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First, for convenience rewrite $J(p,p')$ as\begin{align}J(p,p') &= -D(p\Vert p')+\sum_{i}p_{i}\sum_{j}Q_{ij}\log\frac{Q_{ij}}{q_{j}}+\sum_{j}q_{j}\log\frac{q_{j}}{q'_{j}} \\&= I({p})-\left[D(p\Vert p')-D(q\Vert q')\right]\\& = I(p) - \Delta D(p\Vert p')\end{align}where I have used your definition of $I(p)$, and defined... |
How do we check exactly that a distribution is involutive?
I have the following definition in my book: A $k-$dimensional distribution $\Delta$ on a manifold $M$ is a smooth choice of a k-dimensional subspace $\Delta_{p} \subseteq T_{p}M$. The distribution is called $involutive$ if $\left [ \Delta , \Delta \right ]\subs... |
Categorical models for linear logic with $\otimes$, $1$, $\&$, $\top$, $\oplus$, $0$, and $\multimap$ are typically symmetric monoidal closed categories (for modeling $\otimes$, $1$, and $\multimap$) with products (for modeling $\&$ and $\top$) and coproducts (for modeling $\oplus$ and $0$). Is it harmful to additional... |
This question already has an answer here:
Limiting shape for Brillouin zones 1 answer
I am having trouble finding a mathematical definition of the Brouillin zone beyond the first, which are basically the Voronoi cells or Wigner-Seitz cells. We could imagine the set of point closer to a particular integer than any other... |
The following analytic continuation for $\zeta(s)$ towards $\Re(s)>-1$ was derived here:
$$\displaystyle \zeta(s) = \frac{1}{2\,(s-1)} \left(\sum _{n=1}^{\infty } {\frac {s-1-2\,n}{{n}^{s}}} + \sum _{n=0}^{\infty } {\frac {s+1+2\,n}{\left( n+1 \right) ^{s}}} \right)$$
I plugged this formula into this question about the... |
Your conclusion is built on the assumption that the bond lengths will be constant. A bond’s dipole moment varies with bond length and thus for the vector addition to give the identical product, all $\ce{C-Cl}$ and all $\ce{C-H}$ bonds would have to be identical. They’re probably not.
Sutton and Brockway studied the bon... |
One of the hyperparameters for LSTM networks is temperature. What is it?
Temperature is a hyperparameter of LSTMs (and neural networks generally) used to control the randomness of predictions by scaling the logits before applying softmax. For example, in TensorFlow’s Magenta implementation of LSTMs, temperature represe... |
I think that the question is why the SI system of units considers one ampere, the unit of current, to be the elementary one, rather than the unit of the electric charge.
Recall that one ampere is defined in SI as
"the constant current that will produce an attractive force of $2\times 10^{–7}$ newton per metre of length... |
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1. Search for heavy ZZ resonances in the ℓ + ℓ - ℓ + ℓ - and ℓ + ℓ - vv - final states using proton–proton collisions at √s=13 TeV with the ATLAS detector
European Physic... |
There are a number of imprecisions in your question, mostly having to do with confusing the Lie group and its Lie algebra. I suppose this will make it hard to read the mathematical literature. Having said that, the first volume of Kobayashi and Nomizu is probably the canonical reference.
Let me try to summarise. Let me... |
In QFT, a representation of the Lorentz group is specified as follows:$$U^\dagger(\Lambda)\phi(x) U(\Lambda)= R(\Lambda)~\phi(\Lambda^{-1}x)$$Where $\Lambda$ is an element of the Lorentz group, $\phi(x)$ is a quantum field with possibly many components, $U$ is unitary, and $R$ an element in a representation of the Lore... |
I am trying to evaluate $$\int_0^1\frac {\{2x^{-1}\}}{1+x}\,\mathrm d x$$
where $\{x\}$ is the fractional part of $x$.
I have tried splitting up the integral but it gets quite complicated and confusing. Is there an easy method for such integrals?
Mathematics Stack Exchange is a question and answer site for people study... |
This is the third part of a series consisting of three articles with the goal to introduce some general concepts and concrete algorithms in the field of neural network optimizers. As a reminder, here is the table of contents:
We covered two important concepts of optimizers in the previous sections, namely the introduct... |
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Production of charged pions, kaons and protons at large transverse momenta in pp and Pb-Pb collisions at $\sqrt{s_{NN}}$ = 2.76 TeV
(Elsevier, 2014-09)
Transverse momentum spectra of $\pi^{\pm}, K^{\pm}$ and $p(\bar{p})$ up to $p_T$ = 20 GeV/c at mid-rapidity, |y| $\le$ 0.8, in pp and ... |
Ex.13.4 Q3 Surface Areas and Volumes Solution - NCERT Maths Class 10 Question
A fez, the cap used by the Turks, is shaped like the frustum of a cone (see Fig. 13.24). If its radius on the open side is \(10\,\rm{cm}\), radius at the upper base is \(4\,\rm{cm}\) and its slant height is \(15\,\rm{cm, }\) find the area of ... |
This question already has an answer here:
A polynomial that is zero on an open set 5 answers
Consider a non constant polynomial $f:\Bbb R^n\to \Bbb R$. Let $S_f\subset \Bbb R^n$ be its solution set i.e. the set of $x\in \Bbb R^n$ such that $f(x)=0$. What's the slickest proof that $S$ can't contain any ball, or equivale... |
I would like to ask if there is a way to find the expected value and the variance of the following process $$ dv_t=(a-be^{\alpha v_t})dt+\sigma dW_t, \quad v_t=v_0 $$ where $a\in (-\infty,+\infty), b>0, \sigma>0, \alpha>0$.
Thank you for your time. I truly appreciate it.
Added (after the question of The Bridge)
Let $V_... |
This is an interactive problem.
Khue and Hanh are obsessed with doughnuts although they are very much overweight. Over the last week, they worked very hard setting up the problems for ICPC Hanoi. To prepare for a long night of coding, they bought a super-large ring-shaped doughnut.
The perimeter of this doughnut is $1$... |
The von Mises yield function is given by:
$ \Phi(\sigma_1,\sigma_2)=\sqrt{\sigma_{1}^{2} +\sigma_{2}^{2}-\sigma_{1} \sigma_{2}} - \sigma_y $
were $\sigma_1$ and $\sigma_2$ are the principal stresses and $\sigma_y$ is the yield stress. If $\Phi(\sigma_1, \sigma_2)=0$, $\sigma_y =200$ and using
ContourPlot:
contourplot =... |
I'm just starting to learn general relativity (GR), and I'm a beginner, but I came out with this situation which is unclear to me: The trajectory of a charged particle in GR is given from the equation:
$$\dot{u}^{\mu} + \Gamma^{\mu}_{\alpha \beta} u^{\alpha} u^{\beta} = \frac{q}{m} F^{\mu}_{\; \nu} \, u^{\nu}$$
So, if ... |
How to Calculate Bending Stress in Beams
In this tutorial we will look at how to calculate the bending stress of a beam using a bending stress formula that relates the longitudinal stress distribution in a beam to the internal bending moment acting on the beam’s cross section. We assume that the beam’s material is
line... |
Colloquia/Fall18 Contents 1 Mathematics Colloquium 1.1 Spring 2018 1.2 Spring Abstracts 1.2.1 January 29 Li Chao (Columbia) 1.2.2 February 2 Thomas Fai (Harvard) 1.2.3 February 5 Alex Lubotzky (Hebrew University) 1.2.4 February 6 Alex Lubotzky (Hebrew University) 1.2.5 February 9 Wes Pegden (CMU) 1.2.6 March 2 Aaron Be... |
We derive a lower bound on the secrecy capacity of a compound wiretap channel with channel state information at the transmitter which matches the general upper bound on the secrecy capacity of general compound wiretap channels given by Liang et al. [1], thus establishing a full coding theorem in this case. We achieve t... |
Difference between revisions of "Geometry and Topology Seminar"
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|Feb 3
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| Rafael Montezuma (University of Chicago)
| Rafael Montezuma (University of Chicago)
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| Lu Wang
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===Rafael Montezuma===
===Rafael ... |
Last edited: March 22nd 2018
This notebook is an introduction to a set of partial differential equations which are widely used to model aerodynamics, atmosphere and climate, explosive detonations and even astrophysics. It only gives a small taste of the world of hyperbolic PDEs, Riemann problems and computational fluid... |
The Annals of Applied Probability Ann. Appl. Probab. Volume 17, Number 1 (2007), 81-101. On the signal-to-interference ratio of CDMA systems in wireless communications Abstract
Let {
s : ij i, j=1, 2, …} consist of i.i.d. random variables in ℂ with $\mathsf{E}s_{11}=0$, $\mathsf{E}|s_{11}|^{2}=1$. For each positive int... |
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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 ... |
The newly realized relationship between the geometric connections in the spacetime and the standard quantum entanglement has been the topic of exciting papers in recent years. One aspect of the papers that have been written down so far made them simple and too special: the entangled systems were always pretty much pair... |
Answer:
Given, Shreya's age = 15 yr and Bhoomika's age = 12 yr \[\therefore \]Ratio of their ages \[\text{=}\frac{\text{Shreya }\!\!'\!\!\text{ age}}{\text{Bhoomika }\!\!'\!\!\text{ s}\,\text{age}}=\frac{15yr}{12yr}=\frac{15}{12}\] \[=\frac{15\div 3}{12\div 3}=\frac{5}{4}=5:4\] [\[\because \]HCF of 15 and 12 = 3] Now, ... |
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Now showing items 1-10 of 26
Kaon femtoscopy in Pb-Pb collisions at $\sqrt{s_{\rm{NN}}}$ = 2.76 TeV
(Elsevier, 2017-12-21)
We present the results of three-dimensional femtoscopic analyses for charged and neutral kaons recorded by ALICE in Pb-Pb collisions at $\sqrt{s_{\rm{NN}}}$ = 2.76 TeV. Femtoscopy is used to... |
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Now showing items 1-10 of 33
The ALICE Transition Radiation Detector: Construction, operation, and performance
(Elsevier, 2018-02)
The Transition Radiation Detector (TRD) was designed and built to enhance the capabilities of the ALICE detector at the Large Hadron Collider (LHC). While aimed at providing electron... |
So we need to show:
$$\overline{M} = X \leftrightarrow \forall V \subseteq X \text{ open and non-empty } : V \cap M \neq \emptyset$$
Now it will depend on how you define $\overline{M}$. If you define it as the smallest closed subset that contains $M$ (one of the usual definitions) I'd go as follows:
Left to right: assu... |
I'll post some elements of answer to my own question from what I understand. Anyone feel free to make a better, less sloppy answer.
First, there are several versions of this document online. They all have some typographic defects at some point. So when in doubt, better check those 3 versions first.
Second, there's a lo... |
Preprints (rote Reihe) des Fachbereich Mathematik Refine Keywords Brownian motion (2) (remove)
296
We show that the occupation measure on the path of a planar Brownian motion run for an arbitrary finite time intervalhas an average density of order three with respect to thegauge function t^2 log(1/t). This is a surprisi... |
My question in short:
Under which scenarios minimising transmission power is beneficial in terms of transmitter energy-efficiency? is there any fundamental reason to keep a low-power oriented design strategy?
In particular, small, low-cost transceivers (such as those used for M2M/IoT communications) are designed accord... |
You are correct. Many methods of echo cancellation exist, but none of them are exactly trivial. The most generic and popular method is echo cancellation via an adaptive filter. In one sentence, the adaptive filter's job is to alter the signal that it's playing back by minimizing the amount of information coming from th... |
I think you are confused with the meaning of the expression for the error. What it states is:
There is a point $c$ in the interval $(a, b)$ such that the error in calculating the integral $\int_{a}^bf(x)~{\rm d}x$ using the trapezoid rule is given by the expression
$$
\epsilon = (b-a)\frac{h^2}{12}f''(c) \tag{1}
$$
her... |
For a project I'm trying to build a sound engine as realistic as possible and I am trying to add more features to enhance the sound localization. So far I've only implemented one of the three main methods to localize sound: time delay. Another main sound localization method is difference in volume. This however, looks ... |
Proceedings of the International Conference on Geometry, Integrability and Quantization Geom. Integrability & Quantization Proceedings of the Eleventh International Conference on Geometry, Integrability and Quantization, Ivaïlo M. Mladenov, Gaetano Vilasi and Akira Yoshioka, eds. (Sofia: Avangard Prima, 2010), 42 - 67 ... |
Solve equations and simplify expressions
In algebra 1 we are taught that the two rules for solving equations are the addition rule and the multiplication/division rule.
The addition rule for equations tells us that the same quantity can be added to both sides of an equation without changing the solution set of the equa... |
I know how to change the phase of a complex number by multiplying by $\cos \theta + i \sin \theta$. And I understand that the phase of a sine wave is reflected in its Fourier transform. So, I am trying to phase-shift a signal by changing the phase of its Fourier transform..
This works for "synthetic" Fourier transforms... |
Burgers equation¶
The Burgers equation is a non-linear equation for the advection and diffusion of momentum. Here we choose to write the Burgers equation in two dimensions to demonstrate the use of vector function spaces:
where \(\Gamma\) is the domain boundary and \(\nu\) is a constant scalar viscosity. The solution \... |
Edit3 April 17, 2018. I would highly recommend using differential evolution instead of BFGS to perform the optimization. The reason is that the maximum likelihood optimization is likely to have multiple local minima, which may be difficult for the BFGS to overcome without careful use. Edit2 October 20, 2016. I was pass... |
First of all, Andreas' comment is right: a coverage gives no specified way to "pull back" a covering family of $U$ to a covering family of $V$. However, if you consider what
Sketches of an Elephant calls "sifted" coverages, meaning that all covering families are sieves, then there is a canonical choice: the pullback of... |
Quanta Magazine's Natalie Wolchover wrote a status report about grand unification,
Grand Unification Dream Kept at Baywhose subtitle – which includes words such as "failed" and "limbo" – is much more negative than the available evidence suggests. No smoking gun – such as the proton decay – that would "almost" prove gra... |
DBSCAN Engine
Given the graph, we extract the alarms from all the vertices and use these as points as input to the DBSCAN algorithm.
DBSCAN requires a constant \(\epsilon\) and a distance function, which we define as follows:
where:
\(a_{1}\) and \(a_{2}\) are the points representing the alarms
\(\alpha \in (0, \infty)... |
Ex.13.1 Q2 Surface Areas and Volumes Solution - NCERT Maths Class 10 Question
A vessel is in the form of a hollow hemisphere mounted by a hollow cylinder. The diameter of the hemisphere is \(14\;\rm{cm}\) and the total height of the vessel is \(13 \;\rm{cm}\). Find the inner surface area of the vessel.
Text Solution Wh... |
Your reasoning is correct, but you need to go a little further to deduce the answer.
The question does not say but we must assume that the mean position O is the same for P and Q. The phase difference between them remains the same, but the separation changes.
Suppose that, at some instant, P and Q are moving in the sam... |
What causes the melting and boiling points of noble gases to rise when the atomic number increases? What role do the valence electrons play in this?
The melting and boiling points of noble gases are very low in comparison to those of other substances of comparable atomic and molecular masses. This indicates that only w... |
Similar questions have been asked before, you may search. (I'm sorry but I cannot refer to one here)
You want to
identify an analog LTI system from analysing its response $y(t)$ to a known input $x(t)$.
One method of analysis involves the use of continous Fourier transforms of the input and output signals. It can be sh... |
Hello Good people of Emacs!
I'm having trouble exporting unicode math symbols from buffer (org-mode) to pdf file.
1. Problem Description:
Here is source code demonstration:
#+TITLE: Unicode characters export test #+AUThor: #+date:Unicode characters:ℝ ℤ ℕ ⇒ ∈ ∀ Same symbols in latex format:$$\Bbb{R} \Bbb{Z} \Bbb{N} \Rig... |
You have forgotten that there is work done by the battery after $t=0$, so that there is energy lost before S1 is opened and S2 is closed.
The work done by the battery to transfer charge $Q$ onto the 1st capacitor is $W=QV=\frac{Q^2}{C}$.
The final charges on the capacitors are $\frac12Q, \frac14Q, \frac{1}{16}Q, \frac{... |
Ex.13.4 Q2 Surface Areas and Volumes Solution - NCERT Maths Class 10 Question
The slant height of a frustum of a cone is \(4\,\rm{cm}\) and the perimeters (circumference) of its circular ends are \(18 \,\rm{cm}\) and \(6\, \rm{cm.}\) Find the curved surface area of the frustum.
Text Solution What is Known?
Slant height... |
A
quadratic equation solver is a free step by step solver for solving the quadratic equation to find the values of the variable. It uses the quadratic equation formula:
The quadratic equation solution is obtained using the quadratic formula
\(x=\frac{-b\pm \sqrt{b^{2}-4ac}}{2a}\)
If an input is given, it easily shows t... |
Let $M>0$. $$\sum_{n=M}^{\infty} \frac {1}{(x-n)^2}$$
How do I show this converges uniformly for $x ≤ \frac{|M|}{2}$
My actual question is how do I determine the interval of uniform convergence for general series like this one.
Am I allowed to use the Weierstrass M test? Because the sum is between $M$ and $\infty$.
$\s... |
Consider the following sequence $a_n$:
\begin{align*} a_0 &= \alpha \\ a_k &= \beta a_{k-1} + \kappa \end{align*}
Now consider the implementation of this sequence via lisp:
(defun an (k) (if (= k 0) alpha (+ (* beta (an (- k 1))) kappa)))
What is the running time to compute
(an k) just as it is written? Also, what woul... |
I have to apologize, in fact the answer to the second question is still unknown. Namely, up to now all known symplectic manifolds of dimension 4 that have negative Euler characteristic are blow ups of ruled surfaces. However it is not known if there are no other examples. I have corrected the answer accordingly.
It is ... |
Question:
How can we solve a first-order differential equation of the form $$ \frac{d}{dt}x(t)=g(x(t),t), $$ with the initial condition $x(t_0)=x_0$, if we cannot solve it analytically?
Example 1:
We want to solve the ordinary differential equation (ODE) \begin{equation} \frac{d}{dt}x(t)=\cos(x(t))+\sin(t)\qquad\qquad\... |
Publications Influence
Claim Your Author Page
Ensure your research is discoverable on Semantic Scholar. Claiming your author page allows you to personalize the information displayed and manage publications.
In this paper, the existence of a nontrivial least energy solution is considered for the nonlinear fractional Sch... |
Main Page The Problem
Let [math][3]^n[/math] be the set of all length [math]n[/math] strings over the alphabet [math]1, 2, 3[/math]. A subset of [math][3]^n[/math] is said to be
line-free if it contains no combinatorial lines. Let [math]c_n[/math] be the size of the largest line-free subset of [math][3]^n[/math]. [math... |
Now I have a breaker which is containing $\ce{CH4}$ of some amount at standard conditions and then I put it on a burner.
In Thermodynamics we are taught about how to find the bond enthalpy of poly-atomic atoms. They say that such molecules (here in this case methane) all four $C-H$ bonds are identical. However, the ene... |
There are many ways to interpolate data. Interpolation in my mind means that you 'draw' lines between some data points. This can be done many ways. One type of interpolation which is useful in DSP (especially in multirate DSP) is 'Bandlimited interpolation'. If you google that you will get many interesting and useful h... |
Experimental Mathematics Experiment. Math. Volume 11, Issue 4 (2002), 527-546. Random Generators and Normal Numbers Abstract
Pursuant to the authors' previous chaotic-dynamical model for random digits of fundamental constants, we investigate a complementary, statistical picture in which pseudorandom number generators (... |
The question states:
Prove that if $S\subseteq T \subseteq V$ and if $T$ is a subspace of $V$, then $L(S)\subseteq T$.
My proof is as follows:
All elements in $S$ are in $T$. Now $T$ is a subspace, $\therefore$ all elements in $S$ spanning $L(S)$ are independent elements in $T$.
$\therefore T$ is spanned by $S$ if $\di... |
Little explorations with HP calculators (no Prime)
03-23-2017, 01:23 PM (This post was last modified: 03-23-2017 01:23 PM by pier4r.)
Post: #21
RE: Little explorations with the HP calculators
(03-23-2017 12:19 PM)Joe Horn Wrote: I see no bug here. Variables which are assigned values should never be used where formal va... |
To avoid confusion, let's clarify some notation. Let $\mathcal{M}^{*}$ denote the $\sigma$-algebra of $\mu^{*}$-measurable subsets of $X$. Let $\bar{\mathcal{M}}$ denote the completion of $\mathcal{M}$ with respect to $\mu$. Let $\widetilde{\bar{\mathcal{M}}}$ denote the $\sigma$-algebra of locally measurable subsets o... |
Magnetic force is a consequence of electromagnetic force and is caused due to the motion of charges. We have learned that moving charges surround itself with a magnetic field. With this context, the magnetic force can be described as a force that arises due to interacting magnetic fields.
What is Magnetic Force?
If we ... |
Mathematics - Functional Analysis and Mathematics - Metric Geometry
Abstract
The following strengthening of the Elton-Odell theorem on the existence of a $(1+\epsilon)-$separated sequences in the unit sphere $S_X$ of an infinite dimensional Banach space $X$ is proved: There exists an infinite subset $S\subseteq S_X$ an... |
Difference between revisions of "De Bruijn-Newman constant"
(→Bibliography)
(→Threads)
Line 83: Line 83:
* [https://terrytao.wordpress.com/2018/01/27/polymath15-first-thread-computing-h_t-asymptotics-and-dynamics-of-zeroes/ Polymath15, first thread: computing H_t, asymptotics, and dynamics of zeroes], Terence Tao, Jan ... |
Let $f:X\mapsto[0,+\infty)$ be a non-negative measurable function defined on the space $X$, endowed with the complete $\sigma$-additive, $\sigma$-finite, measure $\mu$ defined on the $\sigma$-algebra of the measurable subsets of $X$.
I have read that the following equality holds for the Lebesgue integral:
$$\int_X f d\... |
Can I be a pedant and say that if the question states that $\langle \alpha \vert A \vert \alpha \rangle = 0$ for every vector $\lvert \alpha \rangle$, that means that $A$ is everywhere defined, so there are no domain issues?
Gravitational optics is very different from quantum optics, if by the latter you mean the quant... |
I'm trying to understand what are the required conditions for an ideal gas in one spatial dimension to act as a heat reservoir.
I would appreciate answers that don't use the terms heat, temperature, heat capacity, entropy unless they are well defined for the system described in the question. (I'm trying to find reasoni... |
I am using the following formula to calculate the Hann values for a set of points: $$ w(n)=0.5\left(1-\cos\left(2\pi \frac nN\right)\right) $$
To implement this in java, I am using the following code:
private static void applyHannWindow(final double[] points) { for (int i = 0; i < points.length; i++) { points[i] = 0.5 ... |
Let us consider the enthalpy as a function of temperature and pressure, such that $H = H(T,p).$
Now, say we want to exchange the pressure $p$ by the volume $V$ by performing a Legendre transformation. Let's call the result $U = U(T,V)$ (the internal energy). Thus the Legendre transformation should take the form
$$U(T,V... |
A function $f: \mathbb R \to \mathbb R$ is called sequentially continuuous if
$x_n \to x$ implies $f(x_n) \to f(x)$.
Every continuous function is sequentially continuous. Let $f$ be a continuous function on $\mathbb R$.
If $y_n = f(x_n)$ is a convergent sequence does it follow that $x_n$ is a convergent sequence?
At fi... |
I have been told that \[
[\hat x^2,\hat p^2]=2i\hbar (\hat x\hat p+\hat p\hat x)
\] illustrates
. ordering ambiguity
What does that mean?
I tried googling but to no avail.
Thank you.
LM:The ordering ambiguity is the statement – or the "problem" – that for a classical function \(f(x,p)\), or a function of analogous phas... |
Your alternative method uses the non-relativistic approximation twice : first when you insert a value for $v/c$ in the numerator, second when you insert a value for $v$ in the denominator. Because of this your error is compounded, so you get a result which is less accurate than if you inserted the approximation only on... |
Let $b\in \mathbb{R^n}$ and $c>0$. Assume $g \in C(R^n)$ has compact support and $f = f(x,t)$, $f \in C_1^2(R^n \times [0,\infty))$ has compact support. I'm trying to solve the following IBP via fourier transform: $$ \left\{ \begin{array}{rc} u_t+b \cdot \nabla u-c^2 \Delta u &=& f & \text{ in } \mathbb{R^n} \times(0,\... |
Three question about this equation:
$ \displaystyle\nabla\times\mathbf{E}=-\frac{\partial \mathbf{B}}{\partial t} $
1 If I solve this equation with Mathematica, I find the magnetic field $b(x,y,z,t),b:\mathbb{R}^4\rightarrow\mathbb{R}^3$ right? 2 I have put an arbitrary function $e:\mathbb{R}^4\rightarrow\mathbb{R}^3$ ... |
During a discussion with my professor, he asked me about relativistic resistance transformation. Firstly I started with the formula $R=\frac{\rho L}{s}$, where $\rho$ is electric resistivity. So if some resistor moves with relativistic speed its length contracts. And this means that its resistance changes like its leng... |
MathRevolution wrote:
[Math Revolution
GMAT math practice question]
What is the perimeter of a rectangle?
1) The square of the diagonal is \(52\).
2) The area of the rectangle is \(24\).
\(? = {\text{perim}}\left( {{\text{rectangle}}} \right)\)
Excellent opportunity to GEOMETRICALLY BIFURCATE each statement alone:
\(\l... |
Let $S_n$ be the symmetric group of all the permutations of $\{1,\ldots,n\}$. Recall that a permutation $\sigma\in S_n$ is called a derangemnt if $\sigma(k)\not=k$ for all $k=1,\ldots,n$.
Motivated by the well-known result that $\sum_{k=m}^n\frac1k\not\in\mathbb Z$ whenever $n\ge m>1$ (Kurschak, 1918), here I ask the f... |
OpenCV 3.4.7
Open Source Computer Vision
This tutorial demonstrates to you how to use F-transform for image filtering. You will see:
As I shown in previous tutorial, F-transform is a tool of fuzzy mathematics highly usable in image processing. Let me rewrite the formula using kernel \(g\) introduced before as well:
\[ ... |
Let $a$ and $n\ge3$ be integers. Suppose that $a^{n-1} \equiv 1 \pmod n$, while $a^{(n-1)/p} \not\equiv 1 \pmod n$ for every prime $p$ dividing $n-1$, and I want to show that $n$ is prime.
First of all, we know that $(a,n) = 1$ because if $(a,n) = g > 1$, then $g \mid n$ which means $a^{n-1} \equiv 1 \pmod g$, but this... |
I'm studying the construction of the $\mathrm{Sing}$ functor in Morel-Voevodsky ``$\mathbb{A}^1$-homotopy theory of schemes'' and I was trying to understand the properties of its left adjoint, the realization functor.
To start with, let $\mathcal{C}$ be a site (with an interval, in the sense of M-V) and let $\mathsf{Sh... |
A potential deviation from ΛCDM described via "eating" At least sixteen news outlets ran stories about "dark energy that is devouring dark matter" in recent two days. I think that the journalists started with a University of Portsmouth press release that described the recent publication of a British-Italian paper in Ph... |
Strategy for Starting a Thesis from Scratch The CLAS Linux Group have posted this information on behalf of others. This information is likely dated. Use at your own risk. Create a file called thesis.texto use as your "master" file. This is the big daddy of them all, and will link together the other files that will make... |
Sines
The law of sines is an equation relating the lengths of the sides of an arbitrary triangle to the sines of its angles.
If we have the following triangel
The following holds true
$$\frac{sin\; A}{a}=\frac{sin\; B}{b}=\frac{sin\; C}{c}$$
Example
If we have a triangle (this example is also shown in our video lesson)... |
I'm looking at continuum mechanics from the perspective of De Groot and Mazur's "Non-Equilibrium Thermodynamics" - the first reference that I've come across that seems to do a good job of bringing together thermodynamics and continuum mechanics. In the course of reading I've started wondering why I've never seen transp... |
Consider a molecule of oxygen in a balloon.You know that at nonzero temperature all those molecules are bouncing around in all directions.Of course, the mass of air doesn't have any net motion in any direction.Indeed, the average velocity of each molecule is zero:$$\langle v \rangle = 0 \, .$$Of course, the average ene... |
Difference between revisions of "De Bruijn-Newman constant"
(Created page with "For each real number <math>t</math>, define the entire function <math>H_t: {\mathbf C} \to {\mathbf C}</math> by the formula :<math>\displaystyle H_t(z) := \int_0^\infty e^{t...")
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It is known that <math>\Phi</math> is even, ... |
A nonlocal concave-convex problem with nonlocal mixed boundary data
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Laboratoire d'Analyse Nonlinéaire et Mathématiques Appliquées, Université Abou Bakr Belkaïd, Tlemcen, Tlemcen 13000, Algeria
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Département de Mathématiques, Université Ibn Khaldoun, Tiaret, Tiaret 14000, Algeria
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University of Melbourne, School o... |
Let X be a normal random variable with mean $\mu$ and standard deviation $\sigma^2$. I am wondering how to calculate the third moment of a normal random variable without having a huge mess to integrate. Is there a quicker way to do this?
This is a general method to calculate any moment:
Let $X$ be standard normal. The ... |
Answer
$$x=-1.25,-1.95$$
Work Step by Step
Using the quadratic formula, we obtain: $$x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$$ $$x=\frac{-80\pm \sqrt{(80)^2-4(25)(61)}}{2(25)}$$ $$x=-1.25,-1.95$$
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Good morning fellow mathematicians! I'm finally back and we are going to dive right in. Today we are going to work with quite the amazing integral, but before we can actually get started, I would like to prove a well-known fact regarding functions. Let us consider some arbitrary function, for example $f:\mathbb{R} \rig... |
Keith Winstein,
EDIT: Just to clarify, this answer describes the example given in Keith Winstein Answer on the King with the cruel statistical game. The Bayesian and Frequentist answers both use the same information, which is to ignore the information on the number of fair and unfair coins when constructing the interva... |
Schedule of the Workshop "Picard-Fuchs Equations and Hypergeometric Motives" Monday, March 26
10:15 - 10:50 Registration & Welcome coffee 10:50 - 11:00 Opening remarks 11:00 - 12:00 Frits Beukers: Some supercongruences of arbitrary length 12:00 - 13:45 Lunch break 13:45 - 14:45 Alexander Varchenko: Solutions of KZ diff... |
I am given the problem to find $B(y)$ by solving the following integral numerically:
$$B(y) = \int_{z=0}^{\infty}\frac{1}{\sigma (y,z)}\frac{\partial^2 A(y,z)}{\partial z^2}+\frac{\partial A(y,z)}{\partial z}\frac{\partial}{\partial y}\frac{1}{\sigma (y,z)}\;\;\partial z$$
Here, $A(y,z)$ and $\sigma(y,z)$ are both know... |
You can do this as follows.
Let $A\subset\mathbb R$ be nonempty and bounded above. Choose $a_0\in A$ and an upper bound $b_0$ for $A$. Then, look at the middle point $m$ of the interval $[a_0,b_0]$. If $m$ is an upper bound for $A$, put $b_1:=m$ and $a_1:=a_0$. Otherwise, put $b_1:=b_0$ and choose a point $a_1\in A$ su... |
One way to convert a real-valued signal into a complex-valued one is to set the complex part to zero. This has the effect of "mirroring" the spectrum: all the negative frequencies are the mirror of the positive frequencies. This can be seen by the Fourier transform property for any real $f(x)$:
$$ \hat f(-\omega) = \ov... |
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