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The Annals of Probability Ann. Probab. Volume 29, Number 1 (2001), 92-122. Power-law corrections to exponential decay of connectivities and correlations in lattice models Abstract
Consider a translation-invariant bond percolation model on the integer lattice which has exponential decay of connectivities, that is, the p... |
TADM2E 2.21
First we should see the dominance relations given in the book as it will help in determining the complexity for cases involving square root of n.
1. True 2. False, sqrt(n) dominates logn. 3. True 4. False 5. True 6. True 7. False
Edit: I'm not sure why (7) is False. It's possible that I'm mistaken but I thi... |
The domain for x, y, z is real numbers.
i) $\forall x \exists y (y^2<x)$
FALSE counterexample: $x=0$
ii) $\forall x \exists y (y^3<x)$
TRUE
iii) $\forall x\exists y \forall z ((y>0) \land ((z^2<y) \rightarrow (z^2+1<x^4)))$ (Not sure how exactly x,y,z relate to each other but from my current understanding it is False) ... |
For a project I'm looking for continuous distributions which have a somewhat simple closed form for upper-truncation expectation ($E[x|x>c]$). Here are two examples I've found so far:
Exponential distribution ($F(x)=1-e^{-\lambda x}$): $c+1/\lambda$
Uniform distribution on $(a,b)$: $\frac{c+b}{2}$
Assuming positive $c$... |
A standard deviation is a number that tells us
to what extent a set of numbers lie apart. A standard deviation can range from 0 to infinity. A standard deviation of 0 means that a list of numbers are all equal -they don't lie apart to any extent at all. Standard Deviation - Example
Five applicants took an IQ test as pa... |
I'll write down the idea of "method of Lagrange multiplier" here for my note. For simplicity, the number of variables would be 3.
Supposedly, a function $\psi: \Omega \to \mathbb{R}$ differential for each variable, and satisfies a restriction $\psi(x,y,z)=0$.
If a function $f : \mathbb{R}^3 \to \mathbb{R}$ realizes ext... |
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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 ... |
Let’s say we took the radon example, and took annual measurements. Let’s ignore the floor part of the problem too, and just think about this model:
radon_{i,c,t} = \mu_t + \alpha_{c,t} + \epsilon_c
so that \mu_t reflects the changing mean across counties over time, and \alpha_{c,t} captures changing county offsets. We ... |
Ex.10.2 Q1 Circles Solution - NCERT Maths Class 10 Question
From a point \(Q,\) the length of the tangent to a circle is \(\text{24 cm} \) and the distance of \(Q\) from the center is \(\text{25 cm.} \)
The radius of the circle is
(A) \(\text{7 cm}\)
(B) \(\text{12 cm}\)
(C) \(\text{15 cm}\)
(D) \(\text{24.5 cm}\)
Text... |
Table of Content: Chemical Equilibrium Ionic Equilibrium – Degree of Ionization and Dissociation Equilibrium Constant – Characteristics and Applications Le Chatelier’s Principle on Equilibrium Solubility and Solubility Product Acid and Base pH Scale and Acidity pH and Solutions Hydrolysis, Salts, and Types Buffer Solut... |
Some convenient notational framework For the formal handling I' propose a slightly different notation: two resistors with $r_1$ and $r_2$ Ohm in serie : $ r_1 \oplus r_2$ two resistors with $r_1$ and $r_2$ Ohm parallel : $ r_1 || r_2$
For convenience (reduction of parentheses) we assume that "$||$" binds stronger than ... |
I saw that two random independent vectors are approximately orthogonal in high dimensional space.
How can I prove this? And is there an intuitive explanation?
Thank you.
MathOverflow is a question and answer site for professional mathematicians. It only takes a minute to sign up.Sign up to join this community
There are... |
It is well known that the Van der Pol equation $$\begin{cases} \dot x=y-(x^3-x)\\\dot y=-x \end{cases}$$ has no an algebraic limit cycle.
According to this fact, we search for a related question in the following form:
We consider the Lienard equation $$\begin{cases} \dot x=y-F(x)\\ \dot y=-x\end{cases}$$
where $F(x)$ i... |
It is easier to think about the flatness problem in the other direction: from the past to the present. First, we need to introduce some quantities: $$E \equiv \frac{H}{H_0},\qquad \bar{\Omega} \equiv \Omega E^2, \qquad \bar{\Omega}_k \equiv \Omega_k E^2, \qquad \Omega_k \equiv -\frac{k}{a^2H^2},$$ where $H_0$ refers to... |
Because the slab extends infinitely in the xy plane, the electric field lies only along the z direction. The differential form of Gauss' Law for such a one-dimensional electric field is $$\frac{dE}{dz}=\frac{\rho(z)}{\epsilon_0}$$ This can be integrated, using the boundary condition that the electric field must be zero... |
I've just finished designing my own laboratory power supply unit. At first I wanted it to be 0-3A current limited, ~1-30V, but I've changed my mind about it - I think I might need more acuracy in the lower current levels instead of higher currents. For ease of design I decided that it'll be powered from a laptop charge... |
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Ex.7.1 Q9 Coordinate Geometry Solution - NCERT Maths Class 10 Question
If \(Q \;(0, 1)\) is equidistant from \(P \;(5, -3)\) and \(R\; (x, 6)\), find the values of x. Also find the distances \(QR\) and \(PR\).
Text Solution Reasoning:
The distance between the two points can be measured using the Distance Formula which ... |
Difference between revisions of "Probability Seminar"
(→April 4, TBA)
(→April 11, Eviatar Procaccia, Texas A&M)
Line 89: Line 89:
== April 11, [https://sites.google.com/site/ebprocaccia/ Eviatar Procaccia], [http://www.math.tamu.edu/index.html Texas A&M] ==
== April 11, [https://sites.google.com/site/ebprocaccia/ Eviat... |
Hello,
I've a problem to calculate the Position of a pendulum as a function of theta.
For example: $\theta (t)$ is a function of time which returns the angle made by the pendulum at a particular instant wrt it's equilibrium Position.
So,
$$ T = \dfrac 12 m l^2 \dot \theta^2 $$$$ U = - mgl \cos \theta $$ $$ L(\theta, \d... |
To demodulate a phase-shift keyed signal, of which BPSK is the simplest, you have to recover the carrier frequency, phase, and symbol timing.Bursty SignalsSome signals are bursty and provide a known data sequence called a preamble or mid-amble (depending on whether it shows up at the beginning or middle of the burst). ... |
First fix the following notations:
$AF:=$ The axiom of foundation
$ZFC^{-}:=ZFC\setminus \left\lbrace AF \right\rbrace $
$G:=$ The proper class of all sets
$V:=$ The proper class of Von neumann's cumulative hierarchy
$L:=$ The proper class of Godel's cumulative hierarchy
$G=V:~\forall x~\exists y~(ord(y) \wedge ``x\in ... |
On the Commutability of Homogenization and Linearization in Finite Elasticity
Article
First Online:
211 Downloads Citations Abstract
We consider a family of non-convex integral functionals
where
$$\frac{1}{h^2}\int_\Omega W(x/\varepsilon,{\rm Id}+h\nabla g(x))\,\,{\rm d}x,\quad g\in W^{1,p}({\Omega};{\mathbb R}^n)$$
Wi... |
We make a few comments only.
$1.$ Note that $2\pi$ is a period of $\sin x$, or, equivalently, $1$ is a period of $\sin(2\pi x)$.
But $\sin x$ has many other periods, such as $4\pi$, $6\pi$, and so on. However, $\sin x$ has no (positive) period
shorter than $2\pi$.
$2.$ If $p$ is a period of $f(x)$, and $H$ is
any funct... |
Last edited: March 22nd 2018
Within this example, we'll consider a resistor network consisting of $N$ repetitive units. Each unit has two resistors of magnitude $R$ and $12R$, respectively. The units are connected to a battery of voltage $V_0$, as shown in the figure below.
The goal of this example is to calculate the ... |
Infinite time blow-up of many solutions to a general quasilinear parabolic-elliptic Keller-Segel system
Institut für Mathematik, Universität Paderborn, Warburger Str. 100, 33098 Paderborn, Germany
$ \begin{align} & {{u}_{t}}=\nabla \cdot ({{(u+1)}^{m-1}}\nabla u)-\nabla \cdot (u{{(u+1)}^{\sigma -1}}\nabla v) \\ & \ 0=\... |
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Now showing items 1-1 of 1
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 ... |
Search
Now showing items 1-3 of 3
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^{⁎+}$... |
so I've been at this for about 3 - 4 hours now. It is an homework assignment (well part of a question which i've already completed). We did not learn this in class. All work is shown below.
An atom in an excited state of $4.9 eV$ emits a photon and ends up in the ground state. The lifetime of the excited state is $1.2 ... |
Answer
The ladder goes up the wall a distance of 9.35 meters above the top of the fire truck.
Work Step by Step
We can convert angle to degrees: $\theta = 43^{\circ}50' = (43+\frac{50}{60})^{\circ} = 43.83^{\circ}$ We can find the height $d$: $\frac{d}{h} = sin ~\theta$ $d = (h)~(sin ~\theta)$ $d = (13.5~m)~sin ~(43.83... |
Many inapproximability factors are $2^{n^\epsilon}$. I don't know why this is
2 instead of 3, 4, ..., etc.
To be precise, given a problem,
theorem 1 says: It's NP-hard to approximate the problem to $2^{n^\epsilon}$ for any $0 \leq \epsilon < 1$;
theorem 2 says: It's NP-hard to approximate the problem to $3^{n^\delta}$ ... |
I'm working on the following question. I'm having trouble with the solution presented in the textbook - specifically weak convergence.
Let $f \in L^p(\mathbb{R}^N), 1<p<\infty$ with $\alpha>0$ real, define $f_n = n^\alpha f(nx)$ for $n = 1,2,3,\dots$. Does $\{f_n\}$ strongly converge? Does it weakly converge?
It can be... |
Finite element simulation of a hyperelastic material with nonlinear Kirchhoff-St. Venant constitutive law. The material is stretched upwards for one second and then released inducing the free vibration shown. Roundoff errors eventually build enough to perturb the material laterally.
The mesh was generated with
gmsh. Ru... |
This is a good question, but at first blush it is hard to answer. This is because there is always an ambiguity in where you put the meaningful definitions - you can put it in the force constant, or you can put it in the units for the magnetic charges.
For magnetic monopoles, the first place one naturally turns to is to... |
Chandra, Poonam and Ray, Alak and Bhatnagar, Sanjay (2004)
Synchrotron aging and the radio spectrum of SN 1993J. [Preprint]
PDF
0402391.pdf
Download (118kB)
Abstract
We combine the GMRT low frequency radio observations of SN 1993J with the VLA high frequency radio data to get a near simultaneous spectrum around day 320... |
In evaluating the vacuum structure of quantum field theories you need to find the minima of the effective potential including perturbative and nonperturbative corrections where possible.
In supersymmetric theories, you often see the claim that the Kähler potential is the suitable quantity of interest (as the superpoten... |
Is the 2-D elevation wave spectrum (as a function of wavenumber and direction, with units of $m^4$) always positive? If so, why would that be the case?
Yes, wave variance or energy spectrum, direcional or non-directional is positive-definite as @aretxabaleta said in the comment.
In linear water-wave theory, the surface... |
EDIT: I notice that the link is hidden, but this post is made with reference to
THIS PAPER
I'm trying to solve quite an old problem (once again) - to find the distance between a point (in 3d space) and the ellipse. - Or actually the furthest distance on said ellipse (but the algorithm is similar so...). The first step ... |
Negate and simplify the the quantified statement: $$\forall_x[p(x) \to \neg q(x)] $$
My answer:
$ \neg\forall_x[p(x) \to \neg q(x)] \tag 1$
$ \exists_x\neg [p(x) \to \neg q(x)] \tag 2$
$ \exists _x[\neg p(x)\leftrightarrow \neg(¬q(x))] \tag 3$
$ \exists _x[\neg p(x) \leftrightarrow q(x)] \tag 4$
My answer is not correc... |
This question relates to a discussion on another message board. Euclid's proof of the infinitude of primes is an indirect proof (a.k.a. proof by contradiction, reductio ad absurdum, modus tollens). My understanding is that Intuitionists reject such proofs because they rely on the Law of the Excluded Middle, which they ... |
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... |
I am looking for a version of Suslin's Stability Theorem for Chevalley groups. The version of the theorem for $G=SL_n({\mathbb Z}[x_1, \dots , x_m])$ states that the if $n\ge m+2$, the elementary matrices generate $G$. I think by embedding many copies of $SL_n$, one can prove a similar statement, but probably with a ba... |
On the LUQ decomposition
The algorithm implemented in
luq (see reference given below) computes bases for the left/right null spaces of a sparse matrix $A$. Unfortunately, as far as I can tell, there seems to be no thorough discussion of this particular algorithm in the literature. In place of a reference, let us clarif... |
Ex.14.3 Q6 Statistics Solution - NCERT Maths Class 10 Question
\(100\) surnames were randomly picked up from a local telephone directory and the frequency distribution of the number of letters in the English alphabets in the surnames was obtained as follows:
Number of letters \(1 - 4\) \(4 - 7\) \(7 - 10\) \(10 - 13\) ... |
Cosmology, or at least basic cosmology, models the world as perfectly homogeneous and isotropic. Everything in the study of the evolution of the Universe actually works out fine if this is at least true at all times on the largest scales, and observations confirm it pretty much is. But at smaller scales, our Universe d... |
Tokyo Journal of Mathematics Tokyo J. Math. Volume 37, Number 1 (2014), 61-72. Infinitesimal Deformations and Brauer Group of Some Generalized Calabi--Eckmann Manifolds Abstract
Let $X$ be a compact connected Riemann surface. Let $\xi_1: E_1\longrightarrow X$ and $\xi_2: E_2\,\longrightarrow X$ be holomorphic vector bu... |
(5 Marks) Dec-2018
Subject
Fluid Mechanics 2
Topic
Compressible Flow
Difficulty
Medium
(5 Marks) Dec-2018
Subject
Fluid Mechanics 2
Topic
Compressible Flow
Difficulty
Medium Mach number defined as the square root of the ratio of the inertia force of a flowing fluid to the elastic force.
$\therefore \text{Mach Number} =... |
Your task is to take an array of numbers and a real number and return the value at that point in the array. Arrays start at \$\pi\$ and are counted in \$\pi\$ intervals. Thing is, we're actually going to interpolate between elements given the "index". As an example:
Index: 1π 2π 3π 4π 5π 6πArray: [ 1.1, 1.3, 6.9, 4.2, ... |
Let's work over $\mathbb{C}$. Consider the following commutative diagram
\begin{array}{llllllllllll} E_1& \xrightarrow{f} &E_2\\ \downarrow{\pi} &&\downarrow{\pi}\\ P_1 & \xrightarrow{g} &P_2 \end{array} Here $E_1=E_2=E$ is an elliptic curve, $P_1=P_2=\mathbb{P}^1$, $f$ is the multiplication map defined by $f(x)=2x$. L... |
As already mentioned by
TheSimpliFire you cannot simply change from real to complex variables without any changes within your solution. I will present you a solution which does not rely on complex analysis at all.
Recently reading this post dealing with related integrals I have finally found a way to evaluate your inte... |
The Annals of Statistics Ann. Statist. Volume 8, Number 3 (1980), 457-487. Minimum Chi-Square, not Maximum Likelihood! Abstract
The sovereignty of MLE is questioned. Minimum $\chi^2_\lambda$ yields the same estimating equations as MLE. For many cases, as illustrated in presented examples, and further algorithmic explor... |
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Journal of High Energy Physics, ISSN 1029-8479, 01/2010, Volume 2010, Issue 1, pp. 1 - 63
A combination is presented of the inclusive deep inelastic cross sections measur... |
Perturbed fractional eigenvalue problems
1.
Department of Mathematics, University of Craiova, 200585 Craiova, Romania
2.
"Simion Stoilow" Institute of Mathematics of the Romanian Academy, 010702 Bucharest, Romania
3.
Department of Mathematics and Computer Science, University Politehnica of Bucharest, 060042 Bucharest, ... |
Nodal bubble-tower solutions to radial elliptic problems near criticality
1.
Departamento de Ingeniería Matemática, Universidad de Chile, Casilla 170, Correo 3, Santiago, Chile, Chile
$ -\Delta u =|u|^{\frac 4{N-2} -\varepsilon} u \quad \text{in } B $
where $B$ is the unit ball in $\R^N$, $N\ge 3$, under zero Dirichlet... |
Here is one way to make the connection you are hinting at more rigorous. Throughout this answer, $\log$ denotes only the real logarithm (defined for positive real numbers only, so there is no ambiguity in how it is interpreted).
Recall that $$|e^w| = e^{\operatorname{Re} w}, \qquad w \in \mathbb{C}.$$If there were an a... |
Usually, the Stirling numbers of the first kind are defined as the coefficients of the rising factorial: $(*) \prod_{i=0}^{n-1}(x+i) = \sum_{i=0}^{n} S(n,i) x^i$.
With this definition, a recursive relation of $S(n,i)$ be derived, and it can be shown that is coincides with the recursive relation on the number of permuta... |
I know that the spectral radius is $\rho(A) = max |\lambda_l| = \S_{max}^2$ and that the Frobenius norm is $||A|| = \sqrt{tr(A^*A)} = (\sum_{k}S_k^2)^{1/2}$, which means I want to find the matrix A for which the following is true
$$ ||A||_F = \sqrt{tr(A^*A)} = (\sum_{k}S_k^2)^{1/2} = S_{max}^2 $$
So is the spectral rad... |
A simple illustration of the trapezoid rule for definite integration:$$ \int_{a}^{b} f(x)\, dx \approx \frac{1}{2} \sum_{k=1}^{N} \left( x_{k} - x_{k-1} \right) \left( f(x_{k}) + f(x_{k-1}) \right). $$
First, we define a simple function and sample it between 0 and 10 at 200 points
%matplotlib inlineimport numpy as npim... |
Gold Member
16 0
I'm reading through Lancaster & Blundell's
It seems to me that the energy of the harmonic oscillator in its "one-particle" state is ##\omega_0##, and the general energy (off the mass shell) is given by ##\omega## so that the position-space propagator would be given by $$G\left(x,y\right)=\int\frac{d^{4... |
In this Notebook we explore the Lorenz system of differential equations:$$ \begin{aligned} \dot{x} & = \sigma(y-x) \\ \dot{y} & = \rho x - y - xz \\ \dot{z} & = -\beta z + xy \end{aligned} $$
This is one of the classic systems in non-linear differential equations. It exhibits a range of different behaviors as the param... |
Young's Modules is defined as,
$Y = \frac{\sigma}{\epsilon}$
where $\sigma$ is the strain defined as $\sigma = F/A$ and $\epsilon$ is the stress defined as $\epsilon = \frac{\Delta L}{L_0}$.
In this case we require the stress, thus re-arranging the first equation gives,
$\sigma = \epsilon Y$
After plugging in the defin... |
Hydrogenic Wavefunctions:
A hydrogenic wavefunction, $\psi_{nlm}(\boldsymbol{r})$, can be written as the product$$\psi_{nlm}(r,\theta,\phi) = R_{nl}(r) Y_{lm}(\theta,\phi)$$where $R_{nl}$ is a radial wavefunction and $ Y_{lm}$ is a spherical harmonic.
$R_{nl}$ is a radial wavefunction $ Y_{lm}$ is a spherical harmonic ... |
I specify a function in terms of an integral and then try to evaluate it with
Simplify. However, the answer is not really simplified to what it should be.
assumptions := {l > 0, Element[NN, Integers], NN > 0, b > 0, a > 0, l > b, a > l, α > 0, β > 0};Φ = Function[x, If[x < l, (NN*π*α*b^2 *(l^2 ArcCos[x/l] - x Sqrt[l^2 ... |
Let $c_{q}(n)=\displaystyle \sum_{\substack{a=1,...,q\\ (a,q)=1}} e\left(\frac{an}{q}\right)$ be the Ramanujan's sum and consider the following series:
$$\displaystyle\sum_{q>r} \frac{\mu^{2}(q)c_{q}(n)}{\varphi^{2}(q)}$$
It's possible to find an upper bound explicitly in $n$ and $r$?
I want to find a form such as $\fr... |
Ex.13.5 Q5 Surface Areas and Volumes Solution - NCERT Maths Class 10 Question
An oil funnel made of tin sheet consists of a \(10\,\rm{cm}\) long cylindrical portion attached to a frustum of a cone. If the total height is \(22 \,\rm{cm,}\) diameter of the cylindrical portion is \(8\rm{cm}\) and the diameter of the top o... |
This shows you the differences between two versions of the page.
— separation_algebras [2018/08/04 22:44] (current)
jipsen created
Line 1: Line 1: + =====Separation algebras===== + + Abbreviation: **SepAlg** + + ====Definition==== + A \emph{separation algebra} is a [[generalized separation algebra]] such that + + $\cdo... |
Contents
Strong Dirichlet boundary conditions are imposed by providing a listof
DirichletBC objects. The classdocumentation provides the syntax, this document explains themathematical formulation of the boundary conditions in Firedrake, andtheir implementation.
To understand how Firedrake applies strong (Dirichlet) bou... |
You not only can, but also must treat symbols for units by the ordinary rules of algebra, since unit symbols are mathematical entities and not abbreviations.
The
value of a quantity is expressed as the product of a number and a unit. That number is called the numerical value of the quantity expressed in this unit.
This... |
Probably i've an answer for this problem, but i'm not sill sure that it works.
It is not important to "find" the two path, the only important thing is to "know" if they exist or not. I don't think that this is an NP complete problem.
So, take the adjacency matrix $\textbf A$. We can easily suppose that it is filled wit... |
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Now showing items 1-1 of 1
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 ... |
De Bruijn-Newman constant
For each real number [math]t[/math], define the entire function [math]H_t: {\mathbf C} \to {\mathbf C}[/math] by the formula
[math]\displaystyle H_t(z) := \int_0^\infty e^{tu^2} \Phi(u) \cos(zu)\ du[/math]
where [math]\Phi[/math] is the super-exponentially decaying function
[math]\displaystyle... |
Edge at \(m_{\rm inv}=79\GeV\) in dilepton events There were virtually no deviations of the LHC from the Standard Model a month ago. But during the last month, there has been an explosion of so far small excesses. Off-topic: Have you ever played 2048? Flash 2048. A pretty good game. Cursor arrow keys.One day after Tomm... |
I've seen other posts (Inner automorphisms form a normal subgroup of $\operatorname{Aut}(G)$) about the topic of $\operatorname{Inn}(G) \simeq G/Z(G)$, but what I want to ask is a detail. When we ensure that $\operatorname{Inn}(G) \simeq G/Z(G)$, we want to say that there exists some isomorphism $F$ such that:
$$F: G/Z... |
The simplest forcing to add a dominating function is Hechler forcing $\newcommand{\D}{\mathbb{D}}\D$. In set-theoretic circles, conditions in $\D$ are pairs $(s,f)$ where $s$ is a finite sequence of natural numbers and $\newcommand{\N}{\mathbb{N}}f:\N\to\N$, extension is defined by $(s,f) \leq_{\D} (t,g)$ if $t \supset... |
Experimental Mathematics Experiment. Math. Volume 17, Issue 3 (2008), 375-383. Subrings of the Asymptotic Hecke Algebra of Type $H_4$ Abstract
The structure of the subring $J^{\Gamma \cap \Gamma^-1$ of the asymptotic Hecke algebra is described for $\Gamma$}a left cell of the Coxeter group of type $H_4$. A small set of ... |
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Kaon femtoscopy in Pb-Pb collisions at $\sqrt{s_{\rm{NN}}}$ = 2.76 TeV
(Elsevier, 2017-12-21)
We present the results of three-dimensional femtoscopic analyses for charged and neutral kaons recorded by ALICE in Pb-Pb collisions at $\sqrt{s_{\rm{NN}}}$ = 2.76 TeV. Femtoscopy is used to... |
Here are the schematic and naming conventions used :
simulate this circuit – Schematic created using CircuitLab Charge and discharge bounds
You probably know that already, but the theory of operation is as follows :When TRIGGER is pulled at \$2/3 \cdot V_{CC}\$, the output goes \$\text{LOW}\$, and the DISCHARGE pin bec... |
If we have an equation we want to solve such as $\sqrt{x} = 3$, we can say something such as
square both sides or " raise both sides to the power of 2", to arrive at $x = 9$. So $3 \rightarrow 3^2$ with this action.
Is there any standard terminology which can be used for taking a number (or each side of an equation) an... |
Let $S^n$ be the standard unit $n$-sphere, embedded in Euclidian space as $S^n = \{ x \in {\mathbb{R}}^{n+1} | \| x \| = 1 \}$. Define geodesic distance as $d(x, y) = \arccos (x \cdot y)$, where $\cdot$ is the Euclidian dot product.
My lecture notes introduce geodesic distance on page 11, but they're quite hand-wavy ab... |
We know that quantum tunneling is the reason behind several natural phenomenon like alpha decay and thermonuclear fusion inside the stars. How can it influence chemical reactions by tunnelling a species through the activation energy? If so how does it influence the kinetics and fraction of molecules taking part in the ... |
From: Robert Waldmann, Brad DeLong
To: Interested Parties Date: 2019-04-12
This note tries to dot some of the i's and cross some of the t's in Olivier Blanchard's excellent, thoughtful, and provocative American Economic Association Presidential Address "Public Debt and Low Interest Rates" https://www.aeaweb.org/aea/201... |
Ex.9.1 Q2 Some Applications of Trigonometry Solution - NCERT Maths Class 10 Question
A tree breaks due to storm and the broken part bends so that the top of the tree touches the ground making an angle \(30^{\circ}\) with it. The distance between the foot of the tree to the point where the top touches the ground is \(8\... |
This was given as a homework problem but I have already submitted the assignment. I'd like to resolve it at this point for my own satisfaction.
Given that $L_1$ is a linear language and $L_2$ is a regular language, show that $L=L_1L_2$ is a linear language.
Recall that a linear grammar $G=(\Sigma, V, P, \sigma)$ has pr... |
Is there a simple example of a Boolean function $f:\{0,1\}^m \to \{0,1\}$ that we know can be computed by a polynomial-size circuit, but cannot be computed by any polynomial-size monotone circuit? Ideally, I'd be especially interested in a simple example where there is an exponential gap between the size of the smalles... |
I have been trying to understand Discrete Fourier Time Series (NOT Transform).
It is defined as
$$a_k = \sum_{n=0}^{N-1} x[n]e^{jk\frac{2\pi}{N}n}$$
where N is the Time period and an integer (by definition), and $n$ goes from $0 ... N-1$.
Fair enough. But when N = 0.2 second as the time period of the wave, then how we ... |
This answer is based on a comment by J. Kynčl. It gives a bound roughly $\rho_{min}(S) \leq \left(\frac{1}{1.074}\right)^d$ which is already exponentially decreasing, but perhaps still far from the optimum. Thus, a better bound would still be of interest.
Let $AB$ one of the longest edges of $S$. Without loss of genera... |
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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-... |
There ought to be a diagram showing how the angle $\theta$ is defined. Nevertheless, the boundary condition which you have been given is confusing.
The diagram above shows a vertical plane through the centre of the spherical electrode. There is
cylindrical symmetry here, so a cylindrical co-ordinate system is the obvio... |
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... |
I have an issue with the following problem:
Two quadratic equations have real roots $\alpha$ and $\beta$ such that $$\alpha - \beta = 3$$ and $$\alpha \beta = 2(\alpha + \beta).$$ Find the two possible quadratic equations that satisfy these conditions.
Since $\alpha$ is larger than $\beta$, in the general solution to t... |
Essay and Opinion A new graph density
Version 1Released on 08 April 2015 under Creative Commons Attribution 4.0 International License Authors' affiliations Laboratoire Electronique, Informatique et Image (Le2i). CNRS : UMR6306 - Université de Bourgogne - Arts et Métiers ParisTech Keywords Community discovery Density @G... |
In reading about the inversion of sucrose I came across the equation for the reaction rate constant below:
$$k = \left(\frac{2.303}{t}\right) \log\left[\frac{\alpha(0) - \alpha(\infty)}{\alpha(t) - \alpha(0)}\right] \tag{5}$$
What is the logic for difference of the rotations' sign for the logarithmic term? i.e conceptu... |
We know that quantum tunneling is the reason behind several natural phenomenon like alpha decay and thermonuclear fusion inside the stars. How can it influence chemical reactions by tunnelling a species through the activation energy? If so how does it influence the kinetics and fraction of molecules taking part in the ... |
Here is yet another problem I can't seem to do by myself... I am supposed to prove that $$\sum_{n \le x} \frac{\varphi(n)}{n^2}=\frac{\log x}{\zeta(2)}+\frac{\gamma}{\zeta(2)}-A+O \left(\frac{\log x}{x} \right),$$ where $\gamma$ is the Euler-Mascheroni constant and $A= \sum_{n=1}^\infty \frac{\mu(n) \log n}{n^2}$. I mi... |
I'm solving a problem involving a Fermi gas. There is a specific sum I cannot figure my way around.
A set of equidistant levels, indexed by $m=0,1,2 \ldots$, is populated by spinless fermions with population numbers $\nu_m =0 $ or $1$. I need to compute the following sum over the set of all possible configurations $\{ ... |
Ex.12.3 Q14 Areas Related to Circles Solution - NCERT Maths Class 10 Question
\({AB}\) and \({CD}\) are respectively arcs of two concentric circles of radii \(\text{21 cm}\) and \(\text{7 cm}\) and center \({O}\) (see Figure). If \(\angle {AOB} = 30^\circ \), find the area of the shaded region
.
Text Solution What is k... |
Ex.6.3 Q5 Triangles Solution - NCERT Maths Class 10 Question
\(S\) and \(T\) are points on sides \(PR\) and \(QR\) of \(\Delta PQR\) such that \( \angle P{\rm{ }} = \angle RTS\). Show that
Diagram
Text Solution Reasoning:
If two angles of one triangle are respectively equal to two angles of another triangle, then the t... |
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J/Ψ production and nuclear effects in p-Pb collisions at √sNN=5.02 TeV
(Springer, 2014-02)
Inclusive J/ψ production has been studied with the ALICE detector in p-Pb collisions at the nucleon–nucleon center of mass energy √sNN = 5.02TeV at the CERN LHC. The measurement is performed in... |
The lemma 13.1 of CLRS proves that the height of a red black tree with $n$ nodes is
$$h(n) \leq 2\log_2(n+1)$$
There's a subtle step I don't understand. The property 4 reported at the beginning of the chapter states:
If a node is red, then both its children are black.
And because of such property it is later stated
Acc... |
The
amsmath package provides a handful of options for displaying equations. You can choose the layout that better suits your document, even if the equations are really long, or if you have to include several equations in the same line.
Contents
The standard LaTeX tools for equations may lack some flexibility, causing o... |
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