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In this section we consider the continuous version of the problem posed in the previous section: How are sums of independent random variables distributed?
Definition \(\PageIndex{1}\): convolution
Let \(X\) and \(Y\) be two continuous random variables with density functions \(f(x)\) and \(g(y)\), respectively. Assume t... |
Prove that $ \phi(n) =11 \cdot 3^n + 3 \cdot 7^n - 6 $ is divisible by 8 for all $n \in N$.
Base: $ n = 0 $
$ 8 | 11 + 3 - 6 $ is obvious.
Now let $\phi(n)$ be true we now prove that is also true for $ \phi(n+1)$.
So we get $ 11 \cdot 3^{n+1} + 3 \cdot 7^{n+1} - 6$ and I am stuck here, just can't find the way to rewrit... |
Lets say I have point P1(10,10) and P2(20,20).
I want to find a P3 which is on between this two points and 3 units away from P1.
What is the formula to find P3 ?
Known values: X1, X2, Y1 , Y2, distance.
Wanted values: X3, Y3
Mathematics Stack Exchange is a question and answer site for people studying math at any level ... |
The numerical aperture with respect to a point
P
dependson the half-angle
θ
of the maximum cone of light that canenter or exit the lens.
In optics
, the
numericalaperture
(
NA
) of an optical system is adimensionless number
thatcharacterizes the range of angles over which the system can acceptor emit light. The exact d... |
This is a question from a book that I am reading:
Prove that a monotone non-decreasing sequence of real numbers which is bounded above converges to a limit $a$, and that limit is the least upper bound of the set $\{a_1, a_2, ...\}$. (Similarly, prove the same with non-increasing sequences bounded below, ie $\lim_{n\rig... |
Here is a closely related pair of examples from operator theory, von Neumann's inequality and the theory of unitary dilations of contractions on Hilbert space, where things work for 1 or 2 variables but not for 3 or more.
In one variable, von Neumann's inequality says that if $T$ is an operator on a (complex) Hilbert s... |
I need to solve a Reaction-Diffusion using Finite Elements, piecewise linear elements. In this problem, a reaction $A \rightarrow B$, with rate law $ r_A = - k_A \cdot u_A $, takes part, where $u_i$ denotes concentration. Initially, $u_A = u_B = 0$. The time dependent formulation for the conservation of $A$ and $B$ is:... |
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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... |
Here's one solution:I assumed the radius of the hole's curvature matches the curvature radius of the circle, the hole's straight side is equal to the circle's radius, and its curved edges meet the straight edge at right angles.Used Flash Pro to solve this, of all things: it has the useful feature that as you paint whil... |
Let $G$ be an acyclic, context-free grammar over a fixed alphabet $\Sigma=\{a_1,\dots,a_k\}$ with the restriction (without loss of generality) that $|w|=2$ for each rule $A\to w$ in the grammar. Acyclic means that if $N$ is the set of nonterminals, then $$\{(A,B)\in N^2\mid A\to xBy\text{ is a rule in }G\text{; }x,y\in... |
Assume that the instantaneous utility function $u(C)$ in equation $(2.1)$ is $\ln(C(t))$. Consider the problem of a household maximizing $(2.1)$ subject to $(2.6)$. Find an expression for $C$ at each time as a function of initial wealth plus the present value of labor income, the path of $r(t)$, and the parameters of t... |
Skills to Develop
By the end of this chapter, the student should be able to:
Recognize the normal probability distribution and apply it appropriately. Recognize the standard normal probability distribution and apply it appropriately. Compare normal probabilities by converting to the standard normal distribution.
The no... |
Differential Equations
An equation involving derivatives of one or more dependent variables with respect to one or more independent variables is called a
. For example: differential equation
\begin{equation} \frac{d^{2}y}{dx^2} + xy \left( \frac{dy}{dx}\right)^2 = 0 \end{equation} \begin{equation} \frac{d^{4}x}{dt^4} +... |
p I∣Φ + ⟩⟨Φ + ∣ + p x∣Ψ + ⟩⟨Ψ + ∣ + p y∣Ψ − ⟩⟨Ψ − ∣ + p z∣Φ − ⟩⟨Φ − ∣.
In matrix form it looks like
$$\frac{1}{2} \begin{bmatrix} p_I + p_z & 0 & 0 & p_I - p_z \\ 0 & p_x + p_y & p_x - p_y & 0 \\ 0 & p_x - p_y & p_x + p_y & 0 \\ p_I - p_z & 0 & 0 & p_I + p_z \\ \end{bmatrix}$$ where the matrix is in the computational b... |
Chemical Kinetics Integrated Rate Equations and Half-life Integrated rate law for zero order reaction: \tt k = \frac{\left[A\right]_0-\left[A\right]}{t} [A] 0 = Initial concentration of reactant [A] = concentration of reactant at a particular time. Half life period: For zero order reaction half-life is directly proport... |
I will start from very beginning. So having signal: $ x[n] = [0; \ 0.7071; \ 1; \ 0.7071; \ 0; \ -0.7071; \ -1; \ -0.7071] $ and given exponent: $ w[n] = [1; \ 0.7071 - 0.7071i; \ -i; \ -0.7071 - 0.7071i;\ -1;\ -0.7071 + 0.7071i; \ i; \ 0.7071 + 0.7071i]$.
First we need to inverse the bits and rearrange our signal. For... |
suppose
x(n1,n2) = {1 ,n1=0,n2=0 ; 2 ,n1=1,n2=0 ; 3 ,n1=0,n2=1 ; 6 ,n1=1,n2=1 }
then, how do i prove it is separable.
Signal Processing Stack Exchange is a question and answer site for practitioners of the art and science of signal, image and video processing. It only takes a minute to sign up.Sign up to join this comm... |
I originally posted this on math.stackexchange, but it quickly got buried. I removed it not too long after, thinking of rewriting it for MO, but I didn’t have a chance to post it until now. Apologies if you were one of the lucky 24 people who already saw it there.
Background
The Cauchy-Binet formula states that
$$ \det... |
Spectral analysis of the blazars Markarian 421 and Markarian 501 with the HAWC Gamma-Ray Observatory
Pre-published on: 2019 July 22
Published on: —
Abstract
The High Altitude Water Cherenkov (HAWC) Gamma-Ray Observatory surveys the very high energy sky in the $\sim300$ to 100 TeV energy range and has detected two high-... |
Let us first recall the definition of a group homomorphism.A group homomorphism from a group $G$ to a group $H$ is a map $f:G \to H$ such that we have\[f(gg’)=f(g)f(g’)\]for any elements $g, g\in G$.
If the group operations for groups $G$ and $H$ are written additively, then a group homomorphism $f:G\to H$ is a map suc... |
The package
Clustgeo is used here for clustering \(n=303\) french cities. The R dataset estuary is a list of three objects: a matrix dat with the description of the 303 cities on 4 socio-demographic variables, a matrix D.geo with the distances between the town hall of the 303 cities, and an object map of class “Spatial... |
I was given this answer:
So I was told that
$$\tan(x) = 2$$ Then, they said from this statement they could know that: $$\cos(x) = \frac{1}{\sqrt{5}}$$ $$\sin(x) = \frac{2}{\sqrt{5}}$$
Now, I understand that if I do
$$\tan^{-1}(2) = 63.4$$
And then after that I can get the ratio of cosine and sine. However, I don't know... |
In your second edit, you ask whether there exists an example of such a bundle over a lower-dimensional manifold.
Four-dimensional example
Let $M = (\mathbb{RP}^2\times\mathbb{RP}^2)\#(S^1\times S^3)$. Note that
$$H^1(M; \mathbb{Z}_2) \cong H^1(\mathbb{RP}^2\times\mathbb{RP}^2; \mathbb{Z}_2)\oplus H^1(S^1\times S^3;\mat... |
Beautiful Formulas for pi=3.14…
The number $\pi$ is defined a s the ratio of a circle’s circumference $C$ to its diameter $d$:
\[\pi=\frac{C}{d}.\]
$\pi$ in decimal starts with 3.14… and never end.
I will show you several beautiful formulas for $\pi$.
Contents
Art Museum of formulas for $\pi$ Beautiful formula of $\pi$... |
ISSN:
1556-1801
eISSN:
1556-181X
All Issues
Networks & Heterogeneous Media
September 2009 , Volume 4 , Issue 3
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Abstract:
We first develop non-oscillatory central schemes for a traffic flow model with Arrhenius look-ahead dynamics, proposed in [ A. Sopasakis and M.A. Katsoulakis, SI... |
Bharadwaj, BVS and Chandran, LS and Das, Anita (2008)
Isoperimetric Problem and Meta-fibonacci Sequences. In: 14th Annual International Conference on Computing and Combinatorics (COCOON 2008), JUN 27-29, 2008, Dalian.
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So now that we know how to get the least common multiple (LCM) of two numbers, let’s apply this knowledge to add two fractions together that have different denominators.
So let’s look at:\[
\frac{3}{4}\hspace{0.33em}{+}\hspace{0.33em}\frac{3}{18}
\]
In my last post, we found the LCM of the two numbers 4 and 18 to be 36... |
Given a map $F:X \to X$ on a complete metric space $(X,d)$, and let $K<1$ such that:
$$ d(F(x), F(y)) \le K d(x,y), \quad \forall x,y \in X $$
then the contraction mapping theorem tells us that $F$ has a unique fixed point, and we can iteratively solve for this fixed point.
My question is, if we take $K=1$, then it is ... |
Lars Olsen
[1], [2] (2005, 2005) has proved some results about this notion. Let $E \subseteq {\mathbb R}^{n}$ and $x \in {\mathbb R}^{n},$ where $n$ is a fixed positive integer. Let $\dim_{H}(E,x)$ and $\dim_{P}(E,x)$ denote the local Hausdorff and local packing dimensions of $E$ at $x,$ defined as in your question. Di... |
I think I've figured this out. The point is that, the rigorous meaning one can draw from the formal covariance of $J^\mu$ is that the momentum-space coefficient functions of $J^\mu$ (i.e. the functions in front of monomials of $a_p$ and $a^\dagger_p$) transform covariantly under the change of variable $p\to \Lambda p$.... |
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Now showing items 1-10 of 26
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... |
Ray Optics and Optical Instruments Total Internal Reflection Critical angle is the angle of incidence in denser for which angle of refraction in rarer medium is 90° \tt \mu = \frac{1}{\sin C} \tt \sin C = \frac{\mu_{rarer}}{\mu_{denser}} = \frac{V_{denser}}{V_{rarer}} = \frac{\lambda_{denser}}{\lambda_{rarer}} C Red> C... |
I want to extend the following to work on a solid angle:
Suppose we have a volume filled with small surfaces. If we cast a ray from a given point, the probability that the ray will not hit a surface (i.e. is visible to the sky) is given as
$P(ray\ does\ not\ hit) = {e}^{-\alpha d/\cos\theta}$
where $\alpha$ is some dec... |
I'm trying to reconcile some conflicting results that I've found in publications that address the idea of the current in a vacuum diode in the case where the cathode has a non-zero potential, in other words, the electrons are emitted with a non-zero initial velocity.
The traditional Child-Langmuir Space Charge Law, als... |
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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 ... |
EDIT: Let $S$ be a closed orientable 2-dimensional surface equipped with a metric with curvature $\geq \kappa$ in the sense of Alexandrov. Questions 1. Can one define a measure $K$ on $S$ (thought to be an analogue of the Gauss curvature) satisfying the following properties:
(a) if the metric on $S$ is smooth then $K$ ... |
Let $a \in \Bbb{R}$. Let $\Bbb{Z}$ act on $S^1$ via $(n,z) \mapsto ze^{2 \pi i \cdot an}$. Claim: The is action is not free if and only if $a \Bbb{Q}$. Here's an attempt at the forward direction: If the action is not free, there is some nonzero $n$ and $z \in S^1$ such that $ze^{2 \pi i \cdot an} = 1$. Note $z = e^{2 \... |
The Rotation Matrix is an Orthogonal Transformation
Problem 684
Let $\mathbb{R}^2$ be the vector space of size-2 column vectors. This vector space has an inner product defined by $ \langle \mathbf{v} , \mathbf{w} \rangle = \mathbf{v}^\trans \mathbf{w}$. A linear transformation $T : \R^2 \rightarrow \R^2$ is called an o... |
Abbreviation:
MonA
A
is a structure $\mathbf{A}=\langle A, \vee, 0, \wedge, 1, \neg, f\rangle$ of type $\langle 2, 0, 2, 0, 1, 1\rangle$ such that monadic algebra
$\langle A, \vee, 0, \wedge, 1, \neg\rangle$ is a Boolean algebra
$f$ is a
: $f(x\vee y)=f(x)\vee f(y)$, $f(0)=0$, $x\le f(x)=f(f(x))$ unary closure operator... |
I don't
actually have an answer, just ideas, but since this is a riddle, I might of contribute these as (hidden as spoiler text) hints for others, which might have ideas that I miss:
So, MSK is often introduced as
represented by a half-symbol time-offset BPSK on the I and Q components. That comes in very handy here (av... |
This article is about $ 2^n-n $ numbers, that is, numbers that are produced by replacing '$n$' in $ 2^n-n $ with a positive integer $ (1,2,3...) $. I came across these numbers while studying Mersenne numbers $ (2^n-1) $. It got me thinking about $ 2^n-n $ numbers, if there are any interesting properties to them, and wh... |
Skills to Develop
To learn what the coefficient of determination is, how to compute it, and what it tells us about the relationship between two variables \(x\) and \(y\).
If the scatter diagram of a set of \((x,y)\) pairs shows neither an upward or downward trend, then the horizontal line \(\hat{y} =\overline{y}\) fits... |
Well you might suspect that there is a connection between the roots of a number and exponents given my last couple of posts, and you would be correct. Now in my post on roots, I limited myself to using numbers that are perfect roots. For example, \[
\sqrt[3]{8}\hspace{0.33em}{=}\hspace{0.33em}{2} \]. But many roots do ... |
Let $p$ be a real polynomial and $N$ be a positive integer. Suppose I tell you that $|p(\frac{1}{k})| \le 1$ for all $k\in\{1,\ldots,N\}$, and also that $p(\frac{1}{N})\le -\frac{1}{2}$ while $p(\frac{2}{N})\ge \frac{1}{2}$. What bounds can you give me on the minimal possible degree $\deg(p)$?
An upper bound of $O(\sqr... |
I work on an inverse problem for my Ph.D. research, which for simplicity's sake we'll say is determining $\beta$ in
$L(\beta)u \equiv -\nabla\cdot(k_0e^\beta\nabla u) = f$
from some observations $u^o$; $k_0$ is a constant and $f$ is known. This is typically formulated as an optimization problem for extremizing
$J[u, \l... |
Question
Manufacturer can sell x items at a price of rupees \[\left( 5 - \frac{x}{100} \right)\] each. The cost price is Rs \[\left( \frac{x}{5} + 500 \right) .\] Find the number of items he should sell to earn maximum profit.
Solution
\[\text { Profit =S.P. - C.P.}\]
\[ \Rightarrow P = x\left( 5 - \frac{x}{100} \right... |
Measurement of the $D\to K^-\pi^+$ strong phase difference in $\psi(3770)\to D^0\overline{D}{}^0$ 2014 (English)In: PHYSICS LETTERS B, ISSN 0370-2693, Vol. 734Article in journal (Refereed) Published Resource typeText Abstract [en]
We study $D^0\overline{D}{}^0$ pairs produced in $e^+e^-$ collisions at $\sqrt{s}=3.773$ ... |
Alcohols, Phenols and Ethers Methods for Preparation of Alcohols and Phenols Preparations of alcohols: From alkenes: (i) Acid catalysed hydration From alkynes: \tt CH\equiv CH\xrightarrow[kucherer(or)kucherov\ reaction]{H_2O/Hg^{2+},-H^+}CH_3CHO\xrightarrow[\Delta]{O_2/(CH_3COO)_2Mg}CH_3COOH From haloalkanes:
Trick: Re... |
I have this SDE
$$ dX(t) = [X(t)(u(t)(\delta-r)+r-\beta(t))+\theta(t)(1-\alpha(t))]dt+X(t)u(t)\sigma dW(t), t \in [0,T] \\ X(0) = X_0(1-\alpha(0)) $$
I've checked some books and I find the solution is this: $$ X_t=\Phi_{t,0}.\left( X_0(1-\alpha_0)+\int_{0}^{t}\frac{\theta(s)(1-\alpha(s))}{\Phi_{s,0}}ds + \int_{0}^{t} \... |
Hi! I need help with this problem. I tried to solve it by saying that it would be the same as the field of a the spherical shell alone plus the field of a point charge -q at A or B. For the field of the spherical shell I got ##E_1=\frac{q}{a\pi\epsilon_0 R^2}=\frac{\sigma}{\epsilon_0}## and for...
V(ρ) = V_o*ln(ρ/0.001... |
1.
2.
3.
Hamilton paths in vertex-transitive graphs of order 10pKlavdija Kutnar
, Dragan Marušič
, Cui Zhang
, 2012, izvirni znanstveni članek
Opis: It is shown that every connected vertex-transitive graph of order ▫$10p$▫, ▫$p \ne 7$▫ a prime, which is not isomorphic to a quasiprimitive graph arising from the action o... |
How can I put a symbol above a comma? For example in
TeX - LaTeX Stack Exchange is a question and answer site for users of TeX, LaTeX, ConTeXt, and related typesetting systems. It only takes a minute to sign up.Sign up to join this community
You can use
\overset from amsmath:
\documentclass{article}\usepackage{amsmath}... |
Let $a \in \Bbb{R}$. Let $\Bbb{Z}$ act on $S^1$ via $(n,z) \mapsto ze^{2 \pi i \cdot an}$. Claim: The is action is not free if and only if $a \Bbb{Q}$. Here's an attempt at the forward direction: If the action is not free, there is some nonzero $n$ and $z \in S^1$ such that $ze^{2 \pi i \cdot an} = 1$. Note $z = e^{2 \... |
I saw that it was already asked, but the book where I'm studying is slightly different. Recall some definition, if $E$ it's $\mathbb{K}$-vector space and let $\mathcal{E}$ be a vector subspace of the algebraic dual of $E$, wich is the vector space of all linear forms on $E$. We say that $(E,\mathcal{E})$ is a dual coup... |
I know how to derive Navier-Stokes equations from Boltzmann equation in case where bulk and viscosity coefficients are set to zero. I need only multiply it on momentum and to integrate it over velocities.
But when I've tried to derive NS equations with viscosity and bulk coefficients, I've failed. Most textbooks contai... |
Skills to Develop
To use the Cochran–Mantel–Haenszel test when you have data from \(2\times 2\) tables that you've repeated at different times or locations. It will tell you whether you have a consistent difference in proportions across the repeats. When to use it
Use the Cochran–Mantel–Haenszel test (which is sometime... |
ISSN:
2156-8472
eISSN:
2156-8499 Mathematical Control & Related Fields
June 2013 , Volume 3 , Issue 2
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Abstract:
Suitable numerical discretizations for boundary control problems of systems of nonlinear hyperbolic partial differential equations are presented. Using a discrete Lyapuno... |
Or Reactive Power to full?
I made a claim about the power consumption of my EL panel earlier that was patently false for a very interesting reason.
Background
So it should be obvious by now that if I open my mouth and say anything about electroluminescent materials, it’s probably wrong. In this case, it has to do with ... |
It's hard to say just from the sheet music; not having an actual keyboard here. The first line seems difficult, I would guess that second and third are playable. But you would have to ask somebody more experienced.
Having a few experienced users here, do you think that limsup could be an useful tag? I think there are a... |
Sandbox From PsychWiki - A Collaborative Psychology Wiki
tasitricrobaTo see how easy it is to edit pages, we have this
Sandbox:
Sandbox
Welcome to the PsychWiki Sandbox. Feel free to use this page to practice editing or for experiments. After you login, click on the "edit" tab at the top of the page, and scroll down to... |
Can anyone explain how frequency response related to a transfer function?
A discrete-time linear time-invariant (LTI) system is defined by its impulse response, which can be expressed as a list of non-zero coefficients $c_n$ occuring at integer time indices $t_n$. To form its output $y[k]$ all the system can do is sum ... |
The more-geometrically-minded of us take $\cosh u$ and $\sinh u$ to be defined via the "unit hyperbola", $x^2 - y^2 = 1$, in a manner directly analogous to $\cos\theta$ and $\sin\theta$. Specifically, given $P$ a point on the hyperbola with vertex $V$, and defining $u$ as
twice(?!) the area of the hyperbolic sector $OV... |
So last time, I presented the equation that describes the position of a mass on a spring:
The equation is\[ {x}\hspace{0.33em}{=}\hspace{0.33em}{A}\hspace{0.33em}\sin\left({\frac{180t}{\mathit{\pi}}\sqrt{\frac{k}{m}}}\right) \]
where
x is the position of the mass at a given time t in seconds, k is the spring constant, ... |
In the Standard Model, the Higgs boson is expected to have spin 0 and even parity. I know how to get the spin-0 approach, but how do I argue for the even parity? Could you give a simple and a more detailed explanation for this even parity expectation?
One argument could be the Yukawa coupling, which is responsible for ... |
Abbreviation:
MALLA
A
is a structure $\mathbf{A}=\langle A,\vee,\bot,\wedge,\top,+,0,\cdot,1,^\perp\rangle$ of type $\langle2,0,2,0,2,0,1\rangle$ such that multiplicative additive linear logic algebra
$\langle A,\vee,\wedge,\cdot,1,^{\perp}\rangle$ is a commutative involutive residuated lattice
$\bot$ is the least elem... |
There are already some rather good related answers regarding LTL versus CTL. In a nutshell, LTL is first and foremost a logic of traces, and an LTL formula is true for a transition system $S$ if and only if it is true for each trace of $S$. CTL, on the other hand, is a branching-time logic, which can in a sense talk ab... |
What is the indefinite sum of the tangent function, that is, the function $T$ for which
$\Delta_x T = T(x + 1) - T(x) = \tan(x)$
Of course, there are infinitely many answers, who all differ by a function of period 1. Ideally, I would like the solution to be of the form
$T(x) = $ nice_function$(x)$ + possibly_ugly_perio... |
Halloween Season is a seasonal event in Cookie Clicker, that was added in the 1.039 update.
The event was on during versions 1.039 - 1.0403 without a way to turn it off.
The seasonal event upgrade was added in version 1.041.
Since 1.0466 update Halloween season starts automatically and lasts from 24th to 31st of Octobe... |
Commutator Subgroup and Abelian Quotient GroupLet $G$ be a group and let $D(G)=[G,G]$ be the commutator subgroup of $G$.Let $N$ be a subgroup of $G$.Prove that the subgroup $N$ is normal in $G$ and $G/N$ is an abelian group if and only if $N \supset D(G)$.Definitions.Recall that for any $a, b \in G$, the […]
Non-Abelia... |
"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... |
I'm currently reading some books on radiometry. They mention that radiance is constant along a ray. It doesn't change with distance. However, I've seen some raytracer and they put the 1/r² factor when they deal with point sources. I don't get why. I didn't find a great explanation on the Internet.
The concept of a poin... |
Suppose a matrix $X\in\mathbb{R}^{n\times 3}$ is given as a Principal Component Analysis (PCA) projection from some high dimensional space. The 2D PCA solution on X, say $Y\in\mathbb{R}^{n\times 2}$ would simply correspond to the first two columns of $X$.
Now, suppose the configuration is shifted such that the origin c... |
What should I do? Because I have two possibilities. I have ##0=5+at## so ##-5/t =a##. But then I can also say that the acceleration is a negative because it is stopping, so I can write it like ##0=5-kt## and then ##5/t =k##
The first doubt that comes to my mind is "I have to determine the acceleration with respect to w... |
Van Berkel, C. and Lionheart, W. R. B. (2007)
Reconstruction of a grounded object in an electrostatic halfspace with an indicator function. Inverse Problems in Science and Engineering, 15 (6). pp. 585-600. ISSN 1741-5985
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Reconstruction_of_A.pdf
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Abstract
This arti... |
I think I've figured this out. The point is that, the rigorous meaning one can draw from the formal covariance of $J^\mu$ is that the momentum-space coefficient functions of $J^\mu$ (i.e. the functions in front of monomials of $a_p$ and $a^\dagger_p$) transform covariantly under the change of variable $p\to \Lambda p$.... |
Moisture retention in porous materials linked articles This article describes the mechanisms of moisture retention and common approaches for models and material functions, especially the sorption isotherms and the moisture retention capacity (MRC) Contents Introduction
Since porous building materials are capable of ads... |
Abbreviation:
SymRel
A
is a structure $\mathbf{X}=\langle X,R\rangle$ such that $R$ is a symmetric relation (i.e. $R\subseteq X\times X$) that is binary relation on $X$
symmetric: $xRy\Longrightarrow yRx$
Remark: This is a template. If you know something about this class, click on the ``Edit text of this page'' link at... |
So we are working on finding the probability of getting a hand with four aces in a 5-card poker game. To do this, we have to count the total number of possible poker hands. This turns out to be possible using the combination formula:\[{C}{(}{n}{,}\hspace{0.33em}{r}{)}\hspace{0.33em}{=}\hspace{0.33em}\frac{n!}{{r}{!(}{n... |
Consider the following game of Bertrand (price competition):
There are two players, $1$ and $2$. Each has a publicly known marginal cost, $c_i$. A strategy is a price, $p_i\in\mathbb{R}$. Player $i$'s payoff (profit) is $\pi(p_i,p_j)=p_i-c_i$ if $p_i<p_j$, $\pi(p_i,p_j)=\frac{p_i-c}{2}$ if $p_i=p_j$ and $\pi(p_i,p_j)=0... |
I've been working on the following problem:
" Compute the Taylor series of the function $f(x)=\frac{1}{1-x}$ at $x=2$ and determine the radius of convergence $r$ "
I know that the given Taylor series is $\sum_{n=0}^{\infty} \frac{f^{(n)}(2)}{n!}(x-2)^n$, but I don't know how to determine the radius of convergence.
I ha... |
Okay, I guess I can't just
leaveit at that because apparently it's not obviously false.
Two other variations on this phrase: "the whole is more than the sum of its parts" and "the whole is not the sum of its parts". I bring these up because this makes the mathematical error twice as bad. $$whole > \sum parts$$ is the o... |
Does $\text{exp}\bigg(\dfrac{\pi^2}{6 e^{\gamma}}\dfrac{\sigma(p_n\#)}{p_n\#}\bigg)$ bound $p_n$ from above?
(Note: From Daniel Fischer's answer here.)
Update
... and from below by $\log(p_n\#)$?
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related ... |
Electrochemistry Electrochemical Series and Nernst Equation Electrochemical series and its applications: The arrangement of S.R.P values of various elements either in increasing order (or) in decreasing order is called electrochemical series Eg: (i) E_{Mg^{2+}/Mg}^o = − 2.37 V — M (ii) E_{Zn^{2+}/Zn}^o = − 0.76 V — M (... |
This is an example from my text book of a continuous signal: $$x_{in}(t)=\sin \left( 2\pi \cdot 1000 \cdot t\right) + 0.5\sin \left( 2\pi \cdot 2000 \cdot t + \dfrac{3\pi}{4} \right) $$ So to perform a fourier transform on this signal, how to do that, isn't it a bit funny, since it has two sine components. Shouldn't co... |
There are a number of solutions to this problem online that use identities I have not been taught. Here is where I am in relation to my own coursework:
$ \sin(z) = 2 $
$ \exp(iz) - \exp(-iz) = 4i $
$ \exp(2iz) - 1 = 4i \cdot \exp (iz) $
Then, setting $w = \exp(iz),$ I get:
$ w^2 - 4iw -1 = 0$
I can then use the quadrat... |
The standard proof, apparently due to Dedekind, that algebraic numbers form a field is quick and slick; it uses the fact that $[F(\alpha) : F]$ is finite iff $\alpha$ is algebraic, and entirely avoids the (to me, essential) issue that algebraic numbers are roots of some (minimal) polynomial. This seems to be because fi... |
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Now showing items 1-10 of 26
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 ... |
One alternative is to plot several points along the circle using Cartesian coordinates. This has already been suggested, but it can be generalized to deal with many kinds of obstacles.
If you
did have free access to all points in the interior of the circle, you could set up your Cartesian coordinate system by laying tw... |
Here we want to give an easy mathematical bootstrap argument why solutions to the time independent 1D Schrödinger equation (TISE) tend to be rather nice. First formally rewrite the differential form$$-\frac{\hbar^2}{2m} \psi^{\prime\prime}(x) + V(x) \psi(x) ~=~ E \psi(x) \tag{1}$$into the int...
[Some time travel comme... |
It's a little unclear what you're asking here (the wikipedia page is for ordinary covariance but the question relates to covariance
matrices) but I'll try to answer the question with regard to unbiasedness.
Assuming your covariance matrices are computed from the samples $\{ \textbf{a}_i \}_{i=1}^{N_a}$ and $\{ \textbf{... |
If $n^3 < |a_n| < n^4$ find the radius of convergence for $\sum_{n=2}^\infty a_nx^n$
Could someone explain how he got inequality (1)? Theorem 4.1 stated that a power series converges if $|x| <R$.
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related ... |
Suppose we have a smooth manifold M and E--->M is a vector bundle. A connection on E is a linear map from the set of all smooth section on E into the set of smooth sections of the tensor product of E and the cotangent bundle of M , satisfying a condition. Here is the question : We can make the tensor product bundle of ... |
I would like to align the first "+" in the third and fourth lines of the following code. In the third line, I have "= 3 + [a mess]" and in the fourth line, I have "+ [another mess]" - I don't have the "3" in the fourth line. I used the \hphantom command to account for the horizontal space of the "= 3" in the third line... |
ISSN:
1937-5093
eISSN:
1937-5077 Kinetic & Related Models
March 2014 , Volume 7 , Issue 1
Issue on analysis of non-equilibrium evolution problems: Selected topics in material and life sciences
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Abstract:
Robert Glassey (Bob) has decided to withdraw from the Editorial Board of KRM. B... |
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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 ... |
Everything else
Now’s probably a good time to show you the whole schematic:
The battery and charging terminals aren’t actually components; I just drew them out of the traces on the PCB itself.
LEDs
The LEDs on the left are Charlieplexed which allowed me to connect a large number of LEDs with a small number of wires goi... |
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Up a level 55. Article
Aad, G, Abbott, B, Abdallah, J et al. (2883 more authors) (2016)
Addendum to ‘Measurement of the tˉt production cross-section using eμ events with b-tagged jets in pp collisions at √s = 7 and 8 TeV with the ATLAS detector’. European Physical Journal C: Particles and Fields, 76. 6... |
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Full-Text Articles in Physics
Isotropization In Brane Gas Cosmology, Scott Watson, Robert H. Brandenberger
Isotropization In Brane Gas Cosmology, Scott Watson, Robert H. Brandenberger Physics
Brane Gas Cosmology (BGC) is an approach to unifying string theory and cosmology in which matter is descri... |
I'm reading Advanced Global Illumination.
Here is the part confusing me:
What do the second equation and $\delta$-function mean?
Why the third equation is a sufficient condition even though a reason is given?
Computer Graphics Stack Exchange is a question and answer site for computer graphics researchers and programmer... |
Asymptotic behavior for solutions of some integral equations
1.
School of Mathematical Sciences, Nanjing Normal University, Nanjing, 210097, China
2.
Department of Mathematics, University of Colorado at Boulder, Boulder, CO 80309, United States
$u(x) = \frac{1}{|x|^{\alpha}}\int_{R^n} \frac{v(y)^q}{|y|^{\beta}|x-y|^{\l... |
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