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Here are two constructions, showing that the expectation of the min can get down to around $1+1/\sqrt{n}$, and on the other hand can get up to a value approaching $2$ as $n\to\infty$.
Maybe someone can do better!
Let the random variables be $X_1, X_2,\dots, X_n$.
(1) Aiming to make the expected minimum small; the idea ... |
The following question has puzzled me for some time:
Let $(\Omega,\Sigma)$ be a nonempty, measurable space. Does there necessarily exist a probability measure $\mu:\Sigma\to[0,1]$?
If there exists a nonempty measurable set $A$ such that no nonempty subset of $A$ is measurable (an
atom), we can simply let $\mu(B)=1$ if ... |
I decided to start answering this question by building a galaxy (well, a model of a galaxy, but it sounds cooler the first way). A lot of research has already been done in this area, specifically, in density wave theory, which explains the winding arms of spiral galaxies. Before we begin, here’s your 60-second introduc... |
@JosephWright Well, we still need table notes etc. But just being able to selectably switch off parts of the parsing one does not need... For example, if a user specifies format 2.4, does the parser even need to look for e syntax, or ()'s?
@daleif What I am doing to speed things up is to store the data in a dedicated f... |
Although the question is easy to pose, I think some background will help to motivate it, so I'll start with it.
Consider variables $X=(X_1, \ldots, X_n)$ over a field $K$ and the elementary symmetric functions $T=(T_1, \ldots, T_n)$ in $X$. In other words $X$ are the roots of the polynomial $Y^n + T_1 Y^{n-1} + \cdots ... |
In the last few days I thought a lot about (fully) time-constructible functions and I will present what I found out by answering Q1 and Q3. Q2 seems too hard.
Q3:
Kobayashi in his article (the reference is in the question) proved that a function $f:\mathbb{N}\rightarrow\mathbb{N}$, for which there exists an $\epsilon>0... |
I think the work of Dr. Paul Garabedian (and Dr. Schiffer)[1], and Dr. Mel'nikov (who built on Dr. Garabedian's result) are important theorems that were
almost forgotten. I'll share the main theorem from Dr. Mel'nikov's work[2] as it incorporates the main result from Dr Garabedian's:
Given complex numbers $z_1,\ldots,z... |
Let $X$ be an affine holomorphic symplectic variety of dimension $2n$, with the associated Poisson bracket { , }. Let's say it's an integrable system when there are $n$ algebraically independent holomorphic functions $I_i$ ($i=1,\ldots,n$) on $X$ such that they Poisson-commute: $\{I_i,I_j\}=0$.
Pick a simple Lie algebr... |
The path integral formalism doesn't really
replace the operator formalism. You still need to know that the state space is a Hilbert space, that probabilities are computed by norm-squaring inner products in this space, that observables are operators on this space, that time evolution is implemented by a unitary operator... |
We have the matrix Laplacian matrix $G=A^TA$ which has a set of eigenvalues $\lambda_0\leq\lambda_1\leq\ldots\leq \lambda_n$ for $G\in\mathbb{R}^{n\times n}$ where we always know $\lambda_0 = 0$. Thus the Laplacian matrix is always symmetric positive semi-definite. Because the matrix $G$ is not symmetric positive defin... |
And I think people said that reading first chapter of Do Carmo mostly fixed the problems in that regard. The only person I asked about the second pset said that his main difficulty was in solving the ODEs
Yeah here there's the double whammy in grad school that every grad student has to take the full year of algebra/ana... |
Find the parametric equation for the curve.
$$x^{2}+y^{2}=10$$
I haven't learned parametric equations fully yet, so I wanted to check with you guys and see if you can confirm if I'm doing this correctly and possibly go more in depth on the problem if you can?
Because it's centered at (0,0) the origin, and it has a radi... |
Let a (free) particle move in $[0,a]$ with cyclic boundary condition $\psi(0)=\psi(a)$. The solution of the Schrödinger-equation can be put in the form of a plane wave. In this state the standard deviation of momentum is $0$, but $\sigma_x$ must be finite. So we find that $\sigma_x\sigma_p=0$. Is something wrong with t... |
This paper studies fractional integral operator for vector fields in weighted$L^1$. Using the estimates on fractional integral operator and Stein-Weissinequalities, we can give a new proof for a class of Caffarelli-Kohn-Nirenberginequalities and establish new $\divg$-$\curl$ inequalities for vector fields.
A new, exten... |
Short version :
What is the motivation behind the local condition in the definition of a test category ? Why do we want the slice categories $A/a$ to be weak test ?
Long version :
I start with some background.
In
Pursuing stacks, Grothendieck searches for a characterization of modelizers, that is of categories $\mathca... |
I'm interested in maximizing a function $f(\mathbf \theta)$, where $\theta \in \mathbb R^p$.
The problem is that I don't know the analytic form of the function, or of its derivatives. The only thing that I can do is to evaluate the function point-wise, by plugging in a value $\theta_*$ and get a NOISY estimate $\hat{f}... |
There is mathematical justification for setting Dirichlet boundary degrees of freedom to a value. However, you should adjust your variational form accordingly. If you are looking at a general problem, say:
Find $u\in\mathcal{U}$ such that
$a(u,w)=l(w) \ \ \forall w\in\mathcal{V}$
where
$\mathcal{U}=\{u:\int \nabla u^2 ... |
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Now showing items 1-10 of 27
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 ... |
Construct two functions $ f,g: R^+ → R^+ $ satisfying:
$f, g$ are continuous; $f, g$ are monotonically increasing; $f \ne O(g)$ and $g \ne O(f)$.
Computer Science Stack Exchange is a question and answer site for students, researchers and practitioners of computer science. It only takes a minute to sign up.Sign up to jo... |
This question seems to have been specifically designed to make you realise that the homology groups of a space can sometimes pick out homotopical information about a space which is not contained in the fundamental group alone. In this case, we have $X$ which is homotopy equivalent to $S^2\vee S^1\vee S^1\vee S^1$ (as y... |
Could any one give an example of a bijective map from $\mathbb{R}^3\rightarrow \mathbb{R}$?
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 minute to sign up.Sign up to join this community
Could any one give a... |
R C Soni
Articles written in Proceedings – Mathematical Sciences
Volume 100 Issue 1 April 1990 pp 21-24
In this paper we evaluate the inverse Laplace transform of$$\begin{gathered} s^{ - \eta } (s^{l_1 } + \lambda _1 )^{ - \sigma } (s^{l_2 } + \lambda _2 )^{ - \rho } \hfill \\ \times S_n^m [xs^{ - W} (S^{l_1 } + \lambd... |
Concerning partial fraction decomposition I can proof the following theorem:
For two polynomials $f(x),g(x) \ne 0$ with coefficients in $\mathbb C$ one can find the following unique representation:
$$\frac{f(x)}{g(x)}=\sum_{i=1}^{m}\sum_{j=1}^{n_i}\frac{a_{ij}}{(x-\alpha_i)^{j}}+p(x)$$
where $\alpha_1,\dots,\alpha_m$ a... |
I'm told to use Gauss's Theorem to compute the flux of a field $\vec F = <x,y^2,y+z>$ along the boundary of the cylindrical solid $x^2+y^2 \le 4$ below $z=8$ and above $z=x$.
I know by Gauss's Theorem that:
Net Flux = $\iint_{\partial D} \vec F \cdot \vec ndS = \iiint_D \nabla \cdot \vec FdV$
This computation is pretty... |
This question already has an answer here:
We have the result, $\displaystyle{\frac{1}{R}=lim_{n\to\infty}|\frac{a_{n+1}}{a_n}|}$, where $R$ is the radius of the convergence, where $\displaystyle{a_n}$ is the coefficient of the series $\displaystyle{\sum_{n=0}^{\infty}}a_nz^n$,
Here we redefine the series as$\displaysty... |
When working out the maths and solving for the
Level conditional on experience
XP, we obtain:
$$Level = \frac{1 + \sqrt{1 + 8 \times XP \div 50}}{2}$$
For example, what is the player's level for \$XP = 300\$?
$$ \frac{1 + \sqrt{1 + 8 \times 300 \div 50}}{2} = 4 $$
As requested.
Or, what is the level for
XP = 100000?
$$... |
I need to calculate $$\int_{-\infty}^{+\infty} \frac{1}{\left(e^x+ e^{-x}\right)^n} e^{-\rho x^2 + a x} dx$$ where $n \in \mathbb{N}$, $\rho > 0$ and $a \in \mathbb{R}$, but I don't know how to follow. I've tried to include the expression in symbolic software trying to get a result with respect other functions, but not... |
I don't think counting even 1-D holes is appropriate for intuitive understanding of homology. Take a torus for example: its 1st homology $H_1$ is generated by a circle along the torus (the "hole" in this case it the dohnut hole), and a circle across the torus (now the "hole" is the void inside the dohnut surface). The ... |
Background
The
best rational approximations $p/q$ to an irrational $\alpha$ are defined by the property$$\left|\alpha - \frac{p}{q}\right| < \left|\alpha - \frac{p'}{q'}\right|$$for all $q' \leq q$. The approximants $p/q$ are found by simply truncating the continued fraction expansion.
The "most" irrational number is t... |
Short answer: no difference between Primal and Dual - it's only about the way of arriving to the solution. Kernel ridge regression is essentially the same as usual ridge regression, but uses the kernel trick to go non-linear.
Linear Regression
First of all, a usual Least Squares Linear Regression tries to fit a straigh... |
The second Newton's law of motion (fundamental principle of dynamics) say that the sum of the forces \( \vec{F} \) on an object is equal to the mass \( m \) of this object multiplied by the acceleration \( \vec{a} \) of this object:
$$ \sum{\vec{F}}=m.\vec{a} $$
This post illustrates the fundamental principle of dynami... |
As Chandra Chekuri pointed out in a comment, you could just compute the transitive closure via fast matrix multiplication, solving the problem in O($n^\omega$) time (use your favorite method, O($n^{2.376}$) via Coppersmith and Winograd, or more practically using Strassen's O($n^{2.81}$)), and this would be good for den... |
The longitudinal diffusion coefficients $D_L$ in the range of 0.1 to 1.5 kV/cm can be expressed as
defined by the Einstein relation
\[
D_L=\frac{\mu\epsilon_L}{e}=\left(\frac{a_0+a_1E+a_2E^{3/2}+a_3E^{5/2}}{1+(a_1/a_0)E+a_4E^2+a_5E^3}\right)\left(\frac{b_0+b_1E+b_2E^2}{1+(b_1/b_0)E+b_3E^2}\right)\left(\frac{T}{T_0}\rig... |
I stumbled across this question and I cannot figure out how to use the value of $\cos(\sin 60^\circ)$ which would be $\sin 0.5$ and $\cos 0.5$ seems to be a value that you can only calculate using a calculator or estimate at the very best.
$\cos(\sin(\pi/3))=\cos(\sqrt{3}/2)$.
(You can confirm the first step by observi... |
I'm doing some revision using a study guide before the semester starts up again, and have gotten stuck on part of a question. The question I’m having trouble with is as follows:
A rock of mass $m = 1.27kg$ is tied to a string and spun in a circle as it slides on a frictionless horizontal surface. The radius of the circ... |
I am trying to understand the concept of
group velocity of a free particle wave packet: $$\Psi(x,t) = \frac{1}{\sqrt{2 \pi}}\int_{-\infty}^{\infty} \phi(k)e^{ikx}e^{-\frac{i \hbar k^2 t}{2m}}dk.$$
Where $$\omega(k) = \frac{\hbar k^2}{2m}.$$ Assuming that $\phi(k)$ is narrowly peaked about some particular value $k_0$ we... |
The example I'm trying to understand is:
$ \hat{S}_{x} \begin{pmatrix} \frac{1}{\sqrt{2}}\\ \frac{1}{\sqrt{2}} \end{pmatrix} = 1/2 \begin{pmatrix} \frac{1}{\sqrt{2}}\\ \frac{1}{\sqrt{2}} \end{pmatrix} $
My interpretation of this is that the vector shows you the probabilities of a particle being spin up or spin down if ... |
I want to find the equation of motion that comes from the following Lagrangian density $$\mathscr{L}=\mathbf{E}\cdot\left(\nabla^{2}\mathbf{E}\right)$$ where $E_{i}=\partial_{i}\phi\;(i=x,y,z)$ . In this case the $\phi$ and its 3rd derivatives are the independent variables. The Euler-Lagrange equation contains two term... |
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... |
In this appendix we provide the proof of Proposition 26, restated here in a self-contained way.
We shall follow the arguments in Sect. 4.3 (Doubling trick) in [11] almost verbatim. In that paper, the target was a
k-pronged graph with a single vertex; in the present paper, the target is a graph with finitely many vertic... |
I am a little confused about where does the mass and stiff matrix come from. In Discontinuous Galerkin we divide the domain in elements, $\Omega = \cup^K_{k=1} D^k$. Then assume the solution $u$ can be locally approximated by a polynomial as
$$u_h=\sum_{i=1}^{Np}\hat u_i^k \Phi_i$$
We then introduce the approximated so... |
Originally posted on stats.stackexchange, I'll pair the post down to something a bit more general.
Suppose I have vectors $\{\mathbf{\delta}, \mathbf{x}_1, \ldots, \mathbf{x}_J\}$, where $\delta \in \mathbb{R}^{J}$ and $\mathbf{x}_i \in \mathbb{R}^{I}$. Furthermore, let $\mathbf{A} \in \mathbb{R}^{I\times J}$ be such t... |
I wanted to better understand dfa. I wanted to build upon a previous question:Creating a DFA that only accepts number of a's that are multiples of 3But I wanted to go a bit further. Is there any way we can have a DFA that accepts number of a's that are multiples of 3 but does NOT have the sub...
Let $X$ be a measurable... |
Let $\mathcal{C}, \mathcal{D}, \mathcal{E}$ be (symmetric?) monoidal categories, and $H : \mathcal{C} \times \mathcal{D} \to \mathcal{E}$ be a functor that is monoidal in both arguments, ie. $H(C,-)$ and $H(-,D)$ are (strong) monoidal for all objects $C$ and $D$. And take two monoids $M : \Delta \to \mathcal{C}$ and $N... |
I am trying to understand intuition of ADMM (alternating direction methods of multipliers). It combines dual ascent and method of multipliers. Downside of method of multiplier is the loss of decomposability. Why does method of multipliers lose decomposability?
The question is missing some important context about the fo... |
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Now showing items 1-10 of 32
The ALICE Transition Radiation Detector: Construction, operation, and performance
(Elsevier, 2018-02)
The Transition Radiation Detector (TRD) was designed and built to enhance the capabilities of the ALICE detector at the Large Hadron Collider (LHC). While aimed at providing electron... |
Special quasirandom structures¶
Random alloys are often of special interest. This is true in particular forsystems that form random solid solutions below the melting point. It is,however, not always easy to model such structures, because the system sizesthat lend themselves to, for example, DFT calculations, are often ... |
The complex method of interpolation, going back to Calder\'on and Coifman etal., on the one hand, and the Alexander-Wermer-Slodkowski theorem on polynomialhulls with convex fibers, on the other hand, are generalized to a method ofinterpolation of real (finite-dimensional) Banach spaces and of convexfunctions. The under... |
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from collections import OrderedDict
from typing import List
import numpy as np
from ase import Atoms
from icet import ClusterSpace
from icet.core.sublattices import Sublattices
from mc... |
This article will be permanently flagged as inappropriate and made unaccessible to everyone.
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Excessive Violence
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The accelerating universe is the observation that the universe ap... |
The
package is a powerful tool, based on pgfplots
tikz, dedicated to create scientific graphs.
Contents Pgfplots is a visualization tool to make simpler the inclusion of plots in your documents. The basic idea is that you provide the input data/formula and pgfplots does the rest.
\begin{tikzpicture} \begin{axis} \addpl... |
The idea of the argument is this: an integrable function that does not tend to zero may have thinner and thinner pikes, and the integral on each pike needs to tend to zero. If the function is uniformly continuous, these pikes can't get thinner and thinner, and the function can't be integrable, as the integral on pikes ... |
I'd recommend "The Art of Molecular Dynamics Simulation" by D. C. Rapaport. The code samples are written in C. I'm not a huge fan of the programming style of the book, but at least it's not FORTRAN.Having said that, my advise would be to take any book where neighbour lists are explained (for instance the Frenkel & Smit... |
FlashChat Actuarial Discussion Preliminary Exams CAS/SOA Exams Cyberchat Around the World Suggestions
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An Introduction to MimeTex
For those who wish to format math questions on the web using super and subscripting, try using the Tex tags. Tom has been kind enough to impo... |
Consider a Yang-Mills $U(1)$ gauge theory in $d=2+1$ flat dimensions.
It is known that in $d=2+1$ the field strength $F=dA$ can be written in terms of a dual scalar field $a$, in the following way: $F=\star da$. (The star is the hodge dual of forms)
My question is why $a$ is compact, i.e. its target space is a circle (... |
№ 9
All Issues On the Growth of the Maximum of the Modulus of an Entire Function on a Sequence Abstract
Let
M f( r) and μ f( r) be, respectively, the maximum of the modulus and the maximum term of an entire function f and let Φ be a continuously differentiable function convex on (−∞, +∞) and such that x = o(Φ( x)) as x... |
I have no idea how to solve the following
INTEGER problem or prove its hardness. Thanks for any help/comment/open discussion!
Assume there are $N$ startups. For each startup $i$, you can invest $x_i\in \{0,1,...,C_i\}$ dollars where $C_i$ is the maximal investment that it accepts, and you will get a reward as $f_i(x_i)... |
I don't see why you would like to use subgradients for that. Correct me if I'm wrong, but when the problem is fully differentiable (kmeans actually is), the subgradient is the gradient vector $\nabla f$ itself. Then it might just equate to using an EM-like algorithm, iteratively finding the means and solving for the as... |
This is my first question. I have the following data that I'd like to approximate as a parametric function:
\begin{align} y = a + (bx_1 + cx_2 + dx_3 + ex_1x_2 + fx_1x_3 + gx_2x_3 + hx_1x_2x_3 + i)*(j*\sin(kx_1x_2x_3) + l\cos(mx_1x_2x_3)) \end{align}
testdata <- read.csv('..path_to_file/gistfile1.txt', sep = "")plot(1:... |
Flexible equation of state for a hard sphere and Lennard–Jones fluid near critical temperature
Permanent link: https://www.ias.ac.in/article/fulltext/pram/083/06/0955-0962
Author uses the condition in terms of contact point radial distribution function $G(\sigma, \lambda(\eta_c, \alpha))$ containing the self-consistent... |
My original question (posted in https://math.stackexchange.com/questions/1584430/can-all-power-sets-be-limit-cardinals) was:
Is it possible to create a model of ZFC, so that
the cardinality of each power set is a limit cardinal (as opposed to GCH where they are always successor cardinals)?
Obviously, from Easton's theo... |
I am aware of the debate on whether Schrödinger equation was derived or motivated. However, I have not seen this one that I describe below. Wonder if it could be relevant. If not historically but for educational purposes when introducing the equation.
Suppose that we have the time dependent Schrödinger equation for a f... |
Because there are natural computational problems involving many mathematical objects, there are a bunch of implications of complexity class separations like $\mathrm{P} \neq \mathrm{NP}$. I think the first paper to investigate this idea is probably Mike Freedman's
Complexity classes as mathematical axioms, which assume... |
As to the title of your question,
Logistic function: where does it come from?, I can provide an intuition for the logistic function which is the common interpretation from a machine learning perspective. It seems that the underlying question has already been answered above, but I thought this interpretation could help ... |
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
Spanish.
Contents
Spanish language has some special characters, such as the
ñ and some accentuated words. For this reason the preamble of your document must... |
I think the code below meets your requirements. The
\phantom{\phantom{=\int b(x)} command inserts an invisible block of the same width as its contents (i.e., of the line above), and the
\smash{...} command prevents the invisible block from taking up too much vertical space. (Try the code without the
\smash command to s... |
And I think people said that reading first chapter of Do Carmo mostly fixed the problems in that regard. The only person I asked about the second pset said that his main difficulty was in solving the ODEs
Yeah here there's the double whammy in grad school that every grad student has to take the full year of algebra/ana... |
Westergaard is a British scientist. For vertical stress computation, he had proposed a formula in 1938. The formula is presented below.
Westergaard's Equation for Point Loads
If Q is the point load and σ
z is the vertical stress due to the point load,
\[\sigma_{z}=\frac{Q}{2{\pi}z^{2}}\times \frac{\sqrt{(1-2\mu)/(2-2\m... |
Discrete Gaussian Samplers over the Integers¶
This class realizes oracles which returns integers proportionally to\(\exp(-(x-c)^2/(2σ^2))\). All oracles are implemented using rejection sampling.See
DiscreteGaussianDistributionIntegerSampler.__init__() for which algorithms areavailable.
AUTHORS:
Martin Albrecht (2014-06... |
Polya-Hurwitz program.
This may become more interesting in light of the recent progress in the
Polya-Jensen program by Griffin, Ono, Rolen, Zagier.
We will first provide definitions of some functions involved.
The Riemann Xi-function $\Xi(z)$ is related to the Riemann zeta-function $\zeta(s)$ via ([A], [B]): $\Xi(z)=\x... |
Background
I've met this problem when I was trying to convert a elliptic PDE problem into the corresponding variational problem in order to apply finite element method.
The PDE is an elliptic PDE with non-zero Dirichlet boundary condition:
Denote $$ Lu=-\nabla\cdot(a\nabla u)+bu $$ Then the equation is $$ \left\{\!\! \... |
I'm trying to evaluate the integral of the Chebyshev polynomials of the first kind on the interval $-1 \leq x \leq 1 $ . My idea is to use the closed form $$T_n(x) = \frac{z_1^n + z_2^n}{2}, $$ where $z_1 = (x + \sqrt{x^2 - 1})$ and $z_2 = (x - \sqrt{x^2 - 1})$, giving the following integral: $$ \int _{-1}^{1}\!1/2\, \... |
Here I am on thin ice but let me try: I have a feeling (please comment!) that a main difference between statistics and econometrics is that in statistics we tend to consider the regressors as fixed, hence the terminology
design matrix which obviously comes from design of experiments, where the supposition is that we ar... |
This is all just a result of sloppy language on the part of people describing quantum mechanics.The state$$ \left\lvert \Psi \right\rangle = \frac{1}{\sqrt{2}} \left( \left\lvert \uparrow \right\rangle + \left\lvert \downarrow \right\rangle\right) \tag{1}$$is a superposition of the two orthogonal states $\left\lvert \u... |
I have a little question and need some help with the notation. So, the question goes as follows:
A bond with a maturity of ten years that pays annual coupons of 8% has a price of \$90. A bond with a maturity of ten years and annual coupons of 4% has a price of \$80. What is the ten year zero rate?
I don't actually know... |
2018-2019 ICPC, NEERC, Northern Eurasia Finals (Unrated, Online Mirror, ICPC Rules, Teams Preferred) Finished
You are given a positive integer $$$n$$$.
Find a sequence of fractions $$$\frac{a_i}{b_i}$$$, $$$i = 1 \ldots k$$$ (where $$$a_i$$$ and $$$b_i$$$ are positive integers) for some $$$k$$$ such that:
$$$$$$ \begin... |
If a polygon can be cut into $m$ as well as into $n$ triangular pieces of equal area, can it also be cut into $m+n$ triangles of equal area?
(I'm editing after realizing that my conjecture that a convex equidissectable polygon must have an equidissection with all triangles meeting in a common vertex is very wrong.)
Som... |
The Metropolis computer network consists of $$$n$$$ servers, each has an encryption key in the range from $$$0$$$ to $$$2^k - 1$$$ assigned to it. Let $$$c_i$$$ be the encryption key assigned to the $$$i$$$-th server. Additionally, $$$m$$$ pairs of servers are directly connected via a data communication channel. Becaus... |
In the paper, we introduce a quantum random walk polynomial (QRWP) that can be defined as a polynomial $$\{P_{n}(x)\}$$ { P n ( x ) } , which is orthogonal with respect to a quantum random walk measure (QRWM) on $$[-1, 1]$$ [ - 1 , 1 ] , such that the parameters $$\alpha _{n},\omega _{n}$$ α n , ω n are in the recurren... |
Assume $V=L$ and let $\kappa$ be a Mahlo cardinal. Let $L[G]$ be the generic extension obatined by Mitchell forcing to make $2^{\aleph_0}=\aleph_2=\kappa.$ It is known that in the extension there are no special $\aleph_2$-Aronszajn trees but there are $\aleph_2$-Aronszajn trees.
Question 1.Is there any $\aleph_2$-Sousl... |
The Connected Component Process Model
Creates an instance of the Connected Component point process model which can then be fitted to point pattern data.
Usage
Concom(r)
Arguments r
Threshold distance
Details
This function defines the interpoint interaction structure of a point process called the connected component pro... |
I've done a little bit of research and it seems Millikan was able to measure the ratio between the charge of the electron and its mass. But how can one measure one of the two constants to get the value of the other?
The mass-to-charge ratio $m/e$ of the electron was first measured by J.J. Thomson, the discoverer of the... |
SuNem
\(\mathrm{Nem}_{q}(z)=z+z^3+qz^4\)
It is assumed, that \(q\!>\!0\), although the formula can be used for some other values of the parameters too.
SuNem is specific solution of the transfer equation
\(\mathrm{Nem}_{q}\big( \mathrm{SuNem}_{q}(z)\big)=\mathrm{SuNem}_{q}(z\!+\!1)\).
It is assumed that \(\mathrm{SuNem... |
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Now showing items 1-10 of 24
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 ... |
The Full Width Half Maximum (as defined by John Rennie's answer ) can have the following physical meanings:
For a Lorentzian lineshape spectrum, it is proportional to the square magnitude of the strength of the coupling between electromagnetic field and the atomic transition begetting the spectrum in the first place; F... |
Definition: Define the $k$-HamiltonianCycles problem as the decision problem that asks if a given graph has at least $k$ distinct Hamiltonian cycles. Question: Is there some constant $k$ so that the $k$-HamiltonianCycles problem is $NP$-complete on the class of planar $4$ connected graphs? In particular, what about $k ... |
Inspired and intrigued by this question, I decided just for fun to throw in another integer into the factors and look what happens. So for $k\in\mathbb Z$, let us define $$K_r(n,k):=\prod_{\ell_1=1}^n\cdots\prod_{\ell_r=1}^n\left( 4\cos^2\left(\frac{\pi\ell_1}{2n+1}\right)+\cdots+4\cos^2\left(\frac{\pi\ell_r}{2n+1}\rig... |
Three postdoctoral research positions are advertised at University College London:
Research associate to work with Felix Schulze in geometric analysis. The post is partially funded by the project “Regularity and stability of curvature flows and their applicatons to geometric variational problems” of the German Research... |
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A for awesome Posts: 1901 Joined: September 13th, 2014, 5:36 pm Location: 0x-1 Contact:
I have 64-bit Golly 2.8 on Mac, and it crashes when I try to set the rule to
Code: Select all
B4c4e4c4c4c3e3c5c5e6c6e2e2c2i2n2n6n6i6i3i5a3y1e1c5k7c7e4t4q4t6k4w4i88888000005i5y3a1c1e3... |
The unitary discrete Fourier transform (DFT) of a sequence of numbers $x_n$ to $X_k,$ with integer $0 \le n < N$ and $0 \le k < N,$ can be defined as:
$$X_k = \frac{1}{\sqrt{N}} \sum_{n=0}^{N-1} x_n e^{-2\pi ikn/N}\tag{1}$$
and the inverse discrete Fourier transform (IDFT) as:
$$x_n = \frac{1}{\sqrt{N}} \sum_{k=0}^{N-1... |
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... |
Suppose $\gcd(n, \phi(n)) > 1$. If $n$ is not squarefree, there exists a prime $p$ such that $p^2$ divides $n$. Then $H = \mathbb{Z}_p \times \mathbb{Z}_p$ is not cyclic and neither is $H \times \mathbb{Z}_{\frac{n}{p^2}}$. If $n$ is squarefree, there exist prime divisors $p$ and $q$ of $n$ such that $q$ divides $p-1$.... |
The space of ends of a finitely generated group is always homeomorphic to 0, 1, 2 points, or a Cantor set, and in which of these 4 cases it falls is governed by Stallings' characterization (wikipedia link) in terms of amalgam/HNN splittings over finite subgroups. Up to homeomorphism, this provides a complete picture. H... |
Can someone come up with a proof for this little theorem?
Suppose that $F_a(s)$ is a Dirichlet series and $a(n)$ is its associated arithmetic function, that is:
$$F_a(s)=\sum_{n=1}^{\infty}\frac{a(n)}{n^s}$$
Then the $a(n)$ are given by:
\begin{equation} \label{eq:a(n)} \nonumber a(n)=-2\sum_{i=0}^{\infty} (-1)^{i}(2\p... |
I know several papers that treat this, but it seems that most of these papers do things very differently with quite different conclusions, so I am confused.
Basically, when one tries to do classical field theory (as in, the branch of physics) in a mathematically precise manner, one considers a field $\psi$ to be a sect... |
Range searching
Published
Book Section
© 2018 by Taylor & Francis Group, LLC. A central problem in computational geometry, range searching arises in many applications, and a variety of geometric problems can be formulated as range-searching problems. A typical range-searching problem has the following form. Let S be a ... |
In this post I’ll be talking about one of my all-time favorite computer games, Factorio! Specifically: how well it lends itself to automation, and how a lot of benefits can come from using external tools to find the most efficient solutions to many of the challenges the game presents.
Factorio is a game all about autom... |
Fermat left only one proof.
The area of a Pythagorean triangle is never a square number.
Fermat wrote , “If the area of a right-angled triangle were a square, there would exist two biquadrates (fourth powers) the difference of which would be a square number.”
That is,
\( a^4\, -\, b^4 = c^2\)
He used the method of infi... |
I have the solution to problem 2.1 from Bergersen's and Plischke's textbook which I don't quite understand.
I'll post the question itself and its solution.
a) Consider a harmonic oscillator with Hamiltonian $H = 1/2(p^2+q^2)$ show that any phase space trajectory $x(t)$ with energy $E$, on the average, spend equal time ... |
I'm trying to find the best approximation to the function $e^x$ in the finite dimensional polynomial space $P_4$ with respect to the standard basis vectors $B=\{1,x,x^2,x^3,x^4\}$ with inner product $$(f,g)=\int_0^1 \frac{f(x)g(x)}{\left(x(1-x)\right)^{\frac{1}{2}}}dx$$
Let $w=\sum_{j=0}^4a_j\phi_j $ where $\phi_j=x^j$... |
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