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Since my question relates directly to a part of the text from a 2004 book,
Logic in Computer Science: Modelling and Reasoning about Systems (2nd Edition) by Michael Huth and Mark Ryan, in order to provide context for the following discussion, I'm partially quoting the book verbatim:
The decision problem of validity in ... |
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... |
A positive solution for an asymptotically cubic quasilinear Schrödinger equation
School of Mathematical Sciences, Dalian University of Technology, 116024 Dalian, China
$ - \Delta u + V(x)u - \Delta ({u^2})u = q(x)g(u),\;\;\;\;x \in {\mathbb{R}^N}, $
$N≥ 1$
$0 < q(x)≤ \lim_{|x|\to∞}q(x)$
$g∈ C(\mathbb{R}^+, \mathbb{R})$... |
$f\sim g$ does not imply $f'\sim g'$! L'hopital's rule only works in one direction:$$\log x \sim \log \left((5+\sin x)x\right) \quad\text{but}\quad\frac1{x}\nsim\frac{((5+\sin x)x)'}{(5+\sin x)x}$$or if you want,$$\log\log x \sim \log \log \left((5+\sin x)x\right) \quad\text{but}\quad\frac1{x\log x}\nsim\frac{((5+\sin ... |
Is it possible (tractable) to determine if the following system of equations has any nontrivial solutions (ie, none of the unknowns are zero) in the domain of integers?
$$A^2 + B^2=C^2 D^2$$ $$2 C^4 + 2 D^4 = E^2 + F^2$$
Mathematics Stack Exchange is a question and answer site for people studying math at any level and ... |
Conservation of the number of particle is a symmetry of the system. As Akshay Kumar said in his response, when the number of particles operator commutes with the Hamiltonian, it is conserved. It simply means, well, that's the number of particle is conserved. Particles are all what is discussed in condensed matter (bett... |
The two previous answers certainly solve the problem. Soundness of Geoffroy's protocol is fine indeed, but there is the appearance of the witness $x$ in the computation of the announcement $(A',B')$ as $B'=g^{r_x/x} h^r$. This can be avoided, however, and at the same time one can find the protocol maybe in a bit more n... |
The usual formula for euclidean distance that everybody uses is
$$d(x,y):=\sqrt{\sum (x_i - y_i)^2}$$
Now as far as I know, the sum-of-squares usually come with some problems wrt. numerical precision.
There is an obviously equivalent formula:
$$d(x,y):= c \sqrt{\sum \left(\frac{x_i - y_i}{c}\right)^2}$$
Where it seems ... |
A corrected form of the question asks to show that $\int_{\mathbb R^n} e^{-x^tAx}\;dx\;=\; \pi^{n/2}/\sqrt{\det A}$ for symmetric $n$-by-$n$ $A$ with positive-definite real part. First, for $A$
real (positive-definite), there is a (unique) positive-definite square root $S$ of $A$, and the change of variables $x=S^{-1}y... |
I am studying from a set of notes (otherwise quite excellent) which does not explicitly specify some definitions of "ordering."
I have tried to accumulate the various pieces from various discussions and proofs in the text, but am having a hard time putting them together.
In one place it says
strictly well-orderered by ... |
The problem isn't fully solvable in exact form, since it requires the solution of a transcendental equation to get $k$, and with it the energy eigenvalue. This shouldn't be surprising $-$ it's exactly the same situation as for a particle in a ring (i.e. without the internal cutout).
You are correct in all the steps tha... |
Difference between revisions of "Gamma-function"
(Figure 4)
m (Г(x) = (x-1)!)
Line 9: Line 9:
$
$
−
A transcendental function $\Gamma(z)$ that extends the values of the factorial $z!$ to any complex number $z$. It was introduced in 1729 by L. Euler in a letter to Ch. Goldbach, using the infinite product
+
A transcenden... |
Update: Rupert has withdrawn his claim. See the final bullet point below.
Rupert McCallum has posted a new paper to the mathematics arXiv
Rupert McCallum, The choiceless cardinals are inconsistent, mathematics arXiv 2017: 1712.09678.
He is claiming to establish the Kunen inconsistency in ZF, without the axiom of choice... |
A object orbiting the earth has total mechanical energy equal to \begin{align*} E^{mech} = \frac{1}{2} m v^2 - \frac{GMm}{r} \end{align*} with $M$ the mass of the earth and $r$ the distance. My course notes say we have to equal $E^{mech} = 0$ find the escape velocity, which then gives \begin{align*} v = \sqrt{\frac{2GM... |
I'm interested in the pure gauge (no matter fields) case on Minkowski spacetime with simple gauge groups. It would be nice if someone can find a review article discussing all such solutions
EDIT: I think these are relevant to the physics of corresponding QFTs in the high energy / small scale regime. This is because the... |
There are two ways to answer your question. One is direct and has less depth to it, the other is more indirect and has a lot of depth to it. I will begin with the indirect one because it has wide ranging applications beyond finance or economics and because it should serve as a warning to journal editors and so forth. A... |
Numerical simulations of physical processes generally involve solving some
differential equation on a computational domain too complicated to solve analytically. Solving simple systems by “hand” is quite possible in one-dimension. But things get more complicated as you go to higher dimensions. If the domain has a nice ... |
I am trying to understand this paper: http://link.aps.org/doi/10.1103/PhysRevLett.99.236809
(Here is an arXiv version: http://arxiv.org/abs/0709.1274)
In the introduction, they mention certain symmetry arguments (the two paragraphs in the second column of the first page). Unfortunately, I am ill-equipped to understand ... |
That depends on the groups you are working in.
Using a $\Sigma$-protocol
If you have a group $G$ of prime order $q$ where the DDH is hard and you have a DH tuple $(g,g^u,g^v,g^w)$ with $w\equiv uv \pmod q$, then if your prover knows one of these values, say $u$, then we can write the DH tuple as $(g,g^u,h,h^u)$ and he ... |
I just review the following problem:
How to find the limits $\lim\limits_{h\rightarrow 0} \frac{e^{-h}}{-h}$ and $\lim\limits_{h\rightarrow 0} \frac{|\cos h-1|}{h}$?
However, I cannot still know how to solve the following: How to find the following: $$\lim_{x\rightarrow 0^+} \frac{e^{-a/x}}{x}, \ \ a>0$$
By L'hospital'... |
The moments of a continuous distribution, and functions of them like the kurtosis, tell you extremely little about the graph of its density function.
Consider, for instance, the following graphs.
Each of these is the graph of a non-negative function integrating to $1$: they are all PDFs. Moreover, they all have exactly... |
Is this new mathematics?
No. Just an argument over mathematical presentation, bringing together individual observations previously made by e.g. Hatcher 2002.
What mathematical presentation?
It is standard practice to define ‘reduced’ homology after and on the basis of ‘traditional’ homology. But reduced homology is act... |
The process $X$ is not gaussian and its increments are not independent.
Note first that $X$ is a Brownian martingale, hence a Brownian motion with a change of time, thus, it is distributed like $(\beta_{\langle X\rangle_t})$, where $\beta$ is a Brownian motion independent of $X$. For example, $X_1$ has the distribution... |
Assume that the model of computation is a standard Turing machine model with input alphabet $\Sigma = \{0,1\}$, work alphabet $\Gamma = \{0,1,\_\}$, 1 input tape, 1 work tape and 1 output tape.
We can build a Turing machine $U$ that accepts a (reasonable) binary representation of a Turing machine $M$ and
simulates it (... |
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Now showing items 1-10 of 32
The ALICE Transition Radiation Detector: Construction, operation, and performance
(Elsevier, 2018-02)
The Transition Radiation Detector (TRD) was designed and built to enhance the capabilities of the ALICE detector at the Large Hadron Collider (LHC). While aimed at providing electron... |
Let $ f:S→B$ be an elliptic fibration from an integral surface $ S$ to integral curve $ B$
.
Here I use following definitions:
A surface (resp. curve) is a $ 2$ -dim (resp. $ 1$ -dim) proper k scheme over fixed field $ k$ .
Fibration has two properties: 1. $ O_B = f_*O_S$ 2. all fibers of f are geometrically connected
... |
From Folland's
Analysis, suppose $\{E_j\}_1^\infty \subset \mathcal{A}$. Set
$$F_k = E_k \setminus \bigcup_{j=1}^{k-1}E_j$$
Then the $F_k$'s are disjoint, and $\bigcup_1^\infty E_j = \bigcup_1^\infty F_k$.
My question is, what if you let $x \in \bigcap_1^\infty E_j$? Then wouldn't $x \in \bigcup_1^{k-1}E_j$ for all $k$... |
A compact locally connected metric space is "uniformly locally connected"\ That is, for any $\epsilon > 0$, there is some $\delta > 0$ such that whenever $\rho(x, y) < \delta$, then $x$ and $y$ both lie in some connected subset of $X$ of diameter $<\epsilon$.
proof:-
Since $X$ is locally connected metric space then eac... |
I think the question is more about the physical intepretation of the complex expression
$\psi (x,t)=Ae^{i(kx-\omega t)}$
than the mathematical meaning of it. For the physical meaning of it, we think of the probability amplitude like a rotating arrow, which rotates as the particle travels in space. The rotation frequenc... |
For example, I don't understand why the speed of a satellite moving in an orbit of radius 'a' around the Earth must be equal to $\sqrt{GM/a}$ If I release a particle in outer space with a velocity perpendicular to the line joining the particle and Earth but magnitude not equal to $\sqrt{GM/a}$ what will happen? For al ... |
Thank you for using the timer!We noticed you are actually not timing your practice. Click the START button first next time you use the timer.There are many benefits to timing your practice, including:
Hello, Am new here. I just took the m25 GMAT CLub Test and I don't get the solution of a question. (Q19)
If equation \(... |
THE PACE OF SCIENCE -- THE DEVELOPMENT OF EXTENSIONS
Augustin-Louis Cauchy (1789-1857) published his famous inequality in 1821 in the second of two notes on the theory of inequalities that formed the final part of his book
Cours d'Analyse Algébrique, a volume which was perhaps the world's first rigorous calculus text. ... |
arXiv:1906.04715 [math.AP] Asymptotic analysis of exit time for dynamical systems with a single well potential
Published 2019-06-11Version 1
We study the exit time from a bounded multi-dimensional domain $\Omega$ of the stochastic process $\mathbf{Y}_\varepsilon=\mathbf{Y}_\varepsilon(t,a)$, $t\geqslant 0$, $a\in \math... |
A novel scheme suitable for the emulation of fractional-order capacitors and inductors of any order less than 2 is presented in this work. Classically, fractional-order impedances are characterized in the frequency domain by a fractional-order Laplacian of the form \(s^{\pm \alpha }\) with an order \(0<\alpha <1\). The... |
ISSN:
1930-5311
eISSN:
1930-532X
All Issues
Journal of Modern Dynamics
Open Access Articles
Abstract:
This special issue presents some of the lecture notes of the courses held in the 2008 and 2011 Summer Institutes at the Mathematics Research and Conference Center of Polish Academy of Sciences at Będlewo, Poland. The s... |
arXiv:1906.04719 [math.CO] The $h^*$-polynomials of locally anti-blocking lattice polytopes and their $γ$-positivity
Published 2019-06-11Version 1
A lattice polytope $\mathcal{P} \subset \mathbb{R}^d$ is called a locally anti-blocking polytope if for any closed orthant $\mathbb{R}^d_{\varepsilon}$ in $\mathbb{R}^d$, $\... |
Can you all please solve this one?
I was originally thining of $$\int_{-\infty}^{\infty} e^{-iax}\left(\frac{x^2}{n} + 1\right)^{-\frac12(n+1)} \,dx.$$
My mentor has told me that if n is odd you can calculate this and if n is even you will get to use special functions.
If n is odd. $$\int_{-\infty}^{\infty} e^{-iax}\le... |
I understand that a function $f:X\to Y$ is surjective iff $\forall \, y \in Y, \exists x \in X$, such that $f(x)=y$
Basically, every element of $Y$ needs to have at least $1$ pre image.
Intuitively, I can show a function is surjective if I can show that Range = Codomain.
But given my limited skills, I'm not always able... |
Let $f(x)=x^8-16$. Determine the Galois group of the splitting field of $f(x)$ over the field $K$ in each case.
a) $K=\Bbb{Q}$
b) $K=\Bbb{Z}_{17}$.
a) The roots of $f(x)$ are $\alpha$, $\alpha\omega$, $\alpha\omega^2$, ... ,$\alpha\omega^7$ where $\alpha=16^{1/8} = (2^4)^{1/8} = 2^{1/2}$ and $\omega$ is the $8$th primi... |
What do you mean by "pursue"? If you mean trying to produce a full-fledged theory of quantum gravity that can be "directly added" to the standard model, it's most likely not worth to "pursue". See for instance, this "proof".
But often, we can use theories which are actually inconsistent, but can give some meaningful re... |
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Application of the preventive maintenance scheduling to increase the equipment reliability: Case study- bag filters in cement factory Extension of g... |
This one is obviously a little messy, but there is a simple methodology by which the volume may be reduced to a single integral. The idea is to compute the cross sectional area $A(z)$ for each value of $z$ in the volume, and then integrate over $z$ to get the volume.
First, we needs the bounds in $z$. This is done by o... |
The CAPM is an economic theory that expected returns in excess of the risk free rate should be linear in the regression beta on the market.
$$ \operatorname{E}[R_i - R^f] = \beta_i \operatorname{E}[R^m - R^f]$$
Graphically, it would look like this:
As market beta increases, expected returns increase.
Testing the CAPM w... |
Difference between revisions of "Group cohomology of elementary abelian group of prime-square order"
(→Over an abelian group)
Line 33: Line 33:
The homology groups with coefficients in an abelian group <math>M</math> are given as follows:
The homology groups with coefficients in an abelian group <math>M</math> are give... |
While answering a question about the MacLaurin Series Expansion of a composite function I noticed something strange I can not explain to myself. The task was to verify that the MacLaurin Series Expansion of $\ln(1+\sin x)$ is up to the fourth term given by
$$\ln(1+\sin x)=x-\frac{x^2}2+\frac{x^3}6-\frac{x^4}{12}+\left(... |
I am reading Rebonato's Volatility and Correlation (2nd Edition) and I think it's a great book. I'm having difficulty trying to derive a formula he used that he described as the expression for standard deviation in a simple binomial replication example:
\begin{eqnarray}\sigma_S\sqrt{\Delta t}=\frac{\ln S_2-\ln S_1}{2}\... |
I don't understand the difference between the parameter $C$ and $λ$ in terms of the SVM. It seems to me that they are both involved in regulating over-fitting of the data.
What difference between $C$ and $λ$?
Cross Validated is a question and answer site for people interested in statistics, machine learning, data analy... |
Definition:Upper Closure Contents Definition
Let $\left({S, \preccurlyeq}\right)$ be an ordered set.
Let $a \in S$.
The upper closure of $a$ (in $S$) is defined as: $a^\succcurlyeq := \left\{{b \in S: a \preccurlyeq b}\right\}$
Let $T \subseteq S$.
The upper closure of $T$ (in $S$) is defined as: $T^\succeq := \bigcup ... |
First find the molality of solute particles. Assume i = 1; we're just counting how many things are dissolved and it doesn't matter whether they are ions or molecules at this point. I'm using m for mass and b for molality throughout to avoid confusion.
$\Delta T = ibk_f\implies\frac{\Delta T}{k}=b$
$b=\frac{0.768}{1.86}... |
Maybe it could be called book-errata?
I cannot give many examples of discussions from math.SE offhand but at least one example from here https://math.stackexchange.com/questions/34641/find-limit-of-unknown-function
This is an example from a different forum: http://www.sosmath.com/CBB/viewtopic.php?p=181367
I guess ques... |
I am having a hard time understanding the numbers of probing which might occur due to using different collision prevention method such as separate chaining, Linear Probing, double probing, which is given here.
Let $\alpha = N/M$ (the load factor: average number of keys per array index). Analysis is probabilistic, rathe... |
The Radon–Nikodym theorem states that,
given a measurable space $(X,\Sigma)$, if a $\sigma$-finite measure $\nu$ on $(X,\Sigma)$ is absolutely continuous with respect to a $\sigma$-finite measure $\mu$ on $(X,\Sigma)$, then there is a measurable function $f$ on $X$ and taking values in $[0,\infty)$, such that
$$\nu(A) ... |
I'm starting to study elliptic partial differential equations and I just want to know if there are any connections between the following concepts:
An elliptic partial differential equation is given as being a second-order partial differential equation of the form $$Au_{xx} + 2Bu_{xy} + Cu_{yy}+Du_{x} + Eu_{y} + F = 0$$... |
It's been a while since I've done any geometry so I'm a bit confused by this question.
We have a triangle $\triangle PQR$ whose total area is $90 \mathrm{cm}^2$. Another triangle $\triangle PTU$ is formed inside $\triangle PQR$ where the point $T$ is such that $PT=2TQ$ and $U$ is such that $QU = 2UR$. The points $T,U$ ... |
The skew/smile of long term options is flatter than short term options, the reason for this can be explained in several ways.The Vega of a shorter-dated option is smaller than a longer-dated option. Vega is the dollar value of a 1% change in implied volatility.i.e.,30d ATM option, $65 strike, .31 ivol = VEGA .0730d 25 ... |
You can use a supermajority rule to eliminate the possibility of Condorcet cycles. e.g. if you require a \(\frac{2}{3}\) supermajority there is no possibility of creating a Condorcet triple with the majority strictly preferring A to B, B to C and C to A.
Unfortunately that’s only the three candidate case. If you consid... |
The first-ever article on this blog was a quick introduction to the Particle In Cell (PIC) Method. That article (and the follow up example) discussed a two-dimensional Cartesian implementation. The ideas presented there are easily extended to 3D codes. But many engineering applications exhibit azimuthal symmetry. For i... |
Given an ellipse with semi major axis $a$ and semi minor axis $b$. What is the formula to compute the chord length formed by two points, say $P$ and $Q$ on the arc of the ellipse (Euclidean distance between the two points).
The parametric equation for the ellipse are $(x,y)=(a \cos \theta, b \sin \theta)$ and the lengt... |
Advance warning: This is a very boring post.
In my last post I outlined a ludicrously over-simplified model for why you might want to consider high variance strategies.
I’ve been thinking over some of the modelling assumptions and wondering whether it could be made a bit less over-simplified. The only ones that are obv... |
There are several straightforward ways to do this in Excel.
Perhaps the simplest uses
LINEST to fit the lines conditional on a trial value of the x-intercept. One of the outputs of this function is the mean squared residual. Use
Solver to find the x-intercept minimizing the mean squared residual. If you take some care ... |
I'm trying to understand why the following proposition is true:
Let $J$ be a small category and $F, G : J \to \textbf{Top}$ functors. If $\tau : F \Rightarrow G$ is a pointwise homotopy equivalence, then $\operatorname{hocolim}_J F \to \operatorname{hocolim}_J G$ is a homotopy equivalence.
This seems to be such a natur... |
This question deals with Bayesian updating with conjugate prior.Suppose we have a prior distribution of
N~(5, 3) and then we observe 5 data points (8, 9, 10, 8, 7) (assumed to be taken randomly from a N~(9, 3) distribution). What would be the posterior after these observations in the form of N~(x, y)? I read the Wikipe... |
Continued fraction
A continued fraction is an expression of the form
$$a_0+{b_1|\over |a_1}+\cdots+{b_n|\over |a_n}+\cdots,\label{1}$$ where
$$\def\o{\omega}\{a_n\}_{n=0}^\o\label{2}$$ and
$$\{b_n\}_{n=1}^\o\label{3}$$ are finite or infinite sequences of complex numbers. Instead of the expression (1) one also uses the ... |
Layer-adapted Methods for a Singularly Perturbed Singular Problem
Related Articles The Evolution of General Three-Dimensional Disturbances in a Thermally Stratified Couette Flow. Balagondar, P. M.; Vijayalakshmi, A. R. // Global Journal of Pure & Applied Mathematics;2007, Vol. 3 Issue 3, p399
The evolution of general t... |
We will develop conservation of energy relations for electricity that are analogous to those we just developed for flowing fluids. Instead of a real fluid flowing, current electricity (as opposed to static electricity) involves the flow of electric charge. To create intensive energy systems we divide by electric charge... |
The main concepts from this chapter are:
A material wave is a propagating disturbance in a material, while the atoms that make up that material do not travel very far.
Waves describe a large range of phenomena such as ripples in a medium, pressure fluctuations in sound or even fluctuations that describe light.
A wave f... |
I'm trying to go through the proof of rejection sampling and I found a paper ACCEPTANCE-REJECTION SAMPLING MADE EASY which provides several helpful explanations. For Lemma 2, the paper claims that if $Z$ has a uniform distribution $A$, and let $B \subset A$ and then the conditional distribution of $Z$ given $Z \in B$ i... |
At higher loops it certainly isn't true that amplitudes are real. By the optical theorem the imaginary part of an amplitude is related to the intermediate states that can go on-shell. At higher loops lots of intermediate particles can go on shell so one gets an interesting imaginary part.
But here's one interesting way... |
In a paper by Joos and Zeh, Z Phys B 59 (1985) 223, they say:This 'coming into being of classical properties' appears related to what Heisenberg may have meant by his famous remark [7]: 'Die "Bahn" entsteht erst dadurch, dass wir sie beobachten.'Google Translate says this means something ...
@EmilioPisanty Tough call. ... |
Consider the following problem:
Input: lists $X,Y$ of integers Goal: determine whether there exists an integer $x$ that is in both lists.
Suppose both lists $X,Y$ are of size $n$. Is there a deterministic, linear-time algorithm for this problem? In other words, can you solve this problem in $O(n)$ time deterministicall... |
A very basic and very strange question came to me.
Let $D\subseteq\mathbb {R}$, $f:D\to\mathbb{R}$ a continuous function. Then $f$ is uniformly continuous on $D$ iff. $$\forall\epsilon>0\ \exists\delta>0\,\,\text{such that}\,\,\forall\,x,y\in D$$ we have $$|y-x|<\delta\,\Longrightarrow\, |f(y)-f(x)|<\epsilon$$. Now, le... |
Learning Objectives
Explain what an impulse is, physically Describe what an impulse does Relate impulses to collisions Apply the impulse-momentum theorem to solve problems
We have defined momentum to be the product of mass and velocity. Therefore, if an object’s velocity should change (due to the application of a force... |
A common mistake is the thought that the total energy is the sum of all orbital energies $\{\epsilon_i\}$.
From Step #6 of Daniel Crawford's SCF programming project (modified slightly in some places):
The SCF electronic energy may be computed using the density matrix as:
$$
E_{\text{elec}} = \sum_{\mu\nu}^{\text{AO}} D... |
A random person (let's call him Bob) is given 3 cards, containing the names of 3 different countries. Bob is also given the names of the capital cities of these countries (in random order), and his task is to place the country cards with the correct capitals, i.e. to form correct pairs. It just so happens that Bob has ... |
2019-05-20 15:18 Detaljerad journal - Similar records 2019-01-23 09:13
nuSTORM at CERN: Feasibility Study / Long, Kenneth Richard (Imperial College (GB)) The Neutrinos from Stored Muons, nuSTORM, facility has been designed to deliver a definitive neutrino-nucleus scattering programme using beams of $\bar{\nu}_e$ and $\... |
So I have two functions. $f(x) = e^{-x^2+1}$ and $g(x)=\sqrt{x^2-4x+3}$. I am then asked to determine the domain and range of
$a)f∘g,$
$b)g∘f$
I already did part $a)$ and the domain for part $b)$.
For part $a)$, the domain was $(-\infty,1)\cup(3,\infty)$ and the range was $(0,e^2)$.
For part $b$, I figured out that the... |
17 November 2016
Abstracts
Abstract: Finding cycles in graphs is a fundamental problem in algorithmic graph theory. In this paper, we consider the problem of finding and reporting a cycle of length 2k in a graph G with n nodes and m edges for constant k >= 2. A classic result by Bondy and Simonovits [J. Combinatorial T... |
Fields Interact and Propagate as Waves
When we started discussing the electric and magnetic fields they seemed to be quite separate. We knew that any electric charge (moving or not) created an electric field, and that any
moving charge created a magnetic field. Other than that there is not much similarity: the forces p... |
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Up a level 39. Article
Aad, G, Abbott, B, Abdallah, J et al. (2883 more authors) (2016)
Addendum to ‘Measurement of the tˉt production cross-section using eμ events with b-tagged jets in pp collisions at √s = 7 and 8 TeV with the ATLAS detector’. European Physical Journal C: Particles and Fields, 76. 6... |
Let $X:=W^{1,1}(\mathbb{R}^{2})\cap W^{1,\infty}(\mathbb{R}^{2})$ be given. Is it true that $$ X\overset{c}\hookrightarrow L^{1}(\mathbb{R}^{2}),$$ meaning that $X$ is compactly embedded in $L^{1}(\mathbb{R}^{2})$.
The typically Frechet-Kolmogorov Compactness Theorem cannot be applied here directly since we would need ... |
So the question states, Let $B = \{x = (x_1,x_2,x_3) \in \mathbb{R}^3: x_1^2 +x_2^2 +x_3^2 \leq 1 \}$ be the unit ball in $\mathbb{R}^3$. Compute the diameter of $B$ for each of the following metrics.
note: $diam(B) = \sup\{d(x,y): x,y \in B\}$
I know the diameter is 2 but I want to be able to do this in general for an... |
This is only a partial answer - it shows that the sequence converges, but does not give the limit.
Define$$I_n(x) = \int_0^x \cos^{2n+1}(t)dt .$$We have $I_n(\pi) = 0$ because $\cos^{2n+1}(\pi/2 + t) = -\cos^{2n+1}(\pi/2 - t)$. For $a \in (0,2\pi)$ define $$f(n,a) = \int_0^a (1 + 1/4\cos^{2n+1}(t))dt = a + 1/4 I_n(a) .... |
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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 ... |
Your method for solving the problem is correct, but you have made some mistakes.
First, you have assumed that the current $i$ through the inductor towards Earth equals $-\frac{dq}{dt}$ where $q$ is the charge on the sphere. This is not quite correct because charge is also arriving on the sphere from the electron beam a... |
NOTE - I didn't receive any answer in here and I think because my first post is not clear, so I entirely made another example:
$K={\{id,r^2,r^4,s,r^2s,r^4s}\}$ is a proper subgroup of the dihedral group $D_6$. As it is shown here by Gerry Myerson, $K$ is isomorphic to $S_3$. We label the vertices of the hexagon 1 throu... |
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Now showing items 1-10 of 24
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 ... |
While I was working on noise profile creation for darktable, I had to learn how variance stabilization transform work.
So, here is a summary of what I learnt about this What are variance stabilization transform? Noise variance is not constant: the variance depends on the light intensity. Typically, variance is higher i... |
This question was motivated by this related one: How "far" a differential form is from an exterior product .
Let $\mathbb{V}$ be a vector space of dimension $n$ with underlying field $\mathbb{F}$, and say (for lack of a better term) that the
wedge rank of a $k$-form $$\phi \in \Lambda^k \mathbb{V}^*$$ is the minimum nu... |
Dynamical behaviors of stochastic type K monotone Lotka-Volterra systems
Department of Mathematics, Harbin Institute of Technology (Weihai), Weihai 264209, China
Two n-species stochastic type K monotone Lotka-Volterra systems are proposed and investigated. For non-autonomous system, we show that there is a unique posit... |
Let $A(n, B, d)$, $B(n, d)$ be a {Turing machine, random-access machine, C program} with finite tape (which I'm going to denote "Turing machine*" and "random-access machine*" respectively), $n \in \mathbb{N}$. $A$ and $B$ are the same type of machine. For any $N \in \mathbb{N}$, statements where $n \leq N$, don't matte... |
With the spring attached to a wall (and not the ceiling) one might assume that the mass is sliding on a friction-less horizontal surface. Then the starting kinetic energy = the final potential energy: (½) m vo^2 = (½) k x^2 where k is the spring constant and x is the stretch. If the spring is hanging vertically, the re... |
There are cases where the symmetries of a problem ( seem to ) characterize its complexity. One very interesting example is constraint satisfaction problems (CSPs).
Definition of CSP
A CSP is given by a domain $U$, and a constraint language $\Gamma$ ($k$-ary functions from $U^k$ to $\{0, 1\}$). A constraint satisfaction... |
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Now showing items 31-40 of 451
SOME APPLICATIONS OF COMPLEX GEOMETRY TO FIELD THEORY
(1981)
Let be compactified complexified Minkowski space, and ('*) twistor space and dual twistor space, respectively, and ambitwistor space, a complex hypersurface in x ('*). There is a geometric ...
Numerical safeguarded use of... |
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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 ... |
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Now showing items 1-10 of 32
The ALICE Transition Radiation Detector: Construction, operation, and performance
(Elsevier, 2018-02)
The Transition Radiation Detector (TRD) was designed and built to enhance the capabilities of the ALICE detector at the Large Hadron Collider (LHC). While aimed at providing electron... |
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Now showing items 1-7 of 7
Measurement of electrons from beauty hadron decays in pp collisions at root √s=7 TeV
(Elsevier, 2013-04-10)
The production cross section of electrons from semileptonic decays of beauty hadrons was measured at mid-rapidity (|y| < 0.8) in the transverse momentum range 1 < pT <8 GeV/c wit... |
06/04/2011, 09:43 PM (This post was last modified: 06/04/2011, 10:26 PM by tommy1729.)
(06/04/2011, 01:13 PM)Gottfried Wrote: Sometimes we find easter-eggs even after easter...
For the alternating iteration-series
(definitions as copied and extended from previous post, see below)
we find a rational polynomial for p=4. ... |
I currently have a very limited understanding of this topic and would be very grateful if someone could work me through a solution to this question:
Let $\phi : M \to N$ be a diffeomorphism of manifolds. For a vector field $X$ on $M$ define the
push-forwardvector field $Z = \phi_* X$ on $N$ by $$Z|_y = \mathrm{d}\phi_x... |
Let the pdfs of $X$, $Y$, and $Z$ be denoted by $f_X(x)$, $f_Y(y)$, and $f_Z(x)$, respectively.
I don't immediately see how this problem can be solved when $f_X(x)$ and $f_Y(y)$ are
unknown. However, you say that $X$ and $Y$ are mean $0$ as well as Gaussian, so the only missing pieces of information are their variances... |
There is a objective function:
$f(W)$ = $||W||_{2,1}$
For any element $w_{ab}$ in $W$, we apply $F_{w_{ab}}$ to denote the part of $f(W)$ which is only related to $w_{ab}$.
$F'_{w_{ab}}=(DW)_{ab}$
$F''_{w_{ab}}=(D-D^{3}(W\odot W))_{aa}$, (the main problem)
where $D_{ii}$=$\frac{1}{||w^i||_2}$, $\odot$ denotes the eleme... |
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