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In a queuing system, the inter-arrival times are known to be exponentially distributed. My textbook states: "It can be shown that, if the underlying distribution of inter-arrival times { T1, T2, ..., Tn } is exponential, the arrival times are uniformly distributed on the interval (0, T). The arrival times- T1, (T1 + T2... |
This talk is only an introductory overview.
A much more detailed version of this talk given by Lianheng Tong at the 2016 summer school.
We converted the Kohn-Sham equations into matrix form by introducing basis functions.
\begin{align} \mathbf{H C} = \mathbf{E S C}\\ \end{align}
Where
change variables
\begin{align} \ma... |
So far, we’ve been looking at motion that is easily described in Cartesian coordinates, often moving along straight lines. Such kind of motion happens a lot, but there is a second common class as well: rotational motion. It won’t come as a surprise that to describe rotational motion, polar coordinates (or their 3D coun... |
Griffiths,
Introduction to QM, uses $\Psi$ and $\psi$ to denote a solution to the time-dependent and the time-independent Schrödinger eq., respectively.
For a fixed energy $E$, rather than considering a
general solution $\psi$ to the TISE, the book is at this point only interested in finding a generating set $\psi_n$ o... |
Suppose we're selecting points uniformly at random from the $N$-simplex
$S_N = \{x \in \mathbb R^{N+1}: $ all $ x_i \ge 0$ and $x_1 + \ldots x_N = 1\}$.
One way to do this in practice is choose $N-1$ points $a_1, \ldots , a_{N-1}$ uniformly and independently from the unit interval $[0,1]$. Then for $a_0=0$ and $a_1=1$ ... |
The ladder operator method is used to solve the one-particle Schrodinger equation with a harmonic potential.
What other potentials for the one-particle Schrodinger equation may be solved with the ladder operator method?
Physics Stack Exchange is a question and answer site for active researchers, academics and students ... |
with 120v (dc for simplicity) as the input voltage and I have an led that runs on 3.4v and max 20ma ohms law states I=V/R so R=V/I, so R=120v/0.02a = 6000 ohms or 6k is this correct? how do I know the voltage drop across the resistor is correct, and what about power dissipated by the resistor? also, Is there an easy wa... |
Given that the torque is the rotational analog of the force, and the angular momentum is that of the linear momentum, it will not come as a surprise that Newton’s second law of motion has a rotational counterpart that relates the net torque to the time derivative of the angular momentum. To see that this is true, we si... |
An algebraic approach to entropy plateaus in non-integer base expansions
Mathematics Department, University of North Texas, 1155 Union Cir #311430, Denton, TX 76203-5017, USA
For a positive integer $ M $ and a real base $ q\in(1, M+1] $, let $ {\mathcal{U}}_q $ denote the set of numbers having a unique expansion in bas... |
In this paper, we use the thermodynamical formalism to show that there exists a unique equilibrium state $${\mu_\phi}$$ μ ϕ for each expanding Thurston map $${f : S^2\rightarrow S^2}$$ f : S 2 → S 2 together with a real-valued Hölder continuous potential $${\phi}$$ ϕ . Here the sphere S 2 is equipped with a natural met... |
Let $X$ be a quasi-projective variety over a perfect field $k$. Given a projective embedding $j : X\to \mathbf{P}(\mathscr{E})$, the Chow variety $\text{Chow}_r(X, j)$ is a quasi-projective variety parametrizing effective proper cycles on $X$ of codimension $r\ge 0$.
Is there some variant of the Chow construction, so a... |
Rules Use ALL the digits in the year $2019$ (you may not use any other numbers except $2, 0, 1, 9$) to write mathematical expressions that give results for the numbers 50 to 100.
You may use the arithmetic operations $+$, $-$, $\times$, $\sqrt{}$, and $!$ (see below). Indices or exponents may only be made from the digi... |
Neural Style Transfer - Art Generation using Neural networks
A really cool implementation of CNN is the Neural Style Transfer for Art Generation. It basically merges two images - one
Content image and other Style image to create a new image which is a combination of the two.
Some of the generated images are posted on T... |
Given any non-isosceles triangle $ABC$, let denote with $AB$ its longest sides, and draw the two circles with centers in $A$ and $B$ and passing by $C$. They determine two additional points $E$ and $D$ on the side $AB$.
If we draw the circles with centers in $A$ and $B$ and passing by $D$ and $E$, respectively, we obta... |
Optimality conditions for $ E $-differentiable vector optimization problems with the multiple interval-valued objective function
1.
Faculty of Mathematics and Computer Science University of Łódź, Banacha 22, 90-238 Łódź, Poland
2.
Department of Mathematics, Hadhramout University, P.O. BOX : (50511-50512), Al-Mahrah, Ye... |
I am investigating a somewhat obscure area of number theory. Can I post a proposition and a complete proof and ask people to check it?
Say I've proven a theorem or found a solution to a problem. I'm close to being sure that my proof or solution is fine. However, I'm not entirely confident in my jugdement. Maybe I'm new... |
I'm trying to reproduce the results of a paper on Device-to-Device Communication, channel assignment and mode selection (G. Yu, L. Xu, D. Feng, R. Yin, G. Y. Li and Y. Jiang, "Joint Mode Selection and Resource Allocation for Device-to-Device Communications," Nov. 2014.).
I have a couple of questions on the noise spectr... |
When multiple forces act on a body, the (vector) sum of those forces gives the net force, which is the force we substitute in Newton’s second law of motion to get the equation of motion of the body. If all forces sum up to zero, there will be no acceleration, and the body retains whatever velocity it had before. Static... |
Qmechanic's answer has the full details, but I figure it might be useful to break this down in a little more detail.
The proper way to generalize Maxwell's equations to higher-dimensional spaces is to use the field tensor $F^{\mu\nu}$. In our normal 3+1D space, it basically looks like this:
$$F = \begin{pmatrix}0 & E_1... |
I have a very specific difficult on the Problem 3 Item (b)-(c) (page 12) of Landau's book
Course of Theoretical Physics: Volume 1 Mechanics Second Edition. The problem is very straightforward:
Find the Lagrangian of a simple pendulum of length $l$ and mass $m$ whose point of support is (b) oscillating horizontally in t... |
Here is a question from old exam papers I am having trouble with:
Suppose the lifetime of a bulb is distributed exponentially with mean life $\theta$ (in hours). Let $X_i$ be the number of trials required to get a bulb surviving at least $t$ (known) hours for the first time in the $i$th lot, where lot sizes are large e... |
Skip to 0 minutes and 12 secondsHello. It's your turn on trigonometry by the unit circle. OK. Now let us recall some laws that will permit us to reduce our computations to angles between 0 and pi over 2. OK. The laws that I wish to remind you are the antipodal law, which says that the sine of pi plus x is equal to minu... |
Errors in layer thicknesses and instability of the refractive indices of thin film materials are the main reasons of the deviations of experimental spectral characteristics of produced optical coatings from theoretical performances of corresponding multilayer designs.
Errors in layer thicknesses are inevitable even in ... |
I've been trying to teach myself a few modules of my university course in preparation before I start and I'm currently attempting some Vector Calculus, but I'm finding it much more difficult to grasp than previous modules. I was beginning to think I was getting the hang of it until I came across the question below.
The... |
The lifting operator $\mathbf{r}(\mathbf{v_h})$ for the '2nd version' of Bassi-Rebay scheme for elliptic problems in $d$ dimensions is defined as $$ \int_{\Omega_h} \mathbf{w}_h \cdot \mathbf{r}(\mathbf{v}_h)\,\mathrm{d}\mathbf{x} = -\int_{E} \{\mathbf{w}_h\}\cdot \mathbf{v}_h \,\mathrm{d}S, $$ where $$ \mathbf{v}_h \i... |
“One-Dimensional” Sound Waves
We’ll begin by considering sound traveling down a hollow pipe, to avoid unnecessary mathematical complications. Sound is a longitudinal wave—as the wave passes through, the air moves backwards and forwards in the pipe, this oscillatory movement is in the same direction the wave is travelin... |
Differential Equation of Oscillations
Pendulum is an ideal model in which the material point of mass \(m\) is suspended on a weightless and inextensible string of length \(L.\) In this system, there are periodic oscillations, which can be regarded as a rotation of the pendulum about the axis \(O\) (Figure \(1\)).
Dynam... |
I do not believe there is a name for your specific inequality (which I rewrite as following):$$|x|^p+|y|^p\le \big(|x|+|y|\big)^p, \ p \ge1 \iff \boxed{\ \ \left(|x|^p +|y|^p\right)^{\frac{1}{p}} \le |x|+|y|, \quad p \ge 1 \ \ }$$However, it can be viewed as a special case of multiple more general statements, such as J... |
Consider two unshaded circles $C_r$ and $C_s$ with radii $r>s$ that touch at the origin of the complex plane. The shaded circles $C_1,C_2...C_7$ (labeled in counterclockwise direction sequentially) all touch $C_r$ internally and $C_s$ externally. $C_1$ also touches the real axis and $C_i$ and $C_{ i+1}$ touch for $i=1.... |
Kinetic Theory of Gas Molecular nature of matter and Behaviour of Gases A gas consisting of large number of identical, tiny spherical, neutral and elastic particles called molecules. In a gas molecules none in all possible directions with all possible speeds. The pressure of gas is due to elastic collisions of the gas ... |
Contents Post summary: The level set method is a powerful alternative way to represent N-dimensional surfaces evolving through space. (This is a significantly extended blog-post version of three slides from my Medical Visualization lecture on image analysis.)
Imagine that you would like to represent a contour in 2D or ... |
Your loss function would not work because it incentivizes setting $\theta_1$ to any finite value and $\theta_0$ to $-\infty$.
Let's call $r(x,y)=\frac{1}{m}\sum_{i=1}^m {h_\theta\left(x^{(i)}\right)} -y$ the
residual for $h$.
Your goal is to make $r$
as close to zero as possible, not just minimize it. A high negative v... |
In her paper "Quartic rings associated to binary quartic forms" (https://doi.org/10.1093/imrn/rnr070), Wood showed that $\operatorname{GL}_2(\mathbb{Z})$-classes of integral binary quartic forms are in discriminant-preserving bijection to pairs $(Q,C)$ where $Q$ is a quartic ring and $C$ is a monogenic cubic resolvent ... |
A better way to think about this is to think about the Dirac equation being obtained from the action of a fermionic field in curved spacetime. Then a lot of the concepts generalize from the Minkowski metric in a more straightforward manner. In flat spacetime we have
\[\int d^4x ~\bar{\Psi} (i \gamma^{\mu} \partial_{\mu... |
Here are more details than you wanted to know:
Suppose the house has length $l$ and width $w$. The length and with must be non-negative, of course. Then the area is $A(l,w) = lw$. The length of fence required is $2l+2w$ for the exterior wall and $2w$ for the interior separators, hence we have $\lambda(l,w) = 2(l+2w)$. ... |
HTML provides a mnemonic form for 252 of the most common symbols. (See a full list from the W3C.) These are called “character entities.” You can simply put Unicode characters directly into an HTML page as long as you have an input method and the content-type of your HTML page is correctly set. However character entitie... |
Anamoly Detection Algorithms
Anamoly Detection is a class of semi-supervised (close to unsupervised) learning algorithm widely used in Manufacturing, data centres, fraud detection and as the name implies, anamoly detection. Normally this is used when we have a imbalanced classification problem, with, say, y=1(anamoly) ... |
Mechanical Properties of Fluids Pressure Static pressure is the normal force experienced per unit area of cross section P=F/A ⇒ P=ρgh. At the bottom of the liquid pressure is mainly due to the weight of the liquid. Pressure exerted by liquid only is called Gauge pressure. Absolute pressure is equal to atmospheric press... |
The $n-2$ term accounts
for the loss of 2 degrees sample size is increased, but only up to a point. for the critical value, with degrees of freedom (DF) equal to n - 2. The terms in these equations that involve the variance or standard deviation of X merelyyour regression model and continue the analysis.Previously, we ... |
When is a new finding significant? The hypothesis can help answer this question.
The hypothesis testing is composted by a null hypothesis and the alternative hypothesis and helps us to determine if a new finding is significant and thus to see if a parameter is different from what we originally assumed.
Example: Say we ... |
First, let me say that a good place to look at would be [1]. I haven't checked there so I'm not sure, but it contains technology for computing such things even for exceptional groups. It uses a so-called "birdtrack" notation that treats tensor contractions as graphs.
Here however is a way to brute force it. I didn't tr... |
A series in which successive terms have opposite signs is called an alternating series.
The Alternating Series Test (Leibniz’s Theorem)
This test is the sufficient convergence test. It’s also known as the Leibniz’s Theorem for alternating series.
Let \(\left\{ {{a_n}} \right\}\) be a sequence of positive numbers such t... |
ERROR: type should be string, got "https://tex.stackexchange.com/a/88762/17049 provides a beautiful solution for getting spirals like this:\nI've been trying to use this with some mixed text/math content (for a book cover), but I find that even with a tiny excerpt, pdflatex just keeps running and running without terminating. [Using a full core for at least 10 minutes.] The only change I made was to replace\nLorem ipsum ...\nin the code in the linked answer with\nIf $K \\leq G$ and there are inclusions $gKg^-1\\leq K$ for every $g\\in G$, ... .\nIs there any way of getting spirals with mixed text/maths content, either by modifying the linked answer or otherwise?\nMWE:\n\\documentclass{article}\\usepackage{tikz}\\usetikzlibrary{decorations.text}\\makeatletter\\let\\pgf@lib@dec@text@dobox@original=\\pgf@lib@dec@text@dobox%\\def\\pgf@lib@dec@text@dobox{% \\pgf@lib@dec@text@dobox@original% \\ifpgfdecorationtextalongpathscaletext% \\pgfmathparse{\\pgf@lib@dec@text@endscale+(\\pgf@lib@dec@text@startscale-\\pgf@lib@dec@text@endscale)*\\pgfdecoratedremainingdistance/\\pgfdecoratedpathlength}% \\setbox\\pgf@lib@dec@text@box=\\hbox{\\scalebox{\\pgfmathresult}{\\box\\pgf@lib@dec@text@box}}% \\fi%}\\newif\\ifpgfdecorationtextalongpathscaletext\\def\\pgf@lib@dec@text@startscale{1}\\def\\pgf@lib@dec@text@endscale{1}\\pgfkeys{/pgf/decoration/.cd, text path start scale/.code={% \\pgfdecorationtextalongpathscaletexttrue% \\def\\pgf@lib@dec@text@startscale{#1}% }, text path end scale/.code={% \\pgfdecorationtextalongpathscaletexttrue% \\def\\pgf@lib@dec@text@endscale{#1}% }}\\begin{document} \\begin{tikzpicture}[ decoration={ reverse path, text along path, text path start scale=1.5, text path end scale=0, text={If $K \\leq G$ and there are inclusions $gKg^-1\\leq K$ for every $g\\in G$, ... .}}]\\draw [decorate] (0,0) \\foreach \\i [evaluate={\\r=(\\i/2000)^2;}] in {0,5,...,2880}{ -- (\\i:\\r)}; \\useasboundingbox (-2.75,-2.75) rectangle (2.75,2.75); \\end{tikzpicture} \\end{document}" |
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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 ... |
If $X$ is a linear subspace of ${\mathbb R}^n$, $X$ is high-dimensional, and for every $x\in X$ we have
$(1-\epsilon) \sqrt n ||x||_2 \leq ||x||_1 \leq \sqrt n ||x||_2$
for some small $\epsilon >0$, then we say that $X$ is an almost-Euclidean section of $\ell_1^n$, and (the matrix whose image is) X is useful in compres... |
Tagged: nonsingular matrix Problem 509
Using the numbers appearing in
\[\pi=3.1415926535897932384626433832795028841971693993751058209749\dots\] we construct the matrix \[A=\begin{bmatrix} 3 & 14 &1592& 65358\\ 97932& 38462643& 38& 32\\ 7950& 2& 8841& 9716\\ 939937510& 5820& 974& 9 \end{bmatrix}.\]
Prove that the matrix... |
That's probably a good thing. I obviously didn't intend to harm with this link, just wanted to point out that the HTML-on-Catagolue chroniccals reference weren't overA for awesome wrote:Now Chrome blocks as unsafe (which is good because I added an event handler to one of your input fields, which could easily be used fo... |
In his answer on cstheory.SE, Lev Reyzin directed me to Robert Schapire's thesis that improves the bound to $O(n^2 + n\log m)$ membership queries in section 5.4.5. The number of counterexample queries remains unchanged. The algorithm Schapire uses differs in what it does after a counterexample query.
Sketch of the impr... |
I am reading this paper about density estimation (Appendix A), where the authors apply a Fourier transform to the estimated probability density (the $X_j$ are a sample of $N$ data points drawn independently from an unknown probability density function $f(x)$):
$$ \hat{f}(x) = \frac1N \sum^N_{j=1} K(x-X_j) $$
The author... |
I would like to estimate the "harmonicity" (harmonics-to-noise ratio ?) of an audio signal from its spectrum. What kind of algorithm can I use?
Please take a look at this previous answer. Using the semantics and mathematical definitions from that answer...
Let $x[n]$ be the input signal from which you want to measure h... |
Although designing a rocket that will follow a desired trajectory (say to Ceres, Pluto, or Planet Nine) with great accuracy is an enormous engineering challenge, the basic principle behind rocket propulsion is remarkably simple. It essentially boils down to conservation of momentum, or, equivalently, the observation th... |
You might just want to look at
Chapter 2 of Classical Mechanics (Moments of Inertia) before proceeding further with this chapter.
In figure \(\text{VIII.26}\) I draw a massive body whose centre of mass is \(\text{C}\), and an external point \(\text{P}\) at a distance \(R\) from \(\text{C}\). I draw a set of \(\text{C}x... |
Consider a Hermitian field operator $\phi(x)$ with eigenstates satisfying$$\phi(x) |\alpha\rangle = \alpha(x) | \alpha \rangle$$I'm trying to determine the inner product between the eigenstates. To do this, I consider$$\langle\beta|\phi(x)|\alpha\rangle = \alpha(x)\langle\beta|\alpha\rangle = \beta(x)\langle\beta|\alph... |
Oscillations and Waves Simple Harmonic Motion A body is said to be in SHM if it moves to and fro along a straight line about its mean position such that at any point its acceleration is directly proportional to its displacement in magnitude but opposite in direction and is always directed towards the mean position. Pha... |
No, the idea of wealth as something to be created did not originate in the United States. It was part of the mercantilist approach to national economic policy that was widely adopted in Europe in the 16th to 18th centuries.Mercantilism involved a range of policies, many of which were designed to increase the wealth of ... |
Start with the unperturbed gravitational potential for a uniform sphere of mass M and radius R, interior and exterior:
$$ \phi^0_\mathrm{in} = {-3M \over 2R} + {M\over 2R^3} (x^2 + y^2 + z^2) $$$$ \phi^0_\mathrm{out} = {- M\over r} $$
Add a quadrupole perturbation, you get
$$ \phi_\mathrm{in} = \phi^0_\mathrm{in} + {\e... |
We prove the security for the construction given in Sect. 4.2.
Theorem 1
Let \(({\mathsf {KeyGenEnc}},{\mathsf {Enc}},{\mathsf {Dec}})\) be a NM-CPA secure encryption scheme, let \(F_{(\cdot )}\) be a PRP family and let \(({\mathsf {GenCRS}},{\mathsf {Prove}},{\mathsf {VerifyProof}})\) be a NIZK proof system. Then, the... |
Skills to Develop
List of various kinematics equations and identities
In addition to the relations
\[D(v) = \sqrt{\frac{1+v}{1-v}}\]
and
\[v_c = \frac{v_1 + v_2}{1 + v_1 v_2}\]
the following identities can be handy. If stranded on a desert island you should be able to rederive them from scratch. Don’t memorize them.
\[... |
Tagged: symmetric matrix Problem 572
The following problems are Midterm 1 problems of Linear Algebra (Math 2568) at the Ohio State University in Autumn 2017.
There were 9 problems that covered Chapter 1 of our textbook (Johnson, Riess, Arnold). The time limit was 55 minutes. Problem 7. Let $A=\begin{bmatrix} -3 & -4\\ ... |
This is only an extended comment.A few times ago I asked (myself :-) how fast a multitape NTM that accepts a (reasonably encoded) NP-complete language can be. I came up with this idea:
3-SAT remains NP-complete even if variables are represented in unary. In particular we can convert a clause - suppose $(x_i \lor \neg x... |
Let $\pi: \mathcal{X}\to B$ be a complex analytic family of compact complex manifolds, i.e. $\pi$ is a surjective, proper submersion between complex manifolds. For simplicity, we assume $B$ is the open unit disc $\Delta$ in the complex plane. Denote the fibers of $\pi$ by $X_t:=\pi^{-1}(t)$ and the central fiber is $X:... |
I have some problems understanding what the best way of dealing with the delta functions in polar coordinates (I know there are many questions on the subjects on this website but they are all not satisfactory).
In (Delta function integrated from zero), they claim that the delta function is given by $\delta^{(2)}=\frac{... |
The electric potential due to a point charge is given by
\[\varphi=\frac{kq}{r}\label{6-1}\]
where
\(\varphi\) is the electric potential due to the point charge,
\(k=8.99\times 10^9 \frac{Nm^2}{C^2}\) is the Coulomb constant,
\(q\) is the charge of the particle (the source charge, a.k.a. the point charge) causing the e... |
Given a Lagrangian coupling a complex scalar field $\psi$ to a real scalar field $\phi$:
$$\mathcal{L} = \frac{1}{2}\partial_{\mu}\phi\partial^{\mu}\phi + \partial_{\mu}\psi\partial^{\mu}\psi^*+ \frac{1}{2}m^2 \phi^2 + \frac{1}{2}M^2 \psi^2 + g \phi \psi \psi^*$$
I'm struggling to see how there can be any non-zero Feyn... |
The instability and high sensitivity of optimisation results can be augmented by adding another layer of quantitative methodology in the form of Monte Carlo Simulation. The name Monte Carlo alludes to the nature of the simulation procedure, which, in essence, involves drawing random numbers from a distribution, and the... |
Suppose I have two points the unit circle corresponding to 30 and 60 degrees from the x-axis.
I want to draw a line between these two points.
\documentclass[border=5mm]{standalone}\usepackage{tikz} \usepackage{calculator} \usetikzlibrary{rulercompass} \usetikzlibrary{intersections,quotes,angles} \usetikzlibrary{calc}\b... |
In Fourier transform for periodic signal, I checked different books and I found a different explanation in each book. Let's take the explanation in Signals and Systems by Rajeshwari & Rao:
The resulting Fourier transform for a periodic signal consist of a train of impulses in frequency, with areas of impulses proportio... |
This problem is from our recitation which I do not have solutions for, and I'm stuck on the very last part where I need to satisfy the $u_t(x,0)$ initial condition.
The problem is:
$$ \left\{ \begin{split} u_{tt} &= c^2u_{xx}, \quad\qquad x>0,t>0\\ u(&0,t) = 0 \qquad\qquad\qquad t>0\\ u(&x,0) = \sin(x) = f(x)\;\quad x>... |
The Vogt's theorem for plane curves states that if A and B are endpoints of a spiral arc, the curvature nondecreasing from A to B. The angle $\beta$ of the tangent to the arc at B with the chord AB is not less than the angle $\alpha$ of the tangent at A with AB. $\alpha = \beta$ only if the curvature is constant.
Does ... |
This question already has an answer here:
Photons are the force carrier of the electromagnetic force. I do not see how this could result in a transfer of momentum that attracts objects together.
Physics Stack Exchange is a question and answer site for active researchers, academics and students of physics. It only takes... |
I am using the
acronympackage for acronyms, symbols and constants in my report. I would like the list of constants to be slightly different than the other two lists. I want to use the
\acroextra{} macro to add the value of the constants and to print them in a third column.
At the moment I have something like this:
\doc... |
We'll say that a function on $[0,1]$ is uniformly left continuous if for every $\epsilon > 0$ there exists $\delta > 0$ such that $x \in (y - \delta, y)$ implies $|f(x) - f(y)| < \epsilon$ for every $x, y \in [0,1]$. I want to know if the space of all such functions is complete with respect to the uniform norm.
I'm int... |
I'm trying to better understand the causes for the equation of time by deriving an approximation from first principles.
My naive approach, $EOT_{NAIVE}$, is to take the difference between the right ascension of the mean sun, $\alpha_M(t)$, and the right ascension of the "real" sun $$EOT_{NAIVE}(t)=\langle\dot{\alpha }\... |
In this topic, we will learn how to find the volume of a solid object that has known cross sections.
We consider solids whose cross sections are common shapes such as triangles, squares, rectangles, trapezoids, and semicircles.
Definition: Volume of a Solid Using Integration
Let \(S\) be a solid and suppose that the ar... |
Wave energy converters in coastal structures: verschil tussen versies
(→Application for wave energy converters)
(→Application for wave energy converters)
Regel 61: Regel 61:
<p>
<p>
The time-mean wave energy flux per unit crest length is used as one of the main criteria to choose a site for wave energy converters.
The ... |
Angle (argument of a function): \(\alpha\)
Trigonometric functions: \(\sin \alpha, \) \(\cos \alpha ,\) \(\tan \alpha, \) \(\cot \alpha,\) \(\sec \alpha,\) \(\csc \alpha \)
Trigonometric functions: \(\sin \alpha, \) \(\cos \alpha ,\) \(\tan \alpha, \) \(\cot \alpha,\) \(\sec \alpha,\) \(\csc \alpha \)
Coordinates of a ... |
I'm taking a particle physics course and we're using Perkins Introduction to High Energy Physics as the text. I am looking at problem 1.7. It asks whether $$\pi^0\rightarrow e^- + e^+$$ is allowed or forbidden by the Standard Model based off of conservation laws. I feel it doesn't violate any of them. Energy and moment... |
I am attempting to prove a set of results for the products of gamma matrices and traces of products of gamma matrices, but got stuck on this particular one.
$$Tr(\gamma^{\mu_1}...\gamma^{\mu_n})=g^{\mu_1\mu_2}Tr(\gamma^{\mu_3}...\gamma^{\mu_n})-g^{\mu_1\mu_3}Tr(\gamma^{\mu_2}\gamma^{\mu_4}...\gamma^{\mu_n})+...+g^{\mu_... |
Polynomial Long Division
By
Catalin David Introduction The general form of a monomial f(x)=ax n, where:
-
a is the coefficient and can be part of the sets N, Z, Q, R, C
-
x is the variable
-
n is the degree and is part of N Two monomials are equal if they have the same variable and the same degree.
Example:
3x 2 and -5... |
Ray Optics and Optical Instruments Optical Instruments Visual angle is the angle subtended by an object at the eye. Myopia means short sightedness, the distant objects are not clearly visible. Hypermetropia means far sightedness, the near objects are not clearly visible. A convex lens is called simple microscope Magnif... |
This question already has an answer here:
So i was just revising some basic DSP concepts. Just wanted to verify this fact.
Fourier series represents a periodic signal $\hat{x}(t)$ with period P as a countably infinite sum of sinusoids of frequency $0$, $\frac{1}{P},\frac{2}{P},\frac{3}{P}...$. This converges to the sig... |
Thermal Properties of Matter Newton's Law of Cooling From Newtons law of cooling the rate of loss of heat of a hot body is directly proportional to difference in temperature between the body and its surroundings provided the difference is small. \tt \frac{dQ}{dt}\propto \left(\tau -\tau0\right) Newtons law of cooling i... |
@Daniel Fischer already pointed out its relevance to the notion of irrationality measure.
This is related to the following question:
How fast $n$ gets closer to the zero set $\frac{\pi}{2} + \pi \Bbb{Z}$ of $\cos x = 0$?
We do not want a situation where (a subsequence of) $\cos n$ decays so fast that it can even beat t... |
We are considering here binary relations on a set \(A\). Let’s recall that a
binary relation \(R\) on \(A\) is a subset of the cartesian product \(R \subseteq A \times A\). The statement \((x,y) \in R\) is read as \(x\) is \(R\)-related to \(y\) and also denoted by \(x R y \).
Some importants properties of a binary rel... |
I am investigating a somewhat obscure area of number theory. Can I post a proposition and a complete proof and ask people to check it?
Say I've proven a theorem or found a solution to a problem. I'm close to being sure that my proof or solution is fine. However, I'm not entirely confident in my jugdement. Maybe I'm new... |
Take some state variable $X(t)$, which follows the law of motion
$$ \dot X(t) = f(t)X(t) $$
where $f(t)$ is a policy function, and determines the growth rate of $X(t)$. As a second shock, we have $\psi$, which is iid. The agent defaults whenever
$$ g(X(t), \psi) \leq 0$$
Allow the agent to borrow some money that he wil... |
LEARNING OBJECTIVES
Correlate two nearby circuits that carry time-varying currents with the emf induced in each circuit Describe examples in which mutual inductance may or may not be desirable Inductance is the property of a device that tells us how effectively it induces an emf in another device. In other words, it is... |
When adding a
\bar to a relation the spacing around the relation is removed:
\documentclass{article}\begin{document}$x > y$ $x \bar{>} y$\end{document}
So, how does one do this correctly?
TeX - LaTeX Stack Exchange is a question and answer site for users of TeX, LaTeX, ConTeXt, and related typesetting systems. It only ... |
Scrabble?! STATICALLYIs staticallyvalid for Scrabble? Words With Friends? Lexulous? WordFeud? Other games? Definitions of STATICALLY in various dictionaries:
In statics, a structure is statically indeterminate (or hyperstatic) when the static equilibrium equations are insufficient for determining the internal forces an... |
tl;dr: Not without killing everything.
Let's do some maths and actually figure this out.
The specific heat capacity of water is $4.186 \text{ kJkg}^{-1}$. That means it takes 4186 joules of energy to heat 1 kilogram of water up by one degree.
The average temperature of the surface of the sea is 17
oC. It gets a lot col... |
If you look at the recursive combinators in the untyped lambda-calculus, such as the Y combinator or the omega combinator: $$ \begin{array}{lcl} \omega & = & (\lambda x.\,x\;x)\;(\lambda x.\,x\;x)\\ Y & = & \lambda f.\,(\lambda x.\,f\;(x\;x))\; (\lambda x.\,f\;(x\;x)) \\ \end{array} $$ It's clear that all of these comb... |
My attempt :
a) Summation of all values?
b)c)d) Failed
e) Parserval's theorem
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My attempt :
a) Summation of all v... |
Tagged: group Problem 343
Let $G$ be a finite group and let $N$ be a normal abelian subgroup of $G$.
Let $\Aut(N)$ be the group of automorphisms of $G$.
Suppose that the orders of groups $G/N$ and $\Aut(N)$ are relatively prime.
Then prove that $N$ is contained in the center of $G$. Problem 332
Let $G=\GL(n, \R)$ be th... |
Do you know sensible algorithms that run in polynomial time in (Input length + Output length), but whose asymptotic running time in the same measure has a really
huge exponent/constant (at least, where the proven upper bound on the running time is in such a way)?
Do you know sensible algorithms that run in polynomial t... |
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Does GMAT RC seem like an uphill battle? e-GMAT is conducting a free webinar to help you learn reading strategies that ... |
Notation:
\( I_{1}\), \( I_{2}\), \( I_{3}\) are the principal moments of inertia. \( I_{3}\) is the unique moment. If it is the largest of the three, the body is an oblate symmetric top; if it is the smallest, it is a prolate spherical top. \( Ox_{0}\), \( Oy_{0}\), \( Oz_{0}\) are the corresponding body-fixed princip... |
There is no "plain Black Scholes implied surface" because implied volatilities come from options market prices (calls and put). If you had a whole continuum of call prices $C : \mathbb{R}_+ \times \mathbb{R}_+ \to \mathbb{R}_+$, $(T,K) \mapsto C(T,K)$ you would get a implied volatility function $\sigma_I : \mathbb{R}_+... |
In the 19th century it was discovered that the Maxwell Equations describing electric and magnetic fields, a grand synthesis of the results of many different experiments, unlike Newton's laws of motion, are not consistent with Galilean relativity. A priori, the solution was not clear. One possible reason for this incons... |
When the measures of the angles of a triangle are placed in order, the difference between the middle angle and smallest angle is equal to the difference between the middle angle and largest angle. If one of the angles of the triangle has measure 23, then what is the measure in degrees of the largest angle of the triang... |
Can anyone state the difference between frequency response and impulse response in simple English?
The impulse response and frequency response are two attributes that are useful for characterizing linear time-invariant (LTI) systems. They provide two different ways of calculating what an LTI system's output will be for... |
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