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Exercise \(\PageIndex{1}\)
Find expressions for \(\displaystyle oshx+sinhx\) and \(\displaystyle coshx−sinhx.\) Use a calculator to graph these functions and ensure your expression is correct.
Answer
\(\displaystyle e^x\) and \(\displaystyle e^{−x}\)
Exercise \(\PageIndex{2}\)
From the definitions of \(\displaystyle co... |
I'm writing some integrals and I don't like the way the
\int symbol is displayed when it is followed by a big delimiter.Here's the code:
\[\int_S\biggl(\nabla\times\bar B - \mu_0\bar J -\mu_0\varepsilon_0\frac{\partial\bar E}{\partial t}\biggr) \cdot\hat n\,ds = 0\]
And here's the output:
What I'd like to have is an in... |
Newton’s method (or Newton-Raphson method) is an iterative procedure used to find the roots of a function.
Suppose we need to solve the equation \(f\left( x \right) = 0\) and \(x=c\) is the actual root of \(f\left( x \right).\) We assume that the function \(f\left( x \right)\) is differentiable in an open interval that... |
There are a couple of loose ends that need tying up regarding the IT index. One of which is the derivation of the information equilibrium condition (see also the paper) with non-uniform probability distributions. This turns out to be relatively trivial and only involves a change in the IT index formula. The information... |
The title is a bit of a joke, and for the controversy see here. Looking into the Solow model bumps you into the question of what "capital" (K) is, and that met with the titular controversy awhile back where Cambridge, MA said you could add up different stuff in a sensible way while Cambridge, UK said you couldn't.
The ... |
The answer is positive, since $\psi:H_r \to \tilde H_{\binom {r}{k}}$ is proper, and every proper map is closed.
Here is a proof $\psi$ is proper:
Let $K \subseteq \tilde H_{\binom {r}{k}}$ be compact, and let $A_n \in \psi^{-1}(K)$. We shall prove $A_n$ has a convergent subsequence in $\psi^{-1}(K)$. It suffices to pr... |
While searching for more references for the new Wikipedia article (https://en.wikipedia.org/wiki/Sums_of_three_cubes) I found a horrible mistake related to this problem in Wolfram's _A New Kind of Science_, p. 789 (https://www.wolframscience.com/nks/p789--implications-for-mathematics-and-its-foundations/). Wolfram says... |
The OP in this post asked the following:
If you take a regular $n$-sided polygon, which is inscribed in the unit circle and find the product of all its diagonals (including two sides) carried out from one corner you will get $n$ exactly:
$A_1A_2\cdot A_1A_3\cdot ...\cdot A_1A_n = n$
user21820 used the following idea to... |
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Now showing items 1-4 of 4
D-meson nuclear modification factor and elliptic flow measurements in Pb–Pb collisions at $\sqrt {s_{NN}}$ = 5.02TeV with ALICE at the LHC
(Elsevier, 2017-11)
ALICE measured the nuclear modification factor ($R_{AA}$) and elliptic flow ($\nu_{2}$) of D mesons ($D^{0}$, $D^{+}$, $D^{⁎+}$... |
The bounty period lasts 7 days. Bounties must have a minimum duration of at least 1 day. After the bounty ends, there is a grace period of 24 hours to manually award the bounty. Simply click the bounty award icon next to each answer to permanently award your bounty to the answerer. (You cannot award a bounty to your ow... |
Math question on Newton's method and detecting actual zeros
02-07-2017, 05:04 PM
Post: #1
Math question on Newton's method and detecting actual zeros
(Admins: If this is in the wrong forum, please feel free to move it)
This came up during a debugging process in which Newton's method (using backtracking linesearch) gave... |
The $I^2$ statistic was introduced by Higgins and Thompson in their seminal 2002 paper and has become a rather popular statistic to report in meta-analyses, as it facilitates the interpretation of the amount of heterogeneity present in a given dataset.
For a standard random-effects models, the $I^2$ statistic is comput... |
1) Given \(\vecs r(t)=(3t^2−2)\,\hat{\mathbf{i}}+(2t−\sin t)\,\hat{\mathbf{j}}\),
a. find the velocity of a particle moving along this curve.
b. find the acceleration of a particle moving along this curve.
Answer: a. \(\vecs v(t)=6t\,\hat{\mathbf{i}}+(2−\cos t)\,\hat{\mathbf{i}}\) b. \(\vecs a(t)=6\,\hat{\mathbf{i}}+\s... |
The missing step is to show that $v_1,\ldots,v_n$ is linearly independent over $k(x)$. So suppose that there exist rational functions $r_1(x),\ldots,r_n(x)$, not all the zero function, such that
$r_1(x) v_1 + \ldots + r_n(x) v_n = 0$.
We may write $r_i(x) = n_i(x)/d(x)$, i.e., let $d(x)$ be a common denominator of the ... |
For a Banach space $B$, the space $L^1(0,T;B)$ is naturally identified with $L^\infty(0,T;B^*)$
if and only if $B^*$ has the Radon-Nikodym property. The space $L^\infty(\Omega)$ does not have the RNP.
In general, the dual of $L^1(0,T;B)$ is the larger space $\Lambda^\infty(0,T;B^*)$ which consists of
weak*-measurable f... |
As written, it's not clear to me that it's actually fully coupled. That is, the solution to $B$ depends (via its BC2) on the solution to $a$, but assuming $\omega$ is simply some specified function of position and time, it looks like $a$ doesn't depend on the solution to $B$. If that's the case, then simply solve for $... |
Alright, I have this group $\langle x_i, i\in\mathbb{Z}\mid x_i^2=x_{i-1}x_{i+1}\rangle$ and I'm trying to determine whether $x_ix_j=x_jx_i$ or not. I'm unsure there is enough information to decide this, to be honest.
Nah, I have a pretty garbage question. Let me spell it out.
I have a fiber bundle $p : E \to M$ where ... |
I am attempting to solve an equation of the type:
$ \left( -\tfrac{\partial^2}{\partial x^2} - f\left(x\right) \right) \psi(x) = \lambda \psi(x) $
Where $f(x)$ has a simple pole at $0$, for the smallest $N$ eigenvalues and eigenvectors. The boundary conditions are: $\psi(0) = 0$ and $\psi(R)=0$, and I'm only looking at... |
In the discussion of the RCK model on these two posts I realized the Euler equation could be written as a maximum entropy condition. It's actually a fairly trivial application of the entropy maximizing version of the asset pricing equation:
$$
p_{i} = \frac{\alpha_{i}}{\alpha_{j}} \frac{\partial U/\partial c_{j}}{\part... |
Please assume that this graph is a highly magnified section of the derivative of some function, say $F(x)$. Let's denote the derivative by $f(x)$.Let's denote the width of a sample by $h$ where $$h\rightarrow0$$Now, for finding the area under the curve between the bounds $a ~\& ~b $ we can a...
@Ultradark You can try d... |
In papers in physics and mathematics one often encounters longer mathematical expressions which have to be, for intuition and typesetting, expressed using symbols standing for recurring patterns in the expressions.
Consider for instance a set of equations where "$r^2 + a^2 \cos^2\! \vartheta$" and "$r^2 - 2M r + a^2$" ... |
Originally Posted by
kiwiheretic
This video:
Here are my concerns.
On the Youtube clock from:
9:25 Can he really simply draw a sphere around certain galaxies and say only those galaxies matter in the calculations? Why does he assume the other galaxies outside the sphere cancel out?
It's a consequence of how the inverse... |
I was thinking about the relative speed of an observation reference frame and an object which has been accelerated to a speed close to the speed of light. I'm by no mean an expert and the last physics class I took was more than 20 years ago so my question could be silly... If we accelerate a particle, let's say an elec... |
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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... |
In this section, we shall study the concept of divisibility. Let \(a\) and \(b\) be two integers such that \(a \neq 0\). The following statements are equivalent:
\(a\) \(b\), divides \(a\) is a of \(b\), divisor \(a\) is a of \(b\), factor \(b\) is a of \(a\), and multiple \(b\) is \(a\). divisible by
They all mean
The... |
In the early 2000's, I wrote software code to process and recover telemetry data from archived raw telemetry files obtained from the Pioneer 10 and 11 spacecraft between 1972 and 2003. This led to my participation in the investigation of the Pioneer Anomaly, an as-yet unexplained small, anomalous acceleration of these ... |
@egreg It does this "I just need to make use of the standard hyphenation function of LaTeX, except "behind the scenes", without actually typesetting anything." (if not typesetting includes typesetting in a hidden box) it doesn't address the use case that he said he wanted that for
@JosephWright ah yes, unlike the hyphe... |
In using the technique of integration by parts, you must carefully choose which expression is \(u\). For each of the following problems, use the guidelines in this section to choose \(u\). Do not evaluate the integrals.
1) \(\displaystyle ∫x^3e^{2x}\,dx\)
Answer: \( u=x^3\)
2) \(\displaystyle ∫x^3\ln(x)\,dx\)
3) \(\dis... |
First, the interpretation of $\eta=\frac{\partial\log y}{\partial\log x}$ and $\eta'=\frac{\partial y}{\partial x}$ are different. $\eta$ is the ratio of percent change and $\eta'$ is the ratio of absolute change. But you already know that. The real question is not why we define “elasticity” as a ratio of percent chang... |
This is the final one of a series of posts about the manuscript “Finite Part of Operator K-theory for Groups Finitely Embeddable into Hilbert Space and the Degree of Non-rigidity of Manifolds” (ArXiv e-print 1308.4744. http://arxiv.org/abs/1308.4744) by Guoliang Yu and Shmuel Weinberger. In previous posts (most recentl... |
One often hears the words "string tension" in string theory. But what does it really mean? In ordinary physics "tension" in an ordinary classical string arises from the fact that there are elasticity in the string material which is a consequence of the molecular interaction (which is electromagnetic in nature). But str... |
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1. Measurement of the top quark mass with lepton+jets final states using $$\mathrm {p}$$ p $$\mathrm {p}$$ p collisions at $$\sqrt{s}=13\,\text {TeV} $$ s=13TeV
The European Physical Jour... |
Name Last modified Size Description Parent Directory - lgr2licr.lua 2013-07-18 11:57 4.5K greekhyperref.tex 2014-12-12 18:19 5.1K diacritics.tex 2014-12-20 21:13 6.2K alphabeta-lgr.def 2015-08-18 14:50 10K textalpha-doc.tex 2016-09-21 22:15 14K alphabeta-euenc.def 2015-08-18 14:50 15K alphabeta.sty 2019-07-10 11:54 15K... |
10:40 AM
I did not find any posts with \let in the title: data.stackexchange.com/math/query/972169/…\let
Only two where it was removed from the title at some point, in both cases a typo for \left: math.stackexchange.com/posts/399817/revisions math.stackexchange.com/posts/2966236/revisions data.stackexchange.com/math/re... |
Consider a two period, single good, $2$ agent model. Time beings in perios $0$ in a known state (state $0$) but in period $1$ the world may find itself in any one of two states $s = 1,2$ with probabilities $\pi_s = 1/2$ for each state. Both of the consumers agree on the probabilities.
Each consumer as a constant relati... |
Combinatorial conditions for linear systems of projective hypersurfaces
Miguel Marco
Santiago de Compostela, October 8th 2016
Before starting
Ask questions!
Survey of past and current work
Partly joint with J.I. Cogolludo
Two points determine a line.
\(a_{0,0}z+a_{1,0} x + a_{0,1}y\)
One point determines a pencil of li... |
When a change in price results in an infinitely large response in quantity demanded, demand is perfectly elastic. The perfectly elastic demand curve is horizontal. At price P, consumers will buy a quantity Q. If there is an increase in price, quantity demanded drops to zero due to the existence of perfect substitutes. ... |
Cardinality of Infinite Sigma-Algebra is at Least Cardinality of Continuum Theorem $\operatorname{card}\left({\mathcal M }\right) \ge \mathfrak c$ Corollary Then $\mathcal M$ is uncountable. Proof
We first show that $X$ is infinite.
By the definition of a $\sigma$-algebra, $\mathcal M$ is a subset of $\mathcal P(X)$.
W... |
This is part of an old qual problem at my school.
Assume $\{f_n\}$ is a sequence of nonnegative continuous functions on $[0,1]$ such that $\lim_{n\to\infty}\int_0^1 f_n(x)dx=0$. Is it necessarily true that there are points $x_0\in[0,1]$ such that $\lim_{n\to\infty}f_n(x_0)=0$?
I think that there should be some $x_0$. M... |
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Now showing items 1-10 of 24
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 ... |
The bounty period lasts 7 days. Bounties must have a minimum duration of at least 1 day. After the bounty ends, there is a grace period of 24 hours to manually award the bounty. Simply click the bounty award icon next to each answer to permanently award your bounty to the answerer. (You cannot award a bounty to your ow... |
If $$f(x) = \int_x^2{\frac{dy}{\sqrt{1+y^3}}}$$
then find the value of $$\int_0^2{xf(x)}dx$$
I have no idea how to solve this question. Please help.
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It only takes a minute to sign up.Sign ... |
It seems all the answers so far approaching this from a theoretical perspective are approaching this in terms of exact answers, but we can say a lot about when good approximations are possible too. Of course, some answers have already provided silly ways to do this exactly, so approximations may seem unnecessary, but i... |
When I evaluate
Solve[a==Sin[b*c], b] to rearrange the following for $ b $:
$$ a = \sin(bc) $$
I get the following result from Mathematica:
$$\begin{align*} \left\{\left\{b\to \text{ConditionalExpression}\left[\frac{-\sin ^{-1}(a)+2 \pi c_1+\pi }{c},c_1\in \mathbb{Z}\right]\right\},\right.\left.\left\{b\to \text{Condit... |
Sometimes, the best way to do this kind of things is rather simple. If the problem is computing this function a lot of times, then... don't compute it!
Basically, all you have to do is to write a table for a finite set of values $x_j$. If you are going to compute $f(x)$ with $x\in[a,b]$, then you compute $f(x_j)$, wher... |
I am looking for a proof, a hint or an idea to the following problem:
Is the unique solution $x\in (0,2\pi)$ of
$$ x\sin(x) + \cos(x) = 1 $$
which is equivalent to
$$ 2\arctan(x) = x$$
a rational multiple of $\pi$. I.e. is $\frac{x}{\pi} \in \mathbb{Q}$?
I believe that this is not true. This idea is based on the numeri... |
If your interest is in data reduction, PCA, LASSO and ridge regression can all handle categorical predictors in principle. The default is typically to code the dummies as 0/1 numeric variables and standardize them like continuous numeric variables for scaling. Principal-components regression and ridge regression are fu... |
I'm reading
Lambda-Calculus and Combinators: An Introduction, and there's the following definition of $\lambda$-substitution: $FV(P)$ stands for the set containing all free-variables from $P$.
Definition 1.12 (Substitution)For any $M, N, x$, define $[N/x]M$ to be the result of substituting $N$ for every free occurrence... |
The Annals of Statistics Ann. Statist. Volume 24, Number 2 (1996), 862-878. Efficient maximum likelihood estimation in semiparametric mixture models Abstract
We consider maximum likelihood estimation in several examples of semiparametric mixture models, including the exponential frailty model and the errors-in-variable... |
I found a relationship online between the conductivity of electrolyte and current.
$$i = F \sum_i z_i N_i = F^2 \left( \sum_i z_i^2 u_i c_i \right)\nabla\phi = -\kappa\nabla\phi \qquad \kappa = F^2 \sum_i z_i^2 u_i c_i$$
This equation is hard for me to follow. I get what most of the variables mean and I am guessing tha... |
Blog
We can define
roundness in many ways. For example, as you may know, the circle is the shape that given a fixed perimeter maximizes the area. This definition has many problems. One of the problems is that countries generally have chaotic perimeters (also known as borders), so they tend to be much longer than they s... |
Where $f(x,y,z) = xyz$ and the constraint is $g(x,y,z) = x^2+2y^2+3z^2 = 6$
I have tried this problem like three or four times and not gotten the solution, I even asked this question once and got the wrong answer from my one and only answerer. The correct answer is {$\pm\sqrt{2}$,$\pm1$,$\pm\frac{\sqrt{2}}{\sqrt{3}}$} ... |
Let $A(x)$ be a differentiable matrix-valued function with $\det A(x)\ne 0\,\forall x$. I understand that $$\frac{d}{dx}\log A(x)$$ does not have a simple expression in terms of $A$ and $dA/dx$ unless these two things commute, in which case the expression is $$A(x)^{-1}\frac{dA}{dx}.$$ Let's say I don't want to assume ... |
Number theory studies the properties of integers. Some basic results in number theory rely on the existence of a certain number. The next theorem can be used to show that such a number exists.
Theorem \(\PageIndex{1}\label{thm:PWO}\)
Every nonempty subset of \(\mathbb{N}\) has a smallest element.
Proof
The idea is rath... |
I recently attended an internal Convergent Science advanced training course on turbulence modeling. One of the audience members asked one of my favorite modeling questions, and I’m happy to share it here. It’s the sort of question I sometimes find myself asking tentatively, worried I might have missed something obvious... |
Alright, I have this group $\langle x_i, i\in\mathbb{Z}\mid x_i^2=x_{i-1}x_{i+1}\rangle$ and I'm trying to determine whether $x_ix_j=x_jx_i$ or not. I'm unsure there is enough information to decide this, to be honest.
Nah, I have a pretty garbage question. Let me spell it out.
I have a fiber bundle $p : E \to M$ where ... |
First, you don't place any restrictions on $k$. This will turn out to matter.
Second, "$f(x) = k x^{\frac{1}{2}}$" is not a function. A function presented this way is a domain and a rule/formula/expression for converting elements of the domain into elements of the image. When the domain is missing, it is
normally under... |
I am interested in how to do a rotation about the $x$-axis in QM for spin $s = 1$ system. In an answer to the post we have that for a general rotation in QM where spin $s = 1$ we have the equation:\begin{equation} \begin{aligned} \exp(i\alpha \mathbf{J}\cdot\hat{\mathbf{n}}) & = 1 + i\hat{\mathbf{n}}\cdot\mathbf{J}\sin... |
The economist John Hicks wrote out Keynes' prose as an economic model that came to be known as the IS-LM model. I already derived this model before in a way that followed the way it is introduced in macroeconomics classes (as an IS and LM market). This derivation will acheive the same result, but approached fundamental... |
Here's an answer to the general question, which I wrote up a while ago. It's a common interview question.
The question goes like this: "Say you have X,Y,Z three random variables such that the correlation of X and Y is something and the correlation of Y and Z is something else, what are the possible correlations for X a... |
I am trying to solve a system of equations and have a question regarding the validity of my approach when implementing a fifth-order Cash-Karp Runge-Kutta (CKRK) embedded method with the method of lines. To give the questions some context, let me state the problem I am attempting to solve:
$$ \frac {\partial E}{\partia... |
Zeta-function method for regularization zeta-function regularization
Regularization and renormalization procedures are essential issues in contemporary physics — without which it would simply not exist, at least in the form known today (2000). They are also essential in supersymmetry calculations. Among the different m... |
I was playing around with a 3-D potential $V$ such that $V_{(r)} = 0$ for $r<a$, and $V_{(r)} = V_0>0$ otherwise. By using the Schrödinger Equation, I showed that: $$\frac{-\hbar}{2m}\frac{1}{r^2}\frac{d}{dr}\bigl( r^2\frac{d}{dr}\bigr)\psi = E\psi$$
I then used the substitution $\psi_{(r)}=f_{(r)}/r$ and $k=\sqrt{2mE}... |
In my master thesis I used an Algorithm called
Approximative Dynamic Programming [1] to solve equations of the form
$$ \max_{\pi}\mathbb{E}^{\pi}\left\{\sum_{t=0}^{T}\gamma^tC_t^{\pi}(S_t,A_t^{\pi}(S_t))\right\}. $$
It uses Monte-Carlo sampling and an approximation $\overline{V}_t$ of the value function to come around ... |
(Sorry was asleep at that time but forgot to log out, hence the apparent lack of response)
Yes you can (since $k=\frac{2\pi}{\lambda}$). To convert from path difference to phase difference, divide by k, see this PSE for details http://physics.stackexchange.com/questions/75882/what-is-the-difference-between-phase-differ... |
''Diamond Paradox'' by Diamond (1971)
This is a "less-known paradox," usually put as a counter to famous Bertrand paradox. It is a starting point in the literature on informational frictions in consumer markets, and the scientists in the field agree on its significance.
Its idea is diametrically opposite to that of Ber... |
For context, I'm studying the paper Coulomb blockade in superconducting quantum point contacts by Averin from 1998. Specifically, I am trying to find how he obtains equation 11 from equation 10, which gives the Landau Zener probability of ending up in a specific branch of the Josephson potential of a superconducting QP... |
And I think people said that reading first chapter of Do Carmo mostly fixed the problems in that regard. The only person I asked about the second pset said that his main difficulty was in solving the ODEs
Yeah here there's the double whammy in grad school that every grad student has to take the full year of algebra/ana... |
CryptoDB Ke Yang Affiliation: Google Inc Publications Year Venue Title
2005
EPRINT
Resource Fairness and Composability of Cryptographic Protocols
We introduce the notion of {\em resource-fair} protocols. Informally, this property states that if one party learns the output of the protocol, then so can all other parties,... |
We finished covering several tests that help determine the convergence or divergence of a series and I tried them all and I couldn't make progress or produce an answer that I felt was coherent enough to follow.
there are two series up for consideration, the first;
$\sum_{k=1}^{\infty} \frac{\sqrt{k+1}-\sqrt{k}}{\sqrt{k... |
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Now showing items 1-6 of 6
Forward-backward multiplicity correlations in pp collisions at √s = 0.9, 2.76 and 7 TeV
(Springer, 2015-05-20)
The strength of forward-backward (FB) multiplicity correlations is measured by the ALICE detector in proton-proton (pp) collisions at s√ = 0.9, 2.76 and 7 TeV. The measurement... |
I am trying to simulate a robot manipulator dynamics in SciLab.
Basically, I generated a step function that has constant acceleration for half of the time and then the same acceleration but negative for the other half, so I get a smooth transition between the manipulator positions.
This code generates the velocity and ... |
I got a solution for the equation
Simplify[Solve[ 1/(2 q r (-1 + c1 M s1)) (-a q + M q + b c1 q s0 + a c1 M q s1 - c1 M^2 q s1 - c2 M r s1 + \[Sqrt](4 q r (-1 + c1 M s1) (b (cp + c2 s0) + c2 (a - M) M s1) + (b c1 q s0 - c1 M^2 q s1 + a q (-1 + c1 M s1) + M (q - c2 r s1))^2)) == 0 , M ]]
which is $\left\{\left\{M\to \fr... |
Help:Editing
Editing a Wiki page is very easy. Simply click on the "
Edit" tab at the top (or the edit link on the right or bottom) of a Wiki page. This will bring you to a page with a text box containing the editable text of that page. If you want to experiment, please do so in our sandbox, not here. You could open th... |
Your instructor seems to have a rather sloppy approach to the mathematics of microeconomics.
Let's begin with the easiest case, the bundle $(5,1)$. We have $\min\{3\cdot 5,1\}=1$. For $\delta<14$, we have $\min\{3\cdot 5, 1+\delta\}=1+\delta$ so the marginal utility of $y$ is $1$ at the bundle $(5,1)$. Moreover, for an... |
I am trying to solve an assignment on solving the Bogoliubov de Gennes equations self-consistently in Matlab. BdG equations in 1-Dimension are as follows:-
$$\left(\begin{array}{cc} -\frac{\hbar^{2}}{2m}\frac{\delta^{2}}{\delta z^{2}}-\mu+V\left(z\right) & \triangle(z)\\ \triangle(z) & \frac{\hbar^{2}}{2m}\frac{\delta^... |
When we divide a positive integer (the dividend) by another positive integer (the divisor), we obtain a quotient. We multiply the quotient to the divisor, and subtract the product from the dividend to obtain the remainder. Such a division produces two results: a quotient and a remainder.
This is how we normally divide ... |
Suppose that $[U] = [0,...,U-1]$ is the universe from which all elements will be taken, and $A$ a hash table of size $m$.
A hash function $h:[U]\rightarrow[m]$ is truly random if
For any set of distincts elements $\{x_{1},...,x_{k}\} \subseteq [U]$ and any set of values $u_{1},...,u_{k} \subseteq [m]$ we have $Pr_{h}[h... |
I need some help with this proof. A subsequential limit is a limit of a subsequence.
Suppose $a_n$ is a sequence with $\{ L_1, L_2, ...\}$ subsequential limits. Suppose $L_n \to L$. Prove that $L$ is a subsequential limit of $a_n$.
Proof:
We know (1): $\forall_{\epsilon > 0} \exists_{N_0} s.t \forall_{n>N_0} \implies |... |
ISSN:
1531-3492
eISSN:
1553-524X
All Issues
Discrete & Continuous Dynamical Systems - B
November 2009 , Volume 12 , Issue 4
Select all articles
Export/Reference:
Abstract:
We study the existence of travelling-waves and local well-posedness in a subspace of $C_b^1(\R)$ for a nonlinear evolution equation recently propose... |
Let $A$ be a real orthogonal matrix. Then $A^{\text T} A = I.$ Let $\lambda \in \Bbb C$ be an eigenvalue of $A$ corresponding to the eigenvector $X \in \Bbb C^n.$ Then we have
$$\begin{align*} X^{\text T} A^{\text T} A X = X^{\text T} X. \\ \implies (AX)^{\text T} AX & = X^{\text T} X. \\ \implies (\lambda X)^{\text T}... |
Please assume that this graph is a highly magnified section of the derivative of some function, say $F(x)$. Let's denote the derivative by $f(x)$.Let's denote the width of a sample by $h$ where $$h\rightarrow0$$Now, for finding the area under the curve between the bounds $a ~\& ~b $ we can a...
@Ultradark You can try d... |
Please assume that this graph is a highly magnified section of the derivative of some function, say $F(x)$. Let's denote the derivative by $f(x)$.Let's denote the width of a sample by $h$ where $$h\rightarrow0$$Now, for finding the area under the curve between the bounds $a ~\& ~b $ we can a...
@Ultradark You can try d... |
Consideration of the quantum mechanical description of the particle-in-a-box exposed two important properties of quantum mechanical systems. We saw that the eigenfunctions of the Hamiltonian operator are orthogonal, and we also saw that the position and momentum of the particle could not be determined exactly. We now e... |
2018-09-11 04:29
Proprieties of FBK UFSDs after neutron and proton irradiation up to $6*10^{15}$ neq/cm$^2$ / Mazza, S.M. (UC, Santa Cruz, Inst. Part. Phys.) ; Estrada, E. (UC, Santa Cruz, Inst. Part. Phys.) ; Galloway, Z. (UC, Santa Cruz, Inst. Part. Phys.) ; Gee, C. (UC, Santa Cruz, Inst. Part. Phys.) ; Goto, A. (UC,... |
The permanent electric dipole moments of polar molecules can couple to the electric field of electromagnetic radiation. This coupling induces transitions between the rotational states of the molecules. The energies that are associated with these transitions are detected in the far infrared and microwave regions of the ... |
The orbital energy eigenvalues obtained by solving the hydrogen atom Schrödinger equation are given by
\[E_n = -\dfrac {\mu e^4}{8 \epsilon ^2_0 h^2 n^2} \label {8.3.1}\]
where \(\mu\) is the reduced mass of the proton and electron, \(n\) is the principal quantum number and e, \(\epsilon _0\) and h are the usual fundam... |
What, if anything, can we learn about customer switching costs by looking at price, revenue, profit, and quantity responses of producers to cost shocks?
For example, we can define the profit equation as:
$\Pi = \sum^\infty_{t=0} [ -\alpha S + \beta^t(P - C(q))] \cdot q(P,C,S)$
Where $q(P,C,S)$ is demand as as function ... |
Yes, you still use the Nernst equation, but one of your implicit assumptions is not correct.
A point about the Nernst equation that often confuses people is that, at first glance, it doesn't predict any change in $E$ as temperature changes, as long as $Q$ remains equal to $1$, and $\ln Q = 0$.
$$E = E^\circ - \frac{RT}... |
Here's some empirical data for question 2, based on D.W.'s idea applied to bitonic sort. For $n$ variables, choose $j - i = 2^k$ with probability proportional to $\lg n - k$, then select $i$ uniformly at random to get a comparator $(i,j)$. This matches the distribution of comparators in bitonic sort if $n$ is a power o... |
Let's consider an
infinite dimensional space $X$ and a linear operator $T$. The resolvent operator of $T$ is $R_\lambda (T) = (T-\lambda I)^{-1}$. A regular value $\lambda$ of $T$ is a complex number such that:
(R1) $R_\lambda(T)$ exists
(R2) $R_\lambda(T)$ is bounded
(R3) $R_\lambda(T)$ defined on a set which is
dense... |
Let $G$ be group of order $17^4$. I have to find its center $Z(G)$ and $G/Z(G)$.
$|G|=17^4$.
Since $Z(G)$ is subgroup of $G$, the order of center divides the order of the group: $|Z(G)|=17^a$, where $a\leq4$.
$1^{\circ}$ $a=4$ $\Rightarrow |Z(G)|=|G|$. Since center of the group is Abelian, and the group is non-abelian,... |
At this point we will take our information transfer process and apply it the the economic problem of supply and demand. In that case, we will identify the information process source as the demand $Q^d$, the information transfer process destination as the supply $Q^s$, and the process signal detector as the price $p$. T... |
I have $n$-dimensional matrices $\mathrm{\hat{H}}(\vec{k})$ depending on vector parameter $\vec{k}$.
Now, eigenvalue routines return eigenvalues in no particular order (they are usually sorted), but I want to trace eigenvalues $E_i$ as smooth functions of $\vec{k}$. Because eigenvalues are not returned in any particula... |
If a rigid body with the inertia matrix $I_B$, has the angular velocity $\overrightarrow{\omega_1}$ what torque is needed to rotate it around another axis say $\overrightarrow{\omega_2}$ while keeping it's original rotation ... Sort of the torque needed to change the position of the rigid body while it rotates. A know ... |
I'm considering a pulse inside a dispersive medium so its duration depends on the z you are.
... then the concept of transform-limited pulse does not hold globally for your setup. Transform-limited pulses are a 1D (generally time-domain) phenomenon, so in your configuration the question "is the pulse transform-limited"... |
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Production of light nuclei and anti-nuclei in $pp$ and Pb-Pb collisions at energies available at the CERN Large Hadron Collider
(American Physical Society, 2016-02)
The production of (anti-)deuteron and (anti-)$^{3}$He nuclei in Pb-Pb collisions at $\sqrt{s_{\rm NN}}$ = 2.76 TeV has ... |
ddoc latex/formulas? Andrei Alexandrescu via Digitalmars-d digitalmars-d at puremagic.com Thu Sep 15 07:43:56 PDT 2016 On 09/15/2016 10:37 AM, Johan Engelen wrote:
>
> Well, I'm pretty sure just typing \( \) and running `dmd -D` is not
> going to give me the output that I want. Indeed it doesn't.
>
> But, as you write,... |
The production side is modeled as follows:There are $m=1,...,j$ identical firms (the number of firms is not necessarily equal to the number of workers of course), that operate in a perfectly competitive environment. This means that firms are price takers, both in the goods market and in the production input market, i.e... |
The most feasible nuclear reaction for a "first-generation" fusion reaction is the one involving deuterium (D) and tritium (T): $$ \mathrm{D} + \mathrm{T} \rightarrow \alpha (3.5\;\mathrm{MeV}) + n (14.1\;\mathrm{MeV}) $$ Tritium is not a primary fuel and does not exist in significant quantities naturally since it deca... |
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