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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... |
Using residues, try the contour below with $R \rightarrow \infty$ and $$\lim_{R \rightarrow \infty } \int_0^R \frac{1}{1+r^n} dr \rightarrow \int_0^\infty \frac{1}{1+x^n} dx$$
I've attempted the residue summation, but my sum did not converge.
Mathematics Stack Exchange is a question and answer site for people studying ... |
Suppose you have a fair die with 10 sides with numbers from 1 to 10. You roll the die and take the sum until the sum is greater than 100. What is the expected value of this sum?
Well, you can make numbers from 1 to 110, that's 110 possible states you can be in. That's a large transition matrix, but not intractable. Def... |
Is there somewhere on the internet I can find cosmological redshift data. In particular, I would like to know the redshift around the time when the acceleration of the Universe began to accelerate.
One of the main places where data about galaxies gets aggregated is the NASA Extragalactic Database (NED). For example, he... |
Generic classifications by p-group class
This page will contain results for generic classes of
p-groups. It is very much under construction so the list below is not complete. Contents Cyclic p-groups
Morita equivalence classes are labelled by Brauer trees, but it is at present an open problem as to which Brauer trees a... |
Answer
1.47 kg
Work Step by Step
We know that $v=\frac{l}{t}$ and that v is equal to $\sqrt{\frac{F}{\frac{m}{l}}}$. Thus, we combine these equations to find: $m = \frac{Ft^2}{l} = \frac{78.6\times.585^2}{18.3} = 1.47 \ kg$
You can help us out by revising, improving and updating this answer.Update this answer
After you... |
In this chapter, we will discuss regarding the Density and Hubble parameters.
The Hubble parameter is defined as follows −
$$H(t) \equiv \frac{da/dt}{a}$$
which measures how rapidly the scale factor changes. More generally, the evolution of the scale factor is determined by the Friedmann Equation.
$$H^2(t) \equiv \left... |
Tagged: abelian group
Abelian Group Problems and Solutions.
The other popular topics in Group Theory are:
Problem 616
Suppose that $p$ is a prime number greater than $3$.
Consider the multiplicative group $G=(\Zmod{p})^*$ of order $p-1$. (a) Prove that the set of squares $S=\{x^2\mid x\in G\}$ is a subgroup of the mult... |
As I said in the question
I'm trying to find a injection from B to A.
I managed to do it in the following way: Fix some value for $N$ and distribute the values of the set $B = \Bigl\{1, 2, \ldots, \frac{N(N+1)}{2} \Bigr\}$ on the upper-triangular part of a $N \times N$ matrix. For instance, to $N = 5$, $B$ is $\{1, 2, ... |
Let $\{ P_{\gamma} \}$ be a parametric family of probability measures on $(\Omega, \mathcal{F})$, such that $P_{\gamma} \ll \mu$ for all $\gamma$, for some $\sigma$-finite $\mu$. Consider the Radon-Nikodym densities $\{ \frac{d P_{\gamma}}{d \mu} \}$. By the Halmos-Savage factorization criterion, a $\sigma$-subalgebra ... |
Is it possible to take the log of an independent variable in a Poisson regression? What to I have to be aware of, when doing so? (The results are getting better, when assuming that the independent variable is with log link.)
Thanks for the clarification. I agree with @Greg Snow that any transformation should make sense... |
So I used variation of parameter and concluded that the particular solution follows: $$y_p = 2\cos (2t) \int{\tan (t) \sin (2t) dt} + 2 \sin (2t) \int{\tan(t) \cos(2t) dt}$$ I am not sure how to solve the two integrals $\int{\tan (t) \sin (2t) dt}$ and $\int{\tan(t) \cos(2t) dt}$ since it involves the $2t$ term inside ... |
I'm writing a program to generate solar systems but I'm having trouble calculating the expected temperature of a planet. I have found a formula to calculate this, but I haven't been able to get a remotely correct answer out of it as it doesn't clearly state what units your supposed to use.
This formula I found:
$$4 \pi... |
Why do we sandwich operators in quantum mechanics in such a way that the operator acts on the wavefunction and not on its complex conjugate?
$$ \int\psi^* \hat{F} \varphi = \int (\hat{F}^+ \psi)^* \varphi $$
also, if F is an Hermitian operator $$ \int \Psi \hat{F} \Psi^* = \int \Psi^* \hat{F}\Psi $$
Take the kinetic en... |
In free space, $\rho=0$ and $J=0$, so there are no electromagnetic sources/sinks. Maxwell's equations thus reduce to:
$\nabla\cdot E = 0$
$\nabla\cdot B = 0$
$\nabla\times E = -\frac{\partial B}{\partial t}$
$\nabla\times B = \mu_0\epsilon_0 \frac{\partial E}{\partial t} $
Suppose I was writing a simple simulation to v... |
WDM Filters
OptiLayer provides a unique fully automated approach aimed for automatic design of WDM, DWDM, HDWDM and all other types of filters used in modern telecommunication applications. The approach is based on the combination of ideas from classical design approaches with an integer optimization.
This approach tur... |
Logistic regression is widely used in social and behavioral research in analyzing the binary (dichotomous) outcome data. In logistic regression, the outcome can only take two values 0 and 1. Some examples that can utilize the logistic regression are given in the following.
We use an example to illustrate how to conduct... |
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... |
What is a ramjet? Was it used on the SR-71 Blackbird?
Aviation Stack Exchange is a question and answer site for aircraft pilots, mechanics, and enthusiasts. It only takes a minute to sign up.Sign up to join this community
A jet engine compresses air, heats it by mixing it with fuel and burns it, and lets the heated air... |
Published March 2002,February 2011.
When in 1821 the English mathematician Charles Babbage invented what we now recognise as the grandfather of the modern computer he called it the 'Difference Engine' since it was intended to take over the work of making mathematical tables by the techniques described in this article.
... |
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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 ... |
Definitions
The line integral of a vector function \(\mathbf{F} = P\mathbf{i} + Q\mathbf{j} + R\mathbf{k}\) is said to be path independent, if and only if \(P,\) \(Q\) and \(R\) are continuous in a domain \(D,\) and if there exists some scalar function \(u = u\left( {x,y,z} \right)\) in \(D\) such that
\[
{\mathbf{F} =... |
Interior-Point Method
In this post the interior point method described in [1] will be discussed. This algorithm solve the nonlinearly constrained optimization problem:
\begin{eqnarray} \min_x && f(x), \\
\text{subject to } && c_E(x) = 0,\\ && c_I(x) \le 0, \end{eqnarray}
where $x\in \mathbb{R}^n$ is a vector of unknown... |
I suppose you actually suggest
independent hugh haphazard aspects; should they be not really separate, then an answer will have to possibly be conveyed with regards to the articulation submission. Solve for \(k: e Means \dfrac 04.1\) years With Example, the length of a definite computer aspect gets the rapid circulatio... |
Exercise: Suppose a random sample of size n is drawn from a normal pdf where the mean $\mu$ is known ut the variance $\sigma^{2}$ is unknown. Use the method of maximun likelihood to find a formula for $\hat \sigma^2$ Compare your answer to the maximun likelihood estimator found in Example $5.2.4$
I already this this pr... |
Various geometrical figures in three-dimensional space can be described relative to a set of mutually orthogonal axes O\(x\), O\(y\), O\(z\), and a point can be represented by a set of rectangular coordinates \((x, y, z)\). The point can also be represented by cylindrical coordinates \(( ρ , \phi , z)\) or spherical co... |
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... |
My first post of this question is now not on the first page, so I thought I would repost it.
Find all possible integer values of \(z\) such that the following system of equations has a solution for \(z\):
\(\begin{align*} z^n &= 1, \\ \left(z + \frac{1}{z}\right)^n &= 1. \end{align*}\)
Edit: \(z\) can be a complex numb... |
The two operators are not identical, however they approach to each other in the semiclassical limit. To show that, we can compute matrix elements of the two expressions in a complete set of states and show that the matrix elements approach each other. (Strictly speaking this is weak convergence).
I'll perform the compu... |
I've seen various topics here adressing how to turn math symbols bold, but none of them gives a suitable option for
\mathbb characters, as in
\mathbb{ABC}.
I have tested some options to see which commands turn which symbols in bold. Here is my code:
\documentclass{article}\usepackage{amsmath} % some math-related packag... |
Continuity and Differentiability Second Order Derivative
If f'(
x) is differentiable, w.r.t. x. Then, the left hand side becomes \frac{d}{dx}\left(\frac{dy}{dx}\right) which is called the second order derivative of y w.r.t. x and is denoted by \frac{d^2y}{dx^2}. The second order derivative of f( x) is denoted by f''( x... |
1. Right triangle has legs with lengths \(\sqrt7\) on the bottom and 1 on the right side. Use this information to find:
\(\begin{align*} &\sqrt{8}\cdot \cos\left(\arctan\left(\sqrt{7}\right)\right), \\ &\sqrt{8} \cdot \cos\left(\arccos\left(\frac{1}{\sqrt{8}}\right)\right), \\ &\sqrt{8} \cdot \sin\left(\arccos\left(\fr... |
Some Definitions
A function \(f\left( x \right)\) defined on an interval \(\left[ {a,b} \right]\) is said to be piecewise continuous if it is continuous on the interval except for a finite number of jump discontinuities (Figure \(1\)).
A function \(f\left( x \right)\) defined on an interval \(\left[ {a,b} \right]\) is ... |
Let $G$ be a real, connected, non-compact, semisimple Lie group with finite center and real rank $1$. Let $G=KAN$ be an Iwasawa decomposition, then $K\subset G$ is a maximal compact subgroup, and $\dim A=1$ (which is the definition of the real rank of $G$ being $1$). Let $M:=Z_K(A)$ be the centralizer of $A$ in $K$. No... |
Answer
The work done by the crate is approximately $1115\text{ foot-pounds}$.
Work Step by Step
The amount of work done by a force $\mathbf{F}$ on an object from a point A to the point B is denoted by $W=\mathbf{F}\cdot \overrightarrow{AB}$. That is $W=\left\| \mathbf{F} \right\|\overrightarrow{\left\| AB \right\|}\cos... |
257 0
Greetings,
I stumbled across two question that I have no idea on how to answer them.
1) The interaction term in a scalar field theory is [tex]-\frac{\lambda}{4!} \phi^4[/tex]
Why should lambda be positive? (they say look at the energy of the ground state...)
2) Write down the Feynman rules for phi^4
I have no clu... |
I'm currently reading "SAVING RATES AND POVERTY: THE ROLE OF CONSPICUOUS CONSUMPTION AND HUMAN CAPITAL" by Omer Moav and Zvika Neeman, and I encounter some problem deriving one of the equations.
Utility function, where $y$ is income, $\widetilde y$ is the belief of $y$ based on $x$ and human capital $h$, $x$ is the pro... |
Alpha decay: $(Z,A) \rightarrow (Z-2,A-4)+ ^4_2He $
According to the book: "Nuclear and particle physics" by Williams, $Q_\alpha$ is the measure of available energy to permit an alpha decay.
It is defined as:
$$ Q_\alpha = M(Z,A)-M(Z-2,A-4)-M(2,4)$$
(in natural units)
where M is the nuclear mass, defined as: $M(Z,A) = ... |
Determinants Area of a Triangle The area of a triangle whose vertices are (x 1, y 1), (x 2, y 2) and (x 3, y 3), is given by
\Delta=\frac{1}{2}\begin{vmatrix}x_{1} & y_{1} & 1 \\x_{2} & y_{2} & 1 \\x_{3} & y_{3} & 1 \end{vmatrix}
Since area is a positive quantity, we always take the absolute value of the determinant. I... |
I'm currently a third year maths undergrad, writing a dissertation on the application of minimal surfaces in space.
I have recently come across the Penrose Conjecture that the mass of a spacetime is:
$$ m \geq \sqrt{\dfrac{A}{16 \pi}}.$$
What significance does this have in terms of the geometry of a black hole? Also ho... |
Let’s recall Morera’s theorem.
Suppose that \(f\) is a continuous complex-valued function in a connected open set \(\Omega \subset \mathbb C\) such thatMorera’s theorem
\[\int_{\partial \Delta} f(z) \ dz = 0\] for every closed triangle \(\Delta \subset \Omega \setminus \{p\}\) where \(p \in \Omega\). Then \(f\) is holo... |
Background: In machine learning, we often work with graphical models to represent high dimensional probability density functions. If we discard the constraint that a density integrates (sums) to 1, we get an unnormalized graph-structured energy function.
Suppose we have such an energy function, $E$, defined on a graph ... |
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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 ... |
I found what I believe is a valid solution to the following assignment problem but the answer is bothering me.
Let $$H_0(z) = 1+2z^{-1}+3z^{-2}+2z^{-3}+z^{-4}\quad\textrm{and}\quad H_1(z)=H_0(-z).$$
Find causal FIR filters $F_0(z)$ and $F_1(z)$ such that $\hat{x}(n)$ agrees with $x(n)$ except for a possible delay and (... |
We have an equilibrium mixture for the reaction
$$\ce{CO (g) + Cl2 (g) <=> COCl2 (g)}$$
We should recognize that
$$K_\mathrm{eq} = \frac{[\text{products}]}{[\text{reactants}]} = \frac{[\ce{COCl2}]}{[\ce{CO}][\ce{Cl2}]}$$
Note that the reactants and products all have stoichiometric coefficients of 1 so we can write our ... |
I know how to derive Navier-Stokes equations from Boltzmann equation in case where bulk and viscosity coefficients are set to zero. I need only multiply it on momentum and to integrate it over velocities.
But when I've tried to derive NS equations with viscosity and bulk coefficients, I've failed. Most textbooks contai... |
If we assign probabilities to every elementary event such that they sum up to 1 and they're all positive, can we say that this function is a probability function with its domain equal to the set of all subsets of the union of those elementary events? Or should we also specify that P(A or B) = P(A) + P(B) for all A, B w... |
Perhaps it would be helpful to remind ourself of some of the basic properties of orthogonal bases. Let's for this purpose assume the $\{|i\rangle\}$ represents an orthogonal basis of a vector space $V$. In addition to the orthogonality condition$$ \langle j|i\rangle=\delta_{ij} , $$we also have the completeness conditi... |
Normal Nilpotent Matrix is Zero Matrix Problem 336
A complex square ($n\times n$) matrix $A$ is called
normal if \[A^* A=A A^*,\] where $A^*$ denotes the conjugate transpose of $A$, that is $A^*=\bar{A}^{\trans}$. A matrix $A$ is said to be nilpotent if there exists a positive integer $k$ such that $A^k$ is the zero ma... |
On separation of gradient Young measures 43 Downloads Citations Abstract.
Let \(E\subset M^{N\times n}\) be a linear subspace of real \(N\times n\) matrices without rank-one matrices and let \(K = \{A_i\}_{i = 1}^m\subset E\) be a finite set. Suppose \(\Omega \subset \mathbb R^n\) is a bounded arcwise connected Lipschi... |
$PdV$ is boundary work. $VdP$ is
isentropic shaft work in pumps (as you have identified above), gas turbines, etc. Now you must realize that even in a pump or turbine the mechanism of work is still $Pdv$, i.e., the gas pushing on the blade out of its way. But, then there is work required to maintain the flow in and out... |
The Strauss Point Process Model
Creates an instance of the Strauss point process model which can then be fitted to point pattern data.
Keywords spatial Usage
Strauss(r)
Arguments r The interaction radius of the Strauss process Details
The (stationary) Strauss process with interaction radius $r$ and parameters $\beta$ a... |
Algebraic Geometry Seminar Fall 2016
The seminar meets on Fridays at 2:25 pm in Van Vleck B305.
Here is the schedule for the previous semester.
Contents Algebraic Geometry Mailing List Please join the AGS Mailing List to hear about upcoming seminars, lunches, and other algebraic geometry events in the department (it is... |
In fact
any flat coherent sheaf is locally free; see Tag 00NX implication $(1) \Rightarrow (6)$ for the corresponding algebra statement.
Thus, if $\mathscr F$ is flat over $T$, then $\mathscr F$ is locally free over $T$. But because $X_T \to T$ is an isomorphism, we conclude that $\mathscr F$ is locally free on $X_T$ (... |
Given vectors $a_1, \dots, a_n\in \mathbb R^d$ where $n$ is even, I want to find partitions $I$ and $J$ of $[n]$ with $|I|=|J|=\frac n2$ to minimize $$\left\| \sum_{i\in I} a_i - \sum_{j\in J} a_j \right\|.$$ This problem can be written as a binary optimization problem. Given matrix $A = [a_1 \dots a_n]$, I want to min... |
Let $C$ be a cocomplete category. Suppose that $X : A \to B$ is a functor, where $A$ is small. Then every functor $F : A \to C$ admits a left Kan extension $\mathrm{Lan}_X(F) : B \to C$, defined by mapping $b \in B$ to $\mathrm{colim}_{X(a) \to b} F(a)$. The action on morphisms is as follows: If $\iota_{\sigma} : F(a) ... |
Suppose $k$ is a number field and $\sigma:k \hookrightarrow \mathbb{C}$ is an embedding. If $\sim$ is an adequate equivalence relation, we can construct the category of pure motives with rational coefficients, $\textbf{M}_{\sim}(k,\mathbb{Q})$. Let the Hodge realisation functor be $R$, \begin{equation} R:\textbf{M}_{\s... |
When we talked about thin film interference, we said that when light encounters a smooth interface between two transparent media, some of the light gets through, and some bounces off. There we limited the discussion to the case of normal incidence. (Recall that normal means perpendicular to and normal incidence is the ... |
The
electron-volt is a unit of energy or work. An electron-volt (eV) is the work required to move an electron through a potential difference of one volt. Alternatively, an electronvolt is equal to the kinetic energy acquired by an electron when it is accelerated through a potential difference of one volt. Since the mag... |
Let $a>0$. Show that $$\int_0^\pi {dx\over a+\sin^2(x)}={\pi\over \sqrt{a(a+1)}}.$$
I'm not sure how to show this. Any help is greatly appreciated.
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 u... |
I don't think it is difficult to derive analytically the shape of the Earth. Simply look for the shape of the surfaces of equal potential.
The geometrical symmetry reduces the calculation to a 2-dimensional problem. Assume the rotation axis is vertical. The potential is the sum of the gravitational plus centrifugal:
$\... |
Definition and Methods of Solution
An equation of type
\[F\left( {x,y,y’} \right) = 0,\]
where \(F\) is a continuous function, is called the first order implicit differential equation.
If this equation can be solved for \(y’,\) we get one or several explicit differential equations of type
\[y’ = f\left( {x,y} \right),\... |
Gated Recurrent Units (GRUs)
Gated Recurrent Units (GRUs) are a form of RNN which can capture long range dependencies in a sequential data.
A typical RNN unit is represented as the following equation:
$a^{\langle t \rangle}$ = tanh($W_a [a^{\langle t-1 \rangle},x^{\langle t \rangle}] + b_a)$
Sentences:
(1) The cat, whi... |
10:25 PM
Suppose $f,g : [-\infty, \infty] \to [- \infty, \infty]$ are measurable. Prove that the sets $\{x \mid f(x) < g(x) \}$ and $\{x \mid f(x) = g(x)\}$ are measurable.
The first is measurable because $\{x \mid f(x) < g(x) \} = \bigcup_{q \in \Bbb{Q}} \bigg[ \{x \mid f(x) < q \} \cap \{x \mid q < g(x)\} \bigg]$; i.... |
My code solves the incompressible Navier-Stokes equation in a conducting fluid, together with the induction equation:
$ \partial_t u + u \nabla u + 2\Omega \times u = -\nabla p + \nu \Delta u + (\nabla \times b) \times b \\ \partial_t b = \nabla \times (u \times b) + \eta \Delta b$
where $u$ and $b$ are the velocity an... |
Boundary bubbling solutions for a planar elliptic problem with exponential Neumann data
1.
School of Mathematics, Zhejiang University, Hangzhou 310027, China
2.
College of Sciences, Nanjing Agricultural University, Nanjing 210095, China
$\mathbb{R}^2 $
$\left\{ \begin{gathered} \begin{gathered} - \Delta \upsilon + \ups... |
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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 ... |
$L$ isn't recognizable. We'll first establish a couple of preliminary results
I. $\overline{L}$ is recognizable
The complement of $L$,$$\overline{L}=\{\langle M\rangle\mid M \text{ halts on at least one input}\} $$is recognizable. Define a recognizer TM as follows:
R(<M>) =
for n = 1, 2, 3, ...
for each x in {x_1, x_2,... |
Tagged: determinant Problem 548
An $n\times n$ matrix $A$ is said to be
invertible if there exists an $n\times n$ matrix $B$ such that $AB=I$, and $BA=I$,
where $I$ is the $n\times n$ identity matrix.
If such a matrix $B$ exists, then it is known to be unique and called the
inverse matrix of $A$, denoted by $A^{-1}$.
I... |
Notice:
If you happen to see a question you know the answer to, please do chime in and help your fellow community members. We encourage our fourm members to be more involved, jump in and help out your fellow researchers with their questions. GATK forum is a community forum and helping each other with using GATK tools a... |
We can of course also define a four-vector version of the acceleration, by taking the derivative of the four-velocity with respect to the proper time. As with the forces, we’ll see that we’re in for some nasty surprises, this time because the proper time derivative acts on the \(\gamma(u)\) factor in the velocity as we... |
I am following along well several textbooks (Geophysics) that helps me understand the in-depth physics behind the magnetic field of a dipole magnet. I understand that the basic magnetic potential (when observing a dipole magnet where the one of the poles is far enough to have negligible effect on its partner is:
$$W= -... |
Let $T: \R^n \to \R^m$ be a linear transformation.Suppose that the nullity of $T$ is zero.
If $\{\mathbf{x}_1, \mathbf{x}_2,\dots, \mathbf{x}_k\}$ is a linearly independent subset of $\R^n$, then show that $\{T(\mathbf{x}_1), T(\mathbf{x}_2), \dots, T(\mathbf{x}_k) \}$ is a linearly independent subset of $\R^m$.
Let $V... |
Latent Distribution Two-Graph Testing¶
[1]:
import numpy as npimport matplotlib.pyplot as pltnp.random.seed(8888)from graspy.inference import LatentDistributionTestfrom graspy.embed import AdjacencySpectralEmbedfrom graspy.simulations import sbm, rdpgfrom graspy.utils import symmetrizefrom graspy.plot import heatmap, p... |
How to solve these equations using an algebraic method? I need to show my working, don't you do something in reverse, like 7 multiplies by something. I haven't done it in class.
$$\dfrac{5(3y-4)}{2y}=7$$
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in ... |
A body in free motion does not necessarily rotate about the center of mass. The center of mass might have straight linear motion in addition any rotation. The general motion is a screw motion with a rotation about some instantaneous axis and parallel translation at the same time.
Consider an arbitrary body rotating by ... |
The Annals of Applied Probability Ann. Appl. Probab. Volume 5, Number 1 (1995), 128-139. Minimal Positions in a Branching Random Walk Abstract
We consider a branching random walk on the real line, with mean family size greater than 1. Let $B_n$ denote the minimal position of a member of the $n$th generation. It is know... |
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Change to browse by: References & Citations Bookmark(what is this?) Mathematics > Commutative Algebra Title: Totalseparierte Moduln
(Submitted on 1 Apr 2015)
Abstract: Let $(R, \mathfrak{m})$ be a noetherian local ring, $M$ a separated $R$-module (i.e. $\bigcap\limits_{n\geq 1}\mathfrak{... |
উইকিবই:রচনাশৈলী
নিম্নলিখিত উইকিবই:নীতিমালা ও নির্দেশাবলী সম্পর্কিত পাতাটি বর্তমানে ইংরেজিতে আছে বা অনুবাদের কাজ চলছে। দয়া করে এটি অনুবাদ করে আমাদেরকে সহায়তা করুন। যদি অনুবাদ করা শেষ হয়ে থাকে এই নোটিশটি সরিয়ে নিন।
This page contains a draft proposal for a Wikibooks policy or guideline. Discuss changes to this draft ... |
Definition of the Lyapunov Function
A Lyapunov function is a scalar function defined on the phase space, which can be used to prove the stability of an equilibrium point. The Lyapunov function method is applied to study the stability of various differential equations and systems. Below, we restrict ourselves to the aut... |
Layer Sensitivity
The
You can specify relative errors in layer thicknesses on
For each disturbed design, the variations \(\Delta MF_i\) with respect to design target
\[ \Delta MF_i=|MF(d_1,...,d_i(1+\delta_{H,L}),...,d_m)-MF(d_1,...,d_m)|\]
or to theoretical spectral characteristic \(S\) (Eq.(2)):
\[ \Delta MF_i=|S(d_1... |
18 0 Density?! Thinking of it as mass was only an analogy so that you could know to apply the moment of annulus formula, or parallel axis theorem, or whatever. In post #14 you had ##\sigma\omega\tau r^2B^2\int dA##. But the r should have been inside the integral: ##\sigma\omega\tau B^2\int r^2dA##. That integral is the... |
berylium? really? okay then...toroidalet wrote:I Undertale hate it when people Emoji movie insert keywords so people will see their berylium page.
A forum where anything goes. Introduce yourselves to other members of the forums, discuss how your name evolves when written out in the Game of Life, or just tell us how you... |
Let $k\geq2$ be an integer, a graph $G=(V,E)$ is called $k$-partite if $V$ admits a partition into $k$ classes such that every edge of $G$ has its ends in different classes: vertices in the same class must not be adjacent.
Now let $G=(V,E)$ be $k$-partite and $V_1,V_2,\cdots,V_k$ be the $k$ classes into which $V$ Is pa... |
DA recognizes some frequently used values of a multiply-and-accumulate operation, pre-computes these values, and stores them in a lookup table (LUT). Reading these stored values from ROM rather than calculating them leads to an efficient implementation. It should be noted that the DA method is applicable only to cases ... |
CryptoDB Paper: Approx-SVP in Ideal Lattices with Pre-processing
Authors: Alice Pellet-Mary Guillaume Hanrot Damien Stehlé Download: DOI: 10.1007/978-3-030-17656-3_24 Search ePrint Search Google Abstract: We describe an algorithm to solve the approximate Shortest Vector Problem for lattices corresponding to ideals of t... |
Solutions Solubility and Henry's Law, Ideal and Non-Ideal Solutions, Vapour Pressure and Raoult's Law Solubility & Henry's law: Solution of gas in liquid:- (1) In these solutions gas is solute and liquid is solvent (2) The solubility of a gas in a liquid is influenced by the following factors.
(a)
Nature of the gas: Ea... |
Let me answer the second query.
We know $$\mathbf{ B}=\text{curl}\;\mathbf{ A} $$ where $\bf B$ is the magnetic field & $\bf A$ is vector-potential.
Now, using Maxwell's equation, we get $$\text{curl}\;(\text{curl}\; \mathbf A)= \mu_0 \mathbf J . $$ By cracking a bit-algebra, we get, $$-\frac{\partial^2 A_x}{\partial x... |
Period is independent of amplitude. (Vias.org)
But given that,
Simple harmonic motion can be defined by
$$x = A * \sin(\omega t) \tag{1}$$ where $A$ is the amplitude of oscillation, $\omega$ the angular velocity, $t$ the time, and $x$ the displacement from the mean position
And,
$$T = 2 \pi/\omega = 1/f \tag{2}$$ where... |
1IntroductionIn the theory of ordinary differential equations and in particular in the theory of Hamiltonian systems the existence of first integrals is important, because they allow to lower the dimension where the Hamiltonian system is defined. Furthermore, if we know a sufficient number of first integrals, these all... |
In this section we derive how the gas pressure \(P\) depends on the height over sea level \(h\) in the gravitational field of Earth.
If we take an arbitrary gas column with intersection area \(S\) and height \(h,\) then the weight of this column is given by
\[{F = mg = \rho gV }={ \rho ghS,}\]
where \(\rho\) is the gas... |
A railway train trundles towards the east at speed \( \nu_{1}\), and a passenger strolls towards the front at speed \( \nu_{2}\). What is the speed of the passenger relative to the railway station? We might at first be tempted to reply: “Why, \( \nu_{1}+\nu_{2}\) of course.” In this section we shall show that the answe... |
There are many circumstances in which we need to determine the frequency content of a time-domain signal. For example, we may have to analyze the spectrum of the output of an LC oscillator to see how much noise is present in the produced sine wave. This can be achieved by the discrete Fourier transform (DFT). The DFT i... |
Properties of the algorithm: Sequential complexity: [math]O(n^3)[/math] Height of the parallel form: [math]O(n)[/math] Width of the parallel form: [math]O(n^2)[/math] Amount of input data: [math]\frac{n (n + 1)}{2}[/math] Amount of output data: [math]\frac{n (n + 1)}{2}[/math] 1 Properties and structure of the algorith... |
I have a question about the moments generated by torsional springs. Consider an inertial reference frame A and a body fixed reference frame B. The frames are connected by 3 rotational springs acting around all three axes.
For a simple rotation $\psi$ around the $Z_B$-axis the moment will be in the negative $Z_B$ direct... |
There is a huge strand of literature on graph theory in finance which analyzes networks summarized here:Allen, F., and A. Babus (2009): “Networks in Finance,” in Network-based Strategies and Competencies, ed. by P. Kleindorfer, and J. Wind, pp. 367–382.First applications of graph theory in networks focused on credit-ri... |
I don't think I am putting out something truly novel here either; the answer by @MAFIA36790 and the discussion in the link you yourself post it seem quite satisfactory to me, yet I shall try to put a different spin on things so to speak.
Let me define the chemical potential, as the partial molar Gibbs energy of species... |
Diff. Geom, Math. Phys., PDE Seminar: Ali Hyder Date: 11/14/2017 Time: 15:30
University of British Columbia
Conformal metrics on \mathbb{R}^n with arbitrary total Q-curvature
I will talk about the existence of solution to the Q-curvature problem
\begin{align}\label{1}
(-\Delta)^\frac n2 u=Qe^{nu}\quad\text{in }\mathbb{... |
I'm trying to typeset the following
$Q_å=l_å \cdot m$
But LaTeX won't typeset these special or accented letters in my document! Is there a simple way to achieve this?
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 sig... |
Calculations
In this question, I solved for the stresses on an spacecraft passing close to a black hole's event horizon. There isn't some magical barrier that you go through around an event horizon, you just can't get out; you probably wouldn't even notice. I can use the same process to calculate the stresses that a pr... |
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