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can someone please help me with a trivial question?
Write $-3i$ in polar coordinates.
So $z=a+bi=rcis\theta$ with $r=\sqrt{a^{2}+b^{2}}$ and $\theta = arctan\frac{b}{a}$. However, what if $a=0$ such as the case for $-3i$? I am confused!
Mathematics Stack Exchange is a question and answer site for people studying math a... |
I am working with sparse matrices (not particularly huge, <100Mb) and I want to compute the largest independent set on the bipartite graph $(N,E)$ defined as follows: suppose the matrix is named $A$ and is of size $m \times n$.
$m+n$ nodes ($1,\dots,m$ for the rows, $m+1,\dots,m+n$ for the columns) the edge $(i,j) \in ... |
The Art and Science of Electrochemical Plating
Electroplating is commonly used for surface finishing due to its effectiveness across the automotive, electronics, corrosion protection, aerospace, and defense industries. Since WWII, the number of patents claiming to achieve “perfect plating” has increased exponentially. ... |
This is an excellent question! Just to elaborate upon what @porphyrn and @M. Farooq have said, imagine that the universe is entirely empty except for one sodium atom and one photon (particle of light) that has a wavelength of $\pu{242 nm}$. If the photon bumps into the sodium atom, it might just bounce off: this is cal... |
This question is an attempt to make progress on domotorp's interesting challenge. This question was originally asked in two parts; the former of which was answered by Ilya Bogdanov, and the latter of which is still stumping me. I'll keep both parts of the question for the record, but the interesting part is after the s... |
I want to create formulae where the
\rightarrow is enclosed in double quotation marks and appears like any other word in a formula. What I'm getting instead, are formulae where these quotation marks are drawn to adjacent words, leaving a gap between the quotation marks and the
\rightarrow.
Example: I'm getting
Some'' -... |
Help:Editing
This Editing Overview has a lot of examples. You may want to keep this page open in a separate browser window for reference while you edit. If you want the super-quickie help, see the Quickstart Guide.
Each of the topics covered here is covered somewhere else in more detail. See box at right for that
Conte... |
Edit: an earlier version of this answer muddled a distinction between lax limit and 2-limit. I've decided to undelete it in case someone sees how to complete the argument at the end.
If $C$ is locally presentable and $S$ is a semi-monad whose underlying functor is accessible, then there exists a unitalization of $S$. H... |
Renormalization and $\alpha$-limit set for expanding Lorenz maps
1.
Wuhan Institute of Physics and Mathematics, The Chinese Academy of Sciences, Wuhan 430071, China
Mathematics Subject Classification:Primary: 37E05, 37F25; Secondary: 54H2. Citation:Yiming Ding. Renormalization and $\alpha$-limit set for expanding Loren... |
Colossally abundant numbers are positive integers $n$ for which there exists a positive exponent $\epsilon$ such that
$$\frac{\sigma(n)}{n^{1+\epsilon}}>\frac{\sigma(m)}{m^{1+\epsilon}}$$
for all integers $m>1,m\ne n$. Here, $\sigma(n)$ denotes the sum-of-divisors function $\sum_{d|n}d$.
The first few colossally abunda... |
1. Homework StatementShow that f is 2-pi periodic and analytic on the strip \vert Im(z) \vert < \eta, iff it has a Fourier expansion f(z) = \sum_{n = -\infty}^{\infty} a_{n}z^{n}, and that a_n = \frac{1}{2 \pi i} \int_{0}^{2\pi} e^{-inx}f(x) dx. Also, there's something about the lim sup of...
1. Homework StatementShow ... |
LaTeX typesetting is made by using special tags or commands that provide a handful of ways to format your document. Sometimes standard commands are not enough to fulfil some specific needs, in such cases new commands can be defined and this article explains how.
Contents
Most of the LaTeX commands are simple words prec... |
Basic definitions
We now formalize the concepts introduced in the previous lecture. It turns out that it's easiest to deal with events as subsets of a large set called the
probability space, instead of as abstract logical statements. The logical operations of negation, conjunction and disjunction are replaced by the se... |
Restriktor allows for easy-to-use testing of linear equality and inequality restrictions about parameters and effects in linear models.
Many researchers have specific expectations about the relations between theparameters (e.g., means, regression coefficients). These expectations can oftenbe expressed in terms of order... |
Note that by denoting $f(x) = \tan x \sin x -x^2$, you found that $$f'''(x)=-\sin x (1-6\sec^4x+\sec^2x) = \sin x (1+3\sec^2 x)(2\sec^2 x -1 ) \geq 0 $$Hence $f''(x)$ is increasing, with $f''(0)=0$, we conclude that $f''(x) \geq 0$.
Hence $f'(x)$ is increasing, with $f'(0)=0$, we conclude that $f'(x) \geq 0$.
Hence $f(... |
(Disclaimer: I'm a high school student, and my knowledge of mathematics extends only to some elementary high school calculus. I don't know if what I'm about to do is valid mathematics.)
I noticed something really neat the other day.
Suppose we define $L$ as a "left-shift operator" that takes a function $f(x)$ and retur... |
The Problem
Find the absolute minimum and maximum values of the following function on the given interval: $\ f(\theta) = \cos \theta; -\pi \leq \theta \leq {\pi \over 6} $
What I've Done So Far Find the derivative of $\ f(\theta) $. This equals $\ -\sin \theta $. Determine critical points. It won't ever be undefined, b... |
I'm trying to find a formula for the average distance between a point,$\ P$ and a curve segment,$\ C$
When I tried to use the formule for the mean of a function with a distance function $$\frac{1}{a+b}\int_{a}^{b}(\|f(t),P\|)dt$$ where I defined $\ C$ in terms of $\ f:{\rm I\!R} \to {\rm I\!R}^2, C= \{f(i)|a \leq i \le... |
How many solutions does the equation $\cos^2x-\cos x-x=0$ have in the interval $\displaystyle \left[0,\frac\pi2\right]$?
Clearly, $x=0$ is a solution. Are there any other? I couldn't proceed after differentiating it to find the extremes.
Mathematics Stack Exchange is a question and answer site for people studying math ... |
In this section, we use some basic integration formulas studied previously to solve some key applied problems. It is important to note that these formulas are presented in terms of indefinite integrals. Although definite and indefinite integrals are closely related, there are some key differences to keep in mind. A def... |
Research Open Access Published: Convergence rates of nonlinear Stokes problems in homogenization Boundary Value Problems volume 2019, Article number: 96 (2019) Article metrics
242 Accesses
Abstract
In this paper, we study the convergence rates of solutions in homogenization of nonlinear Stokes Dirichlet problems. The m... |
In this second chapter on Taylor Series, we will be studying the case where the n.th derivative of an infinitely differentiable function, does not go to zero. In such cases we therefore have to restrict our values of \(x\) such that for these values the series does converge and not diverge. We will also take a look at ... |
I have a question regarding the uniqueness of the potential flow past a cylinder.
Consider a two dimensional uniform potential flow in $x_1$-direction past the cylinder $B_R = \{ x = (x_1, x_2) \in \mathbb{R}^2 : \vert x \vert < R \}$ for some radius $R > 0$. The velocity potential $\varphi(x)$ is then subject to the b... |
I'm working on a smooth $(d-1)$-dimensional surface $M\subset \mathbb{R}^d$. Let $(\phi_k)_{k\in\mathbb{N}}$ be an orthonormal basis of $L^2(M)$ consisting of the eigenfunctions of the Laplace-Beltrami operator $-\triangle_{M}$, with corresponding eigenvalues $(\lambda_k)_{k\in\mathbb{N}}$.
Claim: the $(\phi_k)$ are $H... |
I don't know how to solve the following:
Let $\alpha$ be a real root of $f(x)=x^4+3x-3\in Q[x]$. Is $\alpha$ a constructible number?
Any help is welcome.
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It only takes a minute to sign up.... |
If you're not quite in the market for a full proof:$$a^n=a\times a\times a\times a...\times a$$$$n!=1\times 2\times 3\times 4...\times n$$Now what happens as $n$ gets much bigger than $a$? In this case, when $n$ is huge, $a$ will have been near some number pretty early in the factorial sequence. The exponential sequenc... |
A sequence of events $A_n, n \in \mathbb{N}$ is said to have a high probability, if $\mathrm{P} (A_n^c) \leq \frac{c}{n^d}$ for some $c, d >0$.
Chernoff bounds are often used to prove some (upper or lower) tail events of a binomial distributed random variable $X$ have a high probability. In such proofs, we are given a ... |
I’m currently getting to grips with the
AdaptiveMonteCarlo method in the
NIntegrate function. I’ve been using the sub-method
MonteCarloRule, however I’m unsure from reading the Mathematica documentation exactly how the option
Points (for this sub-method) actually works. Suppose for example I have the following integral... |
Existence of positive ground state solutions for Choquard equation with variable exponent growth
School of Mathematics and Statistics, Southwest University, Chongqing 400715, China
$ \begin{equation*} -\Delta u = (I_\alpha*|u|^{f(x)})|u|^{f(x)-2}u \ \ \ \ {\rm in} \ \mathbb{R}^N, \end{equation*} $
$ N\geq 3 $
$ \alpha\... |
Show that the Post Correspondence Problem (PCP) is decidable over the unary alphabet ? = {0}.
I will use the following formalization: A PCP-instance is a set $X = \{(a_1, b_1), ..., (a_n, b_n)\}$ where $a_i, b_i \in \Sigma^\ast$ where $\Sigma = \{0\}$ is our alphabet (note that thus every $a_i, b_i$ is of the form $0^k... |
How do I evaluate $$\lim_{x \to 0}\left(\frac{e^{2\sin x}-1}{x}\right)$$
I know it's the indeterminate form since the numerator and denominator both approach 0, but I can't use l'Hopital's rule so I'm not sure how to go about finding the limit.
Mathematics Stack Exchange is a question and answer site for people studyin... |
By Dr Adam Falkowski (Résonaances; Orsay, France)
The title of this post is purposely over-optimistic in order to increase the traffic. A more accurate statement is that a recent analysis
of X-ray spectrum of galactic clusters claims the presence of a monochromatic \(3.5\keV\) photon line which can be interpreted as a ... |
The hyperbolic functions appear with some frequency in applications, and are quite similar in many respects to the trigonometric functions. This is a bit surprising given our initial definitions.
Definition 4.11.1: Hyperbolic Cosines and Sines
The
hyperbolic cosine is the function
\[\cosh x ={e^x +e^{-x }\over2},\]
and... |
Practice Paper 1 Question 10
A circle of radius \(r\) is tangent at two points on the parabola \(y=x^2\) such that the angle between the two radii at the tangent points is \(2\theta\), where \(0<2\theta<\pi\). Find \(r\) as a function of \(\theta\).
Related topics Warm-up Questions What is the slope of the tangent to t... |
In this entry I'll explain and give code for the easiest method I know to reconstruct a surface represented by a scalar field \(f: \mathbb R^3 \rightarrow \mathbb R\) by interpolating a set of point with their normals. The method is called Hermite Radial Basis Function (HRBF) interpolation. The audience aimed is anyone... |
If $f:[-1,1]\to \mathbb{R} $ with $f(x)= \begin{cases}\sin(1/x), & x\neq 0\\ a,& x=0\end{cases} $ , how can I prove that $f$ has intermediate value property if and only if $a$ is between $[-1,1]$?
Let $a\in[-1,1]$. Then:
for $-1\leq b<c<0\,$ (analogously for $0< b<c\leq 1\,$) $f$ on $[b,c]$ is continous, so it has inte... |
Practice Paper 1 Question 11
An organism is born on day \(k=1\) with \(1\) cells. During day \(k=2,3,\ldots\) the organism produces \(\frac{k^2}{k-1}\) times more new cells than it produced on day \(k-1\). Give a simplified expression for the total of all its cells after \(n\) days.
Hint: This is different to the numbe... |
Practice Paper 1 Question 12
Let \(n < 10\) be a non-negative integer. How many integers from \(0\) to \(999\) inclusive have the sum of their digits equal to \(n\)? Give your answer in terms of \(n\).
Hint: Try first for integers from \(0\) to \(99\). Related topics Warm-up Questions
How many \(3\) digit numbers, whos... |
This is joint work with Thomas Hulse, Chan Ieong Kuan, and Alex Walker, and is a sequel to our previous paper.
We have just uploaded a paper to the arXiv on estimating the average size of sums of Fourier coefficients of cusp forms over short intervals. (And by “just” I mean before the holidays). This is the second in a... |
Practice Paper 1 Question 13
On a grid of \(m\times n\) squares, how many ways exist to get from the top-left corner to the bottom-right corner if you can only move right or down on an edge?
Related topics Warm-up Questions
16 tennis players participate in a
doublestournament and are paired at random. How many ways are... |
Practice Paper 3 Question 4
A hiker starts on a path at time \(t=0\) and reaches destination after 1 hour. During the hike, his velocity in km/h varies according to the function \(v(t) = \cos{\big(\frac{t\pi}{2}\big)}.\) Find the time in hours at which the hiker reaches the halfway distance between start and destinatio... |
Category:Examples of Euclidean Algorithm
Jump to navigation Jump to search
This category contains examples of Euclidean Algorithm.
This category contains examples of Euclidean Algorithm.
Let $a, b \in \Z$ and $a \ne 0 \lor b \ne 0$.
The steps are:
$(1): \quad$ Start with $\tuple {a, b}$ such that $\size a \ge \size b$.... |
In order to enable an iCal export link, your account needs to have an API key created. This key enables other applications to access data from within Indico even when you are neither using nor logged into the Indico system yourself with the link provided. Once created, you can manage your key at any time by going to 'M... |
Practice Paper 1 Question 16
Dividing \(x\) by a small annual \(r\)-percent cumulative interest rate approximates the number of years needed to double your investment with a bank. Find \(x\).
Hint: The word "small" may be important. Related topics Warm-up Questions For which real values of \(a\) does \((1+a)^x=e\) yiel... |
Is there a closed-form expression for this nested sum?
$$s(n)=\sum_{i=1}^n\;\; \sum_{j=i+1}^n \sum_{k=i+j-1}^n1$$
If yes, what is it and how can it be derived?
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It only takes a minute to si... |
I recently stumbled across a paper entitled, “Universal Re-Encryption for mix nets,”by P. Golle et al. [1] that I felt is worth exploring. Universal re-encryption (URE), or, perhaps better called
univeral re-randomization, is a primitive that allows some ciphertext to be re-encryptedwithout knowledge of the correspondi... |
When modeling scenarios with a linear function and solving problems involving quantities changing linearly, we typically follow the same problem solving strategies that we would use for any type of function:
problem solving strategy
Identify changing quantities, and then carefully and clearly define descriptive variabl... |
More specifically, I was wondering if there are well-known conditions to put on $X$ in order to make $K_0(X)\simeq K^0(X)$. Wikipedia says they are the same if $X$ is smooth. It seems to me that you get a nice map from the coherent sheaves side to the vector bundle side (the hard direction in my opinion) if you impose ... |
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Multi-strange baryon production at mid-rapidity in Pb-Pb collisions at $\sqrt{s_{\rm NN}}$ = 2.76 TeV
(Elsevier, 2014-01)
The production of ${\rm\Xi}^-$ and ${\rm\Omega}^-$ baryons and their anti-particles in Pb-Pb collisions at $\sqrt{s_{\rm NN}}$ = 2.76 TeV has been measured usin... |
I was asked to prove that $\lim\limits_{x\to\infty}\frac{x^n}{a^x}=0$ when $n$ is some natural number and $a>1$. However, taking second and third derivatives according to L'Hôpital's rule didn't bring any fresh insights nor did it clarify anything. How can this be proven?
Here's a hint: after doing successive applicati... |
I am reading the following proof of a proposition from Royden+Fitzpatrick, 4th edition, and need help in understanding the last half of the proof.
(My comments in italics.) Proposition: Let $A$ be a countable subset of the open interval $(a,b).$ Then there is an increasing function on $(a,b)$ that is continuous only at... |
[exer:7.1.1] For each power series use Theorem [thmtype:7.1.3} to find the radius of convergence \(R\). If \(R>0\), find the open interval of convergence.
\({\displaystyle \sum_{n=0}^\infty {(-1)^n\over2^nn}(x-1)^n}\) \({\displaystyle \sum_{n=0}^\infty 2^nn(x-2)^n}\) \({\displaystyle \sum_{n=0}^\infty {n!\over9^n}x^n}\... |
Answer
False. $\sqrt {f(x)}\ne\frac{1}{2}f(x)$
Work Step by Step
Use the Power Property: $\frac{1}{2}f(x)=\frac{1}{2}\ln x=\ln x^{\frac{1}{2}}=\ln\sqrt x=f(\sqrt x)\ne\sqrt {f(x)}=\sqrt {\ln x}$
You can help us out by revising, improving and updating this answer.Update this answer
After you claim an answer you’ll have
... |
Tutte matrix
In graph theory, the
Tutte matrix $A$ of a graph $G = (V,E)$ is a matrix used to determine the existence of a perfect matching: that is, a set of edges which is incident with each vertex exactly once.
If the set of vertices $V$ has $2n$ elements then the Tutte matrix is a $2n \times 2n$ matrix $A$ with ent... |
Transients
A transient is used to refer to any signal or wave that is short lived. Transient detection has applications in power line analysis, speech and image processing, turbulent flow applications, to name just a few. For instance, in a power system signal, which is highly complicated nowadays because of its consta... |
555851 results
Contributors: Russell, Niamh, Murphy, Thomas Brendan, Raftery, Adrian E
Date: 2015-06-30
... We propose Bayesian model averaging (BMA) as a method for postprocessing the results of model-based clustering. Given a number of competing models, appropriate model summaries are averaged, using the posterior mo... |
Allow me to brief the problem here.
In the graph, assume every edge has weight 1 that the distance can be calculated accordingly. We also define the distance between edges and vertices. For $e = (u,v) \in E$, $d(e,w) = 0.5 + min(d(u,w), d(v,w))$ and the distance between edges immediately follows. It is clear that the d... |
Unit of Ring of Mappings iff Image is Subset of Ring Units/Image is Subset of Ring Units implies Unit of Ring of Mappings Theorem
Let $S$ be a set.
Let $\Img f \subseteq U_R$ where $\Img f$ is the image of $f$.
Then: $f \in R^S$ is a unit of $R^S$ $\forall x \in S : \map {f^{-1}} {x} = \map f x^{-1}$ Proof
From Structu... |
Tsukuba Journal of Mathematics Tsukuba J. Math. Volume 31, Number 1 (2007), 205-215. On double coverings of a pointed non-singular curve with any Weierstrass semigroup Abstract
Let $H$ be a Weierstrass semigroup, i.e., the set $H(P)$ of integers which are pole orders at $P$ of regular functions on $C \setminus \{P\}$ f... |
Roughly speaking there are two ways for a series to converge: As in the case of $\sum 1/n^2$, the individual terms get small very quickly, so that the sum of all of them stays finite, or, as in the case of $\ds \sum (-1)^{n-1}/n$, the terms don't get small fast enough ($\sum 1/n$ diverges), but a mixture of positive an... |
Let $E$ be a smooth vector bundle equipped with an affine connection $\nabla$.
Suppose that $(E,\nabla)$ admits a non-zero parallel section. I think that $(\bigwedge^k E,\bigwedge^k \nabla)$ does not need to admit a non-zero parallel section
even locally. How to construct such an example?
This seems especially interest... |
I searched and wasn't able to find a question similar enough to mine. Here's the problem:
Show that $\sigma=c_1*c_1$, where $c_1$ is the constant function $1$.
Here is my attempt. My argument makes sense to me, but it seems kind of short. I'm wondering if there is anything I need to add to my argument or if I'm sort of... |
Recall that a function \(y=f(x)\) is said to be
one to one if it passes the horizontal line test; that is, for two different \(x\) values \(x_1\) and \(x_2\), we do not have \(f(x_1)=f(x_2)\). In some cases the domain of \(f\) must be restricted so that it is one to one. For instance, consider \(f(x)=x^2\). Clearly, \(... |
I have discovered that the following two tags are too similar to each other:
riemann-zeta-function, with 299 questions tagged, has the description
The Riemann zeta function is the function of one complex variable $s$ defined by the series $\zeta(s) = \sum_{n \geq 1} \frac{1}{n^s}$ when $\operatorname{Re}(s) > 1$. It ad... |
This is a short note written for my students in Math 170, talking about partial fraction decomposition and some potentially confusing topics that have come up. We’ll remind ourselves what partial fraction decomposition is, and unlike the text, we’ll prove it. Finally, we’ll look at some pitfalls in particular. All this... |
Type checking and the inference rules for type theory are
not an algorithm. They do not tell you how to type check. They tell you what is allowed when you perform type checking.
The rule for application should be read as:
If you can prove $\Gamma \vdash t_1 : \forall T . T_{12}$ (and we're not telling you how to do tha... |
We know that 0-1 integer linear programming is NP-Hard. What about 0-1 integer linear programming with only equality constraints? If so, how to prove it
$$\min c^T x \text{ s.t. } Ax = b \quad x_i \in \{0,1\}\quad (i=1,2,...,n)$$
Computer Science Stack Exchange is a question and answer site for students, researchers an... |
Is there a "nice" way to think about the quotient group $\mathbb{C} / \mathbb{Z}$?
Bonus points for $\mathbb{C}/2\mathbb{Z}$ (or even $\mathbb{C}/n\mathbb{Z}$ for $n$ an integer) and how it relates to $\mathbb{C} / \mathbb{Z}$.
By "nice" I mean something like:
$\mathbb{R}/\mathbb{Z}$ is isomorphic to the circle group v... |
I've read so much about it but none of it makes a lot of sense. Also, what's so unsolvable about it?
The prime number theorem states that the number of primes less than or equal to $x$ is approximately equal to $\int_2^x \dfrac{dt}{\log t}.$ The Riemann hypothesis gives a precise answer to how good this approximation i... |
I'm having some beginner problems understanding / proving simple facts about higher inductive type paths.
If you take this higher inductive type for natural numbers modulo 1:
hit N1 := | 0 : N1 | S : N1 -> N1 | mod : 0 = 1
..I have the strong feeling that this corresponds exactly to (is equivalent to) the circle $S^1$ ... |
Symbols:Greek/Pi/Product Notation $\displaystyle \prod_{j \mathop = 1}^n a_j$
Let $\tuple {a_1, a_2, \ldots, a_n} \in S^n$ be an ordered $n$-tuple in $S$.
The composite is called the product of $\tuple {a_1, a_2, \ldots, a_n}$, and is written: $\displaystyle \prod_{j \mathop = 1}^n a_j = \paren {a_1 \times a_2 \times \... |
No, on a general manifold $M$:
there is no preferred linear connection, there is always at least one connection $\nabla$, and the connections on $M$ are precisely the maps $$\bar{\nabla}_X Y := \nabla_X Y + A(X, Y),$$ where $A \in \Gamma(TM \otimes T^*M \otimes T^*M)$ is a $(2, 1)$-tensor on $M$.
As mentioned, given a ... |
First of all, the formulation doesn't make much sense; surely you want to ask for an extension $L/\mathbf{Q}$ such that the inclusion $K \subset L$ induces a
surjection
$$G = \mathrm{Gal}(L/\mathbf{Q}) \rightarrow \mathrm{Gal}(K/\mathbf{Q}) = H.$$
There is then a second ambiguity as to whether you want to fix the choic... |
You have to prove $2$ things here.
Not path connected: To prove that $A\cup B$ is not path connected, you must find $2$ points for which a path between them does not exist. Since it is easy to see that $A$ and $B$ are path connected, it is best to take one point from $A$ and one from $B$. For example, take $$a=(0,0)\in... |
In the integral for surface area, $$\int_a^b\int_c^d |{\bf r}_u\times{\bf r}_v|\,du\,dv,$$ the integrand $|{\bf r}_u\times{\bf r}_v|\,du\,dv$ is the area of a tiny parallelogram, that is, a very small surface area, so it is reasonable to abbreviate it $dS$; then a shortened version of the integral is $$\dint{D} 1\cdot ... |
In Exercises 1–11 a direction field is drawn for the given equation. Sketch some integral curves. In Exercises [exer:1.3.12}-[exer:1.3.22} construct a direction field and plot some integral curves in the indicated rectangular region.
[exer:1.3.12] \(y'=y(y-1); \quad \{-1\le x\le 2,\ -2\le y\le2\}\)
[exer:1.3.13] \(y'=2... |
I'm trying to learn the basics of homotopy theory by studying from Strom's Modern Classical Homotopy Theory, a book in which the proof of every proposition presented is given as a guided exercise to the reader.
Right now I'm working with homotopy colimits, and I've been stuck with Project 6.26 at page 154 since this mo... |
In March, ATLAS has moderately excited us with a 3-sigma SUSY-like excess in final states with a lepton pair, jets, and MET. At the end of another blog post, I mentioned a paper explaining it in terms of a light sbottom.
There's a different explanation on the arXiv now, extending the proposal by Ullwanger 3 weeks ago. ... |
pandas.DataFrame.ewm¶
DataFrame.
ewm(
com=None, span=None, halflife=None, alpha=None, min_periods=0, freq=None, adjust=True, ignore_na=False, axis=0)¶
Provides exponential weighted functions
New in version 0.18.0.
Parameters: com: float, optional
Specify decay in terms of center of mass, \(\alpha = 1 / (1 + com),\text{... |
Here I describe the discreet Laplace-Beltrami operator for a triangle mesh and how to derive the Laplacian matrix for that mesh. Then I provide [ C++ code ] to compute harmonic weights over a triangular mesh by solving the Laplace equation.
Motivation
The goal here is to present the Laplace operator with a concrete app... |
Is there a not identically zero, real-analytic function $f:\mathbb{R}\rightarrow\mathbb{R}$, which satisfies
$$f(n)=f^{(n)}(0),\quad n\in\mathbb{N} \text{ or } \mathbb N^+?$$
What I got so far:
Set
$$f(x)=\sum_{n=0}^\infty\frac{a_n}{n!}x^n,$$
then for $n=0$ this works anyway and else we have
$$a_n=f^{(n)}(0)=f(n)=\sum_... |
If you design trading strategies in a $ \sigma $-algebra space: $ \mathcal {N}(\mu , \sigma^2) $, meaning using averages and standard deviations for data analysis and trading decisions. Then, all you will see will be confined within that space. It implies that you will be dealing most often with a normal distribution o... |
G.9 Linear Independence Worked Example
This video gives some more details behind the example for the following four vectors in \(\mathbb{R}^{3}\). Consider the following vectors in \(\Re^{3}\):
\[ v_{1}=\begin{pmatrix}4\\-1\\3\end{pmatrix}, \qquad v_{2}=\begin{pmatrix}-3\\7\\4\end{pmatrix}, \qquad v_{3}=\begin{pmatrix}... |
Practice Paper 1 Question 20
Evaluate \(\lim\limits_{n\rightarrow\infty} \left(\frac{1}{n+1}+\frac{1}{n+2}+\cdots+\frac{1}{2n}\right)\).
Hint: Graph sketching may help. Related topics Warm-up Questions Sketch \(y=\frac{x}{x^2-a^2}\) for various values of \(a\). Integrate \(y=x\ln x\). Evaluate \(\lim\limits_{x\to\infty... |
$SL(2,R)xSU(2)/R^2$ string model in curved spacetime and exact conformal results
Bars, I and Sfetsos, K (1992)
$SL(2,R)xSU(2)/R^2$ string model in curved spacetime and exact conformal results Phys.Lett. B, 301. pp. 183-190. Abstract
Pursuing further the recent methods in the algebraic Hamiltonian approach to gauged WZW... |
" Find the points $z \in \mathbb{C}$ at which the function $g(z) = \cos(\bar{z})$ satisfies the Cauchy-Riemann equations. "
So I've written $g(z) = g(x,y) = \cos(x-iy)=\cos(x)\cosh(y)+i\sin(x)\sinh(y)$. So that $u(x,y)=\cos(x)\cosh(y)$ and $v(x,y)=\sin(x)\sinh(y)$.
From the first C-R equation I get $-\sin(x)\cosh(y) = \... |
Question:
The closed feedwater heater is to heat feedwater from {eq}5000 kPa {/eq} and {eq}220 ^oC {/eq} (state 1) to a saturated liquid (state 2). The turbine supplies bleed steam at {eq}6000 kPa {/eq} and {eq}320^oC {/eq} (state 3) to this unit. This steam is condensed to a mixture of liquid vapor (97.352% vapor and ... |
There isn't a single way in which one can approach a discrete optimization problem using Differential Evolution (DE).
Widespread techniques listed under the Discrete Differential Evolution label aren't DE-specific.
You can allow variables to take values in a continuous range and use penalty functions to enforce integer... |
Let $S $ be the spectrum of a complete dvr with algebraically closed residue field. Let $\eta$ be its generic point and let $s$ be its closed point with $k(s)$ of positive characteristic. Let $X\to S$ be a smooth proper morphism of schemes whose geometric fibres are connected.
Edit:For all $b$ in $S$, assume that $\mat... |
Based on such demands, I designed a co-pilot which can:
Automatically clustering the clusters; Remove periodic boundary conditions and make the center-of-mass at $(0,0,0)^T$; Adjust the view vector along the minor axis of the aggregate; Classify the aggregate.
After obtaining clusters in step 1, we must remove periodic... |
Consider the finite multisets $\mathbf{Bag}\:X$. Its elements are given by $\{x_1,\ldots,x_n\}$ quotiented by permutations, so that $\{x_1,\ldots,x_n\}=\{x_{\pi 1},\ldots,x_{\pi n}\}$ for any $\pi\in\mathbf{S}_n$. What is a one-hole context for an element in such a thing? Well, we must have had $n>0$ to select a positi... |
555851 results
Contributors: Bianchi, S., Saglimbeni, F., Lepore, A., Di Leonardo, R.
Date: 2015-06-30
... E. coli bacteria swim following a run and tumble pattern. In the run state all flagella join in a single helical bundle that propels the cell body along approximately straight paths. When one or more flagellar mot... |
Errors and residuals
Regression analysis Models Estimation Background
In statistics and optimization,
statistical errors and residuals are two closely related and easily confused measures of the deviation of an observed value of an element of a statistical sample from its "theoretical value". The error (or disturbance)... |
I am generating random 64-bit numbers, in groups of 1000 numbers. How many groups can I expect to generate before there is a collision within one of the groups? Again, I don't care if anything in the first group collides with anything from the second group, only if numbers collide within the same group.
There are $2^{6... |
There is a beautiful formula to count the number of ideals $I$ in the ring of integers $\mathcal{O}_K$ of a number field $K$, given by
$$\sum_{n \leq X} a_n \sim C_K X,$$
where $a_n$ is the number of ideals in $\mathcal{O}_K$ of norm $n$ and $C_K$ is the residue at $s = 1$ of the Dedekind zeta function $\zeta_K$ of $K$... |
1. About Unit-selection Speech Synthesis
Speech synthesis is the artificial production of human speech. A computer system used for this purpose is called a speech computer or speech synthesizer, and can be implemented in software or hardware products. A text-to-speech (TTS) system converts normal language text into spe... |
Finding the lengths of the arcs
If the perimeter of the square is 20 cm, then each side must be 5 cm long.
The sides of the square are the diameters of the semicircles, so the circumferences of the full circles would be $5\times\pi=5\pi$ cm.
As shown in the diagram below, the 4 semicircles make up 2 full circles.
So th... |
Why doesn´t the von Neumann hierarchy to $V_{\omega_1}$ exist in Zermelo set theory if with Scott´s trick you can "count" to $ \omega_1 $
To see what goes wrong, let's try to prove something even simpler: that $\omega_1$ exists.
We definitely have the set of all well-orderings of $\omega$ (via Powerset and Separation).... |
I am wondering about generalisations of the concept of equivalence relations to suplattices.
Here is my motivation: Given a set $X$. The powerset $\mathcal{P}(X)$ is a suplattice. For suplattices there is a tensor product, giving $\mathcal{P}(X)\otimes\mathcal{P}(X)=\mathcal{P}(X\times X)$. Now we can define the diagon... |
The question:
(a) Let $f$ be a continuous periodic complex valued function with period $2\pi $.Then prove that given $\epsilon >0,$ there exists a function $Q(x)=\sum_{k=-M}^{M}c_{k}e^{ikx}$ with $c_k\in \mathbb{C}$ and $M\in \mathbb{N}$ defined on $[-\pi ,\pi ]$ such that $\int_{-\pi }^{\pi }\left | f(x)-Q(x) \right |... |
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