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I'm trying to measure the amplitude of a sinusoidal component in a noisy signal.
Since the signal frequency is known beforehand, I'm calculating scalar product with a sine and cosine base function at the given frequency (see this thread: Measuring amplitude of a spectral component)
$$a = \left<y,\cos(2\pi t f_c/f_s)\ri... |
Update: This implementation is now a package called
CompoundMatrixMethod, hosted on github. It can be installed easily by evaluating:
Needs["PacletManager`"]
PacletInstall["CompoundMatrixMethod", "Site" ->
"http://raw.githubusercontent.com/paclets/Repository/master"]
This version also includes a function
ToMatrixSystem... |
Contents What is a normal?
We briefly mentioned what normals were in the first chapter of this lesson. A surface normal from a surface at P, is a vector perpendicular to the tangent plane to that surface at P. We will learn more about how to compute normals as we get to the lessons on geometric primitives. But lets jus... |
I would like to ask that at what distance from the Earth's surface the curvature of the Earth is visible. What layer of the atmosphere is this?
I've noticed that at the height of 9-12 Km (the view from from aeroplanes) it is not visible.
Earth Science Stack Exchange is a question and answer site for those interested in... |
I have been working on an old problem in one of my finance classes and, since no solution has been provided and I won't be able to contact my teacher anytime soon, I was hoping I could ask you guys to give me some feedback on my solution.
Here's the problem:
Consider a measure Q under which the dynamics of St are:
$\fr... |
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Production of Σ(1385)± and Ξ(1530)0 in proton–proton collisions at √s = 7 TeV
(Springer, 2015-01-10)
The production of the strange and double-strange baryon resonances ((1385)±, Ξ(1530)0) has been measured at mid-rapidity (|y|< 0.5) in proton–proton collisions at √s = 7 TeV with the ... |
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Now showing items 1-10 of 192
J/Ψ production and nuclear effects in p-Pb collisions at √sNN=5.02 TeV
(Springer, 2014-02)
Inclusive J/ψ production has been studied with the ALICE detector in p-Pb collisions at the nucleon–nucleon center of mass energy √sNN = 5.02TeV at the CERN LHC. The measurement is performed i... |
Attainability of the fractional hardy constant with nonlocal mixed boundary conditions: Applications
1.
Laboratoire d'Analyse Nonlinéaire et Mathématiques Appliquées, Université Abou Bakr Belkaïd, Tlemcen, Tlemcen 13000, Algeria
2.
Département de Mathématiques, Université Ibn Khaldoun, Tiaret, Tiaret 14000, Algeria
3.
... |
\(\newcommand{\norm}[1]{\left \lVert #1 \right \rVert}\)
Introduction
So in the world of practical optimization, especially with respect to applications in things like Machine Learning, it is super common to hear about the use of Gradient Descent. Gradient Descent is a simple recursive scheme that is used to finding cr... |
WP 34S vs. DM42 decimal128 differences?
03-20-2018, 09:15 AM (This post was last modified: 03-27-2018 09:51 AM by rkf.)
Post: #1
WP 34S vs. DM42 decimal128 differences?
Today I stumbled about a footnote in Walter's WP 34S Owner's manual, where at Page 319 the result of the Calculator Forensics Test is mentioned. To my ... |
Here is an interesting game I heard a few days ago from one of my undergraduate students; I’m not sure of the provenance.
The game is played with stones on a grid, which extends indefinitely upward and to the right, like the lattice $\mathbb{N}\times\mathbb{N}$. The game begins with three stones in the squares nearest ... |
If $I(\theta)$ is the Fisher Information for $\theta$
Then how do I find $J=I(g(\theta ))$ ?
Currently my thoughts are that:
$$I(\theta) = E\left( \left(\frac{\partial}{\partial \theta}\log f(X;\theta)\right)^2 \right)$$ and if $u=g(\theta)$ where $g( \cdot )$ is differentiable, then $$\frac{\partial}{\partial u}=\frac... |
I think it might be helpful to put the new statement at the beginning and put the original post at the end. This new statement is more mathematically elegant.
Let $f\geq0$ be in $L^1(\mathbb{R}^d)$ and $g(x)=\exp(-\|x\|^2)$. Let $1_{B_1}$ be the indicator function of the unit ball centered at origin. Let $*$ be the con... |
In a physics text book I need help to make sense of the part highlighted in yellow:
This is out of context of course, so just to make it clearer:
$\tau$ is the
mean free time of the electrons in a conductor (the average time between collisions with ions in the material).
This text snippet is part of a derivation of a m... |
What are some examples of functions which are continuous, but whose inverse is not continuous?
nb: I changed the question after a few comments, so some of the below no longer make sense. Sorry.
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fi... |
As mentioned in my other post, I am attempting to learn from Gross'"
Relativistic quantum mechanics and field theory", and I have a question concerning the manipulation of the antisymmetric 4x4 tensors involved.
There are two points where this does not make sense to me. Firstly, when proving that the correct equations ... |
I´ve solved the Exercise 7.1.1 (Bernstein–Vazirani problem) of the book "An introduction to quantum computing" (Mosca et altri). The problem is the following:
Show how to find $a \in Z_2^n$ given one application of a black box that maps $|x\rangle|b\rangle \to |x\rangle |b \oplus x · a\rangle$ for some $b\in \{0, 1\}$.... |
How to Use Circular Ports in the RF Module
The
Port boundary condition in the RF Module, an add-on to the COMSOL Multiphysics® software, can be used to launch and absorb electromagnetic energy. We explain how to set up a circular waveguide port and review the analytical solution that defines the port mode field. We als... |
Inaccessible cardinal Inaccessible cardinals are the traditional entry-point to the large cardinal hierarchy, although weaker notions such as the worldly cardinals can still be viewed as large cardinals.
A cardinal $\kappa$ being inaccessible implies the following:
$V_\kappa$ is a model of ZFC and so inaccessible cardi... |
Stable
Stability was developed as a large countable ordinal property in order to try to generalize the different strengthened variants of admissibility. More specifically, they capture the various assertions that $L_\alpha\models\text{KP}+A$ for different axioms $A$ by saying that $L_\alpha\models\text{KP}+A$ for many ... |
I have a question on the possibility of using Mathematica to plot a convex closed region satisfying a linear system of equalities and inequalities.
Let me first present the linear system. Let $x\equiv (x_1,...,x_{34})$ be a $34\times 1$ vector of unknowns. Let $A,C,E,b,d$ be matrices of known parameters with appropriat... |
V. Gitman, J. D. Hamkins, and A. Karagila, “Kelley-Morse set theory does not prove the class Fodor theorem.” (manuscript under review)
@ARTICLE{GitmanHamkinsKaragila:KM-set-theory-does-not-prove-the-class-Fodor-theorem, author = {Victoria Gitman and Joel David Hamkins and Asaf Karagila}, title = {Kelley-Morse set theor... |
I want to solve the diffusion equation, i.e. $$ \dot{f} - f'' = 0 $$ with a boundary condition $f(0) = f(1) = 0$ and with an initial condition that $f$ is a boxcar function concentrated over some small region of size $d \ll 1$. The units are scaled so that the diffusion constant is equal to unity. Then I want to use th... |
This question already has an answer here:
Consider the following complex power series $$\sum_{n \geq 1} \frac{z^n}{n} \,\,\,\,\,\,\, z \in \mathbb{C}$$
It surely converges conditionally for $z=-1$ (for alternating series test) and for $z=1$ it diverges (it is the harmonic series).
My question is: how can one show that ... |
This is not a solution, but it's too long for a comment.
As I wrote in the comment above, if $n$ is composite, then the statement is easily proved. Write $n=x \cdot y$ and pick $(a,b)=(x, xy-x)$. Since $$a^2+b^2=x^2(1+(y+1)^2)$$is divisible by $x^2$, it's not a prime.
This reduces the study of this problem to primes $n... |
From a categorical perspective, the subcategory of $\mathsf{Top}$ generated by spaces with open connected components does not have pullbacks.
Borceux and Janelidze,
Galois Theories, section 6.4:
The category $\mathsf{Top}$ of topological spaces is extensive, but not of the form $\mathsf{Fam}(\mathcal A)$. On the other ... |
A countable limit ordinal $\kappa$ has cofinality $\omega$. One proves this in
ZF, say, using the usual trick for representing $\kappa$ as a countable set of reals having closed convex span $[0,1]$ (with the usual order) and then comparing with any increasing sequence in $[0,1]$ converging to 1.
Nevertheless, I suspect... |
I found at the beginning of tom Dieck's Book the following (non proved) result
Suppose $X$ is the colimit of the sequence $$ X_1 \subset X_2 \subset X_3 \subset \cdots $$ Suppose points in $X_i$ are closed. Then each compact subset $K$ of $X$ is contained in some $X_k$
Now I really don't know how to prove this fact. Th... |
This is standard theory. Try
Birrell, N. D., & Davies, P. C. W. (1982). Quantum Fields in Curved Space. Cambridge: Cambridge University Press.
Bog standard Curved space QFT text. Don't remember how much is said specifically about spinors though.
Brill, D., & Wheeler, J. (1957). Interaction of Neutrinos and Gravitationa... |
Think of moving volatility in the other direction.
As volatility approaches zero, any call strike strictly smaller than the ATM strike, $K<K_{ATM}$, will have zero probability of ending in the money, and the corresponding option value will be zero. An infinitesimally small change in stock price will not move $K$ past $... |
2019-10-11 14:20
TURBO stream animation /LHCb Collaboration An animation illustrating the TURBO stream is provided. It shows events discarded by the trigger in quick sequence, followed by an event that is kept but stripped of all data except four tracks [...] LHCB-FIGURE-2019-010.- Geneva : CERN, 2019 - 3. Detailed rec... |
Let $B \in \mathbb{R}^{n \times n}$ be symmetric and positive semi-definite such that $B = U\Lambda U^T$, where $U = [u_1,\cdots,u_n]^T$ is an orthogonal matrix with $u_i \in \mathbb{R}^n$, and $\Lambda=\text{diag}(0,\cdots,0,\lambda_k,\cdots,\lambda_n)$ is the diagonal matrix with $0<\lambda_k \leq\cdots \leq \lambda_... |
$\newcommand{\qr}[1]{|#1\rangle}$Grover algorithm's input is a superposition, representing the haystack, and the Bell state $\qr{-}$. The $\qr{-}$ seems utterly important: when I replaced $\qr{-}$ by, say, $\qr{+}$, the oracle became the identity operator and so Grover's algorithm couldn't work with it. So it seems tha... |
14 0
This result isn't in our book, but it is in my notes and I want to make sure it's correct. Please verify if you can.
I have two I.I.D random variables. I want the conditional expectation of Y given Y is less than some other independent random variable Z.
[tex] E(Y \, \vert \, Y < z) = \dfrac{\int_0^{z} y \cdot f(y... |
Positive set theory Positive set theory is the name of a certain group of axiomatic set theories originally created as an example of a (nonstandard) set theories in which the axiom of foundation fails (e.g. there exists $x$ such that $x\in x$). [1] Those theories are based on a weakening of the (inconsistent) comprehen... |
I've just started learning about limits. Why can we say $$ \lim_{x\rightarrow \infty} \frac{\sin x}{x} = 0 $$ even though $\lim_{x\rightarrow \infty} \sin x$ does not exist?
It seems like the fact that sin is bounded could cause this, but I'd like to see it algebraically.
$$ \lim_{x\rightarrow \infty} \frac{\sin x}{x} ... |
Gabriel Romon
Student at ENSAE Paristech and ENS Paris-Saclay (MVA Master's degree). Interested in statistics and machine learning.
A few recent good answers of mine:
DCT for convergence in probability
$\frac{S_n}{\sqrt n}$ is dense in $\mathbb R$ almost surely $\cos(2^n)$ is dense in $[-1,1]$ Showing $(X_n >c_n \text{... |
This will be a talk for the Rutgers Logic Seminar, April 2, 2018. Hill Center, Busch campus.
Abstract. I shall define a certain finite set in set theory $$\{x\mid\varphi(x)\}$$ and prove that it exhibits a universal extension property: it can be any desired particular finite set in the right set-theoretic universe and ... |
I've thought about this question for a while without an answer. The key is to consider the structure of the constructible real numbers. I was actually a bit cavalier with my original definition, "$x$ is irrational if $|x-p/q|<q^{-2}$ has infinitely many coprime solutions". The problem lies in what is meant by "infinite... |
In the original form of Maldacena's AdS/CFT, the bulk is classical supergravity and the boundary is superconformal field theory in the Maldacena's limit. However, in many applications of AdS/CFT, for example in AdS/CMT, we only consider the bulk is classical gravity and the boundary is CFT, which does not include super... |
I've tried to explain the solution using as little math as possible, and to give some intuition as to what makes it tick. Nonetheless there will be a little mathematical notation at the end.
First steps: going beyond the obvious solution in the simplest case (N=2)
The statement of the puzzle as presented here doesn't m... |
@DavidReed the notion of a "general polynomial" is a bit strange. The general polynomial over a field always has Galois group $S_n$ even if there is not polynomial over the field with Galois group $S_n$
Hey guys. Quick question. What would you call it when the period/amplitude of a cosine/sine function is given by anot... |
I was doing some computations for research purposes, which led me to this integral:
$$I(n) = \int_0^{\infty} (t^2+t^4)^n e^{-t^2-t^4}\,dt.$$
This is very suggestively written so as to employ a parametric differentiation technique as so:
$$\left(\frac{\partial^n}{\partial \alpha^n}\right)\int_0^{\infty}e^{-\alpha(t^2+t^... |
Let $\Omega\subset\mathbb{R}^N$ be a bounded smooth domain. Suppose that $0<k<t<1$ and $\Phi$ is a mooth function satisfying: $\Phi(x)=0$ for $x\le k$, $\Phi(x)=1$ for $x\ge t$.
Take $u\in C_0^\infty(\overline{\Omega})$ with $u\ge 0$ and $u$ superharmonic ($-\Delta u\ge 0$). Note that $$\Delta (\Phi\circ u)=(\Phi''\cir... |
since electromagnetic radiation possess the property of both wave and particle(photon). and both theory are applicable but how we have to find out that which theory is suitable or applicable in particular explanation. for example in laser traping of atom we use photon concept rather than wave why?
I'd like to add a sli... |
Rocky Mountain Journal of Mathematics Rocky Mountain J. Math. Volume 44, Number 3 (2014), 1015-1026. On quadratic twists of hyperelliptic curves Abstract
Let $C$ be a hyperelliptic curve of good reduction defined over a discrete valuation field $K$ with algebraically closed residue field $k$. Assume moreover that $\tex... |
A key step in many proofs consists of showing that two possiblydifferent values are in fact the same. The
Pigeonhole principle cansometimes help with this.
Proof. Suppose each box contains at most one object. Then the total number of objects is at most $1+1+\cdots+1=n$, a contradiction.
This seemingly simple fact can b... |
Tverberg Theorem (1965): Let $ x_1,x_2,\dots, x_m$ be points in $ R^d$, $ m \ge (r-1)(d+1)+1$. Then there is a partition $ S_1,S_2,\dots, S_r$ of $ \{1,2,\dots,m\}$ such that $\cap _{j=1}^rconv (x_i: i \in S_j) \ne \emptyset$.
Tverberg's theorem was conjectured by Birch who also proved the planar case. The case $r=2$ i... |
In our day to day lives, we live with uncertainty about what might happen.
What will the weather be like today?
Will there be traffic on my way to work? Will I finally get the recognition and promotion I have been working for?
In life, there’s many things we don’t have enough data to predict. To us, many things might a... |
What are the conditions for formulating a Lagrangian, if the system's state is stochastic?
Some notation: \( x \in X \subset \mathbb{R}^d\) is the control variable, \(u \in \mathbb{R}^n\) is the state vector, \( ( \Omega, S, P ) \) with \( \omega \in \Omega , 0 \leq P(A \in S) \leq 1\) is a probability space. We know t... |
In line with DilipSarwate let me put what I understand from your question and the excerpt you posted.
First of all the excerpt does not say that one can transmit a signal without distortion through a channel whose bandwidth is less than the signal's bandwidth. Rather it says that one can, in principle, perfectly
revers... |
Let $T$ be a linear operator on an inner product space $V$. If $\langle T(x),y \rangle=0$ for all $x,y \in V$ then $T=T_0$ where it means zero transformation.
Prove this result if the equality holds for all $x,y$ in some basis for $V$.
The hint says use the theorem below.
[let $V$ and $W$ be vector spaces over $F$ and ... |
Definition
A two-class classifier.
A Feedforward Neural Network without hidden layers.
More specifically: It maps its input $x$ to output $f(x)$ with parameter $\theta$:
$$ \begin{equation} f(x) = \begin{cases} 0 & \text{if }x \cdot \theta > 0 \\ 1 & \text{otherwise} \end{cases} \end{equation} $$ Learning Algorithm Ran... |
The Annals of Statistics Ann. Statist. Volume 27, Number 3 (1999), 1041-1060. Asymptotics when the number of parameters tends to infinity in the Bradley-Terry model for paired comparisons Abstract
We are concerned here with establishing the consistency and asymptotic normality for the maximum likelihood estimator of a ... |
J. D. Hamkins, “Every countable model of set theory embeds into its own constructible universe,” J. Math. Logic, vol. 13, iss. 2, p. 1350006, 27, 2013.
@article {Hamkins2013:EveryCountableModelOfSetTheoryEmbedsIntoItsOwnL,
AUTHOR = {Hamkins, Joel David},
TITLE = {Every countable model of set theory embeds into its own
... |
"Abstract: We prove, once and for all, that people who don't use superspace are really out of it. This includes QCDers, who always either wave their hands or gamble with lettuce (Monte Zuma calculations). Besides, all nonsupersymmetric theories have divergences which lead to problems with things like renormalons, insta... |
Let $n$ be a square-free integer. Then for a given integer $m$, $m$ is a square modulo $n$ if and only if the sum
$$\displaystyle \sum_{d | n} \left(\frac{m}{d}\right) > 0.$$
In fact one can write the indicator function $\Psi(m,n)$, which equals unity if $m$ is a square mod $n$ and zero otherwise, as
$$\Psi(m,n) = \fra... |
LaTeX supports many worldwide languages by means of some special packages. In this article is explained how to import and use those packages to create documents in
German.
Contents
German language has some special characters. For this reason the preamble of your file must be modified accordingly to support these charac... |
I am confused how to interpret the result of performing a normalized correlation with a constant vector. Since you have to divide by the standard deviation of both vectors (reference: http://en.wikipedia.org/wiki/Cross-correlation ), if one of them is constant (say a vector of all 5's, which has standard deviation of z... |
Please help transcribe this video using our simple transcription tool. You need to be logged in to do so.
Description
We present a fully homomorphic encryption scheme that is based solely on the (standard) learning with errors (LWE) assumption. Applying known results on LWE, the security of our scheme is based on the w... |
Consider a zero-temperature, one-dimensional crystal with allowed electron momenta $k_n = \frac{2\pi n}{L}$.
Question: Which is the more correct way to think about the Fermi sea?
Sharp plane waves --
$$ \prod_{\epsilon_k<\epsilon_f} c_{k\uparrow}^\dagger c_{k\downarrow}^\dagger \lvert 0\rangle$$
or
Wave packets that ar... |
There are other ways that a function might be said to generate asequence, other than as what we have called a generating function. Forexample,$$e^x = \sum_{n=0}^\infty {1\over n!} x^n$$is the generating function for the sequence $1,1,{1\over2}, {1\over3!},\ldots$. But if we write the sum as$$e^x = \sum_{n=0}^\infty 1\c... |
\(R^2\) Statistic M Loecher
It seems to odd to me that we measure the explanatory power of a regression model in “percent of variance explained”, or \(R^2 = cor(\hat{y},y)^2 = r^2\) even though we all know that variance is just an auxiliary quantityto compute the more meaningful measure of uncertainty which is the stan... |
The idea behind this expression is indeed a fairly general one.
$\newcommand{\bs}[1]{\boldsymbol{#1}}\newcommand{\calS}{\mathcal{S}}$An entanglement witness $\mathcal W$ is defined as an operator such that $\operatorname{Tr}(\mathcal W\rho)\ge0$ for all separable $\rho\in\mathcal S$, while for some entangled $\rho_{ent... |
Write the Taylor series of $\text{Log}(1+w)$ with center at $w=0$ on $|w|<1$;
check that if $|z-2|<1$, then $|z|>1$. (If you have difficulties in checking this formally, try to draw a picture of the situation). Use these facts to compute
$$ \int_C \text{Log}\left(1+\frac{1}{z}\right)dz\, $$ $$ C:w(\theta) = 2 + (1/2)e^... |
We know that the sign of the derivative tells us whether a function is increasing or decreasing; for example, when $f'(x)>0$, $f(x)$ is increasing. The sign of the second derivative $f''(x)$ tells us whether $f'$ is increasing or decreasing; we have seen that if $f'$ is zero and increasing at a point then there is a lo... |
\(\)
Time series pervade financial markets and, although some embrace the so-called efficient market hypothesis, stating that current market prices reflect all available information about a security into its price, I’m more inclined to think they provide us with a lot of information that we rarely know how to exploit f... |
What does it mean to measure a qubit (or multiple qubits) in standard basis?
A $1$-qubit system, in general, can be in a state $a|0\rangle+b|1\rangle$ where $|0\rangle$ and $|1\rangle$ are basis vectors of a two dimensional complex vector space. The
standard basis for measurement here is $\{|0\rangle,|1\rangle\}$. When... |
Let $\mathscr C$ be a small category. Necessary and sufficient conditions for a presheaf $F$ to be cofibrant in the global projective model structure on $[\mathscr C^\mathrm{op}, [\Delta^\mathrm{op}, \mathbf{Set}]]$ are that:
(1) Each $F(-)(n) \colon \mathscr C^\mathrm{op} \to \mathbf{Set}$ is projective (i.e., a copro... |
Howto Raytracer: Ray / Triangle Intersection Theory
Besides sphere and plane intersections another important one is the ray / triangle intersection, because most 3D models consist of triangles or can be converted to such a representation. So let’s learn how to do it to be able to model some complex models.
A triangle $... |
Suppose we have a surface given in cylindrical coordinates as $z=f(r,\theta)$ and we wish to find the integral over some region. We could attempt to translate into rectangular coordinates and do the integration there, but it is often easier to stay in cylindrical coordinates.
How might we approximate the volume under s... |
I have a measurement of $x$ coordinates of an oscillating particle at presence of noise taken at constant time steps of 1/60 s.
The corresponding data set can be obtained here:
I would like to measure the power spectrum density (PSD) using the autoregressive (AR) estimation method.
In the paper http://www.measurement.s... |
These results hold for absolutely continuous random variables (see this question for the sample median behavior for discrete random variables). $F$ will be the cumulative distribution function, $f$ the probability density function, $\mu$ the mean. A hat will indicate sample quantities, and a bar sample means. Denote th... |
ISSN:
1078-0947
eISSN:
1553-5231
All Issues
Discrete & Continuous Dynamical Systems - A
January 2006 , Volume 14 , Issue 1
Special Issue
Qualitative theory of nonlinear elliptic and parabolic problems
Select all articles
Export/Reference:
Abstract:
Interaction between nonlinearity and diffusion is a fascinating subject... |
On a question on this site there is an explanation of the algorithm Knuth gives in
The Art Of Computer Programming to compute an approximation of $y = \log_bx$.
Now, I understand why it works; anyway, the only question arising in my mind is: how can we pre-compute a table of logarithms with arguments of the type $\frac... |
equation
Banach Spaces of Solutions of the Helmholtz Equation in the Plane
Time Decay and Regularity of Solutions to the Wave Equation
Mapping Properties of a Projection Related to the Helmholtz Equation
Herglotz Wave Functions are the entire solutions of the Helmholtz equation which have L2-Far-Field-Pattern.
The Ces\... |
Expectations and conditional expectations are either random or fixed points. It depends upon your choice of axioms. Unfortunately, I have never found a good book that fairly describes both well.
On the Bayesian side, I would suggest the very polemical "Probability Theory: The Language of Science" by E.T. Jaynes. On the... |
Can you interchange limits and supremums of functions?
That is, does $$\lim_{n \to \infty} \sup_{x \in X} f_n(x) = \sup_{x \in X} \lim_{n \to \infty} f_n(x) ?$$
Thank you!
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 ... |
Limit ordinal Properties
All limit ordinals are equal to their union.
All limit ordinals contain an ordinal $\alpha$ if and only if they contain $\alpha + 1$.
$\omega$ is the smallest nonzero limit ordinal, and the smallest ordinal of infinite cardinal number.
$(\omega + \omega)$, also written $( \omega \cdot 2 )$, is ... |
The terms can mean almost anything, but I will try to present here
one way in which the terms "parallel algorithms" and "distributed algorithms" are understood. Here we interpret "distributed algorithms" from the perspective of "network computing" (think: algorithms that keep the Internet running).
I will use as a runn... |
A contradiction is usually represented as $A \land \lnot A$. It's typical in intuitionistic logic to
define $\lnot A$ as $A \Rightarrow \bot$. It's clear we can derive $\bot$ from $A \land \lnot A$. Ultimately, a contradiction will be a hypothetical derivation of $\bot$ as the very definition of $\lnot$ suggests. It wi... |
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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 ... |
I would like to generate an isotropic gaussian random field described by a power spectrum $P(k)$ on a 3D grid which represents spherical polar coordinates (i.e., the angular separation between pixels at each slice in the radial direction is equal and each pixel represents a solid angle).
I am currently generating a ran... |
kidzsearch.com > wiki Explore:images videos games
Algebra Algebra is a part of mathematics (often called math in the United States and maths in the United Kingdom [1] ). It uses variables to represent a value that is not yet known. When an equals sign (=) is used, this is called an equation. A very simple equation usin... |
Recall that we were able to analyze all geometric series "simultaneously'' to discover that $$\sum_{n=0}^\infty kx^n = {k\over 1-x},$$ if $|x|< 1$, and that the series diverges when $|x|\ge 1$. At the time, we thought of $x$ as an unspecified constant, but we could just as well think of it as a variable, in which case ... |
We begin with a definition:
Definition 1.4.1 A
partition of a set $S$ is acollection of non-empty subsets $A_i\subseteq S$, $1\le i\le k$ (the parts of the partition), such that $\bigcup_{i=1}^k A_i=S$ andfor every $i\not=j$, $A_i\cap A_j=\emptyset$.
Example 1.4.2 The partitions of the set $\{a,b,c\}$ are $\{\{a\},\{b\... |
There are a number of solutions to this problem online that use identities I have not been taught. Here is where I am in relation to my own coursework:
$ \sin(z) = 2 $
$ \exp(iz) - \exp(-iz) = 4i $
$ \exp(2iz) - 1 = 4i \cdot \exp (iz) $
Then, setting $w = \exp(iz),$ I get:
$ w^2 - 4iw -1 = 0$
I can then use the quadrat... |
Which of these terms is greater ?
$2x-6y+1$ or $1$
if $x^4 + 3y^2=0$
According to the text they are equal ?How is that ?
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 up to join this community
Wh... |
I'm stuck with finding the recursion relation of this differential equation using the power series method. So I started by setting: $$y(x)=\sum\limits_{n=0}^{\infty}{a_n x^n} \\ e^x=\sum\limits_{n=0}^{\infty}{\dfrac{x^n}{n!}}$$
But when I implemented this in the equation, I got stuck with finding the recursion relation... |
Let's first address your comment in response to Igor Rivin's answer: why don't we find this topic addressed in textbooks on Lie groups? Beyond the definite (= compact) case, disconnectedness issues become more complicated and your question is thereby very much informed by the theory of linear algebraic groups $G$ over ... |
Alladi Ramakrishnan Hall
Spinoriality of Representations of Lie Groups
Steven Spallone
IISER Pune
Let $G$ be a connected semisimple complex Lie group and $\pi: G \to SO(V)$ an orthogonal representation with highest weight $\lambda$. We give a polynomial formula in $\lambda$ which determines whether $\pi$ lifts to a hom... |
I recently came across this in a textbook (NCERT class 12 , chapter: wave optics , pg:367 , example 10.4(d)) of mine while studying the Young's double slit experiment. It says a condition for the formation of interference pattern is$$\frac{s}{S} < \frac{\lambda}{d}$$Where $s$ is the size of ...
The accepted answer is c... |
In general, Weierstrass is probably a good idea for such trigonometric integrals. However, your progress left the denominator much more manageable. I would start as in David H's answer up until the step
$$\frac12\int\frac{\sin\theta-\cos\theta}{1+\sin\theta}d\theta$$
Instead of Weierstrass from here, simply multiply by... |
Answer
The male actors can be selected in 116,280 ways for four roles.
Work Step by Step
We know that the order in which the four actors are selected makes a difference as the all the actors would be cast for a different role. Since the order matters, we use permutations. The four officers are to be selected from a clu... |
Coordinate systems are tools that let us use algebraic methods tounderstand geometry. While the
rectangular (also called Cartesian) coordinates that wehave been discussing are the most common, some problems are easier toanalyze in alternate coordinate systems.
A coordinate system is a scheme that allows us to identify ... |
I am working on estimating the position and orientation (pose) of a model (rigid object) from its silhouette in an image. For this, I have constructed an error measure between the model in its pose and the silhouette, which looks roughly like:
$$ \epsilon ( \bar{x} ) = \sum_{\forall i} \| f(\bar{x}, m_i) - s_i \|^2 $$
... |
Interested in the following function:$$ \Psi(s)=\sum_{n=2}^\infty \frac{1}{\pi(n)^s}, $$where $\pi(n)$ is the prime counting function.When $s=2$ the sum becomes the following:$$ \Psi(2)=\sum_{n=2}^\infty \frac{1}{\pi(n)^2}=1+\frac{1}{2^2}+\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{3^2}+\frac{1...
Consider a random binary str... |
The following two facts concerning totally disconnected spaces should (separately) help you demonstrate that your space is totally disconnected.
Fact 1: Every T$_1$-space with a basis consisting of clopen sets ( i.e., every zero-dimensional space) is totally disconnected.
proof. Suppose that $A \subseteq X$ contains at... |
In LaTeX2e,how can I sum two values and assign them to other variable?
I want to compute something like:
var=\textwidth - 1cm
And if both were constants:
var=1+1
TeX - LaTeX Stack Exchange is a question and answer site for users of TeX, LaTeX, ConTeXt, and related typesetting systems. It only takes a minute to sign up.... |
This seems like an interesting question but I am not sure I understand all the details here, so this is more a comment than an answer.Because the preference relation is incomplete, we cannot have a real-valued utility function representing it (recall that indifference is different from indecisiveness because the latter... |
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