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Abbreviation:
CMon
A
is a monoids $\mathbf{M}=\langle M,\cdot,e\rangle $ such that commutative monoid
$\cdot $ is commutative: $x\cdot y=y\cdot x$
A
is a structure $\mathbf{M}=\langle M,\cdot,e\rangle $, where $\cdot $ is an infix binary operation, called the commutative monoid , and $e$ is a constant (nullary operatio... |
I have been searching everywhere online on how to approach these questions. But every example I find, it is said in the question what the density function is. That is what I'm struggling to find with this question, which is as follows:
The density $\rho$ (mass per unit area) of a semi-circular lamina $\Omega$ of radius... |
Measurements of inclusive neutral diboson production with ATLAS
Pre-published on: 2019 July 23
Published on: 2019 October 04
Abstract
We present recent measurements of $ZZ$ and $Z\gamma$ production in proton-proton collisions at $\sqrt{s}=13$ TeV with the ATLAS experiment at LHC. The unfolded differential cross section... |
Current Electricity Combination of Resistors-Series and Parallel R series= R 1+ R 2+ R 3+ ……. When 'n' identical resistances are connected R series= nR. When resistances are connected in series V 1: V 2: V 3= R 1: R 2: R 3. When resistances are connected in series V = V 1+ V 2+ V 3. In parallel combination potential is... |
The halting problem states there is no algorithm that will determine if a given program halts. As a consequence, there should be programs about which we can not tell whether they terminate or not. What are the simplest (smallest) known examples of such programs?
A pretty simple example could be a program testing the Co... |
In Chapter 1: Functions and limits, 1.7 The Precise Definition of a Limit,
Let $f$ be a function ... the limit of $f(x)$ as $x$ approaches $a$ is $L$, and we write $$\lim_{x\to a }f(x)=L$$ if for every number $\epsilon>0$ there is a number $\delta>0$ such that if $0<|x-a|<\delta$ then $|f(x)-L|<\epsilon$.
OK, let's ass... |
How can I calculate the $\alpha$ and $\beta$ parameters for a Beta distribution if I know the mean and variance that I want the distribution to have? Examples of an R command to do this would be most helpful.
I set$$\mu=\frac{\alpha}{\alpha+\beta}$$and$$\sigma^2=\frac{\alpha\beta}{(\alpha+\beta)^2(\alpha+\beta+1)}$$and... |
Electrochemistry Specific conductivity, Equivalent conductivity Specific conductance (K): (i) In C.G.S system: The conducting power of all the ions that are present in 1 cm 3of a solution is called specific conductance. (ii) In M.K.S: The conducting power of all the ions that are present in 1 m 3of a solution is called... |
There are some special functions of 3 or more complex variables that are analytic in some domain (a region in $\mathbb C^n$) with respect to each variable. To give some examples: the incomplete beta function $B(z; a, b)$, the Lerch transcendent $\Phi(z, s, a)$, the Weierstrass elliptic function $\wp(z;g_2,g_3)$, hyperg... |
Continuing with the trigonometry theme, there are other relationships between the angles and the length of the sides of a right triangle. You may have a calculator with buttons labeled as “sin” or “sin
x” or “sin θ”. There would be similar buttons using the prefix “cos” and “tan”. These are the basic trig (trigonometri... |
I'm doing some simulations with phase separations and I have a field $\phi(\mathbf{r},t)$ that takes values in $\phi\in \mathbb{R}$.
What I'd like to do is to obtain the number of separated domains $N(t)$. Let's define a separated domain a connected region for which $\phi_0\leq\phi$.
So I'm looking for an expression $f... |
skills to develop
To understand how to use a chi-square test to judge whether a sample fits a particular population well.
Suppose we wish to determine if an ordinary-looking six-sided die is fair, or balanced, meaning that every face has probability \(1/6\) of landing on top when the die is tossed. We could toss the di... |
The "Elements" of modern lattice theory, from which the terminology spread is Birkhoff's Lattice Theory (1940). After defining lattices and introducing cups and caps (rather than wedges and vees) for inf and sup he says the following on the subject of meets and joins (p.17):
"
A large fraction of the most important par... |
Reference documentation for deal.II version 8.4.1
template<int dim> std::pair< double, double > adjust_refine_and_coarsen_number_fraction (const unsigned int current_n_cells, const unsigned int max_n_cells, const double top_fraction_of_cells, const double bottom_fraction_of_cells) template<int dim, class VectorType , i... |
You can gain some useful insights by visualizing your budget, but creating a chart like the one above this isn’t always worth the effort. That’s why I created a tool called Budgeteer that makes it easy make these charts without tedious work. In this post, I’d like to talk a little bit about how to use the tool as well ... |
I’m starting to feel like the Rocky movie series – will I get to part 7?
Here are more examples of adding fractions with different denominators:
\[ \frac{4}{15}\hspace{0.33em}{+}\hspace{0.33em}\frac{3}{5} \]
So two different denominators. We have to find equivalent fractions that have the same denominator before we can... |
Without loss of generality, we can assume that $M = R/I$, $x = 1 + I$ where $I$ is a proper non-zero ideal of $R$ and $\mathfrak{m}$ is any maximal ideal of $R$ containing $I$ (recall that $R$ is one-dimensional).
We will also assume that
(Condition IIPM) $I$ can be represented as an irredundant intersection $\bigcap_{... |
It is not an answer, but just some hints.
Consider the simplest free QFT with a massless bosonic scalar, the terms in the Lagrangian are local : $\phi(x) \square \phi(x)$. Considering an interacting theory ($\phi^3, \phi^4$). You are interested in calculate scattering amplitudes with incoming particles and outcoming pa... |
To describe the evolution of a (in this example non-relativistic) fluid system, the evolution equations for all relevant variables, conservation laws, the second law of thermodynamics, and appropriate (a)n appropriate equation(s) of state have to be considered.
The evolution equation for momentum is the Navier-Stokes e... |
A particle moves along the x-axis so that at time t its position is given by $x(t) = t^3-6t^2+9t+11$ during what time intervals is the particle moving to the left? so I know that we need the velocity for that and we can get that after taking the derivative but I don't know what to do after that the velocity would than ... |
This is a typical
Euclidean descent. The set $M$ of all positive common multiples of $\,a,b\,$ is closed under positive subtraction, i.e. $\,m> n\in M$ $\Rightarrow$ $\,a,b\mid m,n\,\Rightarrow\, a,b\mid m\!-\!n\,\Rightarrow\,m\!-\!n\in M.\,$ Therefore, further, $\,M\,$ is closed under mod, i.e. remainder, since it ari... |
I was told that Weil reciprocity theorem (one has two meromorphic function $f,g$ on a complex curve $C$, so $\prod\limits_{x\in C} g(x)^{ord_xf}=\prod\limits_{x\in C}f(x)^{ord_xg} \ $ where $ord_xf$ is the smallest degree in Taylor expansion of $f$ at $x$, product is taken only by points in divisors of $f,g$, we assume... |
The object you're talking about is called, in mathematics, a Clifford algebra. The case when the algebra is over the complex field in general has a significantly different structure from the case when the algebra is over the real field, which is important in Physics.
In Physics, in the specific case of 4 dimensions, us... |
I’d like to talk a bit about using
information theory to quantify the intuition that a complex system exhibits structure at multiple scales of organization. My friend and colleague Ben Allen wrote an introduction to this a while ago: “Information and structure in complex systems,” Plektix(24 October 2014).
Ben’s blog p... |
Find Matrix Representation of Linear Transformation From $\R^2$ to $\R^2$ Problem 370
Let $T: \R^2 \to \R^2$ be a linear transformation such that
\[T\left(\, \begin{bmatrix} 1 \\ 1 \end{bmatrix} \,\right)=\begin{bmatrix} 4 \\ 1 \end{bmatrix}, T\left(\, \begin{bmatrix} 0 \\ 1 \end{bmatrix} \,\right)=\begin{bmatrix} 3 \\... |
Ascending Chain of Submodules and Union of its Submodules
Problem 416
Let $R$ be a ring with $1$. Let $M$ be an $R$-module. Consider an ascending chain\[N_1 \subset N_2 \subset \cdots\]of submodules of $M$.Prove that the union\[\cup_{i=1}^{\infty} N_i\]is a submodule of $M$.
Torsion Submodule, Integral Domain, and Zero... |
To show that the matrix $A$ is nonsingular, it suffices to prove that $\det(A)\neq 0$.
One way is to compute the determinant of $A$ directly.
However, as the numbers in $A$ are quite large for hand computation, the direct calculation must be tedious.
So we consider an alternative method.Note that we do not have to find... |
Skills to Develop
To become familiar with the concept of the probability distribution of the sample mean. To understand the meaning of the formulas for the mean and standard deviation of the sample mean.
Suppose we wish to estimate the mean \(μ\) of a population. In actual practice we would typically take just one samp... |
it seems to be possible that you can get the Thomas Precession just through the commutation relations of the Lorentz group. With Thomas Precession i mean, that in general the product of two boosts is a boost with a rotation. The exercise 15b) in this book Lie Groups, Lie Algebras, and Some of Their Applications formula... |
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D-meson nuclear modification factor and elliptic flow measurements in Pb–Pb collisions at $\sqrt {s_{NN}}$ = 5.02TeV with ALICE at the LHC
(Elsevier, 2017-11)
ALICE measured the nuclear modification factor ($R_{AA}$) and elliptic flow ($\nu_{2}$) of D mesons ($D^{0}$, $D^{+}$, $D^{⁎+}$... |
A particle moves along the x-axis so that at time t its position is given by $x(t) = t^3-6t^2+9t+11$ during what time intervals is the particle moving to the left? so I know that we need the velocity for that and we can get that after taking the derivative but I don't know what to do after that the velocity would than ... |
"The general set theory [...] definitely belongs to metaphysics. You can easily convince yourself when examining the categories of cardinal numbers and the order type, these basic notions of set theory, on the degree of their generality. [...] and the fact that my presently written work is issued in mathematical journa... |
Maxwell did not think of the displacement current as a continuation of the conduction current, and his motivations are generally entwined with his mechanical models of ether. But the naming itself comes from the analogy between the added term and the polarization field induced by electric field in a dielectric, caused ... |
Electronic Journal of Probability Electron. J. Probab. Volume 19 (2014), paper no. 98, 35 pp. The harmonic measure of balls in critical Galton-Watson trees with infinite variance offspring distribution Abstract
We study properties of the harmonic measure of balls in large critical Galton-Watson trees whose offspring di... |
Tagged: cofactor expansion Problem 718
Let
\[ A= \begin{bmatrix} 8 & 1 & 6 \\ 3 & 5 & 7 \\ 4 & 9 & 2 \end{bmatrix} . \] Notice that $A$ contains every integer from $1$ to $9$ and that the sums of each row, column, and diagonal of $A$ are equal. Such a grid is sometimes called a magic square.
Compute the determinant of ... |
The Oldenburger infinite sequence [O39]\[K = 1221121221221121122121121221121121221221\ldots\]also known under the name of Kolakoski, is equal to its
exponenttrajectory. The exponent trajectory \(\Delta\) can be obtained by countingthe lengths of blocks of consecutive and equal letters:\[K =1^12^21^22^11^12^21^12^21^22^... |
Previously, we have discussed briefly the simple linear regression. Here we will discuss
multiple regression or multivariable regression and how to get the solution of the multivariable regression. At the end of the post, we will provide the python code from scratch for multivariable regression. Motivation
A single var... |
I have a rather convoluted equation in one variable that I am trying to solve, in terms of many other parameters.
Let $$w(x) = Ax^2 - Bx^4, \quad A,B > 0$$ and $$\varphi = \arccos\left(\rho A^{-2/3}\right),\quad \rho < 0\mbox{ fixed}.$$ I choose here $\arccos\in [0,\pi)$.
Let $$b = \sqrt{\frac{2A}{3B}}\cos{\frac{\varph... |
Please consider the following list:
There is a $(K_n)_{n\in\mathbb N}\subseteq E$ with\begin{itemize} \item $K_n$ is compact; \item $K_n\subseteq\overset\circ K_{n+1}$; and \item $d(\partial K_n,\partial K_{n+1})>0$\end{itemize}for all $n\in\mathbb N$.
This doesn't render well:
There's too much vertical empty space bet... |
Basically 2 strings, $a>b$, which go into the first box and do division to output $b,r$ such that $a = bq + r$ and $r<b$, then you have to check for $r=0$ which returns $b$ if we are done, otherwise inputs $r,q$ into the division box..
There was a guy at my university who was convinced he had proven the Collatz Conject... |
Moving charges and magnetism Magnetic Force and Motion in a Magnetic Field When current is flowing through a conductor only magnetic field is produced around the conductor which is non conservative. If charge +q is moving with velocity \tt \overline{V}, making an angle ‘θ’ with the direction of field, force acting on t... |
This question is a follow up to the gorgeous explanation of how the leaky integrator model becomes a differential equation. The link to that question and answer is below.
I have two questions related to the explanation. Hopefully Fat32 will not mind answering but anyone else is great also.
1) At the bottom of the first... |
The problem in short:
I want to estimate (?) a lag-1 Markovian hidden process for offline multi-variate discrete-time time series with continuous distributions via smoothing, with no dimensionality reduction. The emission model is time invariant.
The data that I have:
I have a dataset of multivariate time series of $N ... |
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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 ... |
Is the impulse response of a LINEAR
TIME-VARIANT system unique? I know that it's unique for the L.T.I case!!! Advance thanks for the HELP....
Is the impulse response of a LINEAR
With the input-output relationship of a linear time-varying system given by
$$y(t)=\int_{-\infty}^{\infty}h(t,\tau)x(t-\tau)d\tau\tag{1}$$
it ... |
Now that an answer has been accepted, I'll spell out the method I hinted at in a comment, leaving only a couple of details to fill in. (I haven't even checked the details myself, so it would be unwise to take my word for them!)
For all $a \in \left(0, \frac{\pi}{2}\right)$, the terms of the alternating series$$\sin a =... |
Brewster’s law is a relationship of light waves at the maximum polarization angle of light. This law is named after Sir David Brewster, a Scottish physicist, who proposed the law in the year 1811. The law states that the p-polarized rays vanish completely on different glasses at a particular angle.
Further, the polariz... |
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... |
Mathematics - Functional Analysis and Mathematics - Metric Geometry
Abstract
The following strengthening of the Elton-Odell theorem on the existence of a $(1+\epsilon)-$separated sequences in the unit sphere $S_X$ of an infinite dimensional Banach space $X$ is proved: There exists an infinite subset $S\subseteq S_X$ an... |
I've noticed that when modelling a continuous action space, the default thing to do is to estimate a mean and a variance where each is parameterized by a neural network or some other model.
I also often see that it is one network $\theta$ models both. The REINFORCE objective can be written as
$$\nabla \mathcal{J}(\thet... |
Here is a closely related pair of examples from operator theory, von Neumann's inequality and the theory of unitary dilations of contractions on Hilbert space, where things work for 1 or 2 variables but not for 3 or more.
In one variable, von Neumann's inequality says that if $T$ is an operator on a (complex) Hilbert s... |
Let $X$ be a topological space endowed with a triangulation $K$. We say that $X$ is a $n$-
dimensional pseudomanifold, if $X$ is the union of all $n$-simplices Every $(n-1)$-simplex is a face of exactle two $n$-simplices for $n>1$ For every pair of $n$-simplices $\sigma$ and $\tau$ in $K$, there is a sequence of $n$-si... |
Skills to Develop
To study the use of G–test of goodness-of-fit (also known as the likelihood ratio test, the log-likelihood ratio test, or the G 2test) when you have one nominal variable To see whether the number of observations in each category fits a theoretical expectation, and the sample size is large When to use ... |
A subset $B$ of a vector space $V$ is called a basis if $B$ is linearly independent spanning set.
Proof.
(a) Prove that if the set $B$ is linearly independent, then $B$ is a basis of the vector space $\R^3$.
To show that $B$ is a basis, we need only prove that $B$ is a spanning set of $\R^3$ as we know that $B$ is line... |
Basic Statistics Mean or Average
The mean or average of a set of values is the sum of the values divided by the number of the values. Symbolically,\[ \overline{x} = \frac{1}{N} \sum_{i=1}^{N} x_i \]
The mean of a number of repeated measurements of an experimental quantity is the best estimate of the true value of the q... |
Hydrocarbons Alkanes
Saturated hydrocarbons
General formula C nH 2n + 2 Also called paraffins (little affinity) Types of preparation Kolbe's electrolysis Decarboxylation Coupling reaction Carbides electrolytes Reduction Others Kolbe's electrolysis : Electrolyte : RCOONa, RCOOK
At anode :
\dot{R} + \dot{R} \rightarrow R... |
Let me illustrate the issue with an simplified example. Suppose we want to solve the following problem with finite difference method (FDM):
$$\frac{\partial u(t,x)}{\partial t}=\frac{\partial^2 u(t,x)}{\partial x^2}$$ $$u(0,x)=x(1-x),\ u(t,0)=0$$ $$t\in[0,1],\ x\in[0,1] $$
One boundary condition (b.c.) is missing, but ... |
A Module $M$ is Irreducible if and only if $M$ is isomorphic to $R/I$ for a Maximal Ideal $I$.
Problem 449
Let $R$ be a commutative ring with $1$ and let $M$ be an $R$-module.Prove that the $R$-module $M$ is irreducible if and only if $M$ is isomorphic to $R/I$, where $I$ is a maximal ideal of $R$, as an $R$-module.
An... |
Logistic regression is a statistical method for analyzing a dataset in which there are one or more independent variables that determine an outcome. The outcome is measured with a dichotomous variable (in which there are only two possible outcomes).
${\pi(x) = \frac{e^{\alpha + \beta x}}{1 + e^{\alpha + \beta x}}}$
Wher... |
Let $f:[a,b]\to \mathbb{R}$ be a monotone function (say strictly increasing).
Then, do for every $\epsilon>0$ exist two step functions $h,g$ so that $g\le f\le h$ and $0\le h-g\le \epsilon$?
Does there exist some closed form of these functions like the one below?
I encountered the problem when trying to prove the Riema... |
Andrei fromTudor Vianu National College, Romania, gives a very clear account of the use of the binomial and normal distributions to solve this problem.
The passengers who have bought tickets either turn up for the flight or do not turn up. Taking $X$ as the random variable for the number of passengers who turn up for t... |
Subspace Spanned by Trigonometric Functions $\sin^2(x)$ and $\cos^2(x)$
Problem 612
Let $C[-2\pi, 2\pi]$ be the vector space of all real-valued continuous functions defined on the interval $[-2\pi, 2\pi]$.Consider the subspace $W=\Span\{\sin^2(x), \cos^2(x)\}$ spanned by functions $\sin^2(x)$ and $\cos^2(x)$.
(a) Prove... |
I need some help with understanding a part of this proof and also writing it up correctly. Given $a_n\geq a_{n+1}\geq b_{n+1} \geq b_n$ with $a_1=a$ and $b_1=b$. I am also given that $$a_{n+1}=\frac{a_n+b_n}{2}$$ and $$b_{n+1}=\sqrt{a_nb_n}$$ I need to show that sequences ${a_n}$ and ${b_n}$ converges and that ${a_n}$ ... |
Let $N$ be a positive integer. Are there known estimates for the product of all numbers that are smaller than $N$ and relatively prime with $N$? One can assume that $N$ is free of squares, if this helps.
For the sake of completeness, here is a proof of Gjergji's formula, which is a cute exercise in elementary number th... |
Creating equations in Sphinx¶ LaTeX¶
The syntax for writing equations is LaTeX.
Only brief examples are included here, since LaTeX as a rather steep learning curve, and AMS LaTeX is only concerned with math support.
The following links are useful:
See ftp://ftp.ams.org/pub/tex/doc/amsmath/short-math-guide.pdf for a not... |
Preprints (rote Reihe) des Fachbereich Mathematik Refine Keywords Brownian motion (2) (remove)
303
We show that the intersection local times \(\mu_p\) on the intersection of \(p\) independent planar Brownian paths have an average density of order three with respect to the gauge function \(r^2\pi\cdot (log(1/r)/\pi)^p\)... |
Note that the identity element $e$ of $G$ has order $1$, hence $e\in H$ and $H$ is not an empty set.
To show that $H$ is a subgroup of $G$, we need to show that $H$ is closed under multiplications and inverses.
Let $a, b\in H$.By definition of $H$, the orders of $a, b$ are finite.So let $m, n \in \N$ be the orders of $... |
ISSN:
2156-8472
eISSN:
2156-8499 Mathematical Control & Related Fields
March 2016 , Volume 6 , Issue 1
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Abstract:
We study a damped semi-linear wave equation in a bounded domain of $\mathbb{R}^3$ with smooth boundary. It is proved that any $H^2$-smooth solution can be stabilised loc... |
Steepest descent method on a Riemannian manifold: the convex case
Related Articles An Estimate for a Fundamental Solution of a Parabolic Equation with Drift on a Riemannian Manifold. Bernatska, J. // Siberian Mathematical Journal;May/Jun2003, Vol. 44 Issue 3, p387
We construct a fundamental solution for a parabolic equ... |
I'm interested in a question regarding the identification of some duals of quasi-Banach spaces. However, I'm not familiar with the quasi-Banach literature, so I'm hoping somebody can point me in the right direction regarding a specific question.
First I'll get the definitions out of the way: a quasi-Banach space is a c... |
ISSN:
1556-1801
eISSN:
1556-181X
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Networks & Heterogeneous Media
June 2012 , Volume 7 , Issue 2
Special Issue
on Mean Field Games
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Abstract:
The theory of Mean Field Games (MFG, in short) is a branch of the theory of Differential Games which aims at modeling and analyzing ... |
Eigenvalues and Eigenvectors of Matrix Whose Diagonal Entries are 3 and 9 Elsewhere Problem 379
Find all the eigenvalues and eigenvectors of the matrix
\[A=\begin{bmatrix} 3 & 9 & 9 & 9 \\ 9 &3 & 9 & 9 \\ 9 & 9 & 3 & 9 \\ 9 & 9 & 9 & 3 \end{bmatrix}.\]
(
Harvard University, Linear Algebra Final Exam Problem) Hint.
Inst... |
1.
Vertex-transitive expansions of (1, 3)-treesMarko Lovrečič Saražin
, Dragan Marušič
, 2010, published scientific conference contribution
Abstract: A nonidentity automorphism of a graph is said to be semiregular if all of its orbits are of the same length. Given a graph ▫$X$▫ with a semiregular automorphism ▫$\gamma$... |
Now eventually, I would like to be able to solve equations like \[
{x}^{2}\hspace{0.33em}{-}\hspace{0.33em}{7}\hspace{0.33em}{=}\hspace{0.33em}{18} \]. But you see that if I am to get x by itself, I need something to get rid of the exponent “2”. This is where square roots come in. But let’s first talk about inverse ope... |
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1556-1801
eISSN:
1556-181X
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Networks & Heterogeneous Media
December 2012 , Volume 7 , Issue 4
Special Issue
dedicated to Hiroshi Matano on the occasion of his 60th birthday: Part I
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Professor Hiroshi Matano was born in Kyoto, Japan, on July 28th, 1952. He s... |
A bank buys
1000 European put options on a $10 non-dividend paying stock at a strike of $12. The bank wishes to hedge this exposure. The bank can trade the underlying stocks and European call options with a strike price of 7 on the same stock with the same maturity. Details of the call and put options are given in the ... |
The biggest challenge to solve the problem is that I can't really picture a pyramid. And it is hard to make a model. The pyramids I am trying to find include those on all tiers.
Some clarification first, to make sure I understand your question correctly: I assume that you mean a step pyramid which has a single unit cub... |
One possible way is using
Lagrange Multiplier.
We want to maximize $f(x,y)$Subject to $g(x,y)=c$
In this case, $f(x,y)=xy$ , $g(x,y)=x^2+y$ and $c=1$
We'll define $L(x,y,\lambda)=f(x,y)+\lambda(g(x,y)-c)=xy+\lambda(x^2+y-1)$
We want to find $x$ and $y$ such that: $\partial L / \partial x = 0$ $\partial L / \partial y =... |
Let $\calO(x)$ denote the orbit of $x\in X$ under the action of the group $P$.
Let $X^P=\{x_1, x_2, \dots, x_m\}$.The orbits of an element in $X^p$ under the action of $P$ is the element itself, that is, $\calO(x_i)=\{x_i\}$ for $i=1,\dots, m$. Let $x_{m+1}, x_{m+2},\dots, x_n$ be representatives of other orbits of $X$... |
Here's a diagram of neutron decay.
Up and down quarks have rest masses of 2-4 MeV. The $W$ boson has a rest mass of 80 GeV.
Where has this extra mass come from?
Physics Stack Exchange is a question and answer site for active researchers, academics and students of physics. It only takes a minute to sign up.Sign up to jo... |
Question
A wire of length 28 m is to be cut into two pieces. One of the pieces is to be made into a square and the other into a circle. What should be the lengths of the two pieces so that the combined area of the circle and the square is minimum?
Solution
\[\text { Suppose the wire, which is to be made into a square a... |
Negative Binomial Distribution
The geometric distribution describes the probability of observing the first success on the \(n^{th}\) trial. The negative binomial distribution is more general: it describes the probability of observing the \(k^{th}\) success on the \(n^{th}\) trial.
Example \(\PageIndex{1}\)
Each day a h... |
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1547-5816
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Journal of Industrial & Management Optimization
October 2007 , Volume 3 , Issue 4
A special issue dedicated to Professor Changyu Wang in recognition of his contributions
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This special issue is dedicated to Professor Changyu Wang ... |
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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 ... |
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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-... |
During Sage Days 31, I worked on theticket #11459 to implement
rst to
sws conversion. This post intends to give some documentationabout this new feature. Here is an example of a ReStructuredText file
calculus.rst:
******** Calculus ******** Let's do some calculus using Sage. Differentiation =============== The derivati... |
In case you're wondering what happened to your feed reader this week: We've decided to retitle all of the arXiv highlights posts to be more attractive. We promise not to do this often, but it seemed like a good time to do it while we're inconveniencing very few people.
This week¶
This week's paper is Discovery of Usefu... |
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:$$ \Psi(2)=\sum_{n=2}^\infty \frac{1}{\pi(n)^2}=1+\frac{1}{2^2}+\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{3^2}+\frac{1...
Consider a random binary str... |
I'm trying to locate my four zeroes of a complex-valued function, in order to apply the Residue Theorem.
After using the quadratic formula, I am left with $$z^2 = [-3 \pm i\sqrt7] / 2$$
writing the left side in exponential form, I get: $$z^2 = 2exp(\pm i\theta)/2$$
which gives $$z=\pm \sqrt2exp(\pm i\theta/2)/2$$
these... |
Setup:
Let $(M, \mathscr A, \mu)$ be a measure space.
$u$ is a non-negative simple function if there exist non-negative real numbers $\alpha_1,\ldots,\alpha_p$ and measurable sets $A_1,\ldots,A_p$ such that $u=\sum_{i=1}^p \alpha_i 1_{A_i}$. The integral of a non-negative simple function $u$ is $\int u\, d\mu = \sum_{i... |
Show that given $A=\left( \begin{array}{cc}\alpha &\beta\\\beta&\delta\\\end{array}\right) \in M_2(\mathbb{R}^2)$, $\langle x,y \rangle = x^TAy, (x,y \in \mathbb{R}^2)$, defines an inner product on $\mathbb{R}^2$ if and only if $\alpha >0$ and det$(A)>0$.
I tried to prove the $\Leftarrow$ direction first:
($\Leftarrow$... |
Chemical Kinetics Effect of Temperature and Catalyst, Activation Energy, Arrhenius Equation, Collision Theory Effect of temperature on rate of reaction: Every increase in temperature by 10°, increases the collision frequency only by about 2% but the rate constant and the rate of reaction become double and in some cases... |
Are two signals are the same if their
auto-convolution functions are the same?
Almost. Look at the autoconvolution in the frequency domain where the autoconvolution of $x$ (with itself) gives us $(X(f))^2$ in the frequency domain while the autoconvolution of $-x$ (with itself) gives us $(-X(f))^2 = (X(f))^2$. So, given... |
What is the limit of this sequence where , $U_n = \frac{(\log n )^p}{n}$ where $p \ge 0$.
I have done this problem when $p$ is an integer. Sorry but I am not too much familiar with writing questions in stack exchange.
Mathematics Stack Exchange is a question and answer site for people studying math at any level and pro... |
Bardsley and Richardson (Etale slices for algebraic transformation groups in characteristic p.Proc. London Math. Soc. (3) 51 (1985), no. 2, 295–317) give a construction which seems to do what you want. It gives less than a "Cayley map" as in Borovoi's answer.
Let $G$ be connected and semisimple over a field of char. 0.... |
FINAL EDIT: There is one main question left: According to the answer, we have choosen $\theta=1$ , where we could choose $0<\theta<\infty$ as we like. His this sufficient, if we regarde the convergence to $\theta$ as a finite positive random variable?
This post seems long, but its almost everything proofed except the l... |
Let $p,q \in (1,\infty)$ with $p\neq q$. Are the Banach spaces $L^p(\mathbb{R})$, $L^q(\mathbb{R})$ isomorphic?
The proof Fabian alludes to in the book reference Mark gave is a modern one using the notions of cotype and type. One way to prove that a Banach space $X$ is not isomorphic to a Banach space $Y$ is to exhibit... |
Let us take two finite duration sequences x
1(n) and x 2(n), having integer length as N. Their DFTs are X 1(K) and X 2(K) respectively, which is shown below −
Now, we will try to find the DFT of another sequence x
3(n), which is given as X 3(K)
$X_3(K) = X_1(K)\times X_2(K)$
By taking the IDFT of the above we get
$x_3(... |
ISSN:
1930-5311
eISSN:
1930-532X
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Journal of Modern Dynamics
January 2007 , Volume 1 , Issue 1
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Abstract:
The paper discusses a number of open questions,which were collected during the AIM workshop “Emerging applications of measure rigidity”. The main emphasis is made on t... |
Work, Energy and Power Potential energy and Law of Conservation of Energy Potential energy of a mass ‘m’ at height ‘h’ u = mgh. Potential energy of a stretched spring \tt u = \frac{1}{2} kx^{2}. Zero potential point is that where gravitational potential = 0. In a conservative force work done in round trip is zero. In a... |
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