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I came across the sum: $$I(m)=\sum_{n=0}^\infty \frac{(-1)^n}{mn+1} $$ where $m>0$.
It's easy to see that this sum is equal to: $$\int_0^1 \frac{1}{1+x^m}dx$$ for $m>0$
So I tried my hardest to find a way of evaluating it. First I thought using Euler's Beta Function but to no avail. Then I decided to brute force a part... |
A geometric series is a sires of the form:$$\sum_{n = 0}^{\infty} ar^n$$
And the only time such a series converges is when $|r|<1$. In that case, what it converges to can be found using the following formula:
$$\sum_{n = 0}^{\infty} ar^n=\frac{a}{1-r}$$
To convert the given series into a geometric one (or ones), just s... |
I have a (simple?) question about Fourier transforms.
Consider a 1D Hamiltonian of the form \begin{equation} H = -JS\sum_{j = 1}^{N-1}a_{j+1}^\dagger a_j + a_j^\dagger a_{j+1} - a^\dagger_{j+1}a_{j+1} - a^\dagger_j a_j \end{equation} where $J$ is a coupling between two nearest neighbours, and $S$ is the spin projection... |
Yes, it has been: , or more stylized , the depression made by the tip of a Babylonian wedge shaped stylus on a clay tablet. When a circular stylus was used (rarely) the symbol was just $\bigcirc$. The earliest positional system was sexagesimal, with base 60, so it had cuneiform symbols for all digits from 1 to 59. Baby... |
The transport equation describes how a scalar quantity is transported in a space. Usually, it is applied to the transport of a scalar field (e.g. chemical concentration, material properties or temperature) inside an incompressible flow. From the mathematical point of view, the transport equation is also called the conv... |
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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... |
Extension of block matrix representation of the geometric mean
J. Korean Math. Soc. Published online August 22, 2019
Hana Choi, Hayoung Choi, Sejong Kim, and Hosoo LeeSungkyunkwan University, ShanghaiTech University, Chungbuk National Universit, Jeju National University
Abstract : To extend the well-known extremal char... |
Let $X$ be a smooth complex projective variety of dimension $n$.
Under the duality between $N_1(X)$ and $N^1(X)$ we know that closure of cone of effective curves $\overline{NE}(X)$ is dual to closure of ample cone $\overline{Amp}(X)$.
It was proved in 2004 that the closure of cone of effective divisors $\overline{Eff}(... |
Discrete Schrödinger equation and ill-posedness for the Euler equation
1.
304 Fine Hall, Princeton, NJ 08544, USA
2.
Kassar House, 151 Thayer street, Providence, RI 02912, USA
DEuler equation with periodic boundary conditions in a family of Banach spaces based on the Fourier coefficients, and show that it is ill-posed ... |
Proceedings of the Thirty-Second Conference on Learning Theory, PMLR 99:299-317, 2019.
Abstract
In the dictionary learning (or sparse coding) problem, we are given a collection of signals (vectors in $\mathbb{R}^d$), and the goal is to find a "basis" in which the signals have a sparse (approximate) representation. The ... |
Sine of Half-Integer Multiple of Pi
Jump to navigation Jump to search
Theorem
Let $x \in \R$ be a real number.
Let $\sin x$ be the sine of $x$.
Then: $\forall n \in \Z: \map \sin {n + \dfrac 1 2} \pi = \paren {-1}^n$
or:
\(\displaystyle \forall m \in \Z: \ \ \) \(\displaystyle \map \sin {2 m + \dfrac 1 2} \pi\) \(=\) \... |
(EDIT: My original post took $p$ to be the smallest prime that divides $k$. This is unnecessary. You can take $p$ to be
any number other than 1 that divides $k$. Doing so gives you not just one solution but $d(k)-1$ solutions, one for each of the divisors of $k$ other than 1.)
(SECOND EDIT: See the answer to this quest... |
I wonder if anybody can help me with this problem.
I'm trying to compute the Mertens function for large $n$. The most obvious algorithm is just to compute all primes up to $\sqrt{n}$ and then to sieve. That takes at least an order of $n\log n$ operations, and really even more.
The most recent article that I could find ... |
Asymptotic behaviour for wave equations with memory in a noncylindrical domains
1.
Departamento de Matemática-DMA, Universidade Estadual de Maringá-UEM, Campus Universitário, Av. Colombo, 5790-Zona 7, CEP 87020-900, Maringá-Pr., Brazil
2.
Departamento de Matemática, Universidade Federal do Pará, Campus Universitário do... |
What are the examples of "confined" $Z_N$ gauge theory?
From these two questions:
Phase Structure of (Quantum) Gauge Theory
http://physics.stackexchange.com/questions/102541
http://physics.stackexchange.com/questions/29359/
We learn that there are deconfined $Z_N$ gauge theory such as the $Z_N$-toric code (Kitaev) or $... |
(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... |
The bounty period lasts 7 days. Bounties must have a minimum duration of at least 1 day. After the bounty ends, there is a grace period of 24 hours to manually award the bounty. Simply click the bounty award icon next to each answer to permanently award your bounty to the answerer. (You cannot award a bounty to your ow... |
One of my discoveries as a physicist was that, despite all attempts at clarity, we still have different meanings for the same words and use different words to refer the the same thing. When Alice says measurement, Bob hears a `quantum to classical channel', but Alice, a hard-core Everettian, does not even believe such ... |
Proceedings of the Thirty-Second Conference on Learning Theory, PMLR 99:1649-1682, 2019.
Abstract
Robust mean estimation is the problem of estimating the mean $\mu \in \mathbb{R}^d$ of a $d$-dimensional distribution $D$ from a list of independent samples, an $\varepsilon$-fraction of which have been arbitrarily corrupt... |
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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 ... |
Semigroup and Blow-Up Dynamics of Attraction Keller-Segel Equations in Scale of Banach Spaces
Semigroup and Blow-Up Dynamics of Attraction Keller-Segel Equations in Scale of Banach Spaces
Abstract
In this paper, we study the asymptotic and blow-up dynamics of the attraction Keller-Segel chemotaxis system of equations i... |
AI News, Machine Learning FAQ Machine Learning FAQ
Without going into much depth regarding information gain and impurity measures, we can think of the decision as “is feature x_i >= some_val?” Intuitively, we can see that it really doesn’t matter on which scale this feature is (centimeters, Fahrenheit, a standardized s... |
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Now showing items 1-2 of 2
Production of charged pions, kaons and protons at large transverse momenta in pp and Pb-Pb collisions at $\sqrt{s_{NN}}$ = 2.76 TeV
(Elsevier, 2014-09)
Transverse momentum spectra of $\pi^{\pm}, K^{\pm}$ and $p(\bar{p})$ up to $p_T$ = 20 GeV/c at mid-rapidity, |y| $\le$ 0.8, in pp and ... |
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Now showing items 11-20 of 26
Measurement of azimuthal correlations of D mesons and charged particles in pp collisions at $\sqrt{s}=7$ TeV and p-Pb collisions at $\sqrt{s_{\rm NN}} = 5.02$ TeV
(Springer, 2017-04)
The azimuthal correlations of D mesons and charged particles were measured with the ALICE detector i... |
If $x,y$ are positive integers satisfying $x^2 - ny^2 = 1$, then $\frac{x}{y}$ is a good rational approximation to $\sqrt{n}$. A
really good rational approximation:
\begin{align}&& x^2 - ny^2 &= 1 \\&\iff& \frac{x^2}{y^2} - n &= \frac{1}{y^2} \\&\iff& \frac{x}{y} - \sqrt{n} &= \frac{1}{y^2\bigl(\sqrt{n} + \frac{x}{y}\b... |
AI News, Memristors power quick-learning neural network On Sunday, June 3, 2018 By Read More Memristors power quick-learning neural network
The network, called a reservoir computing system, could predict words before they are said during conversation, and help predict future outcomes based on the present.
The research ... |
This vignette illustrates the use of
mitml for the treatment of missing data at Level 2. Specifically, the vignette addresses the following topics:
Further information can be found in the other vignettes and the package documentation.
For purposes of this vignette, we make use of the
leadership data set, which contains... |
1. Explain why we can always evaluate the determinant of a square matrix.
2. Examining Cramer’s Rule, explain why there is no unique solution to the system when the determinant of your matrix is 0. For simplicity, use a [latex]2\times 2[/latex] matrix.
3. Explain what it means in terms of an inverse for a matrix to hav... |
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... |
I know that this function ($g$ means coupling) is non-analytical in $g=0$, so this function is only appreciable under non-perturbative calculations, so is a non-perturbative phenomena.This function is present on many critical/cross temperatures like in Kondo problem and Superconductors. This functions happens in QCD, w... |
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... |
Faddeeva Package From AbInitio
Revision as of 22:46, 29 October 2012 (edit)
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Line 26: Line 26: :<math>\mathrm{erfi}(x) = -i\mathrm{erf}(ix) = -i[e^{x^2} w(x) - 1]</math> (imagina... |
Definition:Indexing Set/Term Definition
Let $I$ and $S$ be sets.
Let $x: I \to S$ be a mapping.
The family of elements $x$ of $S$ indexed by $I$ is often seen with one of the following notations:
$\family {x_i}_{i \mathop \in I}$ $\paren {x_i}_{i \mathop \in I}$ $\set {x_i}_{i \mathop \in I}$ There is little consistenc... |
Yu Cheng,Ilias Diakonikolas,Rong Ge,David P. Woodruff;
Proceedings of the Thirty-Second Conference on Learning Theory, PMLR 99:727-757, 2019.
Abstract
We study the problem of estimating the covariance matrix of a high-dimensional distribution when a small constant fraction of the samples can be arbitrarily corrupted. R... |
Let $A = Z[\sqrt{-2}]$ be the ring with elements of the form $\{ a +b \epsilon\mid a,b \in\mathbb Z \}$ and where $\epsilon^2 = -2$.
Let $(1- \epsilon)$ denote the ideal generated by $1- \epsilon$.
I am tasked to show that $A / (1 - \epsilon) \simeq \mathbb Z_3$.
My attempt:
First I see that all elements in the ideal $... |
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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 ... |
Definition:Imaginary Number Informal Definition
In particular, this applies to the equation $x^2 + 1 = 0$.
In order to be able to allow such equations to have solutions, the concept $i = \sqrt {-1}$ is introduced.
$i$ does not exist on the real number line, but is a completely separate concept.
It can be treated as a n... |
It’s been a while, so let’s include a recap : a (transitive) permutation representation of the modular group $\Gamma = PSL_2(\mathbb{Z}) $ is determined by the conjugacy class of a cofinite subgroup $\Lambda \subset \Gamma $, or equivalently, to a dessin d’enfant. We have introduced a
quiver (aka an oriented graph) whi... |
Let ${\mathbb F}:({\mathcal A},{\mathcal E}_{\mathcal A})\to({\mathcal B},{\mathcal E}_{\mathcal B})$ be an exact functor between exact categories, and suppose ${\mathbb F}$ has both a left adjoint ${\mathbb F}_\lambda$ and a right adjoint ${\mathbb F}_\rho$. Then the class
${\mathcal E} := \{X\to Y\to Z\in{\mathcal E}... |
On a second order boundary value problem with singular nonlinearity
DOI: http://dx.doi.org/10.12775/TMNA.2006.001
Abstract
In this paper we investigate in a variational setting, the elliptic
boundary value problem $-\Delta u={\textt{sign}u}/{|u|^{\alpha+1}}$ in $\Omega$, $u=0$ on $\partial\Omega$, where $\Omega$ is an ... |
On the monotonicity of the period function of a quadratic system
1.
Department of Mathematics, Sun Yat-sen University, Guangzhou, 510275
$ \dot x=- y + x y,\quad \dot y=x + 2 y^2-c x^2, \quad -\infty < c < +\infty.$
We show that this system has two isochronous centers for $c=1/2$, and its period function has only one c... |
4 Methods to Account for Radiation in Participating Media
Radiative heat transfer in semitransparent media is described by the radiative transfer equation (RTE). Solving this equation is challenging in terms of computational costs. However, depending on a medium’s radiation properties, simplifications exist that allow ... |
In a continuance of this series today, I wanted to talk about the one-sided limits of calculus. Limits and where they lead are one of the fundamental concepts of calculus. Since limits show what happens near any particular point on a graph we need to take a look at them. Read on with me and I will explain their behavio... |
Definition:Isolated Point (Topology)/Subset
Jump to navigation Jump to search
$x \in H$ is an
Definition
$x \in H$ is an
isolated point of $H$ if and only if: $\exists U \in \tau: U \cap H = \left\{{x}\right\}$ Also see Results about isolated pointscan be found here. |
We can then define the parallel transporter for matter fields to be a linear map \({\parallel_{C}\colon V_{p}\rightarrow V_{q}}\), where \({C}\) is a curve in \({M}\) from \({p}\) to \({q}\). Choosing a gauge, the parallel transporter can be viewed as a (gauge-dependent) map \({\parallel^{\beta}{}_{\alpha}\colon\left\{... |
In what particular situation would the following be true?
$AB = B^TA$
where $A$ is symmetrical, $B$ is not.
I also know that $BB = B$.
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It only takes a minute to sign up.Sign up to join thi... |
I think you mean "perpendicular to", not "parallel to", in the question.
It is clear from the formula for $p(x)$ in terms of $x$, $a$, and the inner product, namely$$
p(x) = \frac{\langle x, a\rangle}{\langle a, a\rangle} a,
$$that $x - p(x)$ is perpendicular to $a$. Just do a short calculation with the formula:$$
\beg... |
The structure of a compound has a big effect on its properties. But how do we know what that structure is? The most useful methods of determining molecular structure involve the interaction of electromagnetic radiation, or light, with matter. Visible light, ultraviolet and infrared radiation, and even microwaves and ra... |
Simple Linear Regression
Let’s continue with the cars data, but this time let’s formally recognize that a car’s weight might have some effect on city MPG. Assume
We again focus on the expected value, not $\sigma$, but we will start dropping the $\mathbb{E}(Y)$ notation because it quickly becomes cumbersome and needless... |
Accelerated Stochastic Power Iteration by Christopher De Sa, Bryan He, Ioannis Mitliagkas, Christopher Ré, and Peng Xu and referencing work by many other members of Hazy Research
and referencing work by many other members of Hazy Research
Surprisingly, standard acceleration doesn’t always work for stochastic PCA. We pr... |
The alternating group $A_5 $ has two conjugacy classes of order 5 elements, both consisting of exactly 12 elements. Fix one of these conjugacy classes, say $C $ and construct a graph with vertices the 12 elements of $C $ and an edge between two $u,v \in C $ if and only if the group-product $u.v \in C $ still belongs to... |
Background
Let $\tau$ be the tension and $\mu$ be a linear mass density (i.e., mass per unit length), then the wave equation for a string is given by:$$\partial_{tt} \psi \left(x,t\right) - \frac{ \tau }{ \mu } \partial_{xx} \psi \left(x,t\right) = 0 \tag{0}$$where $\partial_{jj} \equiv \partial^{2}/\partial j^{2}$ and... |
Differentiating
I want to integrate -ln|cos(x)|+k, I and I should end with tan(x).
However, I'm stuck. I don't know what I need to do after $\displaystyle -x^{-1}*|cos(x)|-ln(x)*sin(x)$
This is how far I've gotten so far: http://img504.imageshack.us/img504/6739/tanjf9.gif Hello
Something I do not understand : the title... |
AliPhysics 608b256 (608b256)
#include <AliFMDCorrNoiseGain.h>
AliFMDCorrNoiseGain () AliFMDCorrNoiseGain (const AliFMDFloatMap &map) Float_t Get (UShort_t d, Char_t r, UShort_t s, UShort_t t) const void Set (UShort_t d, Char_t r, UShort_t s, UShort_t t, Float_t x) const AliFMDFloatMap & Values ()
AliFMDFloatMap fValues... |
In 1934 Witt became Helmut Hasse‘s assistent in Gottingen, where he qualified as a university lecturer in 1936. By 1938 he has made enough of a name for himself to be offered a lecturer position in Hamburg and soon became an associate professor, the down-graded position held by Emil Artin (2) until he was forced to emi... |
When one starts learning about physics, vectors are presented as mathematical quantities in space which have a direction and a magnitude. This geometric point of view has encoded in it the idea that under a change of basis the components of the vector must change contravariantly such that the magnitude and direction re... |
Faddeeva Package From AbInitio
Revision as of 22:53, 29 October 2012 (edit)
Stevenj (Talk | contribs)
(→Usage)
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Revision as of 22:54, 29 October 2012 (edit)
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Line 26: Line 26: :<math>\mathrm{erfi}(x) = -i\mathrm{erf}(ix) = -i[e^{x^2} w(x) - 1]</math> (imagina... |
It’s been a while, so let’s include a recap : a (transitive) permutation representation of the modular group $\Gamma = PSL_2(\mathbb{Z}) $ is determined by the conjugacy class of a cofinite subgroup $\Lambda \subset \Gamma $, or equivalently, to a dessin d’enfant. We have introduced a
quiver (aka an oriented graph) whi... |
(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... |
I have to design a feedback linearization for the model of a car with a single trailer. This picture shows the system:
And this is the kinematic model I got, where
q_dot = [x_dot; y_dot; thA_dot; thP_dot; thR_dot].
I chose
y1 = x and
y2 = y as outputs. I proved that the system is controllable and observable. To complet... |
I want to take the weak gradient operator
$$ \begin{aligned} \nabla: L^2(\Omega) &\to W^{-1,2}(\Omega,\mathbb{R}^d) \\ \langle \nabla u, \phi \rangle_{W^{-1,2},W_0^{1,2}}&:=(u,\text{div}\phi)_{L^2}=\int_\Omega u(x) \,\text{div}\phi(x) ~\text{d}x \end{aligned} $$ for all $\phi \in W_0^{1,2}(\Omega,\mathbb{R}^d)$.
Assume... |
If all numbers are real, it is decidable. This follows, for example from the general result in the paper
Vorobʹev, N. N., Jr. Deciding the consistency of a system of inequalities...
https://link.springer.com/chapter/10.1007%2F978-1-4612-0441-1_33.
If complex numbers are allowed it is not clear to me what the answer is.... |
In Statistics, the researcher checks the significance of the observed result, which is known as
test static. For this test, a hypothesis test is also utilized. The P-value or probability value concept is used everywhere in the statistical analysis. It determines the statistical significance and the measure of significa... |
The quantum mechanical treatment of the hydrogen atom can be extended easily to other one-electron systems such as \(He^+\), \(Li^{2+}\), etc. The Hamiltonian changes in two places. Most importantly, the potential energy term is changed to account for the charge of the nucleus, which is the atomic number of the atom or... |
While the verdict on a neolithic Scottish icosahedron is still open, let us recall Kostant’s group-theoretic construction of the icosahedron from its rotation-symmetry group $A_5 $.
The alternating group $A_5 $ has two conjugacy classes of order 5 elements, both consisting of exactly 12 elements. Fix one of these conju... |
In Part II, we saw how Alice can blindly evaluate the hiding :math:`E(P(s))` of her polynomial :math:`P` of degree :math:`d`, at a point :math:`s` belonging to Bob. We called this “blind” evaluation, because Alice did not learn :math:`s` in the process.
However, there was something missing in that protocol – the fact t... |
Fierz-Pauli action can be written as
$$ \tag{1} S = \int d^Dx \; \frac{1}{2} h_{\mu \nu} \mathcal{O}^{\mu \nu, \alpha \beta}h_{\alpha \beta} $$
where the operator
$$ \tag{2} \mathcal{O}^{\mu \nu} {}_{\alpha \beta} = \left( \eta^{( \mu}{}_{\alpha}\eta^{\nu )}{}_{\beta} - \eta^{\mu \nu} \eta_{\alpha \beta}\right) \left(\... |
Một số bài tập hình học vi phân
Đã gửi 04-11-2006 - 09:11
of latitude on http://dientuvietnam...imetex.cgi?S^2.
Proof:
No loss of generality, we can consider [the latitude tex]c(t)$ to be the
curve http://dientuvietnam...mimetex.cgi?c(t) is the intersection of http://dientuvietnam...mimetex.cgi?S^2
with the hyperplane ... |
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— Written by Triangles on April 01, 2017 • ID 52 —
A collection of practical tips and tricks to improve the gradient descent process and make it easier to understand.
Introduction to machine learning — What machine learning is about, types of learning and classification algorithms, introductory exa... |
In Wikipedia about difference equations, there is some description about correspondence between ODE and difference equation:
If you consider the Taylor series of the solution to a linear differential equation:$$\sum_{n=0}^\infty \frac{f^{(n)}(a)}{n!} (x-a)^n$$ you see that the coefficients of the series are given by th... |
I suppose the right way to do C (charge), T (time reversal), P(parity) transformation on the state $\hat{O}| v \rangle$ with operators $\hat{O}$ is that:
$$C(\hat{O}| v \rangle)=(C\hat{O}C^{-1})(C| v \rangle)\\P(\hat{O}| v \rangle)=(P\hat{O}P^{-1})(P| v \rangle)\\T(\hat{O}| v \rangle)=(T\hat{O}T^{-1})(T| v \rangle)$$
T... |
Normal Distribution Introduction
The first formal model in these notes happened so fast, you might have missed it. By assuming $X_n \sim_{iid} \text{Bernoulli}(p)$, we created a single model. This one statistical model assumed the Bernoulli distribution. Our data consisted of multiple independent observations from the ... |
The classical series $e = \lim_{n \to \infty} X_n$ where $X_n = \sum_{k=0}^n 1/k!$ is incredibly efficient. But is it known to be the most efficient series in terms of denominators for using fractions in the sum? In other words, is it known whether there is another series of fractions $e = \lim_{n \to \infty} Y_n$ wher... |
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... |
Re: Use [tex] and [/tex] tags NOT [math] and [/math] tags for latex.
$\displaystyle \[\sqrt {{b^2} - 4ac} \]$
Re: Use [tex] and [/tex] tags NOT [math] and [/math] tags for latex.
am quite new to this forum and i have little idea on how to use the editor but please this is my question
Please am stuck with the integratio... |
Answer
$A=\frac{1}{2} \times a \times b$ square inch.
Work Step by Step
By using the formula $A=\frac{1}{2} \times a \times b \times sin\gamma$ to calculate the area of the triangle, we can see that we have to maximize the $sin\gamma$. The maximum is 1 where $\gamma = 90^{\circ}$ So the maximum area of the triangle is ... |
L Hospital rule is a general method of evaluating indeterminate forms such as 0/0 or ∞/∞. To evaluate the limits of indeterminate forms for the derivatives in calculus, L Hospital’s rule is used. L’ hospital’s rule states that
If \(\lim_{x\rightarrow c}f(x)= \lim_{x\rightarrow c}g(x)=0 \ or\pm \infty\) and \(\lim_{x\ri... |
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Production of light nuclei and anti-nuclei in $pp$ and Pb-Pb collisions at energies available at the CERN Large Hadron Collider
(American Physical Society, 2016-02)
The production of (anti-)deuteron and (anti-)$^{3}$He nuclei in Pb-Pb collisions at $\sqrt{s_{\rm NN}}$ = 2.76 TeV has ... |
It is messy because you have misunderstood the problem. While $q(\underline{v})$ is induced by the bilinear form $f(\underline{u}, \underline{v})=\underline{v}^TA\underline{u}$, where $A$ is your $3\times 3$ coefficient matrix, $q$ is quadratic, not bilinear, also not a linear transformation. So, what you are asked to ... |
We obtain a partial solution of the problem on the growth of the norms of exponential functions with a continuous phase in the Wiener algebra. The problem was posed by J.-P. Kahane at the International Congress of Mathematicians in Stockholm in 1962. He conjectured that (for a nonlinear phase) one can not achieve the g... |
We try to analyze the average correlation of a portfolio as it can be found here in section 2 b), the same formula which is also used by the CBOE to calculate implied correlations:
$$ \rho_{av(2)} = \frac{\sigma^2 - \sum_{i=1}^N w_i^2\sigma_i^2}{2 \sum_{i=1}^N \sum_{j>i}^N w_i w_j \sigma_i \sigma_j} $$
EDIT:Assuming th... |
Second-order linear structure-preserving modified finite volume schemes for the regularized long wave equation
1.
Graduate School of China Academy of Engineering Physics, Beijing 100088, China
2.
School of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing 210044, China
3.
Col... |
We liberate millions of students and teachers from exam-oriented education by reducing attention and time dissipated on training, with the solution entirely directed by mathematical models.
– Hisen Zhang A lot of wastes for printed past paper booklet Great difficulty to make up a paper for internal assessment No focus ... |
Update: The MathJax Plugin for TiddlyWiki has a new home: https://github.com/guyru/tiddlywiki-mathjax Some time ago I came across MathJax, a nifty, Javascript based engine for displaying TeX and LaTeX equations. It works by “translating” the equation to MathML or HTML+CSS, so it works on all modern browsers. The result... |
Definition:Euler-Mascheroni Constant Contents Definition
The
Euler-Mascheroni Constant $\gamma$ is the real number that is defined as:
\(\displaystyle \gamma\) \(:=\) \(\displaystyle \lim_{n \mathop \to +\infty} \paren {\sum_{k \mathop = 1}^n \frac 1 k - \int_1^n \frac 1 x \rd x}\) \(\displaystyle \) \(=\) \(\displayst... |
After the answers by joshphysics and user37496, it seems to me that a last remark remains.
The quantum relevance of the universal covering Lie group in my opinion is (also) due to a fundamental theorem by Nelson. That theorem relates
Lie algebras of symmetric operators with unitary representations of a certain Lie grou... |
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Production of charged pions, kaons and protons at large transverse momenta in pp and Pb-Pb collisions at $\sqrt{s_{NN}}$ = 2.76 TeV
(Elsevier, 2014-09)
Transverse momentum spectra of $\pi^{\pm}, K^{\pm}$ and $p(\bar{p})$ up to $p_T$ = 20 GeV/c at mid-rapidity, |y| $\le$ 0.8, in pp and ... |
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Production of light nuclei and anti-nuclei in $pp$ and Pb-Pb collisions at energies available at the CERN Large Hadron Collider
(American Physical Society, 2016-02)
The production of (anti-)deuteron and (anti-)$^{3}$He nuclei in Pb-Pb collisions at $\sqrt{s_{\rm NN}}$ = 2.76 TeV has ... |
Q1 T T F, the overlap integral is zero. \(\beta\) pertains to energy, not overlap. T F, \(\beta\) is experimentally found to be negative. F, the resonance integral pertains to energy, so it is \(\beta\) . F, non-adjacent resonance integrals are zero. T Q2
In the ethylene system, there are two p orbitals to consider, \(... |
Overview of Integration Methods in Space and Time
Integration is one of the most important mathematical tools, especially for numerical simulations. Partial Differential Equations (PDEs) are usually derived from integral balance equations, for example. Once a PDE needs to be solved numerically, integration most often p... |
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In this tutorial, we write an Alphabets program, starting from a mathematical equation for LU decomposition. Then we will generate code to execute the alphabets program, and test the generated code for correctness.
The equation for LU Decomposition, derived from first principles... |
Perhaps the most useful feature of thermochemical equations is that they can be combined to determine Δ
H m values for other chemical reactions. Consider, for example, the following two-step sequence. Step 1 is reaction of 1 mol C( s) and 0.5 mol O 2( g) to form 1 mol CO( g):
(Note that since the equation refers to mol... |
The Heat of Reaction (also known and Enthalpy of Reaction) is the change in the enthalpy of a chemical reaction that occurs at a constant pressure. It is a thermodynamic unit of measurement useful for calculating the amount of energy per mole either released or produced in a reaction. Since enthalpy is derived from pre... |
I want to run some simulation studies of (linear) factor models and for that reasons I am wondering about the features such a simulation should contain - every suggestion is welcome, I'll do my best to update my code accordingly to provide some general usable framework at the end of the day. Citations are welcome, too!... |
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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... |
For $k=0,1,...$, let $a_k$ be the rational number defined by the serie expansion
$\frac{1}{e^x -1} = \frac{1}{x}+ \sum_{k=0}^\infty (-1)^k \frac{a_k}{\Gamma(k+1)} x^k$
The computation of the question simply shows that if there would be a "good value" to attach to $\sum_{n=1}^{+ \infty} n^k$, it should be $a_k$. The rea... |
I would like to have the unit circle, centered at the origin, on the Cartesian plane drawn. The origin is to be marked with a dot and labeled "O" and five dots are to be drawn on the circle, one on the x-axis, and the others at
k(2\pi/5) radians from the positive x-axis for each integer
1 \leq k < 5, and they are to be... |
Methods for Enforcing Inequality Constraints
How do you find the shortest overland distance between two points across a lake? Such obstacles and bounds on solutions are often called inequality constraints. Requirements for nonnegativity of gaps between objects in contact mechanics, species concentrations in chemistry, ... |
The luminescence spectrum of the hydrogen atom reveals light being emitted at discrete frequencies. These spectral features appear so sharp that they are called lines. These lines, occurring in groups, are found in different regions of the spectrum; some are in the visible, some in the infrared, and some in the vacuum ... |
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 ... |
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