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In signal processing, cross-correlation is a measure of similarity of two waveforms as a function of a time-lag applied to one of them. This is also known as a sliding dot product or sliding inner-product. It is commonly used for searching a long signal for a shorter, known feature. It has applications in pattern recog... |
Short answer: if $\frac 1 \pi$ is a normal number in base $2$, then the series converges in measure (but not necessarily converges in the usual sense). However, the normality of $\pi$ and $\frac 1 \pi$ has not yet been proved (and it's not known could it be proved). I didn't attempt to prove the reverse, that from conv... |
In a textbook I'm reading, the author states without proof that $$ \zeta(s,mz) = \frac{1}{m^{s}} \sum_{k=0}^{m-1} \zeta \left(s,z+\frac{k}{m} \right), \tag{1}$$ where $\zeta(s,z) $ is the Hurwitz zeta function
Supposedly, this isn't hard to prove. But is it possible to prove $(1)$ using simply the series definition of ... |
In machine learning, the perceptron is an algorithm for supervised learning of binary classifiers.
Its much complex than just drawing some graph and fitting a line to divide these data. I should tell you that you gone entirely wrong about the core concept.
Our brain are capable of solving complex problem, few of which ... |
The ancient
Chinese mathematics ranged from 1400 BC (Shang dynasty) to 6th-century AD. In this period, a positional number system with the basis $10$ was invented, which was equally revolutionary with respect to calculations as the sexagesimal system used by the Sumers and the Babylonians. The decimal system is still u... |
If for each node of a tree, the longest path from it to a leaf node is no more than twice longer than the shortest one, the tree has a red-black coloring.
Here's an algorithm to figure out the color of any node
n
if n is root,
n.color = black
n.black-quota = height n / 2, rounded up.
else if n.parent is red,
n.color = ... |
Let$\ \sigma(n)$ be the sum-of divisors function, with the divisors raised to$\ 1$. If the Riemann Hypothesis is false, Robin proved there are infinitely many counterexamples to the inequality$$\ \sigma(n)<e^\gamma n \log \log n.$$ There are 27 small counterexamples, but the conjecture is that it holds for every$\ n>50... |
As a result of the conservation of charge the current is always constant in a circuit (continuity equation).
We know by Ohm’s law that the current density is proportional to the applied electric field $$\mathbf j=\sigma \mathbf E$$ where $\sigma$ is called the conductivity. Since we apply a constant voltage, the electr... |
Does it make sense to say that the quantum field of a photon is exactly proportional to the photon's electromagnetic field?
\begin{align} \bar{\Psi} = \dfrac{\bar{E}+i\bar{B}}{\sqrt{\int (E^2+B^2)dV}} \end{align}
Physics Stack Exchange is a question and answer site for active researchers, academics and students of phys... |
It is often claimed that spin is a purely quantum property with no classical analogue. However (as was very recently pointed out to me), there is a classical analogue to spin whose action is given (in M. Stone, "Supersymmetry and the quantum mechanics of spin", Nucl. Phys. B 314 (1986), p. 560) by $$S = J\left[\int_\Ga... |
Question:
In a double-slit experiment, the distance between the slits is {eq}0.2\ mm {/eq}, and the distance to the screen is {eq}150\ cm {/eq}. What wavelength (in nm) is needed to have the intensity at a point {eq}1\ mm {/eq} from the central maximum on the screen be {eq}80\% {/eq} of the maximum intensity?
Double Sl... |
As open problems of the month, we state here the two questions discussed in our recent guest post by Oded Goldreich:
Open Problem 1 (obtaining a one-sided error reduction): The reduction from testing affinity of a subspace to that of testing affinity of a function has two-sided error probability. We wonder whether a on... |
The brachistochrone problem is a very famous problem in the history of physics which was first solved by an excellent mathematician named Jean Bernoulli. He posed this problem as a challenge to the greatest mathematicians of Europe during the period of the Renaissance. He stated the problem as such:
We are given two fi... |
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Now showing items 1-10 of 26
Production of light nuclei and anti-nuclei in $pp$ and Pb-Pb collisions at energies available at the CERN Large Hadron Collider
(American Physical Society, 2016-02)
The production of (anti-)deuteron and (anti-)$^{3}$He nuclei in Pb-Pb collisions at $\sqrt{s_{\rm NN}}$ = 2.76 TeV has ... |
This question already has an answer here:
Let $\{x_n\}$ be a bounded sequence such that every convergent subsequence converges to $L$. Prove that $$\lim_{n\to\infty}x_n = L.$$
The following is my proof. Please let me know what you think.
Prove by contradiction: ($A \wedge \lnot B$)
Let {$x_n$} be bounded, and every con... |
April has been kind to us, providing us with a trio of new papers in sublinear algorithms. Also, in case you missed them, be sure to check out Oded Goldreich’s guest post and the associated open problem.
Sparse Fourier Transform in Any Constant Dimension with Nearly-Optimal Sample Complexity in Sublinear Time, by Micha... |
So there are a bunch of "pictures" (that's the technical term!) of quantum mechanics, agreeing in the broad perspective that:
There is some vector space $\{|\phi\rangle\}$ over the field $\mathbb C$ and its canonical dual space $\{\langle\phi|\},$ such that the dual operation $\mathcal D$ maps $$\mathcal D\Big(a |\alph... |
Many optimization procedures are based upon successive approximation: they start with a value of $x$, and try to successively refine $x$ to move it closer and closer to the optimum. For instance, hill climbing and gradient ascent both have this structure.
You can use this structure to solve your problem. Let $x_t$ be t... |
I was wondering: if I were given a matrix $A$, I could calculate its Jordan canonical form. If I considered then $A^2$, I could say that if $\lambda$ is an eigenvalue of $A$, then $\lambda^2$ is an eigenvalue of $A^2$. However I couldn't say anything about the Jordan canonical form of $A^2$. Are there any connections b... |
Can't get integration right
05-31-2016, 12:16 PM (This post was last modified: 06-01-2016 04:23 PM by Marcio.)
Post: #1
Can't get integration right
Hello all,
Would you be king enough as to point out what I am doing wrong with this very simple integration?
\[t = \int_0^{0.515}\frac{1}{0.000273\times exp\left[16306\time... |
Coupling is the way biology makes reactions that 'want' to happen push forward desirable reactions that
don't want to happen. Coupling is achieved through the action of enzymes — but in a subtle way. An enzyme can increase the rate constant of a reaction. However, it cannot change the ratio of forward to reverse rate c... |
To be specific, consider a closed system of $N$ spinless particles described by the Schrodinger equation$$i\frac{d}{dt}\psi(t,\mathbf{x}_1,\mathbf{x}_2,...,\mathbf{x}_N)=H\psi(t,\mathbf{x}_1,\mathbf{x}_2,...,\mathbf{x}_N)\tag{1}$$where the Hamiltonian $H$ is $$H = \frac{\mathbf{P}_1^2}{2m_1} + \frac{\mathbf{P}_2^2}{2m_... |
Absolute Value Function [math]|x| =\left\{\begin{array}{ll}x \quad\textrm{for} \quad x \geq 0\\-x \quad\textrm{for}\quad x \lt 0\end{array}\right.[/math] Example(s): |-3|=3 [math]|(3,0,4)|=\sqrt{3^2+0^2+4^2}=5[/math] [math] |3+i4|=\sqrt{3^2+4^2}=5 [/math] Counter-Example(s): References 2016 (Wikipedia, 2015) ⇒ http://e... |
Chemical Potential The Chemical Potential: Simple Thermodynamics of Chemical Processes
The chemical potential $\mu$, which is simply the free energy per molecule, is probably the most useful thermodynamic quantity for describing and thinking about chemical systems. Because $\mu$ represents an energy for one molecule, i... |
Probability is the extent to which an event is likely to occur, measured by the ratio of the favourable cases to the whole number of cases possible.
When it comes to GMAT exam, all you have to do is make all the cases and select the favourable one.\(Probability = \frac{Number \; of \; Favourable \; Case}{Total \; Numbe... |
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1. Measurement of the top quark mass with lepton+jets final states using $$\mathrm {p}$$ p $$\mathrm {p}$$ p collisions at $$\sqrt{s}=13\,\text {TeV} $$ s=13TeV
The Europ... |
Time Limit: 2 Seconds
Memory Limit: 65536 KB
After a hard struggle, DreamGrid was finally admitted to a university. Now he is having trouble calculating the limit of the ratio of two polynomials. Can you help him?
DreamGrid will give you two polynomials of a single variable \(x\) (eg. x^2-4x+7) or constant integers, an... |
№ 8
All Issues Tri-additive maps and local generalized $(α,β)$-derivations Abstract
Let $R$ be a prime ring with nontrivial idempotents. We characterize a tri-additive map $f : R^3 \rightarrow R$ such that $f(x, y, z) = 0$ for all $x, y, z \in R$ with $xy = yz = 0$. As an application, we show that, in a prime ring with... |
Probability Seminar Spring 2019 Thursdays in 901 Van Vleck Hall at 2:25 PM, unless otherwise noted. We usually end for questions at 3:15 PM.
If you would like to sign up for the email list to receive seminar announcements then please send an email to join-probsem@lists.wisc.edu
January 31, Oanh Nguyen, Princeton
Title:... |
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 ... |
Simple answer: If there does exist a more efficient algorithm that runs in $O(n^{\delta})$ time for some $\delta < 2$, then the strong exponential time hypothesis would be refuted.
We will prove a stronger theorem and then the simple answer will follow.
Theorem: If we can solve the intersection non-emptiness problem fo... |
Let \( A \) be any real square matrix (not necessarily symmetric). Prove that: $$ (x'A x)^2 \leq (x'A A'x)(x'x) $$
The key point in proving this inequality is to recognize that \( x'A A'x \) can be expressed as vector norm of \( A'x \).
Proof:
If \( x=0 \), then the inequality is trival.
Suppose \( x \neq 0 \).
\( \fra... |
Difference between revisions of "NTS ABSTRACT"
(→Dec 17)
(→Dec 17)
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−
In the original Gross-Zagier formula and Zhang's extension to Shimura curves, the modularity of the generating function [[File:
+
In the original Gross-Zagier formula and Zhang's ex... |
Consider for some $0 < \alpha \leq 1$ the space functions $x:[0,1] \to \mathbb{R}^n$ such that $x(0) = 0$ and $\sup_{s,t} \frac{\|f(t)-f(s)\|}{|t-s|^{\alpha}}$ is finite.
There are at least two reasonable norms defined on this space. The first is the Hölder norm which is just the supremum above. Another is the $1/\alph... |
Guessing Game Problem 406
We are trying to find a hidden number selected from the set of integers {1, 2, ...,
n} by asking questions. Each number (question) we ask, we get one of three possible answers:
"Your guess is lower than the hidden number" (and you incur a cost of
a), or
"Your guess is higher than the hidden nu... |
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Now showing items 1-9 of 9
Production of $K*(892)^0$ and $\phi$(1020) in pp collisions at $\sqrt{s}$ =7 TeV
(Springer, 2012-10)
The production of K*(892)$^0$ and $\phi$(1020) in pp collisions at $\sqrt{s}$=7 TeV was measured by the ALICE experiment at the LHC. The yields and the transverse momentum spectra $d^2 ... |
eQuant aims at providing a fast and easy-to-use service for assessing protein model quality. In addition, lightweight visualizations help to quickly catch the information that is of most importance to the user. If users are interested in inspecting and further processing the made assessments, raw output data is also av... |
I am familiar with the
\flushright and
\hfill commands for positioning text to the far right of the page. However throughout my document I am using the terms
(x\rightarrow\infty) on many lines and I wish to send them all to the far right of the page so that they line up nicely. Any ideas?
I am familiar with the
If you'... |
Although machine learning is great for shape classification, for shape recognition, we must still use the old methods. Methods such as Hough Transform, and RANSAC.
In this post, we’ll look into using Hough Transform for recognizing straight lines. The following is taken from E. R. Davies’ book,
Computer Vision: Princip... |
1. Definition
We have seen that a matrix $A$ multiplying a vector $\vec{x}$ is in fact a linear transformation.
We now are interested in the vector $\vec{x}$ whose image $\vec{y}$ (under the linear transformation) is linearly dependent to itself, namely :
$\lambda$ and $\vec{x}$ satisfying $(1)$ are called respectively... |
Introduction to Binary
concept
In the digital world we deal exclusively with "on" and "off" as our only two states. This makes a number system with only two numbers a natural choice. In this topic we'll cover the binary number system, what it is and how to convert between it and our usual decimal numbers.
Our usual num... |
If $B$ is a square matrix whose entries are integers, then the determinant of $B$ is an integer.
The inverse matrix of $A$ can be computed by the formula\[A^{-1}=\frac{1}{\det(A)}\Adj(A).\]
Proof.
Let $I$ be the $n\times n$ identity matrix.
$(\implies)$: If $A^{-1}$ is an integer matrix, then $\det(A)=\pm 1$
Suppose th... |
Equivalences:
The non-orthogonal vectors problem (as defined above) for a set $S$ of $n$ Boolean
vectors each of length $d$ and a positive integer $k$ is equivalent
the following:
Finding a $2$ by $k$ submatrix of 1's in a given $n$ by $d$ Boolean matrix.
Finding a $\mathrm{K}_{2,k}$ complete subgraph in a given bipart... |
There is at Least One Real Eigenvalue of an Odd Real Matrix Problem 407
Let $n$ be an odd integer and let $A$ be an $n\times n$ real matrix.
Prove that the matrix $A$ has at least one real eigenvalue. Proof 1.
Let $p(t)=\det(A-tI)$ be the characteristic polynomial of the matrix $A$.
It is a degree $n$ polynomial and th... |
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 ... |
I am interested in deriving the convergence rate of the smallest eigenvalue of a sequence of random matrices with diverging dimension. More precisely, let $W_n(r)$ represent an $n$-dimensional standard brownian motion at time $r$, and define $\lambda_1(A)$ as the minimum eigenvalue of A. Then, I would like to know how ... |
Fibonacci golden nuggets Problem 137
Consider the infinite polynomial series $A_F(x) = x F_1 + x^2 F_2 + x^3 F_3 + \dots$, where $F_k$ is the $k$th term in the Fibonacci sequence: $1, 1, 2, 3, 5, 8, \dots$; that is, $F_k = F_{k-1} + F_{k-2}$, $F_1 = 1$ and $F_2 = 1$.
For this problem we shall be interested in values of... |
Well-posedness and ill-posedness for the 3D generalized Navier-Stokes equations in $\dot{F}^{-\alpha,r}_{\frac{3}{\alpha-1}}$
1.
School of Mathematics and Statistics, Jiangsu Normal University, Xuzhou, Jiangsu 221116, China
2.
School of Mathematics and Statistics, Central China Normal University, Wuhan, Hubei 430079, C... |
Special isosceles triangles Problem 138
Consider the isosceles triangle with base length, $b = 16$, and legs, $L = 17$.
By using the Pythagorean theorem it can be seen that the height of the triangle, $h = \sqrt{17^2 - 8^2} = 15$, which is one less than the base length.
With $b = 272$ and $L = 305$, we get $h = 273$, w... |
I am your Father!
Time Limit: 2000/1000 MS (Java/Others)
Memory Limit: 65536/65536 K (Java/Others)
Description
> Darth Vader: "Obi-Wan never told you what happened to your father."
> > Luke Skywalker: "He told me enough! He told me you killed him!" > > Darth Vader: "No, I am your father." > > — Vader and Luke, on Cloud... |
And I think people said that reading first chapter of Do Carmo mostly fixed the problems in that regard. The only person I asked about the second pset said that his main difficulty was in solving the ODEs
Yeah here there's the double whammy in grad school that every grad student has to take the full year of algebra/ana... |
Learning Objectives
Explain the following laws within the Ideal Gas Law
The atmosphere of Venus is markedly different from that of Earth. The gases in the Venusian atmosphere are \(96.5\%\) carbon dioxide and \(3\%\) nitrogen. The atmospheric pressure on Venus is roughly 92 times that of Earth, so the amount of nitroge... |
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math-ph
Change to browse by: References & Citations Bookmark(what is this?) Mathematical Physics Title: Covariant Hamiltonian Field Theories on Manifolds with Boundary: Yang-Mills Theories
(Submitted on 1 Jun 2015 (v1), last revised 9 May 2016 (this version, v2))
Abstract: The multisymplectic fo... |
Theorem 2
An nxn matrix A is diagonalizable if and only if A has n linearly independent eigenvectors
Proof
Let A be diagonalizable
Thus, $A = PDP^{-1}$ for some invertible matrix P and diagonal matrix D
$P = \begin{bmatrix} \vec{v}_1&\vec{v}_2&\vec{v}_3,...,\vec{v}_n \end{bmatrix}$ and $D = \begin{bmatrix} d_1&0&0&...&... |
The problem of simulating a multi-path channel where the delays are not integer multiples of the sampling time is not trivial. The simplest method is just to round each tap to the nearest sample, however this is not what happens in reality:
Consider a discrete-time transmit signal $s[n]$ which is transmitted over a rea... |
I should begin by apologizing for rambling on a bit. You've asked questions that are closely related to things I've been thinking about, but I don't know all the literature well, and I clearly haven't figured out how to say things concisely.
I will write $E_d$ for the operad (in spaces) of little $d$-disks, and $G_d$ (... |
Authors: Arnautov Vladimir Abstract
Let $R$ be an associative ring, $S$ is such an element from $R$ that $rs\ne 0$ and $sr\ne 0$ for any $0\ne r\in R$ and $s^kR\subseteq Rs$ for some natural number $k$; $S=\{s^i | i=1,2,\dots \}$. Pseudonorm $\zeta$ of ring $R$ we may extend to pseudonorm on rings quotients $R_s$ of ri... |
3-Uniform Friendship Hypergraphs by Derrick Stolee A very brief welcome to EXCILL2 participants. Thanks for visiting!
Today we discuss On a question of Sós about 3-uniform friendship hypergraphs by Hartke and Vandenbussche. These authors presented several new examples of friendship hypergraphs exhibiting a property tha... |
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Now showing items 1-9 of 9
Production of $K*(892)^0$ and $\phi$(1020) in pp collisions at $\sqrt{s}$ =7 TeV
(Springer, 2012-10)
The production of K*(892)$^0$ and $\phi$(1020) in pp collisions at $\sqrt{s}$=7 TeV was measured by the ALICE experiment at the LHC. The yields and the transverse momentum spectra $d^2 ... |
The following key enhancement to DES was proposed in order to increase the complexity of finding the keys by exhaustive search.
$$\text{DES}^V_{k,k_1}(M)=\text{DES}_k(M)\oplus k_1$$
where the keys’ lengths are $|k|=56$ and $|k_1|=64$ ($k_1$ has the same length as the block length). Show that this proposal do not increa... |
This article is all about the basics of probability. There are two interpretations of a probability, but the difference only matters when we will consider inference.
Frequency The degree of belief Axioms of Probability
A function \(P\) which assigns a value \(P(A)\) to every event \(A\) is a
probability measure or prob... |
Out of the following real numbers, which is the coolest? e (2.7182818...) (38%, 6 Votes) Zero (0) (25%, 4 Votes) pi (3.14159....) (25%, 4 Votes) One (1) (13%, 2 Votes) Golden Ratio (1.61803...) (0%, 0 Votes)
Total Voters:
16
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Some definitions:
pi, also written $\pi$ is defined as the ratio of the circumferen... |
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J/Ψ production and nuclear effects in p-Pb collisions at √sNN=5.02 TeV
(Springer, 2014-02)
Inclusive J/ψ production has been studied with the ALICE detector in p-Pb collisions at the nucleon–nucleon center of mass energy √sNN = 5.02TeV at the CERN LHC. The measurement is performed i... |
September 16th, 2017, 07:05 PM
# 1
Newbie
Joined: Sep 2017
From: San Diego
Posts: 8
Thanks: 0
If P>= 5 is a prime number, then p^2 +2 is composite.
I have seen outlines of the proof, and I tried to fill in the reasons why. Are they right?
If p>=5 is a prime number, then p^2 +2 is composite.
Proof: Suppose p>=5 is a pri... |
I know I promised a post on regression, but then I realized I only have a shallow understanding of Boosting and AdaBoost. So I biked to the nearest public library, when to the index cards, search for ‘Boost’ and after perusing through hundreds of self-help books, I found the greatest resource on AdaBoost: “How to Boost... |
Nearest Neighbour Distance Distribution Function of a Three-Dimensional Point Pattern
Estimates the nearest-neighbour distance distribution function \(G_3(r)\) from a three-dimensional point pattern.
Usage
G3est(X, ..., rmax = NULL, nrval = 128, correction = c("rs", "km", "Hanisch"))
Arguments X
Three-dimensional point... |
Idempotent Matrices are Diagonalizable Problem 429
Let $A$ be an $n\times n$ idempotent matrix, that is, $A^2=A$. Then prove that $A$ is diagonalizable.
The second proof proves the direct sum expression as in proof 1 but we use a linear transformation.
The third proof discusses the minimal polynomial of $A$.
Range=Imag... |
First of all, it is clear that $\Z[\sqrt{2}]$ is an integral domain since it is contained in $\R$.
We use the norm given by the absolute value of field norm.Namely, for each element $a+\sqrt{2}b\in \Z[\sqrt{2}]$, define\[N(a+\sqrt{2}b)=|a^2-2b^2|.\]Then the map $N:\Z[\sqrt{2}] \to \Z_{\geq 0}$ is a norm on $\Z[\sqrt{2}... |
Let \( A \) be any real square matrix (not necessarily symmetric). Prove that: $$ (x'A x)^2 \leq (x'A A'x)(x'x) $$
The key point in proving this inequality is to recognize that \( x'A A'x \) can be expressed as vector norm of \( A'x \).
Proof:
If \( x=0 \), then the inequality is trival.
Suppose \( x \neq 0 \).
\( \fra... |
We have a, b ∈ R \ Q, a < b.A = {x ∈ Q: a < x < b}
Show that A is clopen(open and close) in Q
i have being trying to solve this problem in the last 2hours
i need some hints or examples
thank you in advance
Assuming you give $\displaystyle \mathbb{Q}$ the topology inherited from $\displaystyle \mathbb{R}$ then open sets... |
I know there's a thread similar to this one here, but the OP is asking the reverse of what I'm trying to find here. I've done some research on the web with very few sources coming up with actual solutions to this problem. What techniques are used to give an approximation of an FIR filter given one or more IIR filters w... |
In the introduction to chapter VIII of Dieudonné's
Foundations of Modern Analysis (Volume 1 of his 13-volume Treatise on Analysis), he makes the following argument:
Finally, the reader will probably observe the conspicuous absence of a time-honored topic in calculus courses, the “Riemann integral”. It may well be suspe... |
2019-09-04 12:06
Soft QCD and Central Exclusive Production at LHCb / Kucharczyk, Marcin (Polish Academy of Sciences (PL)) The LHCb detector, owing to its unique acceptance coverage $(2 < \eta < 5)$ and a precise track and vertex reconstruction, is a universal tool allowing the study of various aspects of electroweak an... |
The subgradient algorithm for minimizing a convex function $f(x)$ is the update rule $$ x(t+1) = x(t) - \alpha(t) d(t)$$ where $d(t)$ is any subgradient of $f(x)$ at $x(t)$ and $\alpha(t)$ is a decaying stepsize. Choosing $\alpha(t) = 1/\sqrt{t}$, one usually obtains the bound $$ f \left( \frac{\sum_{j=1}^t \alpha(j) x... |
Since $U$ is not contained in $V$, there exists a vector $\mathbf{u}\in U$ but $\mathbf{u} \not \in V$.Similarly, since $V$ is not contained in $U$, there exists a vector $\mathbf{v} \in V$ but $\mathbf{v} \not \in U$.
Seeking a contradiction, let us assume that the union is $U \cup V$ is a subspace of $\R^n$.The vecto... |
In a previous post I attempted to use the katex plugin to render an old post instead of using Mathjax. It seems that was not actually rendered with KaTex, but (I think) it was rendered with the latex keyword handling in the Jetpack plugin, which I also had installed. I’ve customized the katex plugin I have installed to... |
The Polynomial Rings $\Z[x]$ and $\Q[x]$ are Not Isomorphic Problem 494
Prove that the rings $\Z[x]$ and $\Q[x]$ are not isomoprhic.
Proof.
We give three proofs.
The first two proofs use only the properties of ring homomorphism.
The third proof resort to the units of rings.
If you are familiar with units of $\Z[x]$, th... |
October 25th, 2014, 09:15 AM
# 1
Newbie
Joined: Sep 2014
From: USA
Posts: 8
Thanks: 0
Finding the area inside a cardiod
I messed up towards the end but can't find my error.
$\displaystyle 2[1/2∫ (π/2) to (-π/2) , (1 -2sin(θ) + sin^2(θ))$d(θ)
I made two integrals
$\displaystyle 2[1/2∫(π/2) to (-π/2), (1-sin(θ))] dθ+ 2[1... |
It is often said [e.g. Atiyah, "Bordism and Cobordism" (1961)] that the Thom spectrum $MSO(i)$ represents oriented cobordism, in the following sense: \begin{eqnarray} MSO^n(X,Y) &:=& \lim_{i \rightarrow \infty} \langle \Sigma^{i-n}(X/Y), MSO(i) \rangle\\ &=& \lim_{i \rightarrow \infty} \langle X/Y, \Omega^{i-n} MSO(i) ... |
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Now showing items 1-1 of 1
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 ... |
The question I’d like to explore in this post is how Ampere’s law, the relationship between the line integral of the magnetic field to current (i.e. the enclosed current)
\begin{equation}\label{eqn:flux:20} \oint_{\partial A} d\Bx \cdot \BH = -\int_A \ncap \cdot \BJ, \end{equation} generalizes to geometric algebra wher... |
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This is Calvin Lin's current status:
Gödel has proved it that there is no logical foundation of Mathematics. Discuss.
Gödel has proved it that there is no logical foundation of Mathematics. Discuss.
So, discuss!
Note by Mursalin Habib 5 years, 5 months ago
Easy M... |
I would like to create a math formula as follows. How do I write it in LaTeX?
I recommend reading one of the guides listed here: What are good learning resources for a LaTeX beginner?.
\documentclass{article}\usepackage{amsmath}\begin{document}\[f\sim\mathcal{GP}(\mu(x),K(\mathbf{x},\mathbf{x}';\theta))\] \end{document... |
May 9th, 2017, 09:41 AM
# 1
Newbie
Joined: May 2017
From: California
Posts: 1
Thanks: 0
Green's Theorem and Line Integrals
Hey Everybody,
So I'm doing some line integrals and checking my work with Green's Theorem, but I'm not getting the same answer. Here's the problem:
Evaluate the line integral F · dr over C, where C... |
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 ... |
Regularity in Campanato spaces for solutions of fully nonlinear elliptic systems
1.
Dipartimento di Informatica, Matematica, Elettronica e Trasporti, Università degli Studi Mediterranea di Reggio Calabria, Loc. Feo di Vito, I-89060 Reggio Calabria, Italy
2.
Dipartimento di Matematica “L. Tonelli”, Università di Pisa, L... |
Assume we are given smooth functions $f, g: U \to \mathbb{C}$, where $0 \in U \subset \mathbb{R}^n$ is open and $0 \in g^{-1}(0) \subset \{x_n = 0\}$. Furthermore, suppose that $\nabla g \neq 0$ on the set $g^{-1}(0)$ and let $h = \frac{f}{g}$ defined on $U \setminus g^{-1}(0)$. Assume that all the partial derivatives ... |
We met some common types of inductive argument back in Chapter 2. Now that we know how to work with probability, let’s use what we’ve learned to sharpen our understanding of how those arguments work.
Generalizing from observed instances was the first major form of inductive argument we encountered. Suppose you want to ... |
First Order Transient and Steady State Analysis
concept
When analysing a control system we want to know how it responds to the inputs we're likely to give it when it's running. Unfortunately we often don't know ahead of time exactly what the inputs are going to be. For instance a thermostat system that uses a thermomet... |
(a) Prove that $S=\{x^2\mid x\in G\}$ is a subgroup of $G$.
Consider the map $\phi:G \to G$ defined by $\phi(x)=x^2$ for $x\in G$.Then $\phi$ is a group homomorphism. In fact, for any $x, y \in G$, we have\begin{align*}\phi(xy)=(xy)^2=x^2y^2=\phi(x)\phi(y)\end{align*}as $G$ is an abelian group.
By definition of $\phi$,... |
Continuity of cost functional and optimal feedback controls for the stochastic Navier Stokes equation in 2D
Department of Mathematics, University of Southern California, Los Angeles, CA 90089, USA
We show the continuity of a specific cost functional $J(\phi) =\mathbb{E} \sup_{ t \in [0, T]}(\varphi(\mathcal{L}[t, u_\ph... |
作者：B ANANTHANARAYAN , IRINEL CAPRINI , I SENTITEMSU IMSONG 来源：[J].Pramana(IF 0.562), 2012, Vol.79 (5), pp.1317-1320Springer 摘要：Abstract(#br)Analyticity and unitarity techniques are employed to estimate Taylor coefficients of the pion electromagnetic form factor at t = 0 by exploiting the recently evaluated two-pion con... |
№ 8
All Issues Volume 55, № 9, 2003
Ukr. Mat. Zh. - 2003. - 55, № 9. - pp. 1155-1166
We prove the holomorphy of a function that, at every point, preserves either angles or dilations with respect to a certain set.
Ukr. Mat. Zh. - 2003. - 55, № 9. - pp. 1167-1177
In the case of approximation of periodic functions in the ... |
Consider the action of the group $G$ on the left cosets $G/H$ by left multiplication.
Proof.
Let $H$ be a subgroup of index $p$.Then the group $G$ acts on the left cosets $G/H$ by left multiplication.
It induces the permutation representation $\rho: G \to S_p$.
Let $K=\ker \rho$ be the kernel of $\rho$.Since $kH=H$ for... |
Difference between revisions of "Probability Seminar"
(→Tuesday , May 7, Van Vleck 901, 2:25pm, Duncan Dauvergne (Toronto))
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Title: The directed landscape
+
Title: The directed landscape
Abst... |
Let \( A \) be any real square matrix (not necessarily symmetric). Prove that: $$ (x'A x)^2 \leq (x'A A'x)(x'x) $$
The key point in proving this inequality is to recognize that \( x'A A'x \) can be expressed as vector norm of \( A'x \).
Proof:
If \( x=0 \), then the inequality is trival.
Suppose \( x \neq 0 \).
\( \fra... |
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... |
K Babu Joseph
Articles written in Pramana – Journal of Physics
Volume 4 Issue 1 January 1975 pp 1-18 Mechanics
A new analysis of the nature of the solutions of the Hamilton-Jacobi equation of classical dynamics is presented based on Caratheodory’s theorem concerning canonical transformations. The special role of a prin... |
R K Bhowmik
Articles written in Pramana – Journal of Physics
Volume 55 Issue 3 September 2000 pp L471-L478 Rapid Communication
Excited states of
63Cu were populated via the $^{52}{\rm Cr} + {}^{16}{\rm O}$ (65 MeV) reaction using the gamma detector array equipped with charged particle detector array for reaction channe... |
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