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From what I know of analyzing and designing approximation algorithms, we need to find a lower bound on the optimum (in the case of minimization). For example if our solution is greedy ($SOL_G$) and if we find a lower bound $L_B$ on $OPT$ then $$L_B \leq OPT$$
and if we correctly analyze the following $$SOL_G \leq f . L... |
Viewing posts for the category Featured on frontpage
The magnetic field due to a magnetic dipole moment, $\boldsymbol{m}$ at a point $\boldsymbol{r}$ relative to it may be written $$ \boldsymbol{B}(\boldsymbol{r}) = \frac{\mu_0}{4\pi r^3}[3\boldsymbol{\hat{r}(\boldsymbol{\hat{r}} \cdot \boldsymbol{m}) - \boldsymbol{m}}... |
Graduate seminar on Advanced topics in PDE Organizers
Prof. Dr. Herbert Koch Prof. Dr. Christoph Thiele Dr. Alex Amenta João Pedro Ramos
Schedule
This seminar takes place regularly on Fridays, at 14.00 (c.t.), in Raum 0.011, Endenicher Allee 60.
July 12th - Joris Roos
Title:
Discrete analogues of maximally modulated si... |
An RLC circuit is a simple electric circuit with a resistor, inductor and capacitor in it -- with resistance
R, inductance Land capacitance C, respectively. It's one of the simplest circuits that displays non-trivial behavior.
You can derive an equation for the behavior by using Kirchhoff's laws (conservation of the st... |
Every $LL(k)$ grammar is $LR(k)$, but there are $LL(k)$ grammars which are not $LALR(k)$.
There's a simple example in Parsing Theory by Sippu&Soisalon-Soininen
$$\begin{align}S &\to a A a \mid b A b \mid a B b \mid b B a\\A &\to c \\B &\to c\end{align}$$
The language of this grammar is finite, so it is obviously $LL(k)... |
Is the following true? \begin{equation}\frac{\partial}{\partial X_{t+1}}E_t(f(X_{t+1}))=E_t(\frac{\partial}{\partial X_{t+1}}f(X_{t+1}))\tag{1}\end{equation} where $f$ is some affine function (e.g., $f(x)=a+bx$), $E_t(X_s)=E(X_s|I_t)$ denotes the conditional expectation of $X_s$ given information $I_t$ in time period $... |
Let $A\in\mathbb{R}^{n\times n}$ is symmetric positive definite and consider solving linear system $Ax = b$. Show that the symmetric Gauss-Seidel iteration converges for any $x_0$.
Solution - Since $A$ is symmetric positive definite and $A = D - L - U$ is the usual partitioning into diagonal, strict lower and strict up... |
Sparse probabilistic Boolean network problems: A partial proximal-type operator splitting method
College of Mathematics and Computer Science, Fuzhou University, Fuzhou 350108, China
The sparse probabilistic Boolean network (SPBN) model has been applied in various fields of industrial engineering and management. The goa... |
Sanaris's answer is a great, succinct list of what each term in the free energy expression stands for: I'm going to concentrate on the $T\,S$ term (which you likely find the most mysterious) and hopefully give a little more physical intuition. Let's also think of a chemical or other reaction, so that we can concretely ... |
Bases of a trapezoid: \(a\), \(b\)
Legs of a trapezoid: \(c\), \(d\) Midline of a trapezoid: \(m\) Altitude of a trapezoid: \(h\) Perimeter: \(P\)
Legs of a trapezoid: \(c\), \(d\)
Midline of a trapezoid: \(m\)
Altitude of a trapezoid: \(h\)
Perimeter: \(P\)
Diagonals of a trapezoid: \(p\), \(q\)
Angle between the diag... |
So I wrote somewhat tongue-in-cheek blog post a few years ago titled "Resolving the Cambridge capital controversy with abstract algebra" [RCCC I] that called the Cambridge Capital Controversy [CCC] for Cambridge, UK in terms of the original debate they they were having — summarized by Joan Robinson's claim that you can... |
I'm trying to implement finite-difference WENO method to progressively complex equations and systems. At the moment I'm successful with singular scalar equations (constant advection and Burgers), and trying to advance to 1D system of Euler equations.
I've read that there are two approaches to apply WENO to systems of c... |
This question already has an answer here:
How does one prove that the Dirac Delta distribution is the eigenfunction of the position operator $\hat{x}$? In math, why does $\langle x’|x\rangle = \delta(x’-x)$?
Physics Stack Exchange is a question and answer site for active researchers, academics and students of physics. ... |
Information Theory in Gambling Part I: Variance and the Kelly Criterion
Let’s play a game. Imagine you have $100 and you’d like to maximize your money. You flip a weighted coin that comes up heads 60% of the time, and tails 40% of the time . You can play as many times as you would like. How much would you bet?
The most... |
Let $\mathcal{X}= \{1,-1\}^n$, $E$ the set of edges and $J$ some real-valued matrix. Van der Waerden's theorem gives constant $c$ and set of edge weights such that
$$\sum_\mathbf{x\in \mathcal{X}} \exp \sum_{ij \in E} J_{ij} x_i x_j = c \sum_{A\in C} f(A) $$
Where $C$ consists of Eulerian subgraphs over $E$, $f(A)$ is ... |
Just to clarify notation, I'll be discussing the Gauss-Newton method for the problem
$\min \phi(x)=(1/2) \| F(x) \|_{2}^{2}$
with the search direction $p$ computed as the solution to the linear system of equations
$J(x^{(k)})^{T}J(x^{(k)}) p = - J(x^{(k)})^{T} F(x^{(k)})$
where $J(x)$ is the matrix of partial derivativ... |
CryptoDB Paper: Explicit Construction of Secure Frameproof Codes
Authors: Dongvu Tonien Reihaneh Safavi-Naini Download: URL: http://eprint.iacr.org/2005/275 Search ePrint Search Google Abstract: $\Gamma$ is a $q$-ary code of length $L$. A word $w$ is called a descendant of a coalition of codewords $w^{(1)}, w^{(2)}, \d... |
Deelan Cunden, Fabio, Mezzadri, Francesco, O'Connell, Neil and Simm, Nick (2019)
Moments of random matrices and hypergeometric orthogonal polynomials. Communications in Mathematical Physics. ISSN 0010-3616
PDF - Published Version
Available under License Creative Commons Attribution.
Download (955kB)
PDF - Accepted Vers... |
Let's suppose that we have a polynomial time randomized algorithm $A$ for a decision problem $\Pi$ with the property that$$\mathrm{Pr}[A \text{ is right}] > 1/2$$for all inputs. (In particular, independent of the input length $n$.)
We can use Chernoff bounds to show something stronger, namely that for any fixed $c$, th... |
If the utility is continuous and locally insatiable then the Hicksian demand equals the Walrasian demand.So you'll need to look for a utility function which violates atleast one of these.Lets try a simple violation of non-satiation $$u(x,y) = \left\{\begin{array}{ll}x+y & \quad x+y \leq 1 \\1 & \quad \text{ ...
Convexi... |
Let's say I want to use a Gaussian copula $$C_{R_t}(\eta_1, ..., \eta_n) = N_{R_t}(N^{-1}(\eta_1), ...,N^{-1}(\eta_n))$$ with a time-varying correlation matrix $R_t$. Through DCC we model the correlation which evolves as $$Q_t=(1-\alpha-\beta)\overline{Q}+\beta Q_{t-1} + \alpha \epsilon^{*}_{t-1} \epsilon^{*T}_{t-1}$$ ... |
Here is the answer I had made over on MathOverflow:
Surprisingly, the answer is yes! Well, let me say that the answeris yes for what I find to be a reasonable way to understand whatyou've asked.
Specifically, what I claim is that if PA is consistent, then thereis a consistent theory $T$ in the language of arithmetic wi... |
The main aim of this paper is to present a Stochastic Finite Element Method analysis with reference to principal design parameters of bridges for pedestrians: eigenfrequency and deflection of bridge span. They are considered with respect to random thickness of plates in boxed-section bridge platform, Young modulus of s... |
I would like to numerically solve the following system of coupled nonlinear differential equations:
$$ -\frac{\hbar^2}{2m_a} \frac{\partial^2}{\partial x^2}\psi_a + V_{ext}\psi_a + \left( g_a |\psi_a|^2 + g_{ab} |\psi_b|^2 \right)\psi_a = \mu_a \psi_a $$
$$ -\frac{\hbar^2}{2m_b} \frac{\partial^2}{\partial x^2}\psi_b + ... |
From Paul Romer's extended mathiness appendix [pdf].
I apparently completely misunderstood Paul Romer's comment about "mathiness". My original interpretation was that Romer was upset about obfuscating political assumptions that aren't substantiated empirically by using fancy math. But then I started reading some of his... |
Distances
We have the invariant distance equation for a homogeneous and isotropic universe (an FRW spacetime):
\[
ds^2 = -c^2 dt^2 + a^2(t)\left[\frac{dr^2}{1-kr^2} +r^2\left(d\theta^2 + \sin^2(\theta) d\phi^2\right)\right]. \]
Here we introduce several distance definitions, and how they are related to the coordinate s... |
After visiting some of the applications of different aspects of atomic physics, we now return to the basic theory that was built upon Bohr’s atom. Einstein once said it was important to keep asking the questions we eventually teach children not to ask. Why is angular momentum quantized? You already know the answer. Ele... |
The short answer is: I have no idea. It is fun to think about. Moving along the demand curve is analogous to an isothermal process and there is an additional law for an isoentropic process:$$
P (Q^s)^{1\mp1/\kappa} = \text{constant}
$$
One interesting idea is that if $\kappa \sim 1$, (as might be inferred from the pric... |
Take a Klein-Gordon (KG) equation for a model exercise: \begin{equation}\frac{\partial^2 u}{\partial t^2}=c^2\frac{\partial^2 u}{\partial x^2 } - \Omega^2 u,\end{equation} with boundary and initial conditions: \begin{equation}u(x,t)\in[0,a]\times[0,\infty]\end{equation} \begin{equation}u(x,0)=\alpha(x)\end{equation} \b... |
Answer Wiki
The 4 way stop these occasions (shown in the bottom quit nook where these people overlap) naturally is \=\max(X,Ful)\le x. To accomplish any calculations, you need to realise \(m\), a rot away parameter. How can I find the CDF for F_=\. The cumulative supply function is \(Delaware(A 7 | By 5)\). Say X_i \si... |
1.2E: Exercises Exercises
For the following exercises, for each pair of points, a. find the slope of the line passing through the points and b. indicate whether the line is increasing, decreasing, horizontal, or vertical.
59) \((-2,4)\) and \((1,1)\)
Answer: a. −1 b. Decreasing Answer: \(a. −1 \\b. Decreasing\)
60) \((... |
Newton-Mercator Series Contents Theorem
Let $\ln x$ be the natural logarithm function.
Then:
\(\displaystyle \ln \left({1 + x}\right)\) \(=\) \(\displaystyle x - \dfrac {x^2} 2 + \dfrac {x^3} 3 - \dfrac {x^4} 4 + \cdots\) \(\displaystyle \) \(=\) \(\displaystyle \sum_{n \mathop = 1}^\infty \frac {\left({-1}\right)^{n +... |
An RLC circuit is a simple electric circuit with a resistor, inductor and capacitor in it -- with resistance
R, inductance Land capacitance C, respectively. It's one of the simplest circuits that displays non-trivial behavior.
You can derive an equation for the behavior by using Kirchhoff's laws (conservation of the st... |
Longitude lines are perpendicular and latitude lines are parallel to the equator.
A
geographic coordinate system is a coordinate system that enables every location on the Earth to be specified by a set of numbers or letters. The coordinates are often chosen such that one of the numbers represents vertical position, and... |
One of the things I first noticed when I started studying economics was the strange fact that the macroeconomic AD-AS model has some formal similarities to a simple microeconomic supply and demand model. In the AD-AS model, the sum of hundreds of markets for hundreds of goods behaves a bit like a single market for a si... |
This question already has an answer here:
for (i=1; i<=n ;i=i*2){ for (j=1; j<=i ;j++){ basic_step; }}
Regarding the above nested loops, I can't seem to understand why is the following runtime analysis is correct (specifically the
first equality), when $k$ is defined as $\log i$, meaning $i=2^k$. What is the process th... |
Definition:Differentiable Functional Definition
Let $y, h \in S: \R \to \R$ be real functions.
Let $J \sqbrk y$, $\phi \sqbrk {y; h}$ be functionals.
$\Delta J \sqbrk {y; h} = \phi \sqbrk {y;h} + \epsilon \size h$
Suppose $\phi \sqbrk {y; h}$ is a linear with respect to $h$ and:
$\displaystyle \lim_{\size h \mathop \to... |
I'm a little rusty with my integrals, how may I evaluate the following:
$$ \int_0^1{\frac{y}{\sqrt{y(1-y)}}dy} $$
I've tried:
$$ \int_0^1{\frac{y}{\sqrt{y(1-y)}}dy} = \int_0^1{\sqrt{\frac{y}{1-y}} dy} $$
Make the substitution z = 1-y
$$ = \int_0^1{\sqrt{\frac{1-z}{z}} dz} = \int_0^1{\sqrt{\frac{1}{z} - 1} dz} $$
Which ... |
I have a simple question. I think not a question is, is a request. This month I have been studying how to understand and implement the Kalman filter algorithm for simple models such as the local level.
$ Y_t = \mu_t + \epsilon_t$
$\mu_t = u_{t-1} + \gamma_t$
I managed to implement this model (i don't have ability in pr... |
$w$-Matlis Cotorsion Modules and $w$-Matlis Domains
Bull. Korean Math. Soc. Published online August 6, 2019
yongyan pu, Gaohua Tang, and Fanggui WangPanzhihua University, Qinzhou University, Sichuan Normal University
Abstract : Let $R$ be a domain with its field $Q$ of quotients. An $R$-module $M$ is said to be weak $w... |
Question: A bucket contains $2$ white and $8$ red marbles. A marble is drawn randomly $10$ times in succession with replacement. Find the probability of drawing more than $7$ red marbles?
I think since the marbles are replaced, the probability of selecting a red marble does not change from trial to trail. Am I right on... |
A
density matrix, or density operator, is used in quantum theory to describe the statistical state of a quantum system. The formalism was introduced by John von Neumann (according to other sources independently by Lev Landau and Felix Bloch) in 1927. It is the quantum-mechanical analogue to a phase-space density (proba... |
I have a data set $x_{1}, x_{2}, \ldots, x_{k}$ and want to find the parameter $m$ such that it minimizes the sum $$\sum_{i=1}^{k}\big|m-x_i\big|.$$ that is
$$\min_{m}\sum_{i=1}^{k}\big|m-x_i\big|.$$
Computational Science Stack Exchange is a question and answer site for scientists using computers to solve scientific pr... |
My knowledge of finite difference is very basic so this could be very trivial. I've seen how multidimensional finite difference works for say fluid equations, but they are also dealing with a single variable. How would one solve a coupled multidimensional equation, for example of the form
$$a \nabla a = \nabla b,$$
in ... |
Here is the problem I'm working on (Satan's apple with bounded memory decision problem): Suppose I offer you slices of an apple, first $1/2$, then $1/4$, ... then $1/2^k$, etc. You want to eat as much of the apple as possible without eating the whole thing. For simplicity, lets have the utility $U(A_n) = n$ where $A_n$... |
Let $x_{1}=0,x_{2}=1$ and for $n\geq3,$ define $x_{n}=\frac{x_{n-1}+x_{n-2}}{2}.$
Which of the following is/are true?
$1.\{x_{n}\}$ is a monotone sequence.
$2. \lim_{n\to\infty} x_{n}=\frac{1}{2}.$
$3.\{x_{n}\}$ is a cauchy sequence.
$4.\lim_{n\to\infty} x_{n}=\frac{2}{3}.$
From first three terms it is clear that the s... |
That was an excellent post and qualifies as a treasure to be found on this site!
wtf wrote:
When infinities arise in physics equations, it doesn't mean there's a physical infinity. It means that our physics has broken down. Our equations don't apply. I totally get that
. In fact even our friend Max gets that.http://blo... |
Let $f:G\rightarrow H$ be a group homomorphism such that $f_* :G_{ab}\rightarrow H_{ab}$ is an isomorphism and that $f_* : H_2(G)\rightarrow H_2(H)$ is an epimorphism.
Question is to prove that this induced a monomorphism $$f:\frac{G}{\bigcap_{n=0}^{\infty}G_n}\rightarrow \frac{H}{\bigcap_{n=0}^{\infty}H_n}$$
Define th... |
I've been trying to prove that $\frac{b-a}{1+b}<\ln(\frac{1+b}{1+a})<\frac{b-a}{1+a}$ using the Mean value theorem. What I've tried is setting $f(x)=\ln x$ and using the Mean value theorem on the interval $[1,\frac{1+b}{1+a}]$. I managed to prove that $\ln(\frac{1+b}{1+a})<\frac{b-a}{1+a}$ but not the other part, only ... |
Good morning.I need to create a pdf and estimate its parameters by the MLE method. The distribution is a power law ($f(x)=C(k)\;x^{-k}$) and I need to estimate the $k$ parameter and $C(k)$ is determinated by the normalization condition $\int_a^b\;C(k)\;x^{-k}=1$.I have tried to define the power distribution with
Probab... |
I read this pdf on non inertial frame, in particular I have a question on the deviation of free falling object due to Coriolis effect.
Consider a ball let go from a tower at height $h$. The displacement due to Coriolis effect, calculated with formulas in Earth system, is $(4.19)$, after it there is explanation of the e... |
The key here is that $X = Y\oplus Y^\perp$, i.e. for any $x\in X$ there are unique $y\in Y, z\in Y^\perp$ such that $x = y+z$. This is essential in order for $P(x) = P(y+z) = y$ to be well defined in the first place.
Now, what you showed is that $\alpha x_1 +\beta x_2$ can be uniquely written as $(\alpha y_1 + \beta y_... |
I am interested in solving ODE systems of the form \begin{align} \frac{\partial \vec{u}}{\partial t} = F(\vec{u}) \end{align} where $F$ is a nonlinear operator, $\vec{u}$ is a vector valued function of $t$, and we have initial conditions $\vec{u}(0) = \vec{u}_0$. I am specifically interested in equations of this form t... |
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. ... |
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Now showing items 1-10 of 32
The ALICE Transition Radiation Detector: Construction, operation, and performance
(Elsevier, 2018-02)
The Transition Radiation Detector (TRD) was designed and built to enhance the capabilities of the ALICE detector at the Large Hadron Collider (LHC). While aimed at providing electron... |
We consider the problem of distributed estimation of a Gaussian vector withlinear observation model. Each sensor makes a scalar noisy observation of theunknown vector, quantizes its observation, maps it to a digitally modulatedsymbol, and transmits the symbol over orthogonal power-constrained fadingchannels to a fusion... |
ISSN:
1534-0392
eISSN:
1553-5258
All Issues
Communications on Pure & Applied Analysis
November 2012 , Volume 11 , Issue 6
Select all articles
Export/Reference:
Abstract:
The present volume is dedicated to Michel Pierre. An international Workshop for his 60th birthday, entitled "Partial Dierential Equations and Applicat... |
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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 ... |
ä is in the extended latin block and n is in the basic latin block so there is a transition there, but you would have hoped \setTransitionsForLatin would have not inserted any code at that point as both those blocks are listed as part of the latin block, but apparently not.... — David Carlisle12 secs ago
@egreg you are... |
Let $S$ be the set of all probability distributions on $\mathbb{R}$ and $S_n=\{p_\theta\}$ be an $n$ dimensional submanifold of parameterized family of probability distributions on $\mathbb{R}$ where $\theta=(\theta_1,\dots, \theta_n)\in \Theta$ are called parameters of the probability density $p_\theta(x)$ and $\Theta... |
ISSN:
1547-5816
eISSN:
1553-166X
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Journal of Industrial & Management Optimization
October 2007 , Volume 3 , Issue 4
A special issue dedicated to Professor Changyu Wang in recognition of his contributions
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Abstract:
This special issue is dedicated to Professor Changyu Wang ... |
I want to solve the following exercise from Dummit & Foote. My attempt is down below. Is it correct? Thanks!
Show that the group of rigid motions of a cube is isomorphic to $S_4$.
My attempt:Let us denote the vertices of the cube so that $1,2,3,4,1$ trace a square and $5,6,7,8$ are the vertices opposite to $1,2,3,4$. L... |
OPEN ACCESS
Draglines are heavy and costly machines massively utilised in opencast mines to remove the overburden materials
. Because of harsh operating situations advanced wear, tear, fractures and fatigue failure are generally determined in dragline. The bucket is the main component of the dragline, and it's the far ... |
(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 can't be entirely sure but I'll make an informed guess:
That value doesn't come for a single measurement. Therefore, if the error in the age of a single sample is $\pm125$ kyr, you just need to average 16 samples to get it down to $\pm31$ kyr.
The uncertainty in the addition (or substraction) of two or more quantitie... |
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Forward-backward multiplicity correlations in pp collisions at √s = 0.9, 2.76 and 7 TeV
(Springer, 2015-05-20)
The strength of forward-backward (FB) multiplicity correlations is measured by the ALICE detector in proton-proton (pp) collisions at s√ = 0.9, 2.76 and 7 TeV. The measurement... |
Okay so let me begin.
Mathematica itself does a semi-good job here. It find 2 solutions where one is not applicable for your startingcondition. So it finds the only solution which is
1/Sqrt[1 - 2 HeavisideTheta[-2 + t]]
But this only seems to work for $t<2$ and this is indeed right (we'll see later).
If we apply the Fo... |
I) Recall first the $\phi\phi$-Operator Product Expansion (OPE):
$$\tag{A} {\cal R}\left\{\phi(z,\bar{z})\phi(w,\bar{w})\right\} ~-~: \phi(z,\bar{z})\phi(w,\bar{w}):~=~C(z,\bar{z};w,\bar{w}) ~{\bf 1}, $$
where the contraction is assumed to be a $c$-number:
$$\tag{B} C(z,\bar{z};w,\bar{w})~=~ \langle 0 | {\cal R}\left\{... |
The Navier Stokes equation: apply Newton’s Second Law to a small ‘blob’ of fluid moving with the flow (imagine we can watch it as it goes).
Normal pressure forces in x-direction
Net pressure force in x-direction
Vector pressure force
Viscous forces: take bulk fluid component
u in the x-direction- assume it is independe... |
I don't understand exactly what you are looking for, I'll try to explain the Curry-Howard correspondence in a nutshell, you'll let me know if it helps.
The Curry-Howard correspondence (or isomorphism, if you wish) definitely links the three objects you mention: it actually tells that two of them, IL and $\lambda$c, are... |
I have a package for numerically calculating solutions of eigenvalue problems using the Evans function via the method of compound matrices, which is hosted on github. See my answers to other questions or the github for some more details.
First we install the package (only need to do this the first time):
Needs["PacletM... |
How is this trigonometric relation derived in simple terms?
$$\cos\left(\frac{2\pi}{N}\right) = 1 - 2\sin^2\left(\frac{\pi}{N}\right)$$
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It only takes a minute to sign up.Sign up to join th... |
I'm having a little trouble with correlation functions wick theorem and ordering in the context of OPE and CFT, for string theory.
(1) My first question, the propagator is: $$<X(z) X(w)> = \frac{\alpha}{2} \ln(z-w).$$
In the context of primary operators it's easy to see that $X$ it's not a good conformal field. But $\p... |
We already learnt about the vectors and their notations in the previous physics article. Now, we will discuss vector addition and subtraction.
Vector Addition:
The vector addition is done based on the Triangle law. Let us see what triangle law of vector addition is:
Suppose there are two vectors: \(\overrightarrow{a}\)... |
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... |
Nodes are the points in space around a nucleus where the probability of finding an electron is zero. However, I heard that there are two kinds of nodes,
radial nodes and angular nodes. What are they and what information do they provide of an atom?
Nodes are the points in space around a nucleus where the probability of ... |
A peek through the imaginary looking glass
Plymouth, December 2018
Before starting Thank you very much for the invitation Please ask questions Recalling projective geometry
The set of lines through a point.
Recalling projective geometry
Parametrized by the points in a line.
Recalling projective geometry
Except for one.... |
This is the final one of a series of posts about the manuscript “Finite Part of Operator K-theory for Groups Finitely Embeddable into Hilbert Space and the Degree of Non-rigidity of Manifolds” (ArXiv e-print 1308.4744. http://arxiv.org/abs/1308.4744) by Guoliang Yu and Shmuel Weinberger. In previous posts (most recentl... |
Sometimes finding the volume of a solid of revolution using the disk or washer method is difficult or impossible.
For example, consider the solid obtained by rotating the region bounded by the line \(y = 0\) and the curve \(y = {x^2}-{x^3}\) about the \(y-\)axis.
The cross section of the solid of revolution is a washer... |
Consider a Dp-brane. Compactify $d$ spatial dimensions over a torus $T^d$. Suppose $d\geqslant p$, and that the Dp-brane is completely wrapped around the compactified dimensions.
Look at the open string modes ending on this wrapped D-brane. There is a zero energy open string mode associated with each spatial dimension.... |
Suppose that $\mathcal{L}$ is the language of a simply typed lambda calculus of two base types, $e$ and $t$, with infinitely many constants at each type.
A substitution $j$ is a mapping from constants of type $\sigma$ to arbitrary closed $\mathcal{L}$-terms of type $\sigma$. $j$ extends to a mapping on arbitrary closed... |
Expand $f(x) = \log(1 + x)$ around $x = 0$ to all orders. More precisely, find $a_n$ such that for any positive integer $N$, we have$$f(x) = \left(\sum_{n=0}^{N-1} a_nx^n\right) + E_N(x) \text{ for all }\left|x\right| < {1\over2},$$where $\left|E_N(x)\right| \le C_N\left|x\right|^N$ for $\left| x\right| \le 1/2$. How d... |
Star forming regions Massive stars are born in warm molecular clouds; because of their size, they shape the environment around them through processes such as photoionisation, stellar winds and supernovae. It may also be the case that massive stars trigger or terminate the formation of less massive stars. are born in co... |
Suppose we have the following production function:
$$F(L,K)=\max_{L_K}H(L,L_K,K)=\max_{L_K}\left[(L-L_K+1)^\alpha(L_K+K)^{1-\alpha}\right]=(L-L_K^*+1)^\alpha(L_K^*+K)^{1-\alpha}$$
With the constraint $L_K\in[0,L]$.
We know that $$\frac {dH}{dL_K}=\alpha(L-L_K+1)^{-1}H+(1-\alpha)(L_K+K)^{-1}H=0$$ Hence the value for $L_... |
This question already has an answer here:
Let $f: \mathbb R \rightarrow \mathbb R$ defined by $$f(x) := \begin{cases}x^2 \sin \frac 1 x\ & x \neq 0\\ 0\ & x = 0\end{cases}$$
Show $f$ is differentiable on $\mathbb R$:
Let $\epsilon > 0$.
$x_0 \neq 0$: $\left\lvert\frac {x^2 \sin \frac 1 x - x_0^2 \sin \frac 1 {x_0}}{x-x... |
Intuitively Deriving the Y Combinator$$ \newcommand{\one}[1]{ \color{red}{ #1 } } \newcommand{\two}[1]{ \color{blue}{ #1 } } \newcommand{\three}[1]{ \color{green}{ #1 } } \newcommand{\four}[1]{ \color{magenta}{ #1 } } $$
The $\lambda$ calculus is designed to be a model of computation, so it may be surprising that it ha... |
This story actually starts with Einstein's paper on the photoelectric effect. Einstein proposed that for light waves, $E \propto f$, with a proportionality constant that eventually became known as $h$. Using the relation $E = pc$ from special relativity, you can derive that $pc = hf$, and with $\lambda f = c$ you get $... |
I just have a question concerning the third law of thermodynamics.
The third law describes that the entropy should be a well defined constant if the system reaches the ground state which depends only on the temperature. Beside this fact we now that the temperature is independent on the measurement system we can assume ... |
Let $\mathbf{F}=3y \ \mathbf{i} -3xz \ \mathbf{j} + (x^2-y^2) \ \mathbf{k}.$ Compute the flux of the vectorfield $\text{curl}(\mathbf{F})$ through the semi-sphere $x^2+y^2+z^2=4, \ z\geq 0$, by using direct parameterization of the surface and computation of $\text{curl}(\mathbf{F}).$
Denote the semisphere by $S$. In th... |
I have a question about partitions of unity specifically in the book Calculus on Manifolds by Spivak. In case 1 for the proof of existence of partition of unity, why is there a need for the function $f$? The set $\Phi = \{\varphi_1, \dotsc, \varphi_n\}$ looks like is already the desired partition of unity. Following is... |
Group Action on Subgroup by Left Regular Representation Theorem
Let $G$ be a group.
Let $H$ be a subgroup of $G$.
Let $*: H \times G \to G$ be the operation defined as: $\forall \left({h, g}\right) \in H \times G: h * g = \lambda_h \left({g}\right)$
where $\lambda_h \left({g}\right)$ is the left regular representation ... |
Let's say
I have $10$ biased coins. Each coin has a different probability for head.
$$\text{coins} = [10\%, 20\%, 30\% ...]$$ I flip each coin once
What is the probability of getting:
At least $3$ heads Exactly $3$ heads
Mathematics Stack Exchange is a question and answer site for people studying math at any level and ... |
Traditionally, the null hypothesis is a point value. (It is typically $0$, but can in fact be any point value.) The alternative hypothesis is that the true value is any value other than the null value. Because a continuous variable (such as a mean difference) can take on a value which is indefinitely close to the null ... |
Where priors come from Rob Zinkov 2015-06-09
When reading up on Bayesian modeling papers it can be bewildering to understand why a paricular prior was chosen. The distributions usually are named after people and the density equations are pretty scary. This makes it harder to see why the models were successful.
The real... |
$$\mathfrak{I}=\int\limits_0^1 \left[\log(x)\log(1-x)+\operatorname{Li}_2(x)\right]\left[\frac{\operatorname{Li}_2(x)}{x(1-x)}-\frac{\zeta(2)}{1-x}\right]\mathrm dx=4\zeta(2)\zeta(3)-9\zeta(5)\tag1$$
This integral haunts me for while and I am still unable to evaluate it which annoys me even more. For the first time I h... |
Inner automorphism of a group $G$
An automorphism $\phi$ such that $$ \phi(x) = g^{-1} x g $$
for a certain fixed element $g \in G$: that is, $\phi$ is conjugation by $g$. The set of all inner automorphisms of $G$ forms a normal subgroup $\mathrm{Inn}(G)$ in the group $\mathrm{Aut}(G)$ of all automorphisms of $G$; this... |
Is there a name for the following problem? Is there a measure of quality of a given solution? How can we even define what a proper solution is?
Context: I want to detect long lines (most lines over 1000 pixel long) in an image. It is known that most of the lines have similar alignment. To detect those I use the Standar... |
You can check that there exists a
potential function, $U$, such that $\mathbf{F} = -\nabla U $, since $\nabla \wedge \mathbf{F} = 0$ (then, $\mathbf{F}$ is known as a force field). You can also verify that $U$ is given by:
$$ U(x,y) =- \frac{x^2}{y},$$
which is continuous in its domain, which is the same as the domain ... |
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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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Now showing items 1-9 of 9
Production of $K*(892)^0$ and $\phi$(1020) in pp collisions at $\sqrt{s}$ =7 TeV
(Springer, 2012-10)
The production of K*(892)$^0$ and $\phi$(1020) in pp collisions at $\sqrt{s}$=7 TeV was measured by the ALICE experiment at the LHC. The yields and the transverse momentum spectra $d^2 ... |
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