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Inner Limit in Normed Spaces by Open Balls Theorem Then the inner limit of $\left \langle{C_n}\right \rangle_{n \in \N}$ is: $\displaystyle \liminf_n \ C_n = \left\{{x: \forall \epsilon > 0: \exists N \in \mathcal N_\infty: \forall n \in N: x \in C_n + \epsilon B}\right\}$
where $B$ denotes the open unit ball of the sp... |
HP 17bII+ Silver solver
09-14-2018, 09:20 PM
Post: #1
HP 17bII+ Silver solver
I'm very satisfied with my HP 17bII+ Silver, which I find very powerful, but also nice and not looking too complicated (no [f] and [g] functions on keys like the HP 12c or HP 35s that I used to use at work every day, but a really complete cal... |
By definition supersymmetry transformations square to spacetime translations. In a superspace formalism the supersymmetry operator is constructed from the vector field $\partial_\theta$ with respect to the odd coordinates $\theta$. As this operator has to square to the vector field $\partial_x$ with respect to the even... |
The vector projection is of two types: Scalar projection that tells about the magnitude of vector projection and the other is the Vector projection which says about itself and represents the unit vector.
If the vector veca is projected on vecb then Vector Projection formula is given below:
\[\large proj_{b}\,a=\frac{\v... |
The expression for the acceleration of a near-earth satellite as presented in the IERS Technical note is given by \begin{equation} \label{eq:problemeq} \tag{1} \frac{d^2\mathbf{r}}{dt^2} = \frac{GM_E}{c^2r^3} \left\{\left[2(\beta+\gamma)\frac{GM_E}{r} - \gamma \dot{\mathbf{r}} \cdot \dot{\mathbf{r}} \right] \mathbf{r} ... |
The Grassmann analytic continuation principle says that a real function $f(x,\xi)$ that depends on $n$ real variables $x=(x_1,\ldots,x_n)$ and $n$ nilpotent Grassmann numbers $\xi=(\xi_1,\ldots,\xi_n)$ has the following Taylor expansion containing only a finit ($2n?$) number of terms
$$ f(x+\xi) = \sum_{\alpha}\frac{\x... |
ergm.ego
Last updated: April 05, 2016 This tutorial is a joint product of the Statnet Development Team:
Mark S. Handcock (University of California, Los Angeles)
Carter T. Butts (University of California, Irvine) David R. Hunter (Penn State University) Steven M. Goodreau (University of Washington) Skye Bender de-Moll (O... |
Following up on his previous post, “Is Math a Gift From God?” — calculus students say, “No!” — Jason Rosenhouse has a new essay for your delectation, “Is God Like an Imaginary Number?” Again, the short answer is, “Nope.” The longer answer will take us into the history of mathematics, the role of mysticism in theology a... |
Let $X=[0,+ \infty[ $ and $d(x,y)=|\frac{1}{1+x^2}- \frac{1}{1+y^2}| $
1) Show that $(X,d)$ and $(]0,1], d_{2})$ are homeomorphic (where $d_{2}=|x-y|$)
2) Is the space $(X,d)$ connected? compact? complete ?
To do this it means we need to find any function such as:
$f\colon (\mathbb{R}^+, d)\to (]0,1], d_{2})$ is biject... |
I have a one-semester background in string theory (bosonic string theory, the NSR string, conformal field theory), but I have not taken any full length courses on supersymmetry and supergravity. I'm presently taking a second string theory course, but I'm forced to build the background I lack myself, in an attempt to un... |
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Production of Σ(1385)± and Ξ(1530)0 in proton–proton collisions at √s = 7 TeV
(Springer, 2015-01-10)
The production of the strange and double-strange baryon resonances ((1385)±, Ξ(1530)0) has been measured at mid-rapidity (|y|< 0.5) in proton–proton collisions at √s = 7 TeV with the ... |
Show that the first excited state of 8-Be nucleus fits the experimental value of the rotational band $E(2^+) = 92 keV$ (this is the first excited state, which is 92 keV above the ground state). To do so model 8-Be to be made of 2 alpha particles $4.5 fm$ apart rotating about their center of mass.
The method I used is:
... |
Computing R.M.S. Error
RMS error measures the differences between values predicted by a model or an estimator and the values actually observed.
Learning Objectives
Define and compute root-mean-square error.
Key Takeaways Key Points These individual differences are called residuals when the calculations are performed ov... |
Question:
I want to determine a boolean vector $b \in \{0,1\}^n$ consisting of zeros and ones, but cannot access it directly. I can only call a black-box computer code which will take the dot product of $b$ with a real-valued vector $v \in \mathbb{R}^n$ of my choosing. I.e., access to $b$ is available through evaluatio... |
Journal of Symbolic Logic J. Symbolic Logic Volume 45, Issue 2 (1980), 237-250. Constructible Models of Subsystems of ZF Abstract
One of the main results of Godel [4] and [5] is that, if $M$ is a transitive set such that $\langle M, \epsilon \rangle$ is a model of ZF (Zermelo-Fraenkel set theory) and $\alpha$ is the le... |
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Measurement of $W$ boson angular distributions in events with high transverse momentum jets at $\sqrt{s}=$ 8 TeV using the ATLAS detector
(Elsevier, 2017-02)
The $W$ boson angular distribution in events with high transverse momentum jets is measured using data collected by the ATLAS ... |
amp-mathml
Displays a MathML formula.
Required Script
<script async custom-element="amp-mathml" src="https://cdn.ampproject.org/v0/amp-mathml-0.1.js"></script>
Supported Layouts container Examples amp-mathml.amp.html
This extension creates an iframe and renders a MathML formula.
<amp-mathml layout="container" data-form... |
I was recently thinking about some of my past math classes, and depending on the context I recall my professors would sometimes use the "$\equiv$" symbol in places where I'd feel "$=$" to be more appropriate. For example, since this would often be the case in my classes on differential equations and Fourier series, we ... |
Find the radius of convergence and the convergence at the end points of the series:
$$\sum_{n=1}^\infty(2+(-1)^n)^nx^n$$
This is what I did:
$a_n=(2+(-1)^n)^n\Rightarrow R=\frac{1}{limsup|a_n|^\frac1n}\\ for\ n=2k \to lim(2+1)=3 \\ for\ n= 2k+1 \to lim(2-1)=1 \\ limsup \ a_n^{\frac1n}=3 \Rightarrow R=\frac13$
So the se... |
I have been recently learning a lot about Macdonald polynomials, which have been shown to have probabilistic interpretations, more precisely the eigenfunctions of certain Markov chains on the symmetric group.
To make this post more educational, I will define these polynomials a bit. Consider the 2-parameter family of M... |
Author: Zuguang Gu ( z.gu@dkfz.de ) Date: 2019-05-02
library(EnrichedHeatmap)load(system.file("extdata", "neg_cr.RData", package = "EnrichedHeatmap"))all_genes = all_genes[unique(neg_cr$gene)]all_tss = promoters(all_genes, upstream = 0, downstream = 1)mat_neg_cr = normalizeToMatrix(neg_cr, all_tss, mapping_column = "ge... |
TL; DR: obtaining a reasonably big single crystal of $\ce{ZnSO4 * H2O}$ seems to be a tricky task, whereas one can easily obtain $\ce{ZnSO4 * H2O}$ as a result of thermal dehydration of heptahydtare above $\pu{70 ^\circ C}$ in a form of melt, and above $\pu{120 ^\circ C}$ – as a polycrystalline solid material.
I finall... |
When choosing the public exponent e, it is stressed that $e$ must be coprime to $\phi(n)$, i.e. $\gcd(\phi(n), e) = 1$.
I know that a common choice is to have $e = 3$ (which requires a good padding scheme) or $e=65537$, which is slower but safer.
I also know that for two primes $p,q$, we have $\phi(pq) = (p - 1) (q - 1... |
Every new study presents its own challenges. (I would have to say that one of the great things about being a biostatistician is the immense variety of research questions that I get to wrestle with.) Recently, I was approached by a group of researchers who wanted to evaluate an intervention. Actually, they had two, but ... |
Through the questions below, this post asks whether the concept of
abelian subfactor is relevant. Remark : here abelian qualifies an inclusion of II$_1$ factors $(N \subset M)$, $N$ is not an abelian algebra.
First some useful reminders about groups and lattices :
Definitions: A lattice $(L, \wedge, \vee)$ is :
$(\fora... |
Can I be a pedant and say that if the question states that $\langle \alpha \vert A \vert \alpha \rangle = 0$ for every vector $\lvert \alpha \rangle$, that means that $A$ is everywhere defined, so there are no domain issues?
Gravitational optics is very different from quantum optics, if by the latter you mean the quant... |
Upcoming Events › Discrete Math Seminar Events Search and Views Navigation October 2019
For a graph $H$ and an integer $k\ge1$, the $k$-color Ramsey number $R_k(H)$ is the least integer $N$ such that every $k$-coloring of the edges of the complete graph $K_N$ contains a monochromatic copy of $H$. Let $C_m$ denote the c... |
rencsee wrote:
What is the remainder when the positive integer n is divided by 2?
(1) When n is divided by 13, the remainder is 3 (2) n + 2 is a multiple of 7
\(n \geqslant 1\,\,\,\left( * \right)\)
\(n\,\,\mathop = \limits^? \,\,{\text{even}}\,\,\,\,\,\left[ \begin{gathered}
n\,\,{\text{even}}\,\, \Rightarrow \,\,\,{\... |
I and my friend are thinking about a smooth analog of Rubik's cube. One idea is the following:
Consider the 2-dimensional sphere $S^{2}$. We choose three parameters: $(L, H, \theta)$. Here $L$ is a ray that passes through the origin, $H$ is a plane that intersects with $L$, the sphere, and orthogonal to $L$. $\theta\in... |
If $P(x,y,...,z)$ is a polynomial with integer coefficients then every integer solution of $P=0$ corresponds to a homomorphism from $\mathbb{Z}[x,y,...,z]/(P)$ to $\mathbb{Z}$. So there are infinitely many solutions iff there are infinitely many homomorphisms. If $P$ is homogeneous, we consider solutions up to a scalar... |
Recruiting is the essence of College Football. It is one of the most important factors, if not the most important factor that determines how good a season will be. With this in mind, I dug up some data from 247Sports to see if we could use public recruiting event data to see if we could predict where a player was commi... |
From Sipser,
Language A is mapping reducible to language B, written $A \leq_m B$, if there is a computable function $f : \Sigma^* \rightarrow \Sigma^*$, where for every $w$, $w ∈ A \Leftrightarrow f(w) \in B$. The function $f$ is called the reduction from A to B.
A function is injective if every element in the co-domai... |
Starting, generally, with a commutative ring $R$ and a rank $2$ projectivemodule $P$ given with a quadratic form $\varphi$ we can form its Clifford algebra$C(P)$. Its even part $S:=C^+(P)$ is then a commutative $R$ algebra of rank $2$.If (which we may assume locally) $P=Re_1+Re_2$ we have that $S$ has basis$1,e_1e_2=:h... |
I want to understand what quantum entanglement is and what role does it play in quantum error correction.
NOTE:As per the suggestions of @JamesWootton and @NielDeBeaudrap, I have asked a separate question for the classical analogy here.
Quantum Computing Stack Exchange is a question and answer site for engineers, scien... |
Assume, an extension of the lambda calculus with terms $t$ and values $v$ is defined in big-step operational semantics with evaluation relation $t \Downarrow v$.
It is intuitive to assume that $\beta$-equivalence holds, e.g.
(λx. t) unit $\equiv_\beta$
t when
x is not free in
t
It is however unclear to me, how $\equiv_... |
I am teaching a course on knots for the first time, and this led me to play with an approach which I have not seen in the literature. I would be surprised if no one had used it before, so I am asking whether this approach has a name, and if there are any relevant references.
The basic idea is like this. Let $\Lambda$ b... |
How can I make the symbol of product operator (pi caps) making the extremes remain the same above and below the symbol? (I do not want the extremes on the right side of the symbol) I wanna write this symbol with that conditions in the simplest possible way.
Please be aware that the default behaviour in displaymath mode... |
Find the differential of each of the following expressions, ie. zap each of the following with $d$:
(mbZapWithD) Find the differential of special functions.
$$f=3x-5z^2+2xy$$
$$g=\sin^2(\omega t)$$
$$h=\frac{\mu B}{k_B T}$$
$$j=\exp\left(\frac{\mu B}{k_B T}\right)$$
$$k=\ln\left(e^{\frac{\mu B}{k_B T}} +e^{-\frac{\mu B... |
STANDARD DEVIATION
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, Bunuel
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"The Mathematical Ninja is currently on sabbatical. Leave a message after the tone... or else!" Oh dear! How are we going to figure out $e^e$ now? Let alone $e^{-\frac{1}{e}}$? We'll just have to roll up our sleeves and get our thinking hats on, that's all. OK, $e^e$ First of all,Read More →
The Mathematical Ninja peer... |
Content
Access the CASTELLI-KURUCZ ATLAS
The Castelli AND Kurucz 2004 Stellar Atmosphere Models
The atlas contains about 4300 stellar atmosphere models for a wide range of metal abundances, effective temperatures and gravities. These LTE models with no convective overshooting computed by Fiorella Castelli, have improve... |
Prove that if $ab \equiv 0 \pmod p$, where p is a prime number, then $a \equiv 0 \pmod p$ or $b \equiv 0 \pmod p$.
All I have right now is that the prime divisibility property may help with the then part of this problem.
Mathematics Stack Exchange is a question and answer site for people studying math at any level and ... |
Let $M$ be a complete Riemannian 3-manifold and $\gamma \subset M$ a simple closed curve that bounds a
least-area disc $D$ - a disc that minimizes the area among all discs bounded by $\gamma$. Let $Conv(\gamma)$ be the convex hull of $\gamma$, i.e, the smallest convex subset of $M$ containing $\gamma$. When $M = \mathb... |
Hamiltonian Gromov-Witten theory(see Mundet-Tian paper) corresponds to a new type of Symplectic vortex equations: Such type of models gives a connection to Hitchin-Kobayashi correspondence and Floer theory(for example Donaldson's book: Floer homology groups in Yang–Mills theory).
Question:
Take the vortex equations wit... |
I'm trying to solve this particular equation
$\frac{\partial u}{\partial t} = \frac{\partial}{\partial x} \big[D_{i}(x)\frac{\partial u}{\partial x} \big] + S(x,t)$
where the $i$ index denotes different layers. Let's say that $ i \in \{1,2,3\}$.
The interface conditions are:
$-D_1(x)\frac{\partial u}{\partial x}\bigg|_... |
Can I be a pedant and say that if the question states that $\langle \alpha \vert A \vert \alpha \rangle = 0$ for every vector $\lvert \alpha \rangle$, that means that $A$ is everywhere defined, so there are no domain issues?
Gravitational optics is very different from quantum optics, if by the latter you mean the quant... |
Let $G = ( V_G, E_G )$ be a graph. Let $E_H \subseteq E_G$.
The subgraph of $G$ edge-induced by $E_H$ is $H = ( V_H, E_H)$, where
$V_H = \{ v \in V_G : \exists ( u, w ) \in E_H\ v = u \lor v = w \}$
Let $k_1 \leq |E_G|$ and $k_2 \leq |V_G|$ be given in input.
I would like to determine the number $k_3$ of edge-induced s... |
Allowed by whom? There is no Central Graph Administration that decides what you can and cannot do. You can define objects in any way that's convenient for you, as long as you're clear about what the definition is. If zero-weighted edges are useful to you, then use them; just make sure your readers know that's what you'... |
\defl{Binomial Distribution has the following properties:}
There are a fixed number of trials or observations, $n$, determined in advance. Each trial can take on one of two possible outcomes, labeled ''success'' and ''failure''. Each trial's outcome is determined independently of all the other trials. The probability o... |
Exams can be easily created in LaTeX by means of the class
exam.cls. This class makes it straightforward to typeset questions, and it sets a 1in margin in all paper sizes and provides special commands to write and compute grades. This article explains how to edit with exam.cls.
Contents
Let's see a simple working examp... |
For $n\in\mathbb{N}$ and $q\in(0,1)$, define $$f_{n}(q):=\sum_{i_{1},i_{2},\dots,i_{n}=1}^{\infty}\frac{q^{i_1+i_2+\dots+i_n}}{(1-q^{i_1+i_2})(1-q^{i_2+i_3})\dots(1-q^{i_{n-1}+i_n})(1-q^{i_n+i_1})}.$$
I would like to know something about the asymptotic behavior of $f_{n}(q)$, as $n\to\infty$.
Some remarks on possible w... |
Depth 2 circuits require exponential size to compute addition since a depth 2 circuit must be either DNF or CNF and it is easy to verify that there are exponentially many minterms and maxterms.
Warning: the part below is buggy. See the comments under the answer.
The way I count it, addition can be done in depth 3. Assu... |
Rocky Mountain Journal of Mathematics Rocky Mountain J. Math. Volume 44, Number 4 (2014), 1145-1160. Elliptic curves coming from Heron triangles Abstract
Triangles having rational sides $a, b, c$ and rational area $Q$ are called \textit{Heron triangles}. Associated to each Heron triangle is the quartic \[ v^2=u(u-a)(u-... |
The Annals of Statistics Ann. Statist. Volume 28, Number 3 (2000), 922-947. Maximum likelihood estimation of smooth monotone and unimodal densities Abstract
We study the nonparametric estimation of univariate monotone and unimodal densities usingthe maximum smoothed likelihood approach. The monotone estimator is the de... |
In this paper we study the L p-Minkowski problem for p=鈭n鈭1, which corresponds to the critical exponent in the Blaschke鈥揝antalo inequality. We first obtain volume estimates for general solutions, then establish a priori estimates for rotationally symmetric solutions by using a Kazdan鈥揥arner type obstruction. Finally we... |
First it is easy to see that if $ a_i \leq0 $ at optimal solution we have $x_i = 0$, and we can omit the variable $x_i$ so let's first assume $a_i$ are distinct hence (WLOG by rearranging x_i) $$ 0 < a_1 < a_2 < a_3 ... < a_n $$
Now let assume at the
Unique optimal solution, say $(x^*_1 , x^*_2,..., x^*_n)$, we have $\... |
Since $On⊂L⊆V$, properties of ordinals that depend on the absence of a function or other structure (i.e. $\Pi_1^{ZF}$ formulas) are preserved when going down from $V$ to $L$. Hence initial ordinals of cardinals remain initial in L. Regular ordinals remain regular in $L$. Weak limit cardinals become strong limit cardina... |
In my research I came upon a recursively defined sequence, and I'm pretty sure it converges to $\sqrt{2}$ though I can't prove it easily. I don't think it is a difficult question but I'm not sure.
Consider the following sequence of functions over $\mathbb{R}$, where it makes sense:
$f_0(x)=0$,
$\displaystyle f_{n+1}(x)... |
Such a dramatic change would indeed make it harder to reach space, in a precisely defined sense. The easiest measure of how 'hard' it is to get so space is the escape velocity, which is determined by the planet's mass $M$ and radius $R$ as$$v_\text{esc}=\sqrt{\frac{2GM}R}.$$For a planet like the one you mention, the es... |
If $F$ is continuously differentiable and smooth, you can use the gradient to walk along the contour. In this way you could walk on the contour starting at $x_1$ (tracing both directions of the contour) and see if you reach $x_2$.
In particular, if you're currently at a point $x \in \mathcal{C}$ on the contour, then th... |
Yes, both Theorem 1 and Theorem 2 have constructive proofs.
In the following, I will work with rational numbers, but the same argumentswork for any ordered field. (Note that in constructive logic, fields areautomatically discrete -- i.e., any two elements of a field are either equalor not. Therefore, I don't think that... |
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1. Measurement of the ratio of the production cross sections times branching fractions of B c ± → J/ψπ ± and B± → J/ψK ± and ℬ B c ± → J / ψ π ± π ± π ∓ / ℬ B c ± → J / ψ... |
One of the many lovely things about Big MathsJam is that I’ve found My People - I’ve made several very dear friends there, introduced others to the circle, and get to stay in touch with other maths fans through the year. It’s golden. Adam Atkinson is one of those dearRead More →
Dear Uncle Colin, I’m given that $0 \le ... |
The time energy uncertainty principle arises from the fact that a function can be described as a sum of terms in a conjugate variable, as is the case of any fourier transform. In this case the variables are frequency and time. The time-energy uncertainty does not seem to have any more fundamental meaning than this, unl... |
Model Description NOTE: formulae are not displayed correctly since our wikimedia update. model description Contents 1 Model description 1.1 Overview 1.2 Basic model description 1.3 Introduction of variable climate sensitivities 1.4 Updated carbon cycle 1.5 Other additional capabilities compared to MAGICC4.2 Model descr... |
Complex Impedance
Complex impedances are commonly used quantities in the analysis of AC power systems. A complex impedance is represented by the following relation:
[math] Z = R + jX \, [/math]
Where [math] Z \, [/math] is the complex impedance ([math] \Omega [/math])
[math] R \, [/math] is the resistance ([math] \Omeg... |
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November 24, 2004, 04:52
test cases
#
1
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Hello,
For purposes of my MSc Thesis I am now doing a set of test benchmarks (test cases) for code validation.
I found really nice test case with an analytical solution as presented above:
It has been taken from:
Amara, "Vorticity–velocity–pressure for... |
Edit for clarity: How does Mathematica's function
Series know that
Gamma[x] has a pole at
x=0? When
Series is called to expand near
x=0, it gives the proper
1/x term in its Laurent expansion. I need to copy this behavior of
Series to user-defined functions.
Series[Gamma[x],{x,0,1}]
1/x-EulerGamma+1/12 (6 EulerGamma^2+[... |
We say that the uniformly elliptic operator $$Lu\ =\ -\sum_{i,j=1}^na^{ij}u_{x_ix_j}\ +\ \sum_{i=1}^nb^iu_{x_i}\ +\ cu$$ satisfies the
weak maximum principleif for all $u\in C^2(U)\cap C(\bar{U})$ $$\left\{\begin{array}{rl} Lu \leq 0 & \mbox{in } U\\ u \leq 0 & \mbox{on } \partial U \end{array}\right.$$ implies that $u... |
Let E be a holomorphic bundle over algebra surface X, let $H$ be a Hermitian metric of $E$, recall the Hermitian-Yang-mills equation is $\wedge F_H=\lambda.1$.
Let $H_t$ be Hermitian metrics over $E$ parametrized by $t$, Donaldson in [1] consider the following flow equation: \begin{equation} H_t^{-1}\frac{\partial H_t}... |
I have found the following claim made very clearly at least once in the published literature (see below):
Let $P$ be a linear partial differential operator defined on an open set $\Omega \subset \mathbb{R}^{n+1}$, strictly hyperbolic with respect to the level surfaces of the first coordinate, which I will denote by $t$... |
I find the Frobenius Method quite beautiful, and I would like to be able to apply it. In particular there are three questions in my text book that I have attempted. In each question my limited understanding has stopped me. Only one of these questions (the last) is assigned homework. The rest are examples I found intere... |
Let $X$ be a topological space and $V$ and $N$ are subspaces of $X$ such that $N$ deformation retracts onto $V$. I want to show that $X-V$ deformation retracts onto $X-N$. So i need to construct a retraction $r':X-V\longrightarrow X-N$ and show that there exists a homotopy between $i'\circ r'$ and $id'$ where $i':X-N\r... |
Let $k$ be a field. What is an explicit power series $f \in k[[t]]$ that is transcendental over $k[t]$?
I am looking for elementary example (so there should be a proof of transcendence that does not use any big machinery).
MathOverflow is a question and answer site for professional mathematicians. It only takes a minut... |
In general, this is a hard problem. For classes of expressions for which there is a canonical form, such as polynomials (in any number of variables), the answer is straightforward: two expressions are equal if and only if they have the same canonical form. (A canonical form means that for each expression there is one a... |
According to remark 6.14 in Shigeru Mukai's
An introduction to invariants and moduli (unfortunately, the page is not available on Google Books, so I explain it below), the GIT-quotient of an affine variety $X$ by a reductive group $G$ with respect to a nontrivial character $\chi: G \to \mathbb G_m$ may be considered as... |
A recent question on the notion and notation of multiplicative integrals ( What is the standard notation for a multiplicative integral? ) induced me to play with the Riemann products of the Gamma function, in order to evaluate the multiplicative integral of $\Gamma(x)$, exploiting the multiplicative formula. I will, ho... |
Suppose that $K/\mathbb{Q}_p$ is a finite extension and $k_K$ the residue field of $K$. Let $A/K$ be an abelian variety with good reduction. Suppose that $E\to\mathrm{End}^0_K(A)$ is an inclusion of a number field that sends $1$ to the identity.
Denote by $T_\ell A$ the Tate module for a prime $\ell\neq p$ and let $V_\... |
The electrical power grid operates in equilibrium. The power supply from the generator matches the demand levied by the end-users. The flow of power to enable this demand-supply equilibrium over the transmission lines (T-lines) is governed by the following conditions.
Thermal limitation of T-lines Voltage drop limitati... |
We have to do it without calculus or any complex inequality. Level of complexity is that we cannot even use the AM-GM inequality. So I tried, $$(\sin\theta-\cos\theta)^2\geq0$$ $$1-2\sin\theta\cos\theta\geq0$$ $$\frac12\geq\sin\theta\cos\theta$$ Reverting back to the previous step, $$(\sin\theta+\cos\theta)^2\geq4\sin\... |
Dear Uncle Colin, I have a pair of parametric equations giving $x$ and $y$ each as a function of $t$. I'm happy with the first derivative being $\diff{y}{t} \div \diff{x}{t}$, but I struggle to find the second derivative. How would I do that? - Can't Handle An Infinitesimal Nuance Hi,Read More →
Eagle-eyed friend of th... |
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Now showing items 1-10 of 26
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... |
Answer
parallelogram matches (f) square matches (e) trapezoid matches (d) circle matches (b) rectangle matches (c) triangle matches (a)
Work Step by Step
A=b$\times$h is the formula for the area of a parallelogram. A=s$^2$ is the formula for the area of a square. A=$\frac{1}{2}$ $\times$h$\times$(b+B) is the formula fo... |
\[\]
Exponential Distribution has the following properties:
Equals the distance between successive occurances or arrivals of a Poisson process with mean $\lambda > 0$ $\lambda$ is the average number of occurances or arrivals per unit of time (length, space, etc.) $\frac{1}{\lambda}$ is the average time between occurren... |
so let's say we have: $f''+4f=\frac{1}{\sin(2x)}$
Homogeneous Problem:
We use Euler-Ansatz: $char(\lambda)=\lambda^2+4 \Rightarrow \lambda=\pm 2i$
So we get
$f_h(x)=\hat{A}e^{2ix}+\hat{B}e^{-2ix}=A\cos(2x)+B\sin(2)$
Particular Problem:
We use variaton of constants. From the homogeneous solution we get the basis $\{\cos... |
Context Suppose we have a grid-based game where a unit has a range parameter that serves as the upperbound of the sum of the costs of his movements in a single turn. Moving orthogonally to an adjacent tile costs 1, and moving diagonally to an adjacent tile costs $\sqrt{2}$. So a unit with range 4 can move up to 2 tiles... |
Short Answer
Set
Method -> {"MethodOfLines",
"DifferentiateBoundaryConditions" -> {True, "ScaleFactor" -> 1}}
inside
NDSolve will resolve the problem. It's not necessary to set
"ScaleFactor" to
1, it just needs to be a not-that-small positive number.
Long Answer
The answer for this problem is hidden in this obscure tut... |
This article provides answers to the following questions, among others:
How can the microstructure fraction of a steel be determined from the iron-carbon phase diagram? How is the phase fraction of a steel determined from the iron-carbon phase diagram? Introduction
For many applications it is important to know exactly ... |
Chakradhar, Sreekanth RP and Nagabhushana, BM and Chandrappa, GT and Ramesh, KP and Rao, JL (2004)
EPR of $Ni^{2+}$ ions in macro porous nanocrystalline $CaSiO_3$ ceramic powders. In: DAE Solid State Physics Symposium, Dec 26 - 30, 2004, Amritsar, India.
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Abstract
Porous wollastonite ... |
(Sorry was asleep at that time but forgot to log out, hence the apparent lack of response)
Yes you can (since $k=\frac{2\pi}{\lambda}$). To convert from path difference to phase difference, divide by k, see this PSE for details http://physics.stackexchange.com/questions/75882/what-is-the-difference-between-phase-differ... |
Determining the short-circuit rating of the breaker requires knowledge of the prospective fault current at the panelboard. Following section provides a simple method to obtain this current magnitude.
3-phase circuit breakers
Let’s start with calculating the prospective current from the nearest transformer.
Fault curren... |
103 0 1. Homework Statement
From Resnick and Halliday:
A metal plate 8 cm on a side carries a total charge of 60 microC. Using the infinite plate approximation, calculate the electric field 0.5 mm above the surface of the plate near the plate's center.
2. Homework Equations
(1) [tex]E = \frac{\sigma}{\epsilon_0}[/tex]
... |
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Forward-backward multiplicity correlations in pp collisions at √s = 0.9, 2.76 and 7 TeV
(Springer, 2015-05-20)
The strength of forward-backward (FB) multiplicity correlations is measured by the ALICE detector in proton-proton (pp) collisions at s√ = 0.9, 2.76 and 7 TeV. The measurement... |
Is the volume of solid bounded below by the sphere $$\rho=2 \cos(\phi)$$ and above by the cone $$z=\sqrt{x^2+y^2}$$ will be gotten by the following integration ?
in cylindrical form : $$V =\int_{0}^{2\pi}d\theta\int_{0}^{1}\int_{1+\sqrt{1-r^2}}^{r} r \,dz \, dr$$ (since the projection of their intersection will be a un... |
When I discuss a question with my colleague, he said he has a feeling that the symmetrization of functions should be unique up to a coefficient. However, I keep being critical at the point.
Specifically, symmetrization(standard) of a multivariable function is
$$Sf(x_1,\dots,x_n)=\frac{1}{n!}\sum_{\sigma\in S_n}f(\sigma... |
Topological proof of Benoist-Quint's orbit closure theorem for $ \boldsymbol{ \operatorname{SO}(d, 1)} $
Department of Mathematics, Yale University, New Haven, CT 06520, USA
We present a new proof of the following theorem of Benoist-Quint: Let $ G: = \operatorname{SO}^\circ(d, 1) $, $ d\ge 2 $ and $ \Delta<G $ a cocomp... |
In p-adic properties of modular schemes and modular forms Katz formulates the following base change theorem as Theorem 1.7.1
Let $n\geq 3$ and $\overline{\mathcal{M}}_n$ be the compactified moduli scheme of elliptic curves with level-$n$-structure over $\mathbb{Z}[\frac1n]$. Let $K$ be any $\mathbb{Z}[\frac1n]$-module.... |
Let us consider the simplest isoperimetric inequality. Consider a smooth simple closed curve given by $r=\rho(\theta)$ in polar coordinates, where $\rho(\theta)>0$ can be regarded as a smooth periodic function with period $2\pi$.
As $dA=rdrd\theta$, the area of the region $\Omega$ enclosed by the closed curve is \begin... |
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* [[Siril:Tutorial_import|Convert your images in the FITS format Siril uses (image import)]]
* [[Siril:Tutorial_import|Convert your images in the FITS format Siril uses (image import)]]
* [[Siril:Tutorial_sequence|Work on a sequenc... |
How to Model Moisture Flow in COMSOL Multiphysics®
Computing laminar and turbulent moisture flows in air is both flexible and user friendly with the
Moisture Flow multiphysics interfaces and coupling in the COMSOL Multiphysics® software. Available as of version 5.3a, this comprehensive set of functionality can be used ... |
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