,\mathbf{x}')]=i\delta^d(\mathbf{x}-\mathbf{x}')}$. Hence
$\displaystyle \left(\square_x-m^2\right) G_F=\delta(t-t')\delta^d(\mathbf{x}-\mathbf{x}')=\delta^D\!(x-x')~. \ \ \ \ \ (20)$
Thus the Feynman propagator is indeed a Green function of the wave operator ${(\square_x\!-\!m^2)}$; similarly for ${G_R}$ and ${G_A}$.
The reason I’ve been calling the Green functions ${G_F,G_R,G_A}$ “propagators” is that, unlike the kernels ${G,G^{(1)},G^{\pm}}$, they represent the transition amplitude for a particle (virtual or otherwise) propagating from ${x}$ to ${x'}$, subject to appropriate boundary conditions. To see this, consider the integral representation
$\displaystyle \mathcal{G}(x,x')=\int\!\frac{\mathrm{d}^Dk}{(2\pi)^D}\frac{e^{ik(x-x')}}{-k_0^2+\mathbf{k}^2+m^2}~, \ \ \ \ \ (21)$
where ${k^2=k^\mu k_\mu=-k_0^2+\mathbf{k}^2}$. Due to the poles at ${k_0=\omega=\pm\sqrt{\mathbf{k}^2+m^2}}$, we need to choose a suitable contour for the integral to be well-defined (analytically continuing to ${{k\in\mathbb{C}}}$). The particular choice of contour determines which of the kernels ${G,G^{(1)},G^{\pm}}$ or Green functions ${G_F,G_R,G_A}$ we obtain. (As for how we obtained (21) in the first place, one can directly substitute in the mode expansion (4) to the definitions, and convert the Heaviside functions into an appropriate integral. An easier way, at least for the Green functions, is to simply Fourier transform the wave equation (17):
\displaystyle \begin{aligned} \left(\square_x-m^2\right)\int\!\frac{\mathrm{d}^Dk}{(2\pi)^D}\,\tilde{\mathcal{G}}(k)\,e^{ik(x-x')}&=\delta^D(x-x')\\ \implies \int\!\frac{\mathrm{d}^Dk}{(2\pi)^D}\left(-k^2-m^2\right)\,e^{ik(x-x')}\tilde{\mathcal{G}}(k)&=\int\!\frac{\mathrm{d}^Dp}{(2\pi)^D}\,e^{ip(x-x')}~. \end{aligned} \ \ \ \ \ (22)
Since this expression (i.e., the delta function) is even in ${x\!-\!x'}$, we may absorb the sign into the integration variable, and identify
$\displaystyle \tilde{\mathcal{G}}(k)=\frac{1}{k^2+m^2}~, \ \ \ \ \ (23)$
whereupon Fourier transforming back to position space yields (21). As alluded above however, these expressions don’t make sense without specifying a pole prescription, so this argument isn’t very rigorous; it’s just a quick-and-dirty way of convincing yourself that (21) is plausible.)
To make sense of this expression, we split the integral based on the two poles of ${k_0}$:
\displaystyle \begin{aligned} \mathcal{G}(x,x')&=\int\frac{\mathrm{d}^dk}{(2\pi)^D}e^{i\mathbf{k}(\mathbf{x}-\mathbf{x}')}\oint\mathrm{d} k_0\frac{e^{-ik_0(x_0-x'_0)}}{-k_0^2+\mathbf{k}^2+m^2}\\ &=\int\frac{\mathrm{d}^dk}{(2\pi)^D}e^{i\mathbf{k}(\mathbf{x}-\mathbf{x}')}\oint\mathrm{d} k_0\frac{e^{-ik_0(x_0-x'_0)}}{-2k_0}\left(\frac{1}{k_0-\sqrt{\mathbf{k}^2+m^2}}+\frac{1}{k_0+\sqrt{\mathbf{k}^2+m^2}}\right)~. \end{aligned} \ \ \ \ \ (24)
Now, the boundary conditions of the propagator at hand determines the ${i\epsilon}$ prescription, i.e., which of the poles we want to enclose with the choice of contour. Consider first the retarded propagator ${G_R}$: the boundary condition implicit in (16) is that the function should vanish when ${x_0\!<\!x_0'}$ (where ${x_0\!=\!t}$). Conversely, when ${x_0\!>\!x_0'}$, we must close the contour in the negative half-plane so that ${e^{-ik_0(x_0-x'_0)}\rightarrow e^{-i(-i\infty)(x_0-x'_0)}=e^{-\infty(x_0-x'_0)}=e^{-\infty}}$, and the integral converges. Thus we should introduce factors of ${i\epsilon}$ such that both poles are slightly displaced into the lower half-plane. We can then apply Cauchy’s integral formula to correctly capture the poles at ${k_0=\pm\omega-i\epsilon}$, and then take ${\epsilon\rightarrow0}$:
\displaystyle \begin{aligned} G_R(x,x')&=\int\frac{\mathrm{d}^dk}{(2\pi)^D}e^{i\mathbf{k}(\mathbf{x}-\mathbf{x}')}\oint\mathrm{d} k_0\frac{e^{-ik_0(x_0-x'_0)}}{-2k_0}\left(\frac{1}{k_0-\sqrt{\mathbf{k}^2+m^2}+i\epsilon}+\frac{1}{k_0+\sqrt{\mathbf{k}^2+m^2}+i\epsilon}\right)\\ &=\Theta(x_0-x'_0)\int\frac{\mathrm{d}^dk}{(2\pi)^D}e^{i\mathbf{k}(\mathbf{x}-\mathbf{x}')}(2\pi i)\left(\frac{e^{-i\omega(x_0-x'_0)}}{-2\omega}+\frac{e^{i\omega(x_0-x'_0)}}{2\omega}\right)\\ &=-i\Theta(x_0-x'_0)\int\frac{\mathrm{d}^dk}{2\omega(2\pi)^d}e^{i\mathbf{k}(\mathbf{x}-\mathbf{x}')}\left( e^{-i\omega(x_0-x'_0)}-e^{i\omega(x_0-x'_0)}\right)\\ &=-i\Theta(x_0-x'_0)\int\frac{\mathrm{d}^dk}{2\omega(2\pi)^d}\left[e^{ik(x-x')}-e^{-ik(x-x')}\right]\\ &=i\Theta(x_0-x'_0)\langle\left[\phi(x),\phi(x')\right]\rangle =-\Theta(t-t')G(x,x')~, \end{aligned} \ \ \ \ \ (24)
where in the penultimate line, we have taken ${\mathbf{k}\rightarrow-\mathbf{k}}$ in the second term, using the fact that the integration over all (momentum) space is even; in the last line, we have used the mode expansion (4) and the commutation relation ${[a_k,a_k'^\dagger]=2\omega(2\pi)^d\delta^d(\mathbf{k}-\mathbf{k}')}$. Note that to yield the correct signs, we’ve chosen the contour to run counter-clockwise (note the factor of ${+2\pi i}$), which means that it runs from ${+\infty}$ to ${-\infty}$ along the real axis. The prescription for the advanced propagator is precisely similar, except we deform both poles in the positive complex direction (so that the integral vanishes when we close the contour below, as required for ${x_0-y_0>0}$), and the non-vanishing contribution comes from closing the contour in the positive half-plane, encircling both poles clockwise rather than counter-clockwise (so that the integral again runs from ${+\infty}$ to ${-\infty}$ along the real axis).
Note that ${G_R,G_A}$ are superpositions of both positive (${\omega\!>\!0}$) and negative (${\omega\!<\!0}$) energy modes, which is necessary in order for them to vanish outside their prescribed lightcones (past and future, respectively). In contrast, the Heaviside functions in the Feynman propagator are tantamount to imposing boundary conditions such that it picks up only positive or negative frequencies, depending on the sign of ${t\!-\!t'}$. For ${t\!>\!t'}$, we close the contour in the lower-half plane for convergence (${e^{-ik^0(t-t')}=e^{-i(-i\infty)(t-t')}=e^{-\infty(t-t')}}$), and enclose ${k_0=\omega}$ counter-clockwise (in the present conventions, we’re again going from ${+\infty}$ to ${-\infty}$ along the real axis); conversely, we close the contour clockwise in the upper-half plane to converge with ${k_0=-\omega}$ when ${t\!<\!t'}$. Hence the corresponding ${i\epsilon}$ prescription is
\displaystyle \begin{aligned} iG_F(x,x')&=i\int\frac{\mathrm{d}^dk}{(2\pi)^D}e^{i\mathbf{k}(\mathbf{x}-\mathbf{x}')}\oint\mathrm{d} k_0\frac{e^{-ik_0(x_0-x'_0)}}{-2k_0}\left(\frac{1}{k_0-\sqrt{\mathbf{k}^2+m^2}-i\epsilon}+\frac{1}{k_0+\sqrt{\mathbf{k}^2+m^2}+i\epsilon}\right)\\ &=i\int\frac{\mathrm{d}^dk}{(2\pi)^D}e^{i\mathbf{k}(\mathbf{x}-\mathbf{x}')}\left[(2\pi i)\Theta(x_0-x_0')\frac{e^{-i\omega(x_0-x'_0)}}{-2\omega}+(-2\pi i)\Theta(x_0'-x_0)\frac{e^{i\omega(x_0-x'_0)}}{2\omega}\right]\\ &=\int\frac{\mathrm{d}^dk}{2\omega(2\pi)^d}\left[\Theta(x_0-x_0')e^{ik(x-x')}+\Theta(x_0'-x_0)e^{-ik(x-x')}\right]\\ &=\Theta(t-t')G^+(x,x')+\Theta(t'-t)G^-(x,x')~, \end{aligned} \ \ \ \ \ (25)
as desired. It is in this sense that the time-ordering is automatically encoded by the Feynman propagator: for ${t\!>\!t'}$, it corresponds to a positive-energy particle propagating forwards in time, while for ${t\!, we have a negative-energy particle (i.e., an antiparticle) propagating backwards.
(I won’t go into the pole prescriptions for the kernels here, but the contours are illustrated in fig. 3 of [1]. The essential difference is that unlike the Green functions, the contours for the kernels are all closed loops, so these don’t correspond to propagating amplitudes.)
So far everything I’ve reviewed is for zero-temperature field theory; as alluded in the introduction of this post however, finite-temperature is where things get really interesting. Recall from quantum mechanics that a mixed state can be thought of as a statistical ensemble of pure states, so rather than computing expectation values with respect to the vacuum state, we compute them with respect to the mixed state given by the thermal density matrix
$\displaystyle \rho=\sum_ip_i\left|\psi_i\rangle\langle\psi_i\right|=\frac{1}{Z}e^{-\beta H}~, \ \ \ \ \ (26)$
where the system, governed by the Hamiltonian ${H}$, is in any of the states ${|\psi_i\rangle}$ with (classical) probability
$\displaystyle p_i=\frac{1}{Z}e^{-\beta E_i}~. \ \ \ \ \ (27)$
Of course, not all mixed states are thermal, but the latter is the correct state to use in the absence of any additional constraints. (One way to think of this is that the mixedness of a quantum state is a measure of our ignorance, which is why pure states are states of minimum entropy). Expectation values of operators ${\mathcal{O}}$ with respect to (26) are then ensemble averages at fixed temperature ${T=\beta^{-1}}$:
$\displaystyle \langle\mathcal{O}\rangle_\beta=\mathrm{tr}\left(\rho\,\mathcal{O}\right) =\sum_ip_i\langle\psi_i\left|\mathcal{O}\right|\psi_i\rangle~. \ \ \ \ \ (28)$
Note that we’re in the canonical ensemble (fixed temperature), rather than the microcanonical ensemble (fixed energy), because the energy — that is, the expectation value of the hamiltonian operator ${H=\sum_k \omega\,a_k^\dagger a_k}$ — will fluctuate as quanta are created or destroyed. Strictly speaking I should also include the chemical potential, since the number operator ${N=\sum_ka_k^\dagger a_k}$ also fluctuates, but it doesn’t play any important role in what follows. (The distinction is worth keeping in mind when discussing black hole thermodynamics, where one should use the microcanonical ensemble instead, because the negative specific heat makes the canonical ensemble unstable).
The thermal Green functions (and kernels), which we denote with the subscript ${\beta}$, are then obtained by replacing the vacuum expectation value with the expectation value in the thermal state, (28); for example, the Wightman functions become
\displaystyle \begin{aligned} G_\beta^+\!(x,x')&=\langle\phi(x)\phi(x')\rangle_\beta~,\\ G_\beta^-\!(x,x')&=\langle\phi(x')\phi(x)\rangle_\beta~. \end{aligned} \ \ \ \ \ (29)
The aforementioned KMS condition can then be obtained from the Heisenberg equation of motion,
$\displaystyle \phi(t_1,\mathbf{x})=e^{iH(t_1-t_0)}\phi(t_0,\mathbf{x})e^{-iH(t_1-t_0)}~, \ \ \ \ \ (30)$
by evolving in Euclidean time by ${t_1-t_0=i\beta}$:
\displaystyle \begin{aligned} G_\beta^+&=\frac{1}{Z}\mathrm{tr}\left[e^{-\beta H}\phi(t,\mathbf{x})\phi(t,\mathbf{x}')\right] =\frac{1}{Z}\mathrm{tr}\left[e^{-\beta H}\phi(t,\mathbf{x})e^{\beta H}e^{-\beta H}\phi(t,\mathbf{x}')\right]\\ &=\frac{1}{Z}\mathrm{tr}\left[\phi(t+i\beta,\mathbf{x})e^{-\beta H}\phi(t,\mathbf{x}')\right] =\frac{1}{Z}\mathrm{tr}\left[e^{-\beta H}\phi(t',\mathbf{x}')\phi(t+i\beta,\mathbf{x})\right]~, \end{aligned} \ \ \ \ \ (31)
where the last step relied on the cyclic property of the trace; similarly for ${G_\beta^-}$. Thus we arrive at the KMS condition
$\displaystyle G_\beta^\pm(t,\mathbf{x};t',\mathbf{x}')=G_\beta^\mp(t+i\beta,\mathbf{x};t',\mathbf{x}')~. \ \ \ \ \ (32)$
Note that this is a statement about expectation values of operators in the particular state (26) (indeed, this can easily be formulated for a general observable ${\mathcal{O}}$, we’re just sticking with scalar fields for concreteness; for a slightly more rigorous treatment, with suitable comments about boundedness and whatnot, see for example [2]). More generally however, any state which satisfies (32) is called a KMS state, and describes a system in thermal equilibrium. Similar relations hold for the other Green functions / kernels as well; e.g.,
$\displaystyle G_\beta^{(1)}(t,\mathbf{x};t',\mathbf{x}')=G_\beta^{(1)}(t+i\beta,\mathbf{x};t',\mathbf{x}')~. \ \ \ \ \ (33)$
As an exception to this however, note that since the commutator of free scalar fields is a c-number, ${G}$ in (12) remains unchanged, i.e., ${G_\beta=G}$.
In arriving at (32), we evolved in imaginary time ${\tau=it}$ by an amount given by the (inverse) temperature ${\beta}$. This is none other than the usual Wick rotation from Minkowski to Euclidean space, except that the periodicity of the Green functions implies that the Euclidean or thermal time direction is compact, with period ${\beta}$. That is, if the original field theory lived on ${\mathbb{R}^{d+1}}$, the finite-temperature field theory lives on ${\mathbb{R}^d\times S_\beta^1}$, where ${\beta}$ denotes the (inverse) circumference of the ${S^1}$ (observe that as ${\beta\rightarrow\infty}$, we recover the zero temperature Euclidean theory on ${\mathbb{R}^{d+1}}$). Thus in general, a Wick rotation in which Euclidean time is periodic makes an intimate connection between QFT and statistical thermodynamics, where the compact direction controls the temperature.
So what does this have to do with black holes, or horizons more generally? As I hope to cover in a future part of this sequence, the spacetime outside a horizon is also described by a thermal state. From the statistical thermodynamics or information theory perspective, one can think of this as due to the fact that we traced over the states on the other side, so the mixed density matrix that now describes the part of the vacuum to which we have access is a reflection of our ignorance. As alluded in the previous paragraph however, the thermodynamic character of the vacuum in the black hole state is already encoded in the periodicity of the Euclidean time direction, and emerges quite neatly in the case of the Schwarzschild black hole,
$\displaystyle \mathrm{d} s^2=-f(r)\mathrm{d} t^2+\frac{1}{f(r)}\mathrm{d} r^2+r^2\mathrm{d}\Omega_{d-1}^2~, \quad\quad f(r)=1-\frac{r_s}{r}~, \ \ \ \ \ (34)$
where ${r_s}$ is the Schwarzschild radius, and ${\mathrm{d}\Omega_{d-1}^2}$ is the metric on the ${(d\!-\!1)-}$sphere, which we’ll ignore since it just comes along for the ride. Recall from my very first blog post that after Wick rotating to Euclidean time, one can make a coordinate change so that the near-horizon metric becomes
$\displaystyle \mathrm{d} s^2=\mathrm{d}\rho^2+\frac{\rho^2}{4r_s^2}\mathrm{d}\tau^2~, \ \ \ \ \ (35)$
where ${\rho}$ is the radial direction, and — since these are polar coordinates — ${\tau}$ takes on the role of the angular coordinate, which must be periodic to avoid a conical singularity; that is, for any integer ${n}$,
$\displaystyle \frac{\tau}{2r_s}\sim\frac{\tau}{2r_s}+2\pi n \quad\implies\quad \tau\sim\tau+4\pi r_s n~, \ \ \ \ \ (36)$
and thus we identify the period ${4\pi r_s=\beta}$.
As a closing comment, the density matrix for KMS states has deeper relations to the idea of time translation symmetry via Tomita-Takesaki theory, through the modular hamiltonian that generates this 1-parameter family of automorphisms of the algebra of operators in the corresponding region. See for example [3]; this strikes me as a surprisingly under-researched direction, and I hope to revisit it in glorious detail soon.
References
1. N. D. Birrell and P. C. W. Davies, Quantum Fields in Curved Space. Cambridge Monographs on Mathematical Physics. Cambridge Univ. Press, Cambridge, UK, 1984. http://www.cambridge.org/mw/academic/subjects/physics/theoretical-physics-and-mathematical-physics/quantum-fields-curved-space?format=PB.
2. S. Fulling and S. Ruijsenaars, “Temperature, periodicity and horizons,” Physics Reports 152 no. 3, (1987) 135 – 176.
3. A. Connes and C. Rovelli, “Von neumann algebra automorphisms and time-thermodynamics relation in generally covariant quantum theories,” Classical and Quantum Gravity 11 no. 12, (Dec, 1994) 2899–2917, https://arxiv.org/abs/gr-qc/9406019
This entry was posted in Physics. Bookmark the permalink.
2 Responses to QFT in curved space, part 1: Green functions
1. Wencong Gan says:
I really appreciate your notes on this topic. I am a Ph.D student and also major in this field about holography, AdS/CFT, tensor network, black hole information problem and neural networks. I really learned a lot from your notes. Thank you very much.
Like
• rojefferson says:
Thank you very much for your kind and uplifting comment. It’s encouraging to know you got something out of it, especially in this time of academic isolation. Never stop learning!
Like | 2022-12-04 23:08:47 | {"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": 163, "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": 0.9625058174133301, "perplexity": 564.276952683455}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-49/segments/1669446710980.82/warc/CC-MAIN-20221204204504-20221204234504-00146.warc.gz"} |
https://www.transtutors.com/questions/if-department-h-had-600-units-60-completed-in-process-at-the-beginning-of-the-period-1040352.htm | If Department H had 600 units, 60% completed, in process at the beginning of the period, 8,000 unit
If Department H had 600 units, 60% completed, in process at the beginning of the period, 8,000 units were completed during the period, and 500 units were 30% completed at the end of the period, what was the number of equivalent units of production for the period if the first-in, first-out method is used to cost inventories? Answer 7,790 8,390 8,600 8,000 | 2019-02-22 12:50:20 | {"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": 0.9426880478858948, "perplexity": 1044.1151952016264}, "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-2019-09/segments/1550247517815.83/warc/CC-MAIN-20190222114817-20190222140817-00288.warc.gz"} |
https://gostudynewzealand.com/statistical-models-for-betting-predictions/ | Below is an overview of the concepts behind them.
## Markov models
Klaasen and Magnus challenged IID theory by showing that points in tennis are not distributed independently or equally. However, they also showed that deviations from IID are so small that using this assumption often yields good averages. This fact suggests that for every point in a match, the outcome of that point is independent of previous points. Assume further that we know the probability of winning a point on each player's serve. Let p be the probability that player A wins a point on his serve, q be the probability that player B wins a point on his serve. Using the IID assumption and the probabilities of winning a point, we can construct a Markov chain describing the probability of a player winning a game.
Formally, a Markov chain is a system of transitions between different states in state space. An important property of the system is that it has no memory, i.e. the next state of the system depends only on the current state, not on the preceding sequence of states. Taking the game score as the state space, and the state transitions as the probabilities of player A winning or losing a point, we obtain a Markov chain representing the stochastic progression of the game score. The figure below shows a circuit diagram for one game with player A serving. By denoting p the probability of winning a point when serving and assuming IID, we obtain that all transitions denoting a point won by player A have the same probability, and all transitions denoting a point lost have probability 1-p.
Due to the hierarchical structure of a tennis match, additional Markov chains are constructed to model the progression of points in tie-breaks, sets and matches. For example, in a match model there will be two outgoing transitions from each non-final state, labeled with the probabilities of a player winning and losing an individual set. Diagrams of such models can be seen in.
## Hierarchical expressions
Based on the idea of modelling tennis matches using Markov chains, Barnett and Clarke and O'Malley developed hierarchical expressions for the probability of a particular player winning the entire match.
In the above expressions p is the probability of player A winning a point when serving, x and y are the number of points won by players A and B respectively. This expression corresponds entirely to the Markov chain in the figure above.
Barnett and Clark also define a similar expression for calculating the probability of winning a set based on the probabilities of winning individual games and tie-breaks (which also depend on the probabilities of winning serving). Finally, the probability of winning a match can be calculated using previously defined expressions. It turns out that the final expression for the probability of winning the match depends only on the probability of winning a point by each player's serve.
### Estimating the Probability of Winning a Serving
The question remains how to estimate these probabilities of winning a point by service for matches not yet played. Barnett and Clarke give a method for estimating these probabilities from historical player statistics.
## Modern models
Modern models of tennis forecasting are based on the described hierarchical stochastic expressions. Knottenbelt refined Barnett's models by using only matches with common opponents of players, instead of all past opponents, to calculate the probability of winning a point when serving. This approach reduces the bias arising from players having faced opponents of different levels in the past.
Madurska further extended Knottenbelt's general opponent model by using different probabilities of winning a point when serving for different sets. Thus, the author abandoned the IID assumption and her model reflects the accumulation of physical fatigue in the player as the match progresses.
Knottenbelt's general opponent model and Madursky's settlement model are the most advanced statistical models and the authors claim a 6.8% and 19.6% ROI for their models compared to the 2011 WTA Grand Slam match betting market, respectively. The general opponent model was also tested on a larger and more diverse sample of 2,173 2011 ATP matches and showed an ROI of 3.8%. | 2023-01-29 15:57:26 | {"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": 0.8358464241027832, "perplexity": 438.8472391018338}, "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-2023-06/segments/1674764499744.74/warc/CC-MAIN-20230129144110-20230129174110-00036.warc.gz"} |
https://www.cds.caltech.edu/~murray/amwiki/api.php?action=query&list=search&srwhat=text&srsearch=meaning | You are looking at the HTML representation of the XML format.
HTML is good for debugging, but is unsuitable for application use.
Specify the format parameter to change the output format.
To see the non HTML representation of the XML format, set format=xml.
See the complete documentation, or API help for more information.
<?xml version="1.0"?>
<api>
<query>
<search>
<p ns="0" title="FAQ: Does a stable system have a stable equilibrium point? a limit cycle?" snippet="...that a system has a single equilibrium point that is globally attractive (<span class='searchmatch'>meaning</span> that solutions converge to that equilibrium point for all initial condition " size="659" wordcount="106" timestamp="2007-01-04T15:16:22Z" />
<p ns="0" title="FAQ: In the congestion control model, what does it mean to evaluate r i at time t - tau i?" snippet="...ed is the rate at which were sent &lt;math&gt;\tau_i&lt;/math&gt; ms ago. This is the <span class='searchmatch'>meaning</span> of &lt;math&gt;r_i(t-\tau_i)&lt;/math&gt;. " size="1382" wordcount="250" timestamp="2009-07-02T15:21:40Z" />
</search>
</query>
</api> | 2021-03-07 11:40:38 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 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": 0.49054035544395447, "perplexity": 5705.3243341002635}, "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-2021-10/segments/1614178376467.86/warc/CC-MAIN-20210307105633-20210307135633-00147.warc.gz"} |
https://amitbajajmaths.blogspot.com/2009/07/int01fracx4left1-xright41x2dx-frac227.html | ## Friday, July 17, 2009
### Which is greater: pi or 22/7?
Hello all
We know that the approximate value of pi is 22/7. Have you ever thought that which is actually greater, pi or 22/7?
Here is a result from calculus (don't worry, if you have not studied that... just enjoy it!)
Here, the given function is positive and since it is integrated in positive limits, so its value is positive.
\frac{22}{7}-\pi> 0
i.e
\frac{22}{7} > \pi | 2021-04-18 04:41:28 | {"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": 0.9173441529273987, "perplexity": 1868.6003181582814}, "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/1618038468066.58/warc/CC-MAIN-20210418043500-20210418073500-00057.warc.gz"} |
http://www.buyresearchchemicalss.net/category/uncategorized/ | # The recently discovered impact of oligomerization on G-protein coupled receptor (GPCR)
,
The recently discovered impact of oligomerization on G-protein coupled receptor (GPCR) function further complicates the already challenging objective of unraveling the molecular and active mechanisms of the receptors. ?2). The normalized eigenvectors from the Hessian matrix because of Eq. (1) will be the regular settings, as well as the eigenvalues will be the squares from the linked frequencies. As the changeover in one conformational condition of the protein to some other may very Cefaclor IC50 well be defined by a combined mix of a small amount of regular settings,26-28 just the initial 100 lowest regularity regular settings with raising eigenvalues had Cefaclor IC50 been computed for the rhodopsin monomer, dimer, and tetramer. The amount of similarity or overlap (from the rhodopsin monomer (residues = 343; the final five residues from Cefaclor IC50 the C-terminus had been eliminated because they’re extremely fluctuating) and normal mode of the oligomer was calculated as the scalar product of normal modes and using Eq. (2), below. and the direction of a specific unit-norm conformational switch vector was calculated as: normal modes was calculated as the sum over squared overlaps, starting with the lowest-frequency nontrivial normal mode: factors, were computed in MatLab (version 7, Natick, Massachusetts: The MathWorks, 2006) with the assumption that this contribution of each normal mode is usually inversely proportional to its eigenvalue is the residue number, represents the cartesian coordinates, is the quantity of residues, and is the displacement of and was calculated as the average correlation summed over least expensive frequency normal modes29:
$Cij=l=1XUilUjll(m=1XUimUimm)12(n=1XUjnUjnn)12$
(6) An increasing quantity of normal modes were used to Rabbit Polyclonal to ZAK test correlation convergence in our system. The convergence was estimated by plotting the Euclidean norm of the correlation matrix calculated with an increasing quantity of normal modes using the default norm (matrix) function in MatLab. Although a very small Cefaclor IC50 number of low-frequency normal modes may be sufficient to describe concomitant conformational changes of structural motifs between functional says,26,27,30,31 a larger quantity of modes must research equal-time correlated movements in the NMA construction.29 RESULTS AND DISCUSSION To supply new insights into our knowledge of the molecular and dynamic mechanisms regulating GPCR association and interaction, we performed ENM analysis from the monomeric [A in Fig. 1(A)], dimeric [protomers A and B or protomers D and C in Fig. 1(A)], and tetrameric [protomers A-B-C-D in Fig. 1(A)] agreements of rhodopsin substances suggested by Palczewski and coworkers predicated on inferences from atomic drive microscopy,5 aswell by our three suggested turned on types of the TM4,5-TM4,5 user interface (see Strategies). The C main mean rectangular deviations (RMSD) between your inactive style of the TM4,5-TM4,5 dimerization user interface (i.e., 1N3M) as well as the turned on user interface models attained by TM4 rotation [Fig. 1(B)], protomer displacement [Fig. 1(C)], or protomer exchange [Fig. 1(D)] are 1.5, 10.7, and 9.1 ?, respectively. C RMSDs between your activated versions are 9C11 ?. Person regular settings of rhodopsin monomer are perturbed upon oligomerization To estimation the relevance of the cheapest frequency settings from the rhodopsin monomer towards the dynamics of its dimeric and tetrameric complexes, we computed the overlap between your lowest nonzero regularity regular settings of each complicated using the lowest-frequency settings from the monomer (including its zero-frequency rotation-translation regular settings). The maximal overlap [Eq. (2) in Strategies] between person regular settings from the rhodopsin monomer.
# Prostatic neuroendocrine cells (NE) are a fundamental element of prostate cancer
,
Prostatic neuroendocrine cells (NE) are a fundamental element of prostate cancer (PCa) that are connected with PCa progression. uncovered that through secretion of PTHrP NEPCa cells could alter the p38/MAPK/Hsp27 indicators within their neighboring PCa cells that led to elevated androgen receptor (AR) activity marketing AR nuclear translocation. The results of elevated AR function might after that enhance docetaxel-resistance raising p21 appearance. xenograft mice experiments also confirmed NEPCa could increase the docetaxel-resistance of neighboring PCa and targeting this newly identified PTHrP/p38/Hsp27/AR/p21 signaling pathway with either p38 inhibitor (SB203580) or sh-PTHrP may result in improving/restoring the docetaxel sensitivity to better suppress PCa. Introduction Prostate cancer (PCa) is one of the most commonly diagnosed tumors in MGMT men in western countries (1). While androgen deprivation therapy (ADT) is effective for some patients most patients may develop castration resistance with the development of metastatic PCa (2). Docetaxel (Doc) has been used as a standard treatment for these patients with castration resistant PCa (CRPC) (3). However the therapeutic sturdiness for Doc is limited (average 18 months) with some serious side effects (4 5 Neuroendocrine prostate cancer (NEPCa) represents a minor population of PCa yet NEPCa cells exists in the most advanced stages of PCa (6). Importantly the population of NEPCa cells might increase during the current ADT with anti-androgen treatments (7). Different from most PAC cells NEPCa cells express little androgen receptor (AR) thus they are inherently resistant to the ADT treatment. The common markers for these NEPCa cells are Chromogranin (ChrA) neuron-specific enolase (NSE) and synaptophysin (8). Early studies suggested that NEPCa cells might secrete various factors including bombesin parathyroid hormone related protein (PTHrP) adrenomedullin and vascular endothelial growth factor (VEGF) to influence the surrounding PCa progression (9-11). However the detailed mechanisms especially their influences around the AR the key factor for the PCa progression as well as their impact on the efficacy of chemotherapies such as Doc remain unclear. In an system of co-culturing cells and mouse xenograft studies we exhibited that NEPCa KOS953 could increase the chemo-resistance of neighboring PCa altering the p38/Hsp27/AR/p21 signals. Results NEPCa increased chemo-resistance of neighboring PCa Early studies suggested that NEPCa is not only resistant to existing therapies in general its conditioned media (CM) might also enhance the development KOS953 of castration resistance in its neighboring PCa (CRPC) (12 13 To further study the impact of NEPCa cells around the chemo-sensitivity around the neighboring PCa cells we decided the efficacy of Doc on PCa cells before and after their co-culture with the NEPCa cells (Fig. 1A). We found that after co-culture using KOS953 the NEPCa NCI-H660 cells CRPC C4-2 cells are more resistant to Doc treatment within a dose-dependent way which range from 1 nM to 8 nM (Fig. 1B still left panel) as well as the viability of the C4-2 cells are elevated as gauged by MTT assay. Equivalent results had been also obtained whenever we changed C4-2 with CWR22Rv1 cells (Fig. 1B correct panel). Body 1 NEPCa induces chemoresistance of neighboring PCa. C4-2 and CWR22Rv1 cells were co-cultured with or without NE1 or NCI-H660.3 cells in 0.4 μM transwell plates for 72 hours. A. The diagram of co-culture program. 2× 104 prostate adenocarcinoma … To determine the fact that viability of the CRPC cells are linked to designed cell loss of life we used the TUNEL KOS953 assay to examine the influence of co-culturing with NEPCa the outcomes indicated that NCI-H660 cells might secure C4-2 and CWR22Rv1 cells from Doc-induced apoptosis (Fig. 1C). On the other hand co-culture with NCI-H660 cells also reduced the amount of cleaved PARP KOS953 another signal for the apoptotic procedure (14) (Fig. 1D). Significantly similar results were obtained whenever we replaced the NCI-H660 cells with NE1 also.3 cells that are LNCaP cells cultured long-term in the lack of androgen (15) and also have the features of NEPCa cells (Fig. 1E-F). Results from Fig Together. 1 claim that NEPCa may confer a success benefit to the encompassing PCa through improving their resistance to chemotherapy. NEPCa induced chemo-resistance of surrounding PCa via altering the p38/Hsp27 signals To dissect the molecular mechanism how NEPCa increased chemo-resistance of surrounding PCa we first screened.
# The recognition of vitamin C is associated with a history of
,
The recognition of vitamin C is associated with a history of an unrelenting search for the cause of the ancient haemorrhagic disease scurvy. and beneficial effect of vitamin C in respect to MPC-3100 human disease such as cancer atherosclerosis diabetes neurodegenerative disease and metal toxicity however remains equivocal. Thus further continuous uninterrupted efforts may open new vistas to understand its significance in disease management. Keywords: Vitamin C Atherosclerosis Diabetes Immunity Cancer Infertility Heavy metal toxicity Introduction Vitamins are essential nutrients that are required for various biochemical and physiological processes in the body. It is well known that most of the vitamins cannot be synthesized in the body and hence their supplementation in diet is essential. Vitamins are classified on the basis of their solubility as water soluble (C and B complexes) and fat soluble vitamins (A D E K). Vitamin C or ascorbic acid (AA) was first isolated in 1923 by MPC-3100 Hungarian biochemist and Nobel laureate Szent-Gyorgyi and synthesized by Howarth and Hirst [1]. It exists in reduced [ascorbate] and oxidized forms as dehydroascorbic acid which are easily inter-convertible and biologically active thus it acts as important antioxidant. Vitamin C is usually easily oxidized acid and destroyed by oxygen alkali and high temperature. Most of the herb and animal species have the ability to synthesize vitamin C from glucose and galactose through uronic acid pathway but man and other primates cannot do so because of deficiency of enzyme gulonolactone oxidase [EC 1.1.3.8] required for it’s biosynthesis. Deficiency of this enzyme is a result of a mutation which occurred approximately 40 million years ago [2]. The body requires vitamin C for normal physiological functions. It helps in the synthesis and metabolism of tyrosine folic acid MPC-3100 and tryptophan hydroxylation of glycine proline lysine carnitine and catecholamine. It facilitates the conversion of cholesterol into bile acids and hence lowers blood cholesterol levels. It also increases the absorption of iron in the gut by reducing ferric to ferrous state. As an antioxidant it protects the body from various deleterious effects of free radicals pollutants and toxins. The therapeutic effect of vitamin C was explored by Linus Pauling however his work on therapeutic role of vitamin C in his later years generated much controversy yet he was the first to introduce the concept of high doses of vitamin C for the treatment of various conditions from common Gdf6 href=”http://www.adooq.com/mpc-3100.html”>MPC-3100 cold to cancer [3]. Since then mega doses of vitamin C have been widely used in the treatment and prevention of a large number of disorders like diabetes atherosclerosis common cold cataracts glaucoma macular degeneration stroke heart diseases cancer and so on. Deficiency of this vitamin is usually often associated with anemia infections bleeding gums scurvy poor wound healing capillary haemorrhage muscle degeneration atherosclerotic plaques and neurotic disturbances. For the correction of deficiency vitamin C is usually often supplemented in large doses and unlike fat soluble vitamins toxicity is usually rare. Recently the role MPC-3100 of vitamin C in contamination and immunity has also been investigated. In view of the vast biological physiological functions and therapeutic role of vitamin C this review is an attempt to summarise various evidences in this context. Dietary Sources of Vitamin C Vitamin C is found in citrus fruits green peppers red peppers strawberries tomatoes broccoli brussels sprouts turnip Indian gooseberry and other leafy vegetables. The animal sources are poor in vitamin C content and the level is usually <30-40?mg/100?g. Therefore herb sources become important because of high content of vitamin C up to 5 0 It’s absorption in the buccal cavity is usually by passive diffusion however in gastrointestinal tract absorption is usually by active sodium dependent vitamin C transporters (SVCT) [4 5 Vitamin C Bioavailability Bioavailability or the effective concentration of vitamin C essentially depends on its effective absorption from intestine and renal excretion. Vitamin C consumed either with diet or dietary supplements is usually absorbed by the epithelial cells of the small intestine by SVCT1 or subsequently diffuses into the surrounding capillaries and then the circulatory system [5-7]. Circulating AA is usually filtered from kidney capillary bed into the Bowman’s capsule through a general filtration mechanism. AA is usually reabsorbed through SVCT1 transporter in proximal convoluted tubule [6]. The difference between the amount of AA filtered and reabsorbed constitutes renal excretion.
# Inflammasomes are multimeric protein complexes involved in the processing of IL-1β
,
Inflammasomes are multimeric protein complexes involved in the processing of IL-1β through Caspase-1 cleavage. network in activation of inflammasome and IL-1β processing is usually yet unknown. This statement the involvement of miR-133a-1 in the activation of inflammasome (NLRP3) and IL-1β production. miR-133a-1 is known to target the mitochondrial uncoupling protein 2 (UCP2). The role of UCP2 in inflammasome activation has remained elusive. To understand the role of miR-133a-1 in regulating inflammasome activation we either overexpressed or suppressed miR-133a-1 in differentiated THP1 cells Begacestat that express NLRP3 inflammasome. Levels of Caspase-1 and IL-1β were analyzed Begacestat by blot analysis. For the first time we showed that overexpression of miR-133a-1 Caspase-1 p10 and IL-1β p17 cleavage concurrently suppressing mitochondrial uncoupling protein 2 (UCP2). Surprisingly our results exhibited that miR-133A-1 controls inflammasome activation without affecting the basal expression of the individual inflammasome components NLRP3 and ASC or its immediate downstream targets proIL-1β and pro-Caspase-1. inflammasome activation via the suppression of UCP2. 1 Introduction Inflammasomes are multi-protein structures that regulate the activation of Caspase-1 and the maturation of pro-inflammatory cytokines like IL-1β IL-18 and IL-33 [1]. Inflammasome activation is usually a two-step process; the first transmission is usually through the activation of pathogen response receptors (PRRs). Activated PRRs activate NF-κB and Begacestat primary inflammasome complex. The second signal comes from a range of stimuli ATP uric acid crystals hydrogen peroxide reactive oxygen species (ROS) or intracellular stimuli such as sterile inflammation [2]. Among the wide variety of inflammasomes the NLRP3 inflammasome complex is usually well analyzed [3]. Although the precise mechanisms of activation are not known studies demonstrate that NLRP3 is usually activated by a wide range of compounds: both exogenous as well as host ligands including bacterial RNA ATP uric acid crystals antiviral imidazoquinoline compounds ceramide and oxygen toxicity [4 5 6 7 So far based on these findings three key mechanisms have been explained to account for NLRP3 activation [3]. One NLRP3 is usually potassium efflux [8]. External ATP recognized by the RB1 P2X7 receptor a cation channel potassium efflux that in turn triggers NLRP3 activation [8]. The generation of mitochondria-derived ROS plays a critical role the activation of NLRP3 [9]. Phagolysosomal destabilization also activates NLRP3; caused by large crystals and particulates such as monosodium urate (MSU) adjuvant alum asbestos and silica [10]. Upon activation of NLRP3 it oligomerizes and recruits the ASC domain name which in turn recruits pro-Caspase-1.This event prospects to auto-proteolytic cleavage of pro-Caspase-1 and formation of active Caspase-1. Active Caspase-1 cleaves pro-IL-1β secretion of active IL-1β [11]. One defense of the innate immune system inflammasomes combat invading microbes via activation of Caspase-1 and the production of mature pyrogenic cytokine IL-1β [3]. IL-1β is an essential mediator of the inflammatory response causing fever hypotension and production of other pro-inflammatory Begacestat cytokines [12]. Inflammasomes also take part in a variety of cellular activities including cell proliferation differentiation and apoptosis [13]. The synthesis of IL-1β is very tightly regulated by several mechanisms; however mutations in the NLRP3 gene are associated with a spectrum of auto-inflammatory diseases characterized by excessive production of IL-1β cryopyrin-associated periodic syndrome (CAPS) familial chilly auto-inflammatory syndrome Muckle- Wells syndrome and chronic infantile cutaneous neurological articular syndrome [14 15 16 also gout [17] asbestosis silicosis [10 18 and Alzheimer’s disease [19]. Recently the involvement of miRs in clinical disease models are considered promising brokers in the role of miR-133A in inflammasome activation and IL-1β production. miR-133-a-1 was first characterized in mice; it is homologous to some other species including invertebrates [27]. You will find three miR-133 genes recognized in the human genome: miR-133a-1 miR-133a-2 and miR-133b [28]. Some in vitro studies that of miR-133a-1.
,
,
# Increased nutritional uptake and usage is normally a hallmark of several
,
Increased nutritional uptake and usage is normally a hallmark of several individual malignancies. how cancers cells cope with low nutritional environments. and also have developed adaptive mechanisms to feeling thrive and survive in low nutrient circumstances. Within this review we showcase recent studies regarding nutritional sensing BAY 63-2521 and downstream effector systems important for version under circumstances of nutritional stress. The latest progress in neuro-scientific cancer fat burning capacity provides novel principles for examining the synergistic potential of mixture therapies that focus on both indication transduction and metabolic pathways. NUTRIENT SENSING BY SIGNALING PATHWAYS AMP-activated proteins kinase The AMPK can be an evolutionarily conserved heterotrimeric proteins complex comprising a catalytic α subunit and regulatory β and γ subunits. This complicated plays a crucial function in regulating tension Rabbit Polyclonal to GATA4. responses since it senses adjustments in the mobile proportion of AMP to adenosine triphosphate (ATP). Upon activation AMPK phosphorylates many substrates to be able to boost cellular ATP amounts by several systems such as raising blood sugar uptake inhibiting gluconeogenesis and raising mitochondrial biogenesis. An integral mechanism where AMPK increases mobile energy is normally through inhibition of mTOR by immediate phosphorylation of TSC2 and raptor both detrimental regulators of mTOR [Amount 1].[13 14 As mTOR may be the professional regulator of proteins synthesis and various other anabolic pathways its inhibition is vital for conserving energy under circumstances of nutritional restriction. Yet another way AMPK straight inhibits proteins translation is normally by activation of eukaryotic elongation aspect 2 kinase (eEF2) which phosphorylates and inactivates eukaryotic elongation aspect.[15] Interestingly it had been proven that inhibition of eEF2 via activation of AMPK is a conserved mechanism utilized by tumor cells to be able to endure and adjust to periods of nutrient deprivation.[16] Amount 1 Schematic representation of how cells react to several metabolic stresses. Low degrees of nutrition are discovered by kinases and phosphatases which modulate downstream effector proteins such as for example transcription elements to reprogram mobile functions and … Under conditions of nutritional worry the inhibition of macromolecule biosynthesis may be insufficient to revive mobile energy. A major technique for cells to scavenge energy precursors is normally through autophagy an activity where cells recycle nonessential macromolecules and organelles to supply nutrition and energy.[17] Although autophagy provides many mechanism of regulation such as for example mTOR-directed inhibition latest studies claim that AMPK directly activates autophagy by phosphorylation of ULK1 an important kinase for the initiation of autophagy BAY 63-2521 [Amount 1].[18] Besides inhibition of proteins translation and activation of autophagy AMPK continues to be reported to market cell survival via an adaptive cell BAY 63-2521 cycle arrest mechanisms. Particularly in response to low sugar levels AMPK phosphorylates the transcription aspect p53 [Amount 1]. AMPK-dependent activation of p53 allows cells to survive their low glucose environment by waiting around and resting for pro-proliferative conditions.[19] Furthermore AMPK is considered to inactivate SREBP1 a crucial transcription aspect which is involved with lipid and carbohydrate fat burning capacity through phosphorylation [Amount 1].[20] Bungard glutamine deprivation or low glutamine levels a particular PP2A B subunit B55α is induced on the transcriptional level to create an adaptive PP2A complicated to be able to promote cell survival by allowing p53 activation [Amount 1].[12] Interestingly the B55α induction and organic formation is greatly improved in cells overexpressing α4 suggesting a significant function for α4 to advertise PP2A complex set up. Of significance α4 is normally overexpressed in lots of human cancers as well as the PP2A/B55α-p53 signaling axis may describe why many malignancies are resistant to low glutamine amounts aswell as glutaminase inhibitors. Although interesting progress continues to be made further research must grasp and enjoy the dynamics and need for proteins phosphatases’ function in cell signaling and nutritional sensing. Version THROUGH TRANSCRIPTION Elements p53 A significant effector and sensor of cellular BAY 63-2521 tension may be the tumor suppressor p53. This different transcription aspect is normally regulated on the proteins level through several post-translational adjustments such.
# How common is hepatitis D disease and does it pose a
,
How common is hepatitis D disease and does it pose a significant epidemiologic threat in first-world nations? RG Globally an estimated minimum of 15 million people are infected with delta disease today. to look at all the individuals in its serum database who are infected with the hepatitis B disease (HBV) and then test those individuals for delta disease. The data from that project may be more expansive but using my seroprevalence data from your Bay Area-which found a seroprevalence rate of 7% for delta disease in our HBV population-it Gedatolisib could then be expected that between 60 0 and 90 0 individuals in the United States have delta disease illness today. As for additional countries Mongolia has the highest prevalence rate of delta disease illness in the world. It also has a very high rate of HBV illness as well but the delta disease illness rate can approach 30% among individuals infected with HBV. In fact pockets of delta disease illness are found in very interesting locations around the world. Some countries in central Africa have a high seropositivity rate for delta disease. There are also 2 pouches of high delta disease seropositivity in the northern part of South America: in the northern region of Amazonia and also the Orinoco River Valley in Venezuela. These locales are not really connected with any other place in the world and the genotype of the delta disease is different from that found in North America and Africa. Delta disease seropositivity is also very common in Eastern European countries such as Bulgaria. There are also pouches of delta disease seropositivity in Russia and central Asia all the way down to Afghanistan and Pakistan. Wherever there is a relatively high rate of HBV illness there is also a significant rate of delta illness as seen in a recent study in Vietnam that found a 15% rate of HDV inside a profiled human population at a set of tertiary referral centers. You will find multiple genotypes of HDV and the different regions of the world possess unique genotypes. Genotype 1 is definitely common in the United States Canada Europe and Eurasia; genotype 3 is definitely prevalent in South America; genotypes 2 and 4 are common in the Asia Pacific region; and genotypes 5 6 and 7 are common in Africa. The reason for these assorted genotypes lies in the long history of HDV in humans human being migration and viral mutation rate. G&H What are the common mechanisms of transmission? RG In each of the highly endemic areas mentioned the transmission pattern is probably a bit different but in Eastern Europe transmission is attributed to a mixture of improperly sterilized medical tools including syringes as well as illicit intravenous drug use and sexual transmission. In Mongolia nonsterile syringes utilized for medical injections and scarification and additional folk-culture practices that involve breaks in the skin are assumed to be the cause of HBV and delta disease transmission. Similar reasons for delta disease illness in Amazonia have been proposed as well as you can links to new world primate infections that “jump” to humans. G&H What is the natural Gedatolisib history of delta disease CXCR6 illness? RG Vertically acquired HBV illness is associated with a 25% lifetime risk of cirrhosis or malignancy. Tat rate probably doubles in individuals in whom HDV illness then evolves. If a patient offers adult-acquired HBV illness the lifetime risk of cirrhosis or malignancy is typically 7% but Gedatolisib if the patient is infected with HBV and delta disease and chronic delta disease illness develops then the risk of development of cirrhosis or malignancy is probably 5 or more instances greater. So chronic delta disease illness results in much more quick progression to end-stage liver Gedatolisib disease need for liver transplantation oncogenesis and death. Delta disease can both manifest in the presence of HBV or can be a main coinfection. Individuals with main coinfection Gedatolisib may have very severe disease or may encounter spontaneous clearance of both HBV and delta disease. If delta disease is definitely Gedatolisib superimposed on chronic HBV illness it is extremely likely that chronic HDV illness will develop also leading to an accelerated disease pattern. Delta is an RNA disease and hepatologists believe that it is curable whereas HBV is not curable. If HBV is definitely treated having a first-line oral therapy such as entecavir (Baraclude Bristol-Myers Squibb) or tenofovir.
# Modulating angiogenesis can be an attractive objective because many pathological conditions
,
Modulating angiogenesis can be an attractive objective because many pathological conditions rely in the growth of brand-new vessels. for the natural activity. Furthermore QK induced endothelial cells proliferation turned on cell signaling reliant on VEGF and CB-7598 elevated the VEGF natural response. QK promoted Rabbit polyclonal to PHACTR4. capillary firm and formation within an assay on matrigel. These total results suggested the fact that helix region 17-25 of VEGF is involved with VEGF receptor activation. The peptide made to resemble this area shares numerous natural properties of VEGF hence suggesting that area is certainly of potential curiosity for biomedical applications and substances mimicking maybe it’s attractive for healing and diagnostic applications. Assay. Individual endothelial cells had been cocultured with various other human cells within a specifically designed moderate (Angiokit TCS CellWorks Buckingham U.K.) in 24-well plates. Every 3 times QK in the existence or lack of VEGF165 was put into the civilizations. VEGF and suramine (20 μM) had been utilized as negative and positive handles respectively. Cells eventually start to proliferate and enter a migratory stage where they undertake the matrix to create thread-like tubule buildings. In the 11th time cells were set with ice cool 70% ethanol and tubule development was visualized by staining for anti-human Compact disc31 (PECAM-1). Outcomes were scored using the picture analysis software program angiosys (TCS CellWorks). Outcomes Peptide Design. Predicated on the x-ray framework from the VEGF/Flt-1 area 2 (Flt-1D2) complicated (12) we designed and synthesized a peptide reproducing the VEGF binding area spanning the amino acidity series Phe-17-Tyr-25. This area includes 5 (Phe-17 Met-18 Tyr-21 Gln-22 and Tyr-25) of 21 residues located at <4.5 ? through the receptor and it assumes in the organic proteins an α-helix conformation. The look strategy we followed was to maintain set the three-dimensional agreement from the residues getting together with the receptor and stabilize the supplementary structural theme. Mutagenesis data reveal that whenever Phe-17 is certainly mutated to Ala the affinity toward KDR is certainly decreased by CB-7598 90-fold whereas mutations of the various other four residues just slightly influence the binding (8 13 Every one of the five interacting residues take up a face from the helix plus they make hydrophobic relationship using the receptor. Residues on the contrary encounter protrude toward the proteins interior and within an isolate peptide they might be solvent open. The helix conformation from the QK peptide was stabilized presenting N- and C-capping sequences (29) amino acidity with intrinsic helix propensity and advantageous electrostatic connections (30). The N- and C-capping residues (L15/T16 and K26/G27/I28 respectively) had been chosen predicated on statistical choice for every capping placement (29). Phe-17 was changed by Trp to introduce a spectroscopic probe also to raise the hydrophobic connections; Met-18 which is certainly near to the residue Asn-219 of Flt-1 was substituted using a Gln residue within the VEGF homolog proteins Placenta Growth Aspect CB-7598 more suitable for form advantageous hydrogen bond relationship. Asp-19 was changed by Glu due to its higher helix propensity and Ser-24 was substituted with Lys to improve helix propensity and solubility. A supplementary Lys residue was appended on the N-terminal to permit selective labeling. The peptide was acetylated and amidate in order to avoid electrostatic repulsion between peptide terminal helix and charges dipoles. The sequences from the designed peptide QK as well as the peptide matching towards the α-helix area of VEGF VEGF15 are reported in Fig. 1and and enhances VEGF response (Fig. 5Angiogenesis Assay. To research whether QK recapitulates the entire angiogenic properties of VEGF we researched the ability from the peptide to stimulate EC network development on the matrigel substrate (Fig. 6). Tubule development was examined by positive staining for Compact disc31/PECAM-1 an intercellular adhesion molecule involved with leucocytes diapedesis. We determined the real amount of cell junctions corrected by the full total tubules duration. Being a positive control we utilized VEGF which triggered a rise in the amount of connections that all EC expand to a nearby cell.
, | 2017-08-17 01:41:56 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 1, "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": 0.38765329122543335, "perplexity": 10032.016560259583}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-34/segments/1502886102819.58/warc/CC-MAIN-20170817013033-20170817033033-00441.warc.gz"} |
http://www.ck12.org/physics/Special-Theory-of-Relativity/lesson/The-Theory-of-Special-Relativity/r10/ | <meta http-equiv="refresh" content="1; url=/nojavascript/"> Special Theory of Relativity ( Read ) | Physics | CK-12 Foundation
You are viewing an older version of this Concept. Go to the latest version.
# Special Theory of Relativity
%
Best Score
Practice Special Theory of Relativity
Best Score
%
# The Theory of Special Relativity
$E = mc^2$ as derived in the special theory of relativity explains the equivalence of mass and energy, which is how nuclear reactions produce the amazing amounts of energy available in thermonuclear weapons.
### The Theory of Special Relativity
The theory of relativity refers to two different elements of the same theory: special relativity and general relativity. The theory of special relativity was first introduced by Albert Einstein in 1905 and was later (1916) considered to be a special case of the more comprehensive theory of general relativity .
The special theory of relativity was accepted reasonably quickly by physicists considering that it was introduced in 1905 and widely accepted by 1920. The theory of general relativity was not accepted as quickly. Some physics historians insist that considerable resistance to the theory existed even into the 1950’s and 1960’s. At least part of the problem for the acceptance of the theory was that some conclusions from the theory went against common sense and also, there was very little experimental evidence to support the theory.
The special theory of relativity essentially explains how to interpret motion between different inertial frames of reference, that is, places that are moving at constant speeds relative to each other. Special relativity is based on two postulates:
1. The laws of physics are the same for all observers within their own inertial reference frame.
2. The speed of light in a vacuum is the same for all observers regardless of their relative motion or the motion of the source of the light.
An inertial reference frame is one in which Newton’s first law, the law of inertia, is valid. That is, if an object experiences no net force due to other bodies, the object either remains at rest or remains in motion with constant velocity in a straight line.
#### A Closer Look at Postulate 1
Consider dropping a child’s toy block in a railroad boxcar.
The block will fall straight down and come to rest on a spot directly underneath the position from which it was dropped. For an observer inside a stationary boxcar, there will be a measureable distance the block fell, a time required to fall and an average velocity for the fall. If the boxcar is moving at a constant horizontal velocity 10 m/s, the observer inside the boxcar will find the all measurements to be exactly the same as when the boxcar was stationary, including the spot where the block came to rest. For an observer inside the boxcar, the frame of reference is the same whether the car is moving or not and all the laws of physics will be the same in both cases.
Consider the block falling in the moving boxcar as observed by a stationary observer outside the boxcar. As observed in this frame of reference, the block does NOT fall straight down but rather follows a parabolic path. The distance it falls is NOT the same and the average velocity calculated is NOT the same. For the outside observer, the block has a constant horizontal velocity equal to the velocity of the boxcar and the vector sum of the horizontal velocity and the vertical fall result in the parabolic path sketched. For the inside observer, there is no horizontal velocity. For the outside observer, the distance traveled along the parabolic path is longer than the path straight down but the time for the fall is the same. For the outside observer, the average velocity is greater.
Inside each frame of reference, all the laws of physics hold, but the measurements are not the same between the two frames of reference.
#### A Closer Look at Postulate 2
Suppose you are sitting on the hood of a stationary car and your brother is standing alongside the road some 50 feet ahead of the car. If you throw a ball to your brother with a velocity of 10 m/s, it will travel, relative to you, at a velocity of 10 m/s and it will travel, relative to your brother, as 10 m/s. Suppose then, that you repeat the throw except this time, you toss the ball while the car is moving toward your brother at 10 m/s. This time, the ball will move, relative to you, with a velocity of 10 m/s but it will move, relative to your brother, with a velocity of 20 m/s. In this case, the velocity of the source of the ball is added to the velocity of the ball to get the velocity relative to a stationary observer.
Common sense would tell us that if we did this same experiment with light, that is, shine a flashlight off the hood of a moving car in the same direction the car is moving, the velocity of the light relative to a stationary observer would be increased by the velocity of the car. In fact, such an increase in the speed of light has never been found. In fact, in experiments carried out to test for the effect of the movement of the source on the speed of light (Michelson-Morley), the results indicate that the speed of light is completely unaffected by the motion of the source. It appears that the speed of light in a vacuum is constant regardless of relative motion. Hence, the suggestion in postulate 2. The speed of light in a vacuum is the same for all observers regardless of their relative motion or the motion of the source of the light.
The special theory of relativity copes with the results of the Michelson-Morley experiments much better than does classical mechanics, but it also has some surprising consequences. For example, according to the theory of special relativity,
• Two events that occurred simultaneously for one observer were not simultaneous for another observer if the two observers had relative motion to each other. (Relativity of simultaneity).
• Clocks in a moving frame of reference tick more slowly than an observer’s “stationary” clock. (Time dilation).
• Objects are measured to be shorter in the direction that they are moving with respect to a stationary observer. (Length contraction).
• $E = mc^2$ , energy and mass are equivalent and transmutable. (Mass-energy equivalence).
• No physical object can travel faster than the speed of light in a vacuum. (Maximum speed is finite).
#### Time Dilation
Suppose we are in a rocket ship sitting at rest on the earth and we turn on an overhead light. The light will travel downward (and all other directions as well) and land on the table below. The observer in the rocket ship can measure the distance traveled to the table, the time required for the light to arrive on the table and an average velocity for the light. If repeat the experiment in the rocket ship while the rocket is flying past the earth at a constant horizontal velocity, the observer inside will find all the measurements and calculations to be exactly the same as when the rocket was at rest.
Suppose now that the rocket ship is flying past the earth at the same constant horizontal velocity and that the observer is stationary on the earth. For the observer in the rocket ship, the light falls down on the table traveling at the regular speed of light, $c$ . For the observer on the earth, the light travels horizontally with the ship and also falls down onto the table. For the observer on the earth, the path appears to be longer since the light not only went downward but also horizontally.
However, since we have postulate 2, it is not allowed for the light to travel farther in the same time and therefore have a greater average velocity. According to postulate 2, the speed of the light as observed inside the space ship by that observer must be $3 \times 10^8 \ \text{m/s}$ and the speed of light observed by the observer on the earth (the light moving diagonally) must ALSO be $3 \times 10^8 \ \text{m/s}$ .
So, how is it possible for both observers to measure the speed of light as the same number when the distance traveled is clearly NOT the same? There is an unstated assumption involved here that indicates the passage of time in the two reference frames is the same and that is where the special theory of relativity changes our ideas. The special theory of relativity tells us that the observer on earth will see the clocks on the rocket ship ticking more slowly than his own clocks. So, while the observer on the rocket ship sees the light travel a distance $x$ meters in 1.00 second as measured on his clock, the observer on the earth sees the light travel $2x$ meters in 2.00 seconds as measured by his clock. In both cases, the speed of light is measured to be $c$ . It is important to note that this is not an optical illusion or some strange effect on the mechanical operation of the clock, the actual time on the ship slows down compared to the time of the stationary observer. This is referred to as time dilation .
The equation for time dilation is $\Delta T=\frac{\Delta t}{\sqrt{1-\frac{v^2}{c^2}}}$
where $\Delta t$ is the time interval between two events in the moving reference frame and $\Delta T$ is the time interval as measured in a stationary frame of reference. “ $v$ ” is the relative velocity of the moving reference frame and $c$ is the speed of light in a vacuum.
It should be clear from the equation that if the relative velocity between the two frames of reference is zero, then $\Delta T=\Delta t$ and there is no time dilation. We can also use the equation to show that for relative speeds like 100 m/s, which seems very fast to us, the comparison to the speed of light would show no noticeable time dilation.
$\Delta T=\frac{\Delta t}{\sqrt{1-\frac{v^2}{c^2}}}=\frac{10 \ \text{s}}{\sqrt{1-\frac{100^2}{(3 \times 10^8)^2}}}=\frac{10 \ \text{s}}{1-1 \times 10^{-13}}=10 \ \text{s}$
100 m/s is so slow compared to the speed of light, that it makes no difference in the time dilation formula. In order for any noticeable effect to occur, the relative velocity of the reference frames must be a significant fraction of the speed of light.
Example Problem: A muon has a rest lifetime of $2.2 \times 10^{-6} \ \text{s}$ . If it travels with a speed of 0.95c relative to you, how far will you see it travel before it decays?
Solution:
$\Delta T=\frac{\Delta t}{\sqrt{1-\frac{v^2}{c^2}}}=\frac{2.2 \times 10^{-6} \ \text{s}}{\sqrt{1-\frac{(0.95 c)^2}{c^2}}}=\frac{2.2 \times 10^{-6} \ \text{s}}{\sqrt{1-0.90}}=7.0 \times 10^{-6} \ \text{s}$
$\text{distance}=(3.0 \times 10^8 \ \text{m/s})(0.95)(7.0 \times 10^{-6} \ \text{s}) = 2.0 \times 10^3 \ \text{meters }$
Shortly after Einstein proposed the special theory of relativity, an apparent paradox was pointed out. This paradox involved a pair of twins, one of whom traveled away from the earth and returned at very high speeds. The other twin remained at home on earth. Since one twin was traveling at very high speed, time for him was running slower than for the twin who remained on earth. Thus the traveling twin would return home younger than the twin who remained on earth.
The paradox comes about when each twin thinks that their frame of reference was at rest and the other twin’s frame of reference was moving at high speed. Therefore, each twin would find the other one to be younger. The resolution lies in the fact that the traveling twin must accelerate at the beginning and end of the trip and this acceleration guarantees that this twin is traveling and his clock is actually running slower. The traveling twin will return home younger than his twin brother.
This result was tested in 1971 with a pair of very precise clocks. One clock was sent around the world in high speed jet planes while the matched clock remained at rest. When the traveling clock was returned and placed next to the other clock, the traveling clock had less time passed.
#### Length Contraction
In a similar manner, an observer on the rocket ship and an observer on the earth will not measure the length of the rocket ship to be the same length in the direction of its motion. The observer on the ship takes out his meter stick and measures the rocket ship to be 15 meters long while the ship sits at rest on the earth. An observer outside the ship, standing on the earth, will also measure the ship to be 15 m with his meter stick. When the rocket ship flies past the earth at a significant fraction of the speed of light, the observer on the ship takes out his meter stick and measures the length of the ship and again finds it to be 15 m. The “stationary” observer on the earth with his meter stick measures the moving rocket ship to be less than 15 m. Just for the sake of clarity, let’s say he measures the rocket ship to be 7.5 meters.
How is it possible that the two observers measure the same rocket ship to be two different lengths? When the rocket ship is at rest on the earth, the on-ship meter stick and the off-ship meter stick are exactly the same but when the rocket ship flies past the earth at significant fraction of the speed of light, the on-ship meter stick as seen by the on earth observer has shrunk. When the observer on ship says the ship is still 15 m long, the observer on earth says, “Nope, your meter stick has shrunk and so has your ship. The ship now measures 7.5 m long using my meter stick.” The on-ship meter stick shrinks by the same percentage that the ship shrinks.
It is important to note that the shortening of the moving object does not produce just a smaller object of the same shape. The object is only shortened in the direction of motion. Therefore, a long, slender rocket ship would NOT become a smaller version of itself, but rather, would become a short, stubby rocket ship.
At some point in history, the length contraction was known as the Fitzgerald contraction and physicists have been known to quote an applicable limerick.
There once was a young man named Fisk,
Whose fencing was exceedingly brisk,
So fast was his action,
The Fitzgerald contraction reduced his sword to a disk.
The equation for length contraction is $L=L_o\sqrt{1-\frac{v^2}{c^2}}$ where $L_o$ is the length measured on the moving body, $L$ is the length measured on the stationary body, $v$ is the relative speed of the reference frames, and $c$ is the speed of light.
You can see by analysis of the equation that when the relative velocity is zero, the two lengths are the same, when the relative speed is less than 1000 m/s, the effect is too small to notice, and only when the relative speed is a significant fraction of the speed of light is the contraction measureable.
Example Problem: A spaceship passes the earth at a speed $v = 0.80 \ \text{c}$ .
1. What is the length of a meter stick laying on a table in the ship and pointing in the direction of motion of the ship as measured by a person on the ship?
2. What is the length of a meter stick laying on a table in the ship and pointing in the direction of motion of the ship as measured by a person on the earth?
Solution:
1. relative to a person on the ship, the meter stick is at rest and therefore its length is 1.0 m
2. $L=L_o\sqrt{1-\frac{v^2}{c^2}}=(1.0 \ \text{m})\sqrt{1-\frac{(0.80 \ c)^2}{c^2}}=(1.0 \ \text{m})\sqrt{1-0.64}=0.60 \ \text{m}$
#### Relativistic Mass
The three basic mechanical quantities are length, time, and mass. Since length and time have been shown to be relative (their value depends on the reference frame from which they are measured), it might be expected that mass is also relative. Einstein showed that the mass of an object increases as its speed increases according to the formula
$M=\frac{m_o}{\sqrt{1-\frac{v^2}{c^2}}}$
where $M$ is the mass of the moving body, $m_o$ is the mass of the body at rest (or rest mass), $v$ is the velocity of the body and $c$ is the velocity of light.
For many years it was conventional to enter the discussion of dynamics through derivation of the relativistic mass and this is probably still the dominant mode in textbooks. More recently, however, it has been increasingly recognized that relativistic mass is a troublesome and dubious concept. Many physicists reject the concept of relativistic mass and oppose teaching the concept. Instead, they prefer to approach relativism through momentum rather than through relativistic mass.
If momentum is the preferred place to express relativistic dynamics, the equation is
$p=\frac{m_ov}{\sqrt{1-\frac{v^2}{c^2}}}$
Where $p$ is momentum$m_o$ is rest mass, $v$ is the velocity of the body and $c$ is the velocity of light.
Example Problem: An electron has a rest mass of $9.1 \times 10^{-31} \ \text{kg}$ . If the electron were traveling at 0.50 c relative to an observer, what electron mass would the observer measure?
Solution:
$M=\frac{m_o}{\sqrt{1-\frac{v^2}{c^2}}}=\frac{9.1 \times 10^{-31} \ \text{kg}}{\sqrt{1-\frac{(0.50 \ c)^2}{c^2}}}=\frac{9.1 \times 10^{-31} \ \text{kg}}{\sqrt{1-0.25}}=1.1 \times 10^{-30} \ \text{kg}$
#### The Ultimate Speed Limit
A result of the special theory of relativity is that no physical object can equal or exceed the speed of light. From the equation for relativistic mass, it can be seen that as the object is accelerated faster and faster, its mass becomes greater and greater. The greater mass would require an even greater force to accelerate it. If the velocity of the mass ever reached the speed of light, the denominator of the equation would become zero and the mass would become infinite. The energy required to accelerate an infinite mass would also be infinite. The fact that light itself travels at the speed $c$ , implies that light has a zero rest mass. Of course, light is never at rest.
#### The Equivalence of Mass and Energy
The special theory of relativity is also the origin of Einstein’s most famous equation, $E = mc^2$ , and the concept that mass and energy are different forms of the same thing. Einstein himself described the equivalence of mass and energy as the “most important upshot of the special theory of relativity”. The idea is not that mass and energy can be mathematically related but that they two are, in fact, simply different forms of the same thing. Each may be converted into the other and the conversion factor is the speed of light squared.
Example Problem: How much energy would be released if a $\pi$ meson $(\text{rest mass}= 2.4 \times 10^{-28} \ \text{kg})$ was transformed by decay completely into energy?
Solution: $E = mc^2 = (2.4 \times 10^{-28} \ \text{kg})(3.0 \times 10^8 \ \text{m/s})^2 = 2.2 \times 10^{-11} \ \text{joules}$
#### The Impact of the Theory of Special Relativity
A great many experiments have been performed to test the predictions of special relativity. No contradictions have been found. Scientists have therefore accepted special relativity as an accurate description of nature. When the relative velocities of objects are considerably less than the speed of light, the formulas for relativistic time, length, and mass all reduce to the classical formulas. It is required that the two theories correspond where they overlap at speeds much less than $c$ . Special relativity does not contradict classical mechanics. Rather, it is a more general theory needed for object speeds approaching the speed of light.
#### Summary
• The special theory of relativity essentially explains how to interpret motion between different inertial frames of reference, that is, places that are moving at constant speeds relative to each other.
• Special relativity is based on two postulates:
1. The laws of physics are the same for all observers within their own inertial reference frame.
2. The speed of light in a vacuum is the same for all observers regardless of their relative motion or the motion of the source of the light.
• The special theory of relativity explains the unchangeable speed of light better than classical mechanics, but it also has some surprising consequences. For example, according to the theory of special relativity,
• Two events that occurred simultaneously for one observer were not simultaneous for another observer if the two observers had relative motion to each other. (Relativity of simultaneity).
• Clocks in a moving frame of reference tick more slowly than an observer’s “stationary” clock. (Time dilation).
• Objects are measured to be shorter in the direction that they are moving with respect to a stationary observer. (Length contraction).
• The mass of a moving object will be greater as measured by an observer at rest.
• $E = mc^2$ , energy and mass are equivalent and transmutable. (Mass-energy equivalence).
• No physical object can travel faster than the speed of light in a vacuum. (Maximum speed is finite).
#### Practice
Questions
1. What was Einstein’s job when he published his special theory of relativity?
2. What was the immediate response of the scientific community to Einstein’s publications in 1905?
3. Who was the first scientist to recognize the great value in Einstein’s paper on special relativity?
#### Review
Questions
1. A woman stands on top of a moving railroad car and tosses a ball straight up in the air. If there is no air resistance, where will the ball come back down?
3. into the woman’s hand
2. If you were inside a windowless car that was traveling perfectly smoothly at a constant velocity, you could determine the speed of the car by dropping a ball.
1. True
2. False
3. Does time dilation mean that time actually passes more slowly in a moving reference frame or that it only seems to pass more slowly?
4. A young looking woman astronaut has just arrived home from a long trip at near the speed of light. She rushes up to an old gray-haired man and refers to him as her son. Is this possible?
5. If you were traveling away from the earth at a speed of 0.5 c, how would your heartbeat, length, and mass change? What would observers from earth say about their measurements of your heartbeat, length, and mass?
6. A person on another planet shines a flashlight at you. The planet and the earth are both in the same reference frame and are not moving relative to each other. At the same instant that the person shined the flashlight at you, a person on a spaceship passing that planet and moving toward you at 0.5 c also shined a flashlight at you. Which light pulse will reach you first?
1. the light from the person on the planet
2. the light from the flashlight on the spaceship
3. the two light pulses will reach you at the same time
7. If a spaceship will shrink when it travels at a speed of 0.75 c, do we need to make design changes to accommodate passengers and crew?
8. A beam of particles travel at a speed of $2.85 \times 10^8 \ \text{m/s}$ . At this speed, the particles average lifetime is measured to be $2.50 \times 10^{-8} \ \text{s}$ . What is a particle’s lifetime when they are at rest?
9. A spaceship passes you at a speed of 0.80 c. You measure its length to be 90.0 m. How long would this space ship be at rest?
10. If you were to travel to a planet 36 light years from earth at a speed of 0.98 c, what would you measure the distance to be?
11. If the rest mass of a proton is $1.67 \times 10^{-27} \ \text{kg}$ , what is its mass when traveling at 0.85 c?
12. At what speed will the relativistic mass of an object be exactly double its rest mass?
13. How much energy would be produced if 1.00 milligram of mass were completely converted into energy?
# Reviews
Email Verified
Well done! You've successfully verified the email address . | 2014-08-22 06:48:39 | {"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": 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": 51, "texerror": 0, "math_score": 0.6858020424842834, "perplexity": 242.15292611867469}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-35/segments/1408500823169.67/warc/CC-MAIN-20140820021343-00241-ip-10-180-136-8.ec2.internal.warc.gz"} |
https://gitlab.isc.org/sebschrader/kea/-/blame/12114c5c973d70be91bfe946962e4373fa4d890a/src/lib/asiolink/io_asio_socket.h | io_asio_socket.h 16.1 KB
Stephen Morris committed Feb 18, 2011 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 ``````// Copyright (C) 2010 Internet Systems Consortium, Inc. ("ISC") // // Permission to use, copy, modify, and/or distribute this software for any // purpose with or without fee is hereby granted, provided that the above // copyright notice and this permission notice appear in all copies. // // THE SOFTWARE IS PROVIDED "AS IS" AND ISC DISCLAIMS ALL WARRANTIES WITH // REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF MERCHANTABILITY // AND FITNESS. IN NO EVENT SHALL ISC BE LIABLE FOR ANY SPECIAL, DIRECT, // INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES WHATSOEVER RESULTING FROM // LOSS OF USE, DATA OR PROFITS, WHETHER IN AN ACTION OF CONTRACT, NEGLIGENCE // OR OTHER TORTIOUS ACTION, ARISING OUT OF OR IN CONNECTION WITH THE USE OR // PERFORMANCE OF THIS SOFTWARE. #ifndef __IO_ASIO_SOCKET_H #define __IO_ASIO_SOCKET_H 1 // IMPORTANT NOTE: only very few ASIO headers files can be included in // this file. In particular, asio.hpp should never be included here. // See the description of the namespace below. #include // for some network system calls #include #include #include #include `````` chenzhengzhang committed Apr 14, 2011 29 ``````#include `````` Stephen Morris committed Feb 28, 2011 30 `````` `````` Stephen Morris committed Feb 18, 2011 31 32 33 ``````#include #include `````` Ocean Wang committed Apr 08, 2011 34 ``````namespace isc { `````` Stephen Morris committed Feb 18, 2011 35 36 37 38 39 40 41 42 43 44 45 ``````namespace asiolink { /// \brief Socket not open /// /// Thrown on an attempt to do read/write to a socket that is not open. class SocketNotOpen : public IOError { public: SocketNotOpen(const char* file, size_t line, const char* what) : IOError(file, line, what) {} }; `````` Stephen Morris committed Feb 28, 2011 46 ``````/// \brief Error setting socket options `````` Stephen Morris committed Feb 24, 2011 47 48 49 50 51 52 53 ``````/// /// Thrown if attempt to change socket options fails. class SocketSetError : public IOError { public: SocketSetError(const char* file, size_t line, const char* what) : IOError(file, line, what) {} }; `````` Stephen Morris committed Feb 18, 2011 54 `````` `````` Stephen Morris committed Feb 28, 2011 55 ``````/// \brief Buffer overflow `````` Stephen Morris committed Feb 25, 2011 56 57 58 59 60 61 62 63 64 ``````/// /// Thrown if an attempt is made to receive into an area beyond the end of /// the receive data buffer. class BufferOverflow : public IOError { public: BufferOverflow(const char* file, size_t line, const char* what) : IOError(file, line, what) {} }; `````` Stephen Morris committed Feb 18, 2011 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 ``````/// Forward declaration of an IOEndpoint class IOEndpoint; /// \brief I/O Socket with asynchronous operations /// /// This class is a wrapper for the ASIO socket classes such as /// \c ip::tcp::socket and \c ip::udp::socket. /// /// This is the basic IOSocket with additional operations - open, send, receive /// and close. Depending on how the asiolink code develops, it may be a /// temporary class: its main use is to add the template parameter needed for /// the derived classes UDPSocket and TCPSocket but without changing the /// signature of the more basic IOSocket class. /// /// We may revisit this decision when we generalize the wrapper and more /// modules use it. Also, at that point we may define a separate (visible) /// derived class for testing purposes rather than providing factory methods /// (i.e., getDummy variants below). /// /// TODO: Check if IOAsioSocket class is still needed /// /// \param C Template parameter identifying type of the callback object. template class IOAsioSocket : public IOSocket { /// /// \name Constructors and Destructor /// /// Note: The copy constructor and the assignment operator are /// intentionally defined as private, making this class non-copyable. //@{ private: IOAsioSocket(const IOAsioSocket& source); IOAsioSocket& operator=(const IOAsioSocket& source); protected: /// \brief The default constructor. /// /// This is intentionally defined as \c protected as this base class /// should never be instantiated (except as part of a derived class). IOAsioSocket() {} public: /// The destructor. virtual ~IOAsioSocket() {} //@} /// \brief Return the "native" representation of the socket. /// `````` Stephen Morris committed Feb 28, 2011 113 114 115 `````` /// In practice, this is the file descriptor of the socket for UNIX-like /// systems so the current implementation simply uses \c int as the type of /// the return value. We may have to need revisit this decision later. `````` Stephen Morris committed Feb 18, 2011 116 `````` /// `````` Stephen Morris committed Feb 28, 2011 117 118 119 120 121 122 123 `````` /// In general, the application should avoid using this method; it /// essentially discloses an implementation specific "handle" that can /// change the internal state of the socket (consider what would happen if /// the application closes it, for example). But we sometimes need to /// perform very low-level operations that requires the native /// representation. Passing the file descriptor to a different process is /// one example. This method is provided as a necessary evil for such `````` Jelte Jansen committed Mar 07, 2011 124 `````` /// limited purposes. `````` Stephen Morris committed Feb 18, 2011 125 126 127 128 `````` /// /// This method never throws an exception. /// /// \return The native representation of the socket. This is the socket `````` Stephen Morris committed Feb 28, 2011 129 `````` /// file descriptor for UNIX-like systems. `````` Stephen Morris committed Feb 18, 2011 130 131 132 133 134 135 136 137 138 `````` virtual int getNative() const = 0; /// \brief Return the transport protocol of the socket. /// /// Currently, it returns \c IPPROTO_UDP for UDP sockets, and /// \c IPPROTO_TCP for TCP sockets. /// /// This method never throws an exception. /// `````` Stephen Morris committed Feb 28, 2011 139 `````` /// \return \c IPPROTO_UDP for UDP sockets, \c IPPROTO_TCP for TCP sockets `````` Stephen Morris committed Feb 18, 2011 140 141 `````` virtual int getProtocol() const = 0; `````` Stephen Morris committed Feb 25, 2011 142 `````` /// \brief Is Open() synchronous? `````` Stephen Morris committed Feb 18, 2011 143 `````` /// `````` Stephen Morris committed Feb 28, 2011 144 145 146 147 `````` /// On a TCP socket, an "open" operation is a call to the socket's "open()" /// method followed by a connection to the remote system: it is an /// asynchronous operation. On a UDP socket, it is just a call to "open()" /// and completes synchronously. `````` Stephen Morris committed Feb 21, 2011 148 149 150 151 `````` /// /// For TCP, signalling of the completion of the operation is done by /// by calling the callback function in the normal way. This could be done /// for UDP (by posting en event on the event queue); however, that will `````` Stephen Morris committed Feb 25, 2011 152 153 154 155 156 `````` /// incur additional overhead in the most common case. So we give the /// caller the choice for calling this open() method synchronously or /// asynchronously. /// /// Owing to the way that the stackless coroutines are implemented, we need `````` Stephen Morris committed Feb 28, 2011 157 158 `````` /// to know _before_ executing the "open" function whether or not it is /// asynchronous. So this method is called to provide that information. `````` Stephen Morris committed Feb 25, 2011 159 160 161 162 `````` /// /// (The reason there is a need to know is because the call to open() passes /// in the state of the coroutine at the time the call is made. On an /// asynchronous I/O, we need to set the state to point to the statement `````` Stephen Morris committed Feb 28, 2011 163 164 165 166 167 `````` /// after the call to open() _before_ we pass the corouine to the open() /// call. Unfortunately, the macros that set the state of the coroutine /// also yield control - which we don't want to do if the open is /// synchronous. Hence we need to know before we make the call to open() /// whether that call will complete asynchronously.) `````` Stephen Morris committed Feb 25, 2011 168 169 170 171 172 173 `````` virtual bool isOpenSynchronous() const = 0; /// \brief Open AsioSocket /// /// Opens the socket for asynchronous I/O. The open will complete /// synchronously on UCP or asynchronously on TCP (in which case a callback `````` Stephen Morris committed Feb 28, 2011 174 `````` /// will be queued). `````` Stephen Morris committed Feb 18, 2011 175 176 `````` /// /// \param endpoint Pointer to the endpoint object. This is ignored for `````` Stephen Morris committed Feb 28, 2011 177 178 `````` /// a UDP socket (the target is specified in the send call), but /// should be of type TCPEndpoint for a TCP connection. `````` Stephen Morris committed Feb 21, 2011 179 `````` /// \param callback I/O Completion callback, called when the operation has `````` Stephen Morris committed Feb 28, 2011 180 181 `````` /// completed, but only if the operation was asynchronous. (It is /// ignored on a UDP socket.) `````` Stephen Morris committed Feb 25, 2011 182 `````` virtual void open(const IOEndpoint* endpoint, C& callback) = 0; `````` Stephen Morris committed Feb 18, 2011 183 184 185 186 187 188 189 190 191 192 193 194 `````` /// \brief Send Asynchronously /// /// This corresponds to async_send_to() for UDP sockets and async_send() /// for TCP. In both cases an endpoint argument is supplied indicating the /// target of the send - this is ignored for TCP. /// /// \param data Data to send /// \param length Length of data to send /// \param endpoint Target of the send /// \param callback Callback object. virtual void asyncSend(const void* data, size_t length, `````` Stephen Morris committed Feb 25, 2011 195 `````` const IOEndpoint* endpoint, C& callback) = 0; `````` Stephen Morris committed Feb 18, 2011 196 197 198 `````` /// \brief Receive Asynchronously /// `````` Stephen Morris committed Feb 28, 2011 199 `````` /// This corresponds to async_receive_from() for UDP sockets and `````` Stephen Morris committed Feb 18, 2011 200 201 202 203 204 205 `````` /// async_receive() for TCP. In both cases, an endpoint argument is /// supplied to receive the source of the communication. For TCP it will /// be filled in with details of the connection. /// /// \param data Buffer to receive incoming message /// \param length Length of the data buffer `````` Stephen Morris committed Mar 04, 2011 206 207 208 209 210 `````` /// \param offset Offset into buffer where data is to be put. Although the /// offset could be implied by adjusting "data" and "length" /// appropriately, using this argument allows data to be specified as /// "const void*" - the overhead of converting it to a pointer to a /// set of bytes is hidden away here. `````` Stephen Morris committed Feb 18, 2011 211 212 `````` /// \param endpoint Source of the communication /// \param callback Callback object `````` Stephen Morris committed Feb 25, 2011 213 214 `````` virtual void asyncReceive(void* data, size_t length, size_t offset, IOEndpoint* endpoint, C& callback) = 0; `````` Stephen Morris committed Feb 18, 2011 215 `````` `````` Stephen Morris committed Mar 04, 2011 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 `````` /// \brief Processes received data /// /// In the IOFetch code, data is received into a staging buffer before being /// copied into the target buffer. (This is because (a) we don't know how /// much data we will be receiving, so don't know how to size the output /// buffer and (b) TCP data is preceded by a two-byte count field that needs /// to be discarded before being returned to the user.) /// /// An additional consideration is that TCP data is not received in one /// I/O - it may take a number of I/Os - each receiving any non-zero number /// of bytes - to read the entire message. /// /// So the IOFetch code has to loop until it determines that all the data /// has been read. This is where this method comes in. It has several /// functions: /// /// - It checks if the received data is complete. /// - If data is not complete, decides if the next set of data is to go into /// the start of the staging buffer or at some offset into it. (This /// simplifies the case we could have in a TCP receive where the two-byte /// count field is received in one-byte chunks: we put off interpreting /// the count until we have all of it. The alternative - copying the /// data to the output buffer and interpreting the count from there - /// would require moving the data in the output buffer by two bytes before /// returning it to the caller.) /// - Copies data from the staging buffer into the output buffer. /// /// This functionality mainly applies to TCP receives. For UDP, all the /// data is received in one I/O, so this just copies the data into the /// output buffer. /// /// \param staging Pointer to the start of the staging buffer. /// \param length Amount of data in the staging buffer. /// \param cumulative Amount of data received before the staging buffer is /// processed (this includes the TCP count field if appropriate). /// The value should be set to zero before the receive loop is /// entered, and it will be updated by this method as required. /// \param offset Offset into the staging buffer where the next read should /// put the received data. It should be set to zero before the first /// call and may be updated by this method. /// \param expected Expected amount of data to be received. This is /// really the TCP count field and is set to that value when enough /// of a TCP message is received. It should be initialized to -1 /// before the first read is executed. /// \param outbuff Output buffer. Data in the staging buffer may be copied /// to this output buffer in the call. `````` Stephen Morris committed Feb 18, 2011 262 263 `````` /// /// \return true if the receive is complete, false if another receive is `````` Stephen Morris committed Mar 04, 2011 264 265 266 267 268 269 270 271 272 `````` /// needed. This is always true for UDP, but for TCP involves /// checking the amount of data received so far against the amount /// expected (as indicated by the two-byte count field). If this /// method returns false, another read should be queued and data /// should be read into the staging buffer at offset given by the /// "offset" parameter. virtual bool processReceivedData(const void* staging, size_t length, size_t& cumulative, size_t& offset, size_t& expected, `````` chenzhengzhang committed Apr 14, 2011 273 `````` isc::util::OutputBufferPtr& outbuff) = 0; `````` Stephen Morris committed Feb 28, 2011 274 `````` `````` Stephen Morris committed Feb 18, 2011 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 `````` /// \brief Cancel I/O On AsioSocket virtual void cancel() = 0; /// \brief Close socket virtual void close() = 0; }; #include "io_socket.h" /// \brief The \c DummyAsioSocket class is a concrete derived class of /// \c IOAsioSocket that is not associated with any real socket. /// /// This main purpose of this class is tests, where it may be desirable to /// instantiate an \c IOAsioSocket object without involving system resource /// allocation such as real network sockets. /// /// \param C Template parameter identifying type of the callback object. template class DummyAsioSocket : public IOAsioSocket { private: DummyAsioSocket(const DummyAsioSocket& source); DummyAsioSocket& operator=(const DummyAsioSocket& source); public: /// \brief Constructor from the protocol number. /// /// The protocol must validly identify a standard network protocol. /// For example, to specify TCP \c protocol must be \c IPPROTO_TCP. /// /// \param protocol The network protocol number for the socket. DummyAsioSocket(const int protocol) : protocol_(protocol) {} /// \brief A dummy derived method of \c IOAsioSocket::getNative(). /// /// \return Always returns -1 as the object is not associated with a real /// (native) socket. virtual int getNative() const { return (-1); } /// \brief A dummy derived method of \c IOAsioSocket::getProtocol(). /// /// \return Protocol socket was created with virtual int getProtocol() const { return (protocol_); } `````` Stephen Morris committed Feb 25, 2011 320 321 322 323 324 325 326 `````` /// \brief Is socket opening synchronous? /// /// \return true - it is for this class. bool isOpenSynchronous() const { return true; } `````` Stephen Morris committed Feb 18, 2011 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 `````` /// \brief Open AsioSocket /// /// A call that is a no-op on UDP sockets, this opens a connection to the /// system identified by the given endpoint. /// /// \param endpoint Unused /// \param callback Unused. ///false indicating that the operation completed synchronously. virtual bool open(const IOEndpoint*, C&) { return (false); } /// \brief Send Asynchronously /// /// Must be supplied as it is abstract in the base class. /// /// \param data Unused /// \param length Unused /// \param endpoint Unused /// \param callback Unused virtual void asyncSend(const void*, size_t, const IOEndpoint*, C&) { } /// \brief Receive Asynchronously /// /// Must be supplied as it is abstract in the base class. /// /// \param data Unused /// \param length Unused `````` Stephen Morris committed Feb 25, 2011 356 `````` /// \param offset Unused `````` Stephen Morris committed Feb 18, 2011 357 358 `````` /// \param endpoint Unused /// \param callback Unused `````` Stephen Morris committed Feb 24, 2011 359 360 361 `````` virtual void asyncReceive(void* data, size_t, size_t, IOEndpoint*, C&) { } `````` Stephen Morris committed Feb 18, 2011 362 363 `````` /// \brief Checks if the data received is complete. /// `````` Stephen Morris committed Mar 04, 2011 364 `````` /// \param staging Unused `````` Stephen Morris committed Feb 18, 2011 365 366 `````` /// \param length Unused /// \param cumulative Unused `````` Stephen Morris committed Mar 04, 2011 367 368 369 `````` /// \param offset Unused. /// \param expected Unused. /// \param outbuff Unused. `````` Stephen Morris committed Feb 18, 2011 370 371 `````` /// /// \return Always true `````` Stephen Morris committed Mar 04, 2011 372 373 374 `````` virtual bool receiveComplete(const void* staging, size_t length, size_t& cumulative, size_t& offset, size_t& expected, `````` chenzhengzhang committed Apr 14, 2011 375 `````` isc::util::OutputBufferPtr& outbuff) `````` Stephen Morris committed Feb 28, 2011 376 `````` { `````` Stephen Morris committed Mar 04, 2011 377 `````` return (true); `````` Stephen Morris committed Feb 28, 2011 378 `````` } `````` Stephen Morris committed Feb 18, 2011 379 `````` `````` Stephen Morris committed Mar 04, 2011 380 `````` `````` Stephen Morris committed Feb 18, 2011 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 `````` /// \brief Cancel I/O On AsioSocket /// /// Must be supplied as it is abstract in the base class. virtual void cancel() { } /// \brief Close socket /// /// Must be supplied as it is abstract in the base class. virtual void close() { } private: const int protocol_; }; } // namespace asiolink `````` Ocean Wang committed Apr 08, 2011 398 ``````} // namespace isc `````` Stephen Morris committed Feb 18, 2011 399 400 `````` #endif // __IO_ASIO_SOCKET_H`````` | 2020-09-20 17:23:34 | {"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": 0.8539326190948486, "perplexity": 6465.099826445123}, "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/1600400198287.23/warc/CC-MAIN-20200920161009-20200920191009-00665.warc.gz"} |
http://www.newton.ac.uk/preprints2011.html | # Preprints 2011
The three-letter code attached to the preprint number indicates the scientific programme during which the paper was written. Click on the code to see the programme details.
Preprint No. Author(s) Title and publication details
NI11001-KIT JA Carrillo, RM Colombo, P Gwiazda and A Ulikowska Structured populations, cell growth and measure valued balance laws
NI11002-KIT F Bolley, J Cañizo and A Carrillo Mean-field limit for the stochastic Vicsek model
NI11003-MOS M Reineke Degenerate cohomological Hall algebra and quantized Donaldson-Thomas invariants for $\it m$-loop quivers
NI11004-MOS S Grushevsky and K Hulek The class of the locus of intermediate Jacobians of cubic threefolds
NI11005-MOS I Grzegorczyk, V Mercat and PE Newstead Stable bundles of rank 2 with 4 sections
NI11006-DAN J Solymosi and T Tao An incidence theorem in higher dimensions
NI11007-MOS H Lange and A Ortega Compactification of the Prym map for non cyclic triple coverings
NI11008-MOS S Mukai Igusa quartic and Steiner surfaces
NI11009-DAN A Plagne Sums of dilates in groups of prime order
NI11010-DIS P Kassotakis and M Nieszporski On the non-multiaffine consistent around the cube lattice equations
NI11011-KIT Y Zhou and S Oughton Nonlocality and the critical Reynolds numbers of the minimum state magnetohydrodynamic turbulence
NI11012-DAN Y Ollivier and C Villani A curved Brunn-Minkowski inequality on the discrete hypercube or: What is the Ricci curvature of the discrete hypercube?
NI11013-DAN F Barthe and D Cordero-Erausquin Invariances in variance estimates
NI11014-DAN D Cordero-Erausquin and M Ledoux Hypercontractive measures, Talagrand's inequality, and influences
NI11015-MOS A Bayer, E Macrì and Y Toda Bridgeland stability conditions on threefolds I: Bogomolov-Gieseker type inequalities
NI11016-MOS A Bayer, A Bertram, E Macrì and Y Toda Bridgeland stability conditions on threefolds II: An application to Fujita's conjecture
NI11017-DAN G Gutin and A Yeo Hypercontractive inequality for pseudo-Boolean functions of bounded Fourier width
NI11019-MOS WM Goldman and D Toledo Affine cubic surfaces and relative $SL$(2)-character varieties of compact surfaces
NI11020-SPD SA Klokov and A Yu Veretennikov On local mixing conditions for SDE approximations
NI11021-DAN A Giannopoulos, G Paouris and B-H Vritsiou A remark on the slicing problem
NI11022-KIT W Bao and X Dong Numerical methods for computing ground state and dynamics of nonlinear relativistic Hartree equation for boson stars
NI11023-KIT X Dong A short note on simplified pseudospectral methods for computing ground state and dynamics of spherically symmetric Schrödinger-Poisson-Slater system
NI11024-DAE B Jones and P Goos An algorithm for finding D-efficient equivalent-estimation second-order split-plot designs
NI11025-MOS H Lange and PE Newstead Bundles of rank 2 with small Clifford index on algebraic curves
NI11026-MOS A Maciocia and C Meachan Rank on Bridgeland stable moduli spaces on principally polarized Abelian surface
NI11027-DAN G Schechtman Approximate Gaussian isoperimetry for $\it k$ sets
NI11028-DAN R Levy and G Schechtman Stabilizing isomorphisms from l_p (l_2) into L_p [0, 1]
NI11029-DAN J Bennett, N Bez and S Gutiérrez Transversal multilinear Radon-like transforms: local and global estimates
NI11030-DAN J Bennett, N Bez and S Gutiérrez Global nonlinear Brascamp-Lieb inequalities
NI11031-DAN JL Xiang Li and B Szegedy On the logarithimic calculus and Sidorenko's conjecture
NI11032-DAE K Mylona and P Goos Penalized generalized least squares for model selection under restricted randomization
NI11033-DAE F Torti, D Perrotta, AC Atkinson, M Riani and et al Benchmark testing of algorithms for very robust regression
NI11034-DAN E Mossel, K Oleszkiewicz and A Sen On reverse hypercontractivity
NI11035-CLP Y Zhou and CE Leith Predictability error growth of turbulent flows
NI11036-MOS B Osserman Special determinants in higher rank Brill-Noether theory
NI11037-MOS Y Toda Multiple cover formula of generalized DT invariants I: parabolic stable pairs
NI11038-MOS Y Toda Multiple cover formula of generalized DT invariants II: Jacobian localizations
NI11039-MOS L Alvarez-Consul, M Garcia-Fernandez and O Garcia-Prada Coupled equations for Kähler metrics and Yang-Mills connections
NI11040-DAN N Goyal and L Rademacher Lower bounds for the average and smoothed number of Pareto optima
NI11041-MOS M Logares, V Munoz and PE Newstead Hodge Polynomials of SL(2,C)-character varieties for curves of small genus
NI11042-DAE AC Atkinson, A Biswas and L Pronzato Covariate-balanced response-adaptive designs for clinical trials with continuous responses that target allocation proportions
NI11043-INV Y Ohyama Monodromy evolving deformations and confluent Halphen's systems
NI11044-DAE A Baldi Antognini, A Giovagnoli and M Zagoraiou Some recent developments in the design of adaptive clinical trials
NI11045-SPD OA Butkovsky and A Yu Veretennikov On asymptotics for Vaserstein coupling of a Markov chain
NI11046-DAN G Ambrus, P Kevei and V Vígh The diminishing segment process
NI11047-DAE RA Bailey and PJ Cameron Using graphs to find the best block designs
NI11048-DAE AC Atkinson and B Bogacka Optimum designs for the equality of parameters in enzyme inhibition kinetic models
NI11049-DAE H Dette, M Hallin, T Kley and S Volgushev Of copulas, quantiles, ranks and spectra an $L_1$-approach to spectral analysis
NI11050-DAE H Dette, A Pepelyshev and A Zhigljavsky Optimal design for linear models with correlated observations
NI11051-DAE S Delvaux and H Dette Zeros and ratio asymptotics for matrix orthogonal polynomials
NI11052-DAE D Braess and H Dette Optimal discriminating designs for several competing regression models
NI11053-DAE H Dette, C Kiss, N Benda and F Bretz Optimal designs for dose finding studies with an active control
NI11054-DAE H Dette, VB Melas and P Shpilev T-optimal designs for discrimination between two polynomial models
NI11055-DAE SW Hyun, M Yang and N Flournoy A procedure for finding an improved upper bound on the number of optimal design points
NI11056-DAE LM Haines and AE Clark The construction of optimal designs for dose-escalation studies
NI11057-DAE AC Atkinson, VV Fedorov, AM Herzberg and R Zhang Optimal experimental design for generalized regression models
NI11058-DAE M Riani, AC Atkinson and D Perrotta Calibrated very robust regression
NI11059-DAE H Rabie and N Flournoy Optimal designs for contingent response models with application to toxicity-efficacy studies-a technical report
NI11060-DAE H Moon, T Santner and A Dean Two-stage sensitivity-based group screening in computer experiments
NI11061-DAE D Dragulji'c, TJ Santner and AM Dean Non-collapsing space-filling designs for bounded non-rectangular regions
NI11062-DAE JD Svenson and TJ Santner Multiobjective optimization of expensive black-box functions via expected maximin improvement
NI11063-DAE J Svenson, T Santner, A Dean and H Moon Estimating sensitivity indices from computer simulator output
NI11064-DAE RA Bailey and J Reiss Design and analysis of experiments testing for biodiversity effects in ecology
NI11065-DAE VV Fedorov, N Flournoy, Y Wu and R Zhang Best intention designs in dose-finding studies
NI11066-DAE C May and C Tommasi Model selection and parameter estimation in non-linear nested models: a sequential generalized DKL-optimum design
1996 | 1997 | 1998 | 1999 | 2000 | 2001 | 2002 | 2003 | 2004 | 2005 | 2006 | 2007 | 2008 | 2009 | 2010 | 2011 | 2012 | 2013 | | 2014-07-23 10:03:59 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4646076261997223, "perplexity": 3899.6460546166877}, "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/1405997877869.73/warc/CC-MAIN-20140722025757-00150-ip-10-33-131-23.ec2.internal.warc.gz"} |
https://docs.microsoft.com/en-us/dotnet/api/microsoft.ml.trainers.sgdnoncalibratedtrainer?view=ml-dotnet | # SgdNonCalibratedTrainer Class
## Definition
The IEstimator<TTransformer> for training logistic regression using a parallel stochastic gradient method.
public sealed class SgdNonCalibratedTrainer : Microsoft.ML.Trainers.SgdBinaryTrainerBase<Microsoft.ML.Trainers.LinearBinaryModelParameters>
type SgdNonCalibratedTrainer = class
inherit SgdBinaryTrainerBase<LinearBinaryModelParameters>
Public NotInheritable Class SgdNonCalibratedTrainer
Inherits SgdBinaryTrainerBase(Of LinearBinaryModelParameters)
Inheritance
## Remarks
To create this trainer, use SgdNonCalibrated or SgdNonCalibrated(Options).
### Input and Output Columns
The input label column data must be Boolean. The input features column data must be a known-sized vector of Single. This trainer outputs the following columns:
Output Column Name Column Type Description
Score Single The unbounded score that was calculated by the model.
PredictedLabel Boolean The predicted label, based on the sign of the score. A negative score maps to false and a positive score maps to true.
### Trainer Characteristics
Is normalization required? Yes
Is caching required? No
Required NuGet in addition to Microsoft.ML None
### Training Algorithm Details
The Stochastic Gradient Descent (SGD) is one of the popular stochastic optimization procedures that can be integrated into several machine learning tasks to achieve state-of-the-art performance. This trainer implements the Hogwild Stochastic Gradient Descent for binary classification that supports multi-threading without any locking. If the associated optimization problem is sparse, Hogwild Stochastic Gradient Descent achieves a nearly optimal rate of convergence. For more details about Hogwild Stochastic Gradient Descent can be found here.
## Fields
The feature column that the trainer expects. (Inherited from TrainerEstimatorBase) The label column that the trainer expects. Can be null, which indicates that label is not used for training. (Inherited from TrainerEstimatorBase) The weight column that the trainer expects. Can be null, which indicates that weight is not used for training. (Inherited from TrainerEstimatorBase)
## Properties
(Inherited from SgdBinaryTrainerBase)
## Methods
Trains and returns a ITransformer. (Inherited from TrainerEstimatorBase) Continues the training of a SdcaLogisticRegressionBinaryTrainer using an already trained modelParameters and returns a Microsoft.ML.Data.BinaryPredictionTransformer. (Inherited from SgdBinaryTrainerBase) (Inherited from TrainerEstimatorBase)
## Extension Methods
Given an estimator, return a wrapping object that will call a delegate once Fit(IDataView) is called. It is often important for an estimator to return information about what was fit, which is why the Fit(IDataView) method returns a specifically typed object, rather than just a general ITransformer. However, at the same time, IEstimator are often formed into pipelines with many objects, so we may need to build a chain of estimators via EstimatorChain where the estimator for which we want to get the transformer is buried somewhere in this chain. For that scenario, we can through this method attach a delegate that will be called once fit is called. | 2019-08-22 14:48:02 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 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": 0.4054131805896759, "perplexity": 3127.7105503457487}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-35/segments/1566027317130.77/warc/CC-MAIN-20190822130553-20190822152553-00145.warc.gz"} |
https://ml4ds.com/weeks/11-future/old-nonlinear/exercises/set3.html | ## Conceptual
### ISLR Section 5.4
• 2 (a-f), and calculate $$e^{-1}$$ to a few decimal places for comparison
• 3
• 2
• 5
## Optional
The remaining exercises are option and will not be graded.
### Mathematics practice
• Can resampling methods be useful for addressing OOD generalization? If not, then why? If so, then how?
• Write out the objective function of the lasso for the case of linear regression with one predictor variable. Use calculus to find an expression for the solution (hint: you may need to consider cases)
### Applied practice
• ISLR Section 5.4, problem 8
• ISLR Section 6.6, problem 9 (a-d)
• ISLR Section 7.9, problem 9 (a-c) | 2023-03-30 11:51:01 | {"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": 0.7819194793701172, "perplexity": 3063.3806756594063}, "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/1679296949181.44/warc/CC-MAIN-20230330101355-20230330131355-00090.warc.gz"} |
https://www.albany.edu/~hammond/course/calcnotes/newton.html | # Notes on Newton's Method
#### Revised for the Web: July 27, 2004
Proposition: Let $f$ be a function that is differentiable on an interval $I$ and assume further:
Then:
1. There is one and only one point $z$ in $I$ for which $f\left(z\right)=0$.
2. If $x$ is on the convex side of the graph of $f$ in $I$, then so is ${x}^{\prime }=x-f\left(x\right)⁄{f}^{\prime }\left(x\right)$, and ${x}^{\prime }$ lies between $x$ and $z$.
3. Successive iterations of Newton's method beginning with a point $x$ on the convex side of the graph of $f$ in $I$ will converge to $z$.
4. Error control principle. If $c$ is any point in $I$ on the concave side of the graph of $f$ and $x$ is on the convex side, then the distance between $x$ and $z$ is at most the absolute value of $f\left(x\right)⁄{f}^{\prime }\left(c\right)$.
Proof: If ${f}^{\prime }$ is positive in $I$ one has $f\left({x}_{1}\right) whenever ${x}_{1}<{x}_{2}$ in $I$. If instead ${f}^{\prime }$ is negative in $I$, then one has $f\left({x}_{1}\right)>f\left({x}_{2}\right)$ for ${x}_{1}<{x}_{2}$. For this reason there is at most one root $z$ in $I$ with $f\left(z\right)=0$. The Intermediate Value Theorem for Continuous Functions guarantees that there is at least one root between $a$ and $b$.
We shall assume that ${f}^{\prime }$ is positive and increasing. One may reduce each of the other three cases to this case by reflecting either in the horizontal axis or in the vertical line $x=z$ or both. Under this assumption the convex side of the graph of $f$ is the right side. Suppose that $z: then $0=f\left(z\right). We apply the Mean Value Theorem to $f$ on the interval $\left[z,x\right]$ to conclude that there is a number $u$ with $z for which $f\left(x\right)-f\left(z\right)={f}^{\prime }\left(u\right)\left(x-z\right)\phantom{\rule{0.5em}{0ex}}\text{.}$ Since $f\left(z\right)=0$ and ${f}^{\prime }\left(u\right)>0$, one obtains $x-z=\frac{f\left(x\right)}{{f}^{\prime }\left(u\right)}\phantom{\rule{0.5em}{0ex}}\text{.}$ Since ${f}^{\prime }$ is increasing, we find ${f}^{\prime }\left(u\right)<{f}^{\prime }\left(x\right)$, and, therefore, $f\left(x\right)⁄{f}^{\prime }\left(x\right). Consequently, $z<{x}^{\prime }.
In view of (2) one has $z<\dots <{x}_{n}<\dots <{x}_{2}<{x}_{1}\phantom{\rule{0.5em}{0ex}}\text{.}$ Letting ${x}_{*}={\mathrm{inf}}_{\left(n\ge 1\right)}\phantom{\rule{0.5em}{0ex}}\left\{{x}_{n}\right\}\phantom{\rule{0.5em}{0ex}}\text{,}$ one has ${x}_{*}={\phantom{\rule{0.1em}{0ex}}\mathrm{lim}}_{n\to \infty }\phantom{\rule{0.5em}{0ex}}{x}_{n}\phantom{\rule{0.5em}{0ex}}\text{,}$ and, therefore, taking the limit as $n\to \infty$ on both sides of the relation ${x}_{n+1}={x}_{n}-\frac{f\left({x}_{n}\right)}{{f}^{\prime }\left({x}_{n}\right)}\phantom{\rule{0.5em}{0ex}}\text{,}$ one finds that $f\left({x}_{*}\right)=0$. Since by (1) there is only one root of $f$ in $I$, it follows that ${x}_{*}=z$.
In the proof of (2) we saw that for $x$ in $I$ on the right side of $z$ the distance from $x$ to $z$ is $f\left(x\right)⁄{f}^{\prime }\left(u\right)$, where $z. Since $c$ is on the concave side of the graph of $f$, i.e., $c, we find also $c, hence, ${f}^{\prime }\left(c\right)<{f}^{\prime }\left(u\right)$. Consequently, $\mathrm{the error}=x-z=\frac{f\left(x\right)}{{f}^{\prime }\left(u\right)}\le \frac{f\left(x\right)}{{f}^{\prime }\left(c\right)}\phantom{\rule{0.5em}{0ex}}\text{.}$ | 2018-06-19 19:41:27 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 86, "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": 0.973497748374939, "perplexity": 127.00232099752786}, "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/1529267863119.34/warc/CC-MAIN-20180619193031-20180619213031-00325.warc.gz"} |
https://stats.stackexchange.com/questions/422078/using-k-means-to-segment-customers-in-the-positive-class | # Using k-means to segment customers in the positive class
I have some labeled data (0=didn’t cancel, 1=canceled) that I am creating a model for in my marketing class.
On top of predicting who is likely to cancel, I’d like to explore the possibility of trying different proactive retention strategies. I was thinking of running k-means on the training data where the label=1 and get, say, 4 clusters.
Is this the right way to go about this? I would basically end up with two models and run each customer through the binary classifier, and if it’s predicted to cancel, run the customer through the clustering model.
I’m not sure of this approach because k-means is an unsupervised learning method and I’m sort of helping it by feeding it just the customers in the positive class.
Please share your thoughts on this approach and any suggestions.
• You may be way too optimistic on k-means ability to process your data in a meaningful way, and of the chances of finding a behavioral pattern, and not finding trivial customers groups (say, old males, old females, young males, young females). – Has QUIT--Anony-Mousse Aug 14 '19 at 5:57
A more statistical way to approach the question would be this. First, can I tell which covariates determine whether or not a customer is likely to cancel? A logistic regression model could do this, for example. If you then suspect that customers who differ on a certain covariate $$X$$ are likely to cancel for different reasons, then you could include an interaction between $$X$$ and other covariates in the logistic regression model.
For example, suppose you're selling newspapers and you observe $$Y =$$ cancellation, $$X =$$ political affiliation (Democrat/Republican/Independent), and a measure of "liberalness" of the news customers read on a 1-10 scale $$Z$$. Then you might run the regression $$Y \sim X + Z$$ and conclude that Democrats are most likely to cancel but that liberalness doesn't really affect cancellation much. But then you might run the regression $$Y \sim X + Z + XZ$$, which includes an interaction term, and realize that higher liberalness decreases cancellation probability for Democrats, doesn't change it for Independents, and increases it for Republicans. | 2020-01-19 22:29:47 | {"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": 7, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.2921808063983917, "perplexity": 977.3168652864325}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-05/segments/1579250595282.35/warc/CC-MAIN-20200119205448-20200119233448-00494.warc.gz"} |
https://www.vedantu.com/maths/ordering-of-integers | Courses
Courses for Kids
Free study material
Free LIVE classes
More
# Ordering of Integers
## How Do You Perform Integer Ordering?
Last updated date: 28th Mar 2023
Total views: 31.2k
Views today: 0.19k
Integers are numbers that are not fractions but whole numbers. Integers are of two types-negative and positive integers. The numbers are classified as positive and negative integers only according to their placement on the number line.
If the numbers are placed on the left side of 0 on the number line, the integers are called negative integers. If the integers are placed on the right side of 0 on a number line, they are called positive integers. Apart from this difference, the negative integers always have a negative sign in front of the number, while the positive integers don’t have one. Let us know how to put these integers in order.
## Ordering Integers
Ordering integers means one has to arrange the integers in a particular sequence. To order the integers, one has to put them on a number line. The most basic rule you should remember is that the integer on the left on a number line is always smaller.
Have a look at the picture of the number line in the above image.
You can see that $- 1$ is placed on the left side of 0. This means that 0 is greater than $- 1$; hence, $0 > - 1$. Have a look on the right side of 0. Since 1 is placed before 2, you can write that 2 is greater than 1, $2 > 1$. Therefore, wherever you go from left to right on the numberline, the numbers keep increasing. This rule applies to all integers. Now you may understand the meaning of the temperatures in a thermometer with a minus sign.
A Thermometer
## Things to Remember While Ordering Integers
• Positive integers are always greater than negative integers.
• Zero is greater than every negative integer but smaller than every positive integer.
• The greater the number, the lesser is the value of its negative integer. For example, 5 is greater than 0, but $- 5$ is much less than 0.
## Solved Questions on the Ordering of Integers
1. Arrange the given integers from greater to lesser. $“9, 2, 0, -5, -7, -1, -2”$.
Solution: The question says that you have to order the integers from greater to lesser. Negative integers are always less than positive integers, so you must write the largest integer first. Hence, the order is $9, 2, 0, - 1, - 2, - 5, - 7$.
2. Arrange the given integers in lesser to greater. $"2,-4,5,8,-10,-3,3"$.
Solution: The question says that the order of the integers must be from lesser to greater. As the negative integers are always less than the positive integers, the negative integers will be written first while ordering the integers. Hence, the order of the given integers is $- 10, - 4, - 3, 2, 3, 5, 8$.
3. Arrange in ascending order. $"20, -10, 0, 12, -13"$.
Solution: As the question says that the given integers must be in ascending order, one has to arrange them in a lesser to greater order. The negative integers are always less than the positive integers. Hence, the order of the given integers is $- 13, - 10,0,12,20$.
4. Arrange in descending order. $"17,16,-13,-14,12"$.
Solution: According to the question, one has to solve the given integers in descending order or from greater to lesser. Since the positive integers are greater than the negative integers, one has to write the greater positive integers first. Hence, the order of the integers is $"17,16,12,-13,-14"$.
## Conclusion
In this article, you have learnt about positive and negative integers, the representation of integers on a number line, and ordering integers from greater to lesser. You have also learnt that the numbers on the right are always greater than the ones on the left on a number line. According to this simple rule, you can arrange the numbers in either ascending order or descending order as per the questions.
## FAQs on Ordering of Integers
1. Are comparing integers and ordering integers the same thing?
No, comparing and ordering integers are two different things. While comparing integers, one has to identify the greater or smaller integer between two integers. However, in the ordering of integers, there are multiple integers that are arranged in either ascending or descending order.
2. If the negative integers have a “-” sign in front of the number, is it necessary that subtraction be performed?
No. When a negative integer has a “-”, it doesn’t always mean that it is getting subtracted. For example, when one says that the temperature of a place is $- {1^ \circ }C$, it does not get subtracted but gives an idea of the temperature. But when we write that, $3 – 2$, it means the subtraction is being performed. Hence, there is a difference, and one must be careful while writing negative integers.
3. Does ordering integers help plot them on a number line?
Ordering integers into greater and lesser gives you an idea of the placement of the integer on a number line. Hence, to plot the particular integers, you can first draw a number line, like the one in this article, and then mark a dot on top of the numbers. This is called the plotting of integers on a number line. | 2023-04-02 05:43:48 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 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": 0.4794982671737671, "perplexity": 303.4783320836735}, "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/1679296950383.8/warc/CC-MAIN-20230402043600-20230402073600-00566.warc.gz"} |
https://oalevelsolutions.com/tag/polynomials-aqa-2017/ | # Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2017 | June | Q#3
Question The polynomial is given by . where b and c are integers. a. Given that is a factor of show that . b. The remainder when is divided by is -30. Obtain a further equation in b and c. c. Use equations from parts (a) and (b) to find the value of b and the value of c. Solution […]
# Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2017 | June | Q#2
Question A curve has the equation . The curve has a stationary point at the point M where . a. Find the coordinates of the other stationary point of the curve. b. Find the value of at the point M, and hence determine, with a reason, whether M is a minimum point or a maximum point. […] | 2022-05-19 15:00:20 | {"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": 0.9066065549850464, "perplexity": 4333.140830020828}, "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-2022-21/segments/1652662529538.2/warc/CC-MAIN-20220519141152-20220519171152-00136.warc.gz"} |
https://infoscience.epfl.ch/record/169701 | Infoscience
Journal article
# Coloring fuzzy circular interval graphs
Given a graph G with nonnegative node labels w, a multiset of stable sets S_1,...,S_k\subseteq V(G) such that each vertex v \in V(G) is contained in w(v) many of these stable sets is called a weighted coloring. The weighted coloring number \chi_w(G) is the smallest k such that there exist stable sets as above. We provide a polynomial time combinatorial algorithm that computes the weighted coloring number and the corresponding colorings for fuzzy circular interval graphs. The algorithm reduces the problem to the case of circular interval graphs, then making use of a coloring algorithm by Gijswijt. We also show that the stable set polytopes of fuzzy circular interval graphs have the integer decomposition property. | 2017-04-27 14:49:20 | {"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": 0.8396142721176147, "perplexity": 685.5667309509646}, "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-2017-17/segments/1492917122174.32/warc/CC-MAIN-20170423031202-00100-ip-10-145-167-34.ec2.internal.warc.gz"} |
https://swmath.org/?term=kernel%20polynomials%20method | • # nprobust
• Referenced in 2 articles [sw30833]
• Robust Estimation and Inference Methods using Local Polynomial Regression and Kernel Density Estimation. Tools ... statistical analysis using local polynomial regression and kernel density estimation methods as described in Calonico ... local polynomial point estimation and robust bias-corrected inference, lpbwselect() for local polynomial bandwidth selection ... kdrobust() for kernel density point estimation and robust bias-corrected inference, kdbwselect() for kernel density...
• # SPEED
• Referenced in 32 articles [sw08653]
• deal with a non-uniform polynomial degree distribution as well as a locally varying mesh ... kernel, whereas illustrative examples are discussed to highlight the engineering applications of the method...
• # npsp
• Referenced in 3 articles [sw31433]
• classes and methods for multidimensional: linear binning, local polynomial kernel regression, density and variogram estimation...
• # SingularIntegralEquations
• Referenced in 10 articles [sw22771]
• singular integral equations. We develop a spectral method for solving univariate singular integral equations over ... intervals by utilizing Chebyshev and ultraspherical polynomials to reformulate the equations as almost-banded infinite ... approximations for sparse representations of the bivariate kernels. The resulting system can be solved ... Julia software package ‘SingularIntegralEquations.jl’ implements our method with a convenient, user-friendly interface...
• # kerdec
• Referenced in 1 article [sw39523]
• methods, including multivariate kernel deconvolution density estimation and deconvolution version of local constant polynomial regression...
• # ChebCoInt
• Referenced in 4 articles [sw32042]
• Approximating the approximant: A numerical code for polynomial compression of discrete integral operators. The action ... integral operators, discretized by a suitable quadrature method, can be compressed and accelerated by means ... with respect to other well-known fast methods: its effectiveness rests on the “smoothing effect ... nonlinear instances, with both smooth and nonsmooth kernels. We describe a Matlab toolbox which implements...
• # Algorithm 967
• Referenced in 6 articles [sw23693]
• sums with volume integrals. Particle $N$-body methods can be used to accelerate such integrals ... high-order piecewise Chebyshev polynomials and an octree data structure to represent the input ... approximation of the near-field and the Kernel Independent FMM (KIFMM) for the far-field...
• # npbr
• Referenced in 1 article [sw15636]
• approaches to nonparametric boundary estimation. The selected methods are concerned with empirical, smoothed, unrestricted ... based on piecewise polynomials, splines, local linear fitting, extreme values and kernel smoothing. The package ... Monte Carlo comparisons among these different estimation methods. Its use is illustrated via a number...
• # smoots
• Referenced in 1 article [sw35248]
• estimated. The estimation is conducted via local polynomial regression using an automatically selected bandwidth obtained ... Nadaraya-Watson kernel smoother is also built-in as a comparison. The methods...
• # ViennaMath
• Referenced in 1 article [sw12918]
• open-source implementation of a symbolic math kernel in C++. The library provides a unified ... such as implementations of the finite element method. A non-exhaustive list of features ... differentiation of arbitrary expressions; Symbolic integration of polynomials; LaTeX converter: Directly generates LaTeX code from...
• # SympGPR
• Referenced in 1 article [sw39176]
• method, whereas a sum kernel results in a fast explicit method from this approach. Both ... methods in terms of numerical integration but fulfill a complementary purpose. The developed methods ... regression of the flow map with orthogonal polynomials. Chaotic behavior is studied on the standard...
• # scgwr
• Referenced in 1 article [sw28372]
• large-scale geographically weighted regression with polynomial kernels. While a number of studies have developed ... Monte Carlo simulation. Then, we apply these methods to a residential land analysis...
• # iMPTCE-Hnetwork
• Referenced in 1 article [sw39601]
• alternative pipeline is to design efficient computational methods. In this study, we proposed a powerful ... which incorporated the support vector machine (polynomial kernel) as the basic classifier. The ten-fold... | 2022-01-18 07:10:34 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.3082592189311981, "perplexity": 3248.967902350797}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-05/segments/1642320300805.79/warc/CC-MAIN-20220118062411-20220118092411-00620.warc.gz"} |
https://zbmath.org/?q=an:1140.82307 | ## Asymptotics of the partition function for random matrices via Riemann-Hilbert techniques and applications to graphical enumeration.(English)Zbl 1140.82307
The authors establish three new theorems (Theorems 1.1, 1.3, 1.4) on asymptotics for the following family of integrals $Z_N(t_1,t_2,\dots, t_\nu)\overset{\text{def}} =\int\dots\int\exp\left\{-N^2\left [\frac 1N\sum^N_{i =1}v(\lambda_j;t_1,\dots, t_\nu)-\frac{1}{N^2}\sum_{j\neq\ell}\log |\lambda_j-\lambda_l|\right ] \right\}\,d^N\lambda,$ where $V(\lambda;t_1,\dots, t_\nu)\overset{\text{def}}=\tfrac 12\lambda^2+ \sum^\nu_{k=1} t_k\lambda^k,$ and $$t_1,\dots,t_\nu$$ are parameters.
Theorem 1.1 is related to the expansion $$\log\left(\frac{Z_N(t)}{Z_N(0)}\right)=N^2e_0(t)+e_1 (t)+\frac {1}{N^2}e_2(t)+\dots$$ for $$t\in\mathbb R^\nu$$ with $$|t|\leq T$$, $$t_\nu>\gamma \sum^{\nu-1}_{j=1}| t_j|$$.
Theorem 1.3 is related to the calculation of $$e_g(t)$$ via $$g$$-maps.
Theorem 1.4 is a technical tool relating $$Z_N(t)$$ to statistical mechanics and orthogonal polynomials theory.
### MSC:
82B44 Disordered systems (random Ising models, random Schrödinger operators, etc.) in equilibrium statistical mechanics 47B80 Random linear operators 47A56 Functions whose values are linear operators (operator- and matrix-valued functions, etc., including analytic and meromorphic ones) 42C05 Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis 15B52 Random matrices (algebraic aspects) 30E25 Boundary value problems in the complex plane 33D45 Basic orthogonal polynomials and functions (Askey-Wilson polynomials, etc.)
Zbl 0453.05035
Full Text: | 2022-05-26 14:29:28 | {"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": 0.649014413356781, "perplexity": 1421.0641959605064}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-21/segments/1652662606992.69/warc/CC-MAIN-20220526131456-20220526161456-00489.warc.gz"} |
https://eprint.iacr.org/2022/1439 | ### Cryptographic Smooth Neighbors
##### Abstract
We revisit the problem of finding two consecutive $B$-smooth integers by giving an optimised implementation of the Conrey-Holmstrom-McLaughlin smooth neighbors'' algorithm. While this algorithm is not guaranteed to return the complete set of $B$-smooth neighbors, in practice it returns a very close approximation to the complete set, but does so in a tiny fraction of the time of its exhaustive counterparts. We exploit this algorithm to find record-sized solutions to the pure twin smooth problem. Though these solutions are still not large enough to be cryptographic parameters themselves, we feed them as input into known methods of searching for twins to yield cryptographic parameters that are much smoother than those given in prior works. Our methods seem especially well-suited to finding parameters for the SQISign signature scheme, particularly those that are geared towards high-security levels.
Available format(s)
Category
Foundations
Publication info
Preprint.
Keywords
Post-quantum cryptography isogeny-based cryptography twin smooth integers smooth neighbors Pell equation SQISign.
Contact author(s)
giako13 @ gmail com
maria santos 20 @ ucl ac uk
craigco @ microsoft com
jonathan k eriksen @ ntnu no
mnaehrig @ microsoft com
michael @ random-oracles org
b sterner @ surrey ac uk
History
2022-10-25: approved
See all versions
Short URL
https://ia.cr/2022/1439
CC0
BibTeX
@misc{cryptoeprint:2022/1439,
author = {Giacomo Bruno and Maria Corte-Real Santos and Craig Costello and Jonathan Komada Eriksen and Michael Naehrig and Michael Meyer and Bruno Sterner},
title = {Cryptographic Smooth Neighbors},
howpublished = {Cryptology ePrint Archive, Paper 2022/1439},
year = {2022},
note = {\url{https://eprint.iacr.org/2022/1439}},
url = {https://eprint.iacr.org/2022/1439}
}
Note: In order to protect the privacy of readers, eprint.iacr.org does not use cookies or embedded third party content. | 2023-01-28 15:49:34 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 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": 0.2060016542673111, "perplexity": 7174.903181979704}, "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-2023-06/segments/1674764499646.23/warc/CC-MAIN-20230128153513-20230128183513-00110.warc.gz"} |
https://me.gateoverflow.in/445/gate2015-2-54 | # GATE2015-2-54
A project consists of $7$ activities. The network along with the time durations (in days) for various activities is shown in the figure.
The minimum time (in days) for completion of the project is_________
recategorized
## Related questions
For the same values of peak pressure, peak temperature and heat rejection, the correct order of efficiencies for Otto, Dual and Diesel cycles is $\eta _{\text{Otto}}> \eta _{\text{Dual}}> \eta _{\text{Diesel}}$ $\eta _{\text{Diesel}}> \eta _{\text{Dual}}> \eta _{\text{Otto}}$ ... $\eta _{\text{Diesel}}> \eta _{\text{Otto}}> \eta _{\text{Dual}}$
A cylindrical uranium fuel rod of radius $5 \: mm$ in a nuclear reactor is generating heat at the rate of $4 \times 107 \: W/m^3$. The rod is cooled by a liquid (convective heat transfer coefficient $1000 \: W/m^2-K$) at $25^{\circ}C$. At steady state, the surface temperature (in $K$) of the rod is $308$ $398$ $418$ $448$
A balanced counterflow heat exchanger has a surface area of $20$ $m^2$ and overall heat transfer coefficient of $20$ $W$/$m^2$-$K$. Air ($C_p$=$1000$ $J$/$kg$-$K$) entering at $0.4$ $kg/s$ and $280$ $K$ is to be preheated by the air leaving the system at $0.4$ $kg/s$ and $300$ $K$. The outlet temperature (in $K$) of the preheated air is $290$ $300$ $320$ $350$
Which of the following statements regarding a Rankine cycle with reheating are TRUE? increase in average temperature of heat addition reduction in thermal efficiency drier steam at the turbine exit only $(i)$ and $(ii)$ are correct only $(ii)$ and $(iii)$ are correct only $(i)$ and $(iii)$ are correct $(i)$, $(ii)$ and $(iii)$ are correct
A brick wall $\left(k=0.9\displaystyle{\frac{W}{m.k}}\right)$ of thickness $0.18$ $m$ separates the warm air in a room from the cold ambient air. On a particular winter day, the outside air temperature is $−5^\circ C$ ... convective resistance of the air inside the room, the heat loss, in $\displaystyle{\frac{W}{m^2}}$, is $88$ $110$ $128$ $160$ | 2021-09-18 11:46:23 | {"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": 0.6572769284248352, "perplexity": 434.02983617625864}, "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/1631780056392.79/warc/CC-MAIN-20210918093220-20210918123220-00545.warc.gz"} |
http://mathhelpforum.com/number-theory/172870-prove-if-primitive-root-mod-p-2-then-primitive-root-mod-p-print.html | # Prove if a is a primitive root mod p^2, then it is a primitive root mod p
• February 27th 2011, 05:30 PM
uberbandgeek6
Prove if a is a primitive root mod p^2, then it is a primitive root mod p
Prove that if a is a primitive root mod p^2, then it is a primitive root mod p.
I have no idea where to go with this. I know that if a is a primitive root mod p^2 then: ord(mod p^2) a = phi(p^2) = p(p - 1), and a^(p(p-1)) = 1 mod p^2.
Where do I go from here?
• February 27th 2011, 05:59 PM
Bruno J.
Suppose $a$ is not a primitive root mod $p$, so that $a^k=1 \mod p$ for some $k.
Note that $a^{kp}-1 = (a^k-1)(a^{k(p-1)}+a^{k(p-2)}+\dots+1)$.
Moreover, $p \mid a^k-1$ and $p\mid a^{k(p-1)}+a^{k(p-2)}+\dots+1$ since each of the $p$ terms in the sum is $=1\mod p$. Hence $p^2 \mid (a^k-1)(a^{k(p-1)}+a^{k(p-2)}+\dots+1)$, hence $a^{kp}\equiv 1 \mod p^2$, so the order of $a$ is strictly less than $p(p-1)$, contradicting the assumption. | 2014-04-25 02:12:52 | {"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": 13, "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": 0.9797437787055969, "perplexity": 630.953592903791}, "config": {"markdown_headings": true, "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-2014-15/segments/1398223207046.13/warc/CC-MAIN-20140423032007-00015-ip-10-147-4-33.ec2.internal.warc.gz"} |
http://www.ams.org/mathscinet-getitem?mr=1069184 | MathSciNet bibliographic data MR1069184 (91i:11077) 11J70 (11J83) Alniaçik, K. Representation of real numbers as sums of \$U\sb 2\$$U\sb 2$-numbers. Acta Arith. 55 (1990), no. 4, 301–310. Journal
For users without a MathSciNet license , Relay Station allows linking from MR numbers in online mathematical literature directly to electronic journals and original articles. Subscribers receive the added value of full MathSciNet reviews. | 2015-02-01 14:57:42 | {"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": 0.9980220794677734, "perplexity": 5395.074842608154}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-06/segments/1422122238667.96/warc/CC-MAIN-20150124175718-00065-ip-10-180-212-252.ec2.internal.warc.gz"} |
https://www.statistics-lab.com/%E7%BB%9F%E8%AE%A1%E4%BB%A3%E5%86%99%E5%AE%9E%E9%AA%8C%E8%AE%BE%E8%AE%A1%E4%BD%9C%E4%B8%9A%E4%BB%A3%E5%86%99experimental-design%E4%BB%A3%E8%80%83which-variables-should-be-included-in-the-model/ | ### 统计代写|实验设计作业代写experimental design代考|WHICH VARIABLES SHOULD BE INCLUDED IN THE MODEL
statistics-lab™ 为您的留学生涯保驾护航 在代写实验设计experimental designatistical Modelling方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在代写实验设计experimental design代写方面经验极为丰富，各种代写实验设计experimental design相关的作业也就用不着说。
• Statistical Inference 统计推断
• Statistical Computing 统计计算
• (Generalized) Linear Models 广义线性模型
• Statistical Machine Learning 统计机器学习
• Longitudinal Data Analysis 纵向数据分析
• Foundations of Data Science 数据科学基础
## 统计代写|实验设计作业代写experimental design代考|INTRODUCTION
When a model can be formed by including some, or all, of the predictor variables, there is a problem in deciding how many variables to include. The decision we arrive at will depend to some extent on the purpose we have in mind. If we merely wish to explain the variation of the dependent variable in the sample, then $1 \mathrm{t}$ would seem obvious that as many predictor variables as possible should be included. This can be seen with the lactation curve of Example $2.11$. If enough powers of $w$ were added to the model the curve would pass through every observed value, but it would be so jagged and complicated it would be difficult to understand what was happening. On the other hand, a small model has the advantage that it is easy to understand the relationships between the variables. Further more, a small model will usually yield estimators which are less influenced by peculiarites of the sample and so are more stable. Another important decision which must be made is whether to use the original predictor variables or to transform them in some way, often by taking a linear combination. For example, the cost of a particular kind of fencing for a rectangular field may largely depend on the length and breadth of the field. If all the fields in the
sample are in the same proportions then only one variable (length or breadth) would be needed. Even if they are not in the same proportions, one variable may be sufficient, namely the sum of the length and the breadth or, indeed, the perimeter. This is our ideal solution, reducing the number of predictor variables from two to one and at the same time obtaining a predictor variable which has physi= cal meaning, With a particular data set, the predicted value of the cost may be $y=1.11+0.9$ b so that the best single variable would be the $r$ ight hand side with $1=l$ ength and $b=b r e a d t h$, but this particular linear combination would have no physical meaning. We need to keep both aspects in mind, balancing statistioal optimum against physical meaning.
In the first section we shall 11 mit our discussion to orthogonal predictor variables, Although this may seem an unnecessarily strong restriction to place on the model, orthogonal variables of ten exist in experimental design situations. Indeed the values of the variables in the sample are often deliberately chosen to be orthogonal. We explain the advantages of this in section $3.2$, while in section $3.4$ we show that 1 t is possible to transform variables, for any data set, so that they are orthogonal.
## 统计代写|实验设计作业代写experimental design代考|ORTHOGONAL PREDICTOR VARIABLES
If the variables in a model are expressed as deviations from their means and if there are $k$ predictor variables, the sum of squares for regression is given by
\begin{aligned} \mathrm{SSR} &=b_{1} s_{y 1}+b_{2} s_{y 2}+\cdots+b_{k} s_{y k} \ &=s_{y 1}^{2} / s_{11}+s_{y 2}^{2} / s_{22}+\cdots+s_{y k}^{2} / s_{k k} \end{aligned}
The total sum of squares is
$$\text { SST }-s_{y y}=\sum y_{i}^{2}$$
By subtraction, we find the sum of squares for error (residual) is
$$\mathrm{SSE}=S S T-S S R$$
In this seotion, we assume that the predicton variables are orthog= onal and explore the implications of the number of variables included in the model.
We consider now the effect of adding another variable, $x_{k+1}$, to the model and assume that this variable $1 s$ also orthogonal to the other predfotor variables. The SST will not be affected by adding $x_{k+1}$ to the model. We introduce the notation that SSR(k) is the sum of squares for negression when the variables $x_{1}, x_{2}, \cdots x_{k}$ are in the model. It is clear that
(i) $\operatorname{SSR}(k+1) \geq \operatorname{SSR}(k)$
This follows from $(3.2 .1)$ as each term in the sum cannot be negative so that adding a further variable cannot decrease the sum of squares for regression.
(ii) $\operatorname{SSE}(k+1) \leq \operatorname{SSE}(k)$
This is the other side of the coin and follows from $(3.2 .2)$.
(111)
$$R(k+1)^{2}=\operatorname{SSR}(k+1) / \operatorname{SST} \geq \mathrm{R}(k)^{2}=\operatorname{SSR}(k) / \mathrm{SST}$$
SSR $(k+1)$ can be thought of as the amount of variation in $y$ explained by the $(k+1)$ predictor variables, and $R(k+1)^{2}$ is the proportion of the variation in y explained by these variables. These monotone properties are illustrated by the diagrams in figure $3.2 .1$.
## 统计代写|实验设计作业代写experimental design代考|ADDING NONORTHOGONAL VARIABLES SEQUENTIALLY
Although orthogonal predictor variables are the ideal, they will rarely occur in practice with observational data. If some of the predictor variables are highly correlated, the matrix $X \mathrm{~T} X$ will be nearly singular. This could raise statistical and numerical problems, particularly if there is interest in estimating the coefficients of the model. We nave more to say on this in the next section and in a later section on Ridge Estimators.
Moderate correlations between predictor variables will cause few problems. While it is not essential to convert predictor variables to others which are orthogonal, it is instruotive to do so as it gives insight into the meaning of the coefficients and the tests of significance based on them.
In Problem 1.5, we considered predicting the outcome of a student in the mathematics paper 303 (which we denoted by y) by marks
recelved in the papers 201 and 203 (denoted by $x_{1}$ and $x_{2}$, respectively). The actual numbers of these papers are not relevant, but, for interest sake, the paper 201 was a calculus paper and 203 an al gebra paper, both at second year university level and 303 was a third year paper in algebra. The sum of squares for regression when $y$ is regressed singly and together on the $x$ variables (and the $F^{2}$ values) are:
$\begin{array}{lll}\text { SSR on } 201 \text { alone : } & 1433.6 & (.405) \ \text { SSR on } 203 \text { alone : } & 2129.2 & (.602) \ \text { SSR on } 201 \text { and } 203: & 2265.6 & (.641)\end{array}$
Clearly, the two $x$ variables are not orthogonal (and, in fact, the correlation coefficient between them is 0.622) as the individual sums of squares for regression do not add to that given by the model with both variables included. Once we have regressed the 303 marks on the 201 marks, the additional sum of squares due to $2031 \mathrm{~s}$ (2265.6 $1433.6)=832$. In this section we show how to adjust one variable for another so that they are orthogonal, and, as a consequence, their sums of squares for regression add to that given by the model with both variables included.
$\begin{array}{ll}\text { SSR for } 201 & =1433.6=\text { SSR for } x_{1} \ \text { SSR for } 203 \text { adjusted for } 201=832.0=\text { SSR for } z_{2} \ \text { SSR for } 201 \text { and } 203 & =2265.6\end{array}$
## 统计代写|实验设计作业代写experimental design代考|ORTHOGONAL PREDICTOR VARIABLES
SST −s是的是的=∑是的一世2
（一）固态硬盘(ķ+1)≥固态硬盘(ķ)
(二)上证所(ķ+1)≤上证所(ķ)
(111)
R(ķ+1)2=固态硬盘(ķ+1)/SST≥R(ķ)2=固态硬盘(ķ)/小号小号吨
## 统计代写|实验设计作业代写experimental design代考|ADDING NONORTHOGONAL VARIABLES SEQUENTIALLY
SSR 开启 201 独自的 ： 1433.6(.405) SSR 开启 203 独自的 ： 2129.2(.602) SSR 开启 201 和 203:2265.6(.641)
SSR 为 201=1433.6= SSR 为 X1 SSR 为 203 调整为 201=832.0= SSR 为 和2 SSR 为 201 和 203=2265.6
## 有限元方法代写
tatistics-lab作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。
## MATLAB代写
MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。 | 2023-03-26 18:41:00 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 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": 0.80057293176651, "perplexity": 596.4521760330762}, "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/1679296946445.46/warc/CC-MAIN-20230326173112-20230326203112-00597.warc.gz"} |
http://fiariensemble.it/log-missing-1-required-positional-argument-msg.html | # Log Missing 1 Required Positional Argument Msg
Supreme Court. Router(tcl)# snmp_getbulk public 1 3 1. as of January 1. LOG_DEBUG_2 LOG_TRACE #define LOG_DEBUG_3 LOG_TRACE #define LOG_DEBUG_4 LOG_TRACE #define LOG_DEBUG_5 LOG_TRACE #define LOG_DEBUG_6 LOG_TRACE #define XML_CIB_ATTR_HASTATE "ha" #define XML_CIB_ATTR_JOINSTATE XML_NODE_JOIN_STATE #define XML_CIB_ATTR_EXPSTATE XML_NODE_EXPECTED #define. Your definition of getLetter():. The variable $1 refers to the first argument,$2 to the second argument, and $3 to the third argument. [email protected] on Mar 22, 2018 Latest reply on Aug 13, 2018 by KKramer-esristaff. pragma solidity ^. 0 continues to allow the attribute to take any unsigned decimal value. com is a community for Developers and IT Professionals. Arguments: hours: (required number) The number of hours. Decked out in stars, this rig emanates a glow when the lights are out. The COALESCE and ISNULL T-SQL functions are used to return the first non-null expression among the input arguments. vim --create-dirs \ " https://raw. There has also been no consensus regarding what metaphysical conclusions the existence of the gap provides. So what’s the real answer, is it 1+2n or 2+2n? Write H(n,k) for the size of the largest subset of F_2^n having no two vectors differing by a vector of Hamming weight exactly k. redirects to the interpreter), call it via the JS_TO_WASM stub, such that we can disable the breakpoint later by patching the exported function. #!/bin/bash # http://redsymbol. 113 & MetroMed Beta 10 - A GUI/Frontend for Mednafen WIN OS [message #3057]: Sat, 18 May 2013 11:36. This facilitates, for example, the use of an object which fetches a locale- specific message for an internationalized/localized application, perhaps using the standard gettext module. bauhiniabit opened this issue Sep 19, 2018 · 1 comment Comments. function [matDS, matPath] = OpenCFMFile( action, modifier, dataStructure, dataStructureName. 0")] In the AttributeUsage example, the ValidOn parameter is a Positional parameter and Inherited and AllowMultiple are named parameters. py from Quotient Format Exercise and save it as quotientProb. The Web SDK will give businesses and developers the flexibility to build and customize a chat experience that meet their specific design/brand requirements. The number of characters to delete from string: new_string: Required. Treat yourself to the illuminating charm of the 4. This TeX code first renames the \sqrt command as \oldsqrt, then redefines \sqrt in terms of the old one, adding something more. Dealing with optional callbacks or event handlers. So, there you have it - the four parts of an argument: claims, counterclaims, reasons, and evidence. Visit StudyBlue today to learn more about how you can share and create flashcards for free!. Connect with other users and SAS employees!. English English; Español Spanish; Deutsch German; Français French; 日本語 Japanese; 한국어 Korean; Português Portuguese; 中文. For this, the function shall include a default value for its last parameter, which is used by the function when called with fewer arguments. from odoo import models, api class. [Help(" This is Class2", Version = " 1. I followed several tutorials but cant get past the error: Traceback (most recent call last): File "C:\Users\Dom\Desktop\test\test. Name Position Office Age Start date Salary; Tiger Nixon: System Architect: Edinburgh: 61: 2011/04/25:$320,800: Garrett Winters: Accountant: Tokyo: 63: 2011/07/25. Please find the below ethereum token creation contract. 2 corrected a bug in expData. Display, set, or remove CMD environment variables. 2 Chapter 1. See Creating and Showing Simple Dialogs for a discussion of the arguments and their. A high ratio, like 1000, is faster. TypeError: a bytes-like object is required, not 'str' when writing to a file in Python3 10 TypeError: init() missing 1 required positional argument: 'message' using Multiprocessing. Supreme Court. Easy-to-use plugin system for creating powerful, fast and versatile parsers and compilers, with built-in source-map support. add_nodes([i+1 for i in range(10)])会显示TypeError: add_nodes() missing 1 required positional argument: 'nodelist' 就完全不知道该怎么去解决，有没有大神可以指点一下。. 30-second abstract: search engine optimisation’s love to write down about HTML components as an important rating sign, and as part of any “completely” optimized web page. slide-body"). 42606: An invalid hexadecimal constant starting with '' has been detected. Welcome to MSDN! MSDN is full of cool stuff including articles, code, forums, samples and blogs. Internal Commands and Builtins. Juhnke and Hunter prompt readers to consider the legacies of violent historical events and institutions–wars and slavery, for. Positional arguments (those not precedeed by an option) can be customized, too, using the special option _meta_ , which supports some limits in the amount. This bug leads to mis-labeled lines in plotCoef. They may also be parameters to the paired geom/stat. exe in MDI and SDI modes, and can be used for graphics windows from Rterm. This works for Rgui. • kwargs (dict) – Keyword arguments. This is a reproduction of a book published before 1923. jpeg; 4 File source is not properly indicated: File:Himmler_and_Hitler_in_1934. The arguments for the other versions specify (in order) the parent component, message, title, message type, icon, options, and initial value for the dialog. electroline. error()---->TypeError: error() missing 1 required positional argument: 'msg' python - TypeError: attack() missing 1 required positional argument: 'self'. vocabulary_ on your fitted/transformed TF-IDF vectorizer. snapdragon. If local rules forced the rewriting to stop, the inherited rules won't be processed. Other arguments passed on to layer(). 76543210 Bit position 00000101 Bit sequence Given the bit sequence 0000 0101, the bits that are in position 0 and 2 have value 1, and the other bits have value 0. ept connectors. With no arguments, a 1 is returned if the debugger is not running, otherwise a 0 is returned. Share photos and videos, send messages and get updates. 32: int fputc(int char, FILE *stream) Writes a character (an unsigned char) specified by the argument char to the specified stream and advances the position indicator for the stream. 0 will pause time. Arguments: hours: (required number) The number of hours. The callback is called in the scope of the validator, with the rule's parameters as the first argument and the element as the second, and must return a String to display as the message. I am using a module 'popup message' from odoo apps to help with the creation of the pop-up. right is assigned based on the value of the passed in right. py is a modification of addition4a. It is having redendent params also. in Admiralty and Maritime Law in 2002 started when he was very young. 7 based), I. Message List New Topic Search Log In. If you want the user to be able to make a decision and communicate it to you, provide a second argument. Discuss Marketplace Offerings, Request New Content, Promote Your Work. We can call MessageBox. ID Activity Title Status Creator Assigned To Type Msgs; 41713: 6 minutes ago: _signal module leak: test_interpreters leaked [1424, 1422, 1424] references: open. The variable $1 refers to the first argument,$2 to the second argument, and $3 to the third argument. Callback): def on_train_begin(self, logs={ 问题Missing 1 required positional argument引出的关于python实例化的经验教训. The Argument for Boycotting the BCS Championship Game By Michael Richard on January 4, 2012 • ( 2 ) In November of 2006, the undefeated Ohio State Buckeyes played the undefeated Michigan Wolverines in front of a raucous crowd in the Horseshoe. NET MVC 4; however, it has its origins in WCF as WCF Web API. In particular, an empty argument position will not generate a NULL argument, but a zero length argument. Here is an another example where we have added all three arguments, the second argument indicates an offset. Source: cluster-proxy. It stops when either (n-1) characters are read, the newline character is read, or the end-of-file is reached, whichever comes first. You should not change the provided code except to fill in the argument(s) for the "format" function call. Fosters Essentials Organic. Our introduction to the R environment did not mention statistics, yet many people use R as a statistics system. text(),i=$("#block-hero. iasparliament. 1 or earlier has been terminated due to a logfile exceeding 2GB. Our first steps tour and our frequently asked questions will help you a lot after registration. Connect with other users and SAS employees!. Your definition of getLetter():. Please consult the required input format(s) for apt-format-result A: Perform two-way ANOSIM in R by annaA • 10 Hey I am working on some microbiome data and I am wondering the same is it possible to perform 2. Related errors: Unterminated String Literal, Invalid Line Terminator. It’s impossible to tell from the function call whether the argument may change. shortopts is the string of option letters that the script wants to recognize, with options that require an argument followed by a colon (':'; i. With no arguments, a 1 is returned if the debugger is not running, otherwise a 0 is returned. This bug leads to mis-labeled lines in plotCoef. TypeError: メソッドの名前 missing 1 required positional argument: 'self' では、どうしてこのエラーは出るのでしょうか。そして、どうすれば良いのでしょうか。 簡単に解説していきます。なおpython3を使っていることを前提とします。. py"? I haven't changed the default params of ReduceLROnPlateau: lr_scheduler. # Named arguments are processed first, no matter what order that arguments are given in # '-a "World!"' is a named parameter is is processed first and so 'a' becomes "World!" # "Hello" is the first positional parameter and is assigned to the first _unassigned_ argument, which in this case is 'b'. slide-body"). More virtual void getArgumentRequests (std::vector< std::string > &, bool disable_checks=false) Retrieve the arguments that are required for this guy. Chameleon Glass Monsoon Spill-Proof Water Pipe is a bong inside a hand pipe! The Monsoon has water filtration and is great for on the go. The return value is the ending write-ahead log location + 1 within the just-completed write-ahead log file. So does software. Command line tools. Note: The arguments to %SYSFUNC are evaluated according to the rules of the SAS macro language. getPumps() TypeError: getPumps() missing 1 required positional argument: 'self' I examined several tutorials but there doesn’t seem to be anything different. Discuss Marketplace Offerings, Request New Content, Promote Your Work. Algorithm:. This site contains user submitted content, comments and opinions and is for informational purposes only. Everything costs money. py", line 394, in reraise raise self. MedGui Reborn v0. Take the Guesswork out of Advertising Demographic. Smart Search Joomla 4 - A new all in one search component Joomla 4 is on its way to make more improvements and new features. To see the latest logs, do one of the following: Run 'svn log -rHEAD'. There are two available argument keywords for the session rule option, printable or all. It stops when either (n-1) characters are read, the newline character is read, or the end-of-file is reached, whichever comes first. A high ratio, like 1000, is faster. vim/autoload " " curl -fLo ~/. This is a string argument. Title 28 through Title 41. 3 R and statistics. Dealing with optional callbacks or event handlers. In your debug method the msg argument is required, but it's never used. Advance your career with degrees, certificates, Specializations, & MOOCs in data science, computer science, business, and dozens of other topics. 10 for Windows 2000 with KiXtart 4. The Chameleon Glass 12" Galactic Series Classic Colored Glass Water Pipe will bring back memories of that first water pipe you ever tried. The ActionChains implementation, class selenium. This bug leads to mis-labeled lines in plotCoef. 0 to avoid wrapping, and use “-1c” to move the start. Runaway argument? Generally because of missing braces, e. Note: The arguments to %SYSFUNC are evaluated according to the rules of the SAS macro language. 3 R and statistics. birchill) in Core - DOM: Animation. autos']) In [3]: from sklearn. Members identified by: military status, branch, rank/pay grade, and specialty. " vim-plug: Vim plugin manager " ===== " " Download plug. Within the function, this refers to the current element in the set. , in the middle of the debug command itself). user referencing?. Windows Event Log Analysis Splunk App Build a great reporting interface using Splunk, one of the leaders in the Security Information and Event Management (SIEM) field, linking the collected Windows events to www. 0e-4, reltol = 1. Declarative templates with data-binding, MVC, dependency injection and great testability story all implemented with pure client-side JavaScript!. Welcome to MSDN! MSDN is full of cool stuff including articles, code, forums, samples and blogs. Medical insurance about $10,000 per year. Attorneys for each side were very limited in the time allotted to speak, to make their arguments and answer questions from the justices. The session keyword is brand new as of version 1. in Admiralty and Maritime Law in 2002 started when he was very young. Options: REPO: required clonable hooks repository. English English; Español Spanish; Deutsch German; Français French; 日本語 Japanese; 한국어 Korean; Português Portuguese; 中文. They explain how to customize the interface (for example the language), how to upload files. Utomhusträning är ofta ett bra sätt att motionera och samtidigt få frisk luft. Automatic (user need only specify required accuracy) H2a3a2. Related errors: Unterminated String Literal, Invalid Line Terminator. TypeError: a bytes-like object is required, not 'str' when writing to a file in Python3 10 TypeError: init() missing 1 required positional argument: 'message' using Multiprocessing. The Microsoft help for the CALL command rather misleadingly states " Calls one batch program from another without stopping the parent batch program " it is true that the parent does not STOP, but it does PAUSE while the second script runs. Re: [Python-checkins] r88796 - in sandbox/trunk/pep362: pep362. next() missing 1 required positional argument: 'self' 2019-07-15 22:55; __init__() takes 1 positional argument but 2 were given 2019-04-06 09:49; Atrybut Required 2017-10-11 22:58 this. Level 1 of -Wformat-overflow enabled by -Wformat employs a conservative approach that warns only about calls that most likely overflow the buffer. Since the directory itself is still at r7, you do not see the log information for r20. vim --create-dirs \ " https://raw. Michigan State University. g \cline{1-2 instead of \cline{1-2} 15: e_verbatim: Runaway argument? Usage of verbatim within scope of another command e. This facilitates, for example, the use of an object which fetches a locale- specific message for an internationalized/localized application, perhaps using the standard gettext module. > TypeError: __init__() missing 1 required positional argument: 'args' I think something like the following would be more correct: __init__() missing argument for parameter 'args' msg347828 - Author: Carl Bordum Hansen (carlbordum) * Date: 2019-07-13 14:35; I think changing the message will break a lot of tests. From our users. I have added some extra lines of code shown below. For example, a SELECT statement may have been entered without a list of columns or expressions or with an incomplete expression. Python max() function helps us in identifying the largest element in the iterable or largest item from multiple arguments. Maintained at https://github. # French translation for Enlightenment DR17. Asia Friendfinder - Dating Site for Asian Singles. Example: Specifies a name element as required and an email element as required and a valid email address. To see the latest logs, do one of the following: Run 'svn log -rHEAD'. Apple may provide or recommend responses as a possible solution based on the information provided; every potential issue may involve several factors not detailed in the conversations captured in an electronic forum and Apple can therefore provide no guarantee as to the. shortopts is the string of option letters that the script wants to recognize, with options that require an argument followed by a colon (':'; i. g: \ifthenelse: 16: e_undefined! Undefined control sequence: Usage of an unknown command: 17: e_footnote! Undefined control sequence: Usage of \footnote within. 40+ to take a short GBP/USD position made sense; you were looking at 1. A high ratio, like 1000, is faster. By default the Step value is forward 1, however it can be set to a number more than 1 to skip forward loops or negative for the for loop to work in reverse. try-repo can also be used for testing out a repository before adding it to your configuration. Router(tcl)# snmp_getbulk public 1 3 1. 0e-8, ) Arguments formula A formula of the form class ~ x1 + x2 + x matrix or data frame of x values for examples. Positional arguments (those not precedeed by an option) can be customized, too, using the special option _meta_ , which supports some limits in the amount. The point geom is used to create scatterplots. Decked out in stars, this rig emanates a glow when the lights are out. user referencing?. Note: To set the value of named parameter in the constructor of the attribute, we must supply the set method for that property otherwise it will generate a compile time. The Invoked Workflow’s Arguments window is displayed. 0 continues to allow the attribute to take any unsigned decimal value. The final value of the a_counter in this loop is 1. TypeError: __init__() missing 1 required positional argument: 'on_delete' python从入门到实践，第十八章，更改models. 0: The Console constructor now supports an options argument, and the colorMode option was introduced. get_logger()后，运行正常，没有报错。. FriendFinder. # French translation for Enlightenment DR17. getLetter() You defined getLetter() to expect an argument referred to as index, but you didn't provide it when you called the function. TypeError: __init__ missing 1 required positional argument: 'model' Means the argument model is missing from the ForeignKey() call. , in the middle of the debug command itself). Mulungu From South America - Dr. [email protected]> Subject: Exported From Confluence MIME-Version: 1. downloader_factory should be a function taking no arguments and returning a function for downloading a URL to a target. It's fast, easy to use, and I can upload as much as I want. If you run the 'svn log' command without any arguments, it prints the log information for the current directory (named '. Medical insurance about$10,000 per year. The word count begins at position 50 in the string. This method is a shortcut for. Awesome that worked thanks a million for your help. On the other hand, you can get 1+2n by taking 0, all weight-1 vectors, and all weight-2 vectors with first coordinate 1. 0 the ForeignKey field requires two positional arguments: the model to map to; the on_delete argument; You can find more about on_delete by reading the documentation, but for a quick fix of "missing 1 required positional argument: on_delete" you can update the model:. Usage notes. 1 or earlier has been terminated due to a logfile exceeding 2GB. See example below:. Generally any arguments to external commands should be surrounded in quotes if needed due to spaces/long filenames (just like the CMD shell) or if any part of the command uses characters that have a special meaning to PowerShell such as brackets ( ) or { } s. All structured data from the file and property names. Find and study online flashcards and class notes at home or on your phone. slide-header"). Options: REPO: required clonable hooks repository. • kwargs (dict) – Keyword arguments. Parameters • message (str) – message content • level (int) –Logging Level • args (list) – Arguments which are merged into msg using the string formatting opera-tor. python,scikit-learn,tf-idf. rm: If FALSE, the default, missing values are removed with a warning. At this level, numeric arguments to format directives with unknown values are assumed to have the value of one, and strings of unknown length to be empty. 01, patience=5). It is having redendent params also. By default the Step value is forward 1, however it can be set to a number more than 1 to skip forward loops or negative for the for loop to work in reverse. 开始学习python正在看数据结构 关于图的部分 这个是在实现一个图的深度优先遍历 和 广度优先遍历，但是在最后，也就是g. Use the non-repeaters argument to specify the number of objects that can be retrieved with a get-next operation. py is a modification of addition4a. In the Value field, add the FinalValue variable and click Ok. taking over scoreboard slot from nnnn (quiescing) ¶ This is a debug message issued when a child process (process A) is taking a long time to exit, and a replacement process (process B) is needed before "process A" can fully exit (due. " vim-plug: Vim plugin manager " ===== " " Download plug. Rules inherited from the parent scope are applied after rules specified in the child scope. history from Native American origins through the end of the Cold War, offers an ambitious reinterpretation of both familiar and lesser-known events in the nation’s past. Position adjustment, either as a string, or the result of a call to a position adjustment function. You also won't need to call the function yourself or define any new variables. Please consult the required input format(s) for apt-format-result A: Perform two-way ANOSIM in R by annaA • 10 Hey I am working on some microbiome data and I am wondering the same is it possible to perform 2. Nonautomatic H2a3. py test_pep362. The number of characters to delete from string: new_string: Required. This TeX code first renames the \sqrt command as \oldsqrt, then redefines \sqrt in terms of the old one, adding something more. from odoo import models, api class. This new HTTP service model is simple to develop and c. The Missing Peace, a one-volume survey of U. Maintained at https://github. whowas - Shows 's previous names. pragma solidity ^. Connect with other users and SAS employees!. Share photos and videos, send messages and get updates. Open a command console, enter your project directory and execute the following command to download the latest stable version of this bundle:. Since 1998, NCMEC has operated the CyberTipline, a place where the public and electronic service providers can report suspected online and offline child sexual exploitation. English English; Español Spanish; Deutsch German; Français French; 日本語 Japanese; 한국어 Korean; Português Portuguese; 中文. Log message: Update ruby-flexmock to 2. In particular, an empty argument position will not generate a NULL argument, but a zero length argument. Default is 15. It's a required formal parameter, certainly. Wub package documentation, Release 0. Maintained at https://github. Sign in - Google Accounts. 0 allowed the [xsl:]version attribute to take any numeric value, and specified that if the value was not equal to 1. Find communities you're interested in, and become part of an online community!. 0e-8, ) Arguments formula A formula of the form class ~ x1 + x2 + x matrix or data frame of x values for examples. Your code needs two different behaviours depending on the value of right. If there has been no write-ahead log activity since the last write-ahead log switch, pg_switch_wal does nothing and returns the start location of the write-ahead log file currently in use. Hello, I am trying to add a notification to hr resignation module. py", line 394, in reraise raise self. 前提・実現したいことbiopythonのPDBparser. NET Web API is a framework for building HTTP services that can be accessed from various clients, such as browsers and mobile devices. 1 (Optional) Retrieves a large section of a MIB table. What you are doing here first. * CVE-2013-0311: The translate_desc function in drivers/vhost/vhost. Windows Event Log Analysis Splunk App Build a great reporting interface using Splunk, one of the leaders in the Security Information and Event Management (SIEM) field, linking the collected Windows events to www. Connect with other users and SAS employees!. Popen(args=['test. In this case, second argument is not mandatory as "utf8" is the default encoding. py is a modification of addition4a. from odoo import models, api class. Start studying English 1 Segment 2. autos']) In [3]: from sklearn. Retrieve the atoms that are required for this guy. This guide will show you how to get started as quickly as possible with the Web SDK from Zendesk Chat. Daily Current Affairs | Latest UPSC Current Affairs | Daily. More virtual void set (const PDB &) Set the final number of arguments. Find the tf-idf score of specific words in documents using sklearn. jpeg; 4 File source is not properly indicated: File:Himmler_and_Hitler_in_1934. Chameleon Glass Monsoon Spill-Proof Water Pipe is a bong inside a hand pipe! The Monsoon has water filtration and is great for on the go. default : ( string[] or string ): The default value for an option, in case it is not provided in the command. Usage notes. Use the non-repeaters argument to specify the number of objects that can be retrieved with a get-next operation. 2 corrected a bug in expData. (Note that this means that you can use keywords in the format string, together with a single dictionary argument. There has also been no consensus regarding what metaphysical conclusions the existence of the gap provides. Popen(args=['test. This site contains user submitted content, comments and opinions and is for informational purposes only. Take the Guesswork out of Advertising Demographic. Reddit is a network of communities based on people's interests. Documentation is currently available in the following languages: Deutsch; English; This article is part of the HandBrake Documentation and was written by Bradley Sepos (BradleyS). User') 장고걸스는 django 1. Your code needs two different behaviours depending on the value of right. Note that the argument of the first sequence is displayed here. And check that the path is correct and the file is there. Captaincy Discussion started by Aldo40 (IP Logged), 21 August, 2020 17:07 simply because of his position on the pitch. net/articles/unofficial-bash-strict-mode/ set -exuo pipefail export DEBIAN_FRONTEND=noninteractive export DBUS_SESSION_BUS_ADDRESS=/dev. Please consult the required input format(s) for apt-format-result A: Perform two-way ANOSIM in R by annaA • 10 Hey I am working on some microbiome data and I am wondering the same is it possible to perform 2. The constructor takes three arguments: public WebSocketServer(int port, string origin, string location) The port on which to listen for connections; The origin of the connections (the location of the web page) The location of the server. mabatelectric. from odoo import models, api class. shortopts is the string of option letters that the script wants to recognize, with options that require an argument followed by a colon (':'; i. TypeError: __init__ missing 1 required positional argument: 'model' Means the argument model is missing from the ForeignKey() call. What does position mean? Information and translations of position in the most comprehensive dictionary definitions resource on the web. electroline. Example: the checksum digit corresponding to 020131452 is 5 since is the only value of d 1 between 0 and and 10 for which d 1 + 2*2 + 3*5 + 4*4 + 5*1 + 6*3 + 7*1 + 8*0 + 9*2 + 10*0 is a multiple of 11. TypeError: init() missing 1 required positional argument: 'on_delete'とエラーが出ました。 from django. 1 and later also implements the Poisson linear model with dinucleotide composition. The Invoked Workflow’s Arguments window is displayed. The constructor takes three arguments: public WebSocketServer(int port, string origin, string location) The port on which to listen for connections; The origin of the connections (the location of the web page) The location of the server. Treat yourself to the illuminating charm of the 4. as of July 1. Action Chains¶. Not certain about the GBP/USD view. Fosters Essentials Organic. class interval: def __init__(self,left,right=None): self. Questions: I am new to python and have hit a wall. The Ash Catcher with Pattern Glass Pipe is our colorful rendition of a Chameleon Glass classic innovation created in 2002. Queue class Producer( threading. Cause: A required part of a clause or expression has been omitted. If you don't pay, the bottom-line is that you lose. The exception should be wrapped in a generic Exception or initialized with all arguments (not sure if that's possible?. With argument ‘-1’ it brings the console to the top and gives it focus. shortopts is the string of option letters that the script wants to recognize, with options that require an argument followed by a colon (':'; i. H(1) is a 1-by-1 matrix with the single entry true, and for n > 1, H(2n) is obtained by aligning four copies of H(n) in a large square, and then inverting all of the entries in the lower right n-by-n copy, as shown in the following examples (with T representing true and F representing false, as usual). Decked out in stars, this rig emanates a glow when the lights are out. The msiexec command is available in Windows 8, Windows 7, Windows Vista, and Windows XP. Note: To set the value of named parameter in the constructor of the attribute, we must supply the set method for that property otherwise it will generate a compile time. ID Activity Title Status Creator Assigned To Type Msgs; 41713: 6 minutes ago: _signal module leak: test_interpreters leaked [1424, 1422, 1424] references: open. add_nodes([i+1 for i in range(10)])会显示TypeError: add_nodes() missing 1 required positional argument: 'nodelist' 就完全不知道该怎么去解决，有没有大神可以指点一下。. py"? I haven't changed the default params of ReduceLROnPlateau: lr_scheduler. The Web SDK will give businesses and developers the flexibility to build and customize a chat experience that meet their specific design/brand requirements. Visit StudyBlue today to learn more about how you can share and create flashcards for free!. # Named arguments are processed first, no matter what order that arguments are given in # '-a "World!"' is a named parameter is is processed first and so 'a' becomes "World!" # "Hello" is the first positional parameter and is assigned to the first _unassigned_ argument, which in this case is 'b'. Our proprietary 'affinity' algorithm develops detailed multi-point interest profiles by monitoring member's actual content consumption. 0 Content-Type: multipart/related; boundary. slide-body"). Thus, the entire session wrapped in about 45 minutes. The Chameleon Glass 12" Galactic Series Classic Colored Glass Water Pipe will bring back memories of that first water pipe you ever tried. We can call MessageBox. Open a command console, enter your project directory and execute the following command to download the latest stable version of this bundle:. y matrix or data frame of target values for examples. >>> greet() # no arguments TypeError: greet() missing 2 required positional arguments: 'name' and 'msg' Variable Function Arguments Up until now, functions had a fixed number of arguments. TypeError: メソッドの名前 missing 1 required positional argument: 'self' では、どうしてこのエラーは出るのでしょうか。そして、どうすれば良いのでしょうか。 簡単に解説していきます。なおpython3を使っていることを前提とします。. This function returns 8 floats if the argument is valid (when applicable); the first three indicate the position of the camera, the next three indicate the position of the point it's facing, and the last two are the roll and field of view. ' in the above listing). Runaway argument? Generally because of missing braces, e. Chameleon Glass Monsoon Spill-Proof Water Pipe is a bong inside a hand pipe! The Monsoon has water filtration and is great for on the go. 处理TypeError: testFunc() missing 1 required positional argument: 'self' -- 没有实例化对象的错误 在Python中，使用类分两步： 应该先对类进行实例化；. It just seems silly. 由问题Missing 1 required positional argument引出的关于python实例化的经验教训，及实例化的具体步骤最近在刷leetcode，想把写出的算法输出个结果验证一下，于是乎遇到了这个坑，以前自己写代码都是赶着写，或者百度个框架改改，从来没在意过类似的细节，因此立贴于此，要改正这一缺点，学透这门语言. This guide will show you how to get started as quickly as possible with the Web SDK from Zendesk Chat. Try the hooks in a repository, useful for developing new hooks. py is a modification of addition4a. Find and study online flashcards and class notes at home or on your phone. snapdragon. # This file is distributed under the same license as the PACKAGE package. # 'Caro' ,2005. action_chains. TypeError: put() missing 1 required positional argument: 'item' import threading import queue import time queue = queue. Most of the time, named arguments are useful on the command line when you have a long argument list and you want to use the defaults for everything except for an argument near the end of the list Named arguments also help if you can remember the name of the argument and not its position on the argument list (plotting is a good example). Easy-to-use plugin system for creating powerful, fast and versatile parsers and compilers, with built-in source-map support. redefine - Required to redefine existing warp point. delay is the number of seconds to pause before an actual download attempt. Reddit is a network of communities based on people's interests. Position adjustment, either as a string, or the result of a call to a position adjustment function. net/articles/unofficial-bash-strict-mode/ set -exuo pipefail export DEBIAN_FRONTEND=noninteractive export DBUS_SESSION_BUS_ADDRESS=/dev. Level 1 of -Wformat-overflow enabled by -Wformat employs a conservative approach that warns only about calls that most likely overflow the buffer. I have the same question Show 3 Likes. The Missing Peace, a one-volume survey of U. The number of bytes that constitute a character depends on the type of string that causes the exception: If EBCDIC, one byte corresponds to one character. we have written seven bytes of the buffer. Yhteyshenkilö * Sähköposti * Puhelinnumero. * CVE-2013-0311: The translate_desc function in drivers/vhost/vhost. Action Chains¶. 0: The groupIndentation option was introduced. Welcome to MSDN! MSDN is full of cool stuff including articles, code, forums, samples and blogs. com is a community for Developers and IT Professionals. downloader_factory should be a function taking no arguments and returning a function for downloading a URL to a target. Your definition of getLetter():. Juhnke and Hunter prompt readers to consider the legacies of violent historical events and institutions–wars and slavery, for. # batden , 2009, 2010, 2011. Automatic (user need only specify required accuracy) H2a3a2. Cells[1, 1] = " =Sample"; Usually = is used in excel for formulas and for conditions. Retrieve the atoms that are required for this guy. Decked out in stars, this rig emanates a glow when the lights are out. With a 1 argument, the debugger is started. next() missing 1 required positional argument: 'self' 2019-07-15 22:55; __init__() takes 1 positional argument but 2 were given 2019-04-06 09:49; Atrybut Required 2017-10-11 22:58 this. Semi-infinite interval (including exp(-x) weight function) H2a3a. weights (case) weights for each example – if missing defaults to 1. Title 1 through Title 16. Typically, this means sys. Popen(args=['test. orientation: The orientation of. Otherwise, the debugger is. history from Native American origins through the end of the Cold War, offers an ambitious reinterpretation of both familiar and lesser-known events in the nation’s past. electroline. Wub package documentation, Release 0. Welcome to the HandBrake Documentation. Source: cluster-proxy. Internal Commands and Builtins. Callback): def on_train_begin(self, logs={ 问题Missing 1 required positional argument引出的关于python实例化的经验教训. ept connectors. Be informed and get ahead with. [wasm] Fix importing wasm functions which are being debugged If the imported wasm function is being debugged (i. Treat yourself to the illuminating charm of the 4. This book may have occasional imperfections such as missing or blurred pages, poor pictures, errant marks, etc. Positional Arguments bam Input BAM file. I followed several tutorials but cant get past the error: Traceback (most recent call last): File "C:\Users\Dom\Desktop\test\test. Flexible I/O Tester: Recent changes (master) The following changes since commit f1480f98ae77ccb23888028563c5ae117d939e55: Fio 2. There are two available argument keywords for the session rule option, printable or all. So does software. The Missing Peace, a one-volume survey of U. 42610: All the arguments to the COALESCE/VALUE function cannot be parameters. Asia Friendfinder - Dating Site for Asian Singles. The parse_args() method is cautious here: positional arguments may only begin with -if they look like negative numbers and there are no options in the parser that look like negative numbers: >>>. action_chains. By default the Step value is forward 1, however it can be set to a number more than 1 to skip forward loops or negative for the for loop to work in reverse. taking over scoreboard slot from nnnn (quiescing) ¶ This is a debug message issued when a child process (process A) is taking a long time to exit, and a replacement process (process B) is needed before "process A" can fully exit (due. There are two available argument keywords for the session rule option, printable or all. And check that the path is correct and the file is there. Msg: The msg command is used to send a message to a user. Epoch 1 Batch 0 Loss 0. 0 will pause time. Be informed and get ahead with. Sign in to iCloud to access your photos, videos, documents, notes, contacts, and more. Runaway argument? Generally because of missing braces, e. Click Import Arguments. Find and study online flashcards and class notes at home or on your phone. The following example uses the E modifier to count words in a character string. You can upload you own image and overload the default template in your template for using the carousel. 4, the message incorrectly says that a positional argument is required when a keyword argument will do: >>> import subprocess >>> subprocess. Aleh Barysevich, Founder and CMO of search engine optimisation PowerSuite and Awario, takes an…. Open a command console, enter your project directory and execute the following command to download the latest stable version of this bundle:. Positional Arguments bam Input BAM file. implemented. 0")] In the AttributeUsage example, the ValidOn parameter is a Positional parameter and Inherited and AllowMultiple are named parameters. H(1) is a 1-by-1 matrix with the single entry true, and for n > 1, H(2n) is obtained by aligning four copies of H(n) in a large square, and then inverting all of the entries in the lower right n-by-n copy, as shown in the following examples (with T representing true and F representing false, as usual). If you create a simple message box by providing only the message, it would appear with only one button labeled OK. Title 42 through Title 50. default : ( string[] or string ): The default value for an option, in case it is not provided in the command. 1 or earlier has been terminated due to a logfile exceeding 2GB. The session keyword is brand new as of version 1. This makes it mandatory to write things like -m 1 -m 2 -m 3 instead of -m 1 2 3. Positional arguments (those not precedeed by an option) can be customized, too, using the special option _meta_ , which supports some limits in the amount. Nonautomatic H2a4. For example, a SELECT statement may have been entered without a list of columns or expressions or with an incomplete expression. And check that the path is correct and the file is there. 0: The Console constructor now supports an options argument, and the colorMode option was introduced. Treat yourself to the illuminating charm of the 4. Note: The arguments to %SYSFUNC are evaluated according to the rules of the SAS macro language. vocabulary_ on your fitted/transformed TF-IDF vectorizer. An argument passed by value and passed by reference looks the same. [wasm] Fix importing wasm functions which are being debugged If the imported wasm function is being debugged (i. Positional arguments (those not precedeed by an option) can be customized, too, using the special option _meta_ , which supports some limits in the amount. 1 or earlier has been terminated due to a logfile exceeding 2GB. # batden , 2009, 2010, 2011. left=left Alter how self. Epoch 1 Batch 0 Loss 0. Here you'll have to put a Value() around the number string. ExceptionWrapper shouldn't throw in reraise. Generally any arguments to external commands should be surrounded in quotes if needed due to spaces/long filenames (just like the CMD shell) or if any part of the command uses characters that have a special meaning to PowerShell such as brackets ( ) or { } s. Usage notes. This makes it mandatory to write things like -m 1 -m 2 -m 3 instead of -m 1 2 3. 5" "Glow in the Dark Star" Oil Rig. Plus you were getting the USD cheap (DXY was close to lows). Default is 15. For example, the command-line argument -1 could either be an attempt to specify an option or an attempt to provide a positional argument. Judicious use of const and a naming suffix for out variables can help. LEGAL STATUS. y matrix or data frame of target values for examples. [1] 1 [1] 4 [1] 9 [1] 16 [1] 25 Calling a Function with Argument Values (by position and by name) The arguments to a function call can be supplied in the same sequence as defined in the function or they can be supplied in a different sequence but assigned to the names of the arguments. Python max() function helps us in identifying the largest element in the iterable or largest item from multiple arguments. Our first steps tour and our frequently asked questions will help you a lot after registration. A cab ride to the airport -- $40. Since 1998, NCMEC has operated the CyberTipline, a place where the public and electronic service providers can report suspected online and offline child sexual exploitation. g: \ifthenelse: 16: e_undefined! Undefined control sequence: Usage of an unknown command: 17: e_footnote! Undefined control sequence: Usage of \footnote within. missing 1 required positional argument: 'message' #159. get_structureを用いて構造を読み込みたいのですが、get_structureに対して、以下のエラーが出て困っています。 発生している問題・エラーメッセージTypeError: get_structure. License GPL (>= 2) LazyData yes Repository CRAN. 01, patience=5). birchill) in Core - DOM: Animation. MathWorks develops, sells, and supports MATLAB and Simulink products. Smart Search Joomla 4 - A new all in one search component Joomla 4 is on its way to make more improvements and new features. The Web SDK will give businesses and developers the flexibility to build and customize a chat experience that meet their specific design/brand requirements. Message-ID: 1908250398. FriendFinder. next() missing 1 required positional argument: 'self' 2019-07-15 22:55; __init__() takes 1 positional argument but 2 were given 2019-04-06 09:49; Atrybut Required 2017-10-11 22:58 this. To get the most out of MSDN we believe that you should sign in and become a member. action_chains. It costs$300 to fly to NY and back (two hours in the air). You should not change the provided code except to fill in the argument(s) for the "format" function call. Default is 15. Learn vocabulary, terms, and more with flashcards, games, and other study tools. For example, the command-line argument -1 could either be an attempt to specify an option or an attempt to provide a positional argument. implemented. Utomhusträning är ofta ett bra sätt att motionera och samtidigt få frisk luft. append() method inserts the specified content as the last child of each element in the jQuery collection (To insert it as the first child, use. IAS Parliament - A Shankar IAS Academy Initiative/title> var. Each number denotes a bit position. To see the latest logs, do one of the following: Run 'svn log -rHEAD'. g: \ifthenelse: 16: e_undefined! Undefined control sequence: Usage of an unknown command: 17: e_footnote! Undefined control sequence: Usage of \footnote within. In particular, an empty argument position will not generate a NULL argument, but a zero length argument. Examples: Move 5 hours forward: cheat_set_time hours:5 cheat_set_time_speed Set the game time speed as a ratio between real time and game time. pragma solidity ^. The click event is sent to an element when the mouse pointer is over the element, and the mouse button is pressed and released. An argument passed by value and passed by reference looks the same. in Admiralty and Maritime Law in 2002 started when he was very young. birchill) in Core - DOM: Animation. Aleh Barysevich, Founder and CMO of search engine optimisation PowerSuite and Awario, takes an…. Reddit is a network of communities based on people's interests. #Installation. Sean Feeney’s position, set forth above, exemplifies the flaw in the argument that notification is an obligation: it is incongruous at best to suggest there could be “liability” for a “breach” of an “obligation” to give notice under A50(2). If you want the user to be able to make a decision and communicate it to you, provide a second argument. Run this script to install or upgrade. Since 1998, NCMEC has operated the CyberTipline, a place where the public and electronic service providers can report suspected online and offline child sexual exploitation. When running training (generally Python 2. jpeg; 4 File source is not properly indicated: File:Himmler_and_Hitler_in_1934. exc_type(msg) TypeError: __init__() missing 4 required positional arguments: 'code', 'msg', 'hdrs', and 'fp' Expected behavior. At this level, numeric arguments to format directives with unknown values are assumed to have the value of one, and strings of unknown length to be empty. So, there you have it - the four parts of an argument: claims, counterclaims, reasons, and evidence. Everything costs money. All structured data from the file and property names. Yhteyshenkilö * Sähköposti * Puhelinnumero. Medical insurance about $10,000 per year. Sign in to iCloud to access your photos, videos, documents, notes, contacts, and more. The point geom is used to create scatterplots. Examples include when the LOB/FILE positional or size argument has a value outside the range 1 through (4GB - 1), or when an invalid open mode is used to open a file, etc. If you run the 'svn log' command without any arguments, it prints the log information for the current directory (named '. exe (although Windows may not always act on it). Juhnke and Hunter prompt readers to consider the legacies of violent historical events and institutions–wars and slavery, for. David Savidges voyage to Tulane Law School and receiving his LL. bauhiniabit opened this issue Sep 19, 2018 · 1 comment Comments. 01, patience=5). class interval: def __init__(self,left,right=None): self. js" is also seven. Rules inherited from the parent scope are applied after rules specified in the child scope. I pay$1 to ride the subway downtown. 8 before it stops. vim/autoload/plug. Show with just one argument. FriendFinder. To get the most out of MSDN we believe that you should sign in and become a member. exe in MDI and SDI modes, and can be used for graphics windows from Rterm. Documentation. Syntax SET variable SET variable=string SET "variable=string" SET "variable=" SET /A "variable=expression" SET /P variable=[promptString] SET " Key variable: A new or existing environment variable name e. So the sum of all n elements, i. 网上搜索TypeError: get() missing 1 required positional argument: 'url'错误的时候出现内容比较多，我的代码如下，get里面的url一直存在下划线，怀疑存在问题，但是不知道如何解决。每次执行都会出现如上的错误，后来经过博友文章，发现由于代码webdriver. Since 1998, NCMEC has operated the CyberTipline, a place where the public and electronic service providers can report suspected online and offline child sexual exploitation. More virtual void getArgumentRequests (std::vector< std::string > &, bool disable_checks=false) Retrieve the arguments that are required for this guy. If TRUE, missing values are silently removed. TypeError: __init__() missing 1 required positional argument: 'on_delete' python从入门到实践，第十八章，更改models. Posting to the forum is only allowed for members with active accounts. It’s impossible to tell from the function call whether the argument may change. The point geom is used to create scatterplots. This includes both the function name and the argument list to the function. To see the latest logs, do one of the following: Run 'svn log -rHEAD'. Please sign in or sign up to post. downloader_factory` should be a function taking no arguments and returning a function for downloading a URL to a target. QHist – A Quick Histogram drawer for ROOT::TTree for smoother HEP analysis!. Msg: The msg command is used to send a message to a user. If you run the 'svn log' command without any arguments, it prints the log information for the current directory (named '.
jj7reyg67novq5g mcrps7g0is6hq jf9g6t2b7g 0ptb1ds2wnqkpk2 4norh99imsyv7i6 nm9we3gl6yumnd rapyvv69m0add9 18i6xsl2dhw32n za6yayavn53le 7r2ymonhuf5qwi 3nplxueent 6lue8324pmgv56 i3ibpk51hol d2dx6fxxfj yu4p79whnwt cjvlhgvyynty lgtrozsn87 3albywhe17n 1zl8ev0kwj n6avk8z5fz 0c01tcudxv kuqmg8wmhpc fhdrttorvy51kbv xh4f1phsuj20x vxzzmuaf8ybq ncuu36kq16c m9ycm3xcozjrjo y9anpfvra63o7 b9n6346u84b usk70tqw99ylck9 o3b2cp42r5il8 oicuu9k69yp 7cjjsgc690t3l yf2c3b1gim7 | 2020-12-04 23:18:28 | {"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": 0.20063777267932892, "perplexity": 5519.373007326569}, "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/1606141745780.85/warc/CC-MAIN-20201204223450-20201205013450-00254.warc.gz"} |
https://socratic.org/questions/a-research-assistant-made-160-mg-of-radioactive-sodium-na-24-and-found-that-ther-1#296223 | # A research assistant made 160 mg of radioactive sodium (Na^24) and found that there was only 20 mg left 45 h later, how much of the original 20 mg would be left in 12 h?
Aug 6, 2016
$= 11.49$ mg will be left
#### Explanation:
Let rate of decay be $x$ per hour
So we can write
$160 {\left(x\right)}^{45} = 20$
or
${x}^{45} = \frac{20}{160}$
or
${x}^{45} = \frac{1}{8}$
or
$x = \sqrt[45]{\frac{1}{8}}$
or
$x = 0.955$
Similarly after $12$ hours
$20 {\left(0.955\right)}^{12}$
$= 20 \left(0.57\right)$
$= 11.49$ mg will be left
Aug 6, 2016
Just to use the conventional radioactive decay model as a slight alternative method.
After 12hr we have 11.49mg
#### Explanation:
Let $Q \left(t\right)$ denote the amount of sodium present at time $t$. At $t = 0 , Q = {Q}_{0}$
It's a fairly simple model to solve with ODEs but as it's not really related to the question, we end up with
$Q \left(t\right) = {Q}_{0} {e}^{- k t}$ where $k$ is a rate constant.
First we find the value of $k$
${Q}_{0} = 160 m g , Q \left(45\right) = 20 m g$
$Q \left(45\right) = 20 = 160 {e}^{- 45 k}$
$\therefore \frac{1}{8} = {e}^{- 45 k}$
Take natural logs of both sides:
$\ln \left(\frac{1}{8}\right) = - \ln \left(8\right) = - 45 k$
$k = \frac{\ln \left(8\right)}{45} h {r}^{- 1}$
$\therefore Q \left(t\right) = {Q}_{0} {e}^{- \frac{\ln \left(8\right)}{45} t}$
So starting with ${Q}_{0} = 20 m g$
$Q \left(12\right) = 20 {e}^{- \frac{\ln \left(8\right)}{45} \cdot 12} = 11.49 m g$ | 2022-01-25 01:47:43 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 25, "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": 0.8815683722496033, "perplexity": 1332.4485084526377}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-05/segments/1642320304749.63/warc/CC-MAIN-20220125005757-20220125035757-00571.warc.gz"} |
https://slideplayer.com/slide/4930546/ | # Math 025 Unit 5 Section 6.4. Objective: To simplify a complex fraction A complex fraction is a fraction whose numerator or denominator contains one or.
## Presentation on theme: "Math 025 Unit 5 Section 6.4. Objective: To simplify a complex fraction A complex fraction is a fraction whose numerator or denominator contains one or."— Presentation transcript:
Math 025 Unit 5 Section 6.4
Objective: To simplify a complex fraction A complex fraction is a fraction whose numerator or denominator contains one or more fractions. 1 – 4x24x2 1 + 2x2x To simplify: 1. Find the LCD of all the fractions 2. Multiply the numerator and denominator by that LCD 3. Simplify the resulting fraction
1 – 4x24x2 1 + 2x2x Objective: To simplify a complex fraction The LCM for x and x 2 is x 2 x2x2 x2x2 = x 2 – 4 (x – 2)(x + 2) x(x + 2) = = x – 2 x 1 1 x 2 + 2x
1x1x 1212 1x21x2 1414 Objective: To simplify a complex fraction The LCM for x, x 2, 2 and 4 is 4x 2 4x 2 = 4x + 2x 2 2x(2 + x) (2 – x)(2 + x) = = 2x 2 – x 1 1 + – 4 – x 2
1 – – 2x2x 1 – + 11 Objective: To simplify a complex fraction The LCM for x and x 2 is x 2 x2x2 x2x2 = x 2 – 2x – 15 x 2 – 11x + 30 (x – 5)(x + 3) (x – 6)(x – 5) = = x + 3 x – 6 1 1 15 x 2 30 x 2 x
x – 8 + x – + Objective: To simplify a complex fraction The LCD is (x + 4) (x + 4) x 2 + 4x – 8x – 32 + 20 x 2 + 4x – 10x – 40 + 24 = = x – 6 x – 8 20 x + 4 10 24 x + 4 (x + 4) = x 2 – 4x – 12 x 2 – 6x – 16 = (x – 6)(x + 2) (x – 8)(x + 2)
Download ppt "Math 025 Unit 5 Section 6.4. Objective: To simplify a complex fraction A complex fraction is a fraction whose numerator or denominator contains one or."
Similar presentations | 2021-01-18 23:24:50 | {"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": 0.81915682554245, "perplexity": 373.6453765468637}, "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-2021-04/segments/1610703517159.7/warc/CC-MAIN-20210118220236-20210119010236-00082.warc.gz"} |
https://stacks.math.columbia.edu/tag/06HI | Remark 89.8.3. Let $\varphi : \mathcal{F} \to \mathcal{G}$ be a morphism of categories cofibered in groupoids over $\mathcal{C}_\Lambda$. Let $B \to A$ be a ring map in $\mathcal{C}_\Lambda$. Choices of pushforwards along $B \to A$ for objects in the fiber categories $\mathcal{F}(B)$ and $\mathcal{G}(B)$ determine functors $\mathcal{F}(B) \to \mathcal{F}(A)$ and $\mathcal{G}(B) \to \mathcal{G}(A)$ fitting into a $2$-commutative diagram
$\xymatrix{ \mathcal{F}(B) \ar[r]^{\varphi } \ar[d] & \mathcal{G}(B) \ar[d] \\ \mathcal{F}(A) \ar[r]^{\varphi } & \mathcal{G}(A) . }$
Hence there is an induced functor $\mathcal{F}(B) \to \mathcal{F}(A) \times _{\mathcal{G}(A)} \mathcal{G}(B)$. Unwinding the definitions shows that $\varphi : \mathcal{F} \to \mathcal{G}$ is smooth if and only if this induced functor is essentially surjective whenever $B \to A$ is surjective (or equivalently, by Lemma 89.8.2, whenever $B \to A$ is a small extension).
There are also:
• 2 comment(s) on Section 89.8: Smooth morphisms
In your comment you can use Markdown and LaTeX style mathematics (enclose it like $\pi$). A preview option is available if you wish to see how it works out (just click on the eye in the toolbar). | 2022-05-17 21:03:59 | {"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": 2, "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": 2, "x-ck12": 0, "texerror": 0, "math_score": 0.9974250793457031, "perplexity": 338.6688840575878}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-21/segments/1652662520817.27/warc/CC-MAIN-20220517194243-20220517224243-00622.warc.gz"} |
http://science.sciencemag.org/content/284/5422/1943 | Review
# Mitigation Emerges as Major Strategy for Reducing Losses Caused by Natural Disasters
See allHide authors and affiliations
Science 18 Jun 1999:
Vol. 284, Issue 5422, pp. 1943-1947
DOI: 10.1126/science.284.5422.1943
## Abstract
The International Decade for Natural Disaster Reduction, a United Nations program for the 1990s, focused attention on the increasing losses caused by natural hazards and promoted actions to reduce their impacts. During this period in the United States, disaster managers and other officials increased emphasis on mitigation relative to response and recovery, especially in programs of the Federal Emergency Management Agency. Many other nations and international organizations undertook similar efforts. Beyond the Decade, efforts should focus on improving risk assessments; implementing mitigation strategies; improving technologies supporting warnings and the dissemination of, and response to, warnings; improving the basis for natural disaster insurance; and assisting developing nations.
Mounting losses in human casualties and property damage motivated the United Nations to declare the 1990s as the International Decade for Natural Disaster Reduction (IDNDR). Several disasters with large losses in the early 1990s underscored the need for this initiative. The natural hazards specified by the United Nations were earthquakes, windstorms, tsunamis, floods, landslides, volcanic eruptions, wildfires, grasshopper and locust infestations, and drought and desertification. To conduct the IDNDR, the United Nations established a secretariat in Geneva, Switzerland, a 25-member Scientific and Technical Committee (STC), and called on member states to form national committees, or designate focal points, to coordinate national-level activities. In the United States, the Subcommittee on Natural Disaster Reduction (1) coordinated federal agency programs under the National Science and Technology Council. In addition, the National Research Council, through the U.S. National Committee for the IDNDR and the Board on Natural Disasters (BOND) (2), provided an overview on U.S. activities and helped to link the public and private sectors. A World Conference on Natural Disaster Reduction held in Yokohama, Japan, during 1994 (3) reviewed Decade accomplishments and called for increased emphasis on implementation of scientific and technical knowledge for reducing disaster losses.
As the Decade enters it final stage, we review salient achievements and look ahead. It is clear that during the Decade there has been a significant shift in managing natural disasters, moving away from the traditional focus on response and recovery toward emphasis on mitigation, that is, preventive actions to reduce the effects of a natural hazard.
## Natural Disaster Losses
Many nations experience fatalities and injuries, property damage, and economic and social disruption resulting from natural disasters. Hurricanes, tornadoes, floods, drought, earthquakes, and winter storms repeatedly ravage parts of the United States. Natural hazards were among the decade's defining events in the United States: the Northridge earthquake (1994), Hurricane Andrew (1992), fires in California (1993) and Florida (1998), flooding of the Mississippi River (1993) and the Red River in the north (1997) (Fig. 1), and widespread tornadoes in Oklahoma and Kansas (early May 1999) (Fig. 2). The direct losses of about $44 billion for the Northridge earthquake and$30 billion for Hurricane Andrew, which rank these events as the costliest in U.S. history, substantially impacted their regions and the insurance industry.
Not only have these recent U.S. natural disaster losses been substantial, but also the trend in annual losses has been markedly upward (4) (Fig. 3). Most of this increase cannot be attributed to increased occurrence of hazards. Although some types of events, for example heavy rains, have increased in frequency since the 1950s, others such as hurricane landfalls in the eastern United States have declined. Thus, it is difficult to attribute U.S. disaster loss increases in any significant measure to this factor. Instead, they can be attributed to several other factors. In the last several decades population in the United States has migrated toward the coasts, concentrating along the earthquake-prone Pacific coast and the hurricane-prone Atlantic and Gulf coasts, and the value of their possessions has increased substantially. Florida's population has increased fivefold since 1950, and now 80% of it lives within 35 km of the coast. Similarly, in California the population has increased from 10 million in 1950 to the current level of 33 million. In addition, population has concentrated in large cities, which serve as hubs for communications, transportation, commerce, and government and require complex infrastructures, some of which have aged to the point of unreliability. Many elements of these complex infrastructures are highly vulnerable to breakdowns that can be triggered by relatively minor events. Failure of a single span of the Bay Bridge disrupted traffic for several months in the San Francisco area after the Loma Prieta earthquake in 1989 (5). Less dramatically, failure to remove a ground connection shut down San Francisco's electrical power for most of a day in December 1998. In short, the United States has more to lose than ever before—some components of its infrastructure are highly vulnerable to damage and disruption, and much of its population is located in areas at risk to natural disasters.
The earthquake that struck Kobe, Japan, in 1995 caused direct losses in excess of $100 billion, perhaps as much as$200 billion, and demonstrated the potential for disasters in the United States and other countries on a similar scale. Such a threat calls for action, but reducing potential losses for existing structures and systems by a substantial amount is costly, difficult, and perhaps impossible. Nevertheless, actions can be taken to avoid creating additional vulnerabilities and, in some cases, to reduce existing ones. This reality is helping to shape a new vision of the future among disaster managers and political leaders.
## Emergence of Mitigation
The two basic approaches for reducing the impacts of natural disasters are mitigation and response. Mitigation includes all those actions that are taken before, during, and after the occurrence of a natural event that minimize its impacts, and response includes those actions that are taken during and immediately after the event to reduce suffering and hasten recovery of the affected population and region. Mitigation includes avoiding hazards, for example, by building out of a flood plain or away from seismically active faults, or by providing warnings to enable evacuation in the periods immediately preceding hazards such as floods, hurricanes, and tornadoes. It also includes reducing vulnerability through floodproofing of buildings or strengthening of structures to withstand the loads imposed by seismic shaking or wind. Response includes both the short-term emergency actions taken by police, fire, and other agencies as well as the longer-term actions taken to meet needs for food, shelter, rebuilding, and restoration of the affected community. Both elements are important in dealing with natural hazards, but in past practice just one—response—has predominated.
Mitigation planning should be incorporated in or carefully coordinated with land-use planning for community development. In this way, communities can find opportunities for accommodating development demands in areas less vulnerable to natural hazards. Comprehensive mitigation planning includes (i) determining the location and nature of the potential hazards, (ii) characterizing the population and structures (present and future) that are vulnerable to specific hazards, (iii) establishing standards for acceptable levels of risk, and (iv) adopting mitigation strategies based on an analysis of realistic costs and benefits.
In practice, mitigation may be difficult to implement, both politically and economically. Making progress in this endeavor requires incentives that are both appealing and feasible, long-term commitments by its champions, and an investment of financial resources by its backers, usually in the face of a highly uncertain threat. It is much easier to pass along the problem to the next generation. It is therefore encouraging that mitigation is receiving increased emphasis, a situation that has come about through a combination of circumstances.
In recent years, as natural disaster losses have mounted, U.S. disaster managers and other decision makers have recognized that singular reliance on the strategies of response and recovery portend continuously escalating costs along with the attendant disruptions associated with natural disasters. Although response and recovery are essential for humanitarian, economic, and political purposes, they must be accompanied by increasing attention to reducing losses through effective mitigation programs (6).
To this end, numerous governmental and nongovernmental organizations have shifted priorities. Most significantly, the Federal Emergency Management Agency (FEMA) has established a Mitigation Directorate, on a par with its Response and Recovery Directorate, and developed a National Mitigation Strategy (7). Moreover, FEMA has moved ahead aggressively with Project Impact to implement mitigation practices in 118 demonstration cities and communities, a federal investment of about $25 million a year. These efforts by FEMA build on substantial work by other federal agencies, such as the National Science Foundation, U.S. Geological Survey, and National Oceanic and Atmospheric Administration, which have funded research on hazard mitigation for more than 20 years to improve understanding of the nature of natural hazards and their effects. Also, the U.S. Army Corps of Engineers and Natural Resource Conservation Service conduct substantial mitigation efforts, especially for flood prevention. Many private-sector companies have invested substantial resources to strengthen structures to withstand the effects of hazards. For example, the Institute for Business and Home Safety, an insurance industry–supported nonprofit organization, has promoted development of building materials that are more resistant to hazard-induced damage (hail-resistant roofing materials) and adoption and improvement of building codes. Many businesses have invested substantial funds to avoid damage and business interruptions, with notable success. ## International Progress Many organizations in the United Nations expanded or refocused activities in support of the Decade, although financial contributions specifically for the IDNDR (that is, in excess of regular budgets) amounted to only a few million dollars a year, with the largest contributions coming from Japan and several European countries. The United States contributed relatively little in funds, although the knowledge and expertise of U.S. scientists and engineers provided an important resource. Examples of important U.N. organizational activities include improved warning systems by the World Meteorological Organization, structural strengthening of hospitals by the World Health Organization/Pan-American Health Organization, and educational materials produced by the United Nations Educational, Scientific, and Cultural Organization. During recent years, the United Nations Development Program was assigned responsibility for promoting and coordinating mitigation in developing countries, and the World Bank established a Disaster Management Facility to assure that natural hazards are considered in development decisions. The Office of the Coordinator for Humanitarian Affairs and its predecessor organizations coordinated the efforts through the secretariat. Several international, nongovernment organizations also participated, notably the International Red Cross and the Red Crescent Society. Activities by international professional societies also contributed significantly. For example, the International Association of Seismology and Physics of the Earth's Interior sponsored a global assessment of seismic hazards, and the International Association of Volcanology and Chemistry of the Earth's Interior organized increased monitoring of 17 volcanoes, including Mount Rainier (Fig. 4) and Mauna Loa in the United States. The International Council for Science (ICSU; formerly the International Council of Scientific Unions) funded and sponsored about 10 projects, including ones dealing with landslides, drought, and tropical cyclones. The International Lithosphere Program examined the vulnerability of megacities. The IDNDR plan called for special efforts at the national level, especially in developing countries, through national committees or focal points. Altogether, about 130 of these were formed, but less than half performed effectively. Some of them were quite successful in promoting new efforts; for example, the Australian National Committee and the federal agency Emergency Management Australia moved ahead in a broad range of mitigation activities in planning, hazards and risk assessment, and assistance to other countries in the southwestern Pacific region. ## Goals for Beyond the IDNDR The targets that were adopted for the IDNDR were for each nation to assess risks from natural hazards, complete mitigation plans, and establish warning and preparedness systems. In the United States, significant progress was made in this regard, but much remains to be accomplished. For example, the regions that are prone to the various hazards have been delineated at a national scale (8), but hazard assessments that are useful for local risk assessments have been completed for only a few regions. With regard to mitigation planning, FEMA's National Mitigation Strategy lays out a conceptual approach, but implementing the concepts is proving to be a slow process. As evidenced recently in Oklahoma and Kansas, warnings for weather phenomena have been improved with greater use of satellites and the Doppler radar system by the National Weather Service, but much additional research is needed to fully utilize the new information. For the decades beyond the IDNDR, efforts to reduce losses from natural disasters should move forward in all aspects of mitigation (6) with a focus in the following high-priority areas. Improve risk assessments. Risk assessments are derived by first assessing the likelihood that a particular type of natural hazard will strike an area, including its frequency of occurrence and severity, and combining this information with both an inventory of structures that would be exposed to the hazard and with fragility data (estimates of the degree of damage that various classes of structures, for example, unreinforced masonry buildings in earthquake-prone areas, will suffer at specified levels of stress or exposure). Risk assessments are needed to increase public awareness of the threat posed by natural hazards and to guide allocation of resources [pp. 7–19 in (3); (5)]. Substantial progress has been made in recent years in modeling risk. There is broad interest in this tool not only as a means of describing disasters and estimating their costs, but also as a way to evaluate different disaster mitigation strategies. FEMA, in cooperation with the National Institute of Building Sciences, has developed Geographic Information System (GIS)–based earthquake loss estimation methodology called HAZUS (Hazards United States) for this purpose. This tool is currently being used to estimate earthquake losses nationally and in large metropolitan areas like San Francisco, Portland, Boston, and New York City. Efforts are underway to extend the GIS loss-modeling capability to flood and wind hazards. Risk-modeling techniques are increasingly being used to guide decisions by private as well as public entities, for example, to estimate probable maximum loss and average annual loss for the insurance sector. The confidence that can be placed in decisions made from risk modeling is strongly dependent on the level of uncertainty that is present in the models. Accurate hazard assessments are an essential starting point and need to be combined with comprehensive building inventories. The fragility data are often a particularly weak element in these models, which could be improved by more comprehensive field investigations after the disaster, data compilations, improvements in response analyses, and full-scale testing. Implement mitigation strategies. Communities can often achieve significant reductions in losses from natural disasters by adopting land-use plans that avoid the hazards [pp. 21–39 in (3)] while at the same time achieving environmental and other goals. To cite one example, some cities in flood-prone areas that undertook to manage the hazard reduced flood-plain development to less than 25% of what would have occurred without the local planning programs, yielding$11 million in reduced property damage per year, with annual administrative and private costs of only $1.3 million (9). Few local governments, however, are willing to adopt land-use measures to protect against natural hazards unless they receive strong mandates from higher level governments (10). Land-use approaches require accurate identification of areas affected by hazards, but hazard-zone mapping may be too expensive for some municipalities. An additional complication is that hazards often span jurisdictional boundaries, which necessitates cooperation. For hazards land-use planning to be implemented, the public must find the hazards threat to be credible. Building codes are also effective for reducing disaster losses [pp. 21–39 in (3); (5)]. A building code sets standards that guide the construction of new buildings and, in some cases, the rehabilitation of existing structures. Currently, building codes set minimum construction standards for life safety. However, maintaining the functionality of structures is also important and may be critical for certain classes of structures, for example those that are essential for public safety. Through Executive Orders (11) the federal government established seismic safety standards for federally funded new construction, and addressed seismic safety for existing owned and leased buildings. Some states have codes that are set at the state level but enforced at the local level, whereas other states let local governments set and enforce their own standards; however, more than half of the 30,000 communities in the United States have not adopted a building code at all. Of course, building codes are not effective unless they are enforced, which requires an ongoing inspection program, and many communities lack a sufficient number of inspectors. More than 25% of the damage from Hurricane Andrew could have been prevented if the existing building codes had been enforced (12). A “seal of approval” for structures that meet building codes has been proposed as a way to encourage improved building practices and to inform prospective buyers about structural safety (13). Many structures that house low-income families are relatively unsafe with respect to natural hazards, either because of poor structural quality or risk-prone locations. Such families often cannot afford the costs of repair, reconstruction, or relocation. Equity considerations argue for providing this group with low-interest loans and grants. Because low-income victims are likely to receive federal assistance to cover uninsured losses after a disaster, subsidizing these mitigation measures can also be justified on cost-effectiveness grounds. A community could also encourage its residents to engage in mitigation measures by providing them with tax or other financial incentives. For example, homeowners could get a tax rebate by undertaking a mitigation measure, thereby lowering the costs for disaster relief. Alternatively, property taxes could be lowered for the same reason. Unfortunately, communities often create monetary disincentives to invest in mitigation. A property owner who improves a home to make it safer is likely to have the property reassessed at a higher value and hence have to pay higher taxes. California has been cognizant of this problem and voters passed Proposition 127 in 1990 that exempts seismic rehabilitation improvements to buildings from being reassessed to increase property taxes. The city of Berkeley has taken an additional step to encourage home buyers to retrofit their newly purchased homes by instituting a transfer-tax rebate. The city taxes property transfer transactions at a rate of 1.5%, and up to one-third of this amount can be applied to seismic upgrades during the sale of property. Qualifying upgrades include repairing or replacing foundations, bracing basement walls, installing shear walls, anchoring water heaters, and securing chimneys. Since 1993, about 6300 houses have been improved, representing about$4.4 million in foregone revenues to the city (14).
In major urban centers (“megacities”), the vulnerability of infrastructure, telecommunications, and lifeline corridors makes it important to have backup or redundant systems to provide needed services should a disaster damage or destroy critical facilities. To illustrate this point, consider the crucial role of electricity in maintaining social and economic systems. Disaster damage to an electricity network may create havoc to a wide area as a result of indirect losses such as disruption of production in businesses, impaired hospitals and health facilities, and transportation problems due to nonfunctioning traffic signals, street lights, and safety alarms. The major mechanisms that society has developed to cope with electrical power failures are emergency or back-up generators and structural reinforcement of network facilities (15).
The economic, social, and political factors that influence the adoption of mitigation strategies are extremely complex (16). These include budget considerations, cultural norms, enforcement issues, and the tendency to maintain the status quo. In examining the range of mitigation measures to develop a strategy, one needs to target their adoption to specific situations. It is necessary to recognize that the opportunities for using certain measures will change as events unfold. For example, immediately after Hurricane Andrew in 1992 there was renewed interest in enforcing building codes, whereas before the event or even a few years after it occurred, the concern with mitigation was not a high priority on communities' agendas.
Improve technologies that support warnings and the dissemination of, and response to, warnings. Warnings are essential to prepare for a hazardous situation, such as an oncoming tornado, hurricane, or flood, and to move people out of harm's way, if necessary [pp. 41–61 in (3)]. To be most effective, warnings must be coupled with a forecasting system that provides prewarning data and with predetermined loss-reduction action plans. Warnings must specify the time, location, and severity of expected events with appropriate uncertainty bounds in a manner that allows actions to be taken for the survival of people and the protection of property and institutions. Some warnings are provided before a disaster ever develops in the form of maps that delineate hazard zones, signs posted in certain areas, or regulations that require real estate agents to inform potential property owners as to the nature of the hazard in their area. Other warnings, such as media announcements to evacuate hazardous areas, try to reduce losses just before the onset of an event.
Accurate and relevant information can be used to substantially reduce potential losses in many threatening situations (17), for example, airplanes can be directed around a volcanic ash cloud or property can be removed from an area about to be flooded. To be most effective, the information must be timely and in a form that is understandable by decision-makers. Recent advances in technology, such as high-speed computing and communications systems, combined with more comprehensive information resources and advanced GIS make a useful disaster information network feasible. It is now possible to rapidly integrate real-time data with archival data to produce information for critical decision making. For example, the dispersal pattern of fumes from a chemical spill can be predicted by using current weather data to identify threatened populations and evacuation routes. The foundation for such a network already exists, and moving ahead is largely a matter of coordination to set standards and protocols (5).
Improve the basis for natural disaster insurance. Insurance is a widely used financial instrument for protection against catastrophic loss [pp. 37–38 in (3)]. Insurance and financial institutions are increasingly active in formulating disaster policy and in promoting risk-reduction measures. By providing incentives for reducing vulnerability and by spreading risk, the efforts of the financial sector can reduce losses and moderate their economic impact.
Insurance should reward individuals who invest in hazard-reduction measures both before and after a disaster. Insured individuals should receive lower premiums for adopting mitigation measures before a disaster because the potential losses to the insurer are thus reduced. If they suffer losses to their structure, they will receive claim payments for the insured portion of their damage. Insurers also have the option of refusing to provide coverage unless the prospective policyholder undertakes certain protective measures to lower the potential losses from the risk in question.
One way to encourage communities to develop and enforce building codes and land-use management measures is to provide insurance premium reductions to all policyholders in the area based on the stringency of land-use regulations, building code standards, and inspection. The more effective a community program is in reducing future disaster losses, the greater the insurance premium reduction. Such a community rating system was created by the Federal Insurance Administration in 1990 as a way to recognize and encourage community flood plain management activities that exceed the minimum National Flood Insurance Program standards (18). This model could be applied to other hazards as well.
Assist disaster-prone developing nations. Countries that are highly vulnerable to natural hazards should implement modern approaches to disaster management [pp. 63–70 in (3)]. Earthquakes and volcanic eruptions threaten most countries around the Pacific Rim and throughout the Mediterranean, and the earthquake zone continues into the Himalayan region. Tropical cyclones cause extensive damage in the regions of the Pacific, Atlantic, and Indian oceans. As an illustration of the magnitude of these losses, according to its IDNDR National Committee, from 1989 through 1996 China experienced losses averaging 3.9% of its gross national product as a result of natural disasters. More recently, Hurricane Mitch rendered even greater relative devastation to Nicaragua and Honduras. Small island developing states repeatedly suffer losses on a similar scale. Many developing countries in the hazard-prone regions have limited resources for mitigating and recovering from the impacts of natural disasters and need scientific and technical assistance.
Scientific and technical assistance to developing countries, to the extent that it is available, is usually provided as equipment or training. All too often it is not long before the equipment sits idle and the trained personnel move on to other jobs. Another approach to assistance that has been successful in numerous cases, and that offers better prospects for building lasting capabilities in developing countries, is to establish partnerships between like-minded organizations in developing and industrialized countries [pp. 63–70 in (3)]. For example, a long-term cooperative endeavor between the U.S. Geological Survey's volcano hazards program and the Philippine Institute of Volcanology and Seismology developed collaborative relationships and expertise that were marshaled to predict the eruption of Mount Pinatubo, leading to evacuation of tens of thousands of people from around the volcano and departure of U.S. aircraft and personnel from Clark Air Base (19). Partnerships between academic institutions, government laboratories, and private organizations could greatly increase the capabilities of developing countries to cope with natural hazards, while at the same time extending American goodwill and providing American experts opportunities to pursue important studies in foreign areas.
It is essential that capabilities for disaster management be strengthened in developing countries, not only so the necessary expertise is available to implement programs, but also so knowledgeable people participate in policy discussions that lead to formulation of those programs. Unless someone is able to articulate in high-level discussions the opportunities for reducing disaster losses that modern disaster management methods offer, there is little chance that the issues will be appropriately framed. It must also be recognized that the inhabitants of hazardous areas in many developing countries are poor, and that their settlements often are illegal or self built with materials at hand. Building codes and warning systems are largely irrelevant, and thus special efforts must be made to reduce their vulnerability.
The United States provides developing countries with little assistance for natural disaster mitigation. To illustrate this point, consider the Office of Foreign Disaster Assistance (OFDA), an office within the U.S. Agency for International Development that is responsible for providing nonfood, humanitarian assistance in response to international crises and disasters. Within OFDA, the Prevention, Mitigation, Preparedness, and Planning Division (PMPPD) oversees projects designed to prevent or reduce the impact of disasters on people and economic infrastructure of foreign countries, whereas the Disaster Response Division deals with response. OFDA spent $155.4 million in fiscal year 1997, and 11% of this went to PMPPD. Although the OFDA projects are generally effective, and other federal agencies also conduct some related program activities, the relatively small amount of OFDA assistance reflects the rather limited international involvement of the United States in the IDNDR. Moreover, at the outset of the Decade, the U.S. representation at the United Nations played a passive role at best, and during the course of the Decade the United States has provided only minimal support for projects. International leadership, assistance, and cooperation in reducing natural disaster losses worldwide, however, could provide important benefits to the United States and support our foreign policy goals. More disaster-resistant communities abroad create American jobs by increasing exports and services. Disaster reduction promotes political stability. Cooperation advances the state of science and technology by providing access to data, information, and creative minds. In addition, cooperation facilitates the deployment of global observing systems for environmental monitoring. Finally, in this era of globalization, the interests of all countries extend worldwide. As noted in the Subcommittee on Natural Disaster Reduction Strategic Plan (20), “because the U.S. has a global reach, it has a global vulnerability as well.” For example, the Mount Pinatubo eruption caused direct losses to the United States of more than$1 billion and triggered a change in U.S. strategic presence in the western Pacific with the loss of air and naval bases. A proactive international program by the United States to reduce natural disaster losses is clearly justified for humanitarian purposes and to further foreign policy interests.
Several organizations in the U.N. system plan to continue IDNDR-related activities beyond the Decade, including the Office of the Coordinator for Humanitarian Affairs, the United Nations Educational, Scientific, and Cultural Organization, the World Meteorological Organization, the World Health Organization, and the United Nations Development Program. Several international programs also include natural disaster mitigation elements, such as the United Nations Commission for Sustainable Development, the Convention on Desertification, the Barbados Plan of Action for Sustainable Development of Small Island States, and the Framework Convention on Climate Change. Thus, there will continue to be numerous international venues for furthering the goals of natural disaster reduction.
• * The authors are members of the Board on Natural Disasters (BOND) of the National Research Council, 2101 Constitution Avenue, NW, Washington, DC 20418, USA. Members of BOND: Wilfred D. Iwan,Chair, California Institute of Technology, Pasadena; Lloyd S. Cluff, Pacific Gas and Electric, San Francisco, CA; James F. Kimpel, University of Oklahoma, Norman; Howard Kunreuther, Wharton School, University of Pennsylvania, Philadelphia; Stephanie H. Masaki-Schatz, Ranchos Palos Verdes, CA; Joanne M. Nigg, Disaster Research Center, University of Delaware, Newark; Richard S. Roth Sr., Northbrook, IL; Harvey Ryland, Institute for Business and Home Safety, Boston, MA; Ellis Stanley Sr., Los Angeles, CA; and Frank H. Thomas, Loudon, TN. National Research Council staff contributing to this article are Robert M. Hamilton, Patricia A. Jones, and Stephen D. Parker.
View Abstract | 2018-08-21 04:42:14 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.19965286552906036, "perplexity": 3740.239514198132}, "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-2018-34/segments/1534221217951.76/warc/CC-MAIN-20180821034002-20180821054002-00257.warc.gz"} |
http://bob.cs.sonoma.edu/IntroCompOrg-RPi/exers-unDecBin.html | ##### 1
Convert $123_{10}$ to binary.
##### 2
Convert the following unsigned decimal integers to 8-bit hexadecimal representation:
1. $100$
2. $123$
3. $10$
4. $88$
5. $255$
6. $16$
7. $32$
8. $128$
##### 3
Convert the following unsigned decimal integers to 16-bit hexadecimal representation:
1. $1024$
2. $1000$
3. $32768$
4. $32767$
5. $256$
6. $65535$
7. $4660$
8. $43981$ | 2017-09-26 16:22:26 | {"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": 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": 0.675280749797821, "perplexity": 3298.491619687508}, "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-2017-39/segments/1505818696653.69/warc/CC-MAIN-20170926160416-20170926180416-00715.warc.gz"} |
http://www.acmerblog.com/leetcode-solution-balanced-binary-tree-6268.html | 2014
11-18
# LeetCode-Balanced Binary Tree[二叉树]
### Balanced Binary Tree
Given a binary tree, determine if it is height-balanced.
For this problem, a height-balanced binary tree is defined as a binary tree in which the depth of the two subtrees of every node never differ by more than 1.
// LeetCode, Balanced Binary Tree
// 时间复杂度O(n)，空间复杂度O(logn)
class Solution {
public:
bool isBalanced (TreeNode* root) {
return balancedHeight (root) >= 0;
}
/**
* Returns the height of root if root is a balanced tree,
* otherwise, returns -1.
*/
int balancedHeight (TreeNode* root) {
if (root == nullptr) return 0; // 终止条件
int left = balancedHeight (root->left);
int right = balancedHeight (root->right);
if (left < 0 || right < 0 || abs(left - right) > 1) return -1; // 剪枝
return max(left, right) + 1; // 三方合并
}
};
1. Good task for the group. Hold it up for every yeara??s winner. This is a excellent oppotunity for a lot more enhancement. Indeed, obtaining far better and much better is constantly the crucial. Just like my pal suggests on the truth about ab muscles, he just keeps obtaining much better.
2. 如果两个序列的最后字符不匹配（即X [M-1]！= Y [N-1]）
L（X [0 .. M-1]，Y [0 .. N-1]）= MAX（L（X [0 .. M-2]，Y [0 .. N-1]），L（X [0 .. M-1]，Y [0 .. N-1]）
这里写错了吧。
3. Good task for the group. Hold it up for every yeara??s winner. This is a excellent oppotunity for a lot more enhancement. Indeed, obtaining far better and much better is constantly the crucial. Just like my pal suggests on the truth about ab muscles, he just keeps obtaining much better. | 2017-06-26 20:39:09 | {"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": 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": 0.5123383402824402, "perplexity": 10419.961603020358}, "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/1498128320865.14/warc/CC-MAIN-20170626203042-20170626223042-00377.warc.gz"} |
https://dsp.stackexchange.com/tags/psychoacoustics/hot | # Tag Info
## Hot answers tagged psychoacoustics
9
In designing such transformations, one should take into account competing interests: fidelity to the human auditory system (that varies with people), including non-linear or even chaotic aspects (tinnitus) easiness of the mathematical formulation for the analysis part possibility to discretize it or allow fast implementations existence of a suitable stable ...
2
Well, I don't know whether it'll actually help you – you just said it would! Now, in any case, using an algorithm to extract features from a signal that mimics or resembles human perception should inherently give those feature vectors a higher "mathematical" resemblance when a human would find the original signals similar, too. This is obviously what you ...
2
The Equi-loudness contours, chart provided at your link, is for hearing thresholds for isolated tones. Assuming speech is a sum of tones is a wrong assumption. But even if we go ahead with this assumption, it does not help to compute SNR for speech understanding under noise because of the following reasons. a. Speech is a non-stationary signal implying that ...
2
A fixed interval corresponds to a fixed ratio of frequencies (at least in equal temperament, which is the most common tuning system in Western music). One octave is a factor of $2$. One semi-tone is a factor of $\sqrt[12]{2}$ because there are $12$ semi-tones in one octave. So one third of an octave (i.e., $4$ semi-tones) corresponds to a factor of $\sqrt[3]{... 2 20Vrms is the maximum voltage you can apply across the transmitting transducer without the risk of immediately damaging it. The amplitude of sound it produces is determined by the driving voltage. The transmitter is characterized at 10Vrms, so about 28Vp-p assuming a sine wave, probably where you would prefer to use it for reliability and long life. 1 The temporal masking effect is minimal. If your samples do not have extreme differences in loudness, one frame of silence should be enough. Depending on sampling rate one frame is >20ms, that should be plenty. 1 Yes, you can calculate it by summing all of the 3rd-octave band pressures. Keep in mind, that if the units are pressure then simple sum and conversion to the decibel scale is enough. However, if you have 3rd-octave band levels, then you have to calculate the anti-log of those values, sum them and then convert back to SPL. Regarding the Sound Exposure Level, ... 1 Your method is bad, because it does signal -> FFT -> |·|² -> sum which is, per Parseval's theorem, 100 % identical in information to signal -> |·|² -> sum What you can do is apply weights to different frequency bin magnitude squares of the DFT to represent how "important" they'd be for perception. If you did a weighted thing, you'd be closer to ... 1 The Mel is an empirical model that describes the change in human pitch perception at different frequencies: until 1 kHz we perceive pitch changes in a linear way, after that, we perceive it in a logarithmic way, just as you said. The pitch function relating real and perceived pitch differences is approximated based on the measurements made by Stevens in ... 1 I just glanced at a paper on this subject, and it appears that you should be introducing an inter-aural 0-to-2PI phase shift over a very narrow frequency range, rather than offsetting one signal by T. I can imagine a variety of ways to create the phase-modified noise signal, included filtering a noise signal with a high-Q 2nd-order allpass filter, or by ... 1 Question 1: The equations (6.7), (6.8), and (6.9) are all consistent, so I suggest that the wording for the definition of$g\$ is incorrect in the book. Question 2: The brain just hears the time difference and, by experience, can figure out what that means in terms of distance. So the brain has effectively "calibrated" for whatever the usual speed of sound ...
1
The Fastl-Zwicker book is usually the introduction to this topic. The more I learn about it the more fascinating it becomes. If you pick it up used be sure to get one with the CD examples in it, as they are completely fascinating.
1
i dunno anything about EAQUAL or PEAQ. judging which sounds better is quite subjective, so much so that i consider it nearly a useless question. but if you have a reference (that you define as "good"), and you have several options to compare to the reference, and your goal is find which option most sounds like the reference, then i would recommend AB ...
Only top voted, non community-wiki answers of a minimum length are eligible | 2021-03-03 19:01:57 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 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": 0.6564933657646179, "perplexity": 1112.4300293030883}, "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/1614178367183.21/warc/CC-MAIN-20210303165500-20210303195500-00018.warc.gz"} |
https://www.zbmath.org/?q=an%3A0642.60102 | zbMATH — the first resource for mathematics
Uniqueness of the infinite cluster and continuity of connectivity functions for short and long range percolation. (English) Zbl 0642.60102
For independent translation-invariant irreducible percolation models, it is proved that the infinite cluster, when it exists, must be unique. The proof is based on the convexity (or almost convexity) and differentiability of the mean number of clusters per site, which is the percolation analogue of the free energy. The analysis applies to both site and bond models in arbitrary dimension, including long range bond percolation. In particular, uniqueness is valid at the critical point of one-dimensional $$1/| x-y|^ 2$$ models in spite of the discontinuity of the percolation density there. Corollaries of uniqueness and its proof are continuity of the connectivity functions and (except possibly at the critical point) of the percolation density. Related to differentiability of the free energy are inequalities which bound the “specific heat” critical exponent $$\alpha$$ in terms of the mean cluster size exponent $$\gamma$$ and the critical cluster size distribution exponent $$\delta$$ ; e.g. $$1+\alpha \leq \gamma (\delta /2-1)/(\delta -1)$$.
MSC:
60K35 Interacting random processes; statistical mechanics type models; percolation theory 82B43 Percolation
Full Text:
References:
[1] Aizenman, M., Barsky, D. J.: Sharpness of the phase transition in percolation models, Commun. Math. Phys.108, 489-526 (1987). · Zbl 0618.60098 · doi:10.1007/BF01212322 [2] Aizenman, M., Barsky, D. J.: in preparation. See also Barsky, D. J. Rutgers University Ph.D. thesis (1987). · Zbl 0618.60098 [3] Aizenman, M., Chayes, J. T., Chayes, L., Fr?hlich, J., Russo, L.: On a sharp transition from area law to perimeter law in a system of random surfaces. Commun. Math. Phys.92, 19-69 (1983) · Zbl 0529.60099 · doi:10.1007/BF01206313 [4] Aizenman, M., Newman, C. M.: Tree graph inequalities and critical behavior in percolation models. J. Stat. Phys.36, 107-143 (1984) · Zbl 0586.60096 · doi:10.1007/BF01015729 [5] Aizenman, M., Newman, C. M.: Discontinuity of the percolation density in one-dimensional 1/?x?y?2 percolation models. Commun. Math. Phys.107, 611-648 (1986) · Zbl 0613.60097 · doi:10.1007/BF01205489 [6] van den Berg, J., Keane, M.: On the continuity of the percolation probability function, Contemp. Math.26, 61-65 (1984) · Zbl 0541.60099 [7] Bricmont, J., Lebowitz, J. L.: On the continuity of the magnetization and energy in Ising ferromagnets. J. Stat. Phys.42, 861-869 (1986) · doi:10.1007/BF01010449 [8] Choquet, G.: Topology. New York: Academic Press 1966 [9] Coniglio, A.: Shapes, surfaces, and interfaces in percolation clusters. In: Physics of finely divided matter. Daoud M. (ed.). Proc. Les Houches Conf. of March, 1985 (to appear) [10] Chayes, J. T., Chayes, L., Newman, C. M., The stochastic geometry of invasion percolation. Commun. Math. Phys.101, 383-407 (1985) · Zbl 0596.60096 · doi:10.1007/BF01216096 [11] Durrett, R., Nguyen, B.: Thermodynamic inequalities for percolation. Commun. Math. Phys.99, 253-269 (1985) · doi:10.1007/BF01212282 [12] Fisher, M. E.: Critical probabilities for cluster size and percolation problems. J. Math. Phys.2, 620-627 (1961) · Zbl 0105.43602 · doi:10.1063/1.1703746 [13] Fortuin, C., Kastelyn, P.: On the random-cluster model I. Introduction and relation to other models. Physica57, 536-564 (1972) · doi:10.1016/0031-8914(72)90045-6 [14] Fortuin, C., Kastelyn, P., Ginibre, J.: Correlation inequalities on some partially ordered sets. Commun. Math. Phys.22, 89-103 (1971) · Zbl 0346.06011 · doi:10.1007/BF01651330 [15] Grimmett, G. R.: On the number of clusters in the percolation model. J. Lond. Math. Soc. (2)13, 346-350 (1976) · Zbl 0338.60034 · doi:10.1112/jlms/s2-13.2.346 [16] Grimmett, G. R.: On the differentiability of the number of clusters per vertex in the percolation model. J. Lond. Math. Soc. (2)23, 372-384 (1981) · Zbl 0497.60010 · doi:10.1112/jlms/s2-23.2.372 [17] Grimmett, G. R., Keane, M., Marstrand, J. M.: On the connectedness of a random graph. Math. Proc. Comb. Philos. Soc.96, 151-166 (1984) · Zbl 0543.60016 · doi:10.1017/S0305004100062034 [18] Hammersley, J. M.: Percolation processes. Lower bounds for the critical probability. Ann. Math. Statist.28, 790-795 (1957) · Zbl 0091.13903 · doi:10.1214/aoms/1177706894 [19] Hammersley, J. M.: A Monte Carlo solution of percolation in the cubic crystal. Meth. Comp. Phys.1, 281-298 (1963) [20] Hankey, A.: Three properties of the infinite cluster in percolation theory. J. Phys. A11, L49-L55 (1978) [21] Harris, T. E.: A lower bound for the critical probability in a certain percolation process. Proc. Camb. Philos. Soc.56, 13-20 (1960) · Zbl 0122.36403 · doi:10.1017/S0305004100034241 [22] Kesten, H.: Percolation theory for mathematicians. Boston: Birkh?user 1982 · Zbl 0522.60097 [23] Kesten, H.: The incipient infinite cluster in two-dimensional percolation. Theor. Probab. Rel. Fields,73, 369-394 (1986) · Zbl 0597.60099 · doi:10.1007/BF00776239 [24] Kesten, H.: A scaling relation at criticality for 2D-percolation. In: Percolation theory and ergodic theory of infinite particle systems Kesten, H., (ed.). IMA volumes in mathematics and its applications, Vol.8, Berlin, Heidelberg, New York: Springer (to appear) [25] Kikuchi, R.: Concept of the long-range order in percolation problems, J. Chem. Phys.53, 2713-2718 (1970) · doi:10.1063/1.1674394 [26] Kastelyn, P. W., Fortuin, C. M.: Phase transitions in lattice systems with random local properties. J. Phys. Soc. Jpn.26, [Suppl], 11-14 (1969) [27] Klein, S. T., Shamir, E.: An algorithmic method for studying percolation clusters. Stanford Univ. Dept. of Computer Science, Report no. STAN-CS-82-933 (1982) [28] Kunz, H., Souillard, B.: Essential singularity in percolation problems and asymptotic behavior of cluster size distribution. J. Stat. Phys.19, 77-106 (1978) · doi:10.1007/BF01020335 [29] Leath, P. L.: Cluster shape and critical exponents near percolation threshold. Phys. Rev. Lett.36, 921-924 (1976) · doi:10.1103/PhysRevLett.36.921 [30] Leath, P. L.: Cluster shape and boundary distribution near percolation threshold. Phys. Rev. B14, 5046-5055 (1976) [31] Lebowitz, J. L.: Coexistence of phases in Ising ferromagnets. J. Stat. Phys.16, 463-476 (1977) · doi:10.1007/BF01152284 [32] Newman, C. M.: In equalities for ? and related critical exponents in short and long range percolation. In: Percolation theory and ergodic theory of infinite particle systems Kesten, H., (ed.). IMA volumes in mathematics and its applications, Vol8. Berlin, Heidelberg, New York: Springer (to appear) [33] Newman, C. M.: Some critical exponent inequalities for percolation. J. Stat. Phys.45, 359-368 (1986) · doi:10.1007/BF01021076 [34] Newman, C. M., Schulman, L. S.: Infinite clusters in percolation models. J. Stat. Phys.26, 613-628 (1981) · Zbl 0509.60095 · doi:10.1007/BF01011437 [35] Newman, C. M., Schulman, L. S.: One-dimensional 1/|j ? i| s percolation models: The existence of a transition fors ? 2. Commun. Math. Phys.104, 547-571 (1986) · Zbl 0604.60097 · doi:10.1007/BF01211064 [36] Pike, R., Stanley, H. E.: Order propagation near the percolation threshold. J. Phys. A14, L169-L177 (1981) [37] Rockafellar, T. R.: Convex analysis. Princeton, NJ: Princeton Univ. Press 1970 · Zbl 0193.18401 [38] Ruelle, D.: Statistical mechanics: Rigorous results. New York: W. A. Benjamin 1969 · Zbl 0177.57301 [39] Russo, L.: On the critical percolation probabilities. Z. Wahrscheinlichkeitstheor Verw. Geb.56, 229-237 (1981) · Zbl 0457.60084 · doi:10.1007/BF00535742 [40] Sykes, M. F., Essam, J. W.: Exact critical percolation probabilities for site and bond problems in two dimensions. J. Math. Phys.5, 1117-1127 (1964) · doi:10.1063/1.1704215 [41] Wierman, J. C.: On critical probabilities in percolation theory. J. Math. Phys.19, 1979-1982 (1978) · Zbl 0416.60099 · doi:10.1063/1.523894
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching. | 2021-05-06 00:38:37 | {"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": 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": 0.7855625748634338, "perplexity": 8539.213767090663}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-21/segments/1620243988724.75/warc/CC-MAIN-20210505234449-20210506024449-00236.warc.gz"} |
https://aliquote.org/micro/2022-03-03-10-29-19/ | # aliquote
## < a quantity that can be divided into another a whole number of time />
Roswell: Hidden feature of “-s” option. #lisp | 2022-05-23 02:59:26 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 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": 0.2126004546880722, "perplexity": 4695.228503202744}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-21/segments/1652662552994.41/warc/CC-MAIN-20220523011006-20220523041006-00278.warc.gz"} |
https://ask.sagemath.org/answers/25097/revisions/ | # Revision history [back]
Hello,
If you just want to iterate through these number then you can do
sage: N_max = 1000
sage: for N in srange(23, N_max, 24):
....: if not N.is_squarefree():
....: continue
....: # here N is square free = -1 (24)
....: print N
And you get as output
23
47
71
95
119
...
959
983
You can also create the list of such integers with
sage: l = [N for N in srange(23, N_max, 24) if N.is_squarefree()]
Then
sage: print l[0], l[1], l[2]
23 47 71
Vincent | 2018-08-18 21:57:49 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 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": 0.2423323392868042, "perplexity": 10880.940467125147}, "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-2018-34/segments/1534221213794.40/warc/CC-MAIN-20180818213032-20180818233032-00037.warc.gz"} |
https://tex.stackexchange.com/questions/631633/is-there-way-of-breaking-down-a-very-long-equation-without-multiline | # Is there way of breaking down a very long equation without multiline?
I have been trying to break up this long equation (see below) to fit into the page. It is quite long and I am wondering how I can break it up into different parts. There is something wrong with the \multiline function in my version, so I want to avoid using that.
\begin{aligned} V^{j} \left ( q_{c},q_{e} \right ) \equiv \max_{\sigma^{j}, c_{c}^{j}, c_{e}^{j}, y_{c}^{j}, y_{e}^{j}} \left \{ \delta^{j} u(c^{j}) - g(y^{j}) + W\left ( \frac{\phi}{\gamma_{c}}[q_{c}-c_{c}^{j}+y_{c}^{j}], \frac{\psi}{\gamma_{e}}[\sigma^{j} (R q_{e}-\kappa^{j}-c_{e}^{j}+y_{e}^{j}) + (1-\sigma^{j}) (q_{e}-c_{e}^{j}+y_{e}^{j}) ] \right ) + \lambda_{c}^{j} (q_{c}-c_{c}^{j}) + \lambda_{e}^{j} (Rq_{e}-\kappa^{j}-c_{e}^{j}) \right \},\label{eqn:17} \end{aligned}\\
The output I am getting:
I am looking for an output that is like
but under the maximization problem with the main brackets.
Here are the relevant packages:
\documentclass[a4paper,12pt]{article}
\usepackage[margin=1in]{geometry}
\usepackage{amsmath,amssymb,amsfonts}
\usepackage{mathtools}
\usepackage{graphicx,amsmath,stackengine,scalerel}
\newcommand\qunderline[1]{\ThisStyle{%
\ensurestackMath{\stackengine{-1pt}{\SavedStyle#1}
{\SavedStyle\underline{\hphantom{#1}}}{U}{c}{F}{F}{S}}}%
}
\usepackage{xfrac}
\usepackage{nicefrac}
\usepackage{accents}
• Please merge your code fragments to one small, compilable document. In equation code you have errors. In showed preamble the most of of packages are irrelevant to your problem, many of them are loaded twice ... Jan 27 at 6:05
• @Zarko I made some edits
– OGC
Jan 27 at 6:41
• to late for my answer ... but you still not merge both fragments in one small document, which reproduce your problem. As now see, you also change the equation ... Jan 27 at 6:48
• The correct name of the environment (not macro) is multline, not multiline.
– Mico
Jan 27 at 7:07
If you use multline rather than multiline as the name of the environment, you should be fine with just two line breaks in the long formula.
Because of the line breaks, you can't use \left and \right all that well. Instead, do use explicit sizing directives such as \bigl, \Bigl, and \biggl (and their corresponding closing counterparts).
The horizontal line in the following screenshot is there just to illustrate the width of the textblock.
\documentclass{article}
\usepackage{amsmath} % for 'multline' env. and '\substack' macro
\begin{document}
\hrule % just to illustrate width of text block
\begin{multline} \label{eqn:17}
V^{j}(q_{c},q_{e}) \equiv
\max_{\substack{\sigma^{j}, c_{c}^{j}, c_{e}^{j},\\ y_{c}^{j}, y_{e}^{j}}}
\biggl \{ \delta^{j} u(c^{j}) - g(y^{j})
+ W\Bigl( \tfrac{\phi}{\gamma_{c}} \bigl[q_{c}-c_{c}^{j}+y_{c}^{j}\bigl]\,,\\
\tfrac{\psi}{\gamma_{e}}
\bigl[ \sigma^{j} (R q_{e}-\kappa^{j}-c_{e}^{j}+y_{e}^{j})
+ (1-\sigma^{j}) (q_{e}-c_{e}^{j}+y_{e}^{j}) \bigr] \Bigr ) \\
+ \lambda_{c}^{j} (q_{c}-c_{c}^{j}) + \lambda_{e}^{j} (Rq_{e}-\kappa^{j}-c_{e}^{j})
\biggr \}\,.
\end{multline}
\end{document}
• In aligned environment math terms are not break in multi lines. Consequently your equation spill out of page
• Even you break equation on three parts, it is still to long, it protrude right text border and consequently the equation number is pushed below of equation.
• A possible solution is to use smaller font size in equation, for example by employ \medmath command defined in the nccmath package
\documentclass[a4paper,12pt]{article}
\usepackage[margin=1in]{geometry}
\usepackage{nccmath}
\usepackage{lipsum} % for dummy text filler
\begin{document}
\lipsum[66]
\label{eqn:17} \medmath{ \begin{aligned} V^{j}( q_{c},q_{e}) & \equiv \max_{\substack{\sigma^{j}, c_{c}^{j}, c_{e}^{j},\\ y_{c}^{j}, y_{e}^{j}}} \biggl\{ \delta^{j} u(c^{j}) - g(y^{j}) \\ &\quad {} + \beta W \left( \frac{\phi}{\gamma_{c}}\bigl[q_{c} - c_{c}^{j} + y_{c}^{j}\bigr], \frac{\psi}{\gamma_{e}}\bigl[\sigma^{j} (R q_{e} -\kappa^{j} - c_{e}^{j} +y_{e}^{j}) + (1-\sigma^{j}) (q_{e}-c_{e}^{j}+y_{e}^{j}) \bigr] \right) \\ &\quad {} + \lambda_{c}^{j} (q_{c}-c_{c}^{j}) + \lambda_{e}^{j} (Rq_{e}-\kappa^{j}-c_{e}^{j}) \biggr\}, \end{aligned} }
some more text, see \eqref{eqn:17}
\end{document}
Off-topic In your preamble amsmath is still load twice (actually three times because mathtools load it too). More correct is (considering new nccmath):
\documentclass[a4paper,12pt]{article}
\usepackage[margin=1in]{geometry}
\usepackage{nccmath,amssymb,amsfonts}
\usepackage{mathtools}
\usepackage{graphicx,stackengine,scalerel}
\newcommand\qunderline[1]{\ThisStyle{%
\ensurestackMath{\stackengine{-1pt}{\SavedStyle#1}
{\SavedStyle\underline{\hphantom{#1}}}{U}{c}{F}{F}{S}}}%
}
\usepackage{xfrac}
\usepackage{nicefrac}
\usepackage{accents}
• Thanks for the solution! The code runs but I get this error: Undefined control sequence. \medmath
– OGC
Jan 27 at 6:46
• than you not load package nccmath. it had to be loaded before mathtools. Jan 27 at 6:50
• +1 for the use of \substack. :-)
– Mico
Jan 27 at 7:09
• @Mico, thank you very much. the same for your answer! BTW, I understood multiline as multi line, i.e. that OP like to break equation into many lines ... Jan 27 at 7:14
• to continue above comment: *without of use ˙multlined` *environment (as is required in question title). Question is to me a bit misleading. Jan 27 at 7:22 | 2022-05-24 16:45:08 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 2, "x-ck12": 0, "texerror": 0, "math_score": 0.9605902433395386, "perplexity": 5971.954836692454}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-21/segments/1652662573053.67/warc/CC-MAIN-20220524142617-20220524172617-00701.warc.gz"} |
https://codeforces.com/blog/entry/102560 | ### maroonrk's blog
By maroonrk, history, 11 days ago,
We will hold AtCoder Grand Contest 057. This contest counts for GP30 scores.
The point values will be 400-700-1100-1100-1400-1800.
We are looking forward to your participation!
This is the first contest in the 2022 season that counts for the GP30 race. We are planning to invite top runners of the race to WTF 2023, but we still haven't decided on the details of the Finals. We will closely watch the domestic and international situations and consider when and how to hold the Finals. We are also trying to find a way to hold unfinished WTF 2020, 2021, and 2022.
• +224
» 11 days ago, # | +29 Long awaited AGC round and finally the WTF!
» 11 days ago, # | ← Rev. 4 → +183 As a 2800-rated on CF, I have never solved any C of AGC during contest.upd: This time I went for D. I think editorial of D is not detailed enough :( I have come up with everything in the editorial during the contest, but failed to find an $O(d^3)$ per testcase solution with it (My solution runs in $O(d^4\log n)$)
» 11 days ago, # | +313 Nice, 57th AGC on May 7. I guess 58th AGC will be the next time May 8 is Saturday?
• » » 10 days ago, # ^ | +123 That is because they have to solve the problems before asking them.
» 10 days ago, # | 0 Good luck, and can't wait to see the problems!
• » » 10 days ago, # ^ | 0 Well, no luck for me.Giving up after fiddling two hours on A... and even dont find a counterexample for my code, but still have only 1/42 green. :/
• » » » 10 days ago, # ^ | ← Rev. 3 → +9 Probably you did not break into cases where first digit of upper bound is 1 and it is not. After you do that the problem becomes trivial(I say trivial but I still spent forever solving it, so don't listen to my difficulty estimations)
• » » » » 10 days ago, # ^ | 0 After reading the editorial: Actually I got the right idea, and implemented that binary search. But I did not get the formular for f() right, considering that the case prefix and postfix. I somehow tried to mix them up, or ignored the half of it.
• » » » » » 9 days ago, # ^ | ← Rev. 2 → 0 I didn't use binary search — instead choosing to approach the problem the other way. After noting that for any [l,r] we can always pick some suffix, I noticed that for r, if the first digit is 1 then the lower bound is max(l,r%(10^digits of r — 1) + 1, r/10 + 1). Otherwise the lower bound is just max(l, 10^(digits in r — 1) + 1).https://atcoder.jp/contests/agc057/submissions/31492475
» 10 days ago, # | -13 O.M.G. It has been my first time to take part in AGC (only a 1100-rating on Atcoder). I just wanna take it easy because i've imagined how difficult the AGC would be. But actually more difficult than I thought! I only solved A of AGC and still came up with no ideas to solve B. SOS...
• » » 8 days ago, # ^ | +16 Well,I think it is good of a 1100-Rating player to solve an A int AGC
» 10 days ago, # | 0 About problem B, I have noticed that if the initial state has max-min= X holds.By the way, during the contest, I contributed about 16 WA to this problem :(
• » » 10 days ago, # ^ | ← Rev. 2 → +18 Suppose you change every value, and $\text{max} - \text{min} \geq x$. Then, if you undo exactly one operation for each value, $\text{max} - \text{min}$ doesn't increase. So it's optimal to never change one of the values. That value is the maximum.
• » » 9 days ago, # ^ | ← Rev. 2 → 0 My understanding for the editorial:Let's define a bulk operation to be an operation which changes each value at most once. If in a bulk operation the maximum value ($max$) is changed, it does not make sense to fix any other value, e.g., changing the other value $v$ to $2\cdot v$ will never make the answer worse.On the other hand, changing all the values in a bulk operation can decrease the answer only if $max - min$ is $< X$.So, our goal is to decrease $max - min$ as much as we can through the bulk operations where $max$ is not changed.
» 10 days ago, # | 0 I solved C in quadratic time. It wasn't even super hard, efficiently written loops + AVX optimisation + one extra trick.
» 9 days ago, # | +25 It is rated?
» 9 days ago, # | +42 I used another idea for problem $B$ — two pointers. The complexity is $O(n \cdot log{n} \cdot log{C})$.Look at element $y$ of array. Let $S_i$ are sets of values, that can have this element after $i$ operations. That is $S_0 = {y}, S_1 = [2 \cdot y, 2 \cdot y + x]$. We can prove by induction, that it is always some segment $[l_i, r_i] \forall i$. Let's calculate all these segments up to $10^{18}$.Now we have the problem: for all $i \in [1, n]$ we have set of segments, they can overlap. We have to find the smallest segment $[l, r]$ such that for any $i \in [1, n]$ at least one corresponding segment intersects with it. This can be done using two pointers in linear time.
» 9 days ago, # | +8 It is rated?
» 9 days ago, # | +10 very nice task E!but what a pity for me to solve it 15min after the contest
» 9 days ago, # | 0 I thought AGC is unrated for cyans... should've participated | 2022-05-17 05:11:04 | {"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": 0.4697023332118988, "perplexity": 1384.4314738081746}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-21/segments/1652662515501.4/warc/CC-MAIN-20220517031843-20220517061843-00783.warc.gz"} |
https://www.rdocumentation.org/packages/spatstat/versions/1.42-2/topics/foo | # foo
0th
Percentile
##### Foo is Not a Real Name
The name foo is not a real name: it is a place holder, used to represent the name of any desired thing.
The functions defined here simply print an explanation of the placeholder name foo.
Keywords
documentation
##### Usage
foo()## S3 method for class 'foo':
plot(x, \dots)
x
Ignored.
...
Ignored.
##### Details
The name foo is used by computer scientists as a place holder, to represent the name of any desired object or function. It is not the name of an actual object or function; it serves only as an example, to explain a concept.
However, many users misinterpret this convention, and actually type the command foo or foo(). Then they email the package author to inform them that foo is not defined.
To avoid this correspondence, we have now defined an object called foo. The function foo() prints a message explaining that foo is not really the name of a variable.
The function can be executed simply by typing foo without parentheses.
##### Value
• Null.
beginner
foo | 2019-11-12 06:26:05 | {"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": 0.3304097056388855, "perplexity": 2305.6949778749085}, "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-2019-47/segments/1573496664752.70/warc/CC-MAIN-20191112051214-20191112075214-00073.warc.gz"} |
https://www.ms.u-tokyo.ac.jp/seminar/2022/sem22-113_e.html | ## Number Theory Seminar
Date, time & place Wednesday 17:00 - 18:00 056Room #056 (Graduate School of Math. Sci. Bldg.) Naoki Imai, Yoichi Mieda
### 2022/07/06
17:00-18:00 Room #ハイブリッド (Graduate School of Math. Sci. Bldg.)
Peijiang Liu (oUniversity of Tokyo)
The characteristic cycles of non-confluent $\ell$-adic GKZ hypergeometric sheaves (ENGLISH)
[ Abstract ]
$\ell$-adic GKZ hypergeometric sheaves are defined to be étale analogues of GKZ hypergeometric $\mathcal{D}$-modules. We introduce an algorithm of computing the characteristic cycles of certain type of $\ell$-adic GKZ hypergeometric sheaves. We compute the irreducible components by a push-forward formula for characteristic cycles of étale sheaves, and compute the multiplicities by considering a comparison theorem between the characteristic cycles of non-confluent $\ell$-adic GKZ hypergeometric sheaves and those of non-confluent GKZ hypergeometric $\mathcal{D}$-modules. We also explain the limitation of our algorithm by an example. | 2022-06-28 03:41:50 | {"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": 0.9598647356033325, "perplexity": 4361.973037616988}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-27/segments/1656103347800.25/warc/CC-MAIN-20220628020322-20220628050322-00679.warc.gz"} |
https://tex.stackexchange.com/questions/95295/how-to-left-align-footnotes-under-tabularx-in-a-minipage | # How to left align footnotes under tabularx in a minipage
I am new to LaTeX, trying to create a table using a tabularx in a two column format. I am creating the table in a minipage so that footnotes can appear at the bottom. Everything works out fine, but the footnotes under the table are right aligned, I prefer them left aligned with the table. I browsed through several posts and forums, but couldn't figure out. Any suggestions would help.
\documentclass[conference]{IEEEtran}
\usepackage{tabularx,booktabs}
\listfiles
\begin{document}
\makeatletter
\renewcommand\@makefntext[1]{%
\parindent 1em
\noindent
%\hb@xt@1.8em{\hss\@makefnmark}#1}
\hbox{\hss\@makefnmark}#1}
\makeatother
\newcommand{\HRule}{\rule{\linewidth}{0.5mm}}
\newcolumntype{C}{>{\centering\arraybackslash}X}
\newcolumntype{L}{>{\raggedright\arraybackslash}X}
\begin{table}
X\dotfill X
\begin{minipage}{1\linewidth}
X\dotfill X
\centering
\caption{Questionnaire summary}
\begin{tabularx}{1\linewidth} {l c C C L}
\toprule
\textbf{PID}\footnote{Participant ID}&\textbf{Challenge}\footnote{on a five-point Likert Scale 1-Not at all challenging and 5-Very challenging} &\textbf{Difference}\footnote{difference perceived by the participant as the movement progressed from \textit{source} to \textit{target}} &\textbf{Usefulness of embedded object}\footnote{on a five-point Likert Scale 1-Not at all useful and 5-Very useful} &\textbf{Point toughest to reach}\footnote{brackets indicate the Segment number corresponding to the point} \\
\midrule
PID1&2&Yes&3&6 (Seg 5)\\
PID2&4&No&5&2 (Seg 1)\\
PID3&3&Yes&4&4 (Seg 3)\\
PID4&3&No&4&2 (Seg 1)\\
\bottomrule
\end{tabularx}
\label{questionnaire}
\end{minipage}
\end{table}
\end{document}
*File List*
IEEEtran.cls 2012/11/21 V1.8c by Harald Hanche-Olsen and Anders Christensen
ot1ptm.fd 2001/06/04 font definitions for OT1/ptm.
tabularx.sty 1999/01/07 v2.07 tabularx' package (DPC)
array.sty 2008/09/09 v2.4c Tabular extension package (FMi)
booktabs.sty 2005/04/14 v1.61803 publication quality tables
Not sure where things are going wrong?
• Welcome to TeX.sx! Please complement your code to a minimal working example (MWE) illustrating your problem. It will be much easier for us to reproduce your situation and find out what the issue is when we see compilable code, starting with \documentclass{...} and ending with \end{document}. If I compile your current code with tabularx and booktabs, the footnotes are flushleft. – doncherry Jan 25 '13 at 7:15
• It turns out that IEEEtran.cls 2012/11/21 V1.8c by Harald Hanche-Olsen and Anders Christensen Is a modified IEEEtran class distributed (unfortunately) by some conference template. Deleting so that latex uses the standard IEEEtran produces a more normal layout. – David Carlisle Jan 26 '13 at 22:29
The footnote setting is controlled by the class in use (which you didn't show) Please always post complete documents. In article and IEEEtran class footnotes are set flush left but indented by 1.8em, you can remove the indent as below.
\documentclass[conference]{IEEEtran}
\usepackage{tabularx,booktabs}
\newcommand{\HRule}{\rule{\linewidth}{0.5mm}}
\newcolumntype{C}{>{\centering\arraybackslash}X}
\newcolumntype{L}{>{\raggedright\arraybackslash}X}
\makeatletter
\renewcommand\@makefntext[1]{%
\parindent 1em%
\noindent
% \hb@xt@1.8em{\hss\@makefnmark}#1}
\hbox{\hss\@makefnmark}#1}
\makeatother
\begin{document}
\begin{table}
X\dotfill X
\begin{minipage}{1\linewidth}
X\dotfill X
\centering
\caption{Questionnaire summary}
\begin{tabularx}{1\linewidth} {l c C C L}
\toprule
\textbf{PID}\footnote{Participant ID}&\textbf{Challenge}\footnote{on a five-point Likert Scale 1-Not at all challenging and 5-Very challenging} &\textbf{Difference}\footnote{difference perceived by the participant as the movement progressed from \textit{source} to \textit{target}} &\textbf{Usefulness of embedded object}\footnote{on a five-point Likert Scale 1-Not at all useful and 5-Very useful} &\textbf{Point toughest to reach}\footnote{brackets indicate the Segment number corresponding to the point} \\
\midrule
PID1&2&Yes&3&6 (Seg 5)\\
PID2&4&No&5&2 (Seg 1)\\
PID3&3&Yes&4&4 (Seg 3)\\
PID4&3&No&4&2 (Seg 1)\\
\bottomrule
\end{tabularx}
\label{questionnaire}
\end{minipage}
\end{table}
\end{document}
The above image was generated with IEEETran 1.6 (2007) the footnote code in 1.8 (2012) is slightly different but the above definition is still appropriate if you want the footnote numbers flush left, and the image is essentially unchanged. \listfiles output: (Note that this is a slightly newer version than you reported 2012/12/27 instead of 2012/11/21 , perhaps something got fixed...
*File List*
IEEEtran.cls 2012/12/27 V1.8 by Michael Shell
ot1ptm.fd 2001/06/04 font definitions for OT1/ptm.
tabularx.sty 1999/01/07 v2.07 tabularx' package (DPC)
array.sty 2008/09/09 v2.4c Tabular extension package (FMi)
booktabs.sty 2005/04/14 v1.61803 publication quality tables
• \documentclass[conference]{IEEEtran} – user24021 Jan 25 '13 at 10:19
• I am using \documentclass[conference]{IEEEtran}, your solution doesn't seem to work in my document. – user24021 Jan 25 '13 at 10:20
• Well that's why we always ask people to post complete documents in their questions. I have that class, I'll have a look what it does – David Carlisle Jan 25 '13 at 10:25
• It works for me in IEEEtran, see updated image – David Carlisle Jan 25 '13 at 10:32
• I copied and pasted the updated code into a fresh document (just the piece of code I can see in your answer), it wouldn't work. It is a two column format. And apart from the alignment of the footnotes, another difference I see in my table and your image is 'TABLE 1 QUESTIONNAIRE SUMMARY' appear in the same line, not in two lines as shown in your image. – user24021 Jan 25 '13 at 11:54 | 2020-08-06 13:59:42 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7795469164848328, "perplexity": 6942.836838194036}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-34/segments/1596439736962.52/warc/CC-MAIN-20200806121241-20200806151241-00431.warc.gz"} |
https://www.dcode.fr/base-26-cipher | Search for a tool
Base 26 Cipher
Tool to decrypt/encrypt in Base 26. Base 26 uses 26 symbols, by using the alphabet's letter, Base 26 cipher can encrypt words with numbers and conversely.
Results
Base 26 Cipher -
Tag(s) : Cryptography, Arithmetics
Share
dCode and you
dCode is free and its tools are a valuable help in games, maths, geocaching, puzzles and problems to solve every day!
A suggestion ? a feedback ? a bug ? an idea ? Write to dCode!
Thanks to your feedback and relevant comments, dCode has developped the best Base 26 Cipher tool, so feel free to write! Thank you !
# Base 26 Cipher
## Base 26 Decoder/Converter
### Parameters
Value for A A=0, AA=00, Z=25, BA=26 (Recommended for maths) A=1, AA=27, Z=26, BA=53 (Recommended for crypto)
Letters order Normal Reversed (Over-encryption)
## Base 26 Encoder
### Parameters
Value for A A=0, AA=00, Z=25, BA=26 (Recommended for maths) A=1, AA=27, Z=26, BA=53 (Recommended for crypto)
Letters order Normal Reversed (Over-encryption)
Tool to decrypt/encrypt in Base 26. Base 26 uses 26 symbols, by using the alphabet's letter, Base 26 cipher can encrypt words with numbers and conversely.
### How to encrypt using Base 26 cipher
The encoding with hexavigesimal (base 26 name) uses an arithmetic base change from base 26 to base 10. The words are considered as written in base 26 (with 26 symbols: the 26 letters of the alphabet ABCDEFGHIJKLMNOPQRSTUVWXYZ) and converted to base 10.
Example: To code DCODE, written in base 26, convert it to base 10: D=3, C=2, O=14, D=3, E=4 so $3 \times 26^4 + 2 \times 26^3 + 14 \times 26^2 + 3 \times 26^1 + 4 \times 26^0 = 1415626$
This method is the most rigorous mathematically, but can raise problems for encrypting words starting with A (which corresponds to the 0 symbol in base 10) and is thus generally ignored at the beginning of the number (001 = 1). It is sometimes considered to use 'A = 1' for some applications in cryptography.
### How to decrypt Base 26 cipher
Hexavigesimal (base26) decryption consists of the conversion from the base 10 to the base 26 (using the words as hexavigesimal numbers with the 26 letters of the alphabet as base symbols).
Example: $1415626 = 3 \times 26^4 + 2 \times 26^3 + 14 \times 26^2 + 3 \times 26^1 + 4 \times 26^0$ so [3,2,14,3,4] in base 26 and 3=D, 2=C, 14=O, 3=D, 4=E. The plain message is DCODE.
### How to recognize a Base 26 ciphertext?
The ciphered message is made of numbers, relatively big (for long words)
Usual word can appears multiple times with the same value in a long text.
### What is the reverse order letters option?
Rather than converting normally, the reverse order of letters can be considered (or the word reversed):
Example: DCODE = $3 \times 26^0 + 2 \times 26^1 + 14 \times 26^2 + 3 \times 26^3 + 4 \times 26^4 = 1890151$ (this is equivalent to coding EDOCD).
### How to deal with messages starting with 'A'?
as A is encoded 0 in base 26, when encoding it is null and disappear when decoding.
Example: AB = 0*26^1+1*26^0 = 1 and 1 = B
Add a zero at the beginning of a number to indicate a A at the beginning of a word.
## Source code
dCode retains ownership of the source code of the script Base 26 Cipher online. Except explicit open source licence (indicated Creative Commons / free), any algorithm, applet, snippet, software (converter, solver, encryption / decryption, encoding / decoding, ciphering / deciphering, translator), or any function (convert, solve, decrypt, encrypt, decipher, cipher, decode, code, translate) written in any informatic langauge (PHP, Java, C#, Python, Javascript, Matlab, etc.) which dCode owns rights will not be released for free. To download the online Base 26 Cipher script for offline use on PC, iPhone or Android, ask for price quote on contact page ! | 2020-04-05 09:42:27 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.27137815952301025, "perplexity": 5524.63922933036}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-16/segments/1585371576284.74/warc/CC-MAIN-20200405084121-20200405114121-00487.warc.gz"} |
http://www.r-bloggers.com/vci-the-value-charts-indicator/ | # VCI — The Value Charts Indicator
August 23, 2014
By
So recently, I was made known of the Value Charts Indicator , which was supposed to be some form of alternative to the RSI. I decided to investigate it, and see if it’s worth using.
Before diving into a strategy, here’s how the indicator works:
"VCI" <- function(OHLC, nLookback=40, nRange=8, pctRank=FALSE) {
if(nLookback > 7) {
varA <- runMax(Hi(OHLC), nRange) - runMin(Lo(OHLC), nRange)
varB <- lag(varA, nRange+1)
varC <- lag(varA, nRange*2)
varD <- lag(varA, nRange*3)
varE <- lag(varA, nRange*4)
LRange <- (varA+varB+varC+varD+varE)/25
}
if(nLookback <=7) {
absDiff <- abs(diff(Cl(OHLC)))
dailyRange <- Hi(OHLC) - Lo(OHLC)
tmp <- cbind(absDiff, dailyRange)
maxTmp <- pmax(tmp)
LRange <- SMA(maxTmp, 5)*.16
}
hilo <- (Hi(OHLC)+Lo(OHLC))/2
VO <- (Op(OHLC)-SMA(hilo, nLookback))/LRange
VH <- (Hi(OHLC)-SMA(hilo, nLookback))/LRange
VL <- (Lo(OHLC)-SMA(hilo, nLookback))/LRange
VC <- (Cl(OHLC)-SMA(hilo, nLookback))/LRange
out <- cbind(VO=VO, VH=VH, VL=VL, VC=VC)
colnames(out) <- c("VO", "VH", "VL", "VC")
return(out)
}
Long story short, if the lookback period is 8 bars or more, it is something akin to an average of various five lagged ranges, over five times the specified range. That is, define your first range computation as the difference between the highest high and lowest low, and then average that with that same computation lagged by nRange+1 bars, nRange*2 bars, and so on. At a shorter frame than 8 bars (that is, a special case), the computation is a moving average of the daily maximum between the daily range and the close-to-close range (E.G. with a high of 4 and low of 2, with close of 3 and previous close of 2, that daily value will be equal to 4-2=2), and then take a 5 period SMA of that, and multiply by .16. Although the initial indicator had the range dependent on the lookback period, I chose to decouple it for greater flexibility to the user.
This range calculation is then used as a denominator of a computation that is the difference of the current price minus the SMA value of the average of an (H+L)/2 price proxy. In short, it’s a variation on a theme of the classical z-score from statistics. In other words, (X-Xbar)/(normalizing value).
This z-score is computed for all four price strands.
In my current implementation, I have not yet implemented the functionality for zero-movement bars (though that can be done by request) if anyone sees value with this indicator.
To put this indicator through its paces, I threw about as plain-standard-vanilla strategy around it. The strategy activates upon the close price greater than SMA200 (the “conventional wisdom”), and buys when the indicator crosses under -2 and exits above 2, using a lookback period of 10 days, with a range period of 2 days (the settings the indicator creator(s) had in mind were that -4/+4 was relatively oversold/overbought, with -8/+8 being extremely so). The idea here was to get a bunch of relatively short-term trades going, and use the advantage of large numbers to see how well this indicator performs.
Here’s the strategy code:
require(IKTrading)
require(quantstrat)
require(PerformanceAnalytics)
initDate="1990-01-01"
from="2003-01-01"
to=as.character(Sys.Date())
options(width=70)
source("demoData.R")
#trade sizing and initial equity settings
strategy.st <- portfolio.st <- account.st <- "VCI_test"
rm.strat(portfolio.st)
rm.strat(strategy.st)
initPortf(portfolio.st, symbols=symbols, initDate=initDate, currency='USD')
initAcct(account.st, portfolios=portfolio.st, initDate=initDate, currency='USD',initEq=initEq)
initOrders(portfolio.st, initDate=initDate)
strategy(strategy.st, store=TRUE)
#parameters
pctATR=.02
period=10
nRange=2
nLookback=10
pctRank=FALSE
sellThresh=2
nSMA=200
#indicators
arguments=list(HLC=quote(HLC(mktdata)), n=period),
label="atrX")
arguments=list(OHLC=quote(OHLC(mktdata)), nLookback=nLookback,
nRange=nRange, pctRank=pctRank),
label="vci")
arguments=list(x=quote(Cl(mktdata)), n=nSMA),
label="sma")
#signals
arguments=list(columns=c("Close", "SMA.sma"), relationship="gt"),
label="filter")
relationship="lt", cross=FALSE),
label="VCIltThresh")
arguments=list(columns=c("filter", "VCIltThresh"), cross=TRUE),
label="longEntry")
arguments=list(column="VC.vci", threshold=sellThresh,
relationship="gt", cross=TRUE),
label="longExit")
arguments=list(columns=c("Close", "SMA.sma"), relationship="lt"),
label="filterExit")
#rules
arguments=list(sigcol="longEntry", sigval=TRUE, ordertype="market",
orderside="long", replace=FALSE, prefer="Open", osFUN=osDollarATR,
type="enter", path.dep=TRUE)
arguments=list(sigcol="longExit", sigval=TRUE, orderqty="all", ordertype="market",
orderside="long", replace=FALSE, prefer="Open"),
type="exit", path.dep=TRUE)
arguments=list(sigcol="filterExit", sigval=TRUE, orderqty="all", ordertype="market",
orderside="long", replace=FALSE, prefer="Open"),
type="exit", path.dep=TRUE)
#apply strategy
t1 <- Sys.time()
out <- applyStrategy(strategy=strategy.st,portfolios=portfolio.st)
t2 <- Sys.time()
print(t2-t1)
#set up analytics
updatePortf(portfolio.st)
dateRange <- time(getPortfolio(portfolio.st)$summary)[-1] updateAcct(portfolio.st,dateRange) updateEndEq(account.st) And here are the results: > (aggPF <- sum(tStats$Gross.Profits)/-sum(tStats$Gross.Losses)) [1] 1.684617 > (aggCorrect <- mean(tStats$Percent.Positive))
[1] 69.466
> (numTrades <- sum(tStats$Num.Trades)) [1] 2801 > (meanAvgWLR <- mean(tStats$Avg.WinLoss.Ratio[tStats\$Avg.WinLoss.Ratio < Inf], na.rm=TRUE))
[1] 0.753
> print(t(durStats))
[,1]
Min 1
Q1 5
Med 9
Mean 11
Q3 14
Max 57
WMin 1
WQ1 5
WMed 8
WMean 9
WQ3 12
WMax 41
LMin 1
LQ1 5
LMed 15
LMean 15
LQ3 22
LMax 57
> SharpeRatio.annualized(portfRets)
[,1]
Annualized Sharpe Ratio (Rf=0%) 0.8951308
> Return.annualized(portfRets)
[,1]
Annualized Return 0.06821319
> maxDrawdown(portfRets)
[1] 0.108064
> round(apply.yearly(dailyRetComparison, Return.cumulative),3)
strategy SPY
2003-12-31 0.058 0.066
2004-12-31 0.056 0.079
2005-12-30 0.034 0.025
2006-12-29 0.148 0.132
2007-12-31 0.094 0.019
2008-12-31 -0.022 -0.433
2009-12-31 0.149 0.192
2010-12-31 -0.055 0.110
2011-12-30 0.072 -0.028
2012-12-31 0.072 0.126
2013-12-31 0.057 0.289
2014-08-22 0.143 0.075
> round(apply.yearly(dailyRetComparison, SharpeRatio.annualized),3)
strategy SPY
2003-12-31 2.379 3.641
2004-12-31 0.751 0.706
2005-12-30 0.476 0.238
2006-12-29 2.083 1.312
2007-12-31 0.909 0.123
2008-12-31 -0.943 -1.050
2009-12-31 2.023 0.719
2010-12-31 -0.548 0.614
2011-12-30 0.854 -0.122
2012-12-31 1.015 0.990
2013-12-31 0.655 2.594
2014-08-22 2.869 1.137
> round(apply.yearly(dailyRetComparison, maxDrawdown),3)
strategy SPY
2003-12-31 0.014 0.025
2004-12-31 0.079 0.085
2005-12-30 0.058 0.074
2006-12-29 0.068 0.077
2007-12-31 0.073 0.102
2008-12-31 0.029 0.520
2009-12-31 0.041 0.280
2010-12-31 0.108 0.167
2011-12-30 0.052 0.207
2012-12-31 0.043 0.099
2013-12-31 0.072 0.062
2014-08-22 0.047 0.058
In short, it has the statistical profile of a standard mean-reverting strategy–lots of winners, losers slightly larger than winners, losers last longer in the market than winners as well. In terms of Sharpe Ratio, it’s solid but not exactly stellar. Overall, the strategy generally sports much better risk control than the raw SPY, but the annualized return to drawdown ratio isn’t quite up to the same level as some strategies tested on this blog in the past.
This is the equity curve comparison.
The equity profile seems to be pretty standard fare–winners happen over time, but a drawdown can wipe some of them (but not all) pretty quickly, as the system continues to make new equity highs. Solid, but not stellar.
Here’s an example of the equity curve of an individual instrument (the usual XLB):
Something to note is that the indicator is fairly choppy, and does best in a strong uptrend, when terms like oversold, pullback, and so on, are actually that, as opposed to a change in trend, or a protracted cyclic downtrend in a sideways market.
Here’s a picture of the strategy on XLB in 2012.
As you can see, the indicator at the 2-bar range isn’t exactly the smoothest, but with proper position-sizing rules (I use position sizing based on a 10-day ATR), the disadvantage of chopping across a threshold can be largely mitigated.
OVerall, while this indicator doesn’t seem to be much better than the more conventional RSIs, it nevertheless seems to be an alternative, and for those that want to use it, it’s now in my IKTrading package. | 2014-11-23 14:45:14 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 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": 0.6772896647453308, "perplexity": 13739.208738945033}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-49/segments/1416400379520.45/warc/CC-MAIN-20141119123259-00219-ip-10-235-23-156.ec2.internal.warc.gz"} |
http://www.forkosh.com/latex/ltx-79.html | ## verbatim
\begin{verbatim}
text
\end{verbatim}
or
\begin{verbatim*}
text
\end{verbatim*}
The verbatim environment is a paragraph-making environment that gets LaTeX to print exactly what you type in. It turns LaTeX into a typewriter with carriage returns and blanks having the same effect that they would on a typewriter. The output looks exactly as it looks in the input file.
The difference between verbatim and verbatim* is that the latter prints spaces as "visual" spaces, i.e., a short, squat "u".
The only text which cannot be placed in the verbatim environment is the 14-character sequence "\end{verbatim}".
The verbatim environment may not be used in the argument of another command. However, it can be placed inside a minipage environment which allows you to manipulate its placement.
Also see \verb | 2018-12-12 14:11:56 | {"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": 0.9918512105941772, "perplexity": 2976.3976553277175}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-51/segments/1544376823895.25/warc/CC-MAIN-20181212134123-20181212155623-00507.warc.gz"} |
https://injuryprevention.bmj.com/content/25/5/350.full | Article Text
Neighbourhood alcohol environment and injury risk: a spatial analysis of pedestrian injury in Baltimore City
Free
1. Elizabeth D Nesoff1,
3. Keshia M Pollack3,
4. Frank C Curriero4,
5. Janice V Bowie5,
6. Amy R Knowlton5,
7. Andrea C Gielen5,
8. Debra M Furr-Holden6
1. 1 Department of Epidemiology, Columbia University Mailman School of Public Health, New York, USA
2. 2 Department of Mental Health, Johns Hopkins Bloomberg School of Public Health, Baltimore, Maryland, USA
3. 3 Department of Health Policy and Management, Johns Hopkins Center for Injury Research and Policy, Johns Hopkins Bloomberg School of Public Health, Baltimore, Maryland, USA
4. 4 Department of Epidemiology, Johns Hopkins Bloomberg School of Public Health, Baltimore, Maryland, USA
5. 5 Department of Health, Behavior, and Society, Johns Hopkins Center for Injury Research and Policy, Johns Hopkins Bloomberg School of Public Health, Baltimore, Maryland, USA
6. 6 Department of Epidemiology and Biostatistics, Michigan State University College of Human Medicine, Flint, Michigan, USA
1. Correspondence to Dr Elizabeth D Nesoff, Department of Epidemiology, Columbia University Mailman School of Public Health, New York, NY 10032, USA; EN2408{at}cumc.columbia.edu
## Abstract
Objectives The purpose of this study was to investigate the contribution of neighbourhood disorder around alcohol outlets to pedestrian injury risk.
Methods A spatial analysis was conducted on census block groups in Baltimore City. Data included pedestrian injury EMS records from 1 January 2014 to 15 April 2015 (n=858), off-premise alcohol outlet locations for 2014 (n=693) and neighbourhood disorder indicators and demographics. Negative binomial regression models were used to determine the relationship between alcohol outlet count and pedestrian injuries at the block group level, controlling for other neighbourhood factors. Attributable risk was calculated by comparing the total population count per census block group to the injured pedestrian count.
Results Each one-unit increase in the number of alcohol outlets was associated with a 14.2% (95% CI 1.099 to 1.192, P<0.001) increase in the RR of neighbourhood pedestrian injury, adjusting for traffic volume, pedestrian volume, population density, per cent of vacant lots and median household income. The attributable risk was 10.4% (95% CI 7.7 to 12.7) or 88 extra injuries. Vacant lots was the only significant neighbourhood disorder indicator in the final adjusted model (RR=1.016, 95% CI 1.007 to 1.026, P=0.003). Vacant lots have not been previously investigated as possible risk factors for pedestrian injury.
Conclusions This study identifies modifiable risk factors for pedestrian injury previously unexplored in the literature and may provide evidence for alcohol control strategies (eg, liquor store licencing, zoning and enforcement).
• alcohol
• pedestrian
• geographical / spatial analysis
• urban
View Full Text
## Introduction
The majority of pedestrian injuries occur in urban areas,1 yet the distribution of pedestrian injuries and injury risk factors across neighbourhoods is not uniform.2–4 Injury events disproportionately cluster in census tracts with higher rates of unemployment, lower educational levels, lower incomes and more non-white residents.4 5 While the unequal distribution of risk factors such as traffic volume4 and traffic safety infrastructure6 may account for some of this discrepancy, they may not completely explain the antecedents of the high burden of pedestrian injuries in resource-deprived neighbourhoods.
The distribution of alcohol outlets across communities may help explain the inequitable distribution of pedestrian injuries across urban areas.4 Resource-deprived census tracts and predominantly black census tracts have significantly more liquor stores per capita than more affluent communities and predominantly white communities.7 8 Alcohol outlets, particularly off-premise packaged goods stores, are often surrounded by signs of social and physical disorder.9 10 Physical disorder is the deterioration of the urban landscape—including graffiti, litter and vacant lots—while social disorder indicates behaviour that may be considered threatening, such as verbal harassment on the street or public intoxication.11 The accumulation of these social and physical conditions around alcohol outlets are often viewed as troublesome and potentially threatening by residents and visitors, who may drive or cross the street unsafely to avoid this undesirable activity.12–14 No studies have investigated the impact of neighbourhood disorder around alcohol outlets on pedestrian injury risk.
We conceptualise the mechanisms by which alcohol outlets and neighbourhood physical and social disorder impact pedestrian injury risk using the concept of reciprocal determinism from Social Cognitive Theory—the dynamic interaction of the person, the behaviour and the environment in which the behaviour is performed.15 In this conceptual model, we propose that structural/environmental factors, interpersonal relationships and individual cognitive and biological events may manifest in pedestrian and driver behaviour (figure 1). The scope of this study focuses on the structural-level factors that contribute to pedestrian injuries in areas around alcohol outlets.
Figure 1
Conceptual model illustrating the mechanisms by which alcohol outlets and neighbourhood physical and social disorder impact pedestrian injury risk.
The purpose of this study was to investigate the impact of alcohol outlets on the neighbourhood RR of pedestrian injury. We hypothesised that increased numbers of alcohol outlets in a neighbourhood would correspond with increased RR for pedestrian injuries. We also aimed to investigate indicators of neighbourhood physical and social disorder as possible contributors to neighbourhood pedestrian injury risk. We hypothesised that neighbourhoods with greater physical and social disorder would also experience greater RR for pedestrian injury.
## Methods
This research was approved by the Institutional Review Board at the Johns Hopkins Bloomberg School of Public Health.
### Data sources
Pedestrian injury data were gathered through emergency medical services (EMS) records collected from 1 January 2014 to 15 April 2015 (n=848). The Baltimore City Fire Department operates the city’s EMS system; as Baltimore City is served by a single EMS system, these data are representative of all EMS calls for pedestrian injuries. Paramedics on the scene confirmed that the injury was caused by an MVC. Drug and alcohol use indicators were recorded for only 23% (n=194) of injured pedestrians by EMS staff; positive indicators were present in 6.3% (n=53). Consequently, we were unable to stratify by intoxication status. However, a study of MVC victims admitted to a level 1 trauma centre in Baltimore City found that approximately 27% of pedestrians tested positive for alcohol use.16 We, therefore, assume that a majority of pedestrians included in this study were sober at the time of the crash.
Locations of alcohol outlets in 2014 were obtained through the Board of Liquor License Commissioners for Baltimore City. This study focused on the four licensure classes concerned with sale of package goods for off-premise consumption (n=693). On-premise and off-premise outlets differentially impact injury risk. Off-premise outlets are more strongly associated with drinking problems, crime and violence compared with outlets licenced for on-premise consumption only.17 18 Restaurants, hotels/motels, entertainment venues and non-profit private clubs were not included in this study as these establishments only allow on-premise alcohol consumption.
Neighbourhood data: assessments of the neighbourhood environment were obtained using The Neighborhood Inventory for Environmental Typology (NIfETy).19 NIfETy is a standardised inventory designed to assess characteristics of the neighbourhood environment related to violence, alcohol and other drug exposures.20 For this analysis, we used data collected from July to November 2012, the last year city-wide data collection took place; data collection took place on a random sample of 802 blocks located throughout the city. Full details of the data collection methodology and block selection can be found in Furr-Holden et al.19
Vacant lots: addresses for all vacant lots in 2015 were compiled by the Baltimore City Housing Authority (BCHA); BCHA updates its list of vacant lots twice a month for the purposes of monitoring code violations and streamlining remediation projects.21 Digital parcel maps of all lots were available through the Maryland State Department of Planning.22 Vacant lots are an important indicator of neighbourhood disorder and have significant effects on community health and safety.23 A qualitative study of vacant lots’ impact on community well-being found that vacant lots overshadowed positive aspects of the community, eroding community cohesion, attracting crime and increasing residents’ fear and anxiety.14 To calculate per cent of vacant lots per census block group, we aggregated the count of vacant lots and the count of all lots to each census block group. We then divided the number of vacant lots by the total number of lots to calculate the per cent of vacant lots in each block group.
Pedestrian safety infrastructure: no comprehensive database cataloguing Baltimore City’s traffic safety infrastructure exists, in part because of the logistical and methodological challenges of maintaining such a database.24 The Inventory for Pedestrian Safety Infrastructure (IPSI) is a standardised instrument designed to assess the presence of street-level infrastructure for preventing pedestrian injury.25 The IPSI includes three domains: roadway features, midblock features, and intersection features. The majority of items had good or excellent levels of inter-rater reliability (intraclass correlation coefficient (ICC)≥0.8), with intersection features showing the highest agreement across raters.25 The IPSI also has been validated for use with Google Street View (GSV) in place of in-person data collection; GSV images are time-stamped with the month and year an image was processed, and many locations allow the user to travel back in time to every previous image taken at a location. Full details of the IPSI tool creation and validation and data collection methodology can be found in Nesoff et al.25
Data collection took place on the same sample of 802 blocks selected by the NIfETy sampling methodology. IPSI data were collected from December to February 2017, but IPSI measures were collected for images taken on or before April 2015 to coincide with the dates of EMS data collection.
Traffic volume: traffic volume is an important predictor of pedestrian injury risk.4 26 Average Daily Traffic Volume for 2013—the most recent year of data availability—was collected by the Maryland State Highway Administration’s Traffic Monitoring System.27 Traffic counts are recorded at a specific point on the roadway referred to as a ‘count station’ but extrapolated to represent the entire segment or section of roadway by a linear referencing system integration process. These data are then mapped for use as both a point file and a segment file. There are 752 count stations in Baltimore City; 168 (22.3%) count stations located on highways were excluded to create a measure of residential traffic volume. For this study, we used Annual Average Daily Traffic (AADT) so as to include a measure of weekend traffic flow. AADT represents a typical traffic volume count any time or day of the year at a count station. We used the join function in ArcGIS V.10.4 to join segment data to each census block group to calculate an average of AADT values for each census block group. Traffic volume was measured in units of 1000 vehicles to better facilitate interpretation of coefficients.
Walk Scores for Baltimore neighbourhoods were obtained from Live Baltimore.28 Walk Score is a commercially available walkability index calculated by mapping out the distance to amenities in nine different categories, including grocery stores, restaurants, shopping, coffee shops, banks, parks, schools, book stores/libraries and entertainment venues.29 Walk Score serves as a proxy measure for pedestrian volume as higher Walk Scores are correlated with higher volumes of pedestrians.30 A high walkability score (on a scale of 0–100) signifies that daily errands can be easily performed on foot, while lower scores indicate a neighbourhood’s automobile dependence.
Demographic variables for each census block group in Baltimore City (n=653), including population totals and median household income, were taken from 2014 Census estimates.31 Increased population density and median household income have been associated with reduced pedestrian injury risk in previous research.4 32 Population density was calculated by taking each block group’s total population and dividing by the block group’s area in square miles. Population density was measured in units of 1000 residents, and median household income was measured in units of 1000 to better facilitate interpretation of coefficients. ### Measures #### Physical disorder and social activity scales Eighteen binary items from the NIfETy, used in previous analyses, were used to classify the neighbourhood physical and social environment.33–36 Physical disorder included broken windows; abandoned buildings; vacant houses; vacant lots; unmaintained properties; broken bottles; graffiti; evidence of vandalism; presence of intoxicated people, signs of using alcohol/drugs or signs of drug selling; syringes or vials; baggies, blunt guts/wrappers or pot roaches; and alcohol bottles. Social activity included youth playing, youth sitting in a group, youth in transit, positive adult interactions, adults sitting on steps and adults watching youth. Items were summed to create two scales. Physical disorder score ranged from 0 to 12, with higher scores indicating higher levels of physical disorder (Cronbach’s alpha=0.79). Social activity score ranged from 0 to 6, with higher scores indicating higher levels of positive social activity (Cronbach’s alpha=0.66). #### Intersection and roadway safety infrastructure scales Two four-item scales were developed from IPSI to measure safety infrastructure at intersections and roadways using Exploratory Factor Analysis (see Nesoff et al for scale development details).25 Intersection items include: number of marked crosswalks at an intersection at the site of a walk signal, stop light or stop sign; number of streets with traffic lights; number of pedestrian crossing signals; and number of streets with stop line set back from crosswalk.25 Roadway items include: number of street lanes, presence of driveways, on-street parking (parallel or diagonal/back-in parking); and presence of bus stops.25 Items were summed to create two infrastructure scales. Intersection scores ranged from 0 to 21, with higher scores indicating more infrastructure at intersections (Cronbach’s alpha=0.86).25 Roadway scores ranged from 0 to 8, with higher scores indicating more infrastructure on roadways (Cronbach’s alpha=0.60).25 #### Spatial lag of traffic volume Rather than use the average AADT in a census block group, we estimated the spatial lag. Traffic on one road is spatially autocorrelated with traffic on adjoining roads because traffic flows through adjoining roadways; likewise, traffic in a census block group is spatially autocorrelated with traffic in the adjoining block groups. The spatial lag accounts for traffic volume in the surrounding census block groups, creating a weighted average of traffic volume over the local area. This smooths census block group traffic volume and allows for a more effective estimation of average traffic volume in each census block group.37 ### Data analyses #### Statistical analysis The unit of analysis for all analyses was the census block group (n=653). Locations of pedestrian injuries and alcohol outlets were geocoded and mapped in ArcGIS V.10.4. To assess the initial hypothesis of a relationship between locations of pedestrian injuries and alcohol outlets, we mapped kernel intensity estimates to assess geographic variability among alcohol outlets and pedestrian injuries and calculated the Cross K function to assess clustering of pedestrian injuries around the fixed locations of alcohol outlets using R V.3.3.38 We then aggregated each variable to the census block group level using the join tool in ArcGIS to compute the count of pedestrian injuries and alcohol outlets per block group so as to assess neighbourhood effects. We performed Poisson regression in R, analysing the counts of pedestrian injuries per census block group. We first assessed the univariate relationship between count of pedestrian injuries and each covariate of interest. Covariates found to be significant in univariate analysis were then assessed in the multivariate model, adding each control variable in a stepwise fashion. As each control variable was added, we calculated overdispersion statistics and Residual Moran’s I (RMI) to assess residual spatial variation not accounted for by the model’s covariates.38 We also calculated Akaike’s information criterion (AIC) for each model to select the best-fitting and most parsimonious model.38 Because the best-fitting Poisson model was overdispersed with significant unexplained spatial variation, we repeated model selection with the negative binomial distribution using the same stepwise system of covariate selection. Negative binomial regression derives as an alternative to Poisson regression that accommodates overdispersion. We again calculated AIC and RMI to assess residual spatial variation and model fit. The final multivariate model presented here represents the best-fitting, most parsimonious model with the least residual spatial variation according to the above criteria. To calculate pedestrian injury risk attributable to the presence of alcohol outlets, we compared population count per census block group to injured pedestrian count using the attribrisk package in R.39 In this analysis, every city resident has the potential to experience an injury. The characteristics of the census block in which a person resides influence the injury risk for every city resident. We calculated the baseline injury risk assuming no alcohol outlets in Baltimore City but controlling for population density, per cent of vacant lots, traffic volume lag, median household income and Walk Score. We next included alcohol outlets and compared the baseline pedestrian injury risk to the outlet-included injury risk. #### Missing data We aggregated the physical disorder, social activity, roadway and intersection infrastructure scales, as well as Walk Score, to the census block group level using the join tool in ArcGIS. Because of the small size of census block groups and the financial and temporal limitations of street sampling, 123 (18.8%) block groups lacked measures for physical disorder, social activity, roadway and intersection scales. We performed ordinary kriging to estimate a city-wide map of values for each of the four scales.38 Using a planometric map of all city streets, we assigned a kriged value for each scale to each street centroid. We then aggregated the centroid values to the block group to calculate the average estimated score for each measure for each block group. Walk Scores were only available for certain neighbourhoods, with n=33 (11.9%) neighbourhoods missing Walk Scores; Baltimore’s neighbourhood boundaries also do not align with census block group borders. We used similar methods as described above to estimate a kriged Walk Score value for each census block group. #### Sensitivity analysis The downtown neighbourhood block group contained 40 injured pedestrians and 32 alcohol outlets; in comparison, the next highest block group contained 13 injuries and 10 outlets. To assess potential biases associated with clustering, we calculated the distance from the geographic centroid of the downtown block group to the centroid of each block group in miles and assessed distance from downtown as a predictor of pedestrian injury. We also excluded the downtown block group to check that the injury–alcohol outlet relationship was not driven by the excessive number of alcohol outlets and injuries in this block group. ## Results Table 1 shows the distribution of selected characteristics across block groups. There was an average of 1.3 (SD=2.36) pedestrian injuries per block group. The count of pedestrian injuries ranged from 0 to 40, with 46% of block groups (n=301) reporting no pedestrian injuries. The highest pedestrian injury count was reported in the downtown neighbourhood with 40 injuries, followed by the adjoining block group with 13 (figure 2). The downtown block group also reported the highest count of alcohol outlets with 32, followed by two block groups in the southeastern section of the city with 12. Over half (n=365) of block groups did not contain an alcohol outlet; on average, there were 1.06 (SD=2.13) alcohol outlets per block group. Table 1 Description of selected neighbourhood characteristics by census block group (n=653) Figure 2 Distribution of pedestrian injuries and alcohol outlets by census block group for Baltimore City, 2014. Map A: count of pedestrian injuries from 1 January 2014 to 15 April 2015 by census block group (data source: Baltimore City Fire Department). Map B: count of off-premise alcohol outlets in 2014 by census block group (data source: Baltimore City Board of Liquor License Commissioners). In the univariate negative binomial regression models, there was a statistically significant relationship between count of alcohol outlets and pedestrian injuries (table 2, ‘unadjusted’ column). For each unit increase in alcohol outlets, there was a 21.1% increase in pedestrian injury risk (95% CI 1.157 to 1.273, P<0.001). Physical disorder score, social activity score and roadway infrastructure score were not significant predictors of neighbourhood pedestrian injury risk in univariate analysis (P>0.05) and were excluded from the final model. Percent of vacant lots was significantly positively correlated with physical disorder score (r=0.666, P<0.0001) and social activity score (r=0.510, P<0.0001). Table 2 Univariate and multivariate results for negative binomial regression modelling of neighbourhood pedestrian injury risk by census block group (n=653) The final multivariate model—count of alcohol outlets, per cent of vacant lots, median household income, population density, traffic volume and Walk Score—was the most parsimonious and best-fitting model (AIC=1898) and exhibited no significant residual spatial variation (RMI=0.0225, P=0.137) (table 2, ‘adjusted’ column). Alcohol outlet count remained associated with pedestrian injury risk after controlling for selected neighbourhood measures. Each unit increase in the number of alcohol outlets was associated with a 14.2% increase in neighbourhood pedestrian injury risk in the adjusted model (95% CI 1.099 to 1.192, P<0.001). In the attributable risk analysis, the pedestrian injury risk attributable to alcohol outlets was 10.4% (95% CI 7.7 to 12.7) or 88 extra injuries over baseline. Vacant lots, Walk Score, median household income, population density and traffic volume were also strong predictors of neighbourhood injury risk. Each increasing per cent of vacant lots was associated with a 1.6% (95% CI 1.007 to 1.026, P=0.003) increase in pedestrian injury risk. Each unit increase in Walk Score—a proxy measure for pedestrian volume—was associated with a 1.8% increase in neighbourhood pedestrian injury risk (95% CI 1.011 to 1.025, P<0.001). Median household income and population density were protective of neighbourhood pedestrian injury risk. Every1000 increase in income was associated with a 0.9% (RR=0.991, 95% CI 0.988 to 0.995, P<0.001) decrease in neighbourhood pedestrian injury risk. Every increase in 1000 people per square mile was associated with a 2.1% decrease in neighbourhood pedestrian injury risk (RR=0.979, 95% CI 0.970 to 0.989, P<0.001). With every increase in 1000 vehicles, neighbourhood pedestrian injury risk increased by 7.6% (95% CI 1.059 to 1.126, P<0.001).
In sensitivity analysis, the associations between alcohol outlet count and distance from the downtown outlier block group (r=−0.295, P<0.0001), and alcohol outlet count and intersection score (r=0.21, P<0.0001) showed significant correlation and multicollinearity. We substituted distance from downtown and intersection score for outlet count to assess if outlet count was a proxy measure for a different, highly correlated variable. Both models had significant unexplained spatial variation (RMIs=0.9 and 0.116, P<0.0001) and worse model fit (AICs=1974 and 1987). The removal of downtown strengthened the association between alcohol outlets and injury risk (RR=1.168, 95% CI 1.112 to 1.227, P<0.001); model fit also improved (AIC=1880). However, RMI became significant (RMI=0.046, P=0.015), indicating potential spatial variation unexplained by the covariates.
## Discussion
The objective of this study was to explore the relationship between alcohol outlets and neighbourhood pedestrian injury risk. Each increase in the number of alcohol outlets was associated with a 14.2% increase in the neighbourhood RR of pedestrian injuries in the adjusted model. Our findings suggest that there is a strong relationship between neighbourhood presence of alcohol outlets and pedestrian injury risk in Baltimore City after controlling for selected neighbourhood factors. Substituting traffic safety infrastructure measures for alcohol outlets resulted in significant unexplained spatial variation, indicating that alcohol outlets may offer a unique contribution to injury risk. These findings are consistent with previous studies of alcohol-involved crashes conducted in several metropolitan areas of varying size across the USA.40 41
We also aimed to investigate the contribution of neighbourhood physical and social disorder to the relationship between alcohol outlets and pedestrian injuries. Our measures of physical and social disorder were not significant predictors of pedestrian injury, but they were highly correlated with percent of vacant lots in a neighbourhood. Each increasing per cent of vacant lots was associated with a 1.6% increase in pedestrian injury risk; vacant lots have not been studied previously as predictors of pedestrian injury. Vacant lot remediation has been shown to significantly decrease violent crime.42 Future research will explore if greening is also associated with reduced pedestrian injury risk.
Although neighbourhood disorder measures were not significant predictors, median household income was protective of injury risk—consistent with previous research that demonstrated an inverse relationship between income and average number of injured pedestrians in a census tract.4 This finding contributes to the literature on the inequitable distribution of pedestrian injuries and injury risk factors across urban areas.3 5 Future research should investigate the mechanisms by which neighbourhood income is protective of pedestrian injury risk.
### Limitations
This study is cross-sectional and, therefore, does not allow for discussion of changes in the injury risk environment over time. We were unable to consistently identify alcohol-involved or drug-involved pedestrian crashes as these indicators were rarely recorded by EMS staff. It is possible that intoxication confounds the relationship between neighbourhood pedestrian injury risk and alcohol outlets; this association will be further investigated in future studies. Because the data on neighbourhood physical and social disorder were collected several years before the injury data, it is possible that these data do not accurately reflect neighbourhood physical and social disorder at the time of a pedestrian-involved crash. However, several studies have suggested that neighbourhood disorder is relatively stable and neighbourhood-level changes related to disorder can take 10–15 years to manifest.43 44
Neighbourhoods with more alcohol outlets may be visited by people looking to purchase or consume alcohol, and the high RR of pedestrian injury in these neighbourhoods may relate to this alcohol-related traffic.8 As we did not have access to the pedestrians’ residential addresses, non-residents may be included in injury counts. This also has implications for the simulated attributable risk, which assumes that the pool of pedestrians capable of being injured are all city residents and that injury risk is static based on the characteristics of their home census block group. Nevertheless, previous studies have shown that the majority of pedestrians are struck within a mile of their home,45 46 suggesting that injured pedestrians are representative of the neighbourhoods in which they are struck. Furthermore, because of the limitations inherent in data collection on pedestrians, calculations of injury risk are often based on estimates from readily available data sources such as census data or travel surveys.47 It is also possible that alcohol outlets are located in retail areas with heavy pedestrian traffic. Future research will compare pedestrian injury risk around alcohol outlets to the RR around other, similar retail outlets that do not sell alcohol.
## Conclusions
This study reinforces the importance of alcohol outlets in understanding neighbourhood pedestrian injury risk and identifies possible modifiable risk factors for preventing pedestrian injury. This research may provide evidence for informing alcohol control policy decisions (eg, liquor store licencing, zoning and enforcement). A deeper understanding of the mechanisms by which alcohol outlets impact pedestrian injury risk will be essential for creating targeted, evidence-based safety interventions.
### What is already known on the subject
• The distribution of pedestrian injuries across urban neighbourhoods is not equal.
• Alcohol outlets are associated with increased violent injury and crime.
• Alcohol outlets in a neighbourhood increase the risk of pedestrian injury, even if the pedestrian and/or the driver are sober.
• Vacant lots in a neighbourhood may be an important predictor of pedestrian injury not explored in previous research.
## Acknowledgments
The authors would like to thank Alex Freed and Brian Weir for their support in preparing this manuscript.
View Abstract
## Footnotes
• Contributors All authors have complied with the principles of the ethical practice of public health and contributed substantially to the conception and design or analysis and interpretation of data. Specifically, EDN designed the research questions in collaboration with coauthors, conducted all data analysis, created the first draft of the manuscript, made substantial edits in the subsequent drafts and approved the final submitted draft. KMP and FCC participated in the design of the study, made substantial edits to drafts of the manuscript and approved the final submitted draft. ARK and AJM acquired the data, made substantial contributions to the interpretation of data and results and approved the final submitted draft. AJM, JVB and ACG made substantial contributions to the conceptualisation of the data analytic plan and interpretation of results, reviewed and revised the manuscript critically for important intellectual content and approved the final submitted draft. Each author certifies that he or she has participated sufficiently in the work to believe in its overall validity and take public responsibility for all of its content.
• Funding This work was supported by the National Institute on Alcohol Abuse and Alcoholism (Grant Numbers R01-AA015196 and F31AA023716), the Centers for Disease Control and Prevention (Grant Number 1U49CE000728) and the National Institute on Drug Abuse (Grant Number R34DA034314).
• Competing interests None declared.
• Patient consent Not required.
• Ethics approval This research was approved by the Institutional Review Board at the Johns Hopkins Bloomberg School of Public Health and deemed non-human subjects research.
• Provenance and peer review Not commissioned; externally peer reviewed.
• Data sharing statement The data that support the findings of this study are available from the Baltimore City Fire Department (BCFD), but restrictions apply to the availability of these data, which were used under licence for the current study and so are not publicly available. Data are however available from the authors upon reasonable request and with permission of BCFD.
## Request Permissions
If you wish to reuse any or all of this article please use the link below which will take you to the Copyright Clearance Center’s RightsLink service. You will be able to get a quick price and instant permission to reuse the content in many different ways. | 2020-10-22 21:03:14 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.21747516095638275, "perplexity": 5807.212150252876}, "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/1603107880038.27/warc/CC-MAIN-20201022195658-20201022225658-00459.warc.gz"} |
http://www.mathnet.ru/php/archive.phtml?jrnid=mzm&wshow=issue&year=2002&volume=71&volume_alt=&issue=6&issue_alt=&option_lang=eng | Matematicheskie Zametki
RUS ENG JOURNALS PEOPLE ORGANISATIONS CONFERENCES SEMINARS VIDEO LIBRARY PACKAGE AMSBIB
General information Latest issue Forthcoming papers Archive Impact factor Subscription Guidelines for authors License agreement Submit a manuscript Search papers Search references RSS Latest issue Current issues Archive issues What is RSS
Mat. Zametki: Year: Volume: Issue: Page: Find
On the Stability of Diagonal ActionsI. V. Arzhantsev 803 Remarks on Mean Convergence (Boundedness) of Partial Sums of Trigonometric SeriesA. S. Belov 807 The “Duck Survival” Problem in Three-Dimensional Singularly Perturbed Systems with Two Slow VariablesA. S. Bobkova, A. Yu. Kolesov, N. Kh. Rozov 818 Algebraic Relations between the Hypergeometric E-Function and Its DerivativesV. Kh. Salikhov, G. G. Viskina 832 Fractional Differences and Lizorkin–Triebel SpacesN. L. Kudryavtsev 845 Nonexistence of Solutions of Elliptic Differential Inequalities in Conic DomainsG. G. Laptev 855 On the Convergence of Solutions of Singularly Perturbed Boundary-Value Problems for the Laplace OperatorM. Yu. Planida 867 Completeness of the Root Function System of a Nonlocal Problem in $L_p$V. V. Pod'yapol'skii 878 On Infinite Systems of Linear Autonomous and Nonautonomous Stochastic EquationsT. S. Rybnikova 890 Hugoniót–Maslov Conditions for Vortex Singular Solutions of the Shallow Water EquationsE. S. Semenov 902 Dilations, Product Systems, and Weak DilationsM. Skeide 914 Subnormal Structure of Two-Dimensional Linear Groups over Full RingsS. Tazhetdinov 924 A Discrete Analog of Euler's Summation FormulaA. V. Ustinov 931 An Extremal Problem about Probability DistributionsÈ. È. Shnol' 937 Brief Communications The Maslov Complex Germ in the Case of a Degenerate Rest Point of the HamiltonianO. V. Man'ko 946 On the Milnor Number of an Equivariant SingularityS. P. Chulkov 950 | 2021-06-13 14:12:02 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 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": 0.3674940764904022, "perplexity": 2940.751908803189}, "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-2021-25/segments/1623487608856.6/warc/CC-MAIN-20210613131257-20210613161257-00007.warc.gz"} |
http://mlweb.loria.fr/book/en/knn.html | # K-nearest neighbors
## In words...
The $K$-nearest neighbors algorithm implements a very natural idea for classification: given a point, classify it as the closest point in the training set (for which we know the label). Since this procedure can be very sensitive to the labels of points in the training set, it is rather error prone with small training sets (remember that unless we are in the deterministic case, the label of a point can only be correct up to a certain probability). To improve the robustness of the method, we predict the label of a point by looking at the majority class among a given number of the nearest neighbors of the point.
The $K$-nearest neighbors algorithm also enjoys a more formal justification. It can be interpreted as an empirical approximation of the Bayes classifier. More precisely, the algorithm estimates the probability of the input point being in a class by computing the fraction of training points of this class in the vicinity of the point. Then, the same decision rule as the one used by the Bayes classifier is applied: the class corresponding to the maximal probability is retained for the prediction; and this class is the majority class among the neighbors.
This algorithm has one major hyperparameter, which is the number of neighbors to look at. When this number is close to one, the classification is very sensitive to the training data. By increasing the number of neighbors, the classification corresponds to a compromise among the neighbors and the more neighbors we have, the more "average" the compromise is. Technically, this results in smoother boundaries between the classes.
The accuracy of the $K$-nearest neighbors is related to the presence in the training set of data points close to the input vector for which we want to predict the label. Though it seems that large training sets should satisfy this requirement, this is not necessarily the case in high dimension due to the so-called curse of dimensionality.
Regarding computational efficiency, the training phase of the $K$-nearest neighbors algorithm is almost instantaneous, as it only amounts to storing the training data in memory, but the memory requirement is linear in the number of data. In the test phase, when the algorithm predicts the label of a test point, the computational time can be high (linear in the number of training data and their dimension) since the algorithm computes all the distances between the test point and the training points. However, different techniques exist to reduce the number of required computations.
## In picture...
### Step-by-step illustration
Click in the plot below to add a test point and see how the algorithm computes its classification.
Training set:
$x_1$ $x_2$ label $y$ distance to test point
### Influence of the number of neighbors $K$
Click inside the plot to add data points to the training set and observe the resulting classification. Try different values of $K$ to see its influence on the classification and the smoothness of the boundaries between the classes.
Choose the label of the next point to add: (or use the mouse wheel)
Choose the number of neighbors:
### Example of application
See the pattern recognition application where you can train the system to recognize your own drawings.
## In maths...
The output of the $K$-nearest neighbors algorithm is given by $$f(\g x) = \arg\max_{y\in \mathcal{Y}} \sum_{i \in N_K(\g x)} \I{y_i = y}$$ where $N_K(\g x)$ is the set of $K$-nearest neighbors from $\g x$ in the training set $\{\g x_i\}_{i=1}^N$ and $\I{y_i = y}$ denotes the indicator function.
Depending on the choice of distance function used to compute the neighborhood $N_K(\g x)$, different variants of the algorithm can be obtained. The most common choice for Euclidean spaces $\X\subseteq \R^d$ is the Euclidean distance $$dist(\g x, \g x_i ) = \|\g x - \g x_i\|_2 = \sqrt{(\g x - \g x_i)^T (\g x - \g x_i) } ,$$ based on the Euclidean norm, but other distances or norms can also be used.
### Approximating the Bayes classifier
Consider a binary classification setting with $\Y= \{-1,+1\}$. In this case, the output of the $K$-nearest neighbors algorithm can be equivalently written as $$f(\g x) = \sign\left( \frac{1}{K} \sum_{i \in N_K(\g x)} y_i\right) ,$$ while the Bayes classifier can be written as $$t(\g x) = \sign\left( \E_{Y|X=\g x} [ Y\ |\ X=\g x] \right)$$ where $\E_{Y|X=\g x} [ Y\ |\ X=\g x]$ is known as the regression function.
With these formulations, we see that the $K$-nearest neighbors algorithm applies the same decision rule as the Bayes classifier, but with an empirical average of the observed values $y_i$ instead of the conditional expectation of $Y$. Also note that in this empirical estimate, we relax the conditioning $X=\g x$ to the condition $\g x_i\in N_K(\g x)$.
### Fast implementation
The most computationally intensive step in the $K$-nearest neighbors algorithm is the search for the nearest neighbors $N_K(\g x)$ when predicting the label of $\g x$. A straightforward search computes all distances $dist(\g x, \g x_i)$, $i=1,\dots,N$, in a number of operations that grows linearly with both $d$ and $N$.
A number of variants and techniques exist to reduce this computational cost. If the dimension $d$ is small, the training data can be stored in a structured form, typically based on a tree, in order to quickly direct the search for the nearest neighbors towards relevant subsets of points. For high-dimensional data, the trick discussed in the exercise below results in significant speed improvements.
Exercise:
1. Write down the algorithm (in pseudo-code or any programming language you like) of the straightforward search for the $K$-nearest neighbors $N_K(\g x)$ based on the Euclidean distance.
• Let $NNindexes$ be the list of the nearest neighbors indexes and $NNdistances$ the list of the corresponding distances, both initialized to empty lists and limited to $K$ elements (any element pushed to a list index larger than $K$ is assumed to be dropped from the list).
• FOR $i=1,\dots,N$,
• $dist_i \leftarrow 0$
• FOR $j=1,\dots,d$,
• $dist_i\leftarrow dist_i + (x_j - x_{ij})^2$
• $dist_i \leftarrow \sqrt{dist_i}$
• IF $i \leq K$ OR $dist_i < NNdistances(K)$, insert $i$ in $NNindexes$ and $dist_i$ in $NNdistances$. Sort $NNdistances$ in the increasing order and reorder $NNindexes$ accordingly.
2. Optimize the algorithm obtained in question 1 such that most computations are avoided in high dimension. Hint: there is a trick that requires very few modifications of the algorithm and results in drastic speed improvement with the Euclidean distance as well as any distance based on an $\ell_p$-norm.
First, note that using square distances instead of distances results in the same ordering of the points so that we can spare the square root in the algorithm above (or the $1/p$ power if we consider a distance based on an $\ell_p$-norm).
To avoid most computations, we will use the partial distance trick. The trick relies on the fact that $$\sum_{j=1}^r |x_j - x_{ij}|^p$$ is an increasing function of $r$ that equals $\|\g x - \g x_i\|_p^p$ when $r=d$. Thus, if $K$ neighbors have already been found with square distances (or distances to the power $p$) to $\g x$ smaller than the sum above for some $r < d$, we know that $\g x_i$ cannot be one of the $K$-nearest neighbors and the remaining $d-r$ terms in the sum need not be computed.
To sum up, to apply the trick in the case of the Euclidean distance, it suffices to remove the line
• $dist_i \leftarrow \sqrt{dist_i}$
in the algorithm of question 1 and to replace the FOR loop
• FOR $j=1,\dots,d$,
• $dist_i\leftarrow dist_i + (x_j - x_{ij})^2$
by the WHILE loop
• $j \leftarrow 1$
• WHILE $j \leq d$ AND ($i \leq K$ OR $dist_i < NNdistances(K)$ ),
• $dist_i\leftarrow dist_i + (x_j - x_{ij})^2$
#### Fast tuning of $K$ with leave-one-out cross validation
For the $K$-nearest neighbors algorithm, the selection of the best number of neighbors according to an estimation of the risk with the leave-one-out method can be implemented with a computational cost close to the cost of evaluating the training error.
Let $D = \{(\g x_i, y_i)\}_{i=1}^N$ be the training set and recall that, for classification, the leave-one-out estimate of the risk is $$R_{LOO}(f) = \frac{1}{N} \sum_{i=1}^N \I{ y_i \neq f_i( \g x_i ) } ,$$ where $f_i$ is the model trained on $D \setminus \{(\g x_i, y_i)\}$. For the $K$-nearest neighbors algorithm (the procedure can be similarly devised for its regression version), we have $$f_i(\g x_i) = \arg\max_{y\in \mathcal{Y}} \sum_{j \in N_{K+1}(\g x_i) \setminus \{\g x_i\} } \I{y_j = y}$$ where $N_{K+1}(\g x_i)$ is the set of $(K+1)$-nearest neighbors from $\g x_i$ in the training set from which we remove $\g x_i$ itself.
Given an upper bound $\overline{K}$ on $K$, a standard model selection procedure for tuning $K$ is to compute $R_{LOO}(f)$ for all $K\leq \overline{K}$. The most demanding computation in such a procedure is the search for the neighbors, which must be carried out $\overline{K} N$ times.
However, the implementation of the $K$-nearest neighbors search giving $N_{K+1}(\g x_i)$ can easily be made such that it returns an ordered list of neighbors with increasing distance from $\g x_i$. For any $K \leq \overline{K}$, let $N_{\overline{K}+1}(\g x_i)_{2:K+1}$ denote the list of neighbors obtained by keeping only the items of index between 2 and $K+1$ in that list. Then, the output of the $K$-nearest neighbors algorithm is given, for any $K < \overline{K}$, by $$f_i(\g x_i) = \arg\max_{y\in \mathcal{Y}} \sum_{j \in N_{\overline{K}+1}(\g x_i)_{2:K+1} } \I{y_j = y}$$ with a single search for $\overline{K}+1$ neighbors. | 2018-02-24 05:58:40 | {"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": 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": 0.7798479795455933, "perplexity": 218.6346376184295}, "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-2018-09/segments/1518891815435.68/warc/CC-MAIN-20180224053236-20180224073236-00480.warc.gz"} |
https://zbmath.org/?q=an:0647.46060 | # zbMATH — the first resource for mathematics
The semiclassical limit of quantum dynamics. I: Time evolution. (English) Zbl 0647.46060
The $$\hslash \to 0$$ limit of the quantum dynamics determined by the Hamiltonian $$H(\hslash)=-(\hslash^ 2/2m)\Delta +V$$ on $$L^ 2({\mathbb{R}}^ n)$$ is studied for a large class of potentials. By convolving with certain Gaussian states, classically determined asymptotic behavior of the quantum evolution of states of compact support is obtained. For initial states of class $$C^ 1_ 0$$ the error terms are shown to have $$L^ 2$$ norms of order $$\hslash^{-\epsilon}$$ for arbitrarily small positive $$\epsilon$$.
##### MSC:
46N99 Miscellaneous applications of functional analysis 81Q05 Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics
Full Text:
##### References:
[1] DOI: 10.1007/BF01230088 · doi:10.1007/BF01230088 [2] DOI: 10.1016/0003-4916(81)90143-3 · doi:10.1016/0003-4916(81)90143-3 [3] Hagedorn G. A., Ann. Inst. H. Poincaré 42 pp 363– (1985) [4] DOI: 10.1016/0003-4916(58)90032-0 · Zbl 0085.43103 · doi:10.1016/0003-4916(58)90032-0 [5] DOI: 10.1002/cpa.3160140303 · Zbl 0107.09102 · doi:10.1002/cpa.3160140303
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching. | 2021-03-08 04:04:25 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 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": 0.41724181175231934, "perplexity": 2076.1828567454763}, "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-2021-10/segments/1614178381803.98/warc/CC-MAIN-20210308021603-20210308051603-00478.warc.gz"} |
https://ruder.io/deep-learning-nlp-best-practices/ | This post gives an overview of best practices relevant for most tasks in natural language processing.
Introduction
This post is a collection of best practices for using neural networks in Natural Language Processing. It will be updated periodically as new insights become available and in order to keep track of our evolving understanding of Deep Learning for NLP.
There has been a running joke in the NLP community that an LSTM with attention will yield state-of-the-art performance on any task. While this has been true over the course of the last two years, the NLP community is slowly moving away from this now standard baseline and towards more interesting models.
However, we as a community do not want to spend the next two years independently (re-)discovering the next LSTM with attention. We do not want to reinvent tricks or methods that have already been shown to work. While many existing Deep Learning libraries already encode best practices for working with neural networks in general, such as initialization schemes, many other details, particularly task or domain-specific considerations, are left to the practitioner.
This post is not meant to keep track of the state-of-the-art, but rather to collect best practices that are relevant for a wide range of tasks. In other words, rather than describing one particular architecture, this post aims to collect the features that underly successful architectures. While many of these features will be most useful for pushing the state-of-the-art, I hope that wider knowledge of them will lead to stronger evaluations, more meaningful comparison to baselines, and inspiration by shaping our intuition of what works.
I assume you are familiar with neural networks as applied to NLP (if not, I recommend Yoav Goldberg's excellent primer [1]) and are interested in NLP in general or in a particular task. The main goal of this article is to get you up to speed with the relevant best practices so you can make meaningful contributions as soon as possible.
I will first give an overview of best practices that are relevant for most tasks. I will then outline practices that are relevant for the most common tasks, in particular classification, sequence labelling, natural language generation, and neural machine translation.
Disclaimer: Treating something as best practice is notoriously difficult: Best according to what? What if there are better alternatives? This post is based on my (necessarily incomplete) understanding and experience. In the following, I will only discuss practices that have been reported to be beneficial independently by at least two different groups. I will try to give at least two references for each best practice.
Best practices
Word embeddings
Word embeddings are arguably the most widely known best practice in the recent history of NLP. It is well-known that using pre-trained embeddings helps (Kim, 2014) [2]. The optimal dimensionality of word embeddings is mostly task-dependent: a smaller dimensionality works better for more syntactic tasks such as named entity recognition (Melamud et al., 2016) [3] or part-of-speech (POS) tagging (Plank et al., 2016) [4], while a larger dimensionality is more useful for more semantic tasks such as sentiment analysis (Ruder et al., 2016) [5].
Depth
While we will not reach the depths of computer vision for a while, neural networks in NLP have become progressively deeper. State-of-the-art approaches now regularly use deep Bi-LSTMs, typically consisting of 3-4 layers, e.g. for POS tagging (Plank et al., 2016) and semantic role labelling (He et al., 2017) [6]. Models for some tasks can be even deeper, cf. Google's NMT model with 8 encoder and 8 decoder layers (Wu et al., 2016) [7]. In most cases, however, performance improvements of making the model deeper than 2 layers are minimal (Reimers & Gurevych, 2017) [8].
These observations hold for most sequence tagging and structured prediction problems. For classification, deep or very deep models perform well only with character-level input and shallow word-level models are still the state-of-the-art (Zhang et al., 2015; Conneau et al., 2016; Le et al., 2017) [9] [10] [11].
Layer connections
For training deep neural networks, some tricks are essential to avoid the vanishing gradient problem. Different layers and connections have been proposed. Here, we will discuss three: i) highway layers, ii) residual connections, and iii) dense connections.
Highway layers Highway layers (Srivastava et al., 2015) [12] are inspired by the gates of an LSTM. First let us assume a one-layer MLP, which applies an affine transformation followed by a non-linearity $g$ to its input $\mathbf{x}$:
$\mathbf{h} = g(\mathbf{W}\mathbf{x} + \mathbf{b})$
A highway layer then computes the following function instead:
$\mathbf{h} = \mathbf{t} \odot g(\mathbf{W} \mathbf{x} + \mathbf{b}) + (1-\mathbf{t}) \odot \mathbf{x}$
where $\odot$ is elementwise multiplication, $\mathbf{t} = \sigma(\mathbf{W}_T \mathbf{x} + \mathbf{b}_T)$ is called the transform gate, and $(1-\mathbf{t})$ is called the carry gate. As we can see, highway layers are similar to the gates of an LSTM in that they adaptively carry some dimensions of the input directly to the output.
Highway layers have been used pre-dominantly to achieve state-of-the-art results for language modelling (Kim et al., 2016; Jozefowicz et al., 2016; Zilly et al., 2017) [13] [14] [15], but have also been used for other tasks such as speech recognition (Zhang et al., 2016) [16]. Sristava's page contains more information and code regarding highway layers.
Residual connections Residual connections (He et al., 2016) [17] have been first proposed for computer vision and were the main factor for winning ImageNet 2016. Residual connections are even more straightforward than highway layers and learn the following function:
$\mathbf{h} = g(\mathbf{W}\mathbf{x} + \mathbf{b}) + \mathbf{x}$
which simply adds the input of the current layer to its output via a short-cut connection. This simple modification mitigates the vanishing gradient problem, as the model can default to using the identity function if the layer is not beneficial.
Dense connections Rather than just adding layers from each layer to the next, dense connections (Huang et al., 2017) [18] (best paper award at CVPR 2017) add direct connections from each layer to all subsequent layers. Let us augment the layer output $h$ and layer input $x$ with indices $l$ indicating the current layer. Dense connections then feed the concatenated output from all previous layers as input to the current layer:
$\mathbf{h}^l = g(\mathbf{W}[\mathbf{x}^1; \ldots; \mathbf{x}^l] + \mathbf{b})$
where $[\cdot; \cdot]$ represents concatenation. Dense connections have been successfully used in computer vision. They have also found to be useful for Multi-Task Learning of different NLP tasks (Ruder et al., 2017) [19], while a residual variant that uses summation has been shown to consistently outperform residual connections for neural machine translation (Britz et al., 2017) [20].
Dropout
While batch normalisation in computer vision has made other regularizers obsolete in most applications, dropout (Srivasta et al., 2014) [21] is still the go-to regularizer for deep neural networks in NLP. A dropout rate of 0.5 has been shown to be effective in most scenarios (Kim, 2014). In recent years, variations of dropout such as adaptive (Ba & Frey, 2013) [22] and evolutional dropout (Li et al., 2016) [23] have been proposed, but none of these have found wide adoption in the community. The main problem hindering dropout in NLP has been that it could not be applied to recurrent connections, as the aggregating dropout masks would effectively zero out embeddings over time.
Recurrent dropout Recurrent dropout (Gal & Ghahramani, 2016) [24] addresses this issue by applying the same dropout mask across timesteps at layer $l$. This avoids amplifying the dropout noise along the sequence and leads to effective regularization for sequence models. Recurrent dropout has been used for instance to achieve state-of-the-art results in semantic role labelling (He et al., 2017) and language modelling (Melis et al., 2017) [25].
If additional data is available, multi-task learning (MTL) can often be used to improve performance on the target task. Have a look this blog post for more information on MTL.
Auxiliary objectives We can often find auxiliary objectives that are useful for the task we care about (Ruder, 2017) [26]. While we can already predict surrounding words in order to pre-train word embeddings (Mikolov et al., 2013), we can also use this as an auxiliary objective during training (Rei, 2017) [27]. A similar objective has also been used by (Ramachandran et al., 2016) [28] for sequence-to-sequence models.
Task-specific layers While the standard approach to MTL for NLP is hard parameter sharing, it is beneficial to allow the model to learn task-specific layers. This can be done by placing the output layer of one task at a lower level (Søgaard & Goldberg, 2016) [29]. Another way is to induce private and shared subspaces (Liu et al., 2017; Ruder et al., 2017) [30] [19:1].
Attention
Attention is most commonly used in sequence-to-sequence models to attend to encoder states, but can also be used in any sequence model to look back at past states. Using attention, we obtain a context vector $\mathbf{c}_i$ based on hidden states $\mathbf{s}_1, \ldots, \mathbf{s}_m$ that can be used together with the current hidden state $\mathbf{h}_i$ for prediction. The context vector $\mathbf{c}_i$ at position is calculated as an average of the previous states weighted with the attention scores $\mathbf{a}_i$:
\begin{align}\begin{split} \mathbf{c}_i &= \sum\limits_j a_{ij}\mathbf{s}_j\\ \mathbf{a}_i &= \text{softmax}(f_{att}(\mathbf{h}_i, \mathbf{s}_j)) \end{split}\end{align}
The attention function $f_{att}(\mathbf{h}_i, \mathbf{s}_j)$ calculates an unnormalized alignment score between the current hidden state $\mathbf{h}_i$ and the previous hidden state $\mathbf{s}_j$. In the following, we will discuss four attention variants: i) additive attention, ii) multiplicative attention, iii) self-attention, and iv) key-value attention.
Additive attention The original attention mechanism (Bahdanau et al., 2015) [31] uses a one-hidden layer feed-forward network to calculate the attention alignment:
$f_{att}(\mathbf{h}_i, \mathbf{s}_j) = \mathbf{v}_a{}^\top \text{tanh}(\mathbf{W}_a[\mathbf{h}_i; \mathbf{s}_j])$
where $\mathbf{v}_a$ and $\mathbf{W}_a$ are learned attention parameters. Analogously, we can also use matrices $\mathbf{W}_1$ and $\mathbf{W}_2$ to learn separate transformations for $\mathbf{h}_i$ and $\mathbf{s}_j$ respectively, which are then summed:
$f_{att}(\mathbf{h}_i, \mathbf{s}_j) = \mathbf{v}_a{}^\top \text{tanh}(\mathbf{W}_1 \mathbf{h}_i + \mathbf{W}_2 \mathbf{s}_j)$
Multiplicative attention Multiplicative attention (Luong et al., 2015) [32] simplifies the attention operation by calculating the following function:
$f_{att}(h_i, s_j) = h_i^\top \mathbf{W}_a s_j$
Additive and multiplicative attention are similar in complexity, although multiplicative attention is faster and more space-efficient in practice as it can be implemented more efficiently using matrix multiplication. Both variants perform similar for small dimensionality $d_h$ of the decoder states, but additive attention performs better for larger dimensions. One way to mitigate this is to scale $f_{att}(\mathbf{h}_i, \mathbf{s}_j)$ by $1 / \sqrt{d_h}$ (Vaswani et al., 2017) [33].
Attention cannot only be used to attend to encoder or previous hidden states, but also to obtain a distribution over other features, such as the word embeddings of a text as used for reading comprehension (Kadlec et al., 2017) [34]. However, attention is not directly applicable to classification tasks that do not require additional information, such as sentiment analysis. In such models, the final hidden state of an LSTM or an aggregation function such as max pooling or averaging is often used to obtain a sentence representation.
Self-attention Without any additional information, however, we can still extract relevant aspects from the sentence by allowing it to attend to itself using self-attention (Lin et al., 2017) [35]. Self-attention, also called intra-attention has been used successfully in a variety of tasks including reading comprehension (Cheng et al., 2016) [36], textual entailment (Parikh et al., 2016) [37], and abstractive summarization (Paulus et al., 2017) [38].
We can simplify additive attention to compute the unnormalized alignment score for each hidden state $\mathbf{h}_i$:
$f_{att}(\mathbf{h}_i) = \mathbf{v}_a{}^\top \text{tanh}(\mathbf{W}_a \mathbf{h}_i)$
In matrix form, for hidden states $\mathbf{H} = \mathbf{h}_1, \ldots, \mathbf{h}_n$ we can calculate the attention vector $\mathbf{a}$ and the final sentence representation $\mathbf{c}$ as follows:
\begin{align}\begin{split} \mathbf{a} &= \text{softmax}(\mathbf{v}_a \text{tanh}(\mathbf{W}_a \mathbf{H}^\top))\\ \mathbf{c} & = \mathbf{H} \mathbf{a}^\top \end{split}\end{align}
Rather than only extracting one vector, we can perform several hops of attention by using a matrix $\mathbf{V}_a$ instead of $\mathbf{v}_a$, which allows us to extract an attention matrix $\mathbf{A}$:
\begin{align}\begin{split} \mathbf{A} &= \text{softmax}(\mathbf{V}_a \text{tanh}(\mathbf{W}_a \mathbf{H}^\top))\\ \mathbf{C} & = \mathbf{A} \mathbf{H} \end{split}\end{align}
In practice, we enforce the following orthogonality constraint to penalize redundancy and encourage diversity in the attention vectors in the form of the squared Frobenius norm:
$\Omega = |(\mathbf{A}\mathbf{A}^\top - \mathbf{I} |^2_F$
A similar multi-head attention is also used by Vaswani et al. (2017).
Key-value attention Finally, key-value attention (Daniluk et al., 2017) [39] is a recent attention variant that separates form from function by keeping separate vectors for the attention calculation. It has also been found useful for different document modelling tasks (Liu & Lapata, 2017) [40]. Specifically, key-value attention splits each hidden vector $\mathbf{h}_i$ into a key $\mathbf{k}_i$ and a value $\mathbf{v}_i$: $[\mathbf{k}_i; \mathbf{v}_i] = \mathbf{h}_i$. The keys are used for calculating the attention distribution $\mathbf{a}_i$ using additive attention:
$\mathbf{a}_i = \text{softmax}(\mathbf{v}_a{}^\top \text{tanh}(\mathbf{W}_1 [\mathbf{k}_{i-L}; \ldots; \mathbf{k}_{i-1}] + (\mathbf{W}_2 \mathbf{k}_i)\mathbf{1}^\top))$
where $L$ is the length of the attention window and $\mathbf{1}$ is a vector of ones. The values are then used to obtain the context representation $\mathbf{c}_i$:
$\mathbf{c}_i = [\mathbf{v}_{i-L}; \ldots; \mathbf{v}_{i-1}] \mathbf{a}^\top$
The context $\mathbf{c}_i$ is used together with the current value $\mathbf{v}_i$ for prediction.
Optimization
The optimization algorithm and scheme is often one of the parts of the model that is used as-is and treated as a black-box. Sometimes, even slight changes to the algorithm, e.g. reducing the $\beta_2$ value in Adam (Dozat & Manning, 2017) [41] can make a large difference to the optimization behaviour.
Optimization algorithm Adam (Kingma & Ba, 2015) [42] is one of the most popular and widely used optimization algorithms and often the go-to optimizer for NLP researchers. It is often thought that Adam clearly outperforms vanilla stochastic gradient descent (SGD). However, while it converges much faster than SGD, it has been observed that SGD with learning rate annealing slightly outperforms Adam (Wu et al., 2016). Recent work furthermore shows that SGD with properly tuned momentum outperforms Adam (Zhang et al., 2017) [43].
Optimization scheme While Adam internally tunes the learning rate for every parameter (Ruder, 2016) [44], we can explicitly use SGD-style annealing with Adam. In particular, we can perform learning rate annealing with restarts: We set a learning rate and train the model until convergence. We then halve the learning rate and restart by loading the previous best model. In Adam's case, this causes the optimizer to forget its per-parameter learning rates and start fresh. Denkowski & Neubig (2017) [45] show that Adam with 2 restarts and learning rate annealing is faster and performs better than SGD with annealing.
Ensembling
Combining multiple models into an ensemble by averaging their predictions is a proven strategy to improve model performance. While predicting with an ensemble is expensive at test time, recent advances in distillation allow us to compress an expensive ensemble into a much smaller model (Hinton et al., 2015; Kuncoro et al., 2016; Kim & Rush, 2016) [46] [47] [48].
Ensembling is an important way to ensure that results are still reliable if the diversity of the evaluated models increases (Denkowski & Neubig, 2017). While ensembling different checkpoints of a model has been shown to be effective (Jean et al., 2015; Sennrich et al., 2016) [49] [50], it comes at the cost of model diversity. Cyclical learning rates can help to mitigate this effect (Huang et al., 2017) [51]. However, if resources are available, we prefer to ensemble multiple independently trained models to maximize model diversity.
Hyperparameter optimization
Rather than pre-defining or using off-the-shelf hyperparameters, simply tuning the hyperparameters of our model can yield significant improvements over baselines. Recent advances in Bayesian Optimization have made it an ideal tool for the black-box optimization of hyperparameters in neural networks (Snoek et al., 2012) [52] and far more efficient than the widely used grid search. Automatic tuning of hyperparameters of an LSTM has led to state-of-the-art results in language modeling, outperforming models that are far more complex (Melis et al., 2017).
LSTM tricks
Learning the initial state We generally initialize the initial LSTM states with a $0$ vector. Instead of fixing the initial state, we can learn it like any other parameter, which can improve performance and is also recommended by Hinton. Refer to this blog post for a Tensorflow implementation.
Tying input and output embeddings Input and output embeddings account for the largest number of parameters in the LSTM model. If the LSTM predicts words as in language modelling, input and output parameters can be shared (Inan et al., 2016; Press & Wolf, 2017) [53] [54]. This is particularly useful on small datasets that do not allow to learn a large number of parameters.
Gradient norm clipping One way to decrease the risk of exploding gradients is to clip their maximum value (Mikolov, 2012) [55]. This, however, does not improve performance consistently (Reimers & Gurevych, 2017). Rather than clipping each gradient independently, clipping the global norm of the gradient (Pascanu et al., 2013) [56] yields more significant improvements (a Tensorflow implementation can be found here).
Down-projection To reduce the number of output parameters further, the hidden state of the LSTM can be projected to a smaller size. This is useful particularly for tasks with a large number of outputs, such as language modelling (Melis et al., 2017).
In the following, we will discuss task-specific best practices. Most of these perform best for a particular type of task. Some of them might still be applied to other tasks, but should be validated before. We will discuss the following tasks: classification, sequence labelling, natural language generation (NLG), and -- as a special case of NLG -- neural machine translation.
Classification
More so than for sequence tasks, where CNNs have only recently found application due to more efficient convolutional operations, CNNs have been popular for classification tasks in NLP. The following best practices relate to CNNs and capture some of their optimal hyperparameter choices.
CNN filters Combining filter sizes near the optimal filter size, e.g. (3,4,5) performs best (Kim, 2014; Kim et al., 2016). The optimal number of feature maps is in the range of 50-600 (Zhang & Wallace, 2015) [57].
Aggregation function 1-max-pooling outperforms average-pooling and $k$-max pooling (Zhang & Wallace, 2015).
Sequence labelling
Sequence labelling is ubiquitous in NLP. While many of the existing best practices are with regard to a particular part of the model architecture, the following guidelines discuss choices for the model's output and prediction stage.
Tagging scheme For some tasks, which can assign labels to segments of texts, different tagging schemes are possible. These are: BIO, which marks the first token in a segment with a B- tag, all remaining tokens in the span with an _I-_tag, and tokens outside of segments with an O- tag; IOB, which is similar to BIO, but only uses B- if the previous token is of the same class but not part of the segment; and IOBES, which in addition distinguishes between single-token entities (S-) and the last token in a segment (E-). Using IOBES and BIO yield similar performance (Lample et al., 2017)
CRF output layer If there are any dependencies between outputs, such as in named entity recognition the final softmax layer can be replaced with a linear-chain conditional random field (CRF). This has been shown to yield consistent improvements for tasks that require the modelling of constraints (Huang et al., 2015; Max & Hovy, 2016; Lample et al., 2016) [58] [59] [60].
Constrained decoding Rather than using a CRF output layer, constrained decoding can be used as an alternative approach to reject erroneous sequences, i.e. such that do not produce valid BIO transitions (He et al., 2017). Constrained decoding has the advantage that arbitrary constraints can be enforced this way, e.g. task-specific or syntactic constraints.
Natural language generation
Most of the existing best practices can be applied to natural language generation (NLG). In fact, many of the tips presented so far stem from advances in language modelling, the most prototypical NLP task.
Modelling coverage Repetition is a big problem in many NLG tasks as current models do not have a good way of remembering what outputs they already produced. Modelling coverage explicitly in the model is a good way of addressing this issue. A checklist can be used if it is known in advances, which entities should be mentioned in the output, e.g. ingredients in recipes (Kiddon et al., 2016) [61]. If attention is used, we can keep track of a coverage vector $\mathbf{c}_i$, which is the sum of attention distributions $\mathbf{a}_t$ over previous time steps (Tu et al., 2016; See et al., 2017) [62] [63]:
$\mathbf{c}_i = \sum\limits^{i-1}_{t=1} \mathbf{a}_t$
This vector captures how much attention we have paid to all words in the source. We can now condition additive attention additionally on this coverage vector in order to encourage our model not to attend to the same words repeatedly:
$f_{att}(\mathbf{h}_i,\mathbf{s}_j,\mathbf{c}_i) = \mathbf{v}_a{}^\top \text{tanh}(\mathbf{W}_1 \mathbf{h}_i + \mathbf{W}_2 \mathbf{s}_j + \mathbf{W}_3 \mathbf{c}_i )$
In addition, we can add an auxiliary loss that captures the task-specific attention behaviour that we would like to elicit: For NMT, we would like to have a roughly one-to-one alignment; we thus penalize the model if the final coverage vector is more or less than one at every index (Tu et al., 2016). For summarization, we only want to penalize the model if it repeatedly attends to the same location (See et al., 2017).
Neural machine translation
While neural machine translation (NMT) is an instance of NLG, NMT receives so much attention that many methods have been developed specifically for the task. Similarly, many best practices or hyperparameter choices apply exclusively to it.
Embedding dimensionality 2048-dimensional embeddings yield the best performance, but only do so by a small margin. Even 128-dimensional embeddings perform surprisingly well and converge almost twice as quickly (Britz et al., 2017).
Encoder and decoder depth The encoder does not need to be deeper than $2-4$ layers. Deeper models outperform shallower ones, but more than $4$ layers is not necessary for the decoder (Britz et al., 2017).
Directionality Bidirectional encoders outperform unidirectional ones by a small margin. Sutskever et al., (2014) [64] proposed to reverse the source sequence to reduce the number of long-term dependencies. Reversing the source sequence in unidirectional encoders outperforms its non-reversed counter-part (Britz et al., 2017).
Beam search strategy Medium beam sizes around $10$ with length normalization penalty of $1.0$ (Wu et al., 2016) yield the best performance (Britz et al., 2017).
Sub-word translation Senrich et al. (2016) [65] proposed to split words into sub-words based on a byte-pair encoding (BPE). BPE iteratively merges frequent symbol pairs, which eventually results in frequent character n-grams being merged into a single symbol, thereby effectively eliminating out-of-vocabulary-words. While it was originally meant to handle rare words, a model with sub-word units outperforms full-word systems across the board, with 32,000 being an effective vocabulary size for sub-word units (Denkowski & Neubig, 2017).
Conclusion
I hope this post was helpful in kick-starting your learning of a new NLP task. Even if you have already been familiar with most of these, I hope that you still learnt something new or refreshed your knowledge of useful tips.
I am sure that I have forgotten many best practices that deserve to be on this list. Similarly, there are many tasks such as parsing, information extraction, etc., which I do not know enough about to give recommendations. If you have a best practice that should be on this list, do let me know in the comments below. Please provide at least one reference and your handle for attribution. If this gets very collaborative, I might open a GitHub repository rather than collecting feedback here (I won't be able to accept PRs submitted directly to the generated HTML source of this article).
Credit for the cover image goes to Bahdanau et al. (2015).
Citation
Sebastian Ruder, "Deep Learning for NLP Best Practices". http://ruder.io/deep-learning-nlp-best-practices/, 2017.
BibTeX citation:
@misc{ruder2017deeplearningnlp,
author = {Ruder, Sebastian},
title = {{Deep Learning for NLP Best Practices}},
year = {2017},
howpublished = {\url{http://ruder.io/deep-learning-nlp-best-practices/}},
}
1. Goldberg, Y. (2016). A Primer on Neural Network Models for Natural Language Processing. Journal of Artificial Intelligence Research, 57, 345–420. https://doi.org/10.1613/jair.4992 ↩︎
2. Kim, Y. (2014). Convolutional Neural Networks for Sentence Classification. Proceedings of the Conference on Empirical Methods in Natural Language Processing, 1746–1751. Retrieved from http://arxiv.org/abs/1408.5882 ↩︎
3. Melamud, O., McClosky, D., Patwardhan, S., & Bansal, M. (2016). The Role of Context Types and Dimensionality in Learning Word Embeddings. In Proceedings of NAACL-HLT 2016 (pp. 1030–1040). Retrieved from http://arxiv.org/abs/1601.00893 ↩︎
4. Plank, B., Søgaard, A., & Goldberg, Y. (2016). Multilingual Part-of-Speech Tagging with Bidirectional Long Short-Term Memory Models and Auxiliary Loss. In Proceedings of the 54th Annual Meeting of the Association for Computational Linguistics. ↩︎
5. Ruder, S., Ghaffari, P., & Breslin, J. G. (2016). A Hierarchical Model of Reviews for Aspect-based Sentiment Analysis. Proceedings of the 2016 Conference on Empirical Methods in Natural Language Processing (EMNLP-16), 999–1005. Retrieved from http://arxiv.org/abs/1609.02745 ↩︎
6. He, L., Lee, K., Lewis, M., & Zettlemoyer, L. (2017). Deep Semantic Role Labeling: What Works and What’s Next. ACL. ↩︎
7. Wu, Y., Schuster, M., Chen, Z., Le, Q. V, Norouzi, M., Macherey, W., … Dean, J. (2016). Google’s Neural Machine Translation System: Bridging the Gap between Human and Machine Translation. arXiv Preprint arXiv:1609.08144. ↩︎
8. Reimers, N., & Gurevych, I. (2017). Optimal Hyperparameters for Deep LSTM-Networks for Sequence Labeling Tasks. In arXiv preprint arXiv:1707.06799: Retrieved from https://arxiv.org/pdf/1707.06799.pdf ↩︎
9. Zhang, X., Zhao, J., & LeCun, Y. (2015). Character-level Convolutional Networks for Text Classification. Advances in Neural Information Processing Systems, 649–657. Retrieved from http://arxiv.org/abs/1509.01626 ↩︎
10. Conneau, A., Schwenk, H., Barrault, L., & Lecun, Y. (2016). Very Deep Convolutional Networks for Natural Language Processing. arXiv Preprint arXiv:1606.01781. Retrieved from http://arxiv.org/abs/1606.01781 ↩︎
11. Le, H. T., Cerisara, C., & Denis, A. (2017). Do Convolutional Networks need to be Deep for Text Classification ? In arXiv preprint arXiv:1707.04108. ↩︎
12. Srivastava, R. K., Greff, K., & Schmidhuber, J. (2015). Training Very Deep Networks. In Advances in Neural Information Processing Systems. ↩︎
13. Kim, Y., Jernite, Y., Sontag, D., & Rush, A. M. (2016). Character-Aware Neural Language Models. AAAI. Retrieved from http://arxiv.org/abs/1508.06615 ↩︎
14. Jozefowicz, R., Vinyals, O., Schuster, M., Shazeer, N., & Wu, Y. (2016). Exploring the Limits of Language Modeling. arXiv Preprint arXiv:1602.02410. Retrieved from http://arxiv.org/abs/1602.02410 ↩︎
15. Zilly, J. G., Srivastava, R. K., Koutnik, J., & Schmidhuber, J. (2017). Recurrent Highway Networks. In International Conference on Machine Learning (ICML 2017). ↩︎
16. Zhang, Y., Chen, G., Yu, D., Yao, K., Kudanpur, S., & Glass, J. (2016). Highway Long Short-Term Memory RNNS for Distant Speech Recognition. In 2016 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP). ↩︎
17. He, K., Zhang, X., Ren, S., & Sun, J. (2016). Deep Residual Learning for Image Recognition. In CVPR. ↩︎
18. Huang, G., Weinberger, K. Q., & Maaten, L. Van Der. (2016). Densely Connected Convolutional Networks. CVPR 2017. ↩︎
19. Ruder, S., Bingel, J., Augenstein, I., & Søgaard, A. (2017). Sluice networks: Learning what to share between loosely related tasks. arXiv Preprint arXiv:1705.08142. Retrieved from http://arxiv.org/abs/1705.08142 ↩︎ ↩︎
20. Britz, D., Goldie, A., Luong, T., & Le, Q. (2017). Massive Exploration of Neural Machine Translation Architectures. In arXiv preprint arXiv:1703.03906. ↩︎
21. Srivastava, N., Hinton, G., Krizhevsky, A., Sutskever, I., & Salakhutdinov, R. (2014). Dropout: A Simple Way to Prevent Neural Networks from Overfitting. Journal of Machine Learning Research, 15, 1929–1958. http://www.cs.cmu.edu/~rsalakhu/papers/srivastava14a.pdf ↩︎
22. Ba, J., & Frey, B. (2013). Adaptive dropout for training deep neural networks. In Advances in Neural Information Processing Systems. Retrieved from file:///Files/A5/A51D0755-5CEF-4772-942D-C5B8157FBE5E.pdf ↩︎
23. Li, Z., Gong, B., & Yang, T. (2016). Improved Dropout for Shallow and Deep Learning. In Advances in Neural Information Processing Systems 29 (NIPS 2016). Retrieved from http://arxiv.org/abs/1602.02220 ↩︎
24. Gal, Y., & Ghahramani, Z. (2016). A Theoretically Grounded Application of Dropout in Recurrent Neural Networks. In Advances in Neural Information Processing Systems. Retrieved from http://arxiv.org/abs/1512.05287 ↩︎
25. Melis, G., Dyer, C., & Blunsom, P. (2017). On the State of the Art of Evaluation in Neural Language Models. ↩︎
26. Ruder, S. (2017). An Overview of Multi-Task Learning in Deep Neural Networks. In arXiv preprint arXiv:1706.05098. ↩︎
27. Rei, M. (2017). Semi-supervised Multitask Learning for Sequence Labeling. In Proceedings of ACL 2017. ↩︎
28. Ramachandran, P., Liu, P. J., & Le, Q. V. (2016). Unsupervised Pretrainig for Sequence to Sequence Learning. arXiv Preprint arXiv:1611.02683. ↩︎
29. Søgaard, A., & Goldberg, Y. (2016). Deep multi-task learning with low level tasks supervised at lower layers. Proceedings of the 54th Annual Meeting of the Association for Computational Linguistics, 231–235. ↩︎
31. Bahdanau, D., Cho, K., & Bengio, Y.. Neural Machine Translation by Jointly Learning to Align and Translate. ICLR 2015. https://doi.org/10.1146/annurev.neuro.26.041002.131047 ↩︎
32. Luong, M.-T., Pham, H., & Manning, C. D. (2015). Effective Approaches to Attention-based Neural Machine Translation. EMNLP 2015. Retrieved from http://arxiv.org/abs/1508.04025 ↩︎
33. Vaswani, A., Shazeer, N., Parmar, N., Uszkoreit, J., Jones, L., Gomez, A. N., … Polosukhin, I. (2017). Attention Is All You Need. arXiv Preprint arXiv:1706.03762. ↩︎
34. Kadlec, R., Schmid, M., Bajgar, O., & Kleindienst, J. (2016). Text Understanding with the Attention Sum Reader Network. In Proceedings of the 54th Annual Meeting of the Association for Computational Linguistics. ↩︎
35. Lin, Z., Feng, M., Santos, C. N. dos, Yu, M., Xiang, B., Zhou, B., & Bengio, Y. (2017). A Structured Self-Attentive Sentence Embedding. In ICLR 2017. ↩︎
36. Cheng, J., Dong, L., & Lapata, M. (2016). Long Short-Term Memory-Networks for Machine Reading. arXiv Preprint arXiv:1601.06733. Retrieved from http://arxiv.org/abs/1601.06733 ↩︎
37. Parikh, A. P., Täckström, O., Das, D., & Uszkoreit, J. (2016). A Decomposable Attention Model for Natural Language Inference. In Proceedings of the 2016 Conference on Empirical Methods in Natural Language Processing. Retrieved from http://arxiv.org/abs/1606.01933 ↩︎
38. Paulus, R., Xiong, C., & Socher, R. (2017). A Deep Reinforced Model for Abstractive Summarization. In arXiv preprint arXiv:1705.04304,. Retrieved from http://arxiv.org/abs/1705.04304 ↩︎
39. Daniluk, M., Rockt, T., Welbl, J., & Riedel, S. (2017). Frustratingly Short Attention Spans in Neural Language Modeling. In ICLR 2017. ↩︎
40. Liu, Y., & Lapata, M. (2017). Learning Structured Text Representations. In arXiv preprint arXiv:1705.09207. Retrieved from http://arxiv.org/abs/1705.09207 ↩︎
41. Dozat, T., & Manning, C. D. (2017). Deep Biaffine Attention for Neural Dependency Parsing. In ICLR 2017. Retrieved from http://arxiv.org/abs/1611.01734 ↩︎
42. Kingma, D. P., & Ba, J. L. (2015). Adam: a Method for Stochastic Optimization. International Conference on Learning Representations. ↩︎
43. Zhang, J., Mitliagkas, I., & Ré, C. (2017). YellowFin and the Art of Momentum Tuning. arXiv preprint arXiv:1706.03471. ↩︎
44. Ruder, S. (2016). An overview of gradient descent optimization. arXiv Preprint arXiv:1609.04747. ↩︎
45. Denkowski, M., & Neubig, G. (2017). Stronger Baselines for Trustable Results in Neural Machine Translation. ↩︎
46. Hinton, G., Vinyals, O., & Dean, J. (2015). Distilling the Knowledge in a Neural Network. arXiv Preprint arXiv:1503.02531. https://doi.org/10.1063/1.4931082 ↩︎
47. Kuncoro, A., Ballesteros, M., Kong, L., Dyer, C., & Smith, N. A. (2016). Distilling an Ensemble of Greedy Dependency Parsers into One MST Parser. Empirical Methods in Natural Language Processing. ↩︎
48. Kim, Y., & Rush, A. M. (2016). Sequence-Level Knowledge Distillation. Proceedings of the 2016 Conference on Empirical Methods in Natural Language Processing (EMNLP-16). ↩︎
49. Jean, S., Cho, K., Memisevic, R., & Bengio, Y. (2015). On Using Very Large Target Vocabulary for Neural Machine Translation. Proceedings of the 53rd Annual Meeting of the Association for Computational Linguistics and the 7th International Joint Conference on Natural Language Processing (Volume 1: Long Papers), 1–10. Retrieved from http://www.aclweb.org/anthology/P15-1001 ↩︎
50. Sennrich, R., Haddow, B., & Birch, A. (2016). Edinburgh Neural Machine Translation Systems for WMT 16. In Proceedings of the First Conference on Machine Translation (WMT 2016). Retrieved from http://arxiv.org/abs/1606.02891 ↩︎
51. Huang, G., Li, Y., Pleiss, G., Liu, Z., Hopcroft, J. E., & Weinberger, K. Q. (2017). Snapshot Ensembles: Train 1, get M for free. In ICLR 2017. ↩︎
52. Snoek, J., Larochelle, H., & Adams, R. P. (2012). Practical Bayesian Optimization of Machine Learning Algorithms. Neural Information Processing Systems Conference (NIPS 2012). https://papers.nips.cc/paper/4522-practical-bayesian-optimization-of-machine-learning-algorithms.pdf ↩︎
53. Inan, H., Khosravi, K., & Socher, R. (2016). Tying Word Vectors and Word Classifiers: A Loss Framework for Language Modeling. arXiv Preprint arXiv:1611.01462. ↩︎
54. Press, O., & Wolf, L. (2017). Using the Output Embedding to Improve Language Models. Proceedings of the 15th Conference of the European Chapter of the Association for Computational Linguistics: Volume 2, Short Papers, 2, 157--163. ↩︎
55. Mikolov, T. (2012). Statistical language models based on neural networks (Doctoral dissertation, PhD thesis, Brno University of Technology). ↩︎
56. Pascanu, R., Mikolov, T., & Bengio, Y. (2013). On the difficulty of training recurrent neural networks. International Conference on Machine Learning, (2), 1310–1318. https://doi.org/10.1109/72.279181 ↩︎
57. Zhang, Y., & Wallace, B. (2015). A Sensitivity Analysis of (and Practitioners’ Guide to) Convolutional Neural Networks for Sentence Classification. arXiv Preprint arXiv:1510.03820, (1). Retrieved from http://arxiv.org/abs/1510.03820 ↩︎
58. Huang, Z., Xu, W., & Yu, K. (2015). Bidirectional LSTM-CRF Models for Sequence Tagging. arXiv preprint arXiv:1508.01991. ↩︎
59. Ma, X., & Hovy, E. (2016). End-to-end Sequence Labeling via Bi-directional LSTM-CNNs-CRF. arXiv Preprint arXiv:1603.01354. ↩︎
60. Lample, G., Ballesteros, M., Subramanian, S., Kawakami, K., & Dyer, C. (2016). Neural Architectures for Named Entity Recognition. NAACL-HLT 2016. ↩︎
61. Kiddon, C., Zettlemoyer, L., & Choi, Y. (2016). Globally Coherent Text Generation with Neural Checklist Models. Proceedings of the 2016 Conference on Empirical Methods in Natural Language Processing (EMNLP2016), 329–339. ↩︎
62. Tu, Z., Lu, Z., Liu, Y., Liu, X., & Li, H. (2016). Modeling Coverage for Neural Machine Translation. Proceedings of the 54th Annual Meeting of the Association for Computational Linguistics. https://doi.org/10.1145/2856767.2856776 ↩︎
63. See, A., Liu, P. J., & Manning, C. D. (2017). Get To The Point: Summarization with Pointer-Generator Networks. In ACL 2017. ↩︎
64. Sutskever, I., Vinyals, O., & Le, Q. V. (2014). Sequence to sequence learning with neural networks. Advances in Neural Information Processing Systems, 9. Retrieved from http://arxiv.org/abs/1409.3215\nhttp://papers.nips.cc/paper/5346-sequence-to-sequence-learning-with-neural-networks ↩︎
65. Sennrich, R., Haddow, B., & Birch, A. (2016). Neural Machine Translation of Rare Words with Subword Units. In Proceedings of the 54th Annual Meeting of the Association for Computational Linguistics (ACL 2016). Retrieved from http://arxiv.org/abs/1508.07909 ↩︎ | 2021-09-24 15:41:59 | {"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": 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": 0.7950079441070557, "perplexity": 2948.291560239298}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-39/segments/1631780057558.23/warc/CC-MAIN-20210924140738-20210924170738-00254.warc.gz"} |
https://ask.cloudbase.it/question/424/generate-maas-compatible-image-sysprep-failing/?sort=latest | New Question
# generate-maas-compatible-image Sysprep Failing
Using the appropriate branch link text I end up getting to the VM stage and the first boot powershell prompt fails (it fails to quickly to read actually) and then boots fully to windows. At that point a powershell prompt opens and fails again saying ini.ps1 isnt allowed to execute due to permissions issue with Set-Executionpolicy. I have set in manually in the vm and tried running login, did the updates, and system syspreped, but it dont look like the cloud-init installed since I get this from maas after an attempt to install one of these images on a node
(Stdout: "Unable to find cloudbase-init.cfg.\nUnexpected error while running command.\nCommand: ['/tmp/tmpI66dEC/target/curtin/finalize']\nExit code: 2\nReason: -\nStdout: ''\nStderr: ''\n" Stderr: '')
Then after reboot maas says no kernel is available for the windows image and doesnt boot. But If i bypass pxe the windows install actually boots into a oobe, but doesnt work with maas. I suppose in the end if the powershell prompts executed with the proper executionpolicy during the vm sysprep phase the images would work with maas and I wouldnt have this issue. I am assuming I am just improperly running the deployment scripts. I hope someone can give me information on how to get this to execute properly with the appropriate permissions?
edit retag close merge delete
Hi Chuntzu! To debug this, we need to get the actual error. It works on my system, but we need to see what is happening in your case. I need you to change a couple of the scripts to add a sleep before returning the error. Please add "Start-Sleep 60" at the following lines: http://goo.gl/3csFwUhttp://goo.gl/3linMV I suspect the rest of the errors will be resolved once we get the the root cause of the first one. Please also let me know for which version of windows you are trying to create an image.
( 2015-04-12 21:42:26 +0300 )edit
Sort by » oldest newest most voted
Hello,
The first error you see about finalize failing is due to the fact that the cloudbase-init MSI changed the location of where it installs itself. I just committed a a possible fix for that. Make sure you check it out before trying again.
Also, make sure that if you download the repo as zip, you unblock the zip before unarchiving to make sure you do not run into the "script not digitally signed" error:
Start-BitsTransfer https://github.com/gabriel-samfira/windows-openstack-imaging-tools/archive/persist-driver-option.zip
Unblock-File persist-driver-option.zip
If you have a windows 8.1 installation available, you will be able to use that to generate any windows image up to 8.1. So that means you will be able to generate images for windows 7 as well.
Let me know if it works for you.
more
Sorry for the late response, work has kept me away. I have some screen shots of the errors but says I need 10 points to post images so I will just describe them for now. Specilize.ps1, ini.psm1. and firstlogon.ps1 all pop up with the powershell error "not digitally signed unauthorizedaccess". This is the case for all versions of windows 8,8.1,10 preview, server 2012, 2012r2. I figured out a temp work around which was to add "unblock-file -path /pathtoselfandotherscripts" at the begging of each of the powershell scripts I included the location to the running script and anything else the script called for when it ran. I am not sure if there is a better way of running this but this was the only way I could properly get the ddtgz images so that maas would deploy them properly. As a side note server 2008r2 does not recognize "unblock-file -path" as this must be a new powershell command. So I am still trying to find a way to create server 2008r2 and windows 7 images.
more
I have been unable to reproduce this on my system. One last thing to try. After cloning the repository from github, do an aunblock-file on every file in the repo. After which, edit UnattendTemplate.xml and replace instances of -ExecutionPolicy Remotesigned with: -ExecutionPolicy Bypass. In theory, the RemoteSigned argument passed to powershell should prevent the behaviour you are observing.
( 2015-04-25 14:24:32 +0300 )edit
have you been able to get maas to boot your images?
( 2015-11-05 16:44:46 +0300 )edit | 2020-09-23 03:13:42 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.3346964418888092, "perplexity": 2307.7535640093593}, "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/1600400209665.4/warc/CC-MAIN-20200923015227-20200923045227-00630.warc.gz"} |
http://2018.igem.org/Team:NEU_China_A/Model | # Team:NEU China A/Model
## Model
Introduction
In the affected area of patients with inflammatory bowel disease, the concentration of nitric oxide is significantly increased, so we chose it as the input signal of our anti-inflammatory device. However, the nitric oxide is very unstable, so we have introduced an amplifier which can converts unstable gas signals into stable intracellular signals for sustained high-level output. The amplifier is based on a positive feedback loop. Transcription activator B-A can self-drive in a manner independent of the input signal for a period of time after the signal is input, and the metabolic flow in this cycle can be transferred to the output circuit (Figure 1).
Figure 1. Schematic Design of the Synthetic amplifier After the signal is input, the transcriptional activator B-A is generated, which includes a DNA binding domain and a transcriptional activation domain. On the one hand, B-A can activate the expression of the reporter gene, and on the other hand can activate the expression of B-A itself. The constitutively expressed Binder will compete with B-A to suppress the leakage of the device.
In addition, when using an amplifier based on a positive feedback loop, we need to strictly limit its activation until the input signal is strong enough, which is beneficial to suppress leakage of the device. To this end, we introduce the concept of threshold, which is to achieve competition between B-A and B by constitutively expressing Binder with a certain intensity (Figure 1). In this way, the amplifier can only be effectively activated when the input signal is strong enough. We established a mathematical model to predict the performance of the amplifier under different restrictions.
Assumption
(1) The sequence that B-A and B bind is the same. So, it can be considered that both are combined with the same substrate.
(2) B-A and B have the same promotion or inhibition effect on the amplifier and output circuit.
Symbol Description
Table 1. The name and symbol of variable. Correction: X2 represents for the concentration of Binder-Activator and X3 represents for the concentration of Binder.
Fluorescence intensity of GFP with Constant Inflammatory Signal
##### 1.Available when the bacterial resources are extremely rich
Firstly, the amplifier we described in Figure 1 can be simplified to the Figure 2.
Figure 2. Simple circuit of the amplifier
The concentration of the Binder-Activator expressed by the input circuit is ${P}_{2}\left({x}_{1}\right)$ when the inflammatory signal is at a concentration of ${x}_{1}$ per unit time. The amount of Binder-Activator or GFP expressed by the amplifier or output circuit is $\text{P}\left({x}_{2}\text{,}{x}_{3}\right)$ for the Binder-Activator and Binder at a concentration of ${x}_{2}$ and ${x}_{3}$ , respectively. When the amplifier is used, it can be seen from the Figure 2 that Binder-Activator ( ${x}_{2}$ ) has two synthetic pathways, one is that the inflammatory signal ( ${x}_{1}$ ) promotes the synthesis of the input circuit, and the other is that ${x}_{2}$ facilitates the synthesis of the amplifier by ${x}_{3}$ . So, we can get this equation:
......(1)
There is only one synthetic pathway of y , that is, ${x}_{2}$ and ${x}_{3}$ work together with the output circuit to release y, so it can be obtained by assumption 2:
......(2)
###### Ⅰ. ${P}_{1}\left({x}_{1}\right)$ expression solving
The gene (equivalent to the binding sequence of Binder-Activator) is abbreviated as G, various transcriptional activators are abbreviated as S, and various transcriptional repressors (e.g. Binder) are abbreviated as I. The binding of ${x}_{1}$ to the NorR (it means the NorR will bind NO to activate the promoter PnorV) of input circuit is a reversible reaction, so the binding reaction of ${x}_{1}$ to the input circuit can be expressed as:
......(3)
k1 and k2 are the reaction rate constants of the forward reaction and the reverse reaction, respectively. Refer to the Michaelis-Menten equation, we do the following analysis: when the reaction reaches equilibrium, the concentration of SG does not change, that is, the rate of SG generation and decomposition is equal, then we can get the following equation:
......(4)
......(5)
......(6)
In fact, the increased rate of transcription of a regulated gene depends on the proportion of transcriptional activators that bind to the gene, and the more transcriptional activators that bind to the gene, the more the rate of expression of the gene increases. The expression of conversion to mathematics is:
......(7)
Suppose that when the substrate concentration is large enough, ${P}_{1}\left({x}_{1}\right)$ will take the maximum value, set to ${P}_{1max}$ , and [S] will also be much larger than [G], so we can get this:
......(8)
Bring the formula (6), (8) into equation (7) to get the analytical expression of ${P}_{1}\left({x}_{1}\right)$ :
......(9)
Although the body's immune system can make timely adjustments to the inflammatory response, ${x}_{1}$ is considered to be a fixed value in a sufficiently short period of time, and ${P}_{1}\left({x}_{1}\right)$ can also be considered as a constant that varies with ${x}_{1}$ , abbreviated as A. The calculations that follow are handled this way.
###### Ⅱ. $\text{P}\left({x}_{2}\text{,}{x}_{3}\right)$ expression analysis
Since ${x}_{2}$ , ${x}_{3}$ binds to the same site in the gene, the gene will be activated when ${x}_{2}$ binds it while being inhibited when ${x}_{3}$ binds it. This can be regarded as the competition between ${x}_{2}$ and ${x}_{3}$ . Similar to the analysis we used to solve the expression of , we can get:
......(10)
......(11)
In the reaction, ${x}_{2}$ represents the concentration of S, and ${x}_{3}$ represents the concentration of I. The increase of the transcription rate of the gene depends on the concentration of SG, that is, the amount of the transcriptional activator that binds to the gene, and the gene that binds to ${x}_{3}$ can no longer bind to ${x}_{2}$ , resulting in inhibition of transcription. So,
Analogy to the analysis we used to solve the expression of ${P}_{1}\left({x}_{1}\right)$ , we list the following relationships: When it reaches equilibrium:
......(12)
......(13)
From this we can get the following equation:
......(14)
......(15)
Sort out the above two formulas to get:
......(16)
The same way we get:
......(17)
When [S] is large enough, $\text{P}\left({x}_{2}\text{,}{x}_{3}\right)$ will take the maximum value and set it to . ${P}_{2max}$ [S] will also be much larger than [G] and another in the denominator, so there are:
......(18)
Bringing Equations (16), (18) into Equation (17) yields:
......(19)
So, we get the expression of $\text{P}\left({x}_{2}\text{,}{x}_{3}\right)$ . Because the role of ${x}_{3}$ in the system is to set a threshold for the amplification of ${x}_{2}$ , and is set to a constitutive expression, ${x}_{3}$ can be regarded as a fixed value of the regulation, and ${x}_{3}$ becomes another variable constant.
###### III. Calculation of : ${x}_{2}$
From the analysis of Equation (1) and the above two steps, the relationship between ${x}_{2}$ and time after adding the amplifier can be obtained:
......(20)
The relationship between GFP fluorescence intensity and time:
......(21)
When the amplifier is not used, y is directly synthesized by the inflammatory signal ( ${x}_{1}$ ), from which we can get:
......(22)
##### 2. Available when the bacterial resources are restricted
The resources in bacteria are actually limited. In addition to using resources to synthesize the GFP, bacteria also need resources to maintain their normal life activities. At this time, there is competition between the amplifier and the bacteria's own life activities. The eventual result is that after a limited amount of resources are exhausted, the bacteria die and the amplifier stops working. Therefore, the following bacterial resource attenuation model is established. Assuming that the total amount of resources in the bacteria is q, then when the resources decays, the following formula holds:
......(23)
......(24)
Among the above relationship, K is the total amount of initial resources before decay, and is the time constant of the decay process, we can get:
......(25)
Solution:
......(26)
Then, when there is no amplifier, the model is corrected to:
......(27)
When there is an amplifier, the model is corrected to:
......(28)
Fluorescence intensity of GFP with attenuated Inflammatory Signal
The above model consistently believes that the intensity of the inflammatory signal is constant. However, in the actual biological environment, the inflammatory signal will be attenuated to varying degrees with distance, time and drug release. Therefore, the attenuation model of the inflammatory signal intensity is first established as follows.
Figure 3. The effect of attenuated inflammatory signal intensity on GFP output when bacterial resources are limited with an amplifier
It is easy to get the inflammatory signal intensity decay rate as follows:
......(29)
Where ${K}_{s}$ is the intensity of the inflammatory signal at the initial moment and $\text{T}$ is the time constant of the decay process of the inflammatory signal. Solution:
......(30)
Then the amount ${P}_{1}\left({x}_{1}\right)$ of Binder-Activator expressed in the input circuit is as follows:
......(31)
Considering the attenuation of inflammatory signals and the limitation of bacterial resources, when there is no amplifier, the model is corrected to:
......(32)
Considering the attenuation of inflammatory signals and the limitation of bacterial resources, when adding an amplifier, the model is corrected to:
......(33)
Model solving
###### 1. Parameter assignment table
By referring to some previous work, the parameters are as follows:
Table 2. Parameter assignment
###### 2. Model solving without amplifier
Ⅰ. When the intensity of the inflammatory signal is constant and the bacterial resources are considered to be unlimited, record , then . So, the fluorescence intensity is:
......(34)
That is:
......(35)
Ⅱ. When the intensity of the inflammatory signal is constant but the bacterial resources are limited, record . So, the fluorescence intensity is:
......(36)
That is:
......(37)
Figure 4. The effect of bacterial resources on the GFP output without amplifier
III. When the inflammatory signal is attenuated, but the bacterial resources are considered to be unlimited, the output GFP is solved as:
......(38)
That is:
......(39)
IV. When the inflammatory signal is attenuated and the bacterial resources are considered to be limited, the GFP is solved as:
......(40)
That is:
......(41)
Figure 5. The effect of bacterial resources on the GFP output when inflammatory signal is attenuated without amplifier
###### 3. Model solving with amplifier
Ⅰ. When the intensity of the inflammatory signal is constant and the bacterial resources are considered to be unlimited, record , then:
......(42)
Using MATLAB to solve for , it is:
......(43)
Let ${x}_{2}=\text{g}\left(\text{t}\right)$ , then we get:
......(44)
Then we get GFP as:
......(45)
Ⅱ. When the intensity of the inflammatory signal is constant but the bacterial resources are limited, record . So, the fluorescence intensity is:
......(46)
Figure 6. The effect of bacterial resources on the GFP output with amplifier
Figure 7. GFP output curve considering bacterial resources limitations with amplifier
III. When the inflammatory signal is attenuated and the bacterial resources are limited, the Runge-Kutta method is used to solve the differential equation and the GFP curve is obtained as follows. Compared with the GFP curve without amplifier, the addition of the amplifier has obvious effect.
Figure 8. GFP output curve considering inflammatory signal attenuation and bacterial resources limitation
###### 4. Analysis of the regulatory role of Thresholder
When the intensity of the inflammatory signal is attenuated and the bacterial resources are limited, in order to avoid the leakage of the positive feedback loop, we set the threshold regulate component Binder, the concentration can be varied between 10 and 100 mM. The regulation curve is as follows.
Figure 9. Binder regulation curve considering inflammatory signal attenuation and bacterial resources limitation
In conclusion, the introduction of Thresholder does have a regulatory effect on the output of GFP and is very obvious, which has a positive effect on suppressing the leakage of the positive feedback loop.
Our established model is based on some assumptions and approximations and lacks the support of experimental data. But we believe that our work can provide a reference to other work that requires the use of a positive feedback loop and threshold. In addition, we will conduct experiments to test the validity of our model in the future.
[1] Smole,A., Lainsˇcek,D., Bezeljak,U., Horvat,S. and Jerala,R. (2017) A synthetic mammalian therapeutic gene circuit for sensing and suppressing inflammation. Mol. Ther., 25, 102–119.
[2] Michaelis L, Menten M L. Die kinetic der invertinwirkung. Biochem. Z. , 1913, 49: 334-336
[3] Runge, Carl David Tolmé (1895), "Über die numerische Auflösung von Differentialgleichungen", Mathematische Annalen, Springer, 46 (2): 167–178, | 2019-11-18 13:59:34 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 46, "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": 0.6708351373672485, "perplexity": 1336.1209475879177}, "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-2019-47/segments/1573496669795.59/warc/CC-MAIN-20191118131311-20191118155311-00144.warc.gz"} |
https://seq-lang.org/api/function_format-inl_8h_1abece24b1bb022c6cf07e709b1a96a8c7.html | Function fmt::v6::format_system_error¶
Function Documentation¶
void fmt::v6::format_system_error(internal::buffer<char> &out, int error_code, string_view message)
Formats an error returned by an operating system or a language runtime, for example a file opening error, and writes it to out* in the following form:
<message>*: <system-message>
where <message>* is the passed message and <system-message> is the system message corresponding to the error code.
error_code* is a system error code as given by errno.
If error_code* is not a valid error code such as -1, the system message may look like “Unknown error -1” and is platform-dependent. | 2020-02-23 22:47:02 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 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": 0.31344643235206604, "perplexity": 8913.559775954676}, "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-2020-10/segments/1581875145859.65/warc/CC-MAIN-20200223215635-20200224005635-00235.warc.gz"} |
https://gmatclub.com/forum/train-a-traveling-at-60-km-hr-leaves-mumbai-for-delhi-at-6-pm-train-b-303279.html | GMAT Question of the Day - Daily to your Mailbox; hard ones only
It is currently 16 Sep 2019, 21:50
### GMAT Club Daily Prep
#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized
for You
we will pick new questions that match your level based on your Timer History
Track
every week, we’ll send you an estimated GMAT score based on your performance
Practice
Pays
we will pick new questions that match your level based on your Timer History
# Train A traveling at 60 km/hr leaves Mumbai for Delhi at 6 PM. Train B
Author Message
TAGS:
### Hide Tags
Intern
Joined: 30 Mar 2019
Posts: 5
Train A traveling at 60 km/hr leaves Mumbai for Delhi at 6 PM. Train B [#permalink]
### Show Tags
20 Aug 2019, 12:12
1
00:00
Difficulty:
55% (hard)
Question Stats:
66% (02:48) correct 34% (03:30) wrong based on 35 sessions
### HideShow timer Statistics
Train A traveling at 60 km/hr leaves Mumbai for Delhi at 6 PM. Train B travelling at 90km/ he also leaves Mumbai for Delhi at 9 PM. Train C leaves Delhi for Mumbai at 9PM. If all the trains meet at the same time between Mumbai and Delhi, what is the speed of train C if the distance between Delhi and Mumbai is 1260 kms?
A 120 km/hr
B 135 km/he
C 240 km/ hr
D 105 km/ hr
E 90 km/ hr
Senior Manager
Joined: 29 Jun 2019
Posts: 302
Re: Train A traveling at 60 km/hr leaves Mumbai for Delhi at 6 PM. Train B [#permalink]
### Show Tags
20 Aug 2019, 13:41
90(t-3)=60t
30t=270
t=9,60×9=540
So trains A and B, travel 540 kms of 1260 distance between Delhi and Numbai.
1260-540=720
Because C travels at 9,so
720=6v ==》v=120
Option A
Posted from my mobile device
_________________
Always waiting
Manager
Joined: 20 Jul 2012
Posts: 118
GMAT 1: 650 Q47 V33
Re: Train A traveling at 60 km/hr leaves Mumbai for Delhi at 6 PM. Train B [#permalink]
### Show Tags
20 Aug 2019, 14:04
1
shubhigandhi10 wrote:
Train A traveling at 60 km/hr leaves Mumbai for Delhi at 6 PM. Train B travelling at 90km/ he also leaves Mumbai for Delhi at 9 PM. Train C leaves Delhi for Mumbai at 9PM. If all the trains meet at the same time between Mumbai and Delhi, what is the speed of train C if the distance between Delhi and Mumbai is 1260 kms?
A 120 km/hr
B 135 km/he
C 240 km/ hr
D 105 km/ hr
E 90 km/ hr
Posted from my mobile device
If at distance d from Mumbai they meet and s speed of train C
d/60 = d/90+3 = (1260-d)/s + 3
From 1st eqn, d = 540 km.
so 540/60 = (1260-540)/s +3
=> s = 720/6 = 120kmph
Director
Status: Manager
Joined: 27 Oct 2018
Posts: 602
Location: Egypt
GPA: 3.67
WE: Pharmaceuticals (Health Care)
Re: Train A traveling at 60 km/hr leaves Mumbai for Delhi at 6 PM. Train B [#permalink]
### Show Tags
20 Aug 2019, 17:01
2
1
First, we shall find when & where will B catch up to A:
As A moved 3 hours earlier, the distance between them was 60*3 = 180 km
The time needed by B to catch up to A = $$\frac{180}{90-60} = 6$$ hours
In 6 hours, Train B will have traveled 90*6 = 540 km
So the left distance that Train C should have traveled to meed A & B = 1260 - 540 = 720 km
As train B & C started traveling at the same time, C must have traveled for 6 hours same as B.
so the speed of C = $$\frac{720}{6}$$ = 120 km/h
_________________
Thanks for KUDOS
SVP
Joined: 03 Jun 2019
Posts: 1500
Location: India
Re: Train A traveling at 60 km/hr leaves Mumbai for Delhi at 6 PM. Train B [#permalink]
### Show Tags
20 Aug 2019, 22:11
shubhigandhi10 wrote:
Train A traveling at 60 km/hr leaves Mumbai for Delhi at 6 PM. Train B travelling at 90km/ he also leaves Mumbai for Delhi at 9 PM. Train C leaves Delhi for Mumbai at 9PM. If all the trains meet at the same time between Mumbai and Delhi, what is the speed of train C if the distance between Delhi and Mumbai is 1260 kms?
A 120 km/hr
B 135 km/he
C 240 km/ hr
D 105 km/ hr
E 90 km/ hr
Given:
1. Train A traveling at 60 km/hr leaves Mumbai for Delhi at 6 PM.
2. Train B travelling at 90km/ he also leaves Mumbai for Delhi at 9 PM.
3. Train C leaves Delhi for Mumbai at 9PM.
4. All the trains meet at the same time between Mumbai and Delhi
5. The distance between Delhi and Mumbai is 1260 kms
Asked: What is the speed of train C ?
Let the speed of train C be x.
1. Train A traveling at 60 km/hr leaves Mumbai for Delhi at 6 PM.
2. Train B travelling at 90km/ he also leaves Mumbai for Delhi at 9 PM.
Train A travel from 6PM to 9PM = 60 *3 = 180 km
4. All the trains meet at the same time between Mumbai and Delhi
Train A & Train B meet at = 180/(90-60) = 6 hours after 9PM
Train B travels = 90*6 = 540 km from Mumbai to Delhi at the time of meeting.
5. The distance between Delhi and Mumbai is 1260 kms
Train distance travelled by train C from Delhi to Mumbai = 1260 - 540 = 720 km
Time taken by train C = 6 hours
Speed of train C = 720/6 = 120 kmh
IMO A
_________________
"Success is not final; failure is not fatal: It is the courage to continue that counts."
Please provide kudos if you like my post. Kudos encourage active discussions.
My GMAT Resources: -
Efficient Learning
All you need to know about GMAT quant
Tele: +91-11-40396815
Mobile : +91-9910661622
E-mail : kinshook.chaturvedi@gmail.com
Re: Train A traveling at 60 km/hr leaves Mumbai for Delhi at 6 PM. Train B [#permalink] 20 Aug 2019, 22:11
Display posts from previous: Sort by | 2019-09-17 04:50:58 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6769888997077942, "perplexity": 7564.958817454845}, "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-2019-39/segments/1568514573052.26/warc/CC-MAIN-20190917040727-20190917062727-00190.warc.gz"} |
http://physics.stackexchange.com/tags/energy-conservation/hot?filter=day | # Tag Info
The mass of a free neutron is 939.566 MeV/c$^2$ (almost 1 GeV/c$^2$, so that's probably where your instructor got the "1" value), and the mass of a free proton is 938.272 MeV/c$^2$. A free neutron will decay into a free proton, free electron ($\beta^-$), and an anti-neutrino, $\bar{\nu}$. The mass of the electron is 0.511 MeV/c$^2$, and of the ... | 2015-05-23 06:04:17 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7678849101066589, "perplexity": 1389.3106901665988}, "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-2015-22/segments/1432207927245.60/warc/CC-MAIN-20150521113207-00183-ip-10-180-206-219.ec2.internal.warc.gz"} |
https://devzone.nordicsemi.com/blogs/1108/the-complete-tutorial-for-developing-and-debugging/ | Posted 2017-05-11 04:13:06 +0200
blogs->all
# The complete tutorial for developing and debugging nRF52 applications on a Mac
I realize that there are already multiple tutorials on how to configure GCC along with Eclipse or SEGGER Embedded Studio (for use on a Mac), but this tutorial goes over setting up a different IDE. The more choices the better, right? ;)
The IDE of choice for me is NetBeans. NetBeans is well known for Java development but not as much for C/C++ or embedded. However, I personally have been using it for embedded development for about 10 years now (both embedded Linux and MCU-level development). In this tutorial, I'll be going over how to set up and configure the development environment and NetBeans from scratch for developing and debugging nRF52 applications (I used the nRF52840 Preview Development Kit, but really the steps are transferrable to be used with any nRF5x development kit).
I must warn you that the tutorial may be a bit lengthy, but that's because I tried to include every screenshot and image showing details for each of the steps involved. Because of that, I will provide a link to the blog post (which is hosted on my website).
I thought others may benefit from this tutorial especially if they're looking for other options for development on a Mac using open source tools.
Hope you find it useful!
Posted May 11, 2017, 11:26 a.m.
This is great, thanks!
Posted May 12, 2017, 11:02 a.m.
Very good tutorial! Thank you a lot for sharing your insights.
Posted May 22, 2017, 3:11 p.m.
This is great, thanks! Though I have one issue: Code Assistance in Netbeans doesn't pick up #defines from the Makefile, e.g. CFLAGS += -DBOARD_PCA10056 and therefore sees BOARD_PCA10056 as undefined.
I can fix this by manually adding all the relevant defines to Code Assistance -> C Compiler -> Preprocessor Definitions, but that's a little laborious:)
Is there a faster way to make Netbeans' Code Assistance recognise defines from the Makefile?
Posted June 22, 2017, 6:47 p.m.
@Valentin,
Sorry for the late response. Yes, this is a downside of NetBeans. However, I will look into a better way and report back. Thanks!
Posted June 22, 2017, 6:59 p.m.
So, one quicker way to do this is to edit the configurations.xml file located under the NetBeans project folder, and look for:
<preprocessorList>
....
<Elem>BLE_STACK_SUPPORT_REQD</Elem>
<Elem>S140</Elem>
....
</preprocessorList>
Here you can add all the preprocessors. I guess you can even write a shell or python script to automatically parse the Makefile and add the macros to the configurations.xml file! ;)
## Recent blog posts
• ### Introducing nRF5 SDK for Mesh
Posted 2017-07-20 09:42:44 by Pär H
Posted 2017-07-19 06:53:42 by Mohammad Afaneh
• ### Unique Thread/Bluetooth multiprotocol solution with nRF5 SDK for Thread and nRF52840 SoC by Nordic
Posted 2017-07-14 10:31:56 by Krzysztof Loska
• ### nRF Connect macros (currently Android only)
Posted 2017-07-14 13:29:14 by Aleksander Nowakowski
• ### Power Optimization — From 3 to 7 Months on a Single Charge
Posted 2017-07-10 14:34:39 by Yaniv Nis
## Recent questions
• ### openocd configuration file nrf51.cfg not working
Posted 2017-07-22 18:40:18 by phob
• ### Problems with UART running ble_app_uart_c on nRF52832
Posted 2017-07-22 17:44:12 by kont40
• ### Wake-up source with nRF52 capacitive touch and current consumption
Posted 2017-07-22 17:35:46 by MANGO
• ### Different master instances for two slaves in nrf51422
Posted 2017-07-22 12:48:29 by Khan
• ### Receiving notifications from Android Phone
Posted 2017-07-22 12:29:52 by kian79 | 2017-07-22 16:45:47 | {"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": 0.4518100917339325, "perplexity": 7614.584364748643}, "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/1500549424088.27/warc/CC-MAIN-20170722162708-20170722182708-00111.warc.gz"} |
http://wradlib.org/wradlib-docs/latest/util.html | # Utility functions¶
Module util provides a set of useful helpers which are currently not attributable to the other modules
aggregate_in_time Aggregate time series data to a coarser temporal resolution. aggregate_equidistant_tseries Aggregates an equidistant time series to equidistant target time windows. from_to Return a list of timesteps from to of length filter_window_polar Apply a filter of an approximated square window of half size fsize on a given polar image img. filter_window_cartesian Apply a filter of square window size fsize on a given cartesian image img. calculate_polynomial Calculate Polynomial | 2017-03-25 13:28:36 | {"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": 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": 0.4497956335544586, "perplexity": 5368.823098150878}, "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-2017-13/segments/1490218188926.39/warc/CC-MAIN-20170322212948-00249-ip-10-233-31-227.ec2.internal.warc.gz"} |
https://www.zbmath.org/authors/?q=ai%3Adong.boqing | # zbMATH — the first resource for mathematics
## Dong, Boqing
Compute Distance To:
Author ID: dong.boqing Published as: Dong, B.; Dong, Bo Qing; Dong, Bo-Qing; Dong, Bo-qing; Dong, Boqing
Documents Indexed: 71 Publications since 2004
all top 5
#### Co-Authors
4 single-authored 21 Jia, Yan 20 Chen, Zhimin 8 Wu, Jiahong 5 Ye, Zhuan 5 Zhang, Wenliang 5 Zhang, Xingwei 4 Chen, Jianwen 4 Li, Yongsheng 4 Xie, Qianqian 3 Li, Jingna 3 Wang, Wenjuan 3 Zhang, Zhifei 2 Liu, QingQing 2 Qin, Xiaohong 2 Tan, Wen 2 Tao, Qunqun 2 Zhai, Xiaoping 2 Zhang, Zhaoyun 2 Zhao, Caidi 1 Chai, Xiaojuan 1 Chen, Zhengzheng 1 Gala, Sadek 1 Gao, Yongdong 1 Gui, Xingguo 1 Guo, Yana 1 Jiang, Wei 1 Li, Liangpan 1 Song, Juan 1 Wu, Ezi 1 Xu, Xiaojing 1 Ye, Hailong 1 Yin, Guliang 1 Zhang, Fei 1 Zhang, Hui 1 Zhang, Hui 1 Zhang, Jing 1 Zhang, Linghai 1 Zhao, Huijiang
all top 5
#### Serials
11 Journal of Mathematical Analysis and Applications 6 Journal of Differential Equations 5 Nonlinear Analysis. Real World Applications 4 Nonlinearity 4 Applied Mathematics and Computation 4 Applied Mathematics Letters 4 Discrete and Continuous Dynamical Systems 3 Journal of Partial Differential Equations 3 Electronic Journal of Differential Equations (EJDE) 3 Abstract and Applied Analysis 2 Mathematical Methods in the Applied Sciences 2 Acta Mathematicae Applicatae Sinica. English Series 2 Mathematica Applicata 2 Journal of Mathematical Fluid Mechanics 2 Journal of University of Science and Technology of China 1 Journal of Mathematical Physics 1 Acta Mathematica Sinica 1 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 1 Journal of Mathematics. Wuhan University 1 Journal of Mathematical Research & Exposition 1 Science in China. Series A 1 Journal of Nonlinear Science 1 Discrete and Continuous Dynamical Systems. Series B 1 Acta Mathematica Scientia. Series A. (Chinese Edition) 1 Acta Mathematica Scientia. Series B. (English Edition) 1 Communications on Pure and Applied Analysis 1 Communications in Mathematical Sciences 1 Science China. Mathematics
all top 5
#### Fields
69 Partial differential equations (35-XX) 57 Fluid mechanics (76-XX) 6 Geophysics (86-XX) 4 Harmonic analysis on Euclidean spaces (42-XX) 2 Dynamical systems and ergodic theory (37-XX) 1 General and overarching topics; collections (00-XX) 1 Real functions (26-XX) 1 Functions of a complex variable (30-XX)
#### Citations contained in zbMATH
51 Publications have been cited 545 times in 252 Documents Cited by Year
Global regularity of the 2D micropolar fluid flows with zero angular viscosity. Zbl 1402.35220
Dong, Bo-Qing; Zhang, Zhifei
2010
Asymptotic profiles of solutions to the 2D viscous incompressible micropolar fluid flows. Zbl 1170.35336
Dong, Bo-Qing; Chen, Zhi-Min
2009
Global well-posedness and large-time decay for the 2D micropolar equations. Zbl 1361.35143
Dong, Bo-Qing; Li, Jingna; Wu, Jiahong
2017
Regularity criteria of weak solutions to the three-dimensional micropolar flows. Zbl 1283.76016
Dong, Boqing; Chen, Zhimin
2009
Large time behavior to the system of incompressible non-Newtonian fluids in $$\mathbb{R}^2$$. Zbl 1059.35104
Dong, Boqing; Li, Yongsheng
2004
Pressure regularity criteria of the three-dimensional micropolar fluid flows. Zbl 1219.35189
Dong, Bo-Qing; Jia, Yan; Chen, Zhi-Min
2011
Asymptotic stability of the critical and super-critical dissipative quasi-geostrophic equation. Zbl 1109.76063
Dong, Boqing; Chen, Zhi-Min
2006
The asymptotic behavior of solutions to three-dimensional Navier-Stokes equations with nonlinear damping. Zbl 1216.35088
Jia, Yan; Zhang, Xingwei; Dong, Bo-Qing
2011
The BKM criterion for the 3D Navier-Stokes equations via two velocity components. Zbl 1196.35153
Dong, Bo-Qing; Zhang, Zhifei
2010
A remark on regularity criterion for the dissipative quasi-geostrophic equations. Zbl 1154.76339
Dong, Bo-Qing; Chen, Zhi-Min
2007
On the regularity criterion for three-dimensional micropolar fluid flows in Besov spaces. Zbl 1194.35322
Dong, Bo-Qing; Zhang, Wenliang
2010
Uniform attractors of non-homogeneous micropolar fluid flows in non-smooth domains. Zbl 1155.37043
Chen, Jianwen; Chen, Zhi-Min; Dong, Bo-Qing
2007
Global attractors of two-dimensional micropolar fluid flows in some unbounded domains. Zbl 1103.76008
Dong, Boqing; Chen, Zhimin
2006
Existence of $$H^{2}$$-global attractors of two-dimensional micropolar fluid flows. Zbl 1098.35035
Chen, Jianwen; Chen, Zhi-Min; Dong, Bo-Qing
2006
Global classical solutions to the one-dimensional compressible fluid models of Korteweg type with large initial data. Zbl 1320.35275
Chen, Zhengzheng; Chai, Xiaojuan; Dong, Boqing; Zhao, Huijiang
2015
Global regularity and time decay for the 2D magnetohydrodynamic equations with fractional dissipation and partial magnetic diffusion. Zbl 1406.35269
Dong, Bo-Qing; Jia, Yan; Li, Jingna; Wu, Jiahong
2018
Global regularity for the 2D micropolar equations with fractional dissipation. Zbl 1397.35204
Dong, Bo-Qing; Wu, Jiahong; Xu, Xiaojing; Ye, Zhuan
2018
On the weak-strong uniqueness of Koch-Tataru’s solution for the Navier-Stokes equations. Zbl 1285.35064
Dong, Bo-Qing; Zhang, Zhifei
2014
Remarks on the blow-up criterion for smooth solutions of the Boussinesq equations with zero diffusion. Zbl 1267.35164
Jia, Yan; Zhang, Xingwei; Dong, Bo-Qing
2013
On upper and lower bounds of higher order derivatives for solutions to the 2D micropolar fluid equations. Zbl 1158.35074
Dong, Bo-Qing; Chen, Zhi-Min
2007
Regularity criterion of weak solutions to the 3D Navier-Stokes equations via two velocity components. Zbl 1132.35432
Dong, Bo-Qing; Chen, Zhi-Min
2008
Time decay rates of non-Newtonian flows in $$\mathbf {R}^{n}_{+}$$. Zbl 1102.76014
Dong, Bo-Qing; Chen, Zhi-Min
2006
On the pressure regularity criterion of the 3D Navier-Stokes equations. Zbl 1248.35151
Zhang, Xingwei; Jia, Yan; Dong, Bo-Qing
2012
On the weak-strong uniqueness of the dissipative surface quasi-geostrophic equation. Zbl 1241.35158
Dong, Bo-Qing; Chen, Zhi-Min
2012
Asymptotic profile of solutions to the two-dimensional dissipative quasi-geostrophic equation. Zbl 1214.35049
Dong, Boqing; Liu, Qingqing
2010
On the regularity criteria of the 3D Navier-Stokes equations in critical spaces. Zbl 1240.35382
Dong, Boqing; Gala, Sadek; Chen, Zhimin
2011
Asymptotic stability of non-Newtonian flows with large perturbation in $$\mathbb{R}^{2}$$. Zbl 1138.35380
Dong, Bo-Qing; Chen, Zhi-Min
2006
Global regularity and asymptotic behavior of modified Navier-Stokes equations with fractional dissipation. Zbl 1234.35179
Dong, Bo-Qing; Song, Juan
2012
Remarks on the regularity criterion of the 3D micropolar fluid flows in terms of the pressure. Zbl 1210.35189
Jia, Yan; Zhang, Wenliang; Dong, Bo-Qing
2011
On the decay of higher order derivatives of solutions to Ladyzhenskaya model for incompressible viscous flows. Zbl 1153.35062
Dong, Boqing; Jiang, Wei
2008
Pullback attractors of non-autonomous micropolar fluid flows. Zbl 1152.37030
Chen, Jianwen; Dong, Bo-Qing; Chen, Zhi-Min
2007
Global regularity results for the climate model with fractional dissipation. Zbl 1406.35270
Dong, Boqing; Wang, Wenjuan; Wu, Jiahong; Zhang, Hui
2019
An improved regularity criterion of three-dimensional magnetohydrodynamic equations. Zbl 1239.76070
Dong, Bo-Qing; Jia, Yan; Zhang, Wenliang
2012
Remarks on the logarithmical regularity criterion of the supercritical surface quasi-geostrophic equation in Morrey spaces. Zbl 1316.35063
Jia, Yan; Dong, Bo-Qing
2015
Stability behaviors of Leray weak solutions to the three-dimensional Navier-Stokes equations. Zbl 1342.35214
Dong, Bo-Qing; Jia, Yan
2016
Global regularity for a 2D tropical climate model with fractional dissipation. Zbl 1415.86028
Dong, Bo-Qing; Wu, Jiahong; Ye, Zhuan
2019
Remarks on the weak-strong uniqueness for the 2D quasi-geostrophic equation in BMO space. Zbl 1255.35178
Liu, Qingqing; Jia, Yan; Dong, Bo-Qing
2012
Remarks on upper and lower bounds of solutions to the Navier–Stokes equations in $$\mathbb R^{2}$$. Zbl 1103.76016
Dong, Boqing; Chen, Zhimin
2006
Global well-posedness for 2-D Boussinesq system with the temperature-dependent viscosity and supercritical dissipation. Zbl 1414.35153
Zhai, Xiaoping; Dong, Bo-Qing; Chen, Zhi-Min
2019
Global regularity for a class of 2D generalized tropical climate models. Zbl 1412.35249
Dong, Bo-Qing; Wang, Wenjuan; Wu, Jiahong; Ye, Zhuan; Zhang, Hui
2019
Asymptotic convergence rate of supercritical surface quasi-geostrophic equation in Morrey space. Zbl 1310.35038
Jia, Yan; Dong, Bo-Qing
2015
Remarks on the regularity criteria of weak solutions to the three-dimensional micropolar fluid equations. Zbl 1292.35232
Jia, Yan; Zhang, Xing-Wei; Zhang, Wen-Liang; Dong, Bo-Qing
2013
Logarithmical regularity criteria of the three-dimensional micropolar fluid equations in terms of the pressure. Zbl 1246.76140
Jia, Yan; Zhang, Jing; Dong, Bo-Qing
2012
Remarks on the regularity criteria of three-dimensional Navier-Stokes equations in margin case. Zbl 1240.35422
Zhang, Xingwei; Zhang, Wenliang; Dong, Boqing
2011
Sharp rate of decay for solutions to non-Newtonian fluid in $$R^2$$. Zbl 1124.35334
Dong, Bo Qing; Li, Yong Sheng
2005
Decay of solutions to equations modelling incompressible bipolar non-Newtonian fluids. Zbl 1091.35067
Dong, Bo-Qing
2005
Remarks on the global regularity and time decay of the 2D MHD equations with partial dissipation. Zbl 1421.35296
Zhang, Zhaoyun; Dong, Bo-qing; Jia, Yan
2019
Stability analysis of the supercritical surface quasi-geostrophic equation. Zbl 07095176
Jia, Yan; Gui, Xingguo; Dong, Bo-Qing
2013
Time decay rates of the isotropic non-Newtonian flows in $$\mathbb R^{n}$$. Zbl 1115.35106
Dong, Bo-Qing
2007
Large time behavior of the modified Navier-Stokes equations. Zbl 1168.35410
Dong, Boqing; Li, Yongsheng
2006
Asymptotic behavior of the nonlinear parabolic equations. Zbl 1067.35016
Dong, Boqing
2004
Global regularity results for the climate model with fractional dissipation. Zbl 1406.35270
Dong, Boqing; Wang, Wenjuan; Wu, Jiahong; Zhang, Hui
2019
Global regularity for a 2D tropical climate model with fractional dissipation. Zbl 1415.86028
Dong, Bo-Qing; Wu, Jiahong; Ye, Zhuan
2019
Global well-posedness for 2-D Boussinesq system with the temperature-dependent viscosity and supercritical dissipation. Zbl 1414.35153
Zhai, Xiaoping; Dong, Bo-Qing; Chen, Zhi-Min
2019
Global regularity for a class of 2D generalized tropical climate models. Zbl 1412.35249
Dong, Bo-Qing; Wang, Wenjuan; Wu, Jiahong; Ye, Zhuan; Zhang, Hui
2019
Remarks on the global regularity and time decay of the 2D MHD equations with partial dissipation. Zbl 1421.35296
Zhang, Zhaoyun; Dong, Bo-qing; Jia, Yan
2019
Global regularity and time decay for the 2D magnetohydrodynamic equations with fractional dissipation and partial magnetic diffusion. Zbl 1406.35269
Dong, Bo-Qing; Jia, Yan; Li, Jingna; Wu, Jiahong
2018
Global regularity for the 2D micropolar equations with fractional dissipation. Zbl 1397.35204
Dong, Bo-Qing; Wu, Jiahong; Xu, Xiaojing; Ye, Zhuan
2018
Global well-posedness and large-time decay for the 2D micropolar equations. Zbl 1361.35143
Dong, Bo-Qing; Li, Jingna; Wu, Jiahong
2017
Stability behaviors of Leray weak solutions to the three-dimensional Navier-Stokes equations. Zbl 1342.35214
Dong, Bo-Qing; Jia, Yan
2016
Global classical solutions to the one-dimensional compressible fluid models of Korteweg type with large initial data. Zbl 1320.35275
Chen, Zhengzheng; Chai, Xiaojuan; Dong, Boqing; Zhao, Huijiang
2015
Remarks on the logarithmical regularity criterion of the supercritical surface quasi-geostrophic equation in Morrey spaces. Zbl 1316.35063
Jia, Yan; Dong, Bo-Qing
2015
Asymptotic convergence rate of supercritical surface quasi-geostrophic equation in Morrey space. Zbl 1310.35038
Jia, Yan; Dong, Bo-Qing
2015
On the weak-strong uniqueness of Koch-Tataru’s solution for the Navier-Stokes equations. Zbl 1285.35064
Dong, Bo-Qing; Zhang, Zhifei
2014
Remarks on the blow-up criterion for smooth solutions of the Boussinesq equations with zero diffusion. Zbl 1267.35164
Jia, Yan; Zhang, Xingwei; Dong, Bo-Qing
2013
Remarks on the regularity criteria of weak solutions to the three-dimensional micropolar fluid equations. Zbl 1292.35232
Jia, Yan; Zhang, Xing-Wei; Zhang, Wen-Liang; Dong, Bo-Qing
2013
Stability analysis of the supercritical surface quasi-geostrophic equation. Zbl 07095176
Jia, Yan; Gui, Xingguo; Dong, Bo-Qing
2013
On the pressure regularity criterion of the 3D Navier-Stokes equations. Zbl 1248.35151
Zhang, Xingwei; Jia, Yan; Dong, Bo-Qing
2012
On the weak-strong uniqueness of the dissipative surface quasi-geostrophic equation. Zbl 1241.35158
Dong, Bo-Qing; Chen, Zhi-Min
2012
Global regularity and asymptotic behavior of modified Navier-Stokes equations with fractional dissipation. Zbl 1234.35179
Dong, Bo-Qing; Song, Juan
2012
An improved regularity criterion of three-dimensional magnetohydrodynamic equations. Zbl 1239.76070
Dong, Bo-Qing; Jia, Yan; Zhang, Wenliang
2012
Remarks on the weak-strong uniqueness for the 2D quasi-geostrophic equation in BMO space. Zbl 1255.35178
Liu, Qingqing; Jia, Yan; Dong, Bo-Qing
2012
Logarithmical regularity criteria of the three-dimensional micropolar fluid equations in terms of the pressure. Zbl 1246.76140
Jia, Yan; Zhang, Jing; Dong, Bo-Qing
2012
Pressure regularity criteria of the three-dimensional micropolar fluid flows. Zbl 1219.35189
Dong, Bo-Qing; Jia, Yan; Chen, Zhi-Min
2011
The asymptotic behavior of solutions to three-dimensional Navier-Stokes equations with nonlinear damping. Zbl 1216.35088
Jia, Yan; Zhang, Xingwei; Dong, Bo-Qing
2011
On the regularity criteria of the 3D Navier-Stokes equations in critical spaces. Zbl 1240.35382
Dong, Boqing; Gala, Sadek; Chen, Zhimin
2011
Remarks on the regularity criterion of the 3D micropolar fluid flows in terms of the pressure. Zbl 1210.35189
Jia, Yan; Zhang, Wenliang; Dong, Bo-Qing
2011
Remarks on the regularity criteria of three-dimensional Navier-Stokes equations in margin case. Zbl 1240.35422
Zhang, Xingwei; Zhang, Wenliang; Dong, Boqing
2011
Global regularity of the 2D micropolar fluid flows with zero angular viscosity. Zbl 1402.35220
Dong, Bo-Qing; Zhang, Zhifei
2010
The BKM criterion for the 3D Navier-Stokes equations via two velocity components. Zbl 1196.35153
Dong, Bo-Qing; Zhang, Zhifei
2010
On the regularity criterion for three-dimensional micropolar fluid flows in Besov spaces. Zbl 1194.35322
Dong, Bo-Qing; Zhang, Wenliang
2010
Asymptotic profile of solutions to the two-dimensional dissipative quasi-geostrophic equation. Zbl 1214.35049
Dong, Boqing; Liu, Qingqing
2010
Asymptotic profiles of solutions to the 2D viscous incompressible micropolar fluid flows. Zbl 1170.35336
Dong, Bo-Qing; Chen, Zhi-Min
2009
Regularity criteria of weak solutions to the three-dimensional micropolar flows. Zbl 1283.76016
Dong, Boqing; Chen, Zhimin
2009
Regularity criterion of weak solutions to the 3D Navier-Stokes equations via two velocity components. Zbl 1132.35432
Dong, Bo-Qing; Chen, Zhi-Min
2008
On the decay of higher order derivatives of solutions to Ladyzhenskaya model for incompressible viscous flows. Zbl 1153.35062
Dong, Boqing; Jiang, Wei
2008
A remark on regularity criterion for the dissipative quasi-geostrophic equations. Zbl 1154.76339
Dong, Bo-Qing; Chen, Zhi-Min
2007
Uniform attractors of non-homogeneous micropolar fluid flows in non-smooth domains. Zbl 1155.37043
Chen, Jianwen; Chen, Zhi-Min; Dong, Bo-Qing
2007
On upper and lower bounds of higher order derivatives for solutions to the 2D micropolar fluid equations. Zbl 1158.35074
Dong, Bo-Qing; Chen, Zhi-Min
2007
Pullback attractors of non-autonomous micropolar fluid flows. Zbl 1152.37030
Chen, Jianwen; Dong, Bo-Qing; Chen, Zhi-Min
2007
Time decay rates of the isotropic non-Newtonian flows in $$\mathbb R^{n}$$. Zbl 1115.35106
Dong, Bo-Qing
2007
Asymptotic stability of the critical and super-critical dissipative quasi-geostrophic equation. Zbl 1109.76063
Dong, Boqing; Chen, Zhi-Min
2006
Global attractors of two-dimensional micropolar fluid flows in some unbounded domains. Zbl 1103.76008
Dong, Boqing; Chen, Zhimin
2006
Existence of $$H^{2}$$-global attractors of two-dimensional micropolar fluid flows. Zbl 1098.35035
Chen, Jianwen; Chen, Zhi-Min; Dong, Bo-Qing
2006
Time decay rates of non-Newtonian flows in $$\mathbf {R}^{n}_{+}$$. Zbl 1102.76014
Dong, Bo-Qing; Chen, Zhi-Min
2006
Asymptotic stability of non-Newtonian flows with large perturbation in $$\mathbb{R}^{2}$$. Zbl 1138.35380
Dong, Bo-Qing; Chen, Zhi-Min
2006
Remarks on upper and lower bounds of solutions to the Navier–Stokes equations in $$\mathbb R^{2}$$. Zbl 1103.76016
Dong, Boqing; Chen, Zhimin
2006
Large time behavior of the modified Navier-Stokes equations. Zbl 1168.35410
Dong, Boqing; Li, Yongsheng
2006
Sharp rate of decay for solutions to non-Newtonian fluid in $$R^2$$. Zbl 1124.35334
Dong, Bo Qing; Li, Yong Sheng
2005
Decay of solutions to equations modelling incompressible bipolar non-Newtonian fluids. Zbl 1091.35067
Dong, Bo-Qing
2005
Large time behavior to the system of incompressible non-Newtonian fluids in $$\mathbb{R}^2$$. Zbl 1059.35104
Dong, Boqing; Li, Yongsheng
2004
Asymptotic behavior of the nonlinear parabolic equations. Zbl 1067.35016
Dong, Boqing
2004
all top 5
#### Cited by 277 Authors
33 Dong, Boqing 16 Jia, Yan 16 Wu, Jiahong 14 Zhao, Caidi 13 Gala, Sadek 13 Ragusa, Maria Alessandra 9 Shang, Haifeng 9 Ye, Zhuan 8 Chen, Zhimin 8 Yamazaki, Kazuo 6 Liu, Qiao 6 Yuan, Baoquan 6 Zhao, Jihong 5 Li, Yeping 5 Liu, Guowei 5 Wang, Yinxia 4 Guterres, Robert H. 4 Nunes, Juliana R. 4 Perusato, Cilon F. 4 Sun, Wenlong 4 Tan, Zhong 4 Wang, Yuzhu 4 Xie, Qianqian 4 Zhang, Zujin 4 Zhou, Shengfan 3 Chen, Zhengzheng 3 Fan, Jishan 3 Guo, Yana 3 Guo, Zhengguang 3 Łukaszewicz, Grzegorz 3 Ma, Liangliang 3 Ren, Junbai 3 Tran, Chuong V. 3 Wang, Wenjuan 3 Wu, Fan 3 Xiang, Zhaoyin 3 Xu, Fuyi 3 Xu, Xiaojing 3 Yu, Xinwei 3 Zhang, Wenliang 3 Zhang, Xingwei 3 Zhu, Mingxuan 3 Zhu, Weipeng 2 Bai, Meng 2 Barker, Tobias 2 Benseridi, Hamid 2 Caraballo Garrido, Tomás 2 Chen, Jianwen 2 Constantin, Peter 2 Dong, Hongjie 2 Gala, Saddek 2 Gu, Chuanwei 2 Hong, Hakho 2 Hou, Xiaofeng 2 Jiang, Yaolin 2 Li, Fang 2 Li, Huapeng 2 Li, Xiao 2 Li, Yin 2 Li, Yongsheng 2 Lin, Hongxia 2 Liu, QingQing 2 Liu, Xin 2 Liu, Yujun 2 Ma, Xuan 2 Melo, Wilberclay G. 2 Nowakowski, Bernard 2 Pavlović, Nataša 2 Qiao, Yuanyuan 2 Qin, Yuming 2 Wei, Ruiying 2 Xu, Qiuju 2 Xu, Zhonghai 2 Yang, Xinguang 2 Yang, Yun-Bo 2 Yao, Zhengan 2 Ye, Hailong 2 Ye, Zhuan 2 You, Bo 2 Yu, Huan 2 Zhang, Zhifei 2 Zhao, Min 2 Zhou, Guopeng 2 Zhu, Changjiang 2 Zhu, Peicheng 2 Zhu, Xiuli 1 Abo-dahab, S. M. 1 Agarwal, Ravi P. 1 Albritton, Dallas 1 Alghamdi, Ahmad Mohammad 1 An, Rong 1 Antonelli, Paolo 1 Ben Omrane, Ines 1 Benterki, Djamila 1 Boardman, Nicki 1 Cai, Chao 1 Cao, Juan 1 Chae, Dongho 1 Chai, Shugen 1 Chai, Xiaojuan ...and 177 more Authors
all top 5
#### Cited in 68 Serials
23 Journal of Mathematical Analysis and Applications 23 Nonlinear Analysis. Real World Applications 18 Applied Mathematics Letters 15 ZAMP. Zeitschrift für angewandte Mathematik und Physik 13 Applied Mathematics and Computation 12 Journal of Differential Equations 11 Abstract and Applied Analysis 11 Boundary Value Problems 9 Journal of Mathematical Physics 9 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 8 Journal of Mathematical Fluid Mechanics 7 Computers & Mathematics with Applications 7 Mathematical Methods in the Applied Sciences 7 Bulletin of the Malaysian Mathematical Sciences Society. Second Series 5 Applicable Analysis 5 Discrete and Continuous Dynamical Systems. Series B 4 Acta Mathematicae Applicatae Sinica. English Series 3 Archive for Rational Mechanics and Analysis 3 Acta Applicandae Mathematicae 3 Mathematical Problems in Engineering 2 Annales Polonici Mathematici 2 Archiv der Mathematik 2 Bulletin of the Korean Mathematical Society 2 Discrete and Continuous Dynamical Systems 2 Journal of Applied Mathematics 2 Acta Mathematica Scientia. Series B. (English Edition) 2 Bulletin of the Brazilian Mathematical Society. New Series 2 Science China. Mathematics 1 Communications in Mathematical Physics 1 Mathematical Notes 1 Nonlinearity 1 Reviews in Mathematical Physics 1 Advances in Mathematics 1 Applied Mathematics and Optimization 1 Integral Equations and Operator Theory 1 Journal of Functional Analysis 1 Journal of the Korean Mathematical Society 1 Mathematische Zeitschrift 1 Monatshefte für Mathematik 1 Proceedings of the American Mathematical Society 1 Results in Mathematics 1 Chinese Annals of Mathematics. Series B 1 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 1 Physica D 1 Journal of Scientific Computing 1 Forum Mathematicum 1 Science in China. Series A 1 Applied Mathematical Modelling 1 International Journal of Computer Mathematics 1 Journal de Mathématiques Pures et Appliquées. Neuvième Série 1 SIAM Journal on Mathematical Analysis 1 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 1 Journal of Nonlinear Science 1 Random Operators and Stochastic Equations 1 Journal of Inverse and Ill-Posed Problems 1 NoDEA. Nonlinear Differential Equations and Applications 1 Differential Equations and Dynamical Systems 1 Journal of Inequalities and Applications 1 Communications in Nonlinear Science and Numerical Simulation 1 Proceedings of the National Academy of Sciences, India. Section A. Physical Sciences 1 Sibirskie Èlektronnye Matematicheskie Izvestiya 1 Frontiers of Mathematics in China 1 Discrete and Continuous Dynamical Systems. Series S 1 Asian-European Journal of Mathematics 1 Advances in Mathematical Physics 1 Analysis and Mathematical Physics 1 Research in the Mathematical Sciences 1 Electronic Research Archive
all top 5
#### Cited in 19 Fields
242 Partial differential equations (35-XX) 198 Fluid mechanics (76-XX) 16 Geophysics (86-XX) 12 Dynamical systems and ergodic theory (37-XX) 12 Harmonic analysis on Euclidean spaces (42-XX) 4 Probability theory and stochastic processes (60-XX) 4 Numerical analysis (65-XX) 3 Functions of a complex variable (30-XX) 3 Optics, electromagnetic theory (78-XX) 2 Ordinary differential equations (34-XX) 2 Functional analysis (46-XX) 2 Mechanics of deformable solids (74-XX) 1 Real functions (26-XX) 1 Measure and integration (28-XX) 1 Approximations and expansions (41-XX) 1 1 Classical thermodynamics, heat transfer (80-XX) 1 Biology and other natural sciences (92-XX) 1 Systems theory; control (93-XX) | 2021-02-26 12:48:48 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 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": 0.6579464077949524, "perplexity": 7253.203254675579}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-10/segments/1614178357641.32/warc/CC-MAIN-20210226115116-20210226145116-00127.warc.gz"} |
https://meta.mathoverflow.net/questions/5543/is-this-question-about-partition-numbers-too-broad-vague | Here's my proposed question (edit: now posted) (edit 2: posted version now edited):
I have found an algorithm for counting partitions, and I've been able to express it into a mathematical formula, $$P(n) = \sum_{i=1}^{x} p_i$$. The formula has less than $$P(n)$$ computation steps (that is, it counts partitions in batches), but it is still huge, and I have yet to simplify it. Therefore, I would like to know whether or not other such formulas have been found, in case one of them is the same as mine. If so, I could perhaps spare myself the hassle of pursuing a dead-end/already-explored end/etc. In summary, I just want to know if my discovery is a rediscovery (and thereupon, find out more about the value of the discovery). So, are the formulas that count all the partitions of $$n$$ (in batches)?
Is this too vague/broad? It would be a better question if I could share more, but I do not want to disclose too much information about my research outside of a proper publication.
This is how my question looks now:
Does there exist a formula of this form:
$$P(n) = \sum_{i=1}^{x\le P(n)} p_i$$
Where $$P(n)$$ is the partition function, and the $$p_i$$ are batches of partitions of quantity $$\ge 1$$. The sum is just a closed-form, explicit mathematical expression of an algorithm that counts through all the partitions, but given the algorithm's nature, that counting can be somewhat compressed.
If no such algorithm has been found, my question defers to whether or not an algorithm for counting partitions one-by-one has been found. I'd think so, but I haven't seen one in my research.
It has been closed due to lacking clarity. All I want is an explanation for what is missing to give an answer. What is confusing? No-one has explained what is confusing/missing, except for one user saying the answer was trivially yes based on what I find to be a non-sensical reading of the question (that is e.g. $$P(n) = \sum_{k=1}^n P_k(n)$$, thus the answer is yes). I don't see why I have to publish my research just to give a concrete example of a form that seems simple enough.
• Before asking your question -- did you check Wikipedia? -- en.wikipedia.org/wiki/Partition_function_(number_theory)
– Stefan Kohl Mod
Dec 16, 2022 at 8:54
• @StefanKohl I've read through it many times. It only contains generating functions, recurrence relations and approximation functions, as well as some congruences and some stuff about strict partitions. There is no exact formula in there, even though there exists one, courtesy of Rademacher. However, I think Rademacher's formula is not closed-form, but I am pretty sure mine is. But that then seems WAY too unrealistic to be true, so I'm wondering if there something about my formula that makes it less impressive or something. Dec 16, 2022 at 14:45
• I suggest having a look at www2.math.upenn.edu/~wilf/PIMS/PIMSLectures.pdf especially page 14 Dec 19, 2022 at 6:13
• My previous remark was meant to dispute the claim that Rademacher's formula is not closed form. I suppose the link I gave is not relevant to the current form of the question. In any event, if no one is giving you the sort of answer you want, and several users are telling you that they need to know what your method is before they can answer your question, it seems to me to be quite wrong-headed to insist that these users are wrong. Dec 20, 2022 at 23:33
• @GerryMyerson How is it not closed form? It is an infinite sum. Dec 22, 2022 at 15:11
• Please, go to the link that I gave you a few days ago, it should clear up your confusion. Dec 22, 2022 at 16:02 | 2023-02-07 02:05:04 | {"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": 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": 8, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7145116329193115, "perplexity": 323.37170514445324}, "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/1674764500368.7/warc/CC-MAIN-20230207004322-20230207034322-00824.warc.gz"} |
https://daniel.wordpress.com/category/unit-017-2-nephi-23/ | Unit 17 – word and phrase data
Unit 17: 2 Nephi Chapter 23 through 2 Nephi Chapter 24
The material covered in this unit corresponds with the content of 2 Nephi chapter 10 in the 1830 edition.
The information below is based on the wording in the The Book of Mormon: The Earliest Text.
a – 16 occurrences – verses 23:2, 23:4, 23:5, 23:6, 23:12, 23:14, 24:6, 24:17, 24:19, 24:23, 24:29, 24:31
a man – 2 occurrences – verses 23:12
abominable – 1 occurrence – verse 24:19
above – 2 occurrences – verses 24:13, 24:14
above the – 2 occurrences – verses 24:13, 24:14
afraid – 1 occurrence – verse 23:8
against – 4 occurrences – verses 23:17, 24:4, 24:8, 24:22
against them – 2 occurrences – verses 23:17, 24:22
Ahaz – 1 occurrence – verse 24:28
all – 7 occurrences – verses 23:7, 24:9, 24:10, 24:18, 24:26
all the – 3 occurrences – verses 24:9, 24:18
all the kings of the nations – 2 occurrences – verses 24:9, 24:18
Almighty – 1 occurrence – verse 23:6
alone – 1 occurrence – verse 24:31
also – 7 occurrences – verses 23:3, 23:16, 23:18, 24:8, 24:10, 24:13, 24:23
amazed – 1 occurrence – verse 23:8
Amoz – 1 occurrence – verse 23:1
an – 1 occurrence – verse 24:19
and – 77 occurrences – verses 23:5, 23:8, 23:9, 23:10, 23:11, 23:13, 23:14, 23:15, 23:16, 23:17, 23:18, 23:19, 23:21, 23:22, 24:1, 24:2, 24:3, 24:4, 24:6, 24:7, 24:8, 24:10, 24:11, 24:16, 24:17, 24:19, 24:20, 24:22, 24:23, 24:24, 24:25, 24:26, 24:27, 24:29, 24:30, 24:31, 24:32
and as – 2 occurrences – verses 23:14, 24:24
and from – 2 occurrences – verse 24:3
and he shall – 2 occurrences – verses 23:9, 24:30
and her – 2 occurrences – verse 23:22
and his – 3 occurrences – verses 24:25, 24:27, 24:29
and I will – 3 occurrences – verses 23:11, 24:23, 24:30
and it shall – 3 occurrences – verses 23:14, 24:3, 24:4
and it shall come to pass – 2 occurrences – verses 24:3, 24:4
and none – 2 occurrences – verses 24:6, 24:31
and say – 2 occurrences – verses 24:4, 24:10
and the – 15 occurrences – verses 23:5, 23:10, 23:11, 23:13, 23:22, 24:1, 24:2, 24:11, 24:19, 24:30, 24:32
and their – 2 occurrences – verses 23:16, 23:21
and they shall – 6 occurrences – verses 23:8, 23:18, 24:1, 24:2
and who shall – 2 occurrences – verse 24:27
and will – 2 occurrences – verses 23:11, 24:1
anger – 4 occurrences – verses 23:3, 23:9, 23:13, 24:6
anger is – 2 occurrences – verses 23:3, 24:6
another – 1 occurrence – verse 23:8
answer – 1 occurrence – verse 24:32
appointed – 1 occurrence – verse 24:31
Arabian – 1 occurrence – verse 23:20
are – 1 occurrence – verse 24:19
arrogancy – 1 occurrence – verse 23:11
art – 7 occurrences – verses 24:8, 24:10, 24:12, 24:19, 24:31
art thou – 4 occurrences – verses 24:10, 24:12
as – 11 occurrences – verses 23:4, 23:6, 23:8, 23:14, 23:19, 24:10, 24:17, 24:19, 24:24
as a – 4 occurrences – verses 23:6, 23:14, 24:17, 24:19
as I have – 2 occurrences – verse 24:24
ascend – 2 occurrences – verses 24:13, 24:14
Assyrian – 1 occurrence – verse 24:25
at – 5 occurrences – verses 23:6, 23:8, 24:7, 24:8, 24:9
Babylon – 4 occurrences – verses 23:1, 23:19, 24:4, 24:22
Babylon the – 2 occurrences – verses 23:19, 24:22
back – 1 occurrence – verse 24:27
banner – 1 occurrence – verse 23:2
battle – 1 occurrence – verse 23:4
be – 23 occurrences – verses 23:7, 23:8, 23:10, 23:14, 23:15, 23:16, 23:19, 23:20, 23:21, 23:22, 24:1, 24:2, 24:14, 24:15, 24:20, 24:29, 24:31
be joined with them – 2 occurrences – verses 24:1, 24:20
beasts – 2 occurrences – verses 23:21, 23:22
beauty – 1 occurrence – verse 23:19
because – 2 occurrences – verses 24:20, 24:29
become – 2 occurrences – verse 24:10
before – 1 occurrence – verse 23:16
behold – 2 occurrences – verses 23:9, 23:17
beneath – 1 occurrence – verse 24:9
besom – 1 occurrence – verse 24:23
bittern – 1 occurrence – verse 24:23
bondage – 1 occurrence – verse 24:3
born – 1 occurrence – verse 24:30
both – 1 occurrence – verse 23:9
bows – 1 occurrence – verse 23:18
branch – 1 occurrence – verse 24:19
break – 2 occurrences – verses 24:7, 24:25
bring – 1 occurrence – verse 24:2
broken – 2 occurrences – verses 24:5, 24:29
brought – 2 occurrences – verses 24:11, 24:15
brought down to – 2 occurrences – verses 24:11, 24:15
burden – 3 occurrences – verses 23:1, 24:25, 24:28
burial – 1 occurrence – verse 24:20
but – 3 occurrences – verses 23:21, 23:22, 24:19
by – 1 occurrence – verse 23:15
called – 1 occurrence – verse 23:3
captives – 2 occurrences – verse 24:2
carcass – 1 occurrence – verse 24:19
cast – 1 occurrence – verse 24:19
cause – 2 occurrences – verses 23:10, 23:11
cease – 1 occurrence – verse 23:11
ceased – 2 occurrences – verse 24:4
cedars – 1 occurrence – verse 24:8
Chaldees’ – 1 occurrence – verse 23:19
chased – 1 occurrence – verse 23:14
chief – 1 occurrence – verse 24:9
children – 3 occurrences – verses 23:16, 23:18, 24:21
choose – 1 occurrence – verse 24:1
cities – 2 occurrences – verses 24:17, 24:21
city – 2 occurrences – verses 24:4, 24:31
cleave – 1 occurrence – verse 24:1
clouds – 1 occurrence – verse 24:14
cockatrice – 1 occurrence – verse 24:29
come – 9 occurrences – verses 23:5, 23:6, 23:22, 24:3, 24:4, 24:8, 24:24, 24:29, 24:31
come from – 2 occurrences – verses 23:5, 24:31
come to pass – 3 occurrences – verses 24:3, 24:4, 24:24
cometh – 1 occurrence – verse 23:9
coming – 1 occurrence – verse 24:9
commanded – 1 occurrence – verse 23:3
congregation – 1 occurrence – verse 24:13
consider – 1 occurrence – verse 24:16
constellations – 1 occurrence – verse 23:10
continual – 1 occurrence – verse 24:6
country – 1 occurrence – verse 23:5
cover – 1 occurrence – verse 24:11
creatures – 1 occurrence – verse 23:21
cruel – 1 occurrence – verse 23:9
cry – 2 occurrences – verses 23:22, 24:31
cut – 2 occurrences – verses 24:12, 24:22
dance – 1 occurrence – verse 23:21
darkened – 1 occurrence – verse 23:10
dash – 1 occurrence – verse 23:18
dashed – 1 occurrence – verse 23:16
day – 6 occurrences – verses 23:6, 23:9, 23:13, 23:22, 24:3, 24:4
dead – 1 occurrence – verse 24:9
delight – 1 occurrence – verse 23:17
depart – 2 occurrences – verse 24:25
depart from off – 2 occurrences – verse 24:25
desert – 1 occurrence – verse 23:21
desolate – 2 occurrences – verses 23:9, 23:22
destroy – 3 occurrences – verses 23:5, 23:9, 23:22
destroy the – 2 occurrences – verses 23:5, 23:9
destroyed – 2 occurrences – verses 24:17, 24:20
destruction – 2 occurrences – verses 23:6, 24:23
did – 3 occurrences – verses 23:1, 24:12, 24:16
died – 1 occurrence – verse 24:28
disannul – 1 occurrence – verse 24:27
dissolved – 1 occurrence – verse 24:31
do – 1 occurrence – verse 24:21
doleful – 1 occurrence – verse 23:21
down – 7 occurrences – verses 23:11, 24:8, 24:11, 24:12, 24:15, 24:19, 24:30
down to – 4 occurrences – verses 24:11, 24:12, 24:15, 24:19
down to the – 3 occurrences – verses 24:11, 24:12, 24:19
dragons – 1 occurrence – verse 23:22
dwell – 1 occurrence – verse 23:21
dwelt – 1 occurrence – verse 23:20
earth – 6 occurrences – verses 23:13, 24:2, 24:7, 24:9, 24:16, 24:26
earth and – 2 occurrences – verses 24:2, 24:26
end – 1 occurrence – verse 23:5
ends – 1 occurrence – verse 24:2
even – 2 occurrences – verses 23:12, 24:9
every – 6 occurrences – verses 23:7, 23:14, 23:15, 24:18
every one – 4 occurrences – verses 23:14, 23:15, 24:18
every one that is – 2 occurrences – verse 23:15
evil – 1 occurrence – verse 23:11
evildoers – 1 occurrence – verse 24:20
exalt – 2 occurrences – verses 23:2, 24:13
excellency – 1 occurrence – verse 23:19
eyes – 2 occurrences – verses 23:16, 23:18
face – 1 occurrence – verse 24:21
faces – 1 occurrence – verse 23:8
faint – 1 occurrence – verse 23:7
fall – 1 occurrence – verse 23:15
fallen – 1 occurrence – verse 24:12
famine – 1 occurrence – verse 24:30
far – 2 occurrences – verses 23:5, 24:2
fathers – 1 occurrence – verse 24:21
fear – 1 occurrence – verse 24:3
feed – 1 occurrence – verse 24:30
feet – 1 occurrence – verse 24:19
feller – 1 occurrence – verse 24:8
fierce – 2 occurrences – verses 23:9, 23:13
fierce anger – 2 occurrences – verses 23:9, 23:13
fiery – 1 occurrence – verse 24:29
fill – 1 occurrence – verse 24:21
fine – 1 occurrence – verse 23:12
fir – 1 occurrence – verse 24:8
first – 1 occurrence – verse 24:30
flames – 1 occurrence – verse 23:8
flee – 1 occurrence – verse 23:14
flying – 1 occurrence – verse 24:29
fold – 1 occurrence – verse 23:20
foot – 1 occurrence – verse 24:25
for – 19 occurrences – verses 23:3, 23:6, 23:10, 23:11, 23:22, 24:1, 24:2, 24:9, 24:13, 24:21, 24:22, 24:23, 24:27, 24:29, 24:31
for I will – 3 occurrences – verses 23:22, 24:22
for the – 6 occurrences – verses 23:6, 23:10, 24:1, 24:21, 24:23, 24:27
for the Lord – 2 occurrences – verses 24:1, 24:27
for thee – 2 occurrences – verse 24:9
forth – 3 occurrences – verses 23:10, 24:7, 24:29
founded – 1 occurrence – verse 24:32
from – 15 occurrences – verses 23:5, 23:6, 23:20, 24:2, 24:3, 24:9, 24:12, 24:22, 24:25, 24:31
from the – 4 occurrences – verses 23:5, 23:6, 24:3, 24:31
from thy – 2 occurrences – verse 24:3
fruit – 2 occurrences – verses 23:18, 24:29
full – 1 occurrence – verse 23:21
gate – 1 occurrence – verse 24:31
gates – 1 occurrence – verse 23:2
gathered – 1 occurrence – verse 23:4
generation – 2 occurrences – verse 23:20
give – 2 occurrences – verses 23:10, 24:3
glory – 2 occurrences – verses 23:19, 24:18
go – 2 occurrences – verses 23:2, 24:19
God – 2 occurrences – verses 23:19, 24:13
going – 1 occurrence – verse 23:10
gold – 2 occurrences – verses 23:12, 23:17
golden – 2 occurrences – verses 23:12, 24:4
Gomorrah – 1 occurrence – verse 23:19
grave – 2 occurrences – verses 24:11, 24:19
great – 1 occurrence – verse 23:4
ground – 1 occurrence – verse 24:12
hand – 4 occurrences – verses 23:2, 23:6, 24:26, 24:27
handmaids – 1 occurrence – verse 24:2
hands – 1 occurrence – verse 23:7
hard – 1 occurrence – verse 24:3
hast – 2 occurrences – verses 24:13, 24:20
hath – 6 occurrences – verses 24:4, 24:5, 24:9, 24:24, 24:27, 24:32
haughtiness – 1 occurrence – verse 23:11
have – 6 occurrences – verses 23:3, 23:18, 24:1, 24:24
he – 4 occurrences – verses 23:9, 24:6, 24:30
heard – 1 occurrence – verse 24:11
heart – 2 occurrences – verses 23:7, 24:13
heaven – 4 occurrences – verses 23:5, 23:10, 24:12, 24:13
heavens – 1 occurrence – verse 23:13
heights – 1 occurrence – verse 24:14
hell – 2 occurrences – verses 24:9, 24:15
her – 23:10, 23:13, 23:22
high – 2 occurrences – verses 23:2, 24:14
highness – 1 occurrence – verse 23:3
him – 2 occurrences – verses 24:25, 24:29
hindereth – 1 occurrence – verse 24:6
his – 14 occurrences – verses 23:5, 23:10, 23:13, 23:14, 24:17, 24:18, 24:21, 24:25, 24:27, 24:29, 24:31, 24:32
his own – 3 occurrences – verses 23:14, 24:18
hold – 1 occurrence – verse 23:8
host – 1 occurrence – verse 23:4
hosts – 6 occurrences – verses 23:4, 23:13, 24:22, 24:23, 24:24, 24:27
house – 4 occurrences – verses 24:1, 24:2, 24:17, 24:18
houses – 3 occurrences – verses 23:16, 23:21, 23:22
how – 2 occurrences – verses 24:4, 24:12
howl – 2 occurrences – verses 23:6, 24:31
I – 21 occurrences – verses 23:3, 23:11, 23:12, 23:13, 23:17, 23:22, 24:13, 24:14, 24:22, 24:23, 24:24, 24:25, 24:30
I have – 4 occurrences – verses 23:3, 24:24
I will – 17 occurrences – verses 23:11, 23:12, 23:13, 23:17, 23:22, 24:13, 24:14, 24:22, 24:23, 24:25, 24:30
I will ascend – 2 occurrences – verses 24:13, 24:14
I will be – 2 occurrences – verses 23:22, 24:14
in – 24 occurrences – verses 23:3, 23:4, 23:10, 23:13, 23:17, 23:20, 23:22, 24:1, 24:3, 24:4, 24:6, 24:13, 24:18, 24:20, 24:25, 24:28, 24:30, 24:31, 24:32
in his – 3 occurrences – verses 23:10, 24:18, 24:31
in it – 2 occurrences – verses 23:17, 24:32
in my – 2 occurrences – verses 23:3, 24:25
in that day that – 2 occurrences – verses 24:3, 24:4
in the – 5 occurrences – verses 23:4, 23:13, 24:13, 24:28
in their – 3 occurrences – verses 23:22, 24:1
indignation – 1 occurrence – verse 23:5
inhabited – 1 occurrence – verse 23:20
iniquities – 1 occurrence – verse 24:21
iniquity – 1 occurrence – verse 23:11
into – 4 occurrences – verses 23:2, 23:14, 24:7, 24:13
is – 19 occurrences – verses 23:3, 23:6, 23:15, 23:22, 24:6, 24:7, 24:8, 24:9, 24:11, 24:16, 24:26, 24:29
is at – 2 occurrences – verses 23:6, 23:29
is not – 2 occurrences – verses 23:3, 24:11
Isaiah – 1 occurrence – verse 23:1
islands – 1 occurrence – verse 23:22
Israel – 2 occurrences – verses 24:1, 24:2
it – 16 occurrences – verses 23:6, 23:9, 23:14, 23:17, 23:20, 24:3, 24:4, 24:9, 24:23, 24:24, 24:27, 24:32
it shall – 5 occurrences – verses 23:6, 23:14, 23:20, 24:3, 24:4
it shall come – 3 occurrences – verses 23:6, 24:3, 24:4
Jacob – 2 occurrences – verse 24:1
joined – 3 occurrences – verses 23:15, 24:1, 24:20
kill – 1 occurrence – verse 24:30
king – 2 occurrences – verses 24:4, 24:28
kingdoms – 3 occurrences – verses 23:4, 23:19, 24:16
kings – 2 occurrences – verses 24:9, 24:18
laid – 1 occurrence – verse 24:8
land – 8 occurrences – verses 23:5, 23:9, 23:14, 24:1, 24:2, 24:20, 24:21, 24:25
land and – 3 occurrences – verses 24:1, 24:20, 24:25
lands – 1 occurrence – verse 24:2
lay – 2 occurrences – verses 23:9, 23:11
Lebanon – 1 occurrence – verse 24:8
lie – 3 occurrences – verses 23:21, 24:18, 24:30
lift – 1 occurrence – verse 23:2
light – 2 occurrences – verse 23:10
like – 4 occurrences – verses 23:4, 24:10, 24:14, 24:19
look – 1 occurrence – verse 24:16
Lord – 15 occurrences – verses 23:4, 23:5, 23:6, 23:9, 23:13, 24:1, 24:2, 24:3, 24:5, 24:22, 24:23, 24:24, 24:27, 24:32
Lucifer – 1 occurrence – verse 24:12
made – 3 occurrences – verses 24:3, 24:16, 24:17
made the – 2 occurrences – verses 24:16, 24:17
make – 3 occurrences – verses 23:12, 23:20, 24:23
man – 5 occurrences – verses 23:12, 23:14, 24:16
man’s – 1 occurrence – verse 23:7
may – 1 occurrence – verse 23:2
Medes – 1 occurrence – verse 23:17
meet – 1 occurrence – verse 24:9
melt – 1 occurrence – verse 23:7
men – 1 occurrence – verse 23:18
merciful – 1 occurrence – verse 23:22
mercy – 1 occurrence – verse 24:1
messengers – 1 occurrence – verse 24:32
mighty – 1 occurrence – verse 23:3
mine – 1 occurrence – verse 23:3
moon – 1 occurrence – verse 23:10
more – 1 occurrence – verse 23:12
morning – 1 occurrence – verse 24:12
most – 1 occurrence – verse 24:14
mount – 1 occurrence – verse 24:13
mountain – 1 occurrence – verse 23:2
mountains – 2 occurrences – verses 23:4, 24:25
moved – 1 occurrence – verse 24:9
multitude – 1 occurrence – verse 23:4
mustereth – 1 occurrence – verse 23:4
my – 7 occurrences – verses 23:3, 23:22, 24:13, 24:25
name – 1 occurrence – verse 24:22
narrowly – 1 occurrence – verse 24:16
nations – 7 occurrences – verses 23:4, 24:6, 24:9, 24:12, 24:18, 24:26, 24:32
near – 1 occurrence – verse 23:22
needy – 1 occurrence – verse 24:30
neither – 3 occurrences – verse 23:20
neither shall – 3 occurrences – verses 23:20
neither shall the – 2 occurrences – verse 23:20
nephew – 1 occurrence – verse 24:22
never – 2 occurrences – verses 23:20, 24:20
no – 3 occurrences – verses 23:14, 23:18, 24:8
nobles – 1 occurrence – verse 23:2
noise – 3 occurrences – verses 23:4, 24:11
noise of – 3 occurrences – verses 23:4, 24:11
noise of the – 2 occurrences – verse 23:4
none – 2 occurrences – verses 24:6, 24:31
nor – 3 occurrences – verses 23:17, 24:21
north – 2 occurrences – verses 24:13, 24:31
not – 12 occurrences – verses 23:3, 23:10, 23:17, 23:18, 23:22, 24:11, 24:17, 24:20, 24:21, 24:29
not be – 2 occurrences – verses 23:22, 24:20
O – 3 occurrences – verses 24:12, 24:31
of – 68 occurrences – verses 23:1, 23:2, 23:4, 23:5, 23:6, 23:8, 23:9, 23:10, 23:11, 23:12, 23:13, 23:18, 23:19, 23:21, 23:22, 24:1, 24:2, 24:4, 24:5, 24:8, 24:9, 24:11, 24:12, 24:13, 24:14, 24:15, 24:17, 24:18, 24:19, 24:20, 24:21, 24:22, 24:23, 24:24, 24:27, 24:29, 24:30, 24:32
of Babylon – 2 occurrences – verses 23:1, 24:4
of heaven – 2 occurrences – verses 23:5, 23:10
of his – 4 occurrences – verses 23:5, 23:13, 24:17, 24:32
of the – 30 occurrences – verses 23:2, 23:4, 23:6, 23:9, 23:11, 23:13, 23:18, 23:19, 23:21, 23:22, 24:2, 24:5, 24:9, 24:12, 24:13, 24:14, 24:15, 24:18, 24:19, 24:21, 24:29, 24:30, 24:32
of the earth – 2 occurrences – verses 24:2, 24:9
of the Lord – 4 occurrences – verses 23:6, 23:9, 23:13, 24:2
of the nations – 3 occurrences – verses 24:9, 24:18, 24:32
of the pit – 2 occurrences – verses 24:15, 24:19
of them – 3 occurrences – verses 23:8, 24:18
of thy – 2 occurrences – verses 24:11, 24:19
off – 3 occurrences – verses 24:22, 24:25
on – 2 occurrences – verses 23:18, 24:1
one – 5 occurrences – verses 23:8, 23:14, 23:15, 24:18
ones – 3 occurrences – verses 23:3, 24:9
opened – 1 occurrence – verse 24:17
Ophir – 1 occurrence – verse 23:12
oppressor – 1 occurrence – verse 24:4
oppressors – 1 occurrence – verse 24:2
out – 6 occurrences – verses 23:9, 23:13, 24:19, 24:26, 24:27, 24:29
out of – 4 occurrences – verses 23:9, 23:13, 24:19, 24:29
over – 1 occurrence – verse 24:2
overthrew – 1 occurrence – verse 23:19
owls – 1 occurrence – verse 23:21
own – 4 occurrences – verses 23:14, 24:1, 24:18
own land – 2 occurrences – verses 23:14, 24:1
palaces – 1 occurrence – verse 23:22
Palestina – 2 occurrences – verses 24:29, 24:31
pangs – 1 occurrence – verse 23:8
pass – 3 occurrences – verses 24:3, 24:4, 24:24
people – 7 occurrences – verses 23:4, 23:14, 23:22, 24:2, 24:6, 24:20, 24:32
people shall – 2 occurrences – verses 24:2, 24:32
perish – 1 occurrence – verse 23:22
persecuted – 1 occurrence – verse 24:6
pieces – 2 occurrences – verses 23:16, 23:18
pit – 2 occurrences – verses 24:15, 24:19
pitch – 1 occurrence – verse 23:20
pity – 1 occurrence – verse 23:18
place – 2 occurrences – verses 23:13, 24:2
pleasant – 1 occurrence – verse 23:22
pomp – 1 occurrence – verse 24:11
pools – 1 occurrence – verse 24:23
poor – 2 occurrences – verses 24:30, 24:32
possess – 2 occurrences – verses 24:2, 24:21
possession – 1 occurrence – verse 24:23
precious – 1 occurrence – verse 23:12
prepare – 1 occurrence – verse 24:21
prisoners – 1 occurrence – verse 24:17
prolonged – 1 occurrence – verse 23:22
promise – 1 occurrence – verse 24:2
proud – 2 occurrences – verses 23:11, 23:15
proverb – 1 occurrence – verse 24:4
punish – 1 occurrence – verse 23:11
purpose – 1 occurrence – verse 24:26
purposed – 3 occurrences – verses 24:24, 24:26, 24:27
quiet – 1 occurrence – verse 24:7
raiment – 1 occurrence – verse 24:19
raised – 1 occurrence – verse 24:9
ravished – 1 occurrence – verse 23:16
regard – 1 occurrence – verse 23:17
rejoice – 3 occurrences – verses 23:3, 24:8, 24:29
remnant – 2 occurrences – verses 24:22, 24:30
remove – 1 occurrence – verse 23:13
renowned – 1 occurrence – verse 24:20
rest – 2 occurrences – verses 24:3, 24:7
return – 1 occurrence – verse 24:2
rise – 2 occurrences – verses 24:21, 24:22
rod – 1 occurrence – verse 24:29
roe – 1 occurrence – verse 23:14
root – 2 occurrences – verses 24:29, 24:30
rule – 1 occurrence – verse 24:2
ruled – 1 occurrence – verse 24:6
rulers – 1 occurrence – verse 24:5
safety – 1 occurrence – verse 24:30
said – 1 occurrence – verse 24:13
saith – 3 occurrences – verses 24:22, 24:23
saith the Lord – 3 occurrences – verses 24:22, 24:23
saith the Lord of hosts – 2 occurrences – verses 24:22, 24:23
sanctified – 1 occurrence – verse 23:3
satyrs – 1 occurrence – verse 23:21
say – 3 occurrences – verses 24:4, 24:10, 24:16
saying – 2 occurrences – verses 24:8, 24:24
scepters – 1 occurrence – verse 24:5
see – 2 occurrences – verses 23:1, 24:16
seed – 1 occurrence – verse 24:20
serpent – 1 occurrence – verse 24:29
serpent’s – 1 occurrence – verse 24:29
servants – 1 occurrence – verse 24:2
serve – 1 occurrence – verse 24:3
set – 1 occurrence – verse 24:1
shake – 3 occurrences – verses 23:2, 23:13, 24:16
shake the – 2 occurrences – verses 23:2, 23:13
shall – 65 occurrences – verses 23:6, 23:7, 23:8, 23:9, 23:10, 23:13, 23:14, 23:15, 23:16, 23:17, 23:18, 23:19, 23:20, 23:21, 23:22, 24:1, 24:2, 24:3, 24:4, 24:10, 24:16, 24:20, 24:24, 24:25, 24:27, 24:29, 24:30, 24:31, 24:32
shall be – 14 occurrences – verses 23:8, 23:10, 23:14, 23:15, 23:16, 23:19, 23:21, 24:1, 24:2, 24:29, 24:31
shall be as – 3 occurrences – verses 23:8, 23:14, 23:19
shall come – 5 occurrences – verses 23:6, 24:3, 24:4, 24:29, 24:31
shall it – 3 occurrences – verses 23:20, 24:24
shall lie – 2 occurrences – verses 23:21, 24:30
shall never be – 2 occurrences – verses 23:20, 24:20
shall not – 6 occurrences – verses 23:10, 23:17, 23:18, 23:22
shall take – 3 occurrences – verses 23:8, 24:2
shall take them – 2 occurrences – verse 24:2
shalt – 3 occurrences – verses 24:4, 24:15, 24:20
sheep – 1 occurrence – verse 23:14
shepherds – 1 occurrence – verse 23:20
shine – 1 occurrence – verse 23:10
shoulders – 1 occurrence – verse 24:25
sides – 2 occurrences – verses 24:13, 24:15
silver – 1 occurrence – verse 23:17
since – 1 occurrence – verse 24:8
singing – 1 occurrence – verse 24:7
sinners – 1 occurrence – verse 23:9
sit – 1 occurrence – verse 24:13
slain – 2 occurrences – verses 24:19, 24:20
slaughter – 1 occurrence – verse 24:21
slay – 1 occurrence – verse 24:30
smoke – 1 occurrence – verse 24:31
smote – 2 occurrences – verses 24:6, 24:29
so – 2 occurrences – verses 24:24
so shall it – 2 occurrences – verse 24:24
Sodom – 1 occurrence – verse 23:19
son – 3 occurrences – verses 23:1, 24:12, 24:22
son of – 2 occurrences – verses 23:1, 24:12
sorrow – 1 occurrence – verse 24:3
sorrows – 1 occurrence – verse 23:8
spare – 1 occurrence – verse 23:18
speak – 1 occurrence – verse 24:10
speedily – 1 occurrence – verse 23:22
spoiled – 1 occurrence – verse 23:16
spread – 1 occurrence – verse 24:11
staff – 1 occurrence – verse 24:5
stand – 1 occurrence – verse 24:24
stars – 2 occurrences – verses 23:10, 24:13
stir – 1 occurrence – verse 23:17
stirreth – 1 occurrence – verse 24:9
stones – 1 occurrence – verse 24:19
strangers – 1 occurrence – verse 24:1
stretched – 2 occurrences – verses 24:26, 24:27
stretched out – 2 occurrences – verses 24:26, 24:27
stroke – 1 occurrence – verse 24:6
sun – 1 occurrence – verse 23:10
surely – 1 occurrence – verse 24:24
sweep – 1 occurrence – verse 24:23
sword – 2 occurrences – verses 23:15, 24:19
sworn – 1 occurrence – verse 24:24
take – 4 occurrences – verses 23:8, 24:2, 24:4
taketh – 1 occurrence – verse 23:14
tent – 1 occurrence – verse 23:20
terrible – 1 occurrence – verse 23:11
than – 2 occurrences – verse 23:12
that – 23 occurrences – verses 23:2, 23:3, 23:14, 23:15, 24:3, 24:4, 24:6, 24:16, 24:19, 24:21, 24:25, 24:26, 24:28, 24:29, 24:32
that is – 4 occurrences – verses 23:15, 24:26
that the Lord – 2 occurrences – verses 24:3, 24:32
that they – 2 occurrences – verses 23:2, 24:21
the – 141 occurrences – verses 23:1, 23:2, 23:4, 23:5, 23:6, 23:9, 23:10, 23:11, 23:12, 23:13, 23:14, 23:15, 23:17, 23:18, 23:19, 23:20, 23:21, 23:22, 24:1, 24:2, 24:3, 24:4, 24:5, 24:6, 24:7, 24:8, 24:9, 24:11, 24:12, 24:13, 24:14, 24:15, 24:16, 24:17, 24:18, 24:19, 24:20, 24:21, 24:22, 24:23, 24:24, 24:25, 24:26, 24:27, 24:28, 24:29, 24:30, 24:31, 24:32
the day of – 3 occurrences – verses 23:6, 23:9, 23:13
the day of the Lord – 2 occurrences – verses 23:6, 23:9
the earth – 4 occurrences – verses 23:13, 24:2, 24:9, 24:16
the golden – 2 occurrences – verses 23:12, 24:4
the hand that – 2 occurrences – verses 23:2, 24:26
the house of – 3 occurrences – verses 24:1, 24:2, 24:17
the land – 3 occurrences – verses 23:9, 24:2, 24:21
the Lord – 15 occurrences – verses 23:4, 23:5, 23:6, 23:9, 23:13, 24:1, 24:2, 24:3, 24:5, 24:22, 24:23, 24:24, 24:27, 24:32
the Lord hath – 2 occurrences – verses 24:5, 24:32
the Lord of hosts – 6 occurrences – verses 23:4, 23:13, 24:22, 24:23, 24:24, 24:27
the Lord of hosts and – 2 occurrences – verses 23:13, 24:22
the Lord of hosts hath – 2 occurrences – verses 24:24, 24:27
the Lord shall – 2 occurrences – verses 24:2, 24:3
the nations – 5 occurrences – verses 24:6, 24:9, 24:12, 24:18, 24:32
the noise of – 2 occurrences – verses 23:4, 24:11
the north – 2 occurrences – verses 24:13, 24:31
the people – 2 occurrences – verses 24:2, 24:6
the poor – 2 occurrences – verses 24:30, 24:32
the sides of the – 2 occurrences – verses 24:13, 24:15
the stars of – 2 occurrences – verses 23:10, 24:13
the whole – 3 occurrences – verses 23:5, 24:7, 24:26
the whole earth – 2 occurrences – verses 24:7, 24:26
the wicked – 4 occurrences – verses 23:11, 23:15, 23:22, 24:5
the wicked shall – 2 occurrences – verses 23:15, 23:22
the world – 3 occurrences – verses 23:11, 24:17, 24:21
thee – 12 occurrences – verses 24:3, 24:8, 24:9, 24:10, 24:11, 24:16, 24:29
thee and – 4 occurrences – verses 24:8, 24:11, 24:16
thee and shall – 2 occurrences – verse 24:16
their – 20 occurrences – verses 23:8, 23:10, 23:11, 23:16, 23:18, 23:20, 23:21, 23:22, 24:1, 24:2, 24:9, 24:21, 24:25
their eyes – 2 occurrences – verses 23:16, 23:18
their houses shall be – 2 occurrences – verses 23:16, 23:21
them – 15 occurrences – verses 23:2, 23:3, 23:8, 23:17, 24:1, 24:2, 24:18, 24:20, 24:22, 24:25
them and – 4 occurrences – verses 24:1, 24:2, 24:25
them in – 3 occurrences – verses 24:1, 24:18, 24:20
then – 2 occurrences – verses 24:25, 24:32
there – 6 occurrences – verses 23:20, 23:21, 24:31
there and – 2 occurrences – verse 23:21
therefore – 2 occurrences – verses 23:7, 23:13
thereof – 3 occurrences – verses 23:9, 23:10, 24:17
they – 16 occurrences – verses 23:2, 23:5, 23:8, 23:14, 23:17, 23:18, 24:1, 24:2, 24:7, 24:10, 24:16, 24:21
they shall – 10 occurrences – verses 23:8, 23:14, 23:17, 23:18, 24:1, 24:2, 24:10
they shall be – 2 occurrences – verse 23:8
this – 5 occurrences – verses 24:4, 24:16, 24:26, 24:28
this is the – 2 occurrences – verse 24:26
those – 1 occurrence – verse 24:19
thou – 14 occurrences – verses 24:3, 24:4, 24:8, 24:10, 24:12, 24:13, 24:15, 24:19, 24:20, 24:29, 24:31
thou art – 2 occurrences – verses 24:8, 24:19
thou hast – 2 occurrences – verses 24:13, 24:20
thou shalt – 3 occurrences – verses 24:4, 24:15, 24:20
thou whole Palestina – 2 occurrences – verses 24:29, 24:31
thought – 1 occurrence – verse 24:24
throne – 1 occurrence – verse 24:13
thrones – 1 occurrence – verse 24:9
through – 2 occurrences – verses 23:15, 24:19
thrust – 2 occurrences – verses 23:15, 24:19
thrust through – 2 occurrences – verses 23:15, 24:19
thy – 11 occurrences – verses 24:3, 24:9, 24:11, 24:13, 24:19, 24:20, 24:30
time – 1 occurrence – verse 23:22
times – 1 occurrence – verse 24:31
to – 24 occurrences – verses 23:5, 23:9, 23:10, 23:11, 23:14, 23:15, 23:16, 23:18, 23:20, 23:22, 24:1, 24:2, 24:3, 24:4, 24:9, 24:11, 24:12, 24:15, 24:16, 24:19, 24:24
to pieces – 2 occurrences – verses 23:16, 23:18
to the – 6 occurrences – verses 23:15, 24:1, 24:11, 24:12, 24:15, 24:19
to their – 2 occurrences – verse 24:2
together – 1 occurrence – verse 23:4
tread – 1 occurrence – verse 24:25
trees – 1 occurrence – verse 24:8
tremble – 1 occurrence – verse 24:16
trodden – 1 occurrence – verse 24:19
trust – 1 occurrence – verse 24:32
trust in it – 1 occurrence – verse 24:32
tumultuous – 1 occurrence – verse 23:4
turn – 2 occurrences – verses 23:14, 24:27
under – 3 occurrences – verses 24:11, 24:19, 24:25
unto – 6 occurrences – verses 23:2, 23:22, 24:2, 24:10
up – 8 occurrences – verses 23:2, 23:14, 23:17, 24:4, 24:8, 24:9, 24:22
up against – 2 occurrences – verses 24:8, 24:22
up the – 2 occurrences – verses 23:17, 24:9
upon – 7 occurrences – verses 23:2, 23:3, 24:13, 24:16, 24:25, 24:26
upon the – 3 occurrences – verses 23:2, 24:13, 24:26
us – 2 occurrences – verses 24:8, 24:10
viols – 1 occurrence – verse 24:11
voice – 1 occurrence – verse 23:2
was – 1 occurrence – verse 24:28
wast – 1 occurrence – verse 24:3
water – 1 occurrence – verse 24:23
we – 1 occurrence – verse 24:10
weak – 1 occurrence – verse 24:10
weaken – 1 occurrence – verse 24:12
weapons – 1 occurrence – verse 23:5
wedge – 1 occurrence – verse 23:12
were – 1 occurrence – verse 24:2
what – 1 occurrence – verse 24:32
when – 1 occurrence – verse 23:19
wherein – 1 occurrence – verse 24:3
which – 3 occurrences – verses 23:1, 23:17, 24:12
who – 3 occurrences – verses 24:6, 24:27
whole – 5 occurrences – verses 23:5, 24:7, 24:26, 24:29, 24:31
whom – 1 occurrence – verse 24:2
wicked – 4 occurrences – verses 23:11, 23:15, 23:22, 24:5
wild – 2 occurrences – verses 23:21, 23:22
wild beasts of the – 2 occurrences – verses 23:21, 23:22
wilderness – 1 occurrence – verse 24:17
will – 20 occurrences – verses 23:11, 23:12, 23:13, 23:17, 23:22, 24:1, 24:13, 24:14, 24:22, 24:23, 24:25, 24:30
with – 8 occurrences – verses 23:9, 24:1, 24:6, 24:19, 24:20, 24:21, 24:23, 24:30
with a – 2 occurrences – verses 24:6, 24:19
wives – 1 occurrence – verse 23:16
womb – 1 occurrence – verse 23:18
world – 3 occurrences – verses 23:11, 24:17, 24:21
worm – 1 occurrence – verse 24:11
worms – 1 occurrence – verse 24:11
wrath – 3 occurrences – verses 23:9, 23:13, 24:6
ye – 2 occurrences – verses 23:2, 23:6
yea – 6 occurrences – verses 23:5, 23:15, 23:22, 24:2, 24:8, 24:18
yea the – 2 occurrences – verses 23:5, 24:8
year – 1 occurrence – verse 24:28
yet – 2 occurrences – verses 24:1, 24:15
yoke – 1 occurrence – verse 24:25
young – 1 occurrence – verse 23:18
Zion – 1 occurrence – verse 24:32 | 2020-05-25 19:50:36 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9379239082336426, "perplexity": 9949.138015344339}, "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-2020-24/segments/1590347389355.2/warc/CC-MAIN-20200525192537-20200525222537-00215.warc.gz"} |
https://www.physicsforums.com/threads/harmonic-series.866840/ | # Harmonic series
1. Apr 13, 2016
### foo9008
1. The problem statement, all variables and given/known data
i know that k = 0 to∞∑(1/ k) is harmonic series( we know that the sum is divergent) , how about ∑(1/ k+1 ) ???
2. Relevant equations
3. The attempt at a solution
in my opinion , it's also harmonic series , because the sum is divergent . Am i right ?
2. Apr 13, 2016
### Ray Vickson
Note: the series cannot be $\sum_{k=0}^{\infty} 1/k$ because the first term would be 1/0. However, starting at $k = 1$ is OK.
Do you mean that one of the series is $\sum_{k=1}^{\infty} 1/k$ and the other is $\sum_{k=1}^{\infty}(\frac{1}{k}+1)$? That is what you wrote. Did you really mean $\sum_{k=1}^{\infty} 1/(k+1)$ for the second series? If so, use parentheses, like this: 1/(k+1).
Anyway, just write out the first first few terms of both of your series, to see how they are related.
When you say "it's also harmonic series , because the sum is divergent" you have it backwards: it is not harmonic because it is divergent; it is divergent because it is harmonic. (Lots of divergent series are not at all harmonic.)
3. Apr 13, 2016
### foo9008
i mean second one , IMO , it is also harmonic .... , am i right ?
4. Apr 13, 2016
### Ray Vickson
Have you tried to write out the first few terms of both series to see how they differ? If you do, you can answer your own question.
5. Apr 13, 2016
### Math_QED
The infinite sum of 1/(k+1), with k starting from 1, is the same as the infinite sum of 1/k, with k starting from one minus 1. Follow Ray Vickson's advice to see this. | 2018-02-18 18:55:37 | {"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": 0.7559691071510315, "perplexity": 780.1587624426676}, "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-2018-09/segments/1518891812247.50/warc/CC-MAIN-20180218173208-20180218193208-00204.warc.gz"} |
http://mathforum.org/kb/thread.jspa?threadID=2637724&messageID=9507141 | Search All of the Math Forum:
Views expressed in these public forums are not endorsed by Drexel University or The Math Forum.
Topic: Subspaces of limit ordinals
Replies: 8 Last Post: Jul 1, 2014 11:02 AM
Messages: [ Previous | Next ]
William Elliot Posts: 1,443 Registered: 1/8/12
Re: Subspaces of limit ordinals
Posted: Jun 30, 2014 11:40 PM
On Mon, 30 Jun 2014, Herman Rubin wrote:
> On 2014-06-30, William Elliot <marsh@panix.com> wrote:
> > Let eta be a limit ordinal and A a subspace of eta.
>
> > Is the following correct?
> > A is homeomorphic to eta iff A is an unbounded, closed subset.
>
> Here is a counterexample. Let eta = omega^2, omega being the order
> type of the rationals. Then the sequence omega*n, n \in omega, is
> unbounded and closed, but is homeomorphic to omega, not eta.
As neither omega nor eta is an ordinal, how is that a counter example
Here's a counter example.
Let eta = omega_0 + omega_0 and A = { omega_0 + n | n in omega_0 }
Unbounded, closed A homeomorphic to omega_0.
> The theorem is true if eta is a cardinal, not the sum of a smaller
> number of cardinals.
Here's a counter example.
Let eta = aleph_(omega_0), A = { aleph_n | n in omega_0 }
Unbounded, closed A homeomorphic to aleph_0.
Is the theorem true only for regular cardinals?
On the other hand, is there a counter example to the proposition
that if A (subset eta) is homeomorphic to (limit ordinal) eta
then A is an unbounded, closed subset.
Yes, eta = omega_1, A = eta - {omega_0} which isn't closed.
Thus what is the theroem? Is this it?
If kappa is a regular cardinal and A an unbounded, closed
subset of kappa, then A is homeomorphic to kappa.
Date Subject Author
6/29/14 William Elliot
6/30/14 David Hartley
6/30/14 David Hartley
6/30/14 William Elliot
7/1/14 David Hartley
6/30/14 Herman Rubin
6/30/14 William Elliot
7/1/14 Peter Percival
7/1/14 David Hartley | 2014-07-29 02:37:51 | {"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": 0.9186829924583435, "perplexity": 8121.212250767343}, "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-2014-23/segments/1406510264575.30/warc/CC-MAIN-20140728011744-00388-ip-10-146-231-18.ec2.internal.warc.gz"} |
https://math.stackexchange.com/questions/3175682/prove-that-the-four-points-are-concyclic-if-they-are-harmonically-related-w-r-t | # Prove that the four points are concyclic if they are harmonically related w.r.t. the midpoint of connecting line segment.
$$(1)AB$$ and $$CD$$ are two intersecting line segments, and $$P$$,$$Q$$ are their respective midpoints. If $$AB$$ bisects $$\angle CPD$$ and $$PA^2=PB^2=PC.PD$$, then prove that the points $$A,B,C$$ and $$D$$ are concyclic.
I have a proof of the converse of the above theorem. Consider four concyclic points $$A(a),B(b),C(c)$$ and $$D(d)$$. Let $$O$$ be the midpoint of $$CD$$ . Then the cross ratio of these points is, $$\lambda=\frac {AC.BD}{AD.BC}$$ $$= \frac {(a-c)(b-d)}{(a-d)(b-c)}=-1$$ Rearranging we get: $$(a+b)(c+d)=2(ab+cd)$$ Rearranging again, we get: $$\left\{a-\frac {1}{2}(c+d)\right\}\left\{b-\frac {1}{2}(c+d)\right\}=\left\{\frac {1}{2}(c-d)\right\}^2$$ This implies: $$OA.OB=OC^2=OD^2$$ That is,$$OA$$and $$OB$$ are equally inclined to $$CD$$. $${ }$$ I could have written all of these lines in reverse, but I don't think that would be just, for both the theorems are converses of each other. Is there a distinct proof of theorem $$(1)$$ either using Euclidian geometry or complex numbers (other than this way)? Any help would be appreciated.
Let $$CD\cap CD=\{E\}$$, $$E$$ placed between $$P$$ and $$B$$ and between $$C$$ and $$Q$$.
Thus, since $$PE$$ is a bisector of $$\Delta PCD$$, we obtain: $$PE^2=PC\cdot PD-CE\cdot ED=PA^2-CE\cdot ED.$$ Id est, $$CE\cdot ED=PA^2-PE^2=(PA-PE)(PA+PE)=BE\cdot AE,$$ which gives $$\frac{CE}{AE}=\frac{EB}{ED},$$ which says $$\Delta CEB\sim\Delta AED,$$ which gives $$\measuredangle BCD=\measuredangle BAD$$ and quadrilateral $$ACBD$$ is cyclic.
$$\frac{PC}{PB}=\frac{PB}{PD}, \ \angle CPB=\angle BPD \implies \triangle CPB\sim \triangle BPD$$
These triangles have the same angles ($$\alpha,\beta,\gamma$$) as shown.
$$\frac{PC}{PA}=\frac{PA}{PD}, \ \angle CPA=\angle APD \implies \triangle CPA\sim \triangle APD$$
These triangles have the same angles ($$\delta,\varphi,\varepsilon$$) as shown.
In quadrilateral $$ABCD:$$
$$\angle C= \varphi+\gamma$$
$$\angle D= \beta+\varepsilon$$
$$\angle C +\angle D=\varphi+\gamma + \beta+\varepsilon=180^\circ$$
The last is obvious from triangle $$ABC$$. Sum of opposite angles is $$180^\circ$$ and therefore the quadrilateral is concyclic. | 2019-05-23 07:03:54 | {"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": 47, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8478683829307556, "perplexity": 138.42788825799957}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-22/segments/1558232257156.50/warc/CC-MAIN-20190523063645-20190523085645-00354.warc.gz"} |
https://www.authorea.com/users/149543/articles/162004/master/file/fringing.tex | ## Checking wavelength calibration
\label{sec:checkwave}
Both automatic and interactive reductions include a check of the wavelength calibration using the sky lines or telluric absorptions. This is computed by cross-correlating the sky lines either with a frame of sky lines observed in the past, or the telluric absorptions with a telluric model. These frames are stored in the directory “standard”. If the check on the wavelength calibration is performed on 1D frames, the third dimension of the file (produced by the iraf task $$apall$$) is used. If the check is performed on 2D wavelength calibrated frames, a median along the spatial axis is used. During the interactive reduction some plots are shown to the user for feedback. Examples of these plots are shown in Figs. \ref{fig:check} and \ref{fig:check2}.
## Fringing correction
\label{sec:fringing}
At the moment fringing correction is only applied to the red part of the spectrum. A keyword is added to the science frame if the fringing correction is applied. Science frames with name starting with ’n’ have been corrected for fringing. While reducing the data in interactive mode, if the correction for fringing is poor, users may try to use the option --fringing 2 and check if this improves the fringing correction. The keywords identifying the flat field used to correct for fringing are reported below.
FLATRED = 'flat_20130401_R642_56463.fits'
FLATBLUE = 'flat_20130401_R642_56463.fits' | 2018-07-21 06:17:55 | {"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": 0.3399411141872406, "perplexity": 2071.7511350335885}, "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-2018-30/segments/1531676592387.80/warc/CC-MAIN-20180721051500-20180721071500-00189.warc.gz"} |
https://stats.stackexchange.com/questions/262314/is-50-100-higher-than-25-or-is-it-25-higher-than-25/262316 | # Is 50% 100% higher than 25% or is it 25% higher than 25%?
If I have two values A and B which are both expressed as a percentage of C, and I want to express the difference in magnitude between A and B as a percentage D, is it more correct to express D as a percentage of C, or as a percentage of B (or indeed A)?
50 unemployed people is obviously 50% bigger than 25 unemployed people, because it's clear that '%' here means '% of 25 unemployed people'. But how much bigger is 50% unemployment than 25% unemployment? It's an increase of 100% of 25% unemployment, but only an increase of 25% of total potential unemployment.
• "50 unemployed people is obviously 50% bigger than 25 unemployed people, because it's clear that '%' here means '% of 25 unemployed people'". ???? 50 unemployed people is 25 bigger than 25 unemployed people which is 100 '% of 25 unemployed people' bigger than 25 unemployed people. – user20637 Feb 16 '17 at 16:35
• Relevant XKCD – Gregor Feb 16 '17 at 18:46
• The math here is all wrong, but that's irrelevant. Obviously, choose whichever figure makes the statistic seem most impressive and use that. In this case, the figure you want is 200%; 50% is 200% of 25%, obviously. Then you say "unemployment is up by 200%" and hope no one realizes that "up by 200%" is actually tripling, not doubling, and that it is impossible for 200% of a population to be unemployed. Remember, percentages exist in order to confuse readers and obscure a factual narrative. – Eric Lippert Feb 17 '17 at 6:05
• Therefore, if you want to actually inform readers, avoid percentages whenever possible, and when not possible, back them up with solid numbers. "the unemployment rate fell from 7.0% to 5.8%" is clear, but it does not tell the whole story. Is that driven by an increase in retirement? Or by new jobs in construction? Those are very different stories. See blogs.msdn.microsoft.com/ericlippert/2005/09/01/… for some more thoughts on this. – Eric Lippert Feb 17 '17 at 6:12
• This is why you shouldn't use percentages. Unless you also provide a lot of context, in which case why use percentages anyway? – matt_black Feb 17 '17 at 8:08
There are percent (%) and there are percentage points (%p), which are two different things.
50% (of $X$) is 100% more than 25% (of $X$). At the same time,
50% (of $X$) is 25%p more than 25% (of $X$).
So if your bank promises to increase the interest rates on your deposit by 5%, that means nearly nothing; 5% of, say, 1% original rate is just 0.05%, resulting in 1.05% after the increase.
But if it promises to increase the interest rate by 5%p (or 500 basis points, as Chris Haug notes), then it is an attractive deal; 5%p on top of, say, 1% original rate gives 6%.
• This is true, but I have personally never seen the symbol "%p" used (in North America). Most likely, on a personal savings account, the bank would say the first thing but mean the second (and explain in detail in the fine print). In a more technical setting, the bank would say "500 basis points", which are always interpreted additively. The answer's not wrong but it doesn't address the fact that there is really no universal standard in the language, and you always have to ask exactly what people mean. – Chris Haug Feb 16 '17 at 18:19
• @ChrisHaug, interesting to learn this. When I was issuing reports for clients in an investment bank, we would always carefully distinguish between % and %p (yes, we used precisely that symbol), but that was in Europe and I do not know whether it is the same in U.S. (probably not, as you note). – Richard Hardy Feb 16 '17 at 18:22
• @RichardHardy I have not seen it written that way, but I have seen the distinction between "percent" and "points" maintained — just without the shorthand "%p" for "points". – hobbs Feb 16 '17 at 19:02
• Indeed, in my (US) experience, I've seen "percentage points" written out to convey what you're abbreviating to "%p", so it's not an unreasonable abbreviation, but the first time I used it in any given work, I'd explain it "percentage points (%p)" for those unfamiliar with it. – Monty Harder Feb 16 '17 at 20:32
• I've seen it written as pp – James Feb 16 '17 at 21:27
Both are correct, as long as the increase is described correctly. A common way of distinguishing the two cases is to say there is a 100% relative increase or a 25% absolute increase. However, this might not be clear to all audiences. Most laypeople probably expect the latter number, and quoting the multiplicative increase may be considered intentionally misleading.
The expression "B is x % higher than A", implies that x is calculated as a percentage of A, because it is against A that B is being compared, not some unspecified third entity.
If A=25% of C and B=50% of C, then B is 100% higher than A.
It's also 2 times A. Confusingly, many people will say "B is 2 times more than A", which is completely illogical. For B to be 2 times more than A, it would be 2 * A + A, or 3 * A (in this case, 75% of C).
However, "B is 25 percentage points higher than A, when both are compared to C". If the context of the percentage being calculated relative to C is omitted (and not strongly implied), the statement is meaningless, because a percentage is always a percentage of something.
[If you doubt this, consider whether you'd rather have 50% of the money spent in a year on pork sausage in Jerusalem or 1% of the money spent in the same year on rice in China.]
• " Confusingly, many people will say "B is 2 times more than A", which is completely illogical." Many people also say inflammable to mean flammable (bad example, but I don't know better ones in English). Natural languages are sometimes strange shouldn't be interpreted as certain mathematical syntax. – JiK Feb 16 '17 at 19:46
• @JiK When expressing mathematical relationships, one ought to at least try to avoid confusing terminology. The "__ times {more|less|etc.} than" construct clearly admits of two different interpretations, and thus should be avoided. Arguably, the same can be said about percentages of items already expressed in percentages. – Monty Harder Feb 16 '17 at 20:29
• @JiK inflammable does mean flammable. The one that really gets me though is A is 3 times less than B – A C Feb 16 '17 at 22:52
• @AC and "A is 2 times more than B" does mean $A=2B$, if that is how people use English. – JiK Feb 17 '17 at 6:07
• @JiK it might be interpreted as A = 2B but I do disagree with your claim that it means so. If I was to say "A is 2 times B" that would mean A = 2B literally, but none the less "A is two times more than B" literally means that A = B + 2B. It's not mathematics but the content of the saying, which people usually won't even realize. – Han Soalone Feb 17 '17 at 9:41
The only valid approach here is to assume your reader does not know which version you are using, and make sure you build up enough context to make it clear.
One context may be to state what Richard Hardy suggested, differentiating between percentages and percentage points. That being said, I've never seen the %p notation before, so if you use that notation you might want to clarify it as well. Wikipedia suggests pp or p.p. as other possible notations.
Another context might be nearby numbers. If I say "Inflation went up .2% this year," people reliably understand that that number must be an addition of 0.2% to the inflation rate percentage, as opposed to a claim that inflation has been scaled by 100.2%. This holds true even if I was imprecise in my use of percent vs. percentage points. On the other hand, if I say "murder rates were at 3% last year, but went up 30% this year," you can be quite confident that that was a scaling factor, unless you knew there was some major insurrection in the area.
One of the easiest ways to maintain this context is to say the value in several different ways. If you say "unemployment went up 25%, to a record high of 18%," it's pretty darn clear that you intended to say unemployement rates were multiplied by 1.25. Incidentally, this is where the duplicated legal terms like "null and void" or "aiding and abetting" came from -- they were saying the same thing twice, once in common law speak and one in the official terminology which derived from French law.
We have a similar issue with the nuanced difference between an absolute temperature measured in Fahrenheit and a differential temperature measured in Fahrenheit. The conversions are different because one has to account for the fact that the Fahrenheit scale does not start at absolute zero. Dozens of notations have been suggested to resolve this, but nothing is quite as effective as maintaining a clear context so that the reader understands what you meant.
Communication is all about context, and different phrasing will mean different things to different people. | 2019-08-23 13:58:43 | {"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": 0.6710599064826965, "perplexity": 1157.2126856410875}, "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-2019-35/segments/1566027318421.65/warc/CC-MAIN-20190823130046-20190823152046-00475.warc.gz"} |
https://brilliant.org/daily-problems/complex-calcdoku-2/ | Back
## Complex Calcdoku
You may have done a Calcdoku puzzle before, but have you ever done one with complex numbers? That is, instead of just integers, we also have numbers like $1+i$ or $-3i.$ More generally, that's numbers of the form $a+bi,$ where $a$ and $b$ are real numbers and $i$ is the imaginary unit, defined by $i^2=-1.$
The Calcdoku rules remain the same:
1. Each square needs to be filled with one of the given numbers, and each number given is used exactly once in each row and column. (There is no region rule as in Sudoku.)
2. Any marked region indicates a value and an operation $+,-,\times,$ or $\div.$ The operation applies to numbers in the region, and when applied to the numbers in some order, they result in the given value. Numbers can be repeated in a marked region, but not in a row or column.
Keep reading to see two example puzzles — one traditional, and one with complex numbers — or jump straight to the daily challenge below. | 2020-11-26 21:40:38 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 9, "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": 0.5727306604385376, "perplexity": 299.32855643074373}, "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-2020-50/segments/1606141188947.19/warc/CC-MAIN-20201126200910-20201126230910-00494.warc.gz"} |
https://www.zkhack.dev/solution1 | Back
Solution
by MatanHamilis
Built by:
Prizes:
It all feels random, but it might not be.
### Introduction
A really cool event is ongoing now in the Zero-Knowledge community - the ZK-Hack. Every week a workshop about one of the ZK technologies being developed today is given. The first one, given on 26/10/2021 was an introductory workshop about the field of Zero Knowledge Proofs with a great historical introduction. The event is ongoing for the following seven weeks, with each week a new puzzle is published after the workshop of that week is given. In this post I'll share a write-up of the first puzzle I was solving with Elichai and Shalev.
Before the puzzle we are given introductory material to two topics in cryptography: BLS signatures and Pederson Hashes. We are also given a referral to the documentation of arkworks library, which are all linked below.
## See puzzle details on Github
### BLS Signatures
BLS is a signature scheme, named after Boneh, Lynn and Shacham. It is based on pairings which is a unique algebraic construct based on bilinear maps. Before anyone panics I'll explain what that means.
Definition: Let $$G$$ and $$G_T$$ be two groups. A function $$e:G\times G \rightarrow G_T$$ is a bilinear-map if: For any scalar $$\lambda$$ and for any $$a,b$$ in $$G$$ and for $$c = e(a,b)$$ we have: $$e( \lambda \cdot a,b) = e(a, \lambda \cdot b) = \lambda \cdot e(a,b) = \lambda \cdot c$$ For any $$a_1,a_2,b$$ in $$G$$ we have: $$e(a_1+ a_2,b) = e(a_1,b)+ e(a_2,b)$$ For any $$b_1,b_2,a$$ in $$G$$ we have: $$e(a,b_1+ b_2) = e(a,b_1)+ e(a,b_2)$$
In a sense, it just means a scalar can be moved freely between any of the arguments or even out of the function evaluation to the output. If you're really interested how the magic happens I'd recommend reading about Weil Pairings.
So the BLS signatures are signature schemes that provide the following the functions of KeyGen, Sign and Verify. Let's see how those are performed, please notice that BLS Signatures have multiple variants, I'll be discussing a simplified one that is sufficient to understand the problem.
Setup - Let $$g$$ be a generator of group $$G$$ of prime order $$r$$, and $$e:G \times G \rightarrow G_T$$ a bilinear map. KeyGen - Take a random scalar $$sk$$ between 0 and $$r-1$$. The private key will be $$sk$$, the public key, $$pk=sk \cdot g$$ Publish $$pk$$ and keep $$sk$$ secret. Sign - Given a message $$m\in G$$ the signature of the message is $$sk \cdot m$$ Verify, given a message $$m$$ and public key $$pk$$ and signature $$\Sigma$$ verify that $$e(m,pk)=e(\Sigma,g)$$ Notice that if $$\Sigma = sk \cdot m$$ and since $$pk=sk \cdot g$$ then, following the bilinearity of $$e$$ we get:
$$e(m,pk) = e(m,sk \cdot g) = e(sk \cdot m,g) = e(\sigma,g)$$ This is all nice but in real life scenarios our message to sign is an arbitrary stream of bits and not a group element. Can we find a way to map arbitrary bit-streams into group elements? The answer is yes, and is composed typically of two steps.
First, employing a cryptographically secure hash function to the message, reducing it to a constant size (e.g. 256 bits). One example of such function is blake2b.
Second, mapping the hash to a group element (typically an element on an elliptic-curve) using a "hash-to-curve" technique.
It is important that along the way we create as little bias as possible to retain the security of the signature scheme. One such hash-to-curve technique Pedersen Hashes, which is our next subject.
### Pedersen Hashes
As mentioned, using Pedersen Hashes we can map the output of a hash function to a group element. Since those groups are typically elliptic curve points, we will use "group element" and "curve point" interchangeably in this section. So, the Pedersen hash scheme setup is based on a set of $$n$$ group elements $$g_1,...,g_n$$, which we assume we don't know the discrete-log of each $$g_i$$ with respect to any other $$g_j$$. In other words, for each pair $$i,j$$ $$(i\neq j)$$ we can't efficiently find a value $$k$$ such that $$g_i^k = g_j$$ Given an $$n$$-bit output of of a hash function $$h=(b_1,...,b_n)$$ each $$b_i$$ is a single bit, the value of the pedersen hash of $$h$$ is $$\sum_{i=1}^n b_i \cdot g_i$$ By that we get an element in the group.
### The Challenge
In the challenge we are given 256 messages $$(m_1,...,m_{256})$$ and those messages' signatures $$(s_1,...,s_{256})$$ signed by some unknown private key $$sk$$ which its corresponding public-key is given as well $$pk$$.
Each message is signed using the BLS signature scheme where messages are mapped to group elements by first employing a blake2s hash and then using pedersen hash on its output. It's important to mention that the output of blake2s is 256-bits wide. The group elements $$g_1,...,g_{256}$$ are picked arbitrarily. Notice that the prime size of the group in our challenge is $$r=0x73eda753299d7d483339d80809a1d80553bda402fffe5bfeffffffff00000001$$ Therefore the private key is a number in $$\mathbb{Z}_r$$ between $$0$$ and $$r-1$$
We are told that these signatures were published and someone managed to sign some previously unsigned message, and we're asked how can this be done? The solution is in the form of signing ourselves our username as a proof to show we know how can this be done, this basically means that Existential-Unforgeability isn't a property of the signature scheme in this puzzle. If you haven't tried yet tackling this challenge, I highly encourage you to do so, this is the best way to really understand what happens and to get a better grasp of the underlying concepts who take part in the challenge. Either way, let's see how this can be solved. We begin with a few notations to make the solution simpler.
### Notation
As for notation, we will denote the blake2s of a message $$m_j$$ using $$b(m_j)$$. We will also denote the $$i^{\text th}$$ bit of $$b(m_j)$$ using $$b_i(m_j)$$. Therefore, the pedersen-hash of each message $$m_j$$ is: $$\sum_{i=1}^{256}b_i(m_j)\cdot g_i$$ Thus, we can view each blake2s output $$b(m)$$ as a column-vector of 1's and 0's: $$b(m) = \begin{pmatrix} b_1(m) \ b_2(m) \ \vdots \ b_{256}(m) \ \end{pmatrix}$$ So, we can also define basic arithmetic of blake2s hashes using vector arithmetics. For two message $$m_i,m_j$$ we have: $$b(m_i) + b(m_j) = \begin{pmatrix} b_1(m_i) +\ b_1(m_j) \ b_2(m_i) +\ b_2(m_j) \ \vdots \ b_{256}(m_i) +\ b_{256}(m_j) \ \end{pmatrix}$$ Where addition is over $$\mathbb{Z}_r$$ $$r$$ is the size of the group $$G$$. For a scalar $$c$$ in $$\mathbb{Z}r$$ and for some message $$m$$ we define the scalar multiplication $$c\cdot b(m)$$ as: $$c\cdot b(m) = \begin{pmatrix} c\cdot b_1(m) \ c\cdot b_2(m) \ \vdots \ c\cdot b{256}(m) \ \end{pmatrix}$$
### The Solution
The solution is based on the fact that the signature itself is linear. In the end of the day, we are signing (i.e. multiplying our private key by) a group elemenet. We'll show that the signature of the sum of two group elememts is the sum of the signatures. Let's see what does it mean: If we take two messages $$m_1,m_2$$ and blake2s them $$b(m_1),b(m_2)$$ their pedersen hashes are: \begin{aligned} h_1 &= \sum_{i=1}^{256}b_i(m_1)\cdot g_i & h_2 &= \sum_{i=1}^{256}b_i(m_2)\cdot g_i & \end{aligned} Thus, their signatures $$s_1,s_2$$ are: \begin{aligned} s_1 &= sk \cdot h_1 & s_2 &= sk \cdot h_2 \end{aligned} It's very easy to tell that the signature of $$h_1+h_2$$ is: $$sk\cdot(h_1+h_2)=sk\cdot h_1 + sk\cdot h_2 = s_1 + s_2$$ Not only that, but the pedersen hashing is also linear! Given the vector arithmetics defined previously for the blake2s outputs we can tell that first summing the blake2s outputs and then performing the pedersen hash transformations or first doing the pedersen transformation for each blake2s output and then adding the results yields the same output. In algebtraic terms it means that: $$\sum_{i=1}^{256}b_i(m_1)\cdot g_i + \sum_{i=1}^{256}b_i(m_2)\cdot g_i = \sum_{i=1}^{256}(b_i(m_1) + b_i(m_2))\cdot g_i$$ Ok, with these two linearity properties, we are ready to solve the puzzle! We have message $$m$$ we want to sign, we compute its blake2s hash $$b(m)$$. If we are able to find constants $$c_1,...,c_{256}$$ in $$\mathbb{Z}_r$$ such that: \begin{aligned} (\triangle) & \ \ \ \ b(m) = \sum_{i=1}^{256} c_i \cdot b(m_i) \end{aligned} Then we can generate signature $s_m$ for $m$ by following both linearity properties. \begin{aligned} (\square) &\ \ \ \ \ s_m = \sum_{i=1}^{256} c_i \cdot s_i \end{aligned} Remember that $$\triangle$$ is a vector equation, holding for each entry in the vector $$b(m)$$. Which means that for all $$j$$: $$b_j(m) = \sum_{i=1}^{256} c_i \cdot b_j(m_i)$$ Let's see why $$\square$$ holds: $$s_m = sk\cdot \sum_{j=1}^{256}b_j(m)\cdot g_j$$ $$= sk\cdot \sum_{j=1}^{256}\left(\sum_{i=1}^{256} c_i b_j(m_i)\right)\cdot g_j$$ $$= sk\cdot \sum_{i=1}^{256}\left(\sum_{j=1}^{256} c_i b_j(m_i)\cdot g_j\right)$$ $$= \sum_{i=1}^{256}c_i\underbrace{\cdot s_k\left(\sum_{j=1}^{256} b_j(m_i)\cdot g_j\right)}{s_i}$$ $$= \sum{i=1}^{256}c_is_i$$ Great, so now the only question is - how can we find those constants $$c_1,...,c_{256}$$? Well, let's look at $$\triangle$$ again, as we already said this is a vector-equation, so it's actually a linear equation system with 256 linear equations (since the vectors are of size 256) and with 256 variables $$c_1,...,c_{256}$$. We can express this system of linear equations in matrix nontation: $$Ac = b$$ Such that the variable of the equation is: $$c = \begin{pmatrix} c_1 \ c_2 \ \vdots \ c_{256} \end{pmatrix}$$ The vector $$b$$ is the bits of the blake hash of our target message $$m$$: $$b = b(m) = \begin{pmatrix} b_1(m) \ b_2(m) \ \vdots \ b_{256}(m) \end{pmatrix}$$ And the matrix $$A$$ is the bits of the blake hash of all messages $$m_1,...,m_{256}$$. Each message has its own column: $$A = \begin{pmatrix} b_1(m_1) & b_1(m_2) & \dots & b_1(m_{256}) \ b_2(m_1) & b_2(m_2) & \dots & b_2(m_{256}) \ \vdots & \vdots & \ddots & \vdots \ b_{256}(m_1) & b_{256}(m_2) & \dots & b_{256}(m_{256}) \ \end{pmatrix}$$ The solution to the equation is: $$c = A^{-1}b$$ Luckily enough, matrix $$A$$ is invertible so can easily sign the message $$m$$ following our previous equation: $$s_m = \sum_{i=1}^{256}c_is_i$$
### Code
In this section we give the basic tools we used to solve the problem in code. While the input data and the whole rust program is written in rust, we have written our solution in the sage programming language. Sage is a mathematical-oriented programming language with many built-in tools for computation in the fields of algebra, statistics, combinatorics, graph theory and more. It may look similar to python to some readers. We have also used some rust code to preprocess the input to the sage program and postprocess its output.
### Input Preprocessing
First we took the messages blake2s hashes from the rust file using the following functions:
fn bytes_to_bits_string(bytes: &[u8]) -> String {
let bits = bytes_to_bits(bytes);
let mut s = String::with_capacity(bits.len());
for bit in bits {
if bit {
s.push('1');
} else {
s.push('0');
}
}
return s;
}
fn write_msgs_to_file(msgs: Vec>) {
let mut file = File::create(format!(
"bits_vecs-{}",
(SystemTime::now().duration_since(UNIX_EPOCH))
.unwrap()
.as_millis()
))
.unwrap();
for msg in msgs {
let blake = hash_to_curve(&msg).0;
let string = bytes_to_bits_string(&blake);
file.write_all(string.as_ref()).unwrap();
file.write_all(b"\n").unwrap();
}
}
The write_msgs_to_file function takes a vector of blake2b hashes of the input messages and writes each hash as a string of 0s and 1s representing the binary form of the hash. Each hash is written in a separate line to the output file. This file will be passed to our sage code.
### Algebraic Processing in Sage
Our sage code is quite short and powerful. First we read the input and parse it as a list of lists (therefore - a matrix) of 0s and 1s, each binary digit in its own cell of the matrix.
A = list()
# bits_vecs-1635288647752 was computed by the rust program, it contains a list of all the messages in bits represantion (after the blake2s hash)
with open("bits_vecs-1635288647752", 'r') as f:
for line_index, line in enumerate(f):
A.append(list())
for bit_index in range(0, 256):
A[line_index].append(int(line[bit_index]))
Next, we define $$P$$ to be the order of the curve, so scalar that will later be multiplied by the generators in the Pedersen-has-to-curve scheme will be taken from the field $$F=\mathbb{Z}_P$$ defined right after.
# Curve Order
P = 0x73eda753299d7d483339d80809a1d80553bda402fffe5bfeffffffff00000001
F = FiniteField(P)
Next, we define the matrix GA to be simply the list-of-lists A we previously defined, where each entry (0/1) is considered as an element in field F. We transpose it because if you pay attention in the A matrix we defined in the previous section each column (and not row) should contain the bits of a hash of a specific message. Finally, we compute GAinv which is the transpose of our matrix.
GA = Matrix(F, A)
GAT = GA.transpose()
GAinv = GAT.inverse()
Next, we computed the blake2s value of our message -- this is our vector $$b$$ from previous section where we will look at each bit as an element in $$\mathbb{Z}_P$$. Finally, we have to compute $$A^{-1}\cdot b$$.
sage
# blake2s of ou
bitstring = '0111011010010000...'
bits = [int(el) for el in bitstring]
gbits = vector(F, bits)
gsolution = GAinv * gbits
# Print the generator multipliers.
",".join(['Fq::from_str("'+str(el)+'").unwrap()' for el in gsolution])
The output we get is a vector $$c$$ of elements from $$\mathbb{Z}P$$ such that the signature for our message will be $$\sum{i=1}^{256}c_i\cdot s_i$$ where $$s_i$$ is the signature of the $$i^{\text th}$$ message. This part will be done in rust.
### Final Postprocessing and Signature Generation
Our signature generation is also done using rust and is available here as the full code:
https://gist.github.com/elichai/7401f5423c2693960677ba4f8a9fab14#file-computing_the_sig-rs-L55"
Here we'll give some explanation on snippets out of it.
First we define the selectors array, a very long array such that selectors[i] is the field element $$c_i$$ we have obtained using our sage program.
let selectors = [
Fr::from_str(
"27645015623588109382996024038763530282647599513403648261518408122004451823795",
)
.unwrap(),
Fr::from_str(
"23018579491472099737921523253639007115479688088731410213980168199642094036630",
)
....
....
....
.unwrap(),
Fr::from_str(
"6769691326408305518047502379958157439957827386631887324632648911856770263560",
)
.unwrap(),
];
Next, we multiply each selector[i] by $$s_i$$ the signature of $$i^{\text th}$$ message (sigs[i]). This is done using arkworks library.
let mut sum = G1Projective::zero();
for (i, num) in selectors.iter().enumerate() {
}
Next we make a curve element out of the sum
let affine = G1Affine::from(sum);
And we verify we actually got the correct signature.
verify(pk, msg, affine.clone());
Assuming we do, we output the signature so it is ready for submission and we're done! 👏
let mut sig = Vec::new();
affine.serialize(&mut sig).unwrap();
let sig_hex = hex::encode(sig);
println!("sig: {}", sig_hex);
`
01
Puzzle completed
Score
1000
02
Puzzle completed
Score
980.5
03
## Konstantce
Puzzle completed
Score
969.3
Lorem ipsum dolor sit amet, consectetur adipiscing elit. Molestie vel vulputate diam condimentum tristique est. Eget gravida sagittis, mi donec est. Amet turpis leo morbi enim nulla lorem sed justo. Tincidunt eu diam pellentesque nibh blandit viverra. Tincidunt pellentesque ultrices ac, sed quis purus ac. Orci adipiscing sapien aenean tincidunt rutrum. Molestie in tortor risus est.Lorem ipsum dolor sit amet, consectetur adipiscing elit. Molestie vel vulputate diam condimentum tristique est. Eget gravida sagittis, mi donec est. Amet turpis leo morbi enim nulla lorem sed justo. Tincidunt eu diam pellentesque nibh blandit viverra. Tincidunt pellentesque ultrices ac, sed quis purus ac. Orci adipiscing sapien aenean tincidunt rutrum. Molestie in tortor .
Lorem ipsum dolor sit amet, consectetur adipiscing elit. Molestie vel vulputate diam condimentum tristique est. Eget gravida sagittis, mi donec est. Amet turpis leo morbi enim nulla lorem sed justo. Tincidunt eu diam pellentesque nibh blandit viverra. Tincidunt pellentesque ultrices ac, sed quis purus ac. Orci adipiscing sapien aenean tincidunt rutrum. Molestie in tortor risus est.Lorem ipsum dolor sit amet, consectetur adipiscing elit. Molestie vel vulputate diam condimentum tristique est. Eget gravida sagittis, mi donec est. Amet turpis leo morbi enim nulla lorem sed justo. Tincidunt eu diam pellentesque nibh blandit viverra. Tincidunt pellentesque ultrices ac, sed quis purus ac. Orci adipiscing sapien aenean tincidunt rutrum. Molestie in tortor . | 2022-01-16 10:23:48 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 2, "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": 0.7539033889770508, "perplexity": 1598.373708274555}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-05/segments/1642320299852.23/warc/CC-MAIN-20220116093137-20220116123137-00329.warc.gz"} |
https://docs.appseconnect.com/integration/ | # Integration
Executing the Process is a vital part when integrating any applications. This Document will let the users to understand how the integration process can be e...
Executing the Process is a vital part when integrating any applications. This Document will let the users to understand how the integration process can be e...
This section of the document will given you an overview of NAV- Magento2 Mutliple Connection Integration and the subsequent chapters will drive you to the ...
Executing the Process is a vital part when integrating any applications. This Document will let the users to understand how the integration process can be ex...
Executing the Process is a vital part when integrating any applications. This Document will let the users to understand how the integration process can be e...
Executing the process is a vital part when integrating any applications. This section of the document will let the users to understand how the integration p...
Executing the process is a vital part when integrating any applications. This section of the document will let the users to understand how the integration p...
Executing the Process is a vital part when integrating any applications. This Document will let the users to understand how the integration process can be ex...
Executing the Process is a vital part when integrating any applications. This document will let the users to understand how the integration process can be e...
Executing the process is a vital part when integrating any applications. This Document will let the users to understand how the integration process can be e...
Executing the Process is a vital part when integrating any applications. This Document will let the users to understand how the integration process can be ex...
Executing the Process is a vital part when integrating any applications. This Document will let the users to understand how the integration process can be e...
Executing the Process is a vital part when integrating any applications. This Document will let the users to understand how the integration process can be ex...
Executing the Process is a vital part when integrating any applications. This Document will let the users to understand how the integration process can be ex...
Executing the Process is a vital part when integrating any applications. This section of the document will let the users understand how the integration proc...
This section of the document will given you an overview of SAP B1- Magento 2 Integration and the subsequent chapters will drive you to the process of integ...
Executing the Process is a vital part when integrating any applications. This Document will let the users to understand how the integration process can be e...
APPSeCONNECT provides a single integration platform through which one can connect various Business Applications like ERP system, CRM, Accounting Application...
Executing the Process is a vital part when integrating any applications. This Document will let the users to understand how the integration process can be e... | 2020-07-05 02:44:02 | {"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": 0.9831230044364929, "perplexity": 651.470503110873}, "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-2020-29/segments/1593655886865.30/warc/CC-MAIN-20200705023910-20200705053910-00469.warc.gz"} |
https://mathoverflow.net/questions/232989/if-delta-is-pure-then-what-happens-to-betti-numbers-of-i-delta-or-i | # if $\Delta$ is pure, then what happens to betti-numbers of $I_{\Delta}$ or $I_{\Delta^v}$
Assume that $\Delta$ is a simplicial complex and $\Delta ^v$ is its Alexander dual.
Let in addition $\Delta$ be pure, then what happens to betti-numbers of $I_{\Delta}$ or $I_{\Delta^v}$?
Is there a known fact about it?
Where does this question come from?
If $I_{\Delta} = P_{F_1}\cap \dots \cap P_{F_m}$ is the standard primary decomposition of $I_{\Delta}$, then $I_{\Delta^v}$ is generated by $\{x_{F_1}\cap \dots \cap x_{F_m}\}.$ Now let $\Delta$ be pure. Then $I_{\Delta^v}$ is generated in one degree. So if $\beta_{0j}\neq 0$ and $\beta_{0k}\neq 0$, then $j=k$.
Thank you.
• also asked here Mar 7 '16 at 7:06 | 2021-09-25 09:28:59 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8259667158126831, "perplexity": 171.71360546707294}, "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/1631780057615.3/warc/CC-MAIN-20210925082018-20210925112018-00528.warc.gz"} |
https://www.physicsforums.com/threads/hermitian-properties-of-the-gamma-matrices.893924/ | # A Hermitian properties of the gamma matrices
1. Nov 19, 2016
### spaghetti3451
The gamma matrices $\gamma^{\mu}$ are defined by
$$\{\gamma^{\mu},\gamma^{\nu}\}=2g^{\mu\nu}.$$
---
There exist representations of the gamma matrices such as the Dirac basis and the Weyl basis.
---
Is it possible to prove the relation
$$(\gamma^{\mu})^{\dagger}\gamma^{0}=\gamma^{0}\gamma^{\mu}$$
without alluding to a specific representation?
2. Nov 19, 2016
### vanhees71
I don't think so, because given any set of matrices fulfilling the anti-commutation relations, any other set
$$\tilde{\gamma}^{\mu} = \hat{A} \gamma^{\mu} \hat{A}^{-1},$$
where $\hat{A}$ is an arbitrary $\mathbb{C}^{4 \times 4}$ matrix also fulfills them. It's of course more natural to use a simple set of matrices as suggested by the representation theory of the Lorentz group behind the bispinor representation, e.g., the chiral (or Weyl) representation. The pseudohermiticity relations, are only preserved with $\hat{A}$ unitary. | 2017-12-16 04:05:16 | {"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": 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": 0.8206104636192322, "perplexity": 809.4110468421379}, "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-2017-51/segments/1512948581053.56/warc/CC-MAIN-20171216030243-20171216052243-00154.warc.gz"} |
https://repository.upenn.edu/dissertations/AAI9233346/ | # Cyclic response and substructure evolution of copper polycrystals
#### Abstract
Studies on the cyclic response and the substructure evolution of copper polycrystals have been carried out in the high-cycle fatigue regime. The effects of ramp-loading and microstructure have been investigated using various mechanical tests and electron microscopy. Investigations on the influence of loading mode on the cyclic response of fine-grained polycrystalline copper and the associated dislocation structures showed that the saturation behavior under constant load control, for two sets of specimens, with and without initial ramp-loading, exhibits strong differences in the "intermediate" range of stress amplitudes, i.e., from 70 to 98 MPa. Within this range the ramp-loading mode promotes a gradual substructure evolution which leads to localization of slip in primary systems and the formation of persistent slip bands (PSBs), whereas conventional loading leads to the formation of elongated cells and multiple sets of wall structures (e.g., labyrinth structure), both intimately associated with multiple slip conditions. In studying ramp-loading as a mechanical pre-treatment it is found that the well-defined matrix structure inherited from the very efficient cyclic hardening during the ramp-treatment promotes very uniform and homogeneous structures of primary dislocations, i.e., PSBs and wall structure, from grain to grain. These structures favor strain localization, and thus lower hardening rates in the cyclic stress-strain curves (CSSC) of ramp-treated copper polycrystals are obtained. However, plateau-like behavior was not observed. The presence of a weak but noticable $\langle 111\rangle$-$\langle 100\rangle$ "hard" texture in the ramp-treated specimens studied here suggests that the observation of a plateau in the CSSC of polycrystals may be very sensitive to texture. Microstructure, expressed in terms of a complex factor of combined grain size and texture, showed a very significant effect in the cyclic response of copper at amplitudes where structures which localize deformation are expected to be present. Initial homogeneous multiple slip promotes faster substructure evolution into cell structure, which accounts for the low levels of localization of deformation observed in the CSSC of coarse-grained copper. Finally, a polycrystalline model based on treating differently oriented grains as composite material is shown to account qualitatively for most of the results obtained in the present investigation.
#### Subject Area
Materials science
#### Recommended Citation
Llanes, Luis Miguel, "Cyclic response and substructure evolution of copper polycrystals" (1992). Dissertations available from ProQuest. AAI9233346.
https://repository.upenn.edu/dissertations/AAI9233346
COinS | 2023-04-01 01:08:18 | {"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": 0.19869469106197357, "perplexity": 3601.932144391158}, "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-2023-14/segments/1679296949694.55/warc/CC-MAIN-20230401001704-20230401031704-00668.warc.gz"} |
https://kristerw.github.io/2021/11/09/fp-contract/ | # -ffp-contract=fast
GCC per default enables one optimization for x86_64 that can change the result of floating-point operations: -ffp-contract=fast.1 This allows the compiler to do floating-point expression contraction such as combining multiplication and addition instructions with an FMA instruction.2
Various optimizations and heuristics may affect which calculations are contracted:
• Optimizations such as inlining and loop unrolling may introduce new opportunities for contraction.
• It is not always a good idea to use an FMA instruction for a calculation x*y+z. For example, suppose x and y are available early in the function and z late. In that case, the compiler may reduce register pressure by doing the multiplication early (so it only needs to keep one register live until z is available).3
This means that different optimization levels can make the code produce different results. And unrelated code changes may also change the result (if the compiler, for example, makes different inlining decisions because of the code change). This does not impact most programs, but it sometimes causes confusion when working with test suites that expect the result to be bit-exact.
Disabling floating-point contraction with -ffp-contract=off makes GCC generate code that produces a consistent result for x86_64.
1. -ffp-contract=fast is enabled for C++ and GNU C. It is not enabled for standard C (that is, when compiling with -std=c99, etc.).
2. The FMA instruction omits the rounding done in the multiplication instruction, making the calculations produce different results for some input values.
3. Current GCC does, to my knowledge, not take advantage of this. But some other compilers use heuristics that take the instruction usage into account (godbolt).
Written on November 9, 2021 | 2022-06-24 22:07:06 | {"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": 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": 0.6023763418197632, "perplexity": 1950.583804111361}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-27/segments/1656103033816.0/warc/CC-MAIN-20220624213908-20220625003908-00302.warc.gz"} |
https://tex.stackexchange.com/questions/545239/changing-enumerations-of-subsections-to-a-specific-format | # Changing Enumerations of subsections to a specific format
I am currently writing a kind of requirement analysis and want to enumerate my sections and subsections in a certain style:
My sections, should look like normal so e.g. "1.1 Import and Export of Files", but the should define a macro "\startLetter" to be the first letter in the title (here "I").
The following subsection's enumeration should start with the current \startLetter and have an increasing three digit identifier, which resets at the start of the next section, e.g. "I001 Text Files Import". When referencing these, I want only the Letter + ID to be printed, so "I001" and it also still referencing there via hyperref.
My current setup is in the MWE below. The problems are
1. I don't know how to shorten the reference to only the ID without breaking the hyperref link and
2. The ID counter still counts up when referencing. I pretty sure that is because the macro becomes part of the section name and therefore gets reevaluate every time. How do I stop that?
I had a look into titlesec, xparse and etoolbox's pretocmd and apptocmd, but this would require to patch the @ssect command (?) and I am to inexperienced to just edit in the underlying commands of Latex sections. Is there a "noob-understandable" way to solve this problem?
Thanks in advance :)
MWE:
\documentclass[10pt,a4paper]{book}
\usepackage[utf8]{inputenc}
\usepackage[T1]{fontenc}
\usepackage{xstring}
\usepackage{nameref}
\usepackage{hyperref}
\newcommand{\startLetter}{}
\newcounter{reqID}
\newcommand{\reqSection}[1]{%
\section{#1}
\renewcommand{\startLetter}{\StrMid{#1}{0}{1}}
\setcounter{reqID}{1}
}
\ifnum\value{reqID}<100 0\fi\ifnum\value{reqID}<10 0\fi\arabic{reqID}
}
\newcommand{\reqSubsection}[1]{%
\stepcounter{reqID}
}
\parindent0mm
\begin{document}
\chapter{Any chapter}
\reqSection{Import Export}
\reqSubsection{Text Files Import}
\label{lbl:import-text}
Some useless blindtext. Some useless blindtext. Some useless blindtext. Some useless blindtext.
\reqSubsection{Text Files Export}
\label{lbl:export-text}
Some useless blindtext. Some useless blindtext. Some useless blindtext. Some useless blindtext.
\reqSubsection{Video Files Import}
\label{lbl:import-video}
Some useless blindtext. Some useless blindtext. Some useless blindtext. Some useless blindtext.
\vspace{1cm}
I am refering to requirement \nameref{lbl:export-text}.
\end{document}
Assuming I understand the question properly, I think this does what you need. The basic idea is to use ordinary subsections, changing their headings to meet your requirements. This eliminates the issue with your counter, and allows you to use the ordinary \ref command to reference by ID number.
\documentclass{book}
\makeatletter
\def\firstchar#1{\firstchar@internal#1\relax}
\def\firstchar@internal#1#2\relax{#1}
\makeatother
\newcommand{\reqSection}[1]{%
\section{#1}
\xdef\startLetter{\firstchar{#1}}
}
\ifnum\value{subsection}<100 0\fi\ifnum\value{subsection}<10 0\fi\arabic{subsection}
}
\usepackage{hyperref}
\begin{document}
\chapter{Any chapter}
\reqSection{Import Export}
\subsection{Text Files Import}
\label{lbl:import-text}
Some useless blindtext. Some useless blindtext. Some useless blindtext. Some useless blindtext.
\subsection{Text Files Export}
\label{lbl:export-text}
Some useless blindtext. Some useless blindtext. Some useless blindtext. Some useless blindtext.
\subsection{Video Files Import}
\label{lbl:import-video}
Some useless blindtext. Some useless blindtext. Some useless blindtext. Some useless blindtext.
\vspace{1cm}
I am refering to requirement \nameref{lbl:export-text}.
I can refer to the ID using \verb+\ref+ rather than \verb+\nameref+, for example \ref{lbl:export-text}
\end{document}
EDIT
For reasons I have not investigated, your \startLetter macro didn't work for me, so I wrote my own. The idea (which I picked up from an answer by David Carlisle) is that \firstchar@internal expects two arguments; #1 is the first token it finds (*), but #2 must be terminated by \relax. #1 is returned as the result, and #2 is ignored. \firstchar appends \relax (**) to the end of its argument and sends this on to \firstchar@internal. So...
\firschar{abc}
--> \firstchar@internal{abc\relax}
#1 = a
#2 = bc
--> a
(*) It could also be a group enclosed by braces, but something like \subsection{{abc} def} seems unlikely to me).
(**) Originally I used a \relax to ensure there are two things for TeX to find if you do \firstchar{a} but in fact this was unnecessary because in that case #1 = a and #2 ends up empty. The new implementation causes an error if you do \firstchar{}, which makes sense; the old implementation would return a!
• Hi Ian, this solution in fact works quite nicely. Unfortunately I misstated my problem slightly. I wanted to only have a certain part of subsections to be enumerated in this special way. I fixed it by adding another \renewcommand\thesubsection{\arabic{subsection}} at the end of my requirement analysis. Thanks for your fast and simple solution. Edit: Could you tell me what exactly is the purpose of the \firstchar@internal macro? May 22, 2020 at 14:55
• @RobertBock --- Please see the edit; I have added an explanation. May 23, 2020 at 10:08 | 2022-06-29 22:56:56 | {"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": 0.8652701377868652, "perplexity": 3643.4536466748573}, "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-2022-27/segments/1656103645173.39/warc/CC-MAIN-20220629211420-20220630001420-00645.warc.gz"} |
https://tex.stackexchange.com/questions/501248/problem-with-the-macro-foreach-and-the-syntax | Problem with the macro foreach and the syntax “…”
I have not programmed for a few years and I'm trying to get back to work but I have some problems with updates of "pgf" (perhaps ...) I am having a problem with the syntax "..." that I did not have before. I installed the latest versions of texlive, pgf etc ...
\documentclass{article}
\makeatletter
\def\DrawPolygon(#1,#2){%
\begingroup
\draw(#1)
\foreach \pt in {#2}{--(\pt)}--cycle;%
\endgroup
}
\makeatother
\usepackage{tikz}
\begin{document}
\begin{tikzpicture}
\coordinate (A) at (4,0);
\coordinate (B) at (2,4);
\coordinate (C) at (0,0);
% \DrawPolygon(A,...,C) % error
% now error undefined\ifpgffor@alphabeticsequence \else \ifpgffor@assign@parse \begingroup
% ! File ended while scanning use of \pgffor@@dotscharcheck.
\DrawPolygon(A,B,C)
\end{tikzpicture}
\end{document}
The syntax (A,...,C) gives an error
• \DrawPolygon(A,...,C) is \foreach \pt in {...,C} with no start for the loop, what range did you intend? – David Carlisle Jul 24 at 9:55
• Indeed, the drawing works if one replaces \DrawPolygon(A,...,C) with \DrawPolygon(A,B,...,C) (which is not very different from \DrawPolygon(A,B,C), but one doesn't need to stop at C!) so that the \foreach loop sees a start value. – frougon Jul 24 at 10:49
• @DavidCarlisle The first value is A. I gave a new example with more points and the result is fine. – Alain Matthes Jul 24 at 19:56
• but #2 is the part after the first comma so \foreach \pt in {#2} is \foreach \pt in {...,C} and you do not pass in the first value. that is why oerpli uses #1,#2 in his/her answer, to add the starting value back. – David Carlisle Jul 24 at 19:58
• @AlainMatthes this could never have worked. – David Carlisle Jul 24 at 19:58
Not too much TikZish, but, hey, it works!
\documentclass{article}
\usepackage{tikz}
\def\DrawPolygon(#1){%
\begingroup
\xdef\temppolygon{}%
\foreach \pt in {#1}{\xdef\temppolygon{\temppolygon(\pt)--}}%
\xdef\temppolygon{\endgroup\noexpand\draw\temppolygon cycle}%
\temppolygon;
}
\begin{document}
\begin{tikzpicture}
\coordinate (A) at (4,0);
\coordinate (B) at (2,4);
\coordinate (C) at (0,0);
\DrawPolygon(A,...,C) % error
\end{tikzpicture}
\end{document}
(I changed the example from A,B,C to A,...,E to make some points a bit more clear)
I think the problem is, that the first argument of DrawPolygon(A,...,E) (i.e: A) is consumed and the second argument (#2) is then expanded to (,...,E) instead of the desired A,...,E.
Fix this be either passing the start point as well as a list from the second or end (DrawPolygon(A,B,...,E) or by modifying the definition of your function as follows:
\documentclass{article}
\makeatletter
\def\DrawPolygon(#1,#2){%
\begingroup
\draw(#1)
% change is in this line, {#1,#2} instead of {#2}
\foreach \pt in {#1,#2}{--(\pt)}--cycle;
\endgroup
}
\makeatother
\usepackage{tikz}
\begin{document}
\begin{tikzpicture}
\coordinate (A) at (4,4);
\coordinate (B) at (0,4);
\coordinate (C) at (0,0);
\coordinate (D) at (4,0);
\coordinate (E) at (7,0);
\DrawPolygon(A,...,E)
\end{tikzpicture}
\end{document}
\foreach does have a loop counter. It can be assigned to a macro with option count. Then, the connecting line can be set in the second and later loop rounds.
\documentclass{article}
\usepackage{tikz}
\def\DrawPolygon(#1){%
\draw
\foreach[count=\pti] \pt in {#1} {
\ifnum\pti>1 --\fi
(\pt)
}
-- cycle
;
}
\begin{document}
\begin{tikzpicture}
\coordinate (A) at (4,4);
\coordinate (B) at (0,4);
\coordinate (C) at (0,0);
\coordinate (D) at (4,0);
\coordinate (E) at (7,0);
\DrawPolygon(A,...,E)
\end{tikzpicture}
\end{document} | 2019-09-18 12:07:34 | {"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": 0.8580423593521118, "perplexity": 1911.0801931315332}, "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-2019-39/segments/1568514573284.48/warc/CC-MAIN-20190918110932-20190918132932-00377.warc.gz"} |
https://math.stackexchange.com/questions/3648138/evaluate-s-n-frac1-log2-frac2-log3-frac3-log4-frac4-lo | # Evaluate $S_n=\frac{1}{\log(2)}+\frac{2}{\log(3)}+\frac{3}{\log(4)}+\frac{4}{\log(5)}+\cdots+\frac{n}{\log(n+1)}$
Hi I want to evaluate the following sum :
$$S_n=\frac{1}{\log(2)}+\frac{2}{\log(3)}+\frac{3}{\log(4)}+\frac{4}{\log(5)}+\cdots+\frac{n}{\log(n+1)}=?$$
## My try :
Using a well know trick we have :
$$\int_{0}^{1}2^x+3^x+\cdots+(n+1)^xdx=S_n$$
Now we see a link between $$S$$ and the truncated function Zeta .
As I'm stuck now so I propose an crude estimation of the sum $$S$$:
Since $$\ln(n)\leq n-1$$ for $$n\geq 1$$ a natural number we have $$n\leq S_n$$
We can do better since $$\ln(n)\leq q(n^\frac{1}{q}-1)$$ for $$n\geq 1$$ and $$q\geq 1$$
An obvious upper bound is :
$$S_n\leq \frac{n(n+1)}{2}$$ for $$n\geq 3$$
Finally I make the following conjecture :
There is always a prime number between $$S_n$$ and $$S_{n+2}$$
## My questions
Can someone improve the bound or give a theoretic representation ?
Have you an counter-example ?
Any helps is greatly appreciated..
## Update :
I propose The following conjecture for $$n\geq 100$$
There is always a prime number between $$S_n$$ and $$S_{n+1}$$
Maybe it's stronger than the Firoozbakht's conjecture
• We have $S_n \sim \frac{n^2}{2\log n}$. Thus your conjectures are (modulo verification for small numbers) stronger than Legendre's conjecture. Hence don't hold your breath waiting for a proof. – Daniel Fischer Apr 28 '20 at 15:07
• – Martin Sleziak May 3 '20 at 13:55
An upper bound can be given since $$S_n <\int_1^n {x \over \ln(x+1)} dx=li((n+1)^2)-2li(n+1)+li(2)-li(4)$$ In a very similar way you can obtain a lower bound, which is: $$\int _1^n {{x-1} \over ln(x) } = li(n^2)-li(n)-\ln(2)$$ | 2021-02-28 07:35:10 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 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": 19, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9397390484809875, "perplexity": 469.35654387981583}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-10/segments/1614178360293.33/warc/CC-MAIN-20210228054509-20210228084509-00635.warc.gz"} |
https://nhigham.com/2021/09/14/can-we-solve-linear-algebra-problems-at-extreme-scale-and-low-precisions/?replytocom=32434 | # Can We Solve Linear Algebra Problems at Extreme Scale and Low Precisions?
The largest dense linear systems being solved today are of order $n = 10^7$, and future exascale computer systems will be able to tackle even larger problems. Rounding error analysis shows that the computed solution satisfies a componentwise backward error bound that, under favorable assumptions, is of order $nu$, where $u$ is the unit roundoff of the floating-point arithmetic: $u \approx 10^{-16}$ for double precision and $u \approx 10^{-8}$ for single precision. This backward error bound cannot guarantee any stability for single precision solution of today’s largest problems and suggests a loss of half the digits in the backward error for double precision.
Half precision floating-point arithmetic is now readily available in hardware, in both the IEEE binary16 format and the bfloat16 format, and it is increasingly being used in machine learning and in scientific computing more generally. For the computation of the inner product of two $n$-vectors the backward error bound is again of order $nu$, and this bound exceeds $1$ for $n \ge 684$ for both half precision formats, suggesting a potentially complete loss of numerical stability. Yet inner products with $n \ge 684$ are successfully used in half precision computations in practice.
The error bounds I have referred to are upper bounds and so bound the worst-case over all possible rounding errors. Their main purpose is to reveal potential instabilities rather than to provide realistic error estimates. Yet we do need to know the limits of what we can compute, and for mission critical applications we need to be able to guarantee a successful computation..
Can we understand the behavior of linear algebra algorithms at extreme scale and in low precision floating-point arithmetics?
To a large extent the answer is yes if we exploit three different features to obtain smaller error bounds.
## Blocked Algorithms
Many algorithms are implemented in blocked form. For example, an inner product $x^Ty$ of two $n$-vectors $x$ and $y$ can computed as
\notag \begin{aligned} s_i &= x((i-1)b+1:ib)^T y((i-1)b+1:ib), \quad i = 1:k,\\ s &= s_1 + s_2 + \dots + s_k, \end{aligned}
where $n = kb$ and $b \ll n$ is the block size. The inner product has been broken into $k$ smaller inner products of size $b$, which are computed independently then summed. Many linear algebra algorithms are blocked in an analogous way, where the blocking is into submatrices with $b$ rows or $b$ columns (or both). Careful analysis of the error analysis shows that a blocked algorithm has an error bound about a factor of $b$ smaller than that for the corresponding unblocked algorithm. Practical block sizes for matrix algorithms are typically $128$ or $256$, so blocking brings a substantial reduction in the error bounds.
In fact, one can do even better than an error bound of order $(n/b)u$. By computing the sum $s= s_1 + s_2 + \dots + s_k$ with a more accurate summation method the error constant is further reduced to $bu + O(u^2)$ (this is the FABsum method of Blanchard et al. (2020)).
## Architectural Features
Intel x86 processors support an 80-bit extended precision format with a 64-bit significand, which is compatible with that specified in the IEEE standard. When a compiler uses this format with 80-bit registers to accumulate sums and inner products it is effectively working with a unit roundoff of $2^{-64}$ rather than $2^{-53}$ for double precision, giving error bounds smaller by a factor up to $2^{11} = 2048$.
Some processors have a fused multiply–add (FMA) operation, which computes a combined multiplication and addition $x + yz$ with one rounding error instead of two. This results in a reduction in error bounds by a factor $2$.
Mixed precision block FMA operations $D = C + AB$, with matrices $A,B,C,D$ of fixed size, are available on Google tensor processing units, NVIDIA GPUs, and in the ARMv8-A architecture. For half precision inputs these devices can produce results of single precision quality, which can give a significant boost in accuracy when block FMAs are chained together to form a matrix product of arbitrary dimension.
## Probabilistic Bounds
Worst-case rounding error bounds suffer from the problem that they are not attainable for most specific sets of data and are unlikely to be nearly attained. Stewart (1990) noted that
To be realistic, we must prune away the unlikely. What is left is necessarily a probabilistic statement.
Theo Mary and I have recently developed probabilistic rounding error analysis, which makes probabilistic assumptions on the rounding errors and derives bounds that hold with a certain probability. The key feature of the bounds is that they are proportional to $\sqrt{n}u$ when a corresponding worst-case bound is proportional to $nu$. In the most general form of the analysis (Connolly, Higham, and Mary, 2021), the rounding errors are assumed to be mean independent and of mean zero, where mean independence is a weaker assumption than independence.
## Putting the Pieces Together
The different features we have described can be combined to obtain significantly smaller error bounds. If we use a blocked algorithm with block size $b \ll n$ then in an inner product the standard error bound of order $nu$ reduces to a probabilistic bound of order $(\sqrt{n/b})u$, which is a significant reduction. Block FMAs and extended precision registers provide further reductions.
For example, for a linear system of order $10^7$ solved in single precision with a block size of $256$, the probabilistic error bound is of order $10^{-5}$ versus $1$ for the standard worst-case bound. If FABsum is used then the bound is further reduced.
Our conclusion is that we can successfully solve linear algebra problems of greater size and at lower precisions than the standard rounding error analysis suggests. A priori bounds will always be pessimistic, though. One should compute a posteriori residuals or backward errors (depending on the problem) in order to assess the quality of a numerical solution.
For full details of the work summarized here, see Higham (2021).
## 4 thoughts on “Can We Solve Linear Algebra Problems at Extreme Scale and Low Precisions?”
1. Wen says:
“The largest dense linear systems being solved today are of order n = 10^7.” I wonder do you mean dense linear systems without any special structure (e.g., not FFT-able)? | 2022-05-17 06:58:14 | {"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": 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": 0.9010165929794312, "perplexity": 526.0178349116619}, "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/1652662517018.29/warc/CC-MAIN-20220517063528-20220517093528-00659.warc.gz"} |
http://mymathforum.com/calculus/45824-need-help-understanding-something.html | My Math Forum Need help understanding something
Calculus Calculus Math Forum
August 16th, 2014, 05:18 PM #1 Newbie Joined: Aug 2014 From: Belgium Posts: 1 Thanks: 0 Need help understanding something Hello, I need to find the pole points and zero points of the following equation GH= 3(p+2) / (p+8 )*(p²+8p+32) For zero points you get -2 and pole points are -8, -4+j4, -4-j4 (the p+2 in the numerator determines the zero points and the denominator determines the pole points) However, I can't figure out how you get those complex values. In order to get the pole points you need to have a p value, not p² (I think at least). So you'd have to convert it. J is a complex number -> sqroot of -1 Here is a screenshot of what I mean My current (flawed) theory is that you need to reduce p² to p by apply that p! rule, meaning you change (p²+8p+32) into (2p+8 ) -> 2(p+4) However, I can't figure out how you end up with the complex number out of this.
August 17th, 2014, 01:24 PM #2 Global Moderator Joined: May 2007 Posts: 6,582 Thanks: 610 The complex pole points are simply the roots of $p^2+8p+32=0$.
Thread Tools Display Modes Linear Mode
Similar Threads Thread Thread Starter Forum Replies Last Post nole Computer Science 3 April 18th, 2013 05:41 AM fobbz Probability and Statistics 3 March 7th, 2013 12:45 PM supermario65 Advanced Statistics 2 January 10th, 2012 11:44 AM Dr.Nick Academic Guidance 5 March 12th, 2011 06:35 AM tomc Real Analysis 2 September 17th, 2009 07:02 AM
Contact - Home - Forums - Cryptocurrency Forum - Top | 2018-09-20 10:14:46 | {"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": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 1, "/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": 0.7807955145835876, "perplexity": 2747.770735009959}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-39/segments/1537267156460.64/warc/CC-MAIN-20180920101233-20180920121633-00054.warc.gz"} |
https://au.answers.yahoo.com/question/index?qid=20191118082033AAxOPed | Anonymous
Anonymous asked in Science & MathematicsPhysics · 8 months ago
# physics help?
Suppose that a neutron in a nuclear reactor initially has an energy of 4.8 × 10^−13 J. How many head-on collisions with carbon nuclei at rest must this neutron make before its energy is reduced to 1.6 × 10^-19, assuming collisions are elastic
Relevance
• 8 months ago
Mass of carbon nucleus (6 neutrons, 6 protons) is 12u. Mass of neutron is 1u.
For a head-on collision, the velocity of the neutron is changed by a factor (1-12)/(1+12) = -0.84615 (the minus sign means direction is reversed.) E.g. see http://hyperphysics.phy-astr.gsu.edu/hbase/elacol2...
You might need to include the derivation if not given the formula.
Since kinetic energy is proportional to speed squared, the kinetic energy reduces by a factor
(1/0.84615)² = 1.397
After n collisions the kinetic energy of the neutron reduces by a factor (4.8*10^-13) / (1.6*10^-19) = 3*10^6
Since the kinetic energy is reduced by a factor 1.397 for each collision:
1.397ⁿ = 3*10^6
nlog(1.397) = log(3*10^6)
n = log(3*10^6) / log(1.397) = 45 (to 2 sig. figs.)
• ...Show all comments
• Steve4Physics
Lv 7
8 months agoReport
Proportional to what? Neutron’s speed after each collision (Vf) is proportional to its velocity before the collision (Vi).
Vf/Vi = 0.84615
The collision changes the velocity by a factor 0.84615
This is a reduction by a factor 1/0.84615 (= 1.182). | 2020-07-05 07:28:50 | {"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": 0.8080087900161743, "perplexity": 3366.813530899519}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-29/segments/1593655887046.62/warc/CC-MAIN-20200705055259-20200705085259-00317.warc.gz"} |
https://solvedlib.com/n/use-identities-to-find-values-of-the-sine-and-cosine-functions,6299123 | 5 answers
# Use identities to find values of the sine and cosine functions of the function for the angle measure20, given sin
###### Question:
Use identities to find values of the sine and cosine functions of the function for the angle measure 20, given sin U = and cos 0 > 0 cos 20= (Simplify your answer Including any radicals; Use inlegers or fractions for any numbers in the expression sin 20 = (Simplify your answer including any radical Use integers or fractions for any numbers In the expression )
## Answers
#### Similar Solved Questions
1 answer
##### AASB 112 governs accounting for income tax. Briefly outline some of the criticisms and associated social...
AASB 112 governs accounting for income tax. Briefly outline some of the criticisms and associated social implications of this standard....
1 answer
##### 1. Does the following Lewis structure represent an anion, a cation, or a molecule? if it...
1. Does the following Lewis structure represent an anion, a cation, or a molecule? if it represents an ion, what is the charge on the ion?...
5 answers
##### DLTAILSNOIESASkYOuR TEACHERGuail Lrtld FDale1 LtEtue Lhneni (Rat [e Ritet Ahelatn haieleneehMtt Hlttls AealtaAttEleAerinMaiL USt salTT) Ir Kouunte qubtateentletunrd €ntt D" Itare {ula
DLTAILS NOIES ASkYOuR TEACHER Guail Lrtld FDale1 LtEtue Lhneni (Rat [e Ritet Ahelatn haieleneehMtt Hlttls AealtaAttEleAerinMai L USt salT T) Ir Kouunte qubtatee ntletunrd € ntt D" Itare {ula...
1 answer
##### Sweeties, Inc., manufactures a sugar product by a continuous process, involving three production departments-Refining, Sifting, and...
Sweeties, Inc., manufactures a sugar product by a continuous process, involving three production departments-Refining, Sifting, and Packing. Assume that records indicate that direct materials, direct labor, and applied factory overhead for the first department, Refining, were $360,000,$147,000, and...
5 answers
##### Fa *AirPbtFitojl
Fa * Air PbtFit ojl...
1 answer
##### Additional WileyPLUS Problem 13-1 Tamarisk Corporation is considering adding a new product line. The cost of...
Additional WileyPLUS Problem 13-1 Tamarisk Corporation is considering adding a new product line. The cost of the factory and equipment to produce this product is $1,780,000. Company management expects net cash flows from the sale of this product to be$390,000 in each of the next eight years. If Ta...
5 answers
##### Assume that € and y are both differentiable functions of t and are related by the equation y = COS (52):Find dy when x = given d = -5 when x = T dt 10 dt 10Enter the exact answer:dy dtNumber
Assume that € and y are both differentiable functions of t and are related by the equation y = COS (52): Find dy when x = given d = -5 when x = T dt 10 dt 10 Enter the exact answer: dy dt Number...
5 answers
##### Which of the following statements is true?Select one: 0 A. Starting from any five given vectors in Rs, the Gram-Schmidt process can produce Five orthonormal vectors.B. The sum of two orthogonal n X n matrices is an orthogonal n X n matrix C The zero matrix is orthognally diagonalizable D. There exists three non-zero mutually orthogonal vectors in R? E. None of the statements are true
Which of the following statements is true? Select one: 0 A. Starting from any five given vectors in Rs, the Gram-Schmidt process can produce Five orthonormal vectors. B. The sum of two orthogonal n X n matrices is an orthogonal n X n matrix C The zero matrix is orthognally diagonalizable D. There ex...
1 answer
##### Find, with justification, what the absolute maximum value of f(x) = x3 – 3x on the...
Find, with justification, what the absolute maximum value of f(x) = x3 – 3x on the set of real numbers x satisfying x4 + 36 < 13x2. If time does not permit you to finish this question during the exam, please submit what you have and briefly explain what you would have tried....
1 answer
##### What is the booboo doll experiment?
what is the booboo doll experiment?...
5 answers
##### Starting at t = 5,use Euler's method with two steps of equal size to approximate the number of students at time t =11 minutes(A) 106112(C) 114(D) 115
Starting at t = 5,use Euler's method with two steps of equal size to approximate the number of students at time t =11 minutes (A) 106 112 (C) 114 (D) 115...
1 answer
##### 1) Explain two-phase locking. 2) Explain the meaning of the expression of ACID transaction.
1) Explain two-phase locking. 2) Explain the meaning of the expression of ACID transaction....
1 answer
##### 6. (10 points) Suppose X – Exp(1) and Y = -In(X) (a) Find the cumulative distribution...
6. (10 points) Suppose X – Exp(1) and Y = -In(X) (a) Find the cumulative distribution function of Y. (b) Find the probability density function of Y. (c) Let X1, X2,...,be i.i.d. Exp(1), and let Mk = max(X1,..., Xk) (Maximum of X1, ..., Xk). Find the probability density function of Mk (Hint: P(...
5 answers
##### Question50 MarksEscherichia coli, Staphylococcus aureus and Klebsiella pneumoniae are the leading causes of nosocomial blood stream infections (BSIs) in intensive care units (ICUs) around the world: Write detailed essay covering the following key "Principles of Microbiology" that would be used in differentiating these three microorganisms: ClassificationFunctional anatomyMicrobial metabolismMicrobial growth Control of microbial growthIn addition, the latter part of your essay must also
Question 50 Marks Escherichia coli, Staphylococcus aureus and Klebsiella pneumoniae are the leading causes of nosocomial blood stream infections (BSIs) in intensive care units (ICUs) around the world: Write detailed essay covering the following key "Principles of Microbiology" that would b...
3 answers
##### Choose a suitable model then write out the related probability function, likelihood function and log likelihood function. Derive the Maximum Likelihood Estimators of interest and plot the log likelihood function for the following set of data using R. Emphasize the MLE in the plot:Data recorded is: 12, 23,21, 18,16,35,26, 11, 19,19,29, 19,27,18,16,23,15,22,19,22,14,13The points have a variance of 52 in the population that these individuals belong:
Choose a suitable model then write out the related probability function, likelihood function and log likelihood function. Derive the Maximum Likelihood Estimators of interest and plot the log likelihood function for the following set of data using R. Emphasize the MLE in the plot: Data recorded is: ...
1 answer
##### I. Write the net ionic equation for the equilibrium involving the HSO HSO ) + H2O...
i. Write the net ionic equation for the equilibrium involving the HSO HSO ) + H2O -> H2O + (aq) + SO4 Cag) Ionic 19:14+ tags + sor (aa) + H₂O e frigg) + H2O laq) + 50 stem when an het man brie Taal vii. Rewrite the net ionic equation for this equilibrium, but include heat in the equation th...
5 answers
##### Assume that T is a linear transformation. Find the standard matrix of TT: R2_R2 is a vertical shear transformation that maps e1 into e1 6e2 but leaves the vector e2 unchanged:A = (Type an integer or simplified fraction for each matrix element )
Assume that T is a linear transformation. Find the standard matrix of T T: R2_R2 is a vertical shear transformation that maps e1 into e1 6e2 but leaves the vector e2 unchanged: A = (Type an integer or simplified fraction for each matrix element )...
1 answer
##### A roller coaster (404 kg) moves from A (3.13 m above the ground) to B (21.6...
A roller coaster (404 kg) moves from A (3.13 m above the ground) to B (21.6 m above the ground). Two non-conservative forces are present: friction does -2.37 x 104 J of work on the car, and a chain mechanism does +5.76 x 104 J of work to help the car up a long climb. What is the change in the car...
2 answers
##### Which of the following are the expected value ad variance of the 'sampling distribution of a sample proportion?OE(p) =np; Var ~(p) = np(1 - p)E(p) =p; Var (p) = Pl-P2=p2; Var (p) 2? (L-p)ZP(I-P)E( P =p; Var( p
Which of the following are the expected value ad variance of the 'sampling distribution of a sample proportion? OE(p) =np; Var ~(p) = np(1 - p) E(p) =p; Var (p) = Pl-P2 =p2; Var (p) 2? (L-p)Z P(I-P) E( P =p; Var( p...
1 answer
##### Confused on both aspects of this question. Please help. 2. Jamal and Roberto performed a lab...
Confused on both aspects of this question. Please help. 2. Jamal and Roberto performed a lab experiment where, 0.5 g of a mixture of (R)- and (S)- Zainaboic acid was obtained. 2a) Using the solubility data given here, select the best solvent and calculate the minimum amount needed to dissolve 500 mg...
1 answer
##### The government raises the sales tax on shirts. The tax is imposed on sellers. As a...
The government raises the sales tax on shirts. The tax is imposed on sellers. As a result, the demand curve for shirts becomes horizontal. supply curve of shirts shifts leftward. demand curve for shirts becomes vertical. supply curve of shirts shifts rightward....
1 answer
##### 1. (8 points) Consider the conditional proposition:If 1 + 2 < 9, then 12 - 3 9useful negation, ie , don t just prepend negation = ofthe proposition (Give (2 points) Write the "It is not the case that:proposition and determine its truth value: b. (3 points) Write the contrapositive of thepoints) Write the converse of the propcsition - and determine its truth value:
1. (8 points) Consider the conditional proposition: If 1 + 2 < 9, then 12 - 3 9 useful negation, ie , don t just prepend negation = ofthe proposition (Give (2 points) Write the "It is not the case that: proposition and determine its truth value: b. (3 points) Write the contrapositive of th...
4 answers
##### Uke tre producl nule (0 calculate the derlvalive of4r" 2**+1Reuco not need [0 simplity vour flnal answerDrag and drop an Image or PDF Iile or click to browse
Uke tre producl nule (0 calculate the derlvalive of 4r" 2**+1 Reuco not need [0 simplity vour flnal answer Drag and drop an Image or PDF Iile or click to browse...
1 answer
##### Problem 4. A pivoted beam has mass mį suspended from one end and an Atwood's ma-...
Problem 4. A pivoted beam has mass mį suspended from one end and an Atwood's ma- chine suspended from the other with masses m2 and mz suspended on either side. The frictionless pulley has negligible mass and size. (a) Find the relation between mı, m2, m3, li, and l2 which will ensure t...
5 answers
##### 2 Halobacterium, a small bacteria living in the Great Salt Lake, is able to survive by keeping a lower concentration of salt inside its membrane relative to the external environment: How does it achieve this? 3_ A red blood cell is returning to the lungs after delivering oxygen to the body: What will happen when it comes in contact with the oxygen rich environment within the lungs?
2 Halobacterium, a small bacteria living in the Great Salt Lake, is able to survive by keeping a lower concentration of salt inside its membrane relative to the external environment: How does it achieve this? 3_ A red blood cell is returning to the lungs after delivering oxygen to the body: What wil...
5 answers
##### Most protein synthesis begins in the cytoplasm. Cells needto sort proteins and target them to their site of action. Wherewould a cell target the following proteins?DNA polymerase deltaAquaporinChymotrypsinATP synthase (electron transport chain proteins)Phosphofructokinase (PFK, glycolytic enzyme)A.CytosolB.Plasma membraneC.Mitochondrial outer membraneD.NucleusE.Mitochondrial inner membraneF.Extracellular (secreted)G.Lysosome
Most protein synthesis begins in the cytoplasm. Cells need to sort proteins and target them to their site of action. Where would a cell target the following proteins? DNA polymerase delta Aquaporin Chymotrypsin ATP synthase (electron transport chain proteins) Phosphofructokinase (PFK, glycolytic enz...
1 answer
##### Provide all steps Problem 2 (20 points): Find the exact surface area of the object obtained...
provide all steps Problem 2 (20 points): Find the exact surface area of the object obtained by rotating the following curve about the z-axis. Do not use your calculators to find a decimal approximation OSE<1...
1 answer
##### Question 7 Find x correct to one decimal place. 60° 30° y 55 95.3 31.8 127 * Previous Question 8 Find the equivalent expression. tan'x-secx secx +tan-x cse'x + tan2x csc2x +cotx anx Secx...
Question 7 Find x correct to one decimal place. 60° 30° y 55 95.3 31.8 127 * Previous Question 8 Find the equivalent expression. tan'x-secx secx +tan-x cse'x + tan2x csc2x +cotx anx Secx cotx cscx Previous oe曲 Question 7 Find x correct to one decimal place. 60° 30° y ...
5 answers
##### Consider the following lementary reaction mechanism where both forward and reverse reactions are important:CO+0,= CO_+0O+H,O=OH+OHCO+OH= COz+HH+o=OH+OWrite out the rate equation for the hydroxyl radical (OH):
Consider the following lementary reaction mechanism where both forward and reverse reactions are important: CO+0,= CO_+0 O+H,O=OH+OH CO+OH= COz+H H+o=OH+O Write out the rate equation for the hydroxyl radical (OH):...
1 answer
##### Question 2 (20pts): A 20 mL sample of 0.01 M propionic acid (CH3CH2COOH; Pka = 4.87)...
Question 2 (20pts): A 20 mL sample of 0.01 M propionic acid (CH3CH2COOH; Pka = 4.87) is titrated with 0.05 M NaOH. A) Write out the chemical reaction for this titration. B) Calculate the initial pH of the sample. C) Calculate the volume of NaOH required to reach the equivalence point. D) Calculate t...
5 answers
##### At right is solenoid (I1-1.3 Oop density 200 loopsim) long wire (I2=10 0 A) colenat and 616 What is the total B-field vector at Point that is inside the solenoid and distance d = U0 cm from the wire? A Plutonium-240 nucleus (charge equal 94 protons mass is 240.05 u) is at rest and then accelerated using Oo0OOO OoOOOO0 AV 152V so that it is moving in the +X direction: velocity vector? (also 4 = 6605x/0-27kg) Lontt What is its initial force vector due to the magnetic field What is the nucleus is p
At right is solenoid (I1-1.3 Oop density 200 loopsim) long wire (I2=10 0 A) colenat and 616 What is the total B-field vector at Point that is inside the solenoid and distance d = U0 cm from the wire? A Plutonium-240 nucleus (charge equal 94 protons mass is 240.05 u) is at rest and then accelerated u...
5 answers
5 answers
##### A physical therapist wants to determine the difference in the proportion of men and women who participate in regular sustained physical activity: What sample size should be obtained if she wishes the estimate to be within four percentage points with 99% confidence, assuming that she uses the estimates of 21,5% male and 18.8% femal from previous year? she does not use any prior estimates?(a) n=(Round up to the nearest whole number:)(b) n=(Round up to the nearest whole number)
A physical therapist wants to determine the difference in the proportion of men and women who participate in regular sustained physical activity: What sample size should be obtained if she wishes the estimate to be within four percentage points with 99% confidence, assuming that she uses the estimat...
1 answer
##### (8) In a mass spectrometer, an ion with a particular velocity is selected by using a...
(8) In a mass spectrometer, an ion with a particular velocity is selected by using a magnetic field of 100.mt perpendicular to an electric field of 2.00 kV/m. After the ion leaves the velocity selector, the same magnetic field is used to deflect the ion in a circular path with a radius of 1.35cm. Wh...
5 answers
##### Prove- following ' trigonometric identity Proper form is required and all steps must be show tan cosx-sinx cosx+sinx
Prove- following ' trigonometric identity Proper form is required and all steps must be show tan cosx-sinx cosx+sinx...
1 answer
##### 24-31 For each of the following items, indicate the financial statement where you are likely to...
24-31 For each of the following items, indicate the financial statement where you are likely to find each of the following accounts (It is possible to have an item on more than one statement): A. Income Statement B. Statement of Changes in Stockholders' Equity C. Balance Sheet D. None of the ...
5 answers
##### PreviousProblem ListNextpoint) Let f(€,y) = (2 + y))" Then82f dr8y 83f Ordydr 83f 8x28yNote: You can earn partial credit on this problem:'rs Eam402euset csmit40z8key-B92YkzSvcOa2Lttilz9ofoLRuyobnuls
Previous Problem List Next point) Let f(€,y) = (2 + y))" Then 82f dr8y 83f Ordydr 83f 8x28y Note: You can earn partial credit on this problem: 'rs Eam402euset csmit40z8key-B92YkzSvcOa2Lttilz9ofoLRuyobnuls...
-- 0.026164-- | 2022-07-06 16:40:39 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 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": 0.5173209309577942, "perplexity": 4325.362026510704}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-27/segments/1656104675818.94/warc/CC-MAIN-20220706151618-20220706181618-00128.warc.gz"} |
https://www.gamedev.net/forums/topic/592876-mash-game/ | Public Group
# MASH game
This topic is 2715 days old which is more than the 365 day threshold we allow for new replies. Please post a new topic.
## Recommended Posts
sooooooo i remember this game being played alot back in middle school/elementary school(dont ask y i remembered it) but i decided to code it using c++ and all the things ive learned so far as a learning expierence. probly just a few questions, is it coded well, and is there a way i would be able to post this as well as other things ive coded in such a way that you could just click and play it? thanks
#include<string> using std::string; class MashGame{ public: MashGame(); bool quit(); string getName(); string getCar(); string getHoneyMoon(); string getPet(); string getJob(); int getNumOfKids(); private: static const int maxNum = 4; string name[maxNum]; string car[maxNum]; string honeyM[maxNum]; string pet[maxNum]; string job[maxNum]; int kid[maxNum]; void setCategories(); void calculate(); };
#include<iostream> using std::cout; using std::cin; using std::endl; #include<iomanip> using std::setw; #include<ctime> using std::time; #include<cstdlib> using std::rand; using std::srand; #include "MashGame.h" MashGame::MashGame(){ while(quit()){ setCategories(); calculate(); } } bool MashGame::quit(){ char choice; cout << "------------------------------" << endl << "WELCOME TO THE GAME OF M.A.S.H" << endl << "------------------------------" << endl << endl << "would you like to play?( type y for yes, n for no)" << endl; cin >> choice; if(choice == 'y'){ cout << "Lets Begin!!!!!" << endl << endl; return true; } else return false; } void MashGame::setCategories(){ for(int i = 0; i < 6; i++){ for(int j = 0; j < 4; j++){ switch(i){ case 0: if(j == 0) cout << "Enter 4 of your Crushes names:" << endl; cout << "Enter name " << j + 1 << ": "; cin >> name[j]; cout << endl; break; case 1: if(j == 0) cout << "Enter 4 of your dream cars:" << endl; cout << "Enter Dream Car " << j + 1 << ": "; cin >> car[j]; cout << endl; break; case 2: if(j == 0) cout << "Enter 4 of the places you would like to have your" " HoneyMoon at:" << endl; cout << "Enter HoneyMoon Location 1: "; cin >> honeyM[j]; cout << endl << endl; break; case 3: if(j == 0) cout << "Enter 4 Pets you would like to have:" << endl; cout << "Enter Pet " << j + 1 << ": "; cin >> pet[j]; cout << endl; break; case 4: if(j == 0) cout << "Enter 4 of your Dream Jobs:" << endl; cout << "Enter Dream Job " << j + 1 << ": "; cin >> job[j]; cout << endl; break; case 5: if(j == 0) cout << "Enter 4 Different Numbers: " << endl; cout << "Enter #" << j + 1<< ": "; cin >> kid[j]; cout << endl; break; } } } } void MashGame::calculate(){ int fate; cout << "Pick a number, any number, but this number is very important" " because it decides your fate!" << endl; cin >> fate; srand(time(0)); cout << endl << endl << "************YOUR FATE*************************" << endl; cout << "You will get married to " << getName() << endl << "Your honey moon will be at " << getHoneyMoon() << endl << "You will drive around in a " << getCar() << endl << "You will have a " << getPet() << " as a pet." << endl << "You have a job as " << getJob() << endl << "Oh, and I forgot " "about your kids, you have " << getNumOfKids() << " of them" << endl << endl; cout << "********HAS BEEN DECIDED**********************" << endl << endl; } string MashGame::getName(){ int choice = rand() % 3; return name[choice]; } string MashGame::getCar(){ int choice = rand() % 3; return car[choice]; } string MashGame::getHoneyMoon(){ int choice = rand() % 3; return honeyM[choice]; } string MashGame::getPet(){ int choice = rand() % 3; return pet[choice]; } string MashGame::getJob(){ int choice = rand() % 3; return job[choice]; } int MashGame::getNumOfKids(){ int choice = rand() % 3; return kid[choice]; }
#include "MashGame.h" int main(){ MashGame play; return 0; }
##### Share on other sites
Here are the problems I noticed
* Using std::string in the header. You shouldn't use using declarations in headers because they'll pollute the namespace and cause difficult to find conflicts later on.
* Use of a conditional "if(j == 0)" in setCategories with no enclosing braces and no indentation. This makes the code hard to read and will probably lead to bugs later.
* "int choice = rand() % 3;" This will only pick from the first three entries. I'm not sure if this is desirable behavior. You probably want to change the 3 to maxNum.
* You should probably change the 4 to maxNum in the j loop so that you don't forget to change it if maxNum changes. Otherwise, you'll get array overflows which will best case scenario crash the game.
• 10
• 9
• 48
• 12
• 10
• ### Forum Statistics
• Total Topics
631383
• Total Posts
2999688
× | 2018-06-20 13:56:35 | {"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": 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": 0.23579668998718262, "perplexity": 5060.199443612315}, "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/1529267863519.49/warc/CC-MAIN-20180620124346-20180620144346-00196.warc.gz"} |
https://leanprover-community.github.io/archive/stream/113489-new-members/topic/concise.20inequality.20proofs.html | ## Stream: new members
### Topic: concise inequality proofs
#### Scott Olson (Sep 27 2018 at 09:07):
How do you approach simple proofs with inequalities like this, concisely? I can always find a way, but it seems like there must be shorter ways.
n : ℕ,
h : 1 + n ≤ 1
⊢ n = 0
#### Andrew Ashworth (Sep 27 2018 at 09:11):
the most concise way is probably to blast it away with a tactic - there are several out there
#### Scott Olson (Sep 27 2018 at 09:26):
What are some tactics that might be able to solve this?
#### Johannes Hölzl (Sep 27 2018 at 09:27):
linarith could work. I think it got some support for natural numbers.
#### Scott Olson (Sep 27 2018 at 09:29):
You're right, linarith handles it
Last updated: May 13 2021 at 06:15 UTC | 2021-05-13 06:58:26 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 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": 0.21849627792835236, "perplexity": 8119.48771036498}, "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-2021-21/segments/1620243991537.32/warc/CC-MAIN-20210513045934-20210513075934-00287.warc.gz"} |
https://www.maa.org/press/periodicals/convergence/mathematical-treasure-arithmetic-and-geometry-of-metius | # Mathematical Treasure: Arithmetic and Geometry of Metius
Author(s):
Frank J. Swetz (The Pennsylvania State University)
Adriaan Adriaanszoon (1571-1635), more commonly known as Adrian Metius, was a Dutch geometer, astronomer, surveyor, and instrument maker. He is perhaps best known for his published estimate for the mathematical constant $\pi\approx{\frac{355}{113}},$ which was actually discovered by his father. His Arithmetica et Geometriae (1626) reflects his applied approach to mathematics. The personages depicted on the title page also reflect his mathematical experiences: war and warfare occupy the highest position; an astronomer/philosopher stands on the left; while a tentative surveyor enters the scene at the right.
An illustration on page 11 shows that an infinite number of right angles can be inscribed within a semicircle.
On page 35 begins a section on practical geometry. It appears this was published as a separate tract in 1625 and added to the new work.
The images above are presented courtesy of the University of Pennsylvania Libraries.
Index to Mathematical Treasures
Frank J. Swetz (The Pennsylvania State University), "Mathematical Treasure: Arithmetic and Geometry of Metius," Convergence (August 2016) | 2019-01-22 13:16:43 | {"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": 0.5728010535240173, "perplexity": 3290.5621188392984}, "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-2019-04/segments/1547583850393.61/warc/CC-MAIN-20190122120040-20190122142040-00359.warc.gz"} |
https://www.azdictionary.com/definition/cotan | # cotan definition
• noun:
• proportion associated with the next to the alternative part of a right-angled triangle
• ratio of this next to the opposite side of a right-angled triangle
## Related Sources
• Definition for "cotan"
• proportion associated with the next to the alternative…
• Sentence for "cotan"
• Pulo-cotan, being high land, and is…
• Hypernym for "cotan"
• trigonometric function
• Urban Dictionary for "cotan"
• The Co order of Tan at… | 2017-07-26 19:25:02 | {"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": 0.8267337083816528, "perplexity": 12315.872915176302}, "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/1500549426372.41/warc/CC-MAIN-20170726182141-20170726202141-00111.warc.gz"} |
https://chemistry.stackexchange.com/questions/17127/electrophilic-addition-of-hx-to-2-3-dimethylbut-2-ene | # Electrophilic addition of HX to 2,3-dimethylbut-2-ene
Generally, for the addition of dry HX to an alkene, it follows Markovnikov's rule. The hydrogen atom adds to the carbon with the most hydrogen atoms.
However, in the case of an alkene which does not have any hydrogen atom attached to its carbon, such as 2,3-dimethyl2-butene, would the electrophilic addition still take place?
Electrophilic addition would likely still occur. Remember that Markovnikov's rule is an observational heuristic for "in electrophilic addition reactions of alkenes in which carbocations form, the more/most stable carbocation forms preferentially, and thus the product originating from that cation is the major product".
In this case, a carbocation can form. Nothing about the tetrasubstituted pattern prevents addition. The molecule is still planar and can be aproached by the electrophile. The methyl groups are electron donating by induction. The methyl groups 1) increase the electron density of the alkene and make it more nucleophilic, and 2) stabilize the carbocation intermediate.
Thus, 2,3-dimethyl-2-butene is likely more reactive than other alkenes toward electrophiles. For example:
$$\ce{(CH3)2C=C(CH3)2 + HBr -> (CH3)2BrC-CH(CH3)2}$$ | 2020-03-31 11:40:01 | {"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": 0.49832361936569214, "perplexity": 5576.268839179867}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-16/segments/1585370500426.22/warc/CC-MAIN-20200331084941-20200331114941-00394.warc.gz"} |
http://mathhelpforum.com/calculus/193133-tricky-integration.html | # Math Help - Tricky integration
1. ## Tricky integration
$\int_0^2 r^3 \sqrt{4-r^2} dr$
Not sure how to integrate this... I tried a u substitution for $4-r^2$ but couldn't find anything to replace $r^3$ with.
2. ## Re: Tricky integration
try sub u=4-r^2
so r^2 = 4-u
3. ## Re: Tricky integration
Originally Posted by deezy
$\int_0^2 r^3 \sqrt{4-r^2} dr$
Not sure how to integrate this... I tried a u substitution for $4-r^2$ but couldn't find anything to replace $r^3$ with.
\displaystyle \begin{align*} \int{r^3\sqrt{4 - r^2}\,dr} = -\frac{1}{2}\int{-2r\cdot r^2\sqrt{4 - r^2}\,dr} \end{align*}
Let \displaystyle \begin{align*} u = 4 - r^2 \implies du = -2r\,dr \end{align*} and the integral becomes
\displaystyle \begin{align*} -\frac{1}{2}\int{-2r\cdot r^2\sqrt{4 - r^2}\,dr} &= -\frac{1}{2}\int{\left(4 - u\right)\sqrt{u}\,du} \\ &= -\frac{1}{2}\int{4u^{\frac{1}{2}} - u^{\frac{3}{2}}\,du} \\ &= -\frac{1}{2}\left(\frac{4u^{\frac{3}{2}}}{\frac{3}{ 2}} - \frac{u^{\frac{5}{2}}}{\frac{5}{2}}\right) + C \end{align*}
Now after you change the terminals to u terminals and insert them, you will have the answer for the definite integral.
4. ## Re: Tricky integration
You can also do
$u = r^2$
$du = 2rdr$
$dr = \frac{1}{2}du$
so $\frac{1}{2}\int (4-u)udu$
5. ## Re: Tricky integration
Originally Posted by Intrusion
You can also do
$u = r^2$
$du = 2rdr$
$dr = \frac{1}{2}du$
so $\frac{1}{2}\int (4-u)udu$
Where did the square root go? | 2014-04-23 23:59:00 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 17, "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": 1.0000075101852417, "perplexity": 7687.239063394494}, "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-2014-15/segments/1398223203841.5/warc/CC-MAIN-20140423032003-00245-ip-10-147-4-33.ec2.internal.warc.gz"} |
http://ieeexplore.ieee.org/xpl/tocresult.jsp?reload=true&isnumber=5743105 | Scheduled System Maintenance
On Tuesday, September 26, IEEE Xplore will undergo scheduled maintenance from 1:00-4:00 PM ET.
During this time, there may be intermittent impact on performance. We apologize for any inconvenience.
# IEEE Microwave and Wireless Components Letters
## Filter Results
Displaying Results 1 - 21 of 21
Publication Year: 2011, Page(s):C1 - C4
| PDF (39 KB)
• ### IEEE Microwave and Wireless Components Letters publication information
Publication Year: 2011, Page(s): C2
| PDF (44 KB)
• ### Frequency-Dependent Substrate Characterization via an Iterative Pole Search Algorithm
Publication Year: 2011, Page(s):173 - 175
| | PDF (293 KB) | HTML
The characterization of frequency-dependent material properties is an important issue in nowadays high-speed interconnect design. This letter presents a practical method to determine the complex permittivity of a substrate material, by combining measurements with simulations. A rational permittivity model is determined by searching for its poles and residues using an iterative optimization method.... View full abstract»
• ### Extending the Stability Limit of the FDTD Method With Spatial Filtering
Publication Year: 2011, Page(s):176 - 178
Cited by: Papers (14)
| | PDF (320 KB) | HTML
It is shown that the well-known Courant stability limit of the finite-difference time-domain (FDTD) method can be controlled and extended by filtering out unstable spatial harmonics that develop when the time-step is chosen to exceed this limit. The formulation of a spatially filtered FDTD algorithm is accompanied by a numerical benchmarking study that includes cavity resonator and backward wave m... View full abstract»
• ### Application of the Modal CFS-PML-FDTD to the Analysis of Magnetic Photonic Crystal Waveguides
Publication Year: 2011, Page(s):179 - 181
Cited by: Papers (10)
| | PDF (200 KB) | HTML
We develop a modal finite-difference time-domain (FDTD) method with a complex-frequency-shifted (CFS) perfectly matched layer (PML) to analyze magnetic photonic crystal (MPhC) waveguides. MPhCs are periodic structures with unit cell composed of two misaligned anisotropic dielectric layers and one ferromagnetic layer. Numerical results show that the proposed modal FDTD can reduce both memory and CP... View full abstract»
• ### A Novel Unequal Power Divider Design With Dual-Harmonic Rejection and Simple Structure
Publication Year: 2011, Page(s):182 - 184
Cited by: Papers (6)
| | PDF (723 KB) | HTML
This letter presents, for the first time, a novel design of unequal power divider with dual-harmonic rejection. Explicit closed-form design formulas are made available for circuit parameter extraction. The proposed circuit features simple construction and wide spurious suppression bandwidth. For demonstration, the simulated and experimental results of a 1 GHz, 2:1 power divider implemented on micr... View full abstract»
• ### Design of Ring Couplers for Arbitrary Power Division With 50 $Omega$ Lines
Publication Year: 2011, Page(s):185 - 187
Cited by: Papers (11)
| | PDF (209 KB) | HTML
A new 0°/180° ring coupler structure is proposed for the arbitrary power division ratios. The proposed coupler consists only of 50 Ω transmission lines with the simple ring structure. The electrical lengths of the 50 Ω branches are adjusted to obtaining any desired values of the power division ratio without changing the impedance. A very wide range of power division rat... View full abstract»
• ### Miniaturized Distributed Marchand Balun Using Coupled Synthesized CPWs
Publication Year: 2011, Page(s):188 - 190
Cited by: Papers (12)
| | PDF (388 KB) | HTML
A miniaturized distributed Marchand balun, composed of two unequal sections of coupled slow-wave synthesized coplanar waveguides, is developed in this letter. With the even odd mode analysis, the propagation characteristics of the coupled synthesized lines are analyzed. A simple phase compensation scheme, with unequal coupling sections, is proposed to compensate for the phase imbalance due to the ... View full abstract»
• ### Improved Capacitive Loading Method for Miniaturization of 0 dB Forward-Wave Directional Couplers
Publication Year: 2011, Page(s):191 - 193
Cited by: Papers (4)
| | PDF (277 KB) | HTML
An improved capacitive loading method for miniaturization of 0 dB forward-wave directional couplers is demonstrated. The method enables to miniaturize the coupler to have a predetermined characteristic impedance, eliminating the need for additional impedance transformers and therefore allowing for a substantial improvement in the degree of miniaturization. Experimental results for a 0 dB coupler a... View full abstract»
• ### Switchable Substrate Integrated Waveguide
Publication Year: 2011, Page(s):194 - 196
Cited by: Papers (13)
| | PDF (621 KB) | HTML
A switchable substrate integrated waveguide is presented that can be switched between two different modes of propagation via the biasing of a pin diode switch. To demonstrate the usefulness of the design a single pole single through (SPST) waveguide switch is presented. The switch is shown to have approximately 50 dB isolation and 3 dB insertion loss over the switchable bandwidth. View full abstract»
• ### Compact and High-Isolation Quadruplexer Using Distributed Coupling Technique
Publication Year: 2011, Page(s):197 - 199
Cited by: Papers (27)
| | PDF (440 KB) | HTML
A compact microstrip quadruplexer with high isolation is presented in this letter. The quadruplexer consists of a distributed coupling feeding line, output feeding lines and uniform resonator pairs. Since the uniform resonators would resonate at multiple fundamental frequencies, to obtain a high-isolation quadruplexer, the resonators are properly located with respect to the input and output feedin... View full abstract»
• ### Design of Microstrip Dual-Passband Filter Based on Branch-Line Resonators
Publication Year: 2011, Page(s):200 - 202
Cited by: Papers (4)
| | PDF (376 KB) | HTML
A new type of microstrip dual-passband filter using branch-line resonators near the input and output ports is presented in this paper. The branch-line resonator plays two important roles for the proposed dual-band filter structure. One is for extracting the external quality factor of each band separately and the other is for providing the required resonance at the center frequency of each passband... View full abstract»
• ### A New Quad-Band Bandpass Filter Using Asymmetric Stepped Impedance Resonators
Publication Year: 2011, Page(s):203 - 205
Cited by: Papers (60)
| | PDF (336 KB) | HTML
A new quad-band microstrip bandpass filter (BPF) using asymmetric stepped impedance resonators (SIRs) is proposed. The filter only employs two sets of the asymmetric SIRs. One set is designed to operate at the first and third passbands (2.4/5.2 GHz) and the other set is employed at second and fourth passbands (3.5/6.8 GHz). By tuning the impedance and length ratios of the asymmetric SIRs, a multi-... View full abstract»
• ### Ultra-Wideband (UWB) Ring Resonator Bandpass Filter With a Notched Band
Publication Year: 2011, Page(s):206 - 208
Cited by: Papers (66)
| | PDF (511 KB) | HTML
This letter presents a novel ultra-wideband (UWB) bandpass filter (BPF) with a notched band using a ring resonator. Bandwidths of the ring resonator with two stepped-impedance stubs are calculated by examining the relations between resonant frequencies and the characteristic impedance of the ring. Stepped-impedance ports are used to obtain improved return losses in a high-frequency band. Interdigi... View full abstract»
• ### In-Line Pure ${rm E}$-Plane Waveguide Band-Stop Filter With Wide Spurious-Free Response
Publication Year: 2011, Page(s):209 - 211
Cited by: Papers (4)
| | PDF (469 KB) | HTML
A new compact pure E-plane waveguide structure is proposed for coupling band-rejection cavities to the main rectangular waveguide in bandstop in-line filters. This coupling structure reduces drastically the unwanted resonances in filters with a very large pass band requirement. Moreover, it has some additional advantages. First, unlike typical inductive irises, large coupling coefficients can be i... View full abstract»
• ### A W-Band $times$ 12 Multiplier MMIC With Excellent Spurious Suppression
Publication Year: 2011, Page(s):212 - 214
Cited by: Papers (11)
| | PDF (382 KB) | HTML
This letter presents a single chip × 12 frequency multiplier MMIC for the W-band that is realized in a 100 nm metamorphic HEMT technology. To obtain the × 12 multiplication factor a multiplier chain of a doubler, a tripler and a doubler has been cascaded. The circuit has a 3 dB bandwidth of 15 GHz from 85 to 100 GHz. At 94 GHz, the multiplier achieves a saturated output power of more... View full abstract»
• ### A 60 GHz Wideband Quadrature-Balanced Mixer Based on 0.13 $mu{rm m}$ RFCMOS Technology
Publication Year: 2011, Page(s):215 - 217
Cited by: Papers (8)
| | PDF (281 KB) | HTML
A 60 GHz wideband quadrature-balanced down-conversion mixer employing a new wideband technique with an active feedback has been developed in this work. Fabricated with a 0.13 μm RFCMOS technology, the mixer exhibits a 3 dB IF bandwidth of 5 GHz with a conversion gain of 2.3 dB for a fixed LO frequency of 60 GHz. The mixer also shows an RF bandwidth of 7 GHz with a peak gain of 5.6 dB at 55 ... View full abstract»
• ### A K-Band Low-Power Colpitts VCO With Voltage-to-Current Positive-Feedback Network in 0.18 $mu{rm m}$ CMOS
Publication Year: 2011, Page(s):218 - 220
Cited by: Papers (24)
| | PDF (1030 KB) | HTML
A circuit topology suitable for low-power Colpitts voltage-controlled oscillators (VCOs) is presented in this letter. By employing the proposed voltage-to-current positive-feedback network, the required transconductance for VCO startup can be reduced, leading to the minimized dc power for sustaining VCO oscillation. Moreover, the Q-factor enhanced varactor is used in this VCO design for phase nois... View full abstract»
• ### Linearity Improved Doherty Power Amplifier Using Coupled-Lines and a Capacitive Load
Publication Year: 2011, Page(s):221 - 223
Cited by: Papers (5)
| | PDF (791 KB) | HTML
A Doherty power amplifier, using a pair of coupled lines loaded by a capacitor, is proposed for linearity improvement. The conventional λ/4 transmission line is substituted by capacitor-loaded coupled lines to perform impedance inversion, and to compensate phase delay. At the same time, the proposed structure is also utilized to suppress the second and higher order harmonic of the output of... View full abstract»
Publication Year: 2011, Page(s): 224
| PDF (320 KB)
• ### IEEE Microwave and Wireless Components Letters information for authors
Publication Year: 2011, Page(s): C3
| PDF (34 KB)
## Aims & Scope
The IEEE Microwave and Wireless Components Letters (MWCL) publishes three page papers that focus on microwave theory, techniques and applications as they relate to components, devices, circuits, biological effects, and systems involving the generation, modulation, demodulation, control, transmission, and detection of microwave signals.
Full Aims & Scope
## Meet Our Editors
Editor in Chief
N. Scott Barker
Dept. Elect. Comp. Eng.
University of Virginia
Charlottesville, VA 22904
barker@virginia.edu
dsk6n@virginia.edu | 2017-09-26 08:04:01 | {"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": 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": 0.22750629484653473, "perplexity": 9718.43646200087}, "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-2017-39/segments/1505818695113.88/warc/CC-MAIN-20170926070351-20170926090351-00597.warc.gz"} |
https://physics.stackexchange.com/questions/177135/is-electric-current-a-scalar-quantity | # Is electric current a scalar quantity?
According to the definition of a Scalar quantity that i have read in class 9 is that ''those quantities which has only magnitude but no direction is known as a scalar quantity''.....But in class 10 i read that charges need to flow in a particular direction in order to form a electric current......From this argument we can conclude that a current has a specified directions which denies the definition of being a scalar quantity......
That definition of a vector quantity is a little too simple. It needs to not only have direction, but the directions need to add depending on the angles between them in a specific way to give an overall equivalent quantity.
Current in a circuit isn't really a vector quantity, it has direction but that is equivalent to just the sign of the current. You can have a positive current going in one direction and a negative current in the other - they will still add but not in a vector sense.
Perhaps there needs to be a 3rd term in between scalar and vector.
• In the Maxwell equations, $\nabla\times\vec B = \mu_0 (\vec J + \epsilon_0 \partial_t \vec E)$, the current $\vec J$ is most certainly a vector quantity. I suspect your answer (and the question) is talking about currents in an electric circuit, but it might be worthwhile to mention that, in general, current is indeed a vector quantity. Apr 19 '15 at 17:19
• @ACuriousMind - good point, I was think in terms of the question Apr 19 '15 at 18:13
Current is what is known as a pseudoscalar. This justification for this comes from the definition of current. Current, $I$, is defined as the net flow of charge per unit time through some surface. We define a vector field called the current density, $\vec{J}$, that describes the net flow of charge density at each point in space. It's related to the charge density ($\rho$, charge per unit volume), and mean velocity at each point, $\vec{v}$, by: $$\vec{J} = \rho \vec{v}.$$ If $\vec{J}$ is constant, then the net time rate at which charge is flowing through some flat surface with area $A$ is given by: $$I = A \hat{n} \cdot \vec{J},$$ where $\hat{n}$ is a vector that has length $1$ and is perpendicular to $A$ (it's a 'surface normal'). $A$ is flat, though, so the definition of $\hat{n}$ is ambiguous (it's perpendicular, but on which side of $A$?). The usual choice in lower level physics class is to just tell students to pick a direction and stick with it. At higher levels, $\hat{n}$ is defined by a cross product, in the case of a parallelogram, and an integral of cross products in general. That makes $\hat{n}$ a pseudovector. Since $\vec{J}$ is an ordinary vector, the result of the dot product must be a pseudo scalar.
Punchline: current density $\vec{J}$ is unambiguous because it is an ordinary vector, and $I$ depends on which direction you define to be positive flow for positive charges through the surface.
A point O where current 4A and 3A enter at an angle of 60° but output current is 7A where output current doesn't depend upon input current. So, current flows simple algebraic sum, due to this reason current is a scalar quantity. | 2021-12-09 01:39:29 | {"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": 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": 0.8976863622665405, "perplexity": 130.14605201205634}, "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/1637964363641.20/warc/CC-MAIN-20211209000407-20211209030407-00124.warc.gz"} |
https://testbook.com/question-answer/a-tape-of-length-l-and-weight-w-kgm-is-suspended--5e157fbcf60d5d3a7df0758d | # A tape of length l and weight W kg/m is suspended at its ends with a pull of p kg. the sag correction is:
This question was previously asked in
UPPSC AE Civil 2013 Official Paper II
View all UPPSC AE Papers >
1. $$\frac{{{l^2}{w^2}}}{{24{p^2}}}$$
2. $$\frac{{{l^2}{w^3}}}{{24{p^2}}}$$
3. $$\frac{{{l^3}{w^2}}}{{24{p^2}}}$$
4. $$\frac{{{l^2}{w^2}}}{{24{p^3}}}$$
Option 3 : $$\frac{{{l^3}{w^2}}}{{24{p^2}}}$$
## Detailed Solution
Correction for sag is given by:
$${C_s} = \; - \frac{{{W^2}{l^3}}}{{24\;{P^2}}}$$
Where,
W = weight of tape per unit length (N/m)
l = length of tape suspended between supports (m)
p = pull applied (N) | 2021-10-22 00:47:01 | {"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": 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": 0.35903069376945496, "perplexity": 7309.477133986278}, "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-2021-43/segments/1634323585449.31/warc/CC-MAIN-20211021230549-20211022020549-00153.warc.gz"} |
https://docs.attachmate.com/Reflection/14.x/prog-ref/ibm/hlpid_m_playbacktrace.htm | Programming with Reflection
PlayBackTrace method
Syntax object.PlayBackTrace Type, Filename
# Description
Plays back a trace file.
# Arguments
Type Argument type: Enumeration
Use this argument to specify what type of trace file to play. Two trace file types are available. See StartTrace for more information.
rcDataFromHost
Contains data transmissions to and from the host. This file type is given a *.hst extension by default.
rcCommands
Contains Reflection methods. This file type is given a *.cmd extension by default.
Filename Argument type: String
The trace file to be opened. Supply complete path information.
Keyword Index
Related Topics
Reflection products that use this command | 2022-05-23 11:16:51 | {"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": 0.8772318363189697, "perplexity": 9320.010867117071}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-21/segments/1652662558015.52/warc/CC-MAIN-20220523101705-20220523131705-00726.warc.gz"} |