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I've been struggling trying to understand how to find the center of a circle given 4 points in the circumference $(x_1,y_1),(x_2,y_2),(x_3,y_3),(x_4,y_4)$
Please help me. I don't understand when the polygon created is not a rectangle p.ex..
Mathematics Stack Exchange is a question and answer site for people studying ma... |
;tldr: You're right about the properties, but the fields don't cause or influence each other in so direct away as a first glimpse of Maxwell's equations might suggest.
Special Relativity is "hidden" in Maxwell's equations. An understanding of their relationship might be useful.
Maxwell's Equations are:
$$\nabla\cdot\ve... |
Science Advisor
Gold Member
2,224 1,255 Summary Wigner's friend seems to lead to certainty in two complimentary contexts Summary:Wigner's friend seems to lead to certainty in two complimentary contexts
This is probably pretty dumb, but I was just thinking about Wigner's friend and wondering about the two contexts invol... |
I'm focusing on practical control engineering and I love to read articles/papers and books about people how tried to take control theory and apply that onto control engineering.
My biggest interest is adaptive control. Unfortunately, adaptive control is not used as practical control engineering due to the danger of let... |
This answer will try and outline all the different possibilities I came across over the last couple of years, including drawbacks. But first, let me outline the problem a little.
To appreciate the problem, a first simplistic starting point is here.What the authors observe is similar to what you observed. "Optimization ... |
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∫0π2arctan(1−cos2xsin2x) dx=π24−πarctan2−12. \int\limits_0^{\frac{\pi}{2}}\arctan\left(1-\cos^2 x\sin^2 x\right)\ \mathrm{d}x=\frac{\pi^2}{4}-\pi\arctan\sqrt{\frac{\sqrt{2}-1}{2}}. 0∫2πarctan(1−cos2xsin2x) dx=4π2−πarctan22−1.Can someone prove this ?
Note by Harou... |
2019-10-11 14:20
TURBO stream animation /LHCb Collaboration An animation illustrating the TURBO stream is provided. It shows events discarded by the trigger in quick sequence, followed by an event that is kept but stripped of all data except four tracks [...] LHCB-FIGURE-2019-010.- Geneva : CERN, 2019 - 3. 详细记录 - 相似记录 ... |
It is often convenient to parametrize the implied volatility curve to allow easy interpolation of volatility for any strike or maturity. What functional form describes the implied volatility curve for options at varying strikes and fixed maturity?
OptionMetrics uses a kernel smoothing algorithm to interpolate the volat... |
I would like to calculate the polar velocity components given the position $(x,y)$ and velocity $(u_x,u_y)$ in Cartesian coordinates. First of all, $$ r=\sqrt{x^2+y^2}\text{ and }\theta=\tan^{-1}\left(\frac yx\right). $$ By now, I know the angle and radius in the global cylindrical coordinate system. I assume that $\ma... |
I am trying to solve an equation in Python. Basically what I want to do is to solve the equation:
$$ \frac{1}{x^2}\frac{d}{dx}\left(Gam \frac{dL}{dx}\right)+L\left(\frac{a^2x^2}{Gam}-m^2\right)=0 $$
This is the Klein-Gordon equation for a massive scalar field in a Schwarzschild spacetime. We know $m$ and $Gam=x^2-2x$.
... |
2019-09-20 08:41
Search for the $^{73}\mathrm{Ga}$ ground-state doublet splitting in the $\beta$ decay of $^{73}\mathrm{Zn}$ / Vedia, V (UCM, Madrid, Dept. Phys.) ; Paziy, V (UCM, Madrid, Dept. Phys.) ; Fraile, L M (UCM, Madrid, Dept. Phys.) ; Mach, H (UCM, Madrid, Dept. Phys. ; NCBJ, Swierk) ; Walters, W B (Maryland U... |
H(w) =1/ (square root of 2) That sounds a bit confusing, we usually refer to the cutoff point as the -3 dB point.
That is the same though, -3 dB is
half the power.
Let me explain: take your \$H(\omega) = \frac{1}{\sqrt2}\$
That means that at that \$\omega\$ the
voltage is divided by \$\sqrt2\$, if this voltage is appli... |
Suppose you have some linear algebra background. The most importantthing you need to know is that the inner product has the same meaningof what you have learnt in linear algebra class. The inner product$$\left\langle \phi|\psi\right\rangle =\int\phi^{*}(x)\psi(x)dx$$
has the meaning related to a projection of one vecto... |
To evaluate detection performance, we plot the
miss-rate $mr(c) = \frac{fn(c)}{tp(c) + fn(c)}$ against the number of false positives per image $fppi(c)=\frac{fp(c)}{\text{#img}}$ in log-log plots. $tp(c)$ is the number of true positives, $fp(c)$ is the number of false positives, and $fn(c)$ is the number of false negat... |
Only the first two sections of this long question are essential. The others are just for illustration. Background
Advanced quadratures such as higher-degree composite Newton–Cotes, Gauß–Legendre, and Romberg seem to be mainly intended for cases where one can finely sample the function but not integrate analytically. Ho... |
Given the standard Ising partition function: $$Z(\theta ,h) = \sum\limits_{\bf{x}} {\exp \left\{ {\theta \sum\limits_{(i,j) \in E} {{x_i}{x_j}} + h\sum\limits_{i \in V} {{x_i}} } \right\}}, $$
is there a closed form expression for the lower bound of the free-energy (Pressure) per-site, defined as,
$$\psi (\theta ,h) = ... |
Evaluation of Binary Classifiers
Evaluation is important:
Baseline
So for evaluating a classifier we need to set some baseline
base rate accuracy of a trivial classifier the one that always predicts the majority class random rate accuracy of random guess need to have some domain knowledge to assign Random Distribution
... |
LaTeX uses internal counters that provide numbering of pages, sections, tables, figures, etc. This article explains how to access and modify those counters and how to create new ones.
Contents
A counter can be easily set to any arbitrary value with
\setcounter. See the example below:
\section{Introduction} This documen... |
HAL8999 – 3/100 Chapter 2 of Hands on ML Cost functions virtualenv setup code to get the dataset
The chapter follows a rudimentary machine learning project from business case to final product. California census data is analyzed to build a model which will predict media housing price in a district based on other factors... |
ABCD is a parallelogram.
Prove the following:
$\frac{BF}{FA} = \frac{AD}{AE}$
$\frac{S_{ADF}}{S_{AEF}} = \frac{AD}{AE}$
$S_{EBF} = S_{ADF}$
$S_{BCE} = \frac{1}{2}S_{ABCD}$
I solved the first 3, but could not solve the 4th:
1.
$$\text{Thale's theorm:}$$ $$\frac{AE}{CB} = \frac{AF}{FB} = \frac{EF}{FC}$$ $$\frac{AE}{AD} =... |
Here is the URL: https://github.com/avaneev/biteopt
I've tested it on numerous global optimization benchmarking functions (included), and on real-world hyperparameter optimization problems I have. Seems to be working quite well except in comparison to deterministic methods it's necessary to make several attempts at dif... |
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Now showing items 1-10 of 33
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... |
LLVM optimizes power sums, such as
int sum(int count) { int result = 0; for (int j = 0; j < count; ++j) result += j*j; return result; }to code that calculates the result without a loop (godbolt) sum(int): test edi, edi jle .LBB0_1 lea eax, [rdi - 1] lea ecx, [rdi - 2] imul rcx, rax lea eax, [rdi - 3] imul rax, rcx shr ... |
Here @gung makes reference to the .632+ rule. A quick Google search doesn't yield an easy to understand answer as to what this rule means and for what purpose it is used. Would someone please elucidate the .632+ rule?
I will get to the 0.632 estimator, but it'll be a somewhat long development:
Suppose we want to predic... |
Self-Assembly Of Dna Graphs And Postman Tours, 2018 University of North Florida
Self-Assembly Of Dna Graphs And Postman Tours, Katie Bakewell UNF Graduate Theses and Dissertations
DNA graph structures can self-assemble from branched junction molecules to yield solutions to computational problems. Self-assembly of graph... |
To form a product, you give me $n$ objects, $A_1,\dots,A_n$, and I give you back an object $A_1\times\dots\times A_n$, together with $n$ maps $\pi_i\colon A_1\times\dots\times A_n\to A_i$ (one to each of the $A_i$) satisfying the universal property of the product.
So what happens if $n=0$? Then you give me $0$ objects,... |
There are tons of examples, but I'll give a few from the context of PDEs.
@daw already gave a very good example. Let me provide a similar one, in the form of the
heat propagator. You may know that the study of the heat equation is fundamental in many fields of PDEs. To that end, let $M$ be a compact, Riemannian manifol... |
I have found a way to enlarged the Erdos-Szekeres Conjecture. I have computationally confirmed what might be the simplest unknown case for some small values, and was reaching out for how to prove this case in general.
Definitions Given a set of points in the general position on the plane,a subset is a "convex polygon" ... |
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1. Measurement of the ZZ production cross section in proton-proton collisions at √s = 8 TeV using the ZZ → ℓ−ℓ+ℓ′−ℓ′+ and ZZ→ℓ−ℓ+νν¯¯¯ decay channels with the ATLAS detec... |
This question is a generalization of the question Volume ratio of $\ell_1$ balls and $\ell_1$ surfaces
For any $p\in[1,\infty]$ define $\|x\|_p := (|x_1|^p+\cdots+|x_d|^p)^{1/p}$ for $p\in[1,\infty)$ and $\|x\|_\infty := \max_{1\leq i\leq d}|x_i|$ for $p=\infty$. Denote $B_p^d := \{x\in\mathbb R^d: \|x\|_p\leq 1\}$ as ... |
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Free keywords: Mathematics, Optimization and Control, math.OC,Computer Science, Distributed, Parallel, and Cluster Computing, cs.DC
Abstract: When solving massive optimization problems in areas such as machine learning,
it is a common practice to seek speedup via massive parallelism. However,
especially in an asyn... |
To extend VorKir's basically correct answer, to derive a priori error estimate for finite element approximations, you need to stack the following three Lego blocks:
The well-posedness of the weak formulation of the PDE. The (global) conformity of the Galerkin approximation. The (local) approximation properties of your ... |
Use environments to cluster mathematical expressions
MathJax provides a basic subset of environments for clustering mathematical expressions. For a complete list, see here, but be warned it is a very big page.
Environments are entered with the following syntax, some of them do not need to be explicitly entered with mat... |
This question is about group/phase velocities and also De Brogilie wavelength.
What I would like to know is how to derive ratio $\lambda_e/\lambda_p$ ($\lambda_e$ and $\lambda_p$ are De Broglie wavelength for electron and proton) if we know that electron and proton have same velocities?
I know that when we say "velocit... |
Regarding the edit: I think natural density should still be easier for Frobenius. Let $G$ be $\mathrm{Gal}(F/\mathbb{Q})$ and let $c$ be a class function $G \to \mathbb{C}$.
Cebatarov with natural density is the statement$$ \sum_{p \leq N} c(\mathrm{Frob}(p)) \sim \left( \sum_{g \in G} c(g) \right) \cdot \pi(N) $$Frobe... |
2 0
Hello,
Consider I have a linear time-invariant (LTI) system, with ##x(t)##, ##y(t)##, and ##h(t)##, as input, output, and impulse response functions, respectively. I have two choices to write the convolution integral to get ##y(t)##: $$ 1)\ \ \ y(t) = \int_{0}^{t} h(t-t')x(t')dt' $$ and $$ 2)\ \ \ y(t) = \int_{-\in... |
Given a real finite-dimensional vector space $V$ with a symmetric bilinear form $b$, we define the
$Cl(V,b)$ as the quotient of the tensor algebra $\bigotimes V$ by the two sided ideal generated by $v\otimes v + b(v,v) \mathbb{1}$ for all $v \in V$. $Cl(V,b)$ is a $\mathbb{Z}_2$-graded unital real associative algebra. ... |
March 18th, 2017, 11:46 AM
# 1
Senior Member
Joined: Jan 2017
From: Toronto
Posts: 209
Thanks: 3
Calculating optimal isosceles trapezoid
Trough is to be formed by bending up two sides of a long metal rectangle so that the
cross-section of the trough is an isosceles trapezoid. If the width of the
metal sheet is 2 meters... |
You start from wrong assumptions, which explains your doubts. The line
the induced drag is due to the tip vortices
is as true as saying that wet streets cause rain. Also, the opinion that the
tip vortices strength will be as same as the bound vortex
is wrong. Unfortunately, many authors don't understand the topic thems... |
I carefully read all circa 70 pages of FEniCS tutorial and I still do not understand how to solve electrostatic problems when I have materials with different dielectric constant. The self contained system of equations in electrostatic $$ \mathrm{div}\boldsymbol{\mathcal{D}}=4\pi\rho,\\ \boldsymbol{\mathcal{D}}=\varepsi... |
This question arises from HNN Embedding Theorem for Amenable Groups?
Recall that a group $G$ is called
SQ-universal if every countable group is isomorphic to a subgroup of a quotient of $G$. The first non-trivial example of an SQ-universal group was provided by Higman, Neumann and Neumann in 1949. They proved that the ... |
I read in reliable sites that GR and classical physics calculate the angle of deflection in the same manner. The formula is almost identical: $$\theta = \frac{4GM}{c^2*r} \rightarrow \frac{4GM}{c*r} = v *\frac{1}{c}$$GR modifies the formula adding a factor $ \theta = \frac{4GM}{c^2r}\times \frac{1+\gamma}{2}$ where gam... |
Defining parameters
Level: \( N \) = \( 9450 = 2 \cdot 3^{3} \cdot 5^{2} \cdot 7 \) Weight: \( k \) = \( 2 \) Character orbit: \([\chi]\) = 9450.dn (of order \(18\) and degree \(6\)) Character conductor: \(\operatorname{cond}(\chi)\) = \( 945 \) Character field: \(\Q(\zeta_{18})\) Sturm bound: \(4320\) Dimensions
The f... |
Bungee Drop
Bungee Drop Engineering & Build Event Forum Threads 2015 2014 There are no tests available for this event Images Images (needs submissions) There are no question marathons for this event This event was not held recently in Division B Division C Champion Mentor High School Bungee Drop is a Division C event l... |
I am wondering if one can relate the KL divergence to the probability of error in a Bayesian binary hypothesis testing setting. That is, we have to decide between hypotheses $A$ and $B$ given observationx, and we have prior probabilities of either being true $p(A)$ and $p(B)$ such that $p(A)+p(B)=1$. Under either $A$ o... |
Most of your question is unclear to me, but I the answer to what I think is the core of your question is
yes: For any hermitian operator $A$ and any well-behaved-enough function $f:\mathbb R\to\mathbb R$, it is possible to construct a new operator $f(A)$ which acts in essentially all important respects as the action of... |
Maass forms of weight $0$ with trivial character
A
Maass form on a subgroup \(\Gamma\) of \(\GL_{2}(\R)\)is a smooth, square-integrable, automorphic eigenfunction of the Laplace-Beltrami operator $\Delta$. In other words, $$f\in C^\infty(\mathcal{H}),\quad f\in L^2(\Gamma\backslash{\mathcal H}),\quad f(\gamma z)=f(z)\ ... |
№ 9
All Issues On One Convolution Equation in the Theory of Filtration of Random Processes Abstract
We study the problems of analytic theory and the numerical-analytic solution of the integral convolution equation of the second kind $$ \begin{array}{cc}\hfill {\varepsilon}^2f(x)+{\displaystyle \underset{0}{\overset{r}{... |
I have a short question about the cap product in cohomology.
Let $X$ be a topological space, $R$ a commutative ring with unit $1_R$. We define the cap product on singular chain- and cochain modules $$\cap: C^p(X;R)\otimes _R C_{p+q}(X;R)\to C_q(X;R)$$ by $$\alpha\cap \sigma:=(-1)^{pq}\alpha (\sigma _{|[q,..,p+q]})\sigm... |
As I have heard, tangent vector to a smooth manifold $M$ in $p \in M$ is the operator $D_{\xi}$:$f \to D_{\xi}f$, where $f$ is a smooth function $f: M \to R$, with the following properties:
$D_{\xi}(f+g)=D_{\xi}f+D_{\xi}g $
$D_{\xi}(fh)=(D_{\xi}f)h(p)+f(p)(D_{\xi}h) $
So, the basis of the tangent space is:
${\frac{\par... |
The force of gravity is constantly being applied to an orbiting object. And therefore the object is constantly accelerating. Why doesn't gravity eventually "win" over the object's momentum, like a force such as friction eventually slows down a car that runs out of gas? I understand (I think) how relativity explains it,... |
So not quite sure what you're missing, but here's how you go about doing this sort of thing.
So first, I am assuming this is 1D due to your description. Second, I'm assuming you know the relationship between points in the physical domain, $x$, and the computational domain, $\xi$, something along the lines of $x=x(\xi)$... |
I've been trying to convince myself that "coherent sheaf" is a natural definition. One way I might be satisfied is the following: for modules over a Noetherian ring $A$, coherent and finitely presented modules agree. For quasicoherent sheaves over a locally Noetherian scheme $X$, coherent and locally finitely presented... |
Answer
5 seconds
Work Step by Step
We use the equation for period to find the length of half of a period: $\frac{1}{2}T = \pi \sqrt{\frac{L}{g}} = \pi \sqrt{\frac{25}{9.81}} \approx 5 s$
You can help us out by revising, improving and updating this answer.Update this answer
After you claim an answer you’ll have
24 hours... |
LaTeX is a great tool for printable professional-looking documents, but can be also used to generate PDF files with excellent navigation tools. This article describes how to create hyperlinks in your document, and how to set up LaTeX documents to be viewed with a PDF-reader.
Contents
Let's start with a minimal working ... |
(1) is true if $char(k)=0$. This follows from a combination of results. First of all, it is true over any field that the spectrum $MGL$ is connective, which means that
$$MGL^{p,q}(X)=0$$
if $p>q+dim(X)$, $X\in Sm/k$ [1, Cor. 2.9]. (Slightly more is true: for any $p\geq q+dim(X)$, the orientation map $MGL\to H\mathbb{Z}... |
Is there ever a practical difference between the notions induction and strong induction?
Edit: More to the point, does anything change if we take strong induction rather than induction in the Peano axioms?
MathOverflow is a question and answer site for professional mathematicians. It only takes a minute to sign up.Sign... |
In the book "Quantum Field theory and the Standard Model" by Matthew Schwartz, page 23-24, the position space wavefunction is defined as
$$\psi(x)=\langle 0|\phi(x)|\psi\rangle, \tag{2.82+2.83}$$
where $|\psi\rangle$ is any state in the Fock space. Then he uses the equations (i) $\partial_t^2\phi_0=(\nabla^2-m^2)\phi_0... |
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Now showing items 21-30 of 51
D-meson nuclear modification factor and elliptic flow measurements in Pb–Pb collisions at $\sqrt {s_{NN}}$ = 5.02TeV with ALICE at the LHC
(Elsevier, 2017-11)
ALICE measured the nuclear modification factor ($R_{AA}$) and elliptic flow ($\nu_{2}$) of D mesons ($D^{0}$, $D^{+}$, $D^{⁎... |
While preparing some lecture notes, I had a basic point of confusion come up that I haven't been able to settle.
The $BP$-Adams spectral sequence (or $p$-local Adams-Novikov spectral sequence) for the sphere begins with $E_2$-page $$E_2^{*, *} = \operatorname{Ext}^{*, *}_{BP_* BP}(BP_*, BP_*)$$ and converges to $\pi_* ... |
I work on modelling high intensity discharge xenon-filled lamps. The model governing the discharge is quite complex and sadly includes fluid dynamics. After some time, I managed to implement a finite-difference particle-tracking lagrangian fluid dynamics for axisymmetric 1D discharge:
$$ \frac{\partial}{\partial t} \le... |
The Annals of Probability Ann. Probab. Volume 23, Number 4 (1995), 1523-1556. The "True" Self-Avoiding Walk with Bond Repulsion on $\mathbb{Z}$: Limit Theorems Abstract
The "true" self-avoiding walk with bond repulsion is a nearest neighbor random walk on $\mathbb{Z}$, for which the probability of jumping along a bond ... |
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Now showing items 1-5 of 5
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... |
In Hajime Urakawa's monograph
The Spectral Geometry of the Laplacian on page 41, we make an assumption that I can't quite justify on my own. The following is our setup:
Let $(M^n,g)$ be a closed connected Riemannian manifold, with $\Delta_g$ the Laplacian (a negative operator), and $0=\lambda_0<\lambda_1\le\lambda_2\le... |
Path integral via discretization
So let me start with what seems to be the point of view of physicists (corrections are highly appreciated since this is what I understood!). Let a quantum system with coordinates $q_a$ and momenta $p_b$ be given satisfying commutation relations $$[q_a,p_b]=i\delta_{ab}.$$
Further suppos... |
Hey guys! I built the voltage multiplier with alternating square wave from a 555 timer as a source (which is measured 4.5V by my multimeter) but the voltage multiplier doesn't seem to work. I tried first making a voltage doubler and it showed 9V (which is correct I suppose) but when I try a quadrupler for example and t... |
Assume you have a smooth quasi-projective scheme $X$ (you can actually assume $X$ is projective over an affine scheme of finite type) defined over $\mathbb Z$ (or if you prefer, a discrete valuation ring), and let $F$ be a locally free tilting sheaf on $X$, that is, a locally free sheaf such that $\mathrm{Ext}^i(F,F)=0... |
With a graduate student, I'm going through the paper (Proc. London Math. Soc. (3) 47 (1983), no. 2, 193–224.)
Here's the background and notation.
We have a quadratic character $\chi$ modulo $q$, with Siegel zero $\beta_0$. $\eta=((1-\beta_0)\log q)^{-1}$, so $3\le \eta\ll q$ is known. Let $L=\log q$. We take $$ q^{250}... |
I'm reading a technical report on Simulated Annealing: On the Convergence Time of Simulated Annealing, by Sanguthevar Rajasekaran. You may find it following this link.
Given $G=(V, E)$ is the graph whose vertices are possible solutions to the given problem, and $E$ is the set of edges between the neighbours, the goal i... |
2.8. Density Estimation¶
Density estimation walks the line between unsupervised learning, featureengineering, and data modeling. Some of the most popular and usefuldensity estimation techniques are mixture models such asGaussian Mixtures (
sklearn.mixture.GaussianMixture), andneighbor-based approaches such as the kerne... |
257 23 Homework Statement There is an infinite charged plate in yz plane with surface charge density ##\sigma = 8*10^8 C/m^2## and negatively charged particle at coordinate (4,0,0) Find magnitude of efield at coordinate (4,4,0) Homework Equations E= E1+E2
So I figured to get e-field at point (4,4,0), I need to find the... |
In the restated problem both $X$ and $Y$ have rank at most $k \ll n$, and the same is true of Gram matrices $A$ and $B$. Also $C=(X+Y)(X+Y)^T$ will have rank at most $k$.
The goal of forming $C$ from $A$ and $B$, even approximately, seems unattainable. To briefly enlarge upon Jack Poulson's example, let $X$ and $Y$ be ... |
Background
I am trying to analyse fourier characteristics of a derivative. For example if I have a first order derivative approximated as following: $$\frac{\partial \Psi(x)}{\partial x} = \frac{\Psi_{i+1}-\Psi_{i-1}}{\Delta x}$$
to get its fourier characteristics, substitute $\Psi(x)= e^{j\, kx}$ in LHS, and its discr... |
Logistic operator
Logistic operator (or
LogisticOperator) is quadratic function of specific kind determined with the single parameter \(s\), which is usulally assumed to be real, \(s\!>\!1\): \(\!\!\!\!\!\!\!\!\!\!\!(1) ~ ~ ~ ~ \mathrm{LogisticOperator}_s(z) = s\,z \,(1\!-\!z)\)
(Parameter \(s\) is often denoted also w... |
Guitar Speaker Power Handling
The power rating of a guitar speaker is an indication of how much power it can handle without being damaged thermally or mechanically. It is not an indication of how loud the speaker will sound in comparison to other speakers. Let us examine the basics of how speakers work, how the power r... |
When a charged particle goes through liquid argon (LAr), it takes about 23.6 eV energy to ionize an electron in average. For minimal ionizing particle (heavy ionizing particle), the mean energy loss is about 2.1 (25) MeV/cm leading to about 100 (10) nm average separation between two adjacent ions.
The
mean rate of ener... |
There is an argument I do not understand given in "Introduction to quantum electrodynamics" by Cohen-Tannoudji (page 111 for the French version of the book).
We are dealing with the
non-relativistic version of the QED Lagrangian.
It takes the following form:
$$ L = \sum_a \frac{1}{2} m_a \dot{\boldsymbol{r}}_a^2 + \int... |
Let $V$ a Hilbert space, $a:V\times V\rightarrow \mathbb{R}$ a bounded, symmetric and positive bilinear form and $f:V\rightarrow\mathbb{R}$ bounded.
Is well known that problem
$$\left\lbrace\begin{array}{l}\textrm{Find }u\textrm{ such that}\\ a(u,v)=f(v)\quad\forall v\in V\end{array}\right.$$
is equivalent to minimize ... |
I'm concerned with equation 2.24 of http://arxiv.org/abs/1601.00482
The superconformal hypermultiplets in this paper have a conic hyperkahler target manifold and the authors want to gauge some isometries of this manifold. Letting the isometry group be $G$ and to have an associated Lie algebra $\mathfrak{g}$ generated b... |
oschvr a blog about software, programming, business, travelling and life. ← Problems Largest prime factor 24 days ago 02/05/2019 The prime factors of 13195 are 5, 7, 13 and 29. What is the largest prime factor of the number 600851475143 ?
We neeed to find the largest prime factor of
600851475143.
We know that the large... |
Advances in Differential Equations Adv. Differential Equations Volume 1, Number 2 (1996), 265-281. Almost periodicity enforced by Coulomb friction Abstract
We describe the influence of Coulomb friction $\mu$ sgn $ \dot x$ on the behavior of the linear oscillator given by $\ddot x+x=\varphi(t)$, where $\varphi$ is conti... |
(This is a cross-post from the Theoretical Computer Science Stack Exchange.)
For the purposes of this question, a
cut in a graph $G$ is the edge-set $\delta (S)\subseteq E(G)$ between some vertex-set $S$ and its complement. A max cut is one with at least as many edges as any other cut. Finding a max cut is NP-hard, but... |
LLVM optimizes power sums, such as
int sum(int count) { int result = 0; for (int j = 0; j < count; ++j) result += j*j; return result; }to code that calculates the result without a loop (godbolt) sum(int): test edi, edi jle .LBB0_1 lea eax, [rdi - 1] lea ecx, [rdi - 2] imul rcx, rax lea eax, [rdi - 3] imul rax, rcx shr ... |
I was thinking about the meaning of location-scale family. My understanding is that for every $X$ member of a location scale family with parameters $a$ location and $b$ scale, then the distribution of $Z =(X-a)/b$ does not depend of any parameters and it's the same for every $X$ belonging to that family.
So my question... |
@Jamal showed a good way to calculate it, and that they can be somewhat intertwined. Still, for the cosmological solution one can easily see what causes the curvature, and what is curved. A good way to understand it is to solve the equations for general relativity. If you do it for d=4, with one of the dimensions timel... |
I am referencing B. Schutz, A First Course in General Relativity. 2009, p. 256-258.
Note first that the line element on a 2-sphere with radius of curvature $r$ is $dl^2=r^2(d\theta^2+\sin^2\theta d\phi^2)$. Since we want a metric that is spherically symmetric about a point in space, say $r'=0$, we must not be able to t... |
Let me first explain what a conjugate prior is. I will then explain the Bayesian analyses using your specific example.Bayesian statistics involve the following steps:Define the prior distribution that incorporates your subjective beliefs about a parameter (in your example the parameter of interest is the proportion of ... |
I'm working through Dr. Pete Clark's convergence notes here: http://math.uga.edu/~pete/convergence.pdfand I've been thinking about Exercise 3.2.2 (a) and I am completely stumped.The exercise says ...
In the definition of Riemann integral or Darboux-integral we first study partitions (or tagged partition) of the given i... |
For a linear system
$$ M \dot{u} = Au \qquad \textrm{or} \qquad \dot{u} = L u $$
The
generalized eigenvalue problem is$$A e = \lambda M e$$
We can use the
time-stepper approach which essentially computes the eigenvalues of the operator
$$ E = \exp(L T) $$
If $\mu$ is an eigenvalue of $E$ then it is related to the origi... |
Inverted logic can be unnatural. Let's move over to quantified logic:
$$\forall x:({duck}(x)\land {quacks}(x))\lor ({dog}(x)\land {barks}(x))\lor(\lnot {duck}(x)\land\lnot{dog}(x))$$
"Everything is either a duck (and quacks), or a dog (and barks) or else it is neither duck nor dog."
If write down the dual, and then use... |
Morias
\(\mathrm{mori}(z)=\displaystyle \frac{ J_0 (L_1 z)}{1-z^2}\)
where \(L_1\approx 2.4\) is first zero of the Bessel function, \(J_0(L_1)\!=\!0~\).
\(u\!+\!\mathrm i v=\mathrm{mori}(x\!+\!\mathrm i y)\)
For integer \(m>0\) and \(|z|\gg 1\), function mori\((z)\) can be approximated with
\(\displaystyle \mathrm{mori... |
Give me a descent direction and a step length to move and I will find the optimum.
To recap the optimization problem from the previous post, in an unconstrained problem, the objective function is:
\(\min f(x) \tag{1}\)
We use iterative approaches to move \(x^k\) to \(x^{k+1}\) such that
\(f(x^{k+1}) < f(x^k) \tag{2}\)
... |
First of all, by a simple geometry principle:$\triangle CED$ and $\triangle AED$ have the same base $|ED|$ and thearea ratio between $\triangle CEF$ and $\triangle CFD$ has to be thesame as the length ratio between $|EF|$ and $|FD|$ so, similarly,you can tell the area ratio between $\triangle AEF$ and $\triangleAFD$ as... |
I am not very familiar with the common discretization schemes for PDEs. I know that Crank-Nicolson is popular scheme for discretizing the diffusion equation.
Is also a good choice for the advection term?
I am interesting in solving the Reaction-Diffusion-Advection equation,
$\frac{\partial u}{\partial t} + \nabla \cdot... |
Can I be a pedant and say that if the question states that $\langle \alpha \vert A \vert \alpha \rangle = 0$ for every vector $\lvert \alpha \rangle$, that means that $A$ is everywhere defined, so there are no domain issues?
Gravitational optics is very different from quantum optics, if by the latter you mean the quant... |
I've tried to explain the solution using as little math as possible, and to give some intuition as to what makes it tick. Nonetheless there will be a little mathematical notation at the end.
First steps: going beyond the obvious solution in the simplest case (N=2)
The statement of the puzzle as presented here doesn't m... |
Sample Quantiles
The generic function
quantile produces sample quantiles corresponding to the given probabilities. The smallest observation corresponds to a probability of 0 and the largest to a probability of 1.
Keywords univar Usage
quantile(x, …)
# S3 method for defaultquantile(x, probs = seq(0, 1, 0.25), na.rm = FA... |
No, I don't think auto-regulation explain much in the population sizes of predators. Group selection may explain such auto-regulation but I don't think it is of any considerable importance for this discussion.The short answer is, as @shigeta said[predators] tend to starve to death as they are too many!To have a better ... |
According to Kennedy's
Robust op-amp realization of Chua's circuit(1992), the differential equations satisfied by several physical quantities in Chua's circuit are
$$\begin{aligned} C_{1} \frac{d v_{C_{1}}}{d t} &=G\left(v_{C_{2}}-v_{C_{1}}\right)-g\left(v_{C_{1}}\right) \\ C_{2} \frac{d v_{C_{2}}}{d t} &=G\left(v_{C_{... |
LaTeX supports many worldwide languages by means of some special packages. In this article is explained how to import and use those packages to create documents in
Italian.
Contents
Italian language has some accentuated words. For this reason the preamble of your document must be modified accordingly to support these c... |
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