text stringlengths 256 16.4k |
|---|
I'm trying to develop some basic intuition here, so this comes mostly as a jumble of commentary/questions. Hope its acceptable.
Helmholtz Free Energy: $A = -{\beta ^{-1}}lnZ$. I find this statement to be incredible profound. Granted, I found it yesterday.
Suppose my system has one energy state with no degeneracy. $Z = ... |
The Annals of Probability Ann. Probab. Volume 23, Number 2 (1995), 501-521. Existence of Quasi-Stationary Distributions. A Renewal Dynamical Approach Abstract
We consider Markov processes on the positive integers for which the origin is an absorbing state. Quasi-stationary distributions (qsd's) are described as fixed p... |
Can somebody point me towards a derivation using
statistical physics for the fact that the Helmholtz free energy $F$ is minimised at equilibrium for a canonical system at constant temperature and volume?
I'll sketch the derivation in a classical setting. Let's say we have a system with $N$ degrees of freedom, with $N$ ... |
My other answer addressed the question in the title. Here I will try to address the two queries at the end of the OP question. @ybeltukov was the first to point out the key issue, which is that
ContourPlot works only when it finds sample points where the values of the function are greater than the contour level and poi... |
Difference between revisions of "Main Page"
(→Threads)
(→Threads)
Line 26: Line 26:
We are also collecting bounds for [[Fujimura's problem]], motivated by a [[hyper-optimistic conjecture]].
We are also collecting bounds for [[Fujimura's problem]], motivated by a [[hyper-optimistic conjecture]].
+ +
Here are some [[unso... |
This will be a talk at the Conference in honor of Arthur W. Apter and Moti Gitik at Carnegie Mellon University, May 30-31, 2015. I am pleased to be a part of this conference in honor of the 60th birthdays of two mathematicians whom I admire very much.
Abstract. The weakly compact embedding property for a cardinal $\kap... |
Well this seems like a basic principle, yet I can't seem to get it. (We're expect to "know" this already).
In a three phase situation I'm given a source voltage of 230V. - So the waveform of each of the phases would be: \$ v_s = \sqrt2 \cdot 230 \cdot \sin(\omega t + \theta_i)\$
Where \$\theta_i\$ is \$0, \tfrac{2}{3} ... |
Many define the likelihood of the data something like $\prod_{x} p(x|\theta)$ others like $p(x|\theta)$. Is the likelihood defined for one sample point/data element (like one document from a collection of documents or one sentence from a collection of sentences), for the whole collection of data elements, or for both?
... |
Let $n$ be the original number and $m$ the number after a digit is deleted. Suppose that the deleted digit is $d$, that $r$ is the number represented by the $k$ digits to the right of $d$, and that $\ell$ is the number represented by the digits to the left of $d$, so that $m=10^k\ell+r$, and $n=10^{k+1}\ell+10^kd+r$.
S... |
Advances in Differential Equations Adv. Differential Equations Volume 13, Number 7-8 (2008), 753-780. Entire solutions and global bifurcations for a biharmonic equation with singular non-linearity in $\Bbb R^3$ Abstract
We study the structure of solutions of the boundary-value problem \begin{equation} \tag*{(0.1)} \Del... |
I am trying to get the maximum likelihood estimate for the parameter $p$. The distribution is the following:
$$ f(x\mid p) = \begin{cases} \frac{p}{x^2} &\text{for} \ p\leq x < \infty \ \\ 0 &\text{if not} \end{cases} $$
The sample has size $n$.
The problem is, when I try to estimate it by the procedure I know, I would... |
Let $f:[0,1]\to[1,3]$ be continuous. Prove $$1 \leq \int_0^1 f(x)\,\mathrm dx \int_0^1 \frac{1}{f(x)}\, \mathrm dx\leq \frac{4}{3}.$$
The left is just Cauchy's inequality with integral form, but what's the right?
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professi... |
We know (for instance : https://en.wikipedia.org/wiki/Poisson%27s_ratio ) that the Poisson ratio is $\nu=1/2-Y/(6B)$, with $Y$ the Young modulus and $B$ the bulk modulus.
Let's assume we have a energy density $f(r)$ that depends on the distance $r$ between 2 particles of the solid. It can thus also be written as depend... |
What you are looking for is the correspondence between algebraic Hecke characters over a number field $F$ and compatible families of $l$-adic characters of the absolute Galois group of $F$. This is laid out beautifully in the first section of Laurent Fargues's notes here.
EDIT: In more detail, as Kevin notes in the com... |
I'm going to combine two criteria to find the wall thickness (the only unknown here).
The first criterion is based on yielding of the wall material prior to to failure as a result of crack formation and propagation, so the inspection team can observe the plastic deformation and the pressure within the tank be released ... |
To answer your first question, one way to define (co)homology with local coefficients is the following.
Let $X$ be a space, let $\Pi(X)$ be the fundamental groupoid of $X$, ie. a category with objects points of $X$ and morphisms $x \rightarrow y$ given by homotopy classes of paths. A
local coefficient system $M$ on $X$... |
You are blindfolded and disoriented, standing exactly 1 mile from the Great Wall of China. How far must you walk to find the wall?
Assume the earth is flat and the Great Wall is infinitely long and straight.
Puzzling Stack Exchange is a question and answer site for those who create, solve, and study puzzles. It only ta... |
In the second answer of this post, Euler-Lagrange equations and friction forces
I see a normal Lagrangian (T-V) times an exponential function. $${\cal L}=e^{t\gamma/m}\left(\frac{m}{2}\dot{x}^2 -U(t,x)\right)\:.$$
And, in the #9 of this post, https://www.physicsforums.com/threads/lagrangian-of-object-with-air-resistanc... |
Difference between revisions of "Moser-lower.tex"
Line 1: Line 1:
\section{Lower bounds for the Moser problem}\label{moser-lower-sec}
\section{Lower bounds for the Moser problem}\label{moser-lower-sec}
−
In this section we discuss lower bounds for $c'_{n,3}$.
+
In this section we discuss lower bounds for $c'_{n,3}$. Cl... |
Consider a regular polygon with $N$ sides (and therefore $N$ vertices) such that the distance between its center $O$ and each of its vertices is $r$. At each vertex of the polygon, a charge $q$ is placed (see figure 1). What is the electric field ${\bf E}$ produced by these charges at the point $O$?
Fig. 1: Regular pen... |
Yours is a subtle question with a rather subtle answer. From the way you ask the question, you seem to be thinking of the photon as a little billiard ball. It is not. It is an excitation of a quantum field, which is described very differently from a "particle" in the classical sense. Even so, the short answer, in some ... |
My question - which is likely stupid or appears due to some confusion - stems from the following considerations: when quantizing canonically we are told (see any book on QFT) that a Dirac fermion field can be expressed as
$$ \psi(x) = \int d\tilde{p} (u \cdot\mathbf{a}\,e^{-ipx} + v\cdot\mathbf{b}^\dagger\, e^{ipx}) $$... |
I) Wigner's Theorem states that a symmetry operation $S: H \to H$ is a unitary or anti-unitary$^{1}$ operator $U(S)$ up to a phase factor $\varphi(S,x)$,
$$ S(x)~=~ \varphi(S,x)\cdot U(S)(x), \qquad x~\in~H,\qquad \varphi(S,x)~\in~\mathbb{C} ,\qquad |\varphi(S,x)|~=~1 .$$
In this context, a
symmetry operation $S$ is by... |
$n$-fold Variants of Large Cardinals This page is a WIP.The $n$-fold variants of large cardinal axioms were created by Sato Kentaro in [1] in order to study and investigate the double helix phenomena. The double helix phenomena is the strange pattern in consistency strength between such cardinals, which can be seen bel... |
Is there a physical limit to data transfer rate (e.g. for USB $3.0$, this rate can be a few Gbit per second)? I am wondering if there is a physical law giving a fundamental limit to data transfer rate, similar to how the second law of thermodynamics tells us perpetual motion cannot happen and relativity tells us going ... |
103 0 1. Homework Statement
Determine the period of oscillations of a simple pendulum ( a particle of mass m suspended by a string of length l in a gravitational field) as a function of the amplitude of oscillations.
2. Homework Equations
[tex] T(E) = \sqrt(2m) \int^{x_2(E)}_{x_1(E)}\frac{dx}{\sqrt(E-U(x)} [/tex]
where... |
I need to solve a problem that tells me to find out the motion of both the pendulums that appear in the first 45 seconds of this video
I think this kind of motion is described by a system of differential equation of the form:
$$\ddot{x} + \omega^2x = \epsilon y$$ $$\ddot{y} + \omega^2 y = \epsilon x$$
where all constan... |
When modeling an ideal transformer, why do we not consider the
inductance of the primary and secondary winding of the transformer.
For an ideal transformer, the primary and secondary inductances are arbitrarily large ('infinite'). This must be so since, for an ideal transformer, there is no frequency dependence.
To see... |
(MWE at the end of the post)
I need to solve a non-linear equation $f(y;x_1,x_2,..,x_5)$ in one variable $y$ and then compute 4 new output expressions, for over 60 different initial parameter inputs of $x_i$. The 4 output variables which are as follows:
$g_m(y,x_1,..,x_5) \; \forall m$
The main equation will solve for ... |
Regularization using methods such as Ridge, Lasso, ElasticNet is quite common for linear regression. I wanted to know the following: Are these methods applicable for logistic regression? If so, are there any differences in the way they need to be used for logistic regression? If these methods are not applicable, how do... |
Introduction to sharpening
Sharpening is an important part of digital image processing. It restores some of the sharpness lost in the lens and image sensor.
Every digital image benefits from sharpening at some point in its workflow— in the camera, the RAW conversion software, and/or image editor. Sharpening has a bad n... |
Home
Integration by PartsIntegration by Parts
Examples
Integration by Parts with a definite integral
Going in Circles
Tricks of the Trade
Integrals of Trig FunctionsAntiderivatives of Basic Trigonometric Functions
Product of Sines and Cosines (mixed even and odd powers or only odd powers)
Product of Sines and Cosines (... |
It is strange to me that for a symmetry which involves $\dot{x}$, there seems to always appear a term with $\dddot{x}$ in the variation of the equations of motion, which doesn't makes much sense. I think that probably the procedure I am following is wrong.
I will show you an example: Consider the simple case of a free ... |
Difference between revisions of "Modes"
(added some info)
m (Copy edit →Packet)
Line 188: Line 188:
This mode was popular in the late 1970's and early 1980's, but has decreased in use since then.
This mode was popular in the late 1970's and early 1980's, but has decreased in use since then.
−
[http://en.wikipedia.org/w... |
Suppose $C$ is a small category and $X_{\bullet}$ is a simplicial object in $C$. In particular, by composing with Yoneda $$y:C \to Set^{C^{op}}$$ $y(X)_{\bullet}$ is a simplicial presheaf. I believe it is true that in (either the injective or projective) model structure on simplicial presheaves, that $y(X)_{\bullet}$ "... |
Limits of iterates of spherical Aluthge transforms
Orateur:
R.E. Curto
Affiliation:
Iwoa
Dates:
Vendredi, 7 Juin, 2019 - 14:00 - 15:00
Résumé:
Let $\mathbf{T} \equiv (T_1,T_2)$ be a commuting pair of Hilbert space operators, and let $P:=\sqrt{T_1^{\ast}T_1+T_2^{\ast}T_2}$ be the positive factor in the
(joint) polar dec... |
The film Circular Reuleaux triangle tells about the figures of constant width. The Reuleuaux triangle —, the simplest figure of constant width will help us to drill square holes. If one moves the center of the this «triangle» along some trajectory, its vertices will draw almost a square and itself will cover the area i... |
My model is the following: I have a 1D-lattice with L sites. Each site can be occupied by either one or zero atoms. The Hamiltonian looks as follows: $$H = T\sum(b^\dagger_i b_{i+1} + h.c.) + V\sum n_i n_{i+1}$$
My question is now of a rather basic quantum mechanical nature. I want to make sure what I'm doing is right ... |
Suppose you are given a nowhere-vanishing exact 2-form $B=dA$ on an open, connected domain $D\subset\mathbb{R}^3$. I'd like to think of $B$ as a magnetic field.
Consider the product $H(A)=A\wedge dA$. At least in the plasma physics literature, $H(A)$ is known as the magnetic helicity density.
How can one determine if t... |
Definition of quasi toric manifolds :
The action of $(S^1)^n$ on $\Bbb C^n$ by pointwise multiplication is called the standard representation. Given a manifold $M^{2n}$ with an $(S^1)^n$-action, a
local isomorphism of $M^{2n}$ with the standard representation consists of an automorphism $\theta:(S^1)^n\to (S^1)^n$ $(S^... |
Let $p_n$ be the $n$-th prime number, as usual: $p_1 = 2$, $p_2 = 3$, $p_3 = 5$, $p_4 = 7$, etc.
For $k=1,2,3,\ldots$, define $$ g_k = \liminf_{n \rightarrow \infty} (p_{n+k} - p_n). $$ Thus the twin prime conjecture asserts $g_1 = 2$.
Zhang's theorem (= weak twin prime conjecture) asserts $g_1 < \infty$.
The prime $m$... |
Literature on Carbon Nanotube Research
I have hijacked this page to write down my views on the literature on Carbon Nanotube (CNT) growths and processing, a procedure that should give us the cable/ribbon we desire for the space elevator. I will try to put as much information as possible here. If anyone has something to... |
As far as I understand it, the first principle of thermodynamics is a mere definition of the quantity “Heat”: $$\text d Q: = \text d L + \text d U.$$ This is somewhat the point of view taken in Fermi's introductory book "Thermodynamics":
[...] $$\Delta U + L=0$$If the system is not thermally isolated, the first member ... |
I’d like to share a simple proof I’ve discovered recently of a surprising fact: there is a universal algorithm, capable of computing any given function!
Wait, what? What on earth do I mean? Can’t we prove that some functions are not computable? Yes, of course.
What I mean is that there is a universal algorithm, a Turin... |
I was given the following formula for the Fourier series of a function with period $2\pi$:
$$ \begin{align*} \hat f(x) = \frac {a_0} 2 + \sum_{n=1}^\infty a_n \cos (nx) + b_n \sin (nx) \end{align*} $$
This formula is awkward because the coefficient $a_0$ is halved, whereas the coefficients $a_n$ and $b_n$ aren't, for $... |
Consider the system:
$\begin{cases}x' = e^{ay} - e^x \\ y' = a x^2 + (a-a^2) x + ay^2 e^{-y}\end{cases}$
Using Lyapunov first method we have, for $a \in ]-\infty,1[ \cup ]0,1[$ $p = (0,0)$ is unestable and for $a \in ]1,+\infty[$ is asymptotically stable.
For $a = 1$ I need to use Chetaev theorem to show that it is une... |
There are proofs that treat the cases of real and non-real $\chi$ on an equal footing. One proof is in Serre's Course in Arithmetic, which the answers by Pete and David are basically about. That method is using the (hidden) fact that the zeta-function of the $m$-th cyclotomic field has a simple pole at $s = 1$, just li... |
This question is about Feynman diagram and vertices in a hadron decay, which comes from Problem 89.5 in Srednicki's textbook Quantum Field Theory. The reaction involved is \begin{equation} d\rightarrow u + e + \overline{\nu}_{e} \tag{1} \end{equation}
After integrating out the $W^{\pm}$ fields, we get an effective inte... |
PCTeX Talk Discussions on TeX, LaTeX, fonts, and typesetting
Author Message zedler Joined: 03 Mar 2006 Posts: 15
Posted: Mon Mar 27, 2006 11:53 am Post subject: spacing of mathrm Hello,
\documentclass{book}
\usepackage{times,mtpro2}
\begin{document}
$(\mathrm j$
\end{document}
gives touching glyphs.
Michael Michael Spi... |
Home
Integration by PartsIntegration by Parts
Examples
Integration by Parts with a definite integral
Going in Circles
Tricks of the Trade
Integrals of Trig FunctionsAntiderivatives of Basic Trigonometric Functions
Product of Sines and Cosines (mixed even and odd powers or only odd powers)
Product of Sines and Cosines (... |
Forgot password? New user? Sign up
Existing user? Log in
Q1Q1Q1 Find the largest y such that
11+x2≥y−xy+xforallx>0\frac { 1 }{ 1+{ x }^{ 2 } } \ge \frac { y-x }{ y+x } \quad for\quad all\quad x>01+x21≥y+xy−xforallx>0
Q2Q2Q2 Find the minimum and maximum values of
x+1xy+x+1+y+1yz+y+1+z+1zx+z+1\frac { x+1 }{ xy+x+1 } +\fr... |
Difference between revisions of "Abstract.tex"
Line 1: Line 1:
\begin{abstract}
\begin{abstract}
−
The Hales--Jewett theorem asserts that for every $r$ and every $k$ there exists $n$ such that every $r$-colouring of the $n$-dimensional grid $\{1, \dotsc, k\}^n$ contains a combinatorial line. This result is a generaliza... |
Forgot password? New user? Sign up
Existing user? Log in
Determine the Taylor series for the function f(x)=sin(x)cos(x) centered at x=π.f(x) = \sin(x)\cos(x) \text{ centered at } x = \pi.f(x)=sin(x)cos(x) centered at x=π.
At a=0 a = 0a=0, what is the Taylor series expansion of
ln(1+x)? \ln ( 1 + x ) ? ln(1+x)?
1(1−x)2?... |
Define the quadratic form $$Q(z_1,z_2,z_3,z_4) = 13 + \sum_{i=1}^4 (10+i)z_i +5 \sum_{1 \le i \le j \le 4} z_iz_j.$$ Then, $r_Q(n) := \left|\{(z_1,z_2,z_3,z_4) \in \mathbb{Z}^4 : Q(z_1,z_2,z_3,z_4) = n \}\right|$ is weakly multiplicative. I can prove this by using the generating function $\sum r_Q(n) q^n$ which is in t... |
Let $(e_n)$ be an orthonormal sequence in an inner product space $X$. Then, for every $x \in X$, we have $$ \sum_{n=1}^\infty \vert \langle x, e_n \rangle \vert^2 \ \leq \ \Vert x \Vert^2.$$
Now $\ell^2$ is the inner product space of all sequences $x\colon=(\xi_n)$ of complex numbers such that $$\sum_{n=1}^\infty \vert... |
Difference between revisions of "Sperner's theorem"
Line 41: Line 41:
<math>\mathbf{E}_{C_1, \dots, C_d} \left[\mathbf{E}_{s_1, \dots, t_d}[f(C_1(s_1), \dots, C_d(s_d)) \cdots f(C_1(t_1), \dots, C_d(t_d))]\right].</math>
<math>\mathbf{E}_{C_1, \dots, C_d} \left[\mathbf{E}_{s_1, \dots, t_d}[f(C_1(s_1), \dots, C_d(s_d)) ... |
PHOTO SERIES PROJECTIVE TRIANGLES TAYLOR SERIES STILLS ANIMATIONS SHORT FILMS
ALLOSPHERE
The Allosphere is a 30ft diameter spherical screen enclosing a wide walkway which can accomodate 30+ visitors for simultaneous fully immersive virtual reality experiences. Designed and operated by Jo Ann Kuchera-Morin of UCSB's Med... |
$\def\Spec{\mathop{\rm Spec}}\def\R{{\bf R}}\def\Ep{{\rm E}^+}\def\L{{\rm L}}\def\EpL{\Ep\L}$One can argue that an object of the right category of spaces in measure theoryis not a set equipped with a σ-algebra of measurable sets,but rather a set $S$ equipped with a σ-algebra $M$ of measurable sets and a σ-ideal $N$ of ... |
Astrid the astronaut is floating in a grid. Each time she pushes off she keeps gliding until she collides with a solid wall, marked by a thicker line. From such a wall she can propel herself either parallel or perpendicular to the wall, but always travelling directly \(\leftarrow, \rightarrow, \uparrow, \downarrow\). F... |
Soliton solutions for quasilinear Schrödinger equations involving supercritical exponent in $\mathbb R^N$
1.
Department of Mathematics, University of British Columbia, Vancouver, BC, Canada
$-\epsilon \Delta u+V(x)u-\epsilon k(\Delta(|u|^2))u=g(u), \quad u>0,x \in \mathbb R^N,$
where g has superlinear growth at infinit... |
Defining differential operator that acts like curl
Hello,
As a newbie in using SAGE (experience with Python and Numpy), I was wondering how to define a differential operator that acts like curl (or $\nabla \times \vec F$). The curl for a vector field $\vec F=(F_x,F_y, F_z)$is defined as a determinant $\mathrm{det} (\na... |
This question already has an answer here:
I am trying to attain an ARIMA model for the following Time Series Data:
There is quite obviously a seasonal component - as the plot seems to oscillate between smaller and larger peaks, its seems to suggest that the pattern repeats every 48 timesteps.
I then took the seasonal d... |
Do you know how a fireman and the direction of a financial time series are related? If your answer is no, you’re reading the right post.
An introduction to k-Means: Voronoi diagram
Suppose that you a work at an emergency center, and your job is to tell the pilots of firefighter helicopters to take off. You receive an e... |
Epsilon naught, $\epsilon_0$ The ordinal $\epsilon_0$, commonly given the British pronunciation "epsilon naught," is the smallest ordinal $\alpha$ for which $\alpha=\omega^\alpha$ and can be equivalently characterized as the supremum
$$\epsilon_0=\sup\{\omega,\omega^\omega,\omega^{\omega^\omega},\ldots\}$$
The ordinals... |
Difference between revisions of "Kakeya problem"
Line 36: Line 36:
since the set of all vectors in <math>{\mathbb F}_3^n</math> such that at least one of the numbers <math>1</math> and <math>2</math> is missing among their coordinates is a Kakeya set.
since the set of all vectors in <math>{\mathbb F}_3^n</math> such th... |
1. How can we "interact" with a photon with a purely mechanical device such as a shutter?
Here is the culprit - the QED vertex:
The mechanical shutter, whether made from metal or plastic, contains charged particles (electrons and atomic nuclei). Charged particles interact with photons via the QED vertex. On the most fu... |
Is there a way to find $\sqrt[n]{x}$ with
Mathematica beside of
x^(1/n)as this is something different, because this is not always the same$$(-1)^{\frac{2}{4}}=i \neq 1= \sqrt[4]{(-1)^2}$$In the help I only found
Sqrt[x] which is the squareroot and
CubeRoot[x] for the cubic root.
Is there a reason that there aren't $n$-... |
I'm trying to find the Fourier Transform of the following rectangular pulse:
$$ x(t) = rect(t - 1/2) $$
This is simply a rectangular pulse stretching from 0 to 1 with an amplitude of 1. It is 0 elsewhere. I tried using the definition of the Fourier Tranform:
$$ X(\omega) = \int_0^1 (1)*e^{-j\omega*t}dt $$
However carry... |
Take your favourite newspaper and write down all the numbers you can find in it. Then take the first, leftmost digit of each number. This is called the most significative digit (MSD). What is the frequency you expect to observe for these digits? If your answer is that all digits from 1 to 9 have the same probability, p... |
Let me introduce to you the topic of modal model theory, injecting some ideas from modal logic into the traditional subject of model theory in mathematical logic.
For example, we may consider the class of all models of some first-order theory, such as the class of all graphs, or the class of all groups, or all fields o... |
Norman Lewis Perlmutter successfully defended his dissertation under my supervision and will earn his Ph.D. at the CUNY Graduate Center in May, 2013. His dissertation consists of two parts. The first chapter arose from the observation that while direct limits of large cardinal embeddings and other embeddings between mo... |
Literature on Carbon Nanotube Research
I have hijacked this page to write down my views on the literature on Carbon Nanotube (CNT) growths and processing, a procedure that should give us the cable/ribbon we desire for the space elevator. I will try to put as much information as possible here. If anyone has something to... |
$A \subset \mathbb{R}^n $ is open $ \iff A \cap \overline{X} \subset \overline{A \cap X} $
The $ \overline{X} $ represents the closure of a set.
If I assume that $A$ is open we have many cases for the left side $ A \cap \overline{X} $.
$ A \cap \overline{X} = \emptyset $ $ A \cap \overline{X} = A $ since $ A \subset \o... |
Literature on Carbon Nanotube Research
I have hijacked this page to write down my views on the literature on Carbon Nanotube (CNT) growths and processing, a procedure that should give us the cable/ribbon we desire for the space elevator. I will try to put as much information as possible here. If anyone has something to... |
Let $\gamma : [0,1] \to \mathbb R^2$ be a finite $C^2$-curve in the plane which does not intersect itself. Let $p(z)$ be a second-degree polynomial in $z \in \mathbb R^2$. Can we construct a Riemannian metric $g$ along $\gamma$ such that
$\gamma$ is a geodesic of $g$, $\gamma$ has length 1, and $p(z)$ is the 2-jet of $... |
If your system is damped, after some periods, the resonance will occur regardless of at which point you apply the harmonic force on the swing and only the resonance frequency. There is a steady state solution: $ x(t)= X \sin{(2 \pi f t +\phi)} $. So if you apply a force with resonant frequency, it will vibrate at reson... |
The
theta function is the analytic function $\theta:U\to\mathbb{C}$ defined on the (open) right half-plane $U\subset\mathbb{C}$ by $\theta(\tau)=\sum_{n\in\mathbb{Z}}e^{-\pi n^2 \tau}$. It has the following important transformation property.
Theta reciprocity: $\theta(\tau)=\frac{1}{\sqrt{\tau}}\theta\left(\frac{1}{\ta... |
Suppose I am given a morphism $f:BG\to BGL_1(R)$ for $R$ some at least $E_1$-ring spectrum and $G$ a loop space. Then This corresponds, I believe, to an action of $G$ on $R$, coming from a morphism $G\to GL_1(R)$. The first part of my question is: does this imply a map of spectra $R[G]\wedge R\to R$ or something like t... |
We owe Paul Dirac two excellent mathematical jokes. I have amended them with a few lesser known variations.
A.
Square root of the Laplacian: we want $\Delta$ to be $D^2$ for some first order differential operator (for example, because it is easier to solve first order partial differential equations than second order PD... |
Bear with me while I try to explain exactly what the question is. The question Can a curvature in time (and not space) cause acceleration? is imagining a coordinate system in which the curvature is only in the time coordinate. I want to be as precise as possible about what we mean by
curvature in the time coordinate.
I... |
I'm a 2nd year physics undergraduate and recently I've volunteered to give a short presentation on the Sackur-Tetrode equation derivation and its use at removing the Gibbs paradox. I've looked on the Internet and in some books and found many methods for deriving this result. The one I'm going with is the derivation fro... |
In this paper, we present quantum algorithms to solve the linear structures of Boolean functions. “Suppose Boolean function $$f$$ f : $$\{0, 1\}^{n}\rightarrow \{0, 1\}$$ { 0 , 1 } n → { 0 , 1 } is given as a black box. There exists an unknown n-bit string $$\alpha $$ α such that $$f(x)=f(x\oplus \alpha )$$ f ( x ) = f... |
I'm working on a 4-layer PCB with a U-Blox module and I'm trying to calculate the space between the fencing vias next to the Antenna trace and for the stitching vias.
According to the datasheet we have the following possible frequencies:
The case which would cause the closest vias is the last one.
According to the calc... |
Forgot password? New user? Sign up
Existing user? Log in
Is there a positive integer nnn such that 2n≡1(mod7) ?2^n \equiv 1 \pmod{7} \, ?2n≡1(mod7)?
115,215,315,…,1415,1515\frac{1}{15}, \frac{2}{15}, \frac{3}{15}, \ldots, \frac{14}{15}, \frac{15}{15}151,152,153,…,1514,1515How many of these fractions cannot be reduced?
... |
What is meant by a "system curve" that is used to determine the operating point of a pump. I know what a "pump curve" is, but I often hear about a "system curve" being generated so that the pump operating point can be determined by where the pump curve and system curve intersect.
Imagine if you were pumping through a s... |
We have an elementary sharp lower bound for the regulator of a real quadratic field as a function of the discriminant
$$R\geq \tfrac{1}{2}(\sqrt{d-4}+\sqrt{d})$$
It is sharp because the equality holds infinitely often for $d=x^2+4$.
The problem of finding a good upper seems much more complicated, but there's still is a... |
PCTeX Talk Discussions on TeX, LaTeX, fonts, and typesetting
Author Message stubner Joined: 14 Mar 2006 Posts: 7
Posted: Wed Apr 19, 2006 2:19 pm Post subject: absolute values Hi everybody,
it seems I ahven't used much absolute values lately since only yesterday I found that things like $|x|$ or $|o|$ look offbalance t... |
Essentially, I want to find a single matrix $X$ such that conjugation by $X$ sends:
$$\begin{bmatrix} 1 & 0 & 0 & 0 & 0 \\ 0 & -1 & 0 & 0 & 0 \\ 0 & 0 & 1 & 0 & 0 \\ 0 & 0 & 0 & -1 & 0 \\ 0 & 0 & 0 & 0 & 1 \end{bmatrix} \mapsto \begin{bmatrix} -1 & 0 & 0 & 0 & 0 \\ 0 & -1 & 0 & 0 & 0 \\ 0 & 0 & 1 & 0 & 0 \\ 0 & 0 & 0 &... |
Let $V,H$ be separable Hilbert spaces such that there are dense injections $V \hookrightarrow H \hookrightarrow V^*$. (For example, $H = L^2(\mathbb{R}^n)$, $V = H^1(\mathbb{R}^n)$, $V^* = H^{-1}(\mathbb{R}^n)$.) We can then define the vector-valued Sobolev space $W^{1,2}([0,1]; V, V^*)$ of functions $u \in L^2([0,1]; ... |
Complex number
A complex number is an ordered pair of real numbers. (A real number may take any value from -infinity to +infinity. Real numbers are commonly represented as points on the "real number line", i.e., a straight line of infinite length.)
The two components of a complex number (a,b) are the real part (a) and ... |
ABSTRACT: This preprint proposes a general framework for studying transitional behavior in geometric topology. A theory of families of geometries is developed, robust enough to contain all currently known transitional geometries arising from conjugacy limits. This is used to construct a theory of Klein geometries over ... |
The Annals of Statistics Ann. Statist. Volume 6, Number 4 (1978), 701-726. Nonparametric Inference for a Family of Counting Processes Abstract
Let $\mathbf{B} = (N_1, \cdots, N_k)$ be a multivariate counting process and let $\mathscr{F}_t$ be the collection of all events observed on the time interval $\lbrack 0, t\rbra... |
Research Open Access Published: Blow-up phenomena and lifespan for a quasi-linear pseudo-parabolic equation at arbitrary initial energy level Boundary Value Problems volume 2018, Article number: 159 (2018) Article metrics
403 Accesses
Abstract
In this paper, we continue to study the initial boundary value problem of th... |
In a comment elsewhere you write that you're interested in understanding how quantum-mechanical theory describes the radiation that a hydrogen atom does and does not emit.In your question you ask about another answer that suggests some significance to the electron having zero total momentum; I think that's a feature of... |
In a previous post, we took a look at the computation of a portfolio’s exposure to its allocations. Then, to show the effects of active management, we compared the return made by two portfolios. But there is so much more to look inside the financial time series.
Since we left a couple of cliffhangers, let’s jump into t... |
I'm reading through "Algorithms for Stochastic Mixed-Integer Programming Models", Elsevier Handbooks in OR&MS Volume 12 (Discrete Optimization), Chapter 9 and I'm stuck. For those without access to the Handbooks, I found a preprint version at: http://server1.tepper.cmu.edu/Seminars/docs/Sen_paper1-2.pdf.
On page 531, S... |
$\newcommand\Q{\mathbf{Q}}\newcommand\OL{\mathcal{O}}\newcommand\I{\mathcal{I}}\newcommand\Z{\mathbf{Z}}\newcommand\eps{\epsilon}\newcommand\p{\mathfrak{p}}\newcommand\PP{\mathfrak{P}}\newcommand\Hom{\mathrm{Hom}}\newcommand\R{\mathbf{R}}\newcommand\q{\mathfrak{q}}\newcommand\Gal{\mathrm{Gal}}$
Summary: I think that it... |
NTS ABSTRACTSpring2019
Return to [1]
Jan 23
Yunqing Tang Reductions of abelian surfaces over global function fields For a non-isotrivial ordinary abelian surface $A$ over a global function field, under mild assumptions, we prove that there are infinitely many places modulo which $A$ is geometrically isogenous to the pr... |
We study a collection of $^4$He atoms confined to strictly one dimension at zero temperature. We use the exact Path Integral Ground State method to evaluate the equation of state and the radial distribution function, and we find that the system behaves as a Luttinger liquid with parameter $K_L = \hbar \pi \rho / m v$ t... |
The separation-of-variables solution you quoted has two indices appearing in it:
n and
j (the subscripts of the coefficient $A_{nj}$). Here,
n is azimuthal mode order, i.e. it counts the number of nodes along the direction in which the polar-angle $\theta$ varies (divided by 2).
The index
j is needed because the wave i... |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.