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Advances in Differential Equations Adv. Differential Equations Volume 22, Number 5/6 (2017), 363-402. The Cauchy problem for the shallow water type equations in low regularity spaces on the circle Abstract
In this paper, we investigate the Cauchy problem for the shallow water type equation \begin{align*} u_{t}+\partial... |
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June 2010 , Volume 5 , Issue 2
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The aim of the paper is to study the asymptotic behavior of solutions to a Neumann boundary value problem for a nonlinear elliptic equation with nonstandard growth co... |
Partly your question relates to more general questions like "buy versus rent a house", or "buy versus lease a machine". Under neoclassical assumptions of competition, full information, etc, you can imagine that arbitrage would make these options equivalent
for the average of the population (or the representative agent)... |
Assemble a formula using the numbers $2$, $0$, $1$, and $8$ in any order that equals 109. You may use the operations $x + y$, $x - y$, $x \times y$, $x \div y$, $x!$, $\sqrt{x}$, $\sqrt[\leftroot{-2}\uproot{2}x]{y}$ and $x^y$, as long as all operands are either $2$, $0$, $1$, or $8$. Operands may of course also be deri... |
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1556-1801
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Networks & Heterogeneous Media
September 2010 , Volume 5 , Issue 3
A special issue
New Trends in Model Coupling, Theory, Numerics and Applications
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Special Issue from the workshop
New Trends in Model Coupling, Theory, Nu- merics ... |
Define a sequence of functions \(P_i:\mathbb{R}^+\rightarrow\mathbb{R}\), \(i\in\mathbb{N}\)
$$P_0(x) = \ln(x)$$
$$P_{n+1}(x) = \int P_{n}(x)\cdot dx$$
I found a beautiful closed formula for \(P_i\), that I haven't seen before.
Integrating by parts, it's easy to calculate first few \(P_i\):
$$P_1(x) = x\cdot\ln x - x$$... |
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December 2010 , Volume 5 , Issue 4
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This paper is devoted to the extension to the full $3\times3$ Euler system of the basic analytical properties of the equations governing a fluid flowing in a duct... |
A particle moves along the x-axis so that at time t its position is given by $x(t) = t^3-6t^2+9t+11$ during what time intervals is the particle moving to the left? so I know that we need the velocity for that and we can get that after taking the derivative but I don't know what to do after that the velocity would than ... |
Ramanujan presented many identities, Hardy chose one which for him represented the best of Ramanujan. There are many proofs for this identity.
(for example, H. H. Chan’s proof, M. Hirschhorn's proof...)
Is there an elementary proof for Ramanujan's "most beautiful" identity?
$$\displaystyle{\sum_{n=0}^\infty p(5n+4)q^n}... |
Category: Group Theory 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, \... |
As part of a larger display, I am placing two tabular environments together, one above the other. These two environments are going to appear in one column of a larger tabular, and I want the two environments to have the same width. I would prefer not to use
tabular*, because I don't want to have to guess the width and ... |
Temperature differential, abbreviated as \(\Delta T\) or TD, is the difference between two specific temperature points of a volume at a given time in a system.
Temperature Differential Formula
(Eq. 1) \(\large{ \Delta T = T_h - T_l }\)
(Eq. 2) \(\large{ \Delta T = \frac {\dot {Q}_t \; l} {k_t} }\)
Where:
\(\large{ \Del... |
The Infona portal uses cookies, i.e. strings of text saved by a browser on the user's device. The portal can access those files and use them to remember the user's data, such as their chosen settings (screen view, interface language, etc.), or their login data. By using the Infona portal the user accepts automatic savi... |
Mathematics 1 - May 2013
First Year Engineering (Semester 1)
TOTAL MARKS:
TOTAL TIME: HOURS 1 Find the eigen values of A -1 where $$ A=\begin{bmatrix}3 &1 &4 \\0 &2 &6 \\0 &0 &5 \end{bmatrix}$$(2 marks) 10 Change the order of Integration in $$ \int^a_0 \int^y_0 f(x, y)dxdy$$(2 marks)
Answer any one question form Q11 (a... |
I believe you are following Royden & Fitzpatrick's
Real Analysis. First let me remind you a couple of definitions pertaining to your question:
Let $f:E\to\Bbb{R}$ be a function. Then
\begin{align}\overline{D}f:&E^\circ\to\Bbb{R}& \underline{D}f:&E^\circ\to\Bbb{R}\\&x\mapsto\limsup_{h\to0} \dfrac{f(x+h)-f(x)}{h}& &x\map... |
Answer
Please see the work below.
Work Step by Step
We know that $H=kA\frac{\Delta T}{\Delta x}$ We plug in the known values to obtain: $H=(1)(8.0\times 12)(\frac{20-10}{0.23})$ $H=4200W$
You can help us out by revising, improving and updating this answer.Update this answer
After you claim an answer you’ll have
24 hour... |
Tagged: subspace criteria Problem 659
Fix the row vector $\mathbf{b} = \begin{bmatrix} -1 & 3 & -1 \end{bmatrix}$, and let $\R^3$ be the vector space of $3 \times 1$ column vectors. Define
\[W = \{ \mathbf{v} \in \R^3 \mid \mathbf{b} \mathbf{v} = 0 \}.\] Prove that $W$ is a vector subspace of $\R^3$. Problem 658
Let $V... |
Moving charges and magnetism Magnetic Field on the Axis of a Circular Current Loop, Ampere’s Circuital Law The magnetic field at the centre of the coil is \tt B = \frac{\mu_{0} ni}{2r} The magnetic field at the centre when conductor is bent in the form of a coil. \tt B = \frac{\mu_{0} ni}{4 \pi r} (\theta) (θ in radius... |
Newform invariants
Coefficients of the \(q\)-expansion are expressed in terms of a basis \(1,\beta_1,\beta_2\) for the coefficient ring described below. We also show the integral \(q\)-expansion of the trace form.
Basis of coefficient ring in terms of a root \(\nu\) of \(x^{3}\mathstrut -\mathstrut \) \(x^{2}\mathstrut... |
As Terry mentions in the comments, the reason for the $\sqrt{5}$ is that the limiting case, the golden ratio, forces it. There is a very neat explanation of all of this in the classic number theory book by Hardy and Wright, pages 209 to 212. I give a brief sketch of the ideas.
Why $\phi$ is the worst case.
As Hardy and... |
This is not true in general: one can prove that if $f \in M_k(\Gamma_0(N),\chi)$ is a non-zero modular form with Nebentypus character $\chi$ (without any newform assumption), then the field generated by the Fourier coefficients of $f$ contains $\mathbf{Q}(\chi)$, see e.g. Corollary 3.6 in this preprint.
On the other ha... |
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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... |
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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 ... |
This question is a follow-up/variant on a previous question.
Supposing that we are trying to generate a
large number of (indistinguishable) ciphertexts of a given plaintext and want to avoid the costly exponentiation of standard re-encryption:
$c \gets c \cdot r^n \mod n^2$ (with $r \in \mathbb{Z}_n$ random)
We could p... |
I would like to know if there exists a polytime probablistic algorithm for the problem described below. It is relevant for construction of a crossvalidation-partitioning in statistics, fulfilling certain constraints.
Or is it maybe NP-complete? I don't see any direct connections to any NP-complete problem I know of.
In... |
How does the transition width of a FIR filter relate to phase delay at the output of the filter?
I have been trying to find information on the subject for days.
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 ... |
If we have complete freedom in picking the phase shifts $a_n$, the answer is clearly affirmative: for some sequence $S=\{a_n\}_{n\geq 0}$, $$ f_S(x) = \sum_{n\geq 0}\frac{\sin((2n+1)x+a_n)}{(2n+1)} $$is a continuous function (proof postponed). On the other hand such continuous function is differentiable at almost no po... |
I found in the book of Murphy, C*- Algebras and Operator Theory, the Theorem 7.1.2 :
Let A be an unital C* algebra, the semi group $V(A)$ of equivalent projections (under Murray Von Neumann equivalence) in $M_∞(A)$ is cancellative.
For the proof he proceeds as follow :
take some projection $p, q, r$ such that $[p] \opl... |
On the regularity of minimizers to degenerate functionals
1.
Dipartimento di Matematica e Informatica Università, degli Studi di Salerno Via Ponte don Melillo, 84084 Fisciano (SA), Italy
2.
Dipartimento di Statistica e Matematica per la Ricerca Economica Università, “Parthenope ”Via Medina 40, 80131 Napoli, Italy
$I(\O... |
I have to solve a set of nonlinear optimization problems in the subspace defined as the orthogonal space to a given vector.
More precisely, $$ \arg\min f(\vec x) \qquad \text{with} \qquad \vec x \cdot \vec n =0 $$
I am thinking of applying the nonlinear conjugate gradient method projecting the direction of descent but ... |
Interested in the following function:$$ \Psi(s)=\sum_{n=2}^\infty \frac{1}{\pi(n)^s}, $$where $\pi(n)$ is the prime counting function.When $s=2$ the sum becomes the following:$$ \Psi(2)=\sum_{n=2}^\infty \frac{1}{\pi(n)^2}=1+\frac{1}{2^2}+\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{3^2}+\frac{1...
Consider a random binary str... |
Oscillations and Waves Some system Executing Simple Harmonic Motion
A point mass suspended from a massless spring or placed on a frictionless horizontal plane attached with spring(fig) constitutes a linear harmonic spring pendulum.
If the point mass is pulled on one side and is released,it then executes a to and fro mo... |
For this series, find the radius of convergence and write it as a geometric series and give a formula if $x>3$
$$\sum_{n=0}^{\infty} \frac{1}{2^{n+1}}(x-3)^n$$
Now finding the radius of convergence wasn't too difficult and I'll save you guys the trouble of doing it because the interval of convergence is $ -1 = 3 - 4< x... |
Prove that: $$6 \not\left|\ \left\lfloor\frac 1 {(\sqrt[3]{28} - 3)^{n}}\right\rfloor \ (n \in Z^+)\right.$$ ($\lfloor x\rfloor$ = largest integer not exceeding $x$)
I am very bad as English and number theory, please help me
Mathematics Stack Exchange is a question and answer site for people studying math at any level ... |
A field $\phi(z)$ has the conformal weight $h$, if it transforms under $z\rightarrow z_1(z)$ as
$$ \phi(z) = \tilde{\phi}(z_1)\left(\frac{dz_1}{dz}\right)^h $$
The (classical) scaling dimension can be obtained for each field by appearing in the Lagrangian by making use of the constraint that has to be dimensionless, re... |
Isoperimetric inequalities for the Robin Laplacian
by James Kennedy (GFMUL, Universidade de Lisboa, Portugal)
Isoperimetric inequalities link partial differential equations with certain basic and fundamental geometric properties of the underlying domains on which they are defined. The typical problem is to identify the... |
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We investigate Palatini \( f( \mathcal{R}, \mathcal{L}_m, \mathcal{R}_{\mu\nu}T^{\mu\nu}) \) modified theories of gravity. As such, the metric and affine connection are treated as independent dynamical fields, and the gravitational Lagrangian is made ... |
Document Type: Original Article
Authors
1
Ivan Franko National University of Lviv, Ukraine
2
Jan Kochanowski University, Poland
Abstract
For a constant $K\geq 1$ let $\mathfrak{B}_K$ be the class of pairs $(X,(\mathbf e_n)_{n\in\omega})$ consisting of a Banach space $X$ and an unconditional Schauder basis $(\mathbf e_n... |
Hi, Can someone provide me some self reading material for Condensed matter theory? I've done QFT previously for which I could happily read Peskin supplemented with David Tong. Can you please suggest some references along those lines? Thanks
@skullpatrol The second one was in my MSc and covered considerably less than my... |
In yesterday’s post, we solved \[\frac{x}{2}\hspace{0.33em}{+}\hspace{0.33em}{3}{x}\hspace{0.33em}{=}\hspace{0.33em}{42}\]. We saw that when we first multiplied both side of the equation by 2, we had to multiply the entire left side. Let’s now look at this equation: \[\frac{{3}\hspace{0.33em}{+}\hspace{0.33em}{3}{x}}{2... |
Interferogram In physics, interference is a phenomenon in which two waves superimpose to form a resultant wave of greater or lower amplitude. Interference usually refers to the interaction of waves that are correlated or coherent with each other, either because they come from the same source or because they have the sa... |
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Measurement of electrons from beauty hadron decays in pp collisions at root √s=7 TeV
(Elsevier, 2013-04-10)
The production cross section of electrons from semileptonic decays of beauty hadrons was measured at mid-rapidity (|y| < 0.8) in the transverse momentum range 1 < pT <8 GeV/c wit... |
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Now showing items 21-27 of 27
Measurement of transverse energy at midrapidity in Pb-Pb collisions at $\sqrt{s_{\rm NN}} = 2.76$ TeV
(American Physical Society, 2016-09)
We report the transverse energy ($E_{\mathrm T}$) measured with ALICE at midrapidity in Pb-Pb collisions at ${\sqrt{s_{\mathrm {NN}}}}$ = 2.76 T... |
Ice dynamics¶
The glaciers in OGGM are represented by a depth integrated flowline model. The equations for the isothermal shallow ice are solved along the glacier centerline, computed to represent best the flow of ice along the glacier (see for example antarcticglaciers.org for a general introduction about the various ... |
In mathematics, we often write relations between $a$ and $b$ in the form $aRb$. I mean this both in the sense that we write that string to represent an abstract relation, as well as using that form to write expressions with particular relations. In almost every case, these are read as "$a$ [relation] $b$." For a few ex... |
To see that $M$ is singular, we will row-reduce the augmented matrix:\[\left[\begin{array}{rr|r} 1 & 4 & 0 \\ 3 & 12 & 0 \end{array} \right] \xrightarrow{R_2 – 3 R_1} \left[\begin{array}{rr|r} 1 & 4 & 0 \\ 0 & 0 & 0 \end{array} \right].\]The row-reduced matrix has a row of all $0$’s, and hence is singular.
(b) Find a n... |
Let $T: \R^n \to \R^m$ be a linear transformation.Suppose that the nullity of $T$ is zero.
If $\{\mathbf{x}_1, \mathbf{x}_2,\dots, \mathbf{x}_k\}$ is a linearly independent subset of $\R^n$, then show that $\{T(\mathbf{x}_1), T(\mathbf{x}_2), \dots, T(\mathbf{x}_k) \}$ is a linearly independent subset of $\R^m$.
Let $V... |
Correlation is the normalized form of covariance. For zero meaned signals, a correlation of 1 means the two signals are proportional to each other, and -1 means they are negatively proportional. A correlation of 0 means they are orthogonal, i.e. linearly independent.
From this, it is fairly easy to intuit what the answ... |
The study of the cellular response to a chemical compound is crucial to the development of new therapeutic drugs. Such an analysis is usually done by a screen experiment where the disease-specific cells (such as leukemia primary cells) are exposed to chemical compound for different concentrations. The response, in the ... |
So now that you know about matrices, we can use them to add a third way to solve a system of equations. You will need to read my previous 3 posts on matrices if you are unfamiliar with how to multiply matrices.
In the last post on System of Equations, I looked at the system:
2
x + 3 y = 51 3 x + 2 y = 49
And in my last... |
I've found Lagrange's
Sur la résolution des équations algébriques to be a very confusing and difficult read, and I think I'm starting to see why: it seems that Lagrange thinks of algebra in a much more formal/symbolic way than I'm used to. Whereas I think of a symbol $x$ as referring to a specific number (which may be ... |
Maths can be a dry subject to learn when you do not know of its many applications.This post will be about one of the many applications of trigonometry. Trigonometry is used extensively in the GPS system to determine your position. But I’d like to go a bit farther out in space and show how distances to stars are determi... |
Class "Beta"
The Beta distribution with parameters
shape1 \(= a\) and
shape2 \(= b\) has density $$f(x)=\frac{\Gamma(a+b)}{\Gamma(a)\Gamma(b)}{x}^{a-1} {(1-x)}^{b-1}% $$ for \(a > 0\), \(b > 0\) and \(0 \le x \le 1\) where the boundary values at \(x=0\) or \(x=1\) are defined as by continuity (as limits).
Keywords dist... |
Let $\mathbf{u}_1, \mathbf{u}_2, \mathbf{u}_3$ are vectors in $\R^n$. Suppose that vectors $\mathbf{u}_1$, $\mathbf{u}_2$ are orthogonal and the norm of $\mathbf{u}_2$ is $4$ and $\mathbf{u}_2^{\trans}\mathbf{u}_3=7$. Find the value of the real number $a$ in $\mathbf{u_1}=\mathbf{u_2}+a\mathbf{u}_3$.
(The Ohio State Un... |
Bad representations and homotopy groups of Character Varieties
Guerin, Clément ; ;
E-print/Working paper (2019)
Let G be a connected, reductive, complex affine algebraic group, and let Xr denote the moduli space of G-valued representations of a rank r free group. We first characterize the singularities in Xr ... [more ... |
A problem in computer vision and 3d reconstruction is getting the camera's intrinsics parameters. A common solution is to use an object in which one knows the measurements of the shape before hand, such as a checker board. The issue with this method is that it must be done every time the camera parameter's change such ... |
Can anyone give a specific example of a diffeomorphism and also of composing a function with a diffeomorphism and how this helps mathematics as a whole? In other words, how does this fit into the grand scheme of mathematics?
Thanks
Mathematics Stack Exchange is a question and answer site for people studying math at any... |
Differential and Integral Equations Differential Integral Equations Volume 22, Number 9/10 (2009), 853-880. Existence and multiplicity results for the prescribed mean curvature equation via lower and upper solutions Abstract
We discuss existence and multiplicity of bounded variation solutions of the mixed problem for t... |
I am trying to use the
nomencl package. I am following an excellentlooking guide available here:
However, I can't for the life of me get even the most basic example working despite the document building with no errors. This is the basic example:
\documentclass{article}\usepackage{nomencl}\makenomenclature\begin{documen... |
Image Dimensions Contents Describing the fields of the Canvas Properties Dialog
The user access the image dimensions in the Canvas Properties Dialog.
The Other tab
Here some properties can simply be locked (such that they can't be changed) and linked (so that changes in one entry simultaneously change other entries as ... |
Given the polynomials $g(t) = t$ and $h(t) = (t-3)^2 \in \mathbb{C}[t]$, I want to find the smallest (in terms of degree) polynomial $f(t) \in \mathbb{C}$ satisfying $f \equiv 0$ mod $g$ and $f \equiv 3$ mod $h$.
However, I've been struggling so far finding
any (not just the smallest) polynomial that satisfies these tw... |
Consider an almost periodic solution $u$ of some differential equation (autonomous, nonautonomous, ordinary or in partial derivatives). There are methods to show the existence and uniqueness of such solution if we have almost periodic functions on right-hand side and initial conditions of differential equation. I'm int... |
I had read a few papers on Laplacian Eigenmaps and have been a bit confused on 1 step in the standard derivation. First I just want to deal with the 1-D case. We are given that we want to find the vector $y\in \mathbb{R}^n$ that minimizes $y^TLy$ where L is an $n$ x $n$ symmetric real matrix (positive semidefinite).
If... |
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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 ... |
vignettes/psm.Rmd
psm.Rmd
An N-state partitioned survival model (PSM) simulates the probability that a patient is in each of N distinct health states at a given point of time when treated by a particular therapy. State membership is estimated from a set of non-mutually exclusive survival curves; for an N-state model, N... |
Wikipedia's article(https://en.wikipedia.org/wiki/Carath%C3%A9odory%27s_extension_theorem) says:
Let $R$ be a ring on $\Omega$ and $\mu: R \rightarrow [0, +\infty]$ be a pre-measure on $R$. The Carathéodory's extension theorem states that[2] there exists a measure $\mu':\sigma (R) \rightarrow [0, +\infty]$ such that $\... |
Find all possible positive integer values of c that $\frac {a^2+b^2+ab} {ab-1}$=c can take in $\mathbb N$. I know that the solutions are c=7 and c=4 but I don't know how to prove this with Vieta Jumping method.
THIS IS VIETA JUMPING. I RARELY LIE ABOUT MATHEMATICS.
$$ \frac{x^2 + xy + y^2}{xy-1} = c, $$ $$ x^2 + xy + y... |
I've read an article which features the transpose of a bounded linear operator $A$, denoted by $A^{t}$. I have no idea what is this $A^{t}$ all about. Is this actually an adjoint? Are the transpose of an operator and the adjoint of an operator the same thing? Can you please help me on this. I'm a bit confused. Kindly l... |
Some conditions for a representation $999d_1 + 1000d_2 + 1001d_3 = N$ not to be unique.
If $d_2 \ge 2$, then $(d_1+1, d_2-2, d_3+1)$ is also a valid representation of $N$. For $N$ to have a unique representation, we must have $d_2 = 0$ or $1$.
If both $d_1 \ge 1$ and $d_2 \ge 1$, then $(d_1-1, d_2+2, d_3-1)$ is a valid... |
d arithmetic mean of d roots of d equatio n 4Cos3x -4Cos2x -Cos[315pie+x]=1
...
Plz help me in these questions..............(FIITJEE Package) 1. Prob of A wining a game is 0.4 while that of B is 0.6 . What is the probability of A wining a best of 7 games? 2. If Ram and Shyam selects two numbers at ra
...
1) Find the no... |
Preprints (rote Reihe) des Fachbereich Mathematik Refine Year of publication 1998 (5) (remove)
299
We propose a new discretization scheme for solving ill-posed integral equations of the third kind. Combining this scheme with Morozov's discrepancy principle for Landweber iteration we show that for some classes of equati... |
CHAPTER OBJECTIVES
By the end of this chapter, the student should be able to:
Recognize and understand continuous probability density functions in general. Recognize the uniform probability distribution and apply it appropriately. Recognize the exponential probability distribution and apply it appropriately.
Continuous... |
Yes, I think it's expected that setting roughness = 0, combined with using point lights for illumination, leads to no visible specular highlight. The size of the highlight is infinitesimally small, so the sample points (e.g. pixel centers) almost surely miss it. The math breaks down as well, as the reflectance would be... |
I want to know what makes linear approximation so important (or useful). What I am aware of in my current state of limited understanding is that linear approximation is one of the applications of a derivative and that it is used to approximate the value of a function at a point.
Please forgive my naivete. Here I go.
Li... |
You have seen the \(\chi^{2}\) test statistic used in three different circumstances. The following bulleted list is a summary that will help you decide which \(\chi^{2}\) test is the appropriate one to use.
Goodness-of-Fit:Use the goodness-of-fit test to decide whether a population with an unknown distribution "fits" a... |
Engineering Physics - Dec 2015
First Year Engg (Semester 1)
TOTAL MARKS:
TOTAL TIME: HOURS
Solve any one question from Q1 and Q2 1 (a) Prove that in Newton's rings by reflected light the diameter of dark ring is proportional to square root of a natural number.(6 marks) 1 (b) Explain any two factors affecting the acoust... |
Introduction¶
This article will dive into a lot of the math surrounding the gradients of different maximum entropy RL learning methods. Usually we work in the space of objective functions in practice: with both policy gradients and Q-learning, we'll form an objective function and allow an autodiff library to calculate ... |
If the GPS signal is centered (carrier) at 4.309 MHz, and this is sampled at5.714 MHz, then there would be an alias copy at 5.714-4.309 = 1.405 MHz. Toacquire this signal, you would first "down-convert" the signal to baseband, or0 frequency by multiplying by $exp(-j\omega t)$ where $\omega$ is$2\pi(1.405e6)$ Hz. The re... |
We would like to make conclusions about the difference in two population proportions: \(p_1 - p_2\). We consider three examples. In the first, we compare the approval of the 2010 healthcare law under two different question phrasings. In the second application, a company weighs whether they should switch to a higher qua... |
Moving charges and magnetism Biot-Savart Law According to Biot savarts law the magnitude of the intensity of magnetic field due to a smell element “dl” is \tt dB = \frac{\mu_{o}}{4 \pi } \frac{i d l \sin \theta}{r^{2}} The magnetic field due to entire conductor is given by \tt B = \frac{\mu_{o}}{4 \pi} \int \frac{d l \... |
Let the starting number be $n$. Consider the case where $n < 10$.
$$ \begin{align}1 &\to 2 \to 4 \\2 &\to 4 \\3 &\to 6 \to 12 \to 24 \to 2 \to 4\\4 \\5 &\to 10 \to 1 \to 2 \to 4 \\6 &\to 12 \to 24 \to 2 \to 4\\7 &\to 14 \to 1 \to 2 \to 4\\8 &\to 16 \to 32 \to 64 \to 6 \to 12 \to 24 \to 2 \to 4\\9 &\to 18 \to 36 \to 72 ... |
Consider the integer lattice in $2d$, namely the set $\mathbb{Z}^2 = \{(x,y): x,y\in \mathbb{Z}\}$, and let $u:\mathbb{Z}^2 \to \mathbb{R} $ be a function defined on some bounded subset of $\mathbb{Z}^2$. The discrete (graph) Laplace of $u$, denote it by $\Delta^1$, at point $(x,y)$ is defined as $$ \tag{1} \Delta^1 u(... |
So now we know that \[
{x}^{3} \] is shorthand math notation for x × x × x. In exponents, the x is called the base and the 3 is called the exponent or the power of x. Anything to the power of 2 is referred to as squared and anything to the power of 3 is referred to as cubed. These terms come from the formulas for findi... |
Using the main idea of one of the proofs of the famous
Dehn's tiling problem (see for example here), assume that such a cutting of a square is possible.
Let $S$ the unit square, and $S=\cup_{j=1}^n R_j$ and $$[0,r]\times[0,1/r]=T=\cup_{j=1}^n R_j',$$ were $R'_j$ is produced be translating and/or rotating by $\pi/2$ the... |
My question is related to the following OP
How can I evaluate $\lim_{n\rightarrow\infty} \frac{n\cdot 2^n }{3^n}$?
The answer is $0$. But how? I've searched some links but all of them just quite write the answer and no one shows the procedure.
In order to give an answer to the above mentioned OP, I've presumed that the... |
Graph query languages typically feature graph pattern matching. This is the process of finding all matches for a given graph pattern. Graph pattern matching can (partly) be used for schema-instance consistency checking or validation as schema recognition (schema view). Assume a set of graph patterns, together forming t... |
MathJax
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I just came across the post on the Facebook page Art of Mathematics, which says:
13+53+33=153\textcolor{#20A900}{1}^3 + \textcolor{#EC7300}{5}^3 + \textcolor{#3D99F6}{3}^3 = \textcolor{#20A900}{1}\textcolor{#EC7300}{5}\textcolor{#3D99F6}{3}13+53+33=153
163+503+33... |
I derived a form of the gamma function (see here) using some calculus and neat little tricks.
Anyways, define the factorial with two conditions:
$n!=n(n-1)!$
$1!=1$
From this, you can get the factorial for any integer value, but it does nothing to show you fractional values, at least not yet.
Define a function $f(x):=\... |
Let be B(z) the exponential generating function for the number $b_n$ of different rooted unordered binary trees with exactly n leaves labeled only at their leaves (so the internal nodes are unlabeled). Then it's a well know result that $b_n = 1\cdot3\cdot\ldots\cdot(2n-3)=(2n-3)!!$ (see eg. Schröder "Vier combinatorisc... |
I've been reading some code which setups a ray tracer and I've realized I've a doubt regarding what's a screen and what's a window in this context. Here's the relevant code using Qt:
...void CCanvas::paint(){ // check if we have something to draw on if (!image) return; // camera position Point3d camera (0.0, 0.0, 0.0);... |
The Lane-Riesenfeld algorithm subdivides the control polygon of a B-spline to create a new control polygon with the same limit spline. It's made up of two steps: first, duplicating all of the control points $P_i$ into $P^\prime_{2i}$ and $P^\prime_{2i+1}$; then, moving each point to the midpoint between it and the next... |
Main/General Question
Let $L$ be a language. Define the languages $L_i$ with $L_0 = L$ and $$L_i = \{xwy : xy \in L_{i-1}, w \in L\}$$ for $i \geq 1$. Consider $\hat{L} = \bigcup L_i$. So, we repeatedly "embed" $L$ into itself to obtain $\hat{L}$.
Has $\hat{L}$ been studied? Does it have a name?
Examples/Motivation
As ... |
Constraining the Sea Quark Distributions Through W$^\pm$ Cross Section Ratio Measurements at STAR
Pre-published on: 2019 July 24
Published on: 2019 October 04
Abstract
Over the past several years, parton distribution functions (PDFs) have become more precise. However there are still kinematic regions where more data ar... |
Short answer: No. There's no reason to expect that this should be the case.
My standard reference for classical thermodynamics is Callen's
Thermodynamics and an Introduction to Thermostatistics, 2nd ed. Ch. 11 is relevant here.
Planck's statement of the third law is, according to Callen, "The $T=0$ isotherm coincides w... |
We compute\begin{align*}(1-ba)^2&=(1-ba)(1-ba)=1-ba-ba+b\underbrace{ab}_{=1}a\\&=1-ba-ba+ba=1-ba.\end{align*}Thus, we have $(1-ba)^2=1-ba$, and hence $1-ba$ is idempotent.
(b) Prove that $b^n(1-ba)$ is nilpotent for each positive integer $n$.
As a lemma, we show that $(1-ba)b=0$.To see this, we calculate\begin{align*}(... |
Is the Map $T (f) (x) = f(x) – x – 1$ a Linear Transformation between Vector Spaces of Polynomials?
Problem 674
Let $\mathrm{P}_n$ be the vector space of polynomials of degree at most $n$. The set $B = \{ 1 , x , x^2 , \cdots , x^n \}$ is a basis of $\mathrm{P}_n$, called the standard basis. Let $T : \mathrm{P}_4 \righ... |
First, I think your definition of $H_{n}$ does not agree with Newman's definition. Newman says the following: "Let $H_{n} \subset G_{n}$ be the set of functions of $G_{n}$ with non-negative valence at all parabolic points of $Q_{n}$ other than $\tau = i\infty$." Here $G_{n}$ is the set of modular functions that are exp... |
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\\ ... |
Also we can make the following.
Let $x_1=x_2=...=x_{n-1}=0$ and $x_n=1$.
Hence, we get a value $1$ and it's a maximal value because for this we need to probe that$$\sum_{i=1}^nx_i^2+\sqrt{\prod_{i=1}^nx_i}\leq\left(\sum_{i=1}^nx_i\right)^2,$$which is true by AM-GM.
Indeed, let $\prod\limits_{i=1}^nx_i=w^n$, where $w\ge... |
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