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Usually this part of thermodynamics is not presented in the most efficient way. To derive the expression for, e.g., $C_P - C_V$, one goes through a series of steps involving Maxwell's relations and the triple product rule. Figuring out what to do in each step is done mostly by guesswork.
However, all relations of these... |
Existence and uniqueness of positive solutions for a class of logistic type elliptic equations in $\mathbb{R}^N$ involving fractional Laplacian
1.
Departamento de Matemática, Universidad Técnica Federico Santa María, Casilla: V-110, Avda. España 1680, Valparaíso, Chile
2.
Department of Mathematics, Jiangxi Normal Unive... |
What is the best way to approximate how many primes there are less than $2^{43112609}-1$? I know that one can use prime number theorem. I also found that in the Internet that $\pi (10^{24})=18435599767349200867866$ and then one can use Loo's theorem that there are always prime between $3n$ and $4n$ so this method gives... |
2 Methods for Simulating Radiated Fields in COMSOL Multiphysics®
In Part 2 of our blog series on multiscale modeling in high-frequency electromagnetics, we discuss a practical implementation of multiscale techniques in the COMSOL Multiphysics® software. We will simulate radiated fields using two different techniques an... |
Your 1st equation can be interpreted as saying that the flux through the section is equal to $\frac{1}{\epsilon_0}$ times the charge $Q$ contained within a
cone whose base is the section and whose vertex is the centre of the sphere.
This result can be obtained directly using Gauss' Law. The electric field inside a unif... |
Let's reformulate this problem in terms of commutative algebra (its second tag): for an arbitrary field $K$ the ring $K[z_{11},\dots,z_{mn}]/\ker\phi$ is isomorphic to $\text{Im}\ \phi$ which is obviously the subring of $K[x_1,\dots,x_m,y_1,\dots,y_n]$ generated by all the monomials $x_iy_j$.
Now think in terms of affi... |
This is a special case of the following theorem (Lemma 2.1 in this paper on disjunctive sequences), whose proof is along the same lines as that posted in the answer by @EricWofsey:
If $a_1, a_2, a_3, \dots$ is a strictly increasing infinite sequence
of positive integers such that $$\lim_{n\to \infty}
\frac{a_{n+1}}{a_n... |
I am working on an Index and I am trying to price Call options on it. I work with the 3 Months LIBOR as Cash.
I use the following Black-Scholes formula $$C_{t} = S_{t}e^{-q_{t}(T-t)}\mbox{N}[d_{1}(t)] - K e^{-r_{t}(T-t)}\mbox{N}[d_{0}(t)] $$ with the usual notations. $r_{t}$ is the LIBOR rate and $q_{t}$ is the dividen... |
I came across John Duffield Quantum Computing SE via this hot question. I was curious to see an account with 1 reputation and a question with hundreds of upvotes.It turned out that the reason why he has so little reputation despite a massively popular question is that he was suspended.May I ...
@Nelimee Do we need to m... |
The answer is D, the melting points increase. This is absolutely true (source for values):\begin{array}{lrr}\text{Halogen} & \text{Melting point}/^\circ\mathrm{C}& \text{Boiling point}/^\circ\mathrm{C}\\\hline\text{fluorine} & -220 & -188 \\\text{chlorine} & -101 & -35 \\\text{bromine} & -7.2 & 58.8 \\\text{iodine} & 1... |
Let's assume an $xy$ plane and let there be a force field defined by the potential $$V=F_0|x|$$ Though the potential is not differentiable still its a perfectly realisable system. If we solve the force equation with the initial conditions $x = \delta$ and $\dot{x}=0$, we will have to solve it for $x\geq0$ and $x\leq 0$... |
Disclaimer: I come from an academic finance perspective and hence I will definitely have my inherent biases in this question.
How does one think about "alpha" in portfolio management? In particular, in some practitioner's literature, there's this discussion of an "alpha factor" in the linear factor models. Taking an in... |
Dipak Ghosh
Articles written in Pramana – Journal of Physics
Volume 63 Issue 5 November 2004 pp 963-968
In this paper intermittent behaviour of the pions from ‘cold’ and ‘hot’ classes of events from
12C-AgBr interactions at 4.5 A GeV has been studied, separately. The results reveal strong intermittent pattern in case o... |
I'm reading about the mean-variance optimization of active portfolios. A bit of prior background from the book I'm reading: the author discusses the mean-variance optimal portfolios without cash, which amounts to solving the following optimization problem:
Maximize: $w^Tf - \frac{1}{2}\lambda (w^T\Sigma w)$, subject to... |
Lasted edited by Andrew Munsey, updated on June 15, 2016 at 1:21 am.
Mechanical work is a force applied through a distance, defined mathmatically as the
There was an error working with the wiki: Code[1] and displacement vectors. Work is a
There was an error working with the wiki: Code[2] quantity which can be positive ... |
Your calculation assumes that the charges on both capacitors are the same. There is a fixed amount of charge $Q$ which is shared between the two capacitors. When the charge on the spherical capacitor is $q$ that on the other capacitor is $Q-q$.
Another thing which your diagram does not show is that the LH plate of the ... |
The $(M+1)$ peak is often considered in the high-resolution mass spectra of organic molecules as it reveals the number of carbon atoms in the sample. In general, it is known that the ratio of the size of the $M$ to $(M+1)$ peaks is $98.9 : 1.1 \times n $ since the relative abundance in nature of $^{13}$C is $ 1.1$% for... |
NOTE: AFAICT, D.W found a hole in this reduction and it is wrong (see comments). Keeping it here for historical reasons.
Intro: first I will reduce the problem to our problem. Though the Monotone 3SAT problem is trivially satisfiable, our problem can further solve the Monotone 3SAT problem, which is NP-hard; thus this ... |
In relativity, the symmetric energy-momentum tensor is given by $$ T^{ij}, $$ where $T^{00}$ is the energy density and $\frac{1}{c}T^{10}$ is the momentum density. Thus: $$ \left(\frac{1}{c}T^{00}dV, \frac{1}{c}T^{10}dV\right)^{T}$$ is the 4-momentum. Under a Lorentz transformation, this should transform like 4-vectors... |
A. Enayat, J. D. Hamkins, and B. Wcisło, “Topological models of arithmetic,” ArXiv e-prints, 2018. (under review)
@ARTICLE{EnayatHamkinsWcislo2018:Topological-models-of-arithmetic, author = {Ali Enayat and Joel David Hamkins and Bartosz Wcisło}, title = {Topological models of arithmetic}, journal = {ArXiv e-prints}, ye... |
I have a question about deriving Eq. (6.2.13) in Polchinski's string theory book volume I. It is claimed that
Now consider the path integral with a product of tachyon vertex operators, $$A_{S_{2}}^{n}(k,\sigma)=\left\langle [e^{ik_{1}\cdot X(\sigma_{1})}]_{r}[e^{ik_{2}\cdot X(\sigma_{2})}]_{r}\cdots[e^{ik_{n}\cdot X(\s... |
One way to overcome the problem of excessive extrapolation by least squares involves directly executing on the unconfoundedness assumption and nonparametrically matching subjects with similar covariate values together. As we shall see, least squares still plays an important role under this approach, but its scope is re... |
I need to find the following asymptotic expansion as $t\rightarrow \infty$ :
$\int_{0}^{e^{-1}}e^{-t\sqrt{-y\ln y}}{\rm d}y. $
Introducing the new variable (related to the left branch of the Lambert function) : $u=-e^{\ln y}\ln y\Longleftrightarrow y=\exp\left(W_{-1}\left(-u\right)\right)$ and ${\rm d}y=-\frac{{\rm d}u... |
Is it possible to find all polynomials of the form $ an^2 + bn +c $ where a,b, and c are integers and such that
$$ a+b+c \equiv 31 \pmod{54} $$ $$ 4a+2b+c \equiv 3 \pmod{54} $$ $$ 9a+3b+c \equiv 11 \pmod{54} $$
Mathematics Stack Exchange is a question and answer site for people studying math at any level and profession... |
Given the linear diophantine equation
$$ax+by=c $$
I have to show that
it has solution if and only if $gcd(a,b)$ divides $c$.
$$1)\Rightarrow $$
Let $m=gcd(a,b)$ then
$$a'x+b'y=c'$$
where $gcd(a',b')=1$, but how can I continue from here?
$$2) \Leftarrow $$
I don't know even how to start. I've never studied seriously nu... |
In Quantum Field Theory and the Jones Polynomial, Witten showed how to get the Jones polyomial as a Wilson Loop in Chern-Simons theory. The Chern-Simons Lagrangian is $$ \mathcal{L} = \frac{k}{4\pi} \int_M \mathrm{Tr}(A \wedge dA + \frac{2}{3} A \wedge A \wedge A )$$Here you're integrating over a 3-manifold (e.g. $M= S... |
I want to calculate the limit which is above without using L'hopital's rule ;
$$\lim_{x\rightarrow0} \frac{e^x-1}{\sin(2x)}$$
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 this communi... |
PartialStructureFactor¶ class
PartialStructureFactor(
md_trajectory, start_time=None, end_time=None, pair_selection=None, maximum_q_value=None, q_resolution=None, cutoff_radius=None, resolution=None, time_resolution=None, info_panel=None)¶
Constructor for the PartialStructureFactor object.
Parameters: md_trajectory(
MD... |
In an effort to find a proof that builds intuition for students in my proof writing course, I devised the following. Its seems too easy to me, so I am worried something is wrong. The class is very Naive Naive Set Theory so I realize some axioms are needed but that is way too hard for my students. I guess I would just l... |
A very good way to generate normal variables is to start with pairs of uniform variablesand apply a rejection method. If you're considering these normal variables as inputto a rejection method, then, why not start with uniform variables so you only haveto do one level of rejection?
You could generate a random point uni... |
Prove that the following inequality holds for $x\ge0$ :
$$\sin(x) \cos(x) \geq x-x^3$$
This is an inequality often met during my high school classes I also used for this problem yesterday. I'm interested in a non-calculus proof if this is possible.
Proof involving calculus:
Let's consider
$$f(x) = \sin(x) \cos(x)-x+x^3... |
The ODE I'm trying to solve is: $y''+2y'+2y = 3$. I've never tried to solve an ODE with complex roots until this problem so it's challenge for me. These are my steps for getting r: $$a_2r^2 +a_1r+a_0=0$$ $$r^2+2r+2=0$$ $$(r+1)^2 = -1$$ $$r = \pm i-1$$ $Q_2(x) = \frac32$ and these are my last few steps plugging everythi... |
\begin{equation*} \int_{-a}^{a}e^{-\rho x}P_n \left( \frac{x}{a} \right) dx = (-1)^n\sqrt{\frac{2\pi a}{\rho}}J_{n+1/2}(a\rho) ~~~~~~\text{for $a>0$} \end{equation*}
I am just wondering this formula is correct or not? Thanks in advance!
Mathematics Stack Exchange is a question and answer site for people studying math a... |
Modeling of Materials in Wave Electromagnetics Problems
Whenever we are solving a wave electromagnetics problem in COMSOL Multiphysics, we build a model that is composed of domains and boundary conditions. Within the domains, we use various material models to represent a wide range of substances. However, from a mathem... |
Chemical Forums aims at helping chemistry students. That means many of the questions posted require use of formulae - either chemical ones (like H
2
PO
4 -
) or mathematical ones (like [itex]E = E_0 + \frac {RT}{nF}\ln Q[/itex]). You may even need to use a structural formula like
To make your questions easier to unders... |
Linear Regression -- The Basics The basics
Yeah. It’s not a good sign if I’m starting out already repeating myself. But that’s how things seem to be with linear regression, so I guess it’s fitting. It seems like every day one of my professors will talk about linear regression, and it’s not due to laziness or lack of co... |
If $A+B+C=\pi$ :
$$ \sin A + \sin B + \sin C \le \frac{3\sqrt{3}}{2} \\ \cos A + \cos B + \cos C \le \frac{3}{2} \\ \tan A + \tan B + \tan C \le 3\sqrt{3} $$
with the equalities holding in the case of an equilateral triangle ($A=B=C=\frac{\pi}{3}$). I've also found out that of all the triangles inscribed in a circle, a... |
Let $f$ be Riemann-Stieltjes integrable with respect $G$ (increasing function). My definition for Riemann-Stieltjes integration is: for every $\epsilon$ there is a partition $\mathcal{P}_\epsilon$ such that when $\mathcal{P}_\epsilon \subset \mathcal{P}$ then $\left|S(\mathcal{P},f,G, \{t_i\}) - \int_a^bf dG \right| < ... |
Let $\tau$ be a topology on $\mathbb{R}$ under which every absolutely convergent series converges.
Lemma. If $(x_n) \to L$ under the standard topology, then $(x_n) \to L$ under $\tau$.
Proof. Let $(y_n)$ be any subsequence of $(x_n)$. Then there exist $(n_k)$ such that $|y_{n_k} - L| < 2^{-k}$. Now consider the sequenc... |
Let me try to give you the answer in just the right amount of generality. A quantum code is just a short way to say a quantum
error-correcting code. It is a special embedding of one vector space into another larger one that satisfies some additional properties. If we start with a Hilbert space $H$, then a code is a dec... |
To perform the gluing, we need:
two metric spaces $X$ and $Y$ a set $A\subset X$, this is the part of $X$ covered in glue an isometric embedding $f:A\to Y$, which is a way to put the glue-covered part of $X$ over $Y$.
After we firmly press the spaces together and let them sit for a while, a point $x\in A$ becomes ident... |
Let $\mathbf{R}$ be the relation on $Z \times (Z \setminus \{0\})$ given by $m \mathrel{\mathbf{R}} n$ iff $m - n =2k$ for some $k \in\mathbb Z$. I have proven that this is indeed an equivalence relation by meeting the three required properties, yet I am having trouble understanding the meaning of and determining the e... |
Suppose that the matrix $A=\begin{pmatrix}1+ci & w_1 \\ 2+i & z_2\end{pmatrix}$ with $c\in \mathbb{R}$ is hermitian, of order $1$ and the vector $(k_1, k_2)\in \mathbb{C}^2$ with $k_2$ positive real number, belongs to the orthogonal complement of the row space of $A$ and has norm $\sqrt{3}$.
How can we determine the nu... |
ISSN:
1930-5311
eISSN:
1930-532X
All Issues
Journal of Modern Dynamics
July 2010 , Volume 4 , Issue 3
Select all articles
Export/Reference:
Abstract:
In this paper, we study Hölder-continuous linear cocycles over transitive Anosov diffeomorphisms. Under various conditions of relative pinching we establish properties in... |
ISSN:
1930-5311
eISSN:
1930-532X
All Issues
Journal of Modern Dynamics
October 2010 , Volume 4 , Issue 4
Special issue dedicated to Jan Boman
on the occasion of his 75th birthday
Select all articles
Export/Reference:
Abstract:
We prove the local differentiable rigidity of generic partially hyperbolic abelian algebraic ... |
How many real roots does $x^3+9x^2-49x+49=0$ have in the open interval $1\lt x\lt 2$? I've applied the intermediate value theorem and found that it has at least 1 root. But what about other roots? How can you find the exact numbers of real roots in a given interval. I would really appreciate if I could get some example... |
Often statistical models are used in order to determine which of the predictor variables have a significant relationship with the response variable.
LMM has a number of methods to aid with this kind of statistical inference.
Below we will fit a linear mixed model using the Ruby gem mixed_models, and demostrate various ... |
The equation of motion is $$m\frac{d\mathbf{v}}{dt}=q(\mathbf{E}+\mathbf{v} \times \mathbf{B})$$ in which the bold letters represent vectors : $$\mathbf{E}=\mathbf{j}E, \mathbf{B}=\mathbf{j}B, \mathbf{v}=\mathbf{i}\dot x+\mathbf{j}\dot y+\mathbf{k}\dot z$$ $$\mathbf{v}\times \mathbf{B}=\mathbf{k}\dot x B-\mathbf{i}\dot... |
Does anybody have the Bachelier model call option pricing formula for $r > 0$?
All the references I've read assume $r = 0$. I don't speak French, so I can't read Bachelier's original paper.
Quantitative Finance Stack Exchange is a question and answer site for finance professionals and academics. It only takes a minute ... |
Mayghani, M., Alimohammadi, D. (2017). The structure of ideals, point derivations, amenability and weak amenability of extended Lipschitz algebras. International Journal of Nonlinear Analysis and Applications, 8(1), 389-404. doi: 10.22075/ijnaa.2016.493
Maliheh Mayghani; Davood Alimohammadi. "The structure of ideals, p... |
This is a somewhat stupid question..
In my notes, the Arzela-Ascoli theorem is stated like this: Let $X$ be a compact space and let $M\subset C(X,\mathbb R)$. Then $M$ is relatively compact in $C(X,\mathbb R)$ if and only if it is uniformly bounded and equicontinuous. But since every function in $M$ is continuous (belo... |
Given a curve $C$ with parameter $t$ and origin $0$ and an arc length $s$, I am trying to find the point $P$ so that the length from $C(0)$ to $P$ along $C$ is equal to $s$.
In this case, $C$ is a jointed curve of $n+1$ cubic Bézier curves in $\mathbb{R}^2$; with $(a_i), (b_i), (c_i), (d_i)$ denoting vectors of $\mathb... |
Entire case
From the equation we have that $f^2-g^6=(f+g^3)(f-g^3)=-1$.
Therefore, $f+g^3$, and $f-g^3$ don't vanish.
This means that there is an entire $h$ such that $$\begin{align}f+g^3&=-e^{ih}\\f-g^3&=e^{-ih}\end{align}$$
It follows that $$\begin{align}f&=\frac{-e^{ih}+e^{-ih}}{2}\\g^3&=\frac{-e^{ih}-e^{-ih}}{2}\en... |
This question is similar to Is every forest with more than one node a bipartite graph?, but requires a proof by induction.
This was a past exam question.
-
Let P(G) be the predicate that graph G=(V,E) is bipartite, and can be partitioned into G=($V_1,V_2$,E) s.t. $V_1 \lor V_2 = V$, and $\forall e \in E$, e joins a nod... |
I was reading this article on inequalities (which some of you may find useful) here.
On page 7, I came across this question by Titu Andreescu, which I shall reproduce here:
Question:Let f be a convex function on $\mathbb{R}$. If $x_1$, $x_2$ and $x_3$ lie in it's domain, prove that:$$f(x_1)+f(x_2)+f(x_3)+f\left(\frac{x... |
Let $X_n$ be a binomial distribution with parameter $\theta$. Empirically, after $n$ throws, my estimate is $\hat{\theta}_n=\frac{S_n}{S_n+F_n}$, where $S/F$ are the successes and failures $(F_n:=n-S_n)$.
From simulations on my dataset, I've found out that $-\log(\theta)$ is better approximated by a beta distribution, ... |
Let's talk Homotopy and AlgebraTheorem-of-the-day ·
So this post is going to be a bit more terse than most. In fact, the objective of this post will be to develop the theory of Homotopy very briefly, with the goal of proving the Fundamental Theorem of Algebra.
Homotopy
Given two continuous maps \(f,g : \mathbb{R}^n\to\... |
There are a lot of neat little tricks in Machine Learning to make things work better. They can do many different things: make a network train faster, improve performance, etc. Today I’ll discuss
LogSumExp, which is a pattern that comes up quite a bit in Machine Learning. First let’s define the expression: $$LogSumExp(x... |
In the appendix on page 364 of 'String Theory', Polchinski defines the conformal group (Conf) in two dimensions to be the set of all holomorphic maps. On page 85 he explains how Conf is a subgroup of the direct product of the diffeomorphism (diff) and Weyl groups, denoted as (diff $\times$ Weyl) (here, diffeomorphisms ... |
I very much dislike the "Big Oh" notation. It just doesn't stick in my mind. Suppose $f$ is a continuous function and $f \in \text{O}( 1/|x|^{1+\epsilon})$ when $|x| \rightarrow \infty$ and for $0< \epsilon < 1$. Does this mean that $$ \int_{-\infty}^\infty |f(x)|\cdot |x|^\epsilon \; dx < \infty ?$$
No. This only give... |
Solving $x' = 0 = y'$, we get\begin{aligned}x^2 &= \epsilon \\y &= 0 \, .\end{aligned}Therefore, no critical point (or equilibrium point) is obtained with $\epsilon < 0$.
The origin is the only critical point when $\epsilon = 0$. One eigenvalue of the flow's Jacobian matrix at $(0,0)$ is $-1$, the other is zero. Theref... |
Learning Objectives
Describe the differences between rotational and translational kinetic energy Define the physical concept of moment of inertia in terms of the mass distribution from the rotational axis Explain how the moment of inertia of rigid bodies affects their rotational kinetic energy Use conservation of mecha... |
Difference between revisions of "Multi-index notation"
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The partial derivative operators are also abbreviated:
The partial derivative operat... |
An Internet cafe is reached by three kind of clients: type I, type II, type III, according to (independent) Poisson processes of parameters $\lambda_1,~\lambda_2,~\lambda_3$, respectively. Evaluate the probability that $15$ clients of type I reach the cafe, before $6$ of the other categories reach the same cafe, on the... |
Assessment | Biopsychology | Comparative |Cognitive | Developmental | Language | Individual differences |Personality | Philosophy | Social |
Methods | Statistics | Clinical | Educational | Industrial | Professional items | World psychology | $ \operatorname{cov}(X, Y) = \operatorname{E}((X - \mu) (Y - \nu)), \, $
where... |
Given a deterministic infinite word transducer (also called deterministic generalized sequential machine) with the following restriction:
There is exactly one initial state All states are final The transducer is real-time, i.e. reads excactly one input character on each transition The transducer produces zero or more o... |
$\newcommand{\ket}[1]{|#1\rangle}$$\newcommand{\bra}[1]{\langle#1|}$In
Principles of Quantum Mechanics (2nd edition) by Shankar, Exercise 5.1.3 asks to find the wave function of the free particle by means of applying the propagator to an wave function in $x$-space.
The propagator $U(t)$, which satisfies $\ket{\psi(t)} ... |
OpenCV 3.3.0
Open Source Computer Vision
Structured forests for fast edge detection Filters Superpixels Image segmentation Fast line detector
void cv::ximgproc::anisotropicDiffusion (InputArray src, OutputArray dst, float alpha, float K, int niters) Performs anisotropic diffusian on an image. More... void cv::ximgproc:... |
Introduction
This is part 4 of a five part tutorial on our plasma simulation code Starfish. In this part we continue the surface interaction topic introduced in step 3. More specifically, we will learn how to export surface properties, such as surface flux and deposition rate. We will also set up averaging to obtain av... |
I am stuck on the following problem:
Let $f(x,y) = \max \{ x^2 + y^2 , 1 \}$ and define a Borel measure $\mu$ on $\mathbb{R}$ by $\mu(E) : = (m \times m)(f^{-1}(E))$, where $m$ is Lebesgue measure. Find the Radon-Nikodym derivative $d \rho/d m$, where $\rho$ is the absolutely continuous part of $\mu$.
It is easy to see... |
I haven't got much more to explain other than the title of the question itself. This question was written down in my notes that I took while studying Principles of Flight for my EASA commercial license.
Ideally it would not. With increasing Mach number the lift curve slope of the vertical tail goes up proportional to t... |
"Abstract: We prove, once and for all, that people who don't use superspace are really out of it. This includes QCDers, who always either wave their hands or gamble with lettuce (Monte Zuma calculations). Besides, all nonsupersymmetric theories have divergences which lead to problems with things like renormalons, insta... |
Just for fun, I have been attempting to find polynomials with integer coefficients from a given root. I have been able to do this with square roots: for example, if say I wanted to find a polynomial with a root $\sqrt 2$, we would set an equation like this: $$x-\sqrt 2=0$$ Then just move the square root to the other si... |
Suppose that $M$ is a matrix of order $n$ such that entries of matrix $M$ com from finite field $GF(2^n)$. The matrix $M$ is called MDS (Maximum Distance Separable) matrix if and only if every sub-matrix of $M$ is non-singular over $GF(2^n)$.
For a matrix of order $n$, we should obtain $\sum_{i=1}^n \, {n \choose i }^2... |
I'm trying to find conditions on the gluing map between two manifolds so that the quotient space will be a smooth manifold, and the inclusion map will be a diffeomorphism. Specifically,
Suppose $U_j$ is an open subset of a smooth $m$-manifold $M_j$, for $j \in \{1,2\}$, and $h: U_1 \to U_2$ is a diffeomorphism. Let $\s... |
[Questions about Machine Learning] Chapter I Mathematics Fundamentals
In this chapter, we will discuss some basic mathematics knowledge that you need to know for further study.
Q. What are the relations between scalar, vector, matrix, and tensor?
A. A vector is an ordered finite list of numbers. Vectors are usually wri... |
Is it enough to show that MSE = 0 as $n\rightarrow\infty$? I also read in my notes something about plim. How do I find plim and use it to show that the estimator is consistent?
EDIT: Fixed minor mistakes.
Here's one way to do it:
An estimator of $\theta$ (let's call it $T_n$) is consistent if it converges in probabilit... |
I have been reading chapter 13.4. ("Power Spectrum Estimation Using the FFT") of the Numerical Recipies Book.
Some things related to the expectation value of the "periodogram estimate of the power spectrum" became not clear to me though.
Background
Suppose we have an equally-spaced $N$-point sample $ c_0 ... c_{N-1} $ ... |
Thanks to Sudix I found this answer that helped me find out the solution, which I will repeat here for the sake of completeness (I corrected one mistake in the expression for $a_{m,k}$).
So, first let us re-label the summation indices in the conjecture to coincide with the notation of the cited answer that we will use ... |
I was just doing some practice questions for a test, but have been stumped by the following for the past couple of hours.
I'm given a system such that: $$\frac{du}{dt} = v ~ ~ \& ~ ~ \frac{dv}{dt} = -f(u)$$
with Hamiltonian $$H = \frac{1}{2} \left(\frac{du}{dt}\right)^2 + \int f du.$$
I have to show that using the forw... |
The Fourier Transform is one of the most frequently used computational tools in earthquake seismology. Using an FFT requires some understanding of the way the information is encoded (frequency ordering, complex values, real values, etc) and these are generally well documented in the various software packages used in th... |
Unfortunately, as with many `real world' examples, before we can start to actually do any probabilistic calculations we have to determine what model we would like to use.
In this instance, before we pick a distribution for the problem, we would want to know more about how the typos occur. Consider the two following des... |
For a Poisson distribution with mean $\mu$ the variance is also $\mu$. Within the framework of generalized linear models this implies that the
variance function is $$V(\mu) = \mu$$ for the Poisson model. This model assumption can be wrong for many different reasons. Overdispersed count data with a variance larger than ... |
Is the x_e equation in CAMB correct or not?
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3 posts • Page
1of 1
I am looking at the Antony Lewis' paper
https://arxiv.org/pdf/0804.3865.pdf for Eq.(B3) on page 11, there is this equation of number of free electron per hydrogen atom. But for this equation, if [tex]z \rightarrow[/tex] large values, then y=(1+... |
It is well-known that the function
$$f(x) = \begin{cases} e^{-1/x^2}, \mbox{if } x \ne 0 \\ 0, \mbox{if } x = 0\end{cases}$$
is smooth everywhere, yet not analytic at $x = 0$. In particular, its Taylor series exists there, but it equals $0 + 0x + 0x^2 + 0x^3 + ... = 0$, so while it has radius of convergence $\infty$, i... |
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Multiplicity dependence of jet-like two-particle correlations in pp collisions at $\sqrt s$ =7 and 13 TeV with ALICE
(Elsevier, 2017-11)
Two-particle correlations in relative azimuthal angle (Δ ϕ ) and pseudorapidity (Δ η ) have been used to study heavy-ion collision dynamics, inclu... |
Let a (free) particle move in $[0,a]$ with cyclic boundary condition $\psi(0)=\psi(a)$. The solution of the Schrödinger-equation can be put in the form of a plane wave. In this state the standard deviation of momentum is $0$, but $\sigma_x$ must be finite. So we find that $\sigma_x\sigma_p=0$. Is something wrong with t... |
This article introduces simple regression analysis illustrated with a simple example and shows how to calculate it using Python.
Table of Contents
1. Simple regression analysis 1.1 Introduction
In layman’s terms, given a bunch of data points \({(x_i, y_i), i = 1, …, n}\),
simple regression analysis is to find a straigh... |
Integer programming
A branch of mathematical programming in which one investigates problems of optimization (maximization or minimization) of functions of several variables that are related by a number of equations and (or) inequalities and that satisfy the condition of being integral valued. (Other terms are discrete ... |
Functions An online exercise on function notation, inverse functions and composite functions.
This is level 3, solve the equations given in function notation. You can earn a trophy if you get at least 9 correct and you do this activity online.
Instructions
Try your best to answer the questions above. Type your answers ... |
Newspace parameters
Level: \( N \) = \( 2016 = 2^{5} \cdot 3^{2} \cdot 7 \) Weight: \( k \) = \( 1 \) Character orbit: \([\chi]\) = 2016.l (of order \(2\) and degree \(1\)) Newform invariants
Self dual: No Analytic conductor: \(1.00611506547\) Analytic rank: \(0\) Dimension: \(2\) Coefficient field: \(\Q(i)\) Coefficie... |
In mathematics, an
arithmetic progression (AP) or arithmetic sequence is a sequence of numbers such that the difference between the consecutive terms is constant. For instance, the sequence 5, 7, 9, 11, 13, 15 … is an arithmetic progression with common difference of 2.
If the initial term of an arithmetic progression i... |
While the idea of superposition is relatively straightforward, actually adding the displacements of the waves at every point for all time is a lot of tedious work. We are now going to specialize superposition to the interference of two infinite harmonic waves with the same frequency. Instead of keeping track of both th... |
Questions about the reasons aircrafts fly are frequent among scientist. Since the time I was in high school, even if I now work on the other side of the fluid world (Low $Re$ regime), I've kept asking my professors, advisors, colleagues, what was their own explanation of flight. I know about the controversy about the p... |
I'm new to Discrete mathemathics, in particular in generating functions. This is probably easy to determinate. However I'm having trouble.
For $a_n=\frac{n+1}{(-2)^n}$, and $b_n=\frac{n+1}{3^n}$
$$A(x)=\sum_{n=0}^{\infty} a_nx^n $$ $$B(x)=\sum_{n=0}^{\infty} b_nx^n $$
Let $A(x)$ and $B(x)$ be the generating functions o... |
Find $A,B\in\Bbb K^{2\times 2}$ such that $AB\neq BA$ but $e^{A+B}=e^Ae^B$. Hint: $e^{2k\pi i}=1$ for all $k\in\Bbb Z$.
This is the exercise 10 in page 146 of
Analysis II of Amann and Escher. I dont know exactly what to do here more than just try things blindly (trying to guess what is the hint about).
I know that
$$A:... |
So far we have restricted our discussion of waves to waves that travel. In all our examples until this part, one could follow the location of a maximum of the wave, for example, and observe it moving with the rest of the disturbance.
Another important class of waves exist called
standing waves. For a standing wave, the... |
So as part of my new resolution to start reading the books on my shelves, I recently read through Probability with Martingales.
I’d be lying if I said I fully understood all the material: It’s quite dense, and my ability to read mathematics has atrophied a lot (I’m now doing a reread of Rudin to refresh my memory). But... |
Divisor (algebraic geometry) For other meanings of the term 'Divisor' see the page Divisor (disambiguation)
In algebraic geometry, the term
divisor is used as a generalization of the concept of a divisor of an element of a commutative ring. First introduced by E.E. Kummer[Ku] under the name of "ideal divisor" in his st... |
Talk:Kelvin-Stokes Theorem Filling in the details
I appreciate what is being done here, but I wonder whether it would be better to extract the complexity out into another page (where we may be able to invoke some already-documented vector-calculus identities) and hence structure it in a more easily-digested form (e.g. ... |
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