text stringlengths 256 16.4k |
|---|
The integral representation converges for $Re s > 0$. As an improper integral, convergence is indeed uniform for (real) $s \in [\alpha,\beta]$. However, as you suspect, convergence is not uniform for $s \in (0,\infty)$. Problems arise due to singular behavior both at $x = 0$ when $s < 1$ and as $x \to \infty$ when $s >... |
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... |
From the “Simple English Wikipedia”
1: The Lorentz Factoris the name of the factor by which time, length, and “relativistic mass” change for an object while that object is moving and is often written γ (gamma). This number is determined by the object’s speed in the following way: $\gamma = \frac{1}{\sqrt{1 - \frac{v^2}... |
I came across John Duffield Quantum Computing SE via this hot question. I was curious to see an account with 1 reputation and a question with hundreds of upvotes.It turned out that the reason why he has so little reputation despite a massively popular question is that he was suspended.May I ...
@Nelimee Do we need to m... |
Abstract
We give a necessary and sufficient geometric structural condition, which we call the $\alpha$-Structural Hypothesis, for a stable codimension 1 integral varifold on a smooth Riemannian manifold to correspond to an embedded smooth hypersurface away from a small set of generally unavoidable singularities. The $\... |
How to Use the Beam Envelopes Method for Wave Optics Simulations
In the wave optics field, it is difficult to simulate large optical systems in a way that rigorously solves Maxwell’s equation. This is because the waves that appear in the system need to be resolved by a sufficiently fine mesh. The beam envelopes method ... |
I'm solving the exercises of chapter 14 in the book Representations and Characters of groups. (Gordon James, Martin Liebeck) Always working with $\mathbb{R}$ or $\mathbb{C}$.
One of them says:
Suppose that $\chi$ is a non-zero, non trivial character of $G$, and that $\chi(g)$ is a non-negative real number for all $g$ i... |
In this article we investigate some alternative ways of representing integers and performing arithmetic operations directly on these representations. We start from observation of Edouard Zeckendorf that leads to a representation using sums of non-adjacent Fibonacci numbers. Later we show connections of this representat... |
So, I need to prove the identity
$$\int_{-\infty}^\infty \cos t^2 dt = \int_{-\infty}^\infty \sin t^2 dt = \sqrt{\frac{\pi}{2}}$$
and as a hint I have the Gaussian integral
$$\int_{-\infty}^\infty e^{-xt^2} dt = \sqrt{\frac{\pi}{x}} \;\;\;\forall x>0.$$
I suspect I have to take the real/imaginary part of $e^{-t^2}$ at ... |
Background
Consider $BU=colim \, BU_k$ where we take $BU_k$ to be the specific model of classifying space for the group $U(k)\subseteq O(2k)$ given by the quotient space of the infinite real Stiefel manifold $V_{2k}$ by the action of $U(k)$. The spaces $BU_k$ as described come with maps $f_k : BU_k \rightarrow BO_{2k}$... |
On the positive solutions for a perturbed negative exponent problem on $\mathbb{R}^3$
Department of Basic Mathematics, Centro de Investigacióne en Mathematicás, Guanajuato, Mexico
$\begin{align}\left\{\begin{aligned} Δ^2 u&=-\frac{15}{16}(1+ \varepsilon Q)u^{-7} &&\text{ in } \mathbb R^3\\ u &>0 &&\text{ in } \mathbb R... |
Pitor Indyk,Ali Vakilian,Tal Wagner,David P Woodruff;
Proceedings of the Thirty-Second Conference on Learning Theory, PMLR 99:1723-1751, 2019.
Abstract
A distance matrix $A \in \mathbb{R}^{n \times m}$ represents all pairwise distances, $A_{i,j} = d(x_i,y_j)$, between two point sets $x_1,\dotsc,x_n$ and $y_1,\dotsc,y_m... |
Consider the following example: $$ - \Delta u = f \mbox{ in } \Omega, $$ $$ u = 0 \mbox{ on } \Gamma, $$ Here $\Gamma$ is boundary of $\Omega$. To produce weak formulation we multiply by arbitrary $v$ from $H^1(\Omega)$, integrate over $\Omega$ and apply integration by parts: $$ \int_{\Omega} \nabla u \nabla v dx - \in... |
Definition:Lower Closure/Element Definition
Let $\left({S, \preccurlyeq}\right)$ be an ordered set.
Let $a \in S$.
The lower closure of $a$ (in $S$) is defined as: $a^\preccurlyeq := \left\{{b \in S: b \preccurlyeq a}\right\}$ Also known as
The
lower closure of an element $a$ is also known as: the down-setof $a$ the do... |
But if you don't want to have a Google account: Chrome is really good. Much faster than FF (I can't run FF on either of the laptops here) and more reliable (it restores your previous session if it crashes with 100% certainty).
And Chrome has a Personal Blocklist extension which does what you want.
: )
Of course you alr... |
Simulate Neyman-Scott Point Process with Variance Gamma cluster kernel
Generate a random point pattern, a simulated realisation of the Neyman-Scott process with Variance Gamma (Bessel) cluster kernel.
Usage
rVarGamma(kappa, nu, scale, mu, win = owin(), thresh = 0.001, nsim=1, drop=TRUE, saveLambda=FALSE, expand = NULL,... |
Faddeeva Package From AbInitio
Revision as of 22:46, 29 October 2012 (edit)
Stevenj (Talk | contribs)
(→Usage)
← Previous diff
Revision as of 22:47, 29 October 2012 (edit)
Stevenj (Talk | contribs)
(→Usage)
Next diff →
Line 26: Line 26: :<math>\mathrm{erfi}(x) = -i\mathrm{erf}(ix) = -i[e^{x^2} w(x) - 1]</math> (imagina... |
I'd like to start of by saying I am aware of this post, but I think my question is different enough to warrant its own post.
Some notation, because I don't think this is standard:
$N^X_\epsilon(x)$ is just the $\epsilon$-ball centered at $x$ in $X$. So say $X \subseteq \mathbb{R}$, we would have $N^X_\epsilon(x) = (x -... |
VIII - Neural Networks: Representation 8.1 - Non-linear Hypothesis If we train a logistic regression algorithm with n features, including all the quadratic features \(x_ix_j\) we get approximately \(\frac{n^2}{2}\) features in total. 8.2 - Neurons and the Brain Origin of neural networks: try to mimic the brain. Was wid... |
A
tetrahedral snake, sometimes called a Steinhaus snake, is a collection of tetrahedra, linked face to face.
Steinhaus showed in 1956 that the last tetrahedron in the snake can never be a translation of the first one. This is a consequence of the fact that the group generated by the four reflexions in the faces of a te... |
Difference between revisions of "Probability Seminar"
(→May 7, Tuesday Van Vleck 901, 2:25pm,, Duncan Dauvergne (Toronto))
(→Tuesday , May 7, Van Vleck 901, 2:25pm,, Duncan Dauvergne (Toronto))
Line 114: Line 114:
Abstract: The interplay between geometry and probability in high-dimensional spaces is a subject of active... |
In a paper by Joos and Zeh, Z Phys B 59 (1985) 223, they say:This 'coming into being of classical properties' appears related to what Heisenberg may have meant by his famous remark [7]: 'Die "Bahn" entsteht erst dadurch, dass wir sie beobachten.'Google Translate says this means something ...
@EmilioPisanty Tough call. ... |
I am very new to this particular branch of probability theory, I try to be as formal as possible. In this question I consider bernoulli percolation as it is usually introduced as a first model (see for instance Geoffrey Grimmett).
Problem:Let $x,y \in \mathbb{Z}^d$. Prove that $f(p):= \mathbb{P}_p( x \leftrightarrow y)... |
Are
there hidden relations between mathematical and physical constants such as
$\frac{e^2}{4 \pi \epsilon_0 h c} \sim \frac{1}{137} $
or are these numerical relations mere accidents? A couple of years
ago, Pierre Cartier proposed in his paper A mad day’s work : from Grothendieck to Connes and Kontsevich : the evolution... |
In a Hilbert space of dimension $d$, how do I calculate the largest number $N(\epsilon, d)$ of vectors $\{V_i\}$ which satisfies the following properties. Here $\epsilon$ is small but finite compared to 1.
$$<V_i|V_i> = 1$$
$$|<V_i|V_j>| \leq \epsilon, i \neq j$$
Some examples are as follows.
1. $N(0, d)$ = d
2. $N\lef... |
Definition:Linearly Dependent/Set/Real Vector Space Definition
Let $\left({\R^n,+,\cdot}\right)_{\R}$ be a real vector space.
Let $S \subseteq \R^n$.
That is, such that:
$\displaystyle \exists \left\{{\lambda_k: 1 \le k \le n}\right\} \subseteq \R: \sum_{k \mathop = 1}^n \lambda_k \mathbf v_k = \mathbf 0$
where $\left\... |
Trying to align equal signs and get an error message saying
missing } inserted
I can't figure out what I've done wrong?
\begin{align}($b^nn^\alpha$)$^{-1}$=\large$\frac{a^n}{n^\alpha}$$\geq\frac{a^n}{n^p}$\end{align}
TeX - LaTeX Stack Exchange is a question and answer site for users of TeX, LaTeX, ConTeXt, and related ... |
AI News, When Bayes, Ockham, and Shannon come together to define machine learning On Monday, September 17, 2018 By Read More When Bayes, Ockham, and Shannon come together to define machine learning
It is somewhat surprising that among all the high-flying buzzwords of machine learning, we don’t hear much about the one p... |
Definition:Many-to-One Relation Definition $\forall x \in \Dom {\mathcal R}: \forall y_1, y_2 \in \Cdm {\mathcal R}: \tuple {x, y_1} \in \mathcal R \land \tuple {x, y_2} \in \mathcal R \implies y_1 = y_2$
Let $f \subseteq S \times T$ be a many-to-one relation.
Let $s \in S$.
Let $R \subseteq S$.
Also known as
Such a re... |
Update (21 May 18): It turns out this post is one of the top hits on google for “python travelling salesmen”! That means a lot of people who want to solve the travelling salesmen problem in python end up here. While I tried to do a good job explaining a simple algorithm for this, it was for a challenge to make a progam... |
Here’s a tiny problem illustrating our limited knowledge of finite fields : “Imagine an infinite queue of Knights ${ K_1,K_2,K_3,\ldots } $, waiting to be seated at the unit-circular table. The master of ceremony (that is, you) must give Knights $K_a $ and $K_b $ a place at an odd root of unity, say $\omega_a $ and $\o... |
Before we go deeper into Conway’s M(13) puzzle, let us consider a more commonly known sliding puzzle: the 15-puzzle. A heated discussion went on a couple of years ago at sci-physics-research, starting with this message. Lubos Motl argued that group-theory is sufficient to analyze the problem and that there is no reason... |
McNemar's test statistic is given by:
$\chi^{2} = \frac{\left(|r-s|-1\right)^{2}}{r+s}$, where $r$ and $s$ are the counts of discordant pairs (0,1) versus (1,0), distributed $\chi^{2}$ with 1 degree of freedom under the null hypothesis.
I am having a hard time parsing Sribney on the sign test:
The test statistic for th... |
In the 15-puzzle groupoid 1 we have seen that the legal positions of the classical 15-puzzle are the objects of a category in which every morphism is an isomorphism (a groupoid ). Today, we will show that there are exactly 10461394944000 objects (legal positions) in this groupoid. The crucial fact is that positions wit... |
So that finally brings us to our ZSM viewer on the next page of this tutorial.
When you look at the viewer page, you'll see three graphs, two in the top left and one on the right. The two on the top left are time waveforms: the top graph shows the voltage of the three phases as they change over a commutation cycle, wit... |
Rate of change in calculus is a series I have been wanting to do for a while. If you are a student and just starting then your in the right place. This is the very beginning of calculus and where you want to start your learning. Since there are so many topics in school that require some calculus, I felt it was importan... |
Applied/ACMS/absS18 Contents ACMS Abstracts: Spring 2018 Thomas Fai (Harvard) The Lubricated Immersed Boundary Method
Many real-world examples of fluid-structure interaction, including the transit of red blood cells through the narrow slits in the spleen, involve the near-contact of elastic structures separated by thin... |
This splitting occurs due to hyperfine coupling (the EPR analogy to NMR’s J coupling) and further splits the fine structure (occurring from spin-orbit interaction and relativistic effects) of the spectra of atoms with unpaired electrons. Although hyperfine splitting applies to multiple spectroscopy techniques such as N... |
A classical description of the vibration of a diatomic molecule is needed because the quantum mechanical description begins with replacing the classical energy with the Hamiltonian operator in the Schrödinger equation. It also is interesting to compare and contrast the classical description with the quantum mechanical ... |
I am trying to prove the following:
Let $X$ be a normed linear space satisfying the property: $\forall \left\{x_n\right\}, \left\{y_n\right\} \subseteq X $, we have $\|x_n\|=\|y_n\|=1, \|x_n+y_n\|\rightarrow 2 \Rightarrow \|x_n-y_n\|\rightarrow 0.$
If $\left\{z_n\right\} \subseteq X$ converges to $z\in X$ weakly (meani... |
This is from page 17-18 of Trudinger and Gilbarg
Let $\Omega$ be a domain for which the divergence theorem holds. Let $\Gamma(x-y)$ be the normalised fundamental solution of the Laplace's equation, then Green's representation formula
$$u(y)=\int_{\partial\Omega}\bigg(u\frac{\partial\Gamma}{\partial\nu}(x-y)-\Gamma(x-y)... |
Applied/ACMS/absS18 Contents 1 ACMS Abstracts: Spring 2018 ACMS Abstracts: Spring 2018 Thomas Fai (Harvard) The Lubricated Immersed Boundary Method
Many real-world examples of fluid-structure interaction, including the transit of red blood cells through the narrow slits in the spleen, involve the near-contact of elasti... |
(Sorry was asleep at that time but forgot to log out, hence the apparent lack of response)
Yes you can (since $k=\frac{2\pi}{\lambda}$). To convert from path difference to phase difference, divide by k, see this PSE for details http://physics.stackexchange.com/questions/75882/what-is-the-difference-between-phase-differ... |
Given a random vector $X \in \mathbb{R}^k$, with a known pdf given by $f_X$. If $Y, Z \in \mathbb{R}^k$ are defined by $Y = AX$, $Z = BX$, where $A,B \in \mathbb{R}^{k\times k}$ are different, given, real-valued matrices.
I know how to calculate pdfs of $Y$ and $Z$ on their own. But how do I derive the joint pdf of $Y$... |
Integral formulae for codimension-one foliated Finsler spaces
Recent decades brought increasing interest in Finsler spaces $(M,F)$,
especially, in extrinsic geometry of their hypersurfaces. Randers metrics (i.e., $F=\alpha+\beta$, $\alpha$ being the norm of a Riemannian structure and $\beta$ a 1-form of $\alpha$-norm s... |
Stability in representation theory of the symmetric groups
In the finite-dimensional representation theory of the symmetric groups
$$S_n$$ over the base field $$\mathbb{C}$$, there is an an interesting phenomena of "stabilization" as $$n \to \infty$$: some representations of $$S_n$$ appear in sequences $$(V_n)_{n \geq ... |
Learning Objectives
Define the terms wavelength and frequency with respect to wave-form energy. State the relationship between wavelength and frequency with respect to electromagnetic radiation.
During the summer, almost everyone enjoys going to the beach. They can swim, have picnics, and work on their tans. But if you... |
We know that for a position variable $x$ and momentum $p$, the uncertainties of the two quantities are bounded by
$$\Delta x \Delta p \gtrsim \hbar$$
Now, this is usually first explained with $x$ being a simple linearly measured position and $p$ being linear momentum. But it should apply to
any good coordinate and its ... |
Let's see. There are two observations one needs to make in order to "arrive" to F-theory. Let's go back to type IIB string theory and take the lowe energy sugra 7-brane solutions. These 7-branes have an harmonic function that depends logarithmically on the transverse distance from the brane, something distinct to these... |
Probability Seminar Spring 2019 Thursdays in 901 Van Vleck Hall at 2:25 PM, unless otherwise noted. We usually end for questions at 3:15 PM.
If you would like to sign up for the email list to receive seminar announcements then please send an email to join-probsem@lists.wisc.edu
January 31, Oanh Nguyen, Princeton
Title:... |
Definition:Convergent Series/Number Field Contents Definition
Let $S$ be one of the standard number fields $\Q, \R, \C$.
Let $\displaystyle \sum_{n \mathop = 1}^\infty a_n$ be a series in $S$.
Let $\sequence {s_N}$ be the sequence of partial sums of $\displaystyle \sum_{n \mathop = 1}^\infty a_n$.
If $s_N \to s$ as $N ... |
Alexander Gasnikov,Pavel Dvurechensky,Eduard Gorbunov,Evgeniya Vorontsova,Daniil Selikhanovych,César A. Uribe;
Proceedings of the Thirty-Second Conference on Learning Theory, PMLR 99:1374-1391, 2019.
Abstract
We consider convex optimization problems with the objective function having Lipshitz-continuous $p$-th order de... |
Discrete Uniform Distribution Introduction
Since much of this class is about notation, this section attempts to build on your experience about dice in an effort to minimize the mental hurdles that follow the new notation. Expanding on the process of rolling a single die, we introduce a more formal definition of a rando... |
I am aware there are other proofs of line of this statement. But I am interested in the argument outlined here on page 62-63
Corollary II.2.2.9Let $A$ and $B$ be $C^*$ algebras, $\phi:A \rightarrow B$ be injective $*$-homomoprhism. Then $\phi$ is isometric, i.e. $||\phi(x) || = ||x||$ for all $x \in A$.
The proof goes ... |
I want to prove $$S^{\mu \nu}=\frac{i}{4}[\gamma^\mu,\gamma^\nu].$$ I started from $$[\gamma^\mu,S^{\alpha\beta}]=(J^{\alpha\beta})^\mu_\nu \gamma^\nu$$ Putting the value of $(J^{\alpha\beta})^\mu_\nu$ $$=i(\eta^{\alpha\mu}\delta^\beta_\nu-\eta^{\beta\mu}\delta^\alpha_\nu)\gamma^\nu$$ we get $$\gamma^\mu S^{\alpha\beta... |
I'm trying to format an optimization problem but I am having trouble aligning and and labeling it properly in one environment. I have two equations, each written using an \begin{aligned*} environment. The first is
\documentclass{report}\usepackage{amsmath}\begin{document}\begin{equation*} \begin{aligned} & \underset{y ... |
Mathematical background and pre work Mathematical background
We will not assume a lot of mathematical background in this course butwill use some basic notions from
linear algebra, such as vectorspaces (finite dimensional and almost always over the real numbers),matrices, and associated notions such as rank, eigenvalues... |
$$1 - \frac{1}{3 \cdot 2!} + \frac{1}{5 \cdot 3!} - \frac{1}{7 \cdot 4!}+\cdots$$
I am new to math over flow, and I do not know how to format the math, sorry! Also, what should this converge to?
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related f... |
Let $\mu_n$ be a sequence of positive radon measures on $\mathbb{R}^n$ weakly converging (as dual of continuous compactly supported functions) to a measure $\mu$.
Assume that $f_n(z)$ is a sequence of positive, compacly supported functions such that: they are uniformily supported in a ball, i.e.: for every $n$ their su... |
On the asymptotic character of a generalized rational difference equation
1.
Department of Mathematics, Indian Institute of Science, Bangalore, Karnataka, 560012, India
2.
Department of Mathematics, Maligram, Paschim Medinipur, 2421140, India
We investigate the global asymptotic stability of the solutions of $X_{n+1}=\... |
Theory of Thermoviscous Acoustics: Thermal and Viscous Losses
When sound propagates in structures and geometries with small dimensions, the sound waves become attenuated because of thermal and viscous losses. More specifically, the losses occur in the acoustic thermal and viscous boundary layers near the walls. This kn... |
Symmetry of the superconducting gap
First of all, a bit of theory. Superconductivity appears due to theCooper paring of two electrons, making non-trivial correlations betweenthem in space. The correlation is widely known as the gap parameter$\Delta_{\alpha\beta}\left(\mathbf{k}\right)\propto\left\langle c_{\alpha}\left... |
The monstrous moonshine picture is the subgraph of Conway’s big picture consisting of all lattices needed to describe the 171 moonshine groups.
It consists of:
– exactly 218 vertices (that is, lattices), out of which
– 97 are number-lattices (that is of the form $M$ with $M$ a positive integer), and
– 121 are proper nu... |
A neutralization reaction is when an acid and a base react to form water and a salt and involves the combination of H
+ ions and OH - ions to generate water. The neutralization of a strong acid and strong base has a pH equal to 7. The neutralization of a strong acid and weak base will have a pH of less than 7, and conv... |
I'm using the following commands in my preamble to get the fonts I want:
\usepackage{cmbright}\usepackage{amsmath}\usepackage{amssymb}\usepackage{pxfonts}
I recently found that, in math mode, when I use the command
\log or
\exp (as opposed to
\text{log} or
\text{exp}), the logarithmic and exponential functions get reso... |
The Fibonacci sequence reappears a bit later in Dan Brown’s book ‘The Da Vinci Code’ where it is used to login to the bank account of Jacques Sauniere at the fictitious Parisian branch of the Depository Bank of Zurich.
Last time we saw that the Hankel matrix of the Fibonacci series $F=(1,1,2,3,5,\dots)$ is invertible o... |
I am following along Chapter 2 of Takagi's Vacuum Noise and Stress Induced by Uniform Acceleration. For a free real scalar field $\phi$ the stress-energy tensor is:$$T_{\mu\nu} = ( \partial_{\mu} \phi ) ( \partial_{\nu} \phi ) - g_{\mu\nu} \tfrac{1}{2} g^{\alpha\beta} ( \partial_{\alpha} \phi ) ( \partial_{\beta} \phi ... |
The wavefunctions that describe electrons in atoms and molecules are called orbitals. An orbital is a wavefunction for a single electron. When we say an electron is in orbital n, we mean that it is described by a particular wavefunction Ψn and has energy En. All the properties of this electron can be calculated from Ψn... |
(Originally published on October 19th, 2009)
Before using Squarespace, I built my own front page. As I considered the best way to display series of pictures there, I came up with an interesting way to compress a lot of information onto fairly limited screen real estate. The idea was to have a kind of a slide show compo... |
There are different teleparallel gravities, if you noticed in the literature. The one which is equivalent is called
Teleparallel Equivalent of General Relativity (TEGR) and it is a particular action choice that makes it equivalent.
If you decompose the variables, the metric $g_{\mu\nu}$ and the affine connection $\Gamm... |
Let’s try to identify the $\Psi(n) = n \prod_{p|n}(1+\frac{1}{p})$ points of $\mathbb{P}^1(\mathbb{Z}/n \mathbb{Z})$ with the lattices $L_{M \frac{g}{h}}$ at hyperdistance $n$ from the standard lattice $L_1$ in Conway’s big picture.
Here are all $24=\Psi(12)$ lattices at hyperdistance $12$ from $L_1$ (the boundary latt... |
Electrophoresis Contents 1 Background 2 Electrophoretic Techniques 3 Innovations 4 Applications 5 References Background
Electrophoresis is a biochemical technique that separates compounds by administering an electrical current. The current runs from a power source and travels from the anode end of the electrophoretic a... |
It is well know that quantum Yang-Mills theory has a periodic vacuum structure. Consider electroweak theory. For a single generation of fermions, the theory is CP invariant. I would like to know if the periodic vacua of the theory are also CP invariant.
One expects the trivial vacuum with topological charge $n=0$ to be... |
Abstract
Let $T$ be a smooth homogeneous Calderón-Zygmund singular integral operator in $\mathbb{R}^n$. In this paper we study the problem of controlling the maximal singular integral $T^{\star}f$ by the singular integral $Tf$. The most basic form of control one may consider is the estimate of the $L^2(\mathbb{R}^n)$ n... |
Earth Eclipse of Server Sky Arrays
If the Earth was perfectly round, and the poles were not inclined, arrays in the 12789 km, 17280 second radius equatorial orbit would spend 2868 seconds per orbit shaded by the 6371km radius Earth ( = 17280 \times asin( 6371 / 12789 ) / 180^\circ ~ ).
In fact, the Earth has an equator... |
I was trying to understand the proof of the Witt dimension formula for free Lie algebras. I was basically following this proof.
(I'm not posting the complete proof but just the piece where I'm currently stuck on.)
How do we prove the Witt dimension formula? Write $\ell_n = \dim L_n$. In each homogeneous subspace $L_n$ ... |
Multiplying Complex Numbers
Multiplying complex numbers is much like multiplying binomials. The major difference is that we work with the real and imaginary parts separately.
Example 4: Multiplying a Complex Number by a Real Number
Let’s begin by multiplying a complex number by a real number. We distribute the real num... |
Any conic may be determined by three characteristics: a single
focus, a fixed line called the directrix, and the ratio of the distances of each to a point on the graph. Consider the parabola [latex]x=2+{y}^{2}[/latex] shown in Figure 2.
In The Parabola, we learned how a parabola is defined by the focus (a fixed point) ... |
I started by showing that $1\leq a_{n} \leq n$ (by induction) and then $\frac{1}{n}\leq \frac{a_{n}}{n} \leq 1$ which doesn't really get me anywhere.
On a different path I showed that $a_{n} \to \infty$ but can't see how that helps me.
Mathematics Stack Exchange is a question and answer site for people studying math at... |
I have the following question from
Function Theory of One Complex Variable - Greene/Krantz:
Give an example of a series of complex coefficients $ a_n$ such that $\lim_{N \to + \infty} \sum_{n= -N}^{N} a_n$ exists but $\sum_{-\infty}^{+\infty} a_n$ does not converge.
The answer key I have says that $a_n = n$ answers the... |
It is well-known that a polynomial $q \in \mathbb Z[t]$ vanishes modulo $p$ only if it lies in the ideal $J_p$ generated by $p$ and $t^p-t$. This means that either the degree is large (at least $p$) or the coefficients are large (divisible by $p$).
Is there anything useful like this that one can say if a polynomial van... |
Reynolds Number - Blayne Sarazin Contents Reynolds Number
The Reynolds number is a dimensionless quantity in fluid mechanics that is used to help predict flow patterns in different fluid flow situations. The Reynolds Number serves as a guide to the laminar-turbulent transition in a particular flow situation,
1 and for ... |
How would you go about explaining i.i.d (independent and identically distributed) to non-technical people?
It means "Independent and identically distributed".
A good example is a succession of throws of a fair coin: The coin has no memory, so all the throws are "independent".
And every throw is 50:50 (heads:tails), so ... |
In a paper by Joos and Zeh, Z Phys B 59 (1985) 223, they say:This 'coming into being of classical properties' appears related to what Heisenberg may have meant by his famous remark [7]: 'Die "Bahn" entsteht erst dadurch, dass wir sie beobachten.'Google Translate says this means something ...
@EmilioPisanty Tough call. ... |
Displacement and Acceleration
Arrays of satellites cannot maintain a constant displacement above or below the orbital plane without a constant (and significant) acceleration keeping them there. The ΔV needed over the lifetime of a satellite is beyond the range of high Isp engines. Further, it is unnecessary; by using c... |
1 Laplace transform
The Laplace transform is an essential tool in linear dynamic system modeling and control system engineering. A function $F(s)$ of the complex variable $s=\sigma+j\omega$ is called the Laplace transform of the original function $f(t)$ and is defined in the following way:
The original function $f(t)$ ... |
I am giving a talk on String theory to a math undergraduate audience. I am looking for a nice and suprising mathematical computation, maybe just a surprising series expansion, which is motivated by string theory and which can be motivated and explained relatively easily. Examples of what I have in mind are the results ... |
June 30th, 2011, Verimag (CTL), Grenoble download flyer Registration
Registration is free of charge. We only need to know how many participants will attend in order to estimate the number of people during the lunch and coffee breaks. There will also be an informal dinner on the evening of June 30th at the Bombay indian... |
Ampère never wrote down what is confusingly called "
Ampère's circuital law," not even the form without the displacement current term, as Ampère never dealt with the field concept.* Maxwell derived
$$\nabla \times \mathbf{B} = \mu_0\mathbf{J}\qquad(1)$$
in his 1855 paper
On Faraday's Lines of Force, based on analogies ... |
Hello can anyone help with this question Show that the Maclaurin series of the function $$\ln(1+\sin x)$$ up to the term in $x^4$ is $$x-x^2/2 + x^3/6 - x^4/12 + \ldots$$ So I know the expansion for $\ln(1+x)= x - x^2 + x^3/3 +\dots$ and that of $\sin x= x - x^3/3!+x^5/5!-\dots$ hence I tried by substituting the first ... |
User:DOUG/Sandbox Transclusion Tests Testing Math! Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle A + B \div C = Z } Failed... |
Current browse context:
physics.data-an
Change to browse by: Bookmark(what is this?) Physics > Data Analysis, Statistics and Probability Title: Detector resolution correction for width of intermediate states in three particle decays
(Submitted on 5 Aug 2015)
Abstract: We propose a method that allows to take into accoun... |
Beginning calculus problems with limits of a function are a common teaching technique for young students that are just starting their journey in Calculus. Limits problems will help you understand how they work and what is going on when you encounter a function. Repetition is key here to get your brain used to thinking ... |
This is a heuristic explanation of Witten's statement, without going into the subtleties of axiomatic quantum field theory issues, such as vacuum polarization or renormalization.
A particle is characterized by a definite momentum plus possible other quantum numbers. Thus, one particle states are by definition states wi... |
Current browse context:
physics.app-ph
Change to browse by: Bookmark(what is this?) Physics > Applied Physics Title: Improving the Time Stability of Superconducting Planar Resonators
(Submitted on 30 Apr 2019)
Abstract: Quantum computers are close to become a practical technology. Solid-state implementations based, for... |
1 Introduction
The concept of the differentiation operator $\mathscr{D}=\dif/\dif x$ is a well-known fundamental tool of modern calculus. For a suitable function $f$ the $n$-th derivative is well defined as $\mathscr{D}^n f(x)=\dif f(x)/\dif x^n$, where $n$ is a positive integer. However, what would happen if we extend... |
November 10th, 2016, 05:19 PM
# 1
Member
Joined: Aug 2016
From: South Korea
Posts: 55
Thanks: 0
Help!! How do I find table of values for undetermined Limit?
The given problem is 3x^2 + 2x/x , x> 0
and the only ans. Ive got is 0/0
How do I make Table of values for this and how can I determine if the limit exists or not?... |
Search
Now showing items 1-1 of 1
Anisotropic flow of inclusive and identified particles in Pb–Pb collisions at $\sqrt{{s}_{NN}}=$ 5.02 TeV with ALICE
(Elsevier, 2017-11)
Anisotropic flow measurements constrain the shear $(\eta/s)$ and bulk ($\zeta/s$) viscosity of the quark-gluon plasma created in heavy-ion collisions... |
Let me throw some water on your goal and any nice proof. For my article on this, you can find it at:
Harris, D.E. (2017) The Distribution of Returns. Journal of Mathematical Finance, 7, 769-804
Let us use even weaker assumptions than your assumption that $S_t,\forall{t}$ is stationary. Let us use more Markowitz style a... |
Gamma Distribution Introduction
In this chapter we’ll introduce the Exponential Distribution a one parameter distribution that is a special case of the Gamma distribution and, of course, the Gamma distribution. The Gamma distribution is used to model random durations of time until a next event. What each event is, real... |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.