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Definition:Curvature
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Definition $\kappa = \dfrac {\d \psi} {\d s}$
where:
Let $C$ be embedded in a cartesian plane.
$\kappa = \dfrac {y''} {\paren {1 + y'^2}^{3/2} }$
where:
$y' = \dfrac {\d y} {\d x}$ is the derivative of $y$ with respect to $x$ at $P$ $y'' = \dfrac {\d^2 y} {\d x^2}$... |
Cardinal numbers Cardinality is a measure of the size of a set. Two sets have the same cardinality---they are said to be equinumerous---when there is a one-to-one correspondence between their elements. The cardinality assignment problem is the problem of assigning to each equinumerosity class a cardinal number to repre... |
This post has been cross-posted on the Quansight LabsBlog.
As of November, 2018, I have been working at Quansight. Quansight is a new startup founded by the same people who started Anaconda, which aims to connect companies and open source communities, and offers consulting, training, support and mentoring services. I w... |
Modeling Linear Elastic Materials – How Difficult Can It Be?
The most fundamental material model for structural mechanics analysis is the linear elastic model. Trivial as it may sound, there are some important details that may not be obvious at first glance. In this blog post, we will dive deeper into the theory and ap... |
This question already has an answer here:
Are there any solutions to $2^n-3^m=1$? 4 answers
This question arose as an attempt to answer the following question Relaxed Collatz 3x+1 conjecture. I wanted to show that there is a solution of the equation $2^{k}=3^{z}(2n+1)-1$ for each $n\geq 2$, where $k,z,n\in\mathbb{N}$. ... |
If we idealize the scenario enough, this is a simple exercise in differential equations, so let's get to work. First, we know that it's
initial speed is $150 \text{ m/s}$, but that is by no means its final speed - obviously, the bb slows down as it travels through air! Let's suppose that the moment the bb exits the bar... |
I am following Chapter 8 ("Heteroskedasticity" p. 259) in the 6th edition of Woolridge
Introductory Econometrics: A Modern Approach and I don't understand one piece of the transformation of our model.
For fGLS, we assume [1] $Var(u|\boldsymbol{x}) = \sigma^2exp(\delta_0 +\delta_1x_1+\delta_2x_2+...+\delta_kx_k)$, where... |
You want to show that $(n+1)f^\lambda=\sum_{\mu\succ \lambda}f^\mu$, in other words that given an element $i\in\{1,2,\ldots,n+1\}$ and a standard tableau of shape $\lambda$ you can build a standard tableau of some shape obtained by adding a single square to the shape, and do so in a bijective (reversible) way. You may ... |
A-Softmax $L = \frac{1}{N} \sum\limits_{i}{-\log(\frac{e^{ \left| {x_i} \right| \psi(\theta_{y_i,i})}}{e^{ \left| {x_i} \right| \psi(\theta_{y_i,i})} + \sum\limits_{j|j \ne y_i}{e^{ \left| {x_j} \right| \cos(\theta _{j,i})}}})}$
$\psi(\theta_{y_i,i})=(-1)^k\cos(m\theta_{y_i,i})-2k$, $\theta_{y_i,i}\in[\frac{k\pi}{m}, \... |
For an i.i.d sequence of Random Variables $X_1, \dots, X_n$, each with mean $\mu = \mathbb E[X]$, the goal is to estimate some continuous function $f$ evaluated at the mean, $f[\mathbb E[X]]$.
If there is some unbiased estimator, $L$, so that $\mathbb E L = f[\mathbb E[X]]$, then can this unbiased estimator always be t... |
Indiana Jones found ancient Aztec catacombs containing a golden idol. The catacombs consists of $$$n$$$ caves. Each pair of caves is connected with a two-way corridor that can be opened or closed. The entrance to the catacombs is in the cave $$$1$$$, the idol and the exit are in the cave $$$n$$$.
When Indiana goes from... |
Let $f \in F_p[x]$ be an irreducible polynomial of degree $n$, where $p$ is prime. Prove that its roots are independent over $F_p$.
EDIT: It was pointed in the answers that this claim is true only for some irreducible polynomials. My question can be changed to: prove that for any $n$, such irreducible polynomial of deg... |
Definition:Transcendental Element of Ring Extension Definition
Let $\struct {D, +, \circ}$ be an integral subdomain of $R$.
Let $x \in R$.
Then $x$ is transcendental over $D$ if and only if: $\displaystyle \forall n \in \Z_{\ge 0}: \sum_{k \mathop = 0}^n a_k \circ x^k = 0_R \implies \forall k: 0 \le k \le n: a_k = 0_R$... |
A little mixup in notation there. $P_n(x)$ is normally denoting the $n^{th}$ Legendre polynomial, and $L_n(x)$ the $n^{th}$ Laguerre polynomial.
Both $\{ P_n| n \in \mathbb{N} \}$ and $\{ L_n| n \in \mathbb{N} \}$ form sets of orthogonal functions, which means that when taking an inner product of two of its members whi... |
While reading about refractive index 2 terms popped up, group velocity which alway slows down in a medium and phase velocity which may exceed speed of light. Say in a complete vacuum and using laser with only 1 frequency as an example, which of the two kinds of velocity is defined as standard $c$ in physics?
The answer... |
Periodic solutions in a delayed predator-prey models with nonmonotonic functional response
1.
School of Mathematic and Statistics, Lanzhou University, Lanzhou, Gansu 730000, China
2.
School of Mathematics and Information Sciences, Ludong University, Yantai, Shandong 264025, China
$y^{'}(t)=y(t)[ \frac{\mu (t)x(t-\tau )... |
Hello one and all! Is anyone here familiar with planar prolate spheroidal coordinates? I am reading a book on dynamics and the author states If we introduce planar prolate spheroidal coordinates $(R, \sigma)$ based on the distance parameter $b$, then, in terms of the Cartesian coordinates $(x, z)$ and also of the plane... |
Hi,
in this thread, @rbj mentioned that the MathJax implementation in this forum is erratic and I believe him. I had issued in the past and it is always frustrating. I think most problems are due to conflicts between the wysiwyg editor and Mathjax.
If you find a minute or two, would you please use this thread here to r... |
Scientific posters present technical information and are intended for congress or presentations with colleagues. Since LaTeX is the most natural choice to typeset scientific documents, one should be able to create posters with it. This article explains how to create posters with latex
Contents
The two main options when... |
Introduction to Modeling Soap Films and Other Variational Problems
What do soap films, catenary cables, and light beams have in common? They behave in ways that minimize certain quantities. Such problems are prevalent in science and engineering fields such as biology, economics, elasticity theory, material science, and... |
Approaches
There are many methods for Deconvolution (Namely the degradation operator is linear and Time / Space Invariant) out there.
All of them try to deal with the fact the problem is Ill Poised in many cases.
Better methods are those which add some regularization to the model of the data to be restored.
It can be s... |
This is a question from an old exam, I'm trying to understand the key and comments provided by the examiner.
First question is simply determine the Fourier series of the function $f$ defined as $1-x^2$ on $[-\pi,0)$ and as $1+x^2$ on $[0,\pi)$. I got $$f \sim 1+\frac{2}{\pi} \sum \frac{1}{n^3} \left((2-n^2 \pi^2)(-1)^n... |
member 545369 1. Homework Statement
A space explorer travels in a spaceship with v = 0.9c. She goes from Earth to a distant star that is 4 light years away (again, measured from Earth). What is the distance measured by the explorer and how long will she say it took her to get there?
2. Homework Equations
##L=\frac {L_0... |
Partition property
A partition property is an infinitary combinatorical principle in set theory. Partition properties are best associated with various large cardinal axioms (all of which are below measurable), but can also be associated with infinite graphs.
The
pigeonhole principle famously states that if there are $n... |
Challenge
Given an integer, \$s\$, as input where \$s\geq 1\$ output the value of \$\zeta(s)\$ (Where \$\zeta(x)\$ represents the Riemann Zeta Function).
Further information
\$\zeta(s)\$ is defined as:
$$\zeta(s) = \sum\limits^\infty_{n=1}\frac{1}{n^s}$$
You should output your answer to 5 decimal places (no more, no le... |
In synthetic differential geometry, one way to define formally étale morphisms is as follows.
Say $f:M\to N$ is formally étale if $TM\cong TN\times _N M$, in other words if the unique map from $TM$ to the pullback is an isomorphism. (A generalization of) this approach is taken e.g in definition 8.10 of Kostecki's notes... |
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I came across this question on a site and I didn't find any solution to this.....(except to use calculator)
The question was
Which digit doesn't occur in the number 2^29 ?
Plz help.....
Note by Poonayu Sharma 5 years, 4 months ago
Easy Math Editor
This discussion... |
Answer
The angles are as follows: $A = 61^{\circ}, B = 40.7^{\circ},$ and $C = 78.3^{\circ}$ The lengths of the sides are as follows: $a = 5.4, b = 4,$ and $c = 6$
Work Step by Step
Let $b=4$, and let $c = 6$. We can use the law of cosines to find $a$: $a^2 = b^2+c^2-2bc~cos~A$ $a = \sqrt{b^2+c^2-2bc~cos~A}$ $a = \sqrt... |
Correlation quiz
1
Correlation is a __________ type of statistical analysis.
2
Correlation is:
3
What would you expect the correlation between daily calorie consumption and body weight to be?
4
Estimate the correlation between driving performance and blood alcohol levels:
5
Estimate the correlation between use of contr... |
Consider a one dimensional system with fluid in it. Mass and momentum balance equation of the system are (in the absence of external forces and assuming Newtonian behaviour valid for viscocity), \begin{eqnarray} \frac{\partial \rho}{\partial t} + \frac{\partial}{\partial x}(\rho u)= 0\\ \rho\frac{\partial u}{\partial t... |
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Search for new resonances in $W\gamma$ and $Z\gamma$ Final States in $pp$ Collisions at $\sqrt{s}=8\,\mathrm{TeV}$ with the ATLAS Detector
(Elsevier, 2014-11-10)
This letter presents a search for new resonances decaying to final states with a vector boson produced in association with a... |
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Now showing items 1-2 of 2
Anisotropic flow of inclusive and identified particles in Pb–Pb collisions at $\sqrt{{s}_{NN}}=$ 5.02 TeV with ALICE
(Elsevier, 2017-11)
Anisotropic flow measurements constrain the shear $(\eta/s)$ and bulk ($\zeta/s$) viscosity of the quark-gluon plasma created in heavy-ion collisions... |
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Production of Σ(1385)± and Ξ(1530)0 in proton–proton collisions at √s = 7 TeV
(Springer, 2015-01-10)
The production of the strange and double-strange baryon resonances ((1385)±, Ξ(1530)0) has been measured at mid-rapidity (|y|< 0.5) in proton–proton collisions at √s = 7 TeV with the ... |
Let $X$ be a nowhere dense set of circle $S^1$. Here $S^1$ is equipped with the standard topology and measure.
Q Can we say that $X$ is a finite point set? Is there a counterexample?
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It on... |
If you consider the phase space (the space of initial data) ${\cal{M}}$ of a classical system it can be seen as the cotangent bundle $T^{*}Q$ of the configuration space $Q$.
As you say this bundle has a natural symplectic structure $\omega:T{\cal{M}}\times T{\cal{M}}\rightarrow \mathbb{R}$. Now given a Hamiltonian $H:{... |
Although I'm not sure that Piketty ever directly discusses the exact definition of $r$, he does make it clear indirectly. On page 52 of the hardcover English-language edition of his book, Piketty declares his "first fundamental law of capitalism":
Piketty obtains the share of income $\alpha$ from capital in national in... |
Let $(L,h)\to (X, \omega)$ be a compact toric polarized Kähler manifold of complex dimension $n$. For each $k\in N$, the fibre-wise Hermitian metric $h^k$ on $L^k$ induces a natural inner product on the vector space $C^{\infty}(X, L^k)$ of smooth global sections of $L^k$ by integration with respect to the volume form $... |
Rhenium osmium dating site
Some key papers include: Using Re-Os isotopes to determine the deposition age of petroleum source-rock formation (organic-rich shales) is a major research theme, both in terms of technical development and application.This method has been applied to better understand the origins of global Ocea... |
The way that you ask your question confuses the answer because you say "Will the speed of universe expansion will make the sky bright but the red shift make it invisible to our eyes", because the sky is already "bright" in certain wavelengths, particularly the centimeter cosmic background radiation (CMB).
Other than th... |
Division Theorem/Positive Divisor/Uniqueness Theorem $\forall a, b \in \Z, b > 0: \exists! q, r \in \Z: a = q b + r, 0 \le r < b$ In the above equation: $a$ is the dividend $b$ is the divisor $q$ is the quotient $r$ is the principal remainder, or, more usually, just the remainder.
It is given by Division Theorem: Posit... |
First steps to infinity and beyond Contents Axioms
In math, there are several philosophical liberties that could be taken.
The axioms declare the absolute rules of math; what can and can't be done, what exists and what doesn't, and what statements are true and false, are all determined by them. There are many different... |
Let $C$ denote the positively oriented boundary of the half disk $0 \le r \le 1, 0 \le \theta \le \pi$, and let $f(z)$ be a continuous function defined on that half disk by writing $f(0) = 0$ and using the branch \begin{align} f(z) = \sqrt{r} e^{\frac{i \theta}{2}} \end{align} Show that \begin{align} \int_C f(z) \, dz ... |
I have a question about Galerkin method. I don't understand why the Galerkin method weights the residual by the shape functions and sets it equal to zero. I want to know what is reason of this. Why we must set weights residual functions equal to zero?
When I studied the finite element method in graduate school, this no... |
I have to deal with a situation where I am trying to decompose numbers written as $2K^2, K\ge0$ into sums of squares, i.e. find: $$S_K=\{(x, y)\ |\ x^2+y^2 = 2K^2\}$$
One of the obvious solutions is $(K, K)$.
I have looked into several papers and found a number of algorithms pertaining to this. Basically the solution s... |
Since you already have a method of constructing the needed circle $C$, I assume your question is about uniqueness. Here is an informal analytic approach that could be formalized.
Let $M$ be the center of $D$, and $N$ be the center of $C$. Since $C$ passes through $P$ and $Q$, $N$ must lie on the line $\ell = b_{PQ}$. L... |
Bug introduced in or after 10.3, persisting through 11.2.
I'm trying to solve following PDE (heat equation):
$$ \begin{cases} u_t = a \, u_{xx} \\ u(x,0) = 0\\ \lim_{x\to \infty}u(x,t) =0\\ \alpha\, (\theta_0-u(0,t))+\dot{q}_0=-\lambda u_x(0,t) \end{cases}$$
Where basically I have an initial temperature of $0$ everywhe... |
ECE662: Statistical Pattern Recognition and Decision Making Processes
Spring 2008, Prof. Boutin
Collectively created by the students in the class
Contents Lecture 10 Lecture notes
The perceptron algorithm maps an input to a single binary output value.
For a proof of the Perceptron convergence theorem, see this page:
Fi... |
Contents
If you are old enough you might remember a film called Flubber released in 1997. The film depicts small jelly like characters that were digitally modelled, animated and rendered. The jelly/blobby look of the characters is something you can sort of easily produce in CGI using a technique called metaballs. To sa... |
Shrewd
(All information from [1])
Shrewd cardinals are a generalisation of indescribable cardinals. They are called shrewd because they are bigger in size than many large cardinals which much greater consistency strength (for all notions of large cardinal which do not make reference to the totality of all ordinals).
De... |
Possible Duplicate: Series converges implies $\lim{n a_n} = 0$
Someone can help me? If $(a_n)$ is a decreasing sequence and $\sum a_n$ converges. Then $\lim {(n.a_n)} = 0$.
I don't have idea how to solve this.
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professiona... |
Using method of Lagrange multipliers, I am looking to minimise the function
$f(x_1,...,x_n)=\prod_{i=1}^n(1+x_i)$ with the side condition $g(x_1,...,x_n)=\prod_{i=1}^nx_i-q^n=0$.
My goal is to show that $f$ is minimal when $x_i=q$ for all $i$.
I have $$\nabla g=(\prod_{i=1, i \neq j}^nx_i)_{1\leq j \leq n}$$ $$\nabla f... |
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1. Study of the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsf... |
My book is An Introduction to Manifolds by Loring W. Tu. The following is an entire subsection (Subsection 22.5) of the section that introduces manifolds with boundary (Section 22, Manifolds with Boundary).
Note: I believe that all manifolds with or without boundary referred in this subsection have unique dimensions by... |
i need to calculate some expectations which involving the ratio of normal pdf to normal cdf.
Specifically, they are $E\{\phi(x)/\Phi(x)\}$ and $E\{x\phi(x)/\Phi(x)\}$ where $x\sim N(0,1)$.
Written in integral, they should be $\int_{-\infty }^{+\infty }{\dfrac {\phi^2 \left( x\right) } {\Phi \left( x\right) }dx}$ and $\... |
I am trying different methods for finding the retarded time in an electromagnetism problem. I'm getting different results, but I'm not sure what I'm doing wrong.
Consider a charge at the origin that begins moving at time t=0 at uniform velocity in the positive x direction and that it has been moving for quite some time... |
Better viewed on this Dropbox site:
The Hypergeometric Distribution is usually explained via an urn analogy and formulated as the ratio of “favorable outcomes” to all possible outcomes:
\[
\displaystyle \boxed{P(x=a;N,A,n,a) = \frac{{A \choose a} \cdot {N-A \choose n-a} }{{N \choose n}}} \]
where \(N\) is the total num... |
Let $X,Y$ be two disjoint closed sets on $\mathbb{R}$ such that $X\cup Y = [a,b]$. Show that $X= \emptyset$ or $Y = \emptyset$.
Here's what I've got by now:
Let $k \in X\cup Y$. Therefore $k \in X$ or $k \in Y$. Suppose that $X \neq \emptyset$ and $k \in X$, hence $k \notin Y$ which implies that $k \in \mathbb{R} \setm... |
The simplest way to do so (for Pearson correlation) is to use Fisher's z-transformation.
Let
r be the correlation in question.
Let
n be the sample size used to acquire the correlation.
tanh is the hyperbolic tangent
atanh or $\tanh^{-1}$ is the inverse hyperbolic tangent.
Let
z = atanh(r), then
z is normally distribute... |
A
geometric series
is a sum of terms in which two successive terms always have the same ratio
. For example,
4 + 8 + 16 + 32 + 64 + 128 + 256 ...
is a geometric series with common ratio 2. This is the same as 2 * 2
x
where x is increacing by one for each number. It is called a geometric series because it occurs when co... |
I don't think your formula is quite right.
The two complex samples are the locations (at two successive sampling instants)of the tip of the rotating phasor that represents the analog signal. The information that you need is the
angle between phasor positions at thesetwo successive time instants. If $S_{n+1} = r_{n+1}e^... |
You made a mistake in this last equality
$$x[n] = \frac{1}{2\pi jn}\left( e^{-j\pi n/4} -e^{-j\pi n} +2e^{j\pi n/4} -2e^{-j\pi n/4} + e^{j\pi n} -e^{j\pi n/4} \right) \neq \frac{\sin(\pi n/4)}{\pi n}$$
The right way to do this would be:
$$\begin{align}x(n)&=\frac{1}{2\pi jn}\left( e^{-j\pi n/4} -e^{-j\pi n} +2e^{j\pi n... |
Greiner in his book "Field Quantization" page 173, eq.(7.11) did this calculation:
${\mathcal L}^\prime=-\frac{1}{2}\partial_\mu A_\nu\partial^\mu A^\nu+\frac{1}{2}\partial_\mu A_\nu\partial^\nu A^\mu-\frac{1}{2}\partial_\mu A^\mu\partial_\nu A^\nu $
$\space\space\space\space=-\frac{1}{2}\partial_\mu A_\nu\partial^\mu ... |
Ion Temperature in Inductively Coupled Plasmas (ICPs)
When modeling plasmas, various options exist for choosing an ion temperature. Your choice, however, may strongly influence your model’s results. Let’s discuss the theoretical reason behind this phenomenon and study an example involving an
inductively coupled plasma ... |
Joint work with Øystein Linnebo, University of Oslo.
J. D. Hamkins and Ø. Linnebo, “The modal logic of set-theoretic potentialism and the potentialist maximality principles,” to appear in Review of Symbolic Logic, 2018.
@ARTICLE{HamkinsLinnebo:Modal-logic-of-set-theoretic-potentialism, author = {Hamkins, Joel David and... |
We cannot prove it ...
As said in your previous post :
in system $\mathcal L(\neg, \to, \bullet)$, $\bullet$ "acts" as a constant truth, i.e. $\bullet \varphi \approx (\varphi \to \varphi)$.
If we consider the usual truth functional properties of the conncetives : $\lnot, \rightarrow$, and replace $\bullet \varphi$ wit... |
I am having trouble interpreting the following question:
Let $ \{X, || \cdot ||_{X} \} $ and $ \{Y, || \cdot ||_{Y} \} $ be Banach spaces. Let $ T(x,y) \colon X \times Y \to \mathbb{R} $ be a functional linear and continuous in each of the two variables. Then $ T $ is linear and bounded with respect to both variables.
... |
Definition:Bound Variable Contents Definition Examples
In algebra:
$x^2 + 2 x y + y^2 = \paren {x + y}^2$
both $x$ and $y$ are
bound variables.
In the universal statement:
$\forall x: P \paren x$
Thus, the meaning of $\forall x: P \paren x$ does not change if $x$ is replaced by another symbol.
That is, $\forall x: P \p... |
J. D. Hamkins and M. Kikuchi, “The inclusion relations of the countable models of set theory are all isomorphic,” ArXiv e-prints, 2017. (manuscript under review)
@ARTICLE{HamkinsKikuchi:The-inclusion-relations-of-the-countable-models-of-set-theory-are-all-isomorphic, author = {Joel David Hamkins and Makoto Kikuchi}, ti... |
I have the following equation:
$$D=\frac{1}{64} \pi A ^3 B \sin \left(C\right)-\frac{1}{2} \pi A B \sin \left(C\right)$$
which I want to solve for $A$. The equation is cubic in $A$ so this should give me 3 answers and, potentially, imaginary parts to the answers. I know, from the physical meaning of the parameters, tha... |
Edit: I'm a dumbass. The thing below is supposed to be just the motivation of asking. I want to ask for below and in general, hehe.
Assume that we have a general one-period market model consisting of d+1 assets and N states.
Using a replicating portfolio $\phi$, determine $\Pi(0;X)$, the price of a European call option... |
Answer
3.2 revolutions
Work Step by Step
We find: $\Delta \theta = \frac{\omega^2 - \omega_0^2 }{2\alpha}= \frac {0-2.2^2}{2 \times -.12} \approx 20 rads \approx 3.2\ revs $
You can help us out by revising, improving and updating this answer.Update this answer
After you claim an answer you’ll have
24 hours to send in a... |
8.8 #54
Does this indefinite integral converge for anyone? Also, if you are having trouble with the integral, take a look at the derivatives of inverse hyperbolic functions. --John Mason
It does not converge for me. I used direct comparison to test whether it converges or not. I started by comparing $ \sqrt{x^4-1} $ an... |
Frequency domain view of the relationship between a signal and a sampling of that signal
Outline Introduction Main Points Conclusion Introduction
This Slecture will look into the relationship between a signal and the sampling of that signal in the view of the frequency domain. The signal that will be sampled will be in... |
Those guys only make confusion. I will answer you with a very easy method you can use with piecewise functions.
First of all you have two steps functions, which you can easily figure in your mind to be like 2 dimensional boxes of height $2$.
Think about them as two boxes, one of which has to move towards the other. Tho... |
Let $p \in (1, \infty).$ Then there is a sequence $f_k$ satisfying
1) $f_k \in L^q$ for all $1 \leq q < \infty$
2) $f_k$ converges to $0$ in $L^q$ for all $q \in [1,p)$
3) $f_k$ diverges in $L^p$
$\textbf{Attemp}$ Since the integral for $1 \leq q < p$ converges to $0$ and at exactly $p$ it diverges, I think of $\int \f... |
ECE662: Statistical Pattern Recognition and Decision Making Processes
Spring 2008, Prof. Boutin
Collectively created by the students in the class
Lecture 21 Lecture notes
When the number of categories, c is big, decision tress are particularly good.
Example: Consider the query "Identify the fruit" from a set of c=7 cat... |
Science Advisor
Homework Helper
2,559 3
I missed the lectures for this topic, so I don't have the notes, so I was wondering if anyone could give me the idea behind how to solve quartics in radicals. I know its long and messy, so just the basic idea would do. For example:
x
I recall something about getting rid of the cu... |
TensorFlow 1 version View source on GitHub
Solves one or more linear least-squares problems.
Aliases:
tf.compat.v1.linalg.lstsq
tf.compat.v1.matrix_solve_ls
tf.compat.v2.linalg.lstsq
tf.linalg.lstsq( matrix, rhs, l2_regularizer=0.0, fast=True, name=None)
matrix is a tensor of shape
[..., M, N] whose inner-most 2 dimens... |
When one have a curve $\beta(s)$ which is parametrized by arc length (has natural parametrization) one is able to obtain the tangent, normal and binormal vectors by using Frenet-Serret frame equations:
$T = \beta'(s)$, $N=\frac{T'(s)}{|T'(s)|}$, $B = T \times N$
But are those formulas valid for non-regular parametrizat... |
Despite the rather recent progress in prime number theory (see the proof of the ternary Goldbach conjecture by H.A. Helfgott, and the striking result of Yitang Zhang improved by Tao, Maynard and others), to my knowledge, we're still unable to prove rigorously that there exists $N>0$ such that for all integer $n>N$, $2n... |
Tried asking here first, since a similar question had been asked on that site. Seems more relevant for this site however.
It is my current understanding that a quantum XOR gate is the CNOT gate. Is the quantum XNOR gate a CCNOT gate?
Quantum Computing Stack Exchange is a question and answer site for engineers, scientis... |
Currently, I am constructed a bayesian multilevel model to analyze a panel data set which now basically looks like the following: $y_{ijt} = \beta_{0ij} + X\beta + \epsilon_{ijt}$. So, now only a individual specific intercept but I want to extend this to other parameters. I estimate the model using bayesian econometric... |
If $f,g$ are uniformly continuous, then is $\alpha f+\beta g$ uniformly continuous?
So far, I looked at here If $f,g$ are uniformly continuous prove $f+g$ is uniformly continuous, but I didn't understand something. I know that from what I've been told,: 1. $\forall\epsilon >0$ $\exists\delta_1 >0$, if $|x-y|<\delta_1$ ... |
Unconventional analogs of single-parametric method of iterational aggregation Abstract
When we solve practical problems that arise, for example, in mathematical economics, in the theory of Markov processes, it is often necessary to use the decomposition of operator equations using methods of iterative aggregation. In t... |
Seminar
Parent Program: Location: MSRI: Simons Auditorium
The $L^p$-Brunn--Minkowski theory for $p\geq 1$, proposed by Firey and developed by Lutwak in the 90's, replaces the Minkowski addition of convex sets by its $L^p$ counterpart, in which the support functions are added in $L^p$-norm. Recently, B\"{o}r\"{o}czky, L... |
I've been reviewing proofs for a couple of calculus theorems and as I was trying to recall the proof of the Riemann Sum Theorem which uses Lower Sums and Upper Sums I came up with an idea to prove it using The Mean Value Theorem for Integrals.
I just wanted to know if my proof is good since I'm not sure if I've done ev... |
It´s known that for first order theories, it holds $\mathbf{ZFC} \vdash T \vdash \varphi \leftrightarrow T \models \varphi$. Why does this not hold in the higher order case (any simple example?)?
Furthermore if I change models by interpretations, does it hold that $T \vdash \varphi$ iff for all interpretations (in the ... |
Unpolarized light is more properly called light with
random polarization. That makes it more clear what it means: the polarization state (circular, linear, elliptic) varies randomly over space, wavelength, and time.
Consider the scenario below, where a diffuse light source is converted to a collimated beam with a narro... |
My favourite one: $[0, 1]$ is compact, i.e. every open cover of $[0, 1]$ has a finite subcover.
Proof: Suppose for a contradiction that there is an open cover $\mathcal{U}$ which does not admit any finite subcover. Thus, either $\left[ 0, \frac{1}{2} \right]$ or $\left[ \frac{1}{2}, 1 \right]$ cannot be covered with a ... |
Let $n$ be a natural number. I want to calculate $$\int_0^{\infty} \frac{x^n}{1+x^{2n}}$$ using contour integration.
I declare $f(z) = \frac{z^n}{1+z^{2n}}$. This function has $2n$ simple poles of the form $exp(i\frac{-\pi}{2n} + i\frac{\pi k}{n})$ for $k = 0,1,2, ... , 2n-1$.
My problem is to find which contour to use... |
Contents DFT ( Discrete Fourier Transform )
The Discrete Time Fourier Tranform is a good way to analyze discrete time signals in the frequency domain in theory, but in application the infinite range of time and frequency in the conversion formulas can make analysis difficult, especially on the computer. The Discrete Fo... |
Contents What Will We Study in this Chapter?
In the first chapter of this lesson, we said that projection matrices were used in the GPU rendering pipeline. We mentioned that there were two GPU rendering pipelines: the old one, called the fixed-function pipeline and the new one which is generally referred to as the prog... |
Get the noise calibration. That is, the ratio
\[ \frac{\sigma_{i}}{g_{i}k} \]
where \( k\) is a constant determined by the electronics of units DAC/MIP, and \( \sigma_i, g_i\) are the noise and gain of the \( i \) strip respectively.
This correction is needed because some of the reconstructed data (what which have an A... |
I was confused on how to find the derivative of this function:
y = log
2(x/(x-1)
If anyone could help me, please and thank you!!!
\(y=\log_2\left(\dfrac{x}{x-1}\right) = \dfrac{1}{\ln(2)}\ln\left(\dfrac{x}{x-1}\right)\\ \dfrac{dy}{dx} = \dfrac{1}{\ln(2)}\cdot \dfrac{1}{\dfrac{x}{x-1}}\cdot \left(\dfrac{(x-1)-x}{(x-1)^2... |
J. Bagaria, J. D. Hamkins, K. Tsaprounis, and T. Usuba, “Superstrong and other large cardinals are never Laver indestructible,” Arch. Math. Logic, vol. 55, iss. 1-2, pp. 19-35, 2016. (special volume in memory of R.~Laver)
@ARTICLE{BagariaHamkinsTsaprounisUsuba2016:SuperstrongAndOtherLargeCardinalsAreNeverLaverIndestruc... |
also, if you are in the US, the next time anything important publishing-related comes up, you can let your representatives know that you care about this and that you think the existing situation is appalling
@heather well, there's a spectrum
so, there's things like New Journal of Physics and Physical Review X
which are... |
Answer
$65$
Work Step by Step
We know that $ n!=1 \cdot 2 \cdot 3 .....(n-1)n $ Thus, we have $\dfrac{40!}{38!}=\dfrac{40 \cdot 39 \cdot 38!}{4 \cdot 3 \cdot 2 \cdot 1 \times 38! }$ $=\dfrac{40 \cdot 39}{24}$ $=65$
You can help us out by revising, improving and updating this answer.Update this answer
After you claim an... |
Mössbauer spectroscopy is a versatile technique used to study nuclear structure with the absorption and re-emission of gamma rays, part of the electromagnetic spectrum. The technique uses a combination of the Mössbauer effect and Doppler shifts to probe the hyperfine transitions between the excited and ground states of... |
It is well known to us that the Solubility of solute in a solution increases with the increase in the temperature because, when the temperature increases the molecules of the solvent gain more kinetic energy. Thus the molecules move randomly and having greater distance from each other which is responsible for the large... |
Let $$y''-q(x)y=0$$be a differential equation with initial conditions on $0\leq x<\infty,$ as $y(0)=1,y'(0)=1$ where $q(x)$ is a positive monotonically increasing continuous function. Then which of the following are true?
$y(x)\rightarrow\infty$ as $x\rightarrow\infty$.
$y'(x)\rightarrow\infty$ as $x\rightarrow\infty$.... |
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