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Why do the following two methods give different answers (or are they the same) for the Fourier transform of $Y = \cos(\omega_0 t + \phi)$, with respect to $t \to \omega$ ?
They are the same.
Using the Dirac impulse
sifting property $f(x) \delta(x-a) = f(a)\delta(x-a)$ you can also verify that the second method produces... |
I am new to the axiom of choice, and currently working my way through some exercises. I am struggling with the following exercise:
Exercise -Prove the Axiom of Choice (every surjective $f: X \to Y$ has a section) in the following two special cases: Y is finite X is countable
(A section has been previously defined as a ... |
For clarity, I'm going to generalize your question to be over characteristic $p> 0$ (with base field $\mathbb{F}_q$) instead of the specific case of $p=q=2$.I'll take $p$ and $q$ as a fixed constants;I'll leave it to the reader to figure out what the exact dependence on these parameters is,as there are some tradeoffs t... |
Problem Statement
Let's run an election.
$i \in \text{voters}$
$j \in \text{candidates}$
$x_j \in \{ 0, 1 \}$ The candidate is chosen by setting this to 1. This is the election result.
$b_{i,j} \in [0,1]$ Ballot of voter i for candidate j. Voter gives bigger numbers if he likes the candidate. This is the input to the e... |
This problem is a modified version of a problem from Australian mathematics competition 1984:
The problem is let $f:\mathbb Z^+ \to \mathbb Z^+$ be a function from positive integers to positive integers which satisfy the following three conditions.
$f(2)=2$ $f(mn)=f(m) f(n)$ for $m,n \in \mathbb Z^+$ If $m>n$ then $f(m... |
I'm trying to align two equations using
eqnarray.
Sample:
\documentclass{article}\begin{document}\subsubsection*{\begin{center}Variance equations\end{center}}\begin{eqnarray}\mu = \tfrac{1}{NM}\sum\limits_{x=1}^N\sum\limits_{y=1}^MA(y,x)\nonumber\\varTot = \tfrac{1}{NM}\sum\limits_{x=1}^N\sum\limits_{y=1}^M(A(y,x)-\mu)... |
Pacific Northwest Geometry Seminar Start Date: 04/01/2006 End Date: 04/03/2006
Alejandro Adem (University of British Columbia)
Jim Bryan (University of British Columbia) Yong-Geun Oh (University of Wisconsin-Madison) Ben Chow (UC San Diego) Simon Brendle (Stanford University) Gang Tian (Princeton University)
University... |
In the case of a simple pendulum (also called a mathematical pendulum of simple gravity pendulum), one assumes that
all of the mass is the bob and the rest of the pendulum is massless. An example of the simple pendulum is given in the image below.
The simple pendulum (see wikipedia or hyperphysics) leads to a simple di... |
When considering system
\begin{equation*}
\mathbf{x}'=A\mathbf{x} \qquad \text{with } \
A=\begin{pmatrix} a & b \\ c & d\end{pmatrix}
\end{equation*}
and discovering that it has a repeated root $\mu\ne 0$, but only one eigenvector, we know that $\mu>0$ corresponds to an unstable node, and $\mu<0$ t corresponds to a sta... |
fixed in 10.0.2 Update
I have tried like these. I think there is a bug.
Plot[1/Sqrt[-1 + 2^2 Sech[x]^2], {x, 0, ArcCosh[2]}, Ticks -> {{ArcCosh[2]}, Automatic}]
This is the antiderivative.
primitive = Integrate[1/Sqrt[-1 + 2^2*Sech[x]^2], x]; Plot[primitive, {x, 0, ArcCosh[2]}, Ticks -> {{ArcCosh[2]}, {π/4, π/2}}]
Limi... |
I have to determine the potential electric energy from a point charge $q$ who is in an position $r$ inside an uniform electric field $\vec{E}$. I tried to do it by using work definite integral and then use $ V = \frac{U}{q} $, but i'm stuck because one of the integration limits is $\infty$, and the definite integral wo... |
As far as I understand, the Higgs mechanism is a crucial component of the standard model, which is responsible for the weak gauge bosons acquiring mass, otherwise forbidden by renormalizability constraints. However, is there any justification for the fermion masses arising from a Yukawa coupling to the Higgs field, or ... |
I feel like something is off with label smoothing. While the implementation is correct and agrees with the paper, my intuition suggests that the additional eps/N should not be added to the term for the correct class.
In the notebook for label smoothing we see the following explanation:
Another regularization technique ... |
This section might be tough – but don’t be put off by it. I promise that, after we have got over this section, things will be easy. But in this section I don’t like all these summations and subscripts any more than you do.
Suppose that we have a system of \( N\) particles, and that the force on the \( i\)th particle (\... |
I am trying to solve a large scale inverse problem using the Bayesian formulation. To estimate the Maximum a Posteriori Estimation (MAP) solution I will have to minimize the following objective function:
$F(m) = F_d + F_\text{prior} = \frac{(f(m) - d)^T(f(m) - d)}{\sigma^2} + \frac{(m - m_\text{prior})^T(m - m_\text{pr... |
(a) If $AB=B$, then $B$ is the identity matrix. (b) If the coefficient matrix $A$ of the system $A\mathbf{x}=\mathbf{b}$ is invertible, then the system has infinitely many solutions. (c) If $A$ is invertible, then $ABA^{-1}=B$. (d) If $A$ is an idempotent nonsingular matrix, then $A$ must be the identity matrix. (e) If... |
There is a question in my homework on the algebraic topology course asking if two spaces $X$ and $Y$ are weakly homotopy equivalent in case for every
space $Z$ sets $[Z,X]$ and $[Z,Y]$ are naturally bijective. cellular
I'm wondering if converse statement holds at least for cell complexes. Suppose $f\colon K\to K'$ is w... |
Update: Nov 2012: A new pure geometry method was sent in by Sigi. You can see Sigi's method here. Sigi suggests that certain solutions are dependent in that they use different notations for the same underlying contexts. Sigi suggests the following interesting task: Which of the different methods are genuinely mathemati... |
Let $T: \R^n \to \R^m$ be a linear transformation.Suppose that the nullity of $T$ is zero.
If $\{\mathbf{x}_1, \mathbf{x}_2,\dots, \mathbf{x}_k\}$ is a linearly independent subset of $\R^n$, then show that $\{T(\mathbf{x}_1), T(\mathbf{x}_2), \dots, T(\mathbf{x}_k) \}$ is a linearly independent subset of $\R^m$.
Let $V... |
The last three (or ‘spatial’) components of the momentum four-vector give us the regular components of the momentum, times the factor \( \gamma(v) \). What about the zeroth (or ‘temporal’) component? To interpret it, we expand \( \gamma(v) \), and find:
\[ \begin{align} E&=\gamma(v) m c^{2} \\[4pt] &=m c^{2}+K \label{1... |
(a) If $AB=B$, then $B$ is the identity matrix. (b) If the coefficient matrix $A$ of the system $A\mathbf{x}=\mathbf{b}$ is invertible, then the system has infinitely many solutions. (c) If $A$ is invertible, then $ABA^{-1}=B$. (d) If $A$ is an idempotent nonsingular matrix, then $A$ must be the identity matrix. (e) If... |
My differential equations professor gave the class an assignment introducing us to delay differential equations, and he put some questions for us to answer on it. I've been completely stuck on this problem for too long.
$$ y'(t)=\alpha y(t-\tau) $$ Re-scale the independent variable to show that that equation is equival... |
The $c\bar{c}$ meson decays to a lighter meson in the following reactions: $$\psi(3686)\rightarrow J/\psi(3097)+\eta^0$$ $$\psi(3686)\rightarrow J/\psi(3097)+\pi^0.$$
My aim is to find out which conservation law is causing one of these decay channels to be massively suppressed, but my lack of understanding of this nota... |
Electronic Communications in Probability Electron. Commun. Probab. Volume 20 (2015), paper no. 10, 14 pp. Functional limit theorems for divergent perpetuities in the contractive case Abstract
Let $\big(M_k, Q_k\big)_{k\in\mathbb{N}}$ be independent copies of an $\mathbb{R}^2$-valued random vector. It is known that if $... |
Straight Lines Distance of a Point From a Line The perpendicular distance from a point (x 1y 1) to the line ax + by + c = 0 is \tt \begin{vmatrix}\frac{ax_{1}+by_{1}+c}{\sqrt{a^{2}+b^{2}}} \end{vmatrix} A point A (x 1y 1) and origin lies on the same or opposite side of a line L = ax + by + c = 0 according as c. L 11> 0... |
Tagged: finite group If a Half of a Group are Elements of Order 2, then the Rest form an Abelian Normal Subgroup of Odd Order Problem 575
Let $G$ be a finite group of order $2n$.
Suppose that exactly a half of $G$ consists of elements of order $2$ and the rest forms a subgroup. Namely, suppose that $G=S\sqcup H$, where... |
Hi, Can someone provide me some self reading material for Condensed matter theory? I've done QFT previously for which I could happily read Peskin supplemented with David Tong. Can you please suggest some references along those lines? Thanks
@skullpatrol The second one was in my MSc and covered considerably less than my... |
Motion in a Straight Line Relative Velocity in one dimension Motion of one body with respect to another is called concept of Relativity. Velocity of a body a with respect to velocity of “B” is V AB= V A- V B Velocity of an object with respect to itself is always zero. Relative velocity of approach of bodies moving towa... |
Let the Green's function for the gauge field be given (after gauge fixing) as $$G_{\mu \nu}(x,y) = \delta_{\mu \nu}G(x-y) \tag{1}$$ where $$G(x-y)= \int \frac{d^dk}{(2\pi)^d} \frac{e^{ik \cdot (x-y)}}{k^2+m^2} \tag{1'}$$ and a source $$ J_{\mu}(x) = \delta_{0}^{\mu}q\delta(\vec{x})\tag{2}. $$ Then, the gauge field is g... |
Yes, there is a subtlety there. Also notice that in quantum mechanics we have finely resolved energy eigenstates, and in a typical complicated system all degeneracies are broken so that at any given energy there is at most one state ($\Omega = 1$) but most likely there is no state at exactly that energy ($\Omega = 0$).... |
(a) If $AB=B$, then $B$ is the identity matrix. (b) If the coefficient matrix $A$ of the system $A\mathbf{x}=\mathbf{b}$ is invertible, then the system has infinitely many solutions. (c) If $A$ is invertible, then $ABA^{-1}=B$. (d) If $A$ is an idempotent nonsingular matrix, then $A$ must be the identity matrix. (e) If... |
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Hi, this one came in proofathon contest and had an average score of 000.
Problem
Prove that
∣cos(x)∣+∣cos(y)∣+∣cos(z)∣+∣cos(y+z)∣+∣cos(z+x)∣+∣cos(x+y)∣+3∣cos(x+y+z)∣≥3|\cos (x)| + |\cos (y)| + |\cos (z)| + |\cos(y+z)| + |\cos(z+x)| + |\cos(x+y)| + 3|\cos(x+y+z)| ... |
We have seen that the SI definition of magnetic moment is unequivocally defined as the maximum torque experienced in unit external field. Nevertheless some authors prefer to think of magnetic moment as the product of the equatorial field and the cube of the distance. Thus there are two conceptually different concepts o... |
I have been trying to solve a 4x4 matrix and have done a hell a lot of writing. Now I am near the end and I am not getting the requested output out of the LaTeX compiler.
When I write for example:
\begin{minipage}[t]{\textwidth}\begin{equation}\label{e50}R^{-1} = \frac{1}{\left|R\right|} \rm{adj}(R) = \alpha\end{equati... |
Atomic spectroscopy is, of course, a vast subject, and there is no intention in this brief chapter of attempting to cover such a huge field with any degree of completeness, and it is not intended to serve as a formal course in spectroscopy. For such a task a thousand pages would make a good start. The aim, rather, is t... |
Do you know sensible algorithms that run in polynomial time in (Input length + Output length), but whose asymptotic running time in the same measure has a really
huge exponent/constant (at least, where the proven upper bound on the running time is in such a way)?
Do you know sensible algorithms that run in polynomial t... |
I am reading about american option pricing and the variational inequality, and the book I am reading states, in the derivation of the variational inequality, the following is a martingale: $$M_s = U(s,X_s) - \int_t^s(\partial_tU(x,X_r) + \mathcal{L}U(x,X_r))dr$$ where $\mathcal{L}$ is the Ito/infinitesimal generator of... |
In
mathematics, Riemann's differential equation, named after Bernhard Riemann, is a generalization of the hypergeometric differential equation, allowing the regular singular points (RSPs) to occur anywhere on the Riemann sphere, rather than merely at 0, 1, and . The equation is also known as the ∞ {\displaystyle \infty... |
For some information on tides, here's a website:http://www.lhup.edu/~dsimanek/scenario/tides.htmFor some mathematical detail (just algebra):http://mb-soft.com/public/tides.htmlYou only need gravity to explain the tides.Omega is a constant, equal to the angular velocity of the earth...
I'm pretty confused by the post - ... |
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Hi guys...just thought of sharing my time table and I also want to know yours.how to manage time,how to give quality time for studying,are topics that we should always think while writing a time table.
Do share yours.6:00A.M−7:00A.M−wakeupgetfreshedandreviseconce... |
Let $f: \{-1,1\}^n \rightarrow \{-1,1\}$ be a Boolean function.
The Fourier expansion of $f$ is $$f(T) = \sum_{S \subseteq [n]} \widehat{f}(S)\ \chi_S(T)$$ where $\widehat{f}(S)$ are real numbers and $\chi_S(T)=\Pi_{i \in S} T_i$ is a parity function.
Let $d$ be the degree of the the Fourier expansion of $f$, i.e. $d= ... |
Consider the equation
\[\frac{x^2}{a^2} + \frac{z^2}{c^2} = 1, \label{4.3.1} \tag{4.3.1}\]
with \(a > c\), in the \(xz\)-plane. The length of the semi major axis is \(a\) and the length of the semi minor axis is \(c\). If this figure is rotated through \(360^\circ\) about its minor (\(z\)-) axis, the three- dimensional... |
Let $t$ be time and $x$ be the ratio of the cistern filled with water. Assume that the cistern has a constant horizontal cross-section, which implies that the rate of leaking is proportional to the square-root of the amount of water by Torricelli's law, since the leak is at the bottom, and the amount is proportional to... |
We wish to find the potential at a point P at a large distance \(R\) from a charged body, in terms of its total charge and its dipole, quadrupole, and possibly higher-order moments. There will be no loss of generality if we choose a set of axes such that P is on the \(z\)-axis.
\(\text{FIGURE III.14}\)
We refer to Figu... |
The Simple Pendulum
Galileo was the first to record that the period of a swinging lamp high in a cathedral was independent of the amplitude of the oscillations, at least for the small amplitudes he could observe. In 1657, Huygens constructed the first pendulum clock, a vast improvement in timekeeping over all previous ... |
(a) If $AB=B$, then $B$ is the identity matrix. (b) If the coefficient matrix $A$ of the system $A\mathbf{x}=\mathbf{b}$ is invertible, then the system has infinitely many solutions. (c) If $A$ is invertible, then $ABA^{-1}=B$. (d) If $A$ is an idempotent nonsingular matrix, then $A$ must be the identity matrix. (e) If... |
1
Okay, I just figured this out. I believe this is what you do: we know solution is spherically symmetric by the hint and because the boundary conditions show that the solution has no $\theta$ or $\phi$ dependence. So converting to spherical coordinates, the problem looks like:
$$u_{tt}-u_{rr}-\frac{2}{r} u_r =0$$ We s... |
I'm trying to apply Fourier analysis to a specific problem I have. I have essentially an integral like the following
$$ \int_{\Omega} f(t) g(t) dt $$
And I'm trying to assume that $g$ is a narrow band signal (namely the Fourier transform is defined on a compact set). I want to prove that if $g$ is really narrow band th... |
Despite the fact that neural networks have made major advances in many tasks, such as image recognition, video/image generation and the likes, I feel they inevitably suffer from a greater problem. Their intrinsic complexity enables them to make great progress as well as make them very hard to completely understand for ... |
I have the following problem:
given
a directed graph $G=(V,E,d)$, where $d:V\to\mathcal{I}(\mathbb{Q}_0^+\cup\{+\infty\})$ (here $\mathbb{Q}_0^+$ denotes the set of non-negative rationals and $\mathcal{I}(\mathbb{Q}_0^+\cup\{+\infty\})$ the set of intervals, bounded or unbounded above, with non-negative rational bounds... |
Given coprime $a, b$, what is $$ \min_{x, y > 0} |a^x - b^y| $$
Here $x, y$ are integers. Obviously taking $x = y = 0$ gives an uninteresting answer; in general how close can these powers get? Also, how do we quickly compute the minimizing $x, y$?
MathOverflow is a question and answer site for professional mathematicia... |
A time translation invariant system without energy conservation
Noether's theorem relating continuous Lie symmetries to conserved quantities famously implies that given a time translation symmetry\begin{equation} \phi(t, x^i) \to \phi'(t) = \phi(t + T, x^i) \end{equation}
with infinitesimal action\begin{equation} \delt... |
Averaged and Integral Characteristics
These characteristics can be monitor in the course of
design process.
It is possible to monitor minimum and maximum values as well.
Example. As an example, a 6-layer metal-dielectric coating was designed. The corresponding design bar is shown on the bottom of the Evaluation window ... |
I read the definition of work as $$W ~=~ \vec{F} \cdot \vec{d}$$ $$\text{ Work = (Force) $\cdot$ (Distance)}.$$
If a book is there on the table, no work is done as no distance is covered. If I hold up a book in my hand and my arm is stretched, if no work is being done, where is my energy going?
I read the definition of... |
Can anyone see how the following is obtained:
In a section on Perturbation by an oscillating electric field. In book "Atomic Physics" by Foot. The following is stated: Consider the Shrodinger equation $$i \hbar \frac{\partial \Psi}{\partial t} = H \Psi.$$ The Hamiltonian has two parts $$H = H_0 + H_{I}(t).$$
The pertur... |
Let $T: \R^n \to \R^m$ be a linear transformation.Suppose that the nullity of $T$ is zero.
If $\{\mathbf{x}_1, \mathbf{x}_2,\dots, \mathbf{x}_k\}$ is a linearly independent subset of $\R^n$, then show that $\{T(\mathbf{x}_1), T(\mathbf{x}_2), \dots, T(\mathbf{x}_k) \}$ is a linearly independent subset of $\R^m$.
Let $V... |
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Higher harmonic flow coefficients of identified hadrons in Pb-Pb collisions at $\sqrt{s_{\rm NN}}$ = 2.76 TeV
(Springer, 2016-09)
The elliptic, triangular, quadrangular and pentagonal anisotropic flow coefficients for $\pi^{\pm}$, $\mathrm{K}^{\pm}$ and p+$\overline{\mathrm{p}}$ in Pb-... |
In his celebrated paper "Conjugate Coding" (written around 1970), Stephen Wiesner proposed a scheme for quantum money that is unconditionally impossible to counterfeit, assuming that the issuing bank has access to a giant table of random numbers, and that banknotes can be brought back to the bank for verification. In W... |
An unknown element $\ce{Q}$ has two unknown isotopes: $\ce{^60Q}$ and $\ce{^63Q}$. If the average atomic mass is $\pu{61.5 u}$, what are the relative percentages of the isotopes?
closed as off-topic by Loong♦, bon, ron, Klaus-Dieter Warzecha, John Snow Feb 21 '15 at 19:33
This question appears to be off-topic. The user... |
Wave Optics Huygens' Principle, Refraction and Reflection of Plane Waves using Huygens Principle The locus of all the particles of the medium which are in the same phase or in the same state of vibration are called wave front A point source of Light at finite distance can produce spherical wave front. A Line of source ... |
Does the Leibniz (product) rule hold in some sense for the spectral fractional Laplacian (at least in 1 dimension)?
There are precise rules for the composition of pseudo-differential operators and although these fractional derivatives are singular integrals and not always pseudo-differential operators, because of the s... |
We have $X \sim \mathrm{Unif}[0,2]$ and $Y \sim \mathrm{Unif}[3,4]$. The random variables $X,Y$ are independent. We define a random variable $Z = X + Y$ and want to find the PDF of $Z$ using convolution. Here is my work so far:
The definition of convolution is:
$f_Z(z) = \int_{-\infty}^{\infty}f_X(x)f_Y(z-x)\mathrm{d} ... |
MathJax TeX Test PageMathJax.Hub.Config({tex2jax: {inlineMath: [[‘$’,’$’], [‘\\(‘,’\\)’]]}});
Credit: Ancient Origins
Introduction In a previous Math Scholar blog, we presented Archimedes’ ingenious scheme for approximating $\pi$, based on an analysis of regular circumscribed and inscribed polygons with $3 \cdot 2^k$ s... |
In the well-known communication task
EQUALITY, Alice has a string $x$ of $n$ bits, Bob has a string $y$ of $n$ bits, and their task is to determine whether $x = y$. In the public coin model, there is a probabilistic protocol which uses 2 bits, is always correct when $x = y$, and is correct with constant probability whe... |
I would recommend you to look at Jones' survey paper from 1986, entitled
A New Knot Polynomial and Von Neumann Algebras. It is very readable. Let me try to make a brief summary, though.
The basic object you start with is a $II_1$ factor. This is a von Neumann algebra $M$ with trivial center $Z(M)\simeq \mathbb{C}$, pos... |
The classical LSE (least squares estimator) of the regression parameter in a simple regression model, MLE for normally distributed errors, is known to be highly nonrobust for outliers (gross-error contamination) and plausible departures from the assumed normality. The estimator based on the Kendall tau-statistic, known... |
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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 ... |
"La variante di Lüneburg" and China's rice productionIn 1993, Paolo Maurensig, an Italian writer from Gorizia, wrote a novel entitled "La variante di Lüneburg" (Adelphi, 1995, pp. 164, ISBN 88-459-0984-0). The novel is set in Nazi Germany during World War II and the main theme is the game of chess.
At the beginning of ... |
Please explain each step thank you
Solved: y^2-8x +7
(y-4)^2 -9
sqrt(x-9)+4 = y
g(x) is a concave up parabola
\(g(x)=x^2-8x+7\\ g(x)=(x-7)(x-1)\\ \text{roots are at x= 7 and x= 1}\\ \text{Axis of symmetry = 4} \)
x=4 g(4)= -3*3 = -9
So the vertex is (4,-9)
Since the domain is \((4,\infty)\) the range is \((-9,\infty) \... |
The derivative of a function is one of the basic concepts of mathematics. Together with the integral, derivative occupies a central place in calculus. The process of finding the derivative is called differentiation. The inverse operation for differentiation is called integration.
The derivative of a function at some po... |
While this does not answer the question asked (and will therefore not be accepted), I provide this response in hopes it will help others and promote worthwhile discussion.
In his book Experimentation: An Introduction to Measurement Theory and Experiment Design, David Baird provides a simple explanation for doing a line... |
The current (I) - voltage (V) relationship of electrical components can often provide insight into how electronic devices are used. More specifically, many non-linear devices such as diodes and transistors are used in
operating regions in which they behave like ideal components—such as current sources, voltage regulato... |
4.1.1. Center of Mass of a Collection of Particles
So far we’ve only considered two cases - single particles on which a force is acting (like a mass on a spring), and pairs of particles exerting a force on each other (like gravity). What happens if more particles enter the game? Well, then we have to calculate the tota... |
I'm seriously trying to figure out the exact same thing for my dissertation. I can easily solve for reservation (threshold) prices when offered prices are independent, but I haven't yet solved for the case of mean reversion.
There's an example in Bertsekas (1987) page 83 with an autocorrelated asset sale model, but it'... |
I have been highlighting certain parts of text in order to make it easier for me to search through a long document to find parts that need expanded on or some sort of work is left to do; however, I've been having issues with highlighting equations. I have a bit of a workaround (courtesy of this answer). Inserting this ... |
Initial Note
The highest priority input is RESET. If low, the FF is actively
. But you have that tied high. So RESET isn't active. reset 1st Schematic Results
The next highest priority input is TRIG. But only if it is low (below it's \$\frac13\$\$^\text{rd}\$ threshold.) If low, it actively
the FF. If it is above that ... |
Axioms For *
\begin{align} 1 + aa^* &\leq a^* \\ 1 + a^*a &\leq a^* \\ b + ax &\leq x \to a^*b \leq x \\ b + xa &\leq x \to ba^* \leq x \\ \end{align}
Elementary Results
\begin{align} a \leq b &\to a + c \leq b + c \\ a \leq b &\to ac \leq bc\, \wedge\, ca \leq cb \\ a \leq b &\to a^* \leq b^* \end{align}
Problem
Prove... |
Consider the set of all integer linear combinations of permutation matrices of some fixed dimension. Is there a description of the set of unimodular matrices in this lattice?
If you take $\mathbb{Q}$ linear combination of permutation matrices, this is a ring which is the product $M_1(\mathbb{Q})\times M_{n-1}(\mathbb{Q... |
The OP contains the specifications
do not immediately involve graph theory, on the surface,
reduce, after a little translation, into a common problem in graph theory (find a matching, find a colouring...).
there should be a "haha!" effect for the mathematician, and a sigh of relief for the programmer.
The following is ... |
Subquery is a query within another SQL query. A common subquery is embedded within the
FROM clause, for example：
SELECT ID FROM (SELECT * FROM SRC) AS T
The subexpressions in the
FROM clauses can be processed very well by the general SQL optimizers. But when it comes to subqueries in the
WHERE clause or the
SELECT list... |
Difference between revisions of "stat946w18/Implicit Causal Models for Genome-wide Association Studies"
(→Causal Inference with a Latent Confounder)
Line 201: Line 201:
Dustin Tran, Rajesh Ranganath, and David M Blei. Hierarchical implicit models and likelihood-free variational inference. In Neural Information Processi... |
I'm trying to figure out the elasticity of substitution between input $s$ and input $v$. I know that the marginal rate of substitution between these two inputs are $\frac{v^2}{s(v+k)}$, where $k$ is another input.
Then, the elasticity of substitution is,
$$E_{sv}=\dfrac{dln\big(v/s\big)}{dln\bigg(\frac{v^2}{s(v+k)}\big... |
Equation Maker allows you to typeset equations using LaTeX syntax. You can drag and drop the equations into almost any Mac application (including Pages, Numbers, Keynote, and Microsoft Word).
Equation Maker Overview
Helpful tips
Use PDF as the export format for the highest quality resolution. Use PNG only in cases wher... |
Let us consider a (not necessarily finite) Coxeter group $W$ generated by a finite set of involutions $S=\{s_1,...,s_n\}$ subject (as usual) to the relations $(s_is_j)^{m_{i,j}}$ with $m_{i,j}=m_{j,i}$ and $m_{i,j}=1$ if and only if $i=j$ (if necessary you may also assume that $m_{i,j}<\infty$ for all $i,j$ or even tha... |
Introduction
For two identical particles confined to a one-dimensional box, we established earlier that the normalized two-particle wavefunction \(\psi(x_1,x_2)\), which gives the probability of finding simultaneously one particle in an infinitesimal length \(dx_1\) at \(x_1\) and another in \(dx_2\) at \(x_2\) as \(|\... |
As you said, it varies.Imagine I'm in Chicago and you're in London. My little dog is running circles around me. Which is closer to you, me or my dog?While the correct answer is "it depends on where the dog is in its orbit around me", I'd argue that a better answer is "it doesn't matter" - the distance between you and m... |
Astrobiology is the study of origin, evolution, distribution and future of life in the universe. It is concerned with discovering and detecting Extrasolar Planets. Astrobiology addresses the following points −
How does life begin and evolve? (biology + geology + chemistry + atmospheric sciences)
Are there worlds beyond... |
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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... |
I am investigating a somewhat obscure area of number theory. Can I post a proposition and a complete proof and ask people to check it?
Say I've proven a theorem or found a solution to a problem. I'm close to being sure that my proof or solution is fine. However, I'm not entirely confident in my jugdement. Maybe I'm new... |
Difference between revisions of "stat946w18/Implicit Causal Models for Genome-wide Association Studies"
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By way of example, let us use the expression \(\textbf{dA} = \frac{\mu I}{ 4 \pi r}\textbf{ds}\) , to calculate the magnetic vector potential in the vicinity of a long, straight, current-carrying conductor ("wire" for short!). We'll suppose that the wire lies along the \(z\)-axis, with the current flowing in the direct... |
My eldest came home with some interesting maths homework.
We have three bowls containing peas.
Distribute the peas evenly across the bowls, by moving peas from one bowl to another. The only move allowed, is doubling the amount of peas in one bowl by taking them from one other bowl.
For example:
$\begin{array}{rlrlrl} A... |
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Hi Guys, I just want to say that JOMO 5 has started! Please reshare and tell your friends about it. You can check out the paper here. Please read the rules before starting
Note by Yan Yau Cheng 5 years, 4 months ago
Easy Math Editor
This discussion board is a pla... |
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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... |
I'm trying to figure out how to convert any phase response to the corresponding group delay response.
Is there a way to do that, and vice-versa if possible?
Signal Processing Stack Exchange is a question and answer site for practitioners of the art and science of signal, image and video processing. It only takes a minu... |
I think one important thing that you must understand is that a Dirac delta impulse is not an ordinary function that can be evaluated. So you do not multiply your signal with a value of $\infty$. What happens instead is that you weigh the individual shifted Dirac impulses with the corresponding values of the signal due ... |
The maximum principle for Crank-Nicolson will hold if$$\mu \doteq \frac{k}{h^2} \leq 1$$for timestep $k$ and grid spacing $h$. In general, we can consider a $\theta$-scheme of the form$$u^{n+1} = u^n + \frac{\mu}{2}\left( (1-\theta)Au^n + \theta Au^{n+1}\right)$$where $A$ is the standard Laplacian matrix and $0 \leq \t... |
Ultimately, you'll need a mathematical proof of correctness. I'll get to some proof techniques for that below, but first, before diving into that, let me save you some time: before you look for a proof, try random testing.
Random testing
As a first step, I recommend you use random testing to test your algorithm. It's a... |
Instance: an integer j and an n-vertex non-empty simple graph G
Parameter: integer k Output: if there is a 3-coloring of G in which at least one of the colors is used at most min($\hspace{.03 in}$j,k) times then YES else NO
.
Since j is part of the input and the only involvement of k is via min($\hspace{.03 in}$j,k) , ... |
Does there exist a prime 3-manifold such that its mapping class group has an abelian representation in which the 2$\pi$ rotation is represented by -1?
In detail:Let $M$ be a closed orientable prime 3-manifold.Let $D_F(M,p)$ be the group of diffeomorphisms of $M$ that fix a point $p$ of $M$ and a frame there. Define the... |
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