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Is there an efficient algorithm for the following problem?
Given: a $m$-vector $b \in \{0,1,2\}^m$, and a $m \times 2m$ matrix $A$, with the promise that for every $b' \in \{0,1,2\}^m$, there exists $x' \in \{0,1\}^{2m}$ such that $Ax'=b' \pmod 3$ Goal: find $x \in \{0,1\}^{2m}$ such that $Ax'=b' \pmod 3$
In more detai... |
Difference between revisions of "Extendible"
(→$C^{(n)}$-extendible cardinals: I3)
(→Virtually extendible cardinals: start merging)
Line 87: Line 87:
If $κ$ is [[huge|virtually huge*]], then $V_κ$ is a model of proper class many virtually extendible cardinals.
If $κ$ is [[huge|virtually huge*]], then $V_κ$ is a model o... |
The
amsmath package provides a handful of options for displaying equations. You can choose the layout that better suits your document, even if the equations are really long, or if you have to include several equations in the same line.
Contents
The standard LaTeX tools for equations may lack some flexibility, causing o... |
Review Comment:
This manuscript was submitted as 'full paper' and should be reviewed along the usual dimensions for research contributions which include (1) originality, (2) significance of the results, and (3) quality of writing.
In this paper, the authors present a knowledge graph embedding approach based on the idea... |
Hello fellows,
As referred in Wikipedia (see the specified criteria there), L'Hôpital's rule says,
$$ \lim_{x\to c}\frac{f(x)}{g(x)}=\lim_{x\to c}\frac{f'(x)}{g'(x)} $$
As
$$ \lim_{x\to c}\frac{f'(x)}{g'(x)}= \lim_{x\to c}\frac{\int f'(x)\ dx}{\int g'(x)\ dx} $$
Just out of curiosity, can you integrate instead of takin... |
The following question was asked at Math StackExchange but, having attracted some attention, didn't get solved.
Problem 323 from the Mathematical Excalibur Vol. 14, No. 2, May-Sep. 09, linked here (see page 3, where also a solution is given), reads:
$\qquad$
Prove that there are infinitely many positive integers n such... |
The Annals of Probability Ann. Probab. Volume 40, Number 5 (2012), 2069-2105. The functional equation of the smoothing transform Abstract
Given a sequence $T=(T_{i})_{i\geq1}$ of nonnegative random variables, a function $f$ on the positive halfline can be transformed to $\mathbb{E}\prod_{i\geq1}f(tT_{i})$. We study the... |
Linear Lagrange Interpolating Polynomials
We will now begin to discuss various techniques of interpolation. Given a set of discrete points, we sometimes want to construct a function out of polynomials that is an approximation of another known (or possibly unknown) function. Interpolations can be useful as the original ... |
We now present several multiplicative number theoretic functions which will play a crucial role in many number theoretic results. We start by discussing the Euler phi-function which was defined in an earlier chapter. We then define the sum-of-divisors function and the number-of-divisors function along with their proper... |
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Search for new resonances in $W\gamma$ and $Z\gamma$ Final States in $pp$ Collisions at $\sqrt{s}=8\,\mathrm{TeV}$ with the ATLAS Detector
(Elsevier, 2014-11-10)
This letter presents a search for new resonances decaying to final states with a vector boson produced in association with a... |
Standard Unit Vectors
Definition: The vectors $\vec{i} = (1, 0, 0)$, $\vec{j} = (0, 1, 0)$, and $\vec{k} = (0, 0, 1)$ are said to be Standard Unit Vectors, that is a vector that runs on either the $x$, $y$ or $z$-axis and has a magnitude of 1, that is $\mid \mid \vec{i} \mid \mid = \mid \mid \vec{j} \mid \mid= \mid \mi... |
November 18th, 2012, 04:06 PM
# 1
Senior Member
Joined: Aug 2012
From: South Carolina
Posts: 866
Thanks: 0
Finding the Particular Solution of diff eqn
dy/dx = 8x^3 -9x^2 + 4 and y =5, when x = 0
wanted to see this worked out in full
ty
November 18th, 2012, 04:52 PM
# 4
Senior Member
Joined: Nov 2011
Posts: 595
Thanks: ... |
Let $(a_n)_{n \in \mathbb{N}}$ be a convergent sequence with limit $a \in \mathbb{R}$. Show that the arithmetic mean given by: $$s_n:= \frac{1}{n}\sum_{i=1}^n a_i \tag{A.M.} $$ also converges to $a$.
I have read: arithmetic mean of a sequence converges but unfortunately the answers there don't help me much because I do... |
The Seifert-van Kampen Theorem Example 3
On The Seifert-van Kampen Theorem page we stated the very important Seifert-van Kampen theorem. We will now look at some examples of applying the theorem. More examples can be found on the following pages:
The Seifert-van Kampen Theorem Example 3 Example 3 Let $X$ be the Klein b... |
I have the following exercise:
Use Heisenberg's uncertainty principle and the relation $\Delta u = \sqrt{\langle u^2 \rangle - \langle u \rangle^2}$ to find the range of energy an electron has in an atom of diameter 1 amstrong.
This is the attempt at a solution:
From the uncertainty principle: $\Delta p \Delta x \geq \... |
Eigenvalue arguments tend to work well when the base field $\Bbb F$, with $A \in M_{n \times n}(\Bbb F)$, is
algebraically closed, so that all roots of the characteristic polynomial are guaranteed to exist in $\Bbb F$. Here's an inductive demonstration not based on eigenvalues and eigenvectors which works over any fiel... |
Given a mapping in the Sobolev space $f\in W^{2,n}_{\rm loc}(\mathbb{R}^n,\mathbb{R}^n)$ I would like to know what is the Sobolev regularity of the Jacobian $J_f=\operatorname{det} Df$.
It is well known and easy to prove that if $u,v\in W^{1,p}\cap L^\infty(\mathbb{R}^n)$, then $uv\in W^{1,p}\cap L^\infty$. Indeed, pro... |
You need a slightly stronger version of continuity: Lipschitz. Recall Lipschitz continuity implies uniform continuity
Let $f:[a,b]\rightarrow\mathbb{R}$ be a function. $f'(x)$ is bounded if and only if $f$ is Lipschitz.
$\implies)$ $f'(x)$ is bounded. WTS $f$ is Lipschitz.
If the derivative is bounded, we have $|f(x)|\... |
Connectedness of Box Topological Products
Recall from the Connectedness of Finite Topological Products page that if $\{ X_1, X_2, ..., X_n \}$ is a finite collection of connected topological spaces then the topological product $\displaystyle{\prod_{i=1}^{n} X_i}$ is also connected. We also noted that if instead $\{ X_i... |
Let $W$ be a subspace of $\mathbb{R}^n$. For $x \in \mathbb{R}^n$, define
$$\rho (x) = \inf_{y \in W} \Vert x - y \Vert _2$$
Let $\{ u_1, \ldots, u_m \}$ be an orthonormal basis of $W$, where $m$ is the dimension of $W$. Extend this to an orthonormal basis $\{ u_1, \ldots, u_m, \ldots, u_n \}$ of all of $\mathbb{R}^n$.... |
Skills to Develop
The following questions are meant to guide our study of the material in this section. After studying this section, we should understand the concepts mo- tivated by these questions and be able to write precise, coherent answers to these questions. How is the tangent function defined? What is the domain... |
What I am interested in is to find an expression for
$$\frac{\partial^2G(S,\sigma)}{\partial S\partial\sigma}$$
where $G$ is inverse function in the first argument of function $C$ such that $S = C(G(S,\sigma), \sigma)$, and we define $C$ as
\begin{align*} C(V,\sigma) &=V N \left(d_1 \right) - D \exp \left( -rT\right) N... |
Table of Contents
The Boundary of a Set in a Topological Space Examples 1
Recall from The Boundary of a Set in a Topological Space that if $(X, \tau)$ and $A \subseteq X$ then a point $x \in X$ is said to be a boundary point of $A$ if for every $U \in \tau$ with $x \in U$ we have that $U$ intersects $A$ and $A^c$ nontr... |
Can someone explain the reasoning behind the answers given? We reviewed these in class, but I wasn't able to grasp the logic. Especially c, d, and e.
The domain of possible values for variables X and Y is {Jim, Ann, Sal, Pat, Tom}. The following facts define the values for which the child predicate is true. The child p... |
Table of Contents
Systems of First Order Ordinary Differential Equations
Recall from the First Order Ordinary Differential Equations page that if $D \subseteq \mathbb{R}^2$ is a domain (a nonempty, open, connected subset of $\mathbb{R}^2$) and $f \in C(D, \mathbb{R})$ then a first order ordinary differential equation h... |
The Schottky defect (small shot effect) is named after a popular German physicist Walter H. Schottky who was even awarded the Royal Society’s Hughes medal in 1936 for the discovery of this defect. In his model he explains that the defect is formed in ionic crystals when oppositely charged ions leave their lattice sites... |
In my post Trigonometry Yoga, I discussed how defining sine and cosine as lengths of segments in a unit circle helps develop intuition for these functions.
I learned the circle definitions of sine and cosine in my junior year of high school, in the class that would now be called pre-calculus (it was called “Trig Senior... |
The original renewal process has independent and identically disributed (i.i.d.) inter-renewal times $\{T_1, T_2, T_3, ...\}$. Thus, starting from time 0, renewals occur at times $\{T_1, T_1+T_2, T_1+T_2+T_3, ...\}$. Now fix a probability $p >0$. Independently place each renewal time to $P_1$ with prob $p$. So we get n... |
I need help understanding the Mandelbot and Van Ness' definition of Fractional Brownian motion
$ B_H( t , \omega ) - B_H( 0 , \omega ) = \frac{1}{\Gamma(H + \frac{1}{2})} ( \int_{-\infty}^0 [(t - s)^{H - \frac{1}{2}} - (-s)^{H - \frac{1}{2}}t] dB(s, \omega) + \int_0^t (t - s)^{H - \frac{1}{2}} dB(s, \omega) ) $
(from "... |
Your mistake is simply the statement that the state $|j_1 m_1\rangle$ and $|j_2 m_2\rangle$ are the same physical state: these are abstract angular momentum labels, they aren't full descriptions of the state. The two states would only be the same when the two objects carrying these quantum numbers are indistinguishable... |
Westhoff, Andreas and Schmeling, Daniel and Bosbach, Johannes and Claus, Wagner (2010)
OSCILLATIONS OF HEAT TRANSFER AND LARGE-SCALE CIRCULATION IN
TURBULENT MIXED CONVECTION. In: Third Int. Symposium on Bifurcations and Instabilities in Fluid Dynamics, p. 34. The Univercity Nottingham. Third Int. Symposium on Bifurcat... |
I'm using the code
ContourPlot3D[ NumericQ[ Integrate[ Piecewise[ {{Exp[-1/(1 - x^4 - y^4)]* Exp[I*ω*10*({Cos[ϕ], Sin[θ]} - {Cos[π/2], Sin[π/2]})], Sqrt[x^2 + y^2] < 1}, {0, Sqrt[x^2 + y^2] >= 1}}, PerformanceGoal -> "Speed"], {x, -2, 2}, {y, -2, 2}]], {ϕ, 0, 2*π}, {θ, 0, 2*π}, {ω, -2, 2}, PerformanceGoal -> "Speed", M... |
User:Jan A. Sanders/An introduction to Lie algebra cohomology/Lecture 8 The trace and Killing form
Let \( R\) be \(\mathbb{C}\) and \(\dim_\mathbb{C}\mathfrak{a}<\infty\ .\) Then define \(K_\mathfrak{a}\in C^2(\mathfrak{g},\mathbb{C})\) by\[ K_\mathfrak{a}(x,y)=\mathrm{tr}(d_1(x) d_1(y))\]In the case \(\mathfrak{a}=\ma... |
I am stucked at a detail in a constrained optimization problem:
Question
Assume that the objective function is continuous on its domain $D$, but at some points $Z \subseteq D$ it is not differentiable. Further assume that the constraints implicitly force some or all feasible and optimal solutions to take values in $Z$.... |
Let's suppose we have two variables $(\alpha, \beta)$ on two functions $k_1, k_2$ that can be defined in terms of matrix relations:
$$ k_1 = \left| \xi^T \mathcal{F}^T \mathcal{F} \xi \right| $$
$$ k_2 = \left| \xi^T \mathcal{G}^T \mathcal{G} \xi \right| $$
where:
$$ \mathcal{F}= \left( \begin{matrix} c_{11} & c_{12} \... |
This is in fact a tricky matter.As you say one way is to calculate delta by an analytic formula, i.e. calculate the first derivative of the option pricing formula you are using with respect to the underlying's spot price.The second way is to do it numerically, i.e. change the spot price by a small value $dS$, calculate... |
Section 5.5 Exercise
Note: pictures may not be drawn to scale.
In each of the triangles below, find \(\sin \left(A\right),\cos \left(A\right),\tan \left(A\right),\sec \left(A\right),\csc \left(A\right),\cot \left(A\right)\).
1. 2.
In each of the following triangles, solve for the unknown sides and angles.
3. 4.
5. 6.
7... |
Focus Questions
After studying this section, we should understand the concepts motivated by these questions and be able to write precise, coherent answers to these questions.
How do we measure angles using degrees? What do we mean by the radian measure of an angle? How is the radian measure of an angle related to the l... |
Let $n$ be a given arbitrary positive integer, and let $U_n$ denote the group of all the positive integers less than $n$ and relatively prime to $n$ under multiplication mod $n$. Then for which values of $n$ is $U_n$ a cyclic group? And for any such $n$, which elements of $U_n$ generate it?
One key step in this problem... |
I have a hierarchical model that includes a normal distribution and a beta distribution.
For the normal distribution, it has two parameters: $\mu$ and $\tau^2$. However, I want to implement hierarchy such that the $\mu$ and $\tau^2$ parameters are sampled from group-level distributions. What are good distributions to u... |
Workshop II, 3-4th June Proofs, justifications, certificates ***SLIDES***
Friday 3 June, Institut de Recherche en Informatique de Toulouse (IRIT), Salle des thèses Session 1, Friday 3 June, 9h-10h30, 10h45-12h15, PROVABILITY LOGIC Lev BEKLEMISHEV (Steklov Mathematical Institute, Russia), Positive provability logic and ... |
In my probability class we learned the Central Limit Theorem in the following form.
Theorem:Let $\{X_i\}_{i=1}^\infty$ be a sequence of independent identically distributed random variables and suppose that $E(X_i)=\mu$, $\operatorname{Var}(X_i)=\sigma^2<\infty$. Then,
$$\sqrt{n}\frac{\frac{1}{n}\sum_{i=1}^nX_i-\mu}{\si... |
Ultrapower
The intuitive idea behind ultrapower constructions (and ultraproduct constructions in general) is to take a sequence of already existing models and construct new ones from some combination of the already existing models. Ultrapower constructions are used in many major results involving elementary embeddings.... |
Scalar Triple Products
If we have three vectors $\vec{u}$, $\vec{v}$, and $\vec{w}$ in $\mathbb{R}^3$, then the scalar quantity $\vec{u} \cdot (\vec{v} \times \vec{w})$ appears frequently in other areas of mathematics such as Calculus and has a special name which we define below.
Definition: For any three vectors $\vec... |
As other people have pointed out in comments, the correct answer to the question "what is the probability of rolling another 6 given that I have rolled a 6 prior to it?" is indeed $\frac{1}{6}$. This is because the die rolls are assumed (very reasonably so) to be independent of each other. This means that past rolls of... |
Your wife could be right about the rocket.
Whenever we say something is small physically, we need to be sure what it is small with respect to. In the case of a thread, the drag force exerted by air beats the centripetal force keeping it taut. Because centripetal forces scale with mass, a denser thread will work.
The is... |
Consider two options with maturity $T$ that only differ in their exercise styles, one being European (holder can only exercise at $T $), the other American (holder exercises when it's best for him/her). These options need not necessarily be vanilla options.
Let us further denote by $I (S_t) $ the intrinsic value of the... |
Zero sharp
$0^{\#}$ is a $\Sigma_3^1$ real number which cannot be proven to exist in $\text{ZFC}$. It's existence contradicts the Axiom of constructibility, $V=L$. In fact, it's existence is somewhat equivalent to $L$ being completely different from $V$.
Definition
$0^{\#}$ is defined as the set of all Gödel numberings... |
Given that \(p\) and \(q\) are odd primes. Suppose we know whether \(q\) is a quadratic residue of \(p\) or not. The question that this section will answer is whether \(p\) will be a quadratic residue of \(q\) or not. Before we state the law of quadratic reciprocity, we will present a Lemma of Eisenstein which will be ... |
To send this article to your account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account.Find out more about sending content to .
To send this article to y... |
Congratulations to Phong Quach of Debney Park Secondary College, Tomas from Malmesbury School, Guildford, Chor Kiang Tan, Vassil from Lawnswood High School, Tom from Madras College, Adam from King James's School, Knaresborough, Alex from King Edward and Queen Mary School, Lytham and Andaleeb from Woodhouse Sixth Form C... |
Task to determine the charged particle pseudo density from tracks and tracklets.
This class determines
\[ \left.\frac{d^2N_{ch}}{d\eta d\phi}\right|_{central} \]
from tracks and tracklets.
First, global tracks are investigated. The requirements on global tracks are
\( n_{TPC clusters} \ge 70\) \( \chi^2_{TPC cluster} \... |
Vilma Kemešytė, Nijolė Lemežienė, Vaclovas Stukonis and Juozas Kanapeckas
species of the genus Lolium . Gen. Res. Crop Evol. , 47 , 247-255.Brown, R. N., Barker, R. E., Warnke S. E., Cooper, L. D., Brilman, L. A., Rouf Mian, M. A., Jung, G., Sim, S.-C. (2009). Identification of quantitative trait loci for seed traits a... |
can you please help me with this simple question?
I want to know if this is linear or not
$f: \Bbb R^2\to\Bbb R^3$
$f(0,0)=(1,0,0)$
$f(0,1)=(0,0,0)$
If you could explain why it is or it isn’t linear, I’d be really grateful.
All the best.
Mathematics Stack Exchange is a question and answer site for people studying math ... |
I am trying to understand a modal logic countermodel, illustrating that the
QK theorem,$$ \Box (\phi(x) \wedge \forall x \phi (x)) \rightarrow \Box \forall x \phi (x), $$ fails in the alternate semantics for modal logic given by David Lewis's counterpart theory.The countermodel is the following:
It comes from Oliver Ku... |
I was wondering
if Integration by substitution is a method only for Riemann integral? if Integration by substitution is a special case of Radon–Nikodym theorem, and why?
Thanks and regards!
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields... |
Topological insulator is a fermion system with only
short-ranged entanglement, what does the entanglement mean here?
For example, the Hilbert space $V_s$ of a lattice $N$ spin-1/2 system is $V_s=V_1\otimes V_2\otimes...\otimes V_N$, where $V_i$ is the Hilbert space of the spin on site $i$. And the meaning of an entangl... |
Theorem Schmeorem. A Galilean invariant Lagrangian for any number of classical particles interacting with a potential:
$$ S = \int \sum_k {m_k(\dot{x}_k-u)^2\over 2} + \lambda \dot{u} - U(x_k)\;\;\; dt $$
For any Galilean invariant Lagrangian $L(\dot{x}_k, x_k)$, the Lagrangian
$$ L'(\dot{x}_k,x_k, \lambda, u) = L(\dot... |
The applications of solid codes to r-R and r-D languages 12 Downloads Abstract
A language
S on a free monoid \(A^*\) is called a solid code if S is an infix code and overlap-free. A congruence \(\rho \) on \(A^*\) is called principal if there exists \(L\subseteq A^*\) such that \(\rho =P_L\), where \(P_L\) is the synta... |
Norm Minimization Examples 1
Recall from the Norm Minimization page that if $V$ is an inner product space and $U$ is a finite-dimensional vector space of $V$ where $V = U \oplus U^{\perp}$, and if we let $v \in V$ then for every vector $u \in U$ we have that:(1)
Furthermore, evaluating holds if and only if we take $u =... |
Answer
$$\frac{\cos(x+y)+\cos(x-y)}{\sin(x-y)+\sin(x+y)}=\cot x$$ The equation is an identity.
Work Step by Step
$$\frac{\cos(x+y)+\cos(x-y)}{\sin(x-y)+\sin(x+y)}=\cot x$$ We should examine from the left side. $$A=\frac{\cos(x+y)+\cos(x-y)}{\sin(x-y)+\sin(x+y)}$$ As in here, the application of 4 following identities is... |
I was recently asked an interesting elementary question about the number of possible order types of the final segments of an ordinal, and in particular, whether there could be an ordinal realizing infinitely many different such order types as final segments. Since I found it interesting, let me write here how I replied... |
Consider the elliptic second-order PDE on some bounded domain $D$ (in any dimension)
$-\Delta_D u + \alpha u = 0$
subject to the constraint
$\gamma^i \nabla_i u + \beta u = 0$,
where $\Delta_D$ is the Laplacian on $D$ (with respect to some metric), and $\alpha$, $\beta$, and $\gamma^i$ are real smooth functions on $D$.... |
Table of Contents
Infinite / Finite-Dimensional Vector Space Comparison Theorem
Theorem 1: If $U$ is a subspace of a finite-dimensional vector space $V$, then $U$ is finite-dimensional. Proof:First consider the case where $U$ is the zero subspace. In such a case, clearly $\{ 0 \}$ is finite-dimensional since it can be ... |
№ 9
All Issues On Entire Functions Belonging to a Generalized Class of Convergence Abstract
In terms of Taylor coefficients and distribution of zeros, we describe the class of entire functions
f defined by the convergence of the integral \(\int\limits_{r_0 }^\infty {\frac{{\gamma (\ln M_{f} (r))}}{{r^{\rho + 1} }}} dr\... |
markus
2005-01-02 19:40:05 UTC
Hello LaTeX'ers,a simular
<-- --> E and E of course this can be done with \newcommand{\leftvect}[1]{\stackrel{\leftarrow}{#1}} \newcommand{\rightvect}[1]{\stackrel{\rightarrow}{#1}} but I find the arrow used by \vec much nicer. Is there a way to have
<-- -->
E and E
of course this can be ... |
Another way to look at this problem is to consider it in position space, and then transform the solution to it's momentum space representation. While this may seem like an unnecessary amount of work, it may illuminate to you the delta function solution in a different way. So, in position space we have
$$-\frac{\hbar^2}... |
Difference between revisions of "Vopenka"
Line 4: Line 4:
In a set theoretic setting, the most common definition is the following:
In a set theoretic setting, the most common definition is the following:
<blockquote>
<blockquote>
−
For any language $\mathcal{L}$ and any proper class $C$ of $\mathcal{L}$-structures, the... |
I'm having some trouble solving this limit:
$$\lim_{x\to\infty} x\left[\left(\cosh x\right)^ \frac1x - \left(1+\frac1x\right)^x\right]$$
It's part of a set of limits wich should be solved using taylor. I tried this road:
$$\lim_{x\to\infty} x\left[e^{\frac1x\ln(\cosh x)}-e^{\ln\left(1+\frac1x\right)x}\right]$$
I then t... |
I will elaborate on Xi'an's response.
Metropolis-Adjusted Langevin Algorithm, as its name implies, is based on the Langevin diffusion that is represented by the following stochastic differential equation (SDE):
$ d X_t = - \nabla f(X_t) dt + \sqrt{2} d B_t $,
where $B_t$ is the standard Brownian motion and the target d... |
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Measurement of electrons from beauty hadron decays in pp collisions at root √s=7 TeV
(Elsevier, 2013-04-10)
The production cross section of electrons from semileptonic decays of beauty hadrons was measured at mid-rapidity (|y| < 0.8) in the transverse momentum range 1 < pT <8 GeV/c w... |
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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 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... |
The right triangle formulas are the most important ones in the trigonometry. The sin Theta is the ratio of the opposite side to the hypotenuse, If theta (Θ)
is one of the acute angles.
Sin x Formula:
It is one of the formulae of the Sin function from the six other trigonometric functions.
Sin \(\Theta\) = \(\frac{Oppos... |
In my post Trigonometry Yoga, I discussed how defining sine and cosine as lengths of segments in a unit circle helps develop intuition for these functions.
I learned the circle definitions of sine and cosine in my junior year of high school, in the class that would now be called pre-calculus (it was called “Trig Senior... |
Search
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 ... |
December 4th, 2018, 08:19 PM
# 1
Senior Member
Joined: Sep 2015
From: USA
Posts: 2,574
Thanks: 1422
removable discontinuities in rational functions
So I was taught that
$f(x) = \dfrac{(x+1)(x-2)}{x+1} = x-2$ is continuous.
I'm reading online now that $x=-1$ is considered a removable discontinuity, i.e. a "hole"
If this... |
Journées d'Etude II, 3-4 juin Preuves, justifications, certificats ***TRANSPARENTS***
Vendredi 3 juin, Institut de Recherche en Informatique de Toulouse (IRIT), Salle des thèses Session 1, vendredi 3 juin, 9h-10h30, 10h45-12h15, PROVABILITY LOGIC Lev BEKLEMISHEV (Steklov Mathematical Institute, Russia), Positive provab... |
In the Grothendieck universe approach to category theory, as you say, we replace all small sets with $\mathcal{U}$-small sets. Let's look at the definition of a locally presentable $\mathcal{U}$-category, for example, since that's in the conclusion of the theorem you mentioned: a locally presentable $\mathcal{U}$-categ... |
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J/Ψ production and nuclear effects in p-Pb collisions at √sNN=5.02 TeV
(Springer, 2014-02)
Inclusive J/ψ production has been studied with the ALICE detector in p-Pb collisions at the nucleon–nucleon center of mass energy √sNN = 5.02TeV at the CERN LHC. The measurement is performed in... |
Table of Contents
The Fundamental Group of a Topological Space at a Point
Definition: Let $X$ be a topological space. A path $\alpha : I \to X$ is a Loop at $x$ if $\alpha(0) = x$ and $\alpha(1) = x$.
Recall the material on the following pages:
In particular, if $\alpha, \beta, \gamma : I \to X$ are loops at $x$ then t... |
Vector Subspace Sums
We will now look at an important definition regarding vector subspaces.
Definition: Let $U_1, U_2, ..., U_m$ all be vector subspaces of the $\mathbb{F}$-vector space $V$. We define the Vector Sum of these subspaces $\sum_{i=1}^{m} = U_1 + U_2 + ... + U_m$ is defined to be the set of all possible su... |
Your body has a strange property: you can learn information about the
entire organism from a single cell. Pick a cell, dive into the nucleus, and extract the DNA. You can now regrow the entire creature from that tiny sample.
There's a math analogy here. Take a function, pick a specific point, and dive in. You can pull ... |
Suppose that we run the simple linear regression $Y = \alpha + \beta X + \epsilon$. I want to test whether the independent variable $X$ is exogenous. If the correlation between the independent variable $X$ and the residual of linear regression $\epsilon$ is almost zero, i.e. $cor(X, \epsilon) \approx 0$, can I then con... |
Source Extent and Errors
The apparent sizes and associated errors of sources reported in version 2 of the Chandra Source Catalog are determined using a Mexican-Hat optimization method, which uses a wavelet transform to define elliptical source regions. This is a refinement of the source extent results produced by wavde... |
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A bumble bee charged to 1 C1 \text{ C}1 C flies from (0 m,0 m)(0 \text{ m}, 0\text{ m}) (0 m,0 m) to (1 m,1 m)(1 \text{ m}, 1\text{ m})(1 m,1 m) through a region with electric field E⃗=(x^+y^)NC\vec{E}=(\hat{x}+\hat{y})\dfrac{N}{C}E=(x^+y^)CN. Find the work done ... |
We now discuss the concept of divisibility and its properties.
Integer Divisibility
If \(a\) and \(b\) are integers such that \(a\neq 0\), then we say "\(a\) divides \(b\)" if there exists an integer \(k\) such that \(b=ka\).
If \(a\) divides \(b\), we also say "\(a\) is a factor of \(b\)" or "\(b\) is a multiple of \(... |
This was requested on meta.SO for the Audio & Video Production site. As balpha says, audio clips uploaded to SoundCloud and lined to in a post will automatically be converted into an embedded player like this. Of course, a dev has to turn on the feature for this site, and I'm sure they will when they see this post.
Whi... |
I have recently acquired a couple of mysterious ultra/super capacitors from my brother. Apparently he doesn't remember any of the specifications or even brand... To further complicate matters, they have no meaningful identification information stamped or printed on them. (There is a bar code label with alphanumeric cod... |
Let $\alpha$ and $\beta$ be two isomorphic ordinals. Then $\alpha = \beta$.
I want to whether the following proof is correct.
I already know that there are three prossible cases: $\alpha \in \beta, \alpha=\beta$ or $\beta\in\alpha$. Without loss of generality, assume that $\alpha \in \beta$. Let $f: \beta \to \alpha$ b... |
A few days ago, my math teacher (I hold him in high faith) said that $2\pi$ radians is not exactly $360^{\circ}$. His reasoning is the following.
$\pi$ is irrational (and transcendental). $360$ is a whole number. Since no multiple of $\pi$ can equal a whole number, $2\pi$ radians is not exactly $360^{\circ}$.
His logic... |
What is $f'(a)$ of the function $f(x)$?
$$f(x) = 2x^2 − 3x + 1$$
I have been trying to do it but I cannot figure out how to do it. Please somebody can help me.
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... |
An urn contains $r$ Red and $b$ Blue marbles. A fair coin is flipped. If the flip is Heads then $h$ Red marbles are added to the urn. If the flip is Tails then $t$ Blue marbles are add to the urn. Now a random marble $M$ is drawn from the urn.
(a) What is the probability that $M$ is Red?
(b) What is the probability tha... |
Is it true that all zeros of the Riemann Zeta Function are of order 1?
Let $h(z) = \frac{\zeta'(z)}{\zeta(z)}\frac{x^z}{z}$, where $x$ is a positive real number ($x > 1$, probably?) , and $\zeta$ is the Riemann zeta function. I'm computing the residues of $h$.
The only place I'm having problems computing the residue of... |
When trying to find the Lorentz transformation in matrix form in the $x^2+x^3$-direction, I tried simply mapping the Lorentz boost in the $x^2$-direction to the $x+x^3$-direction by rotating it $45°$ around the $x^1$ axis:
$$ R_{x}^{-1}(\theta=45°)\left(\begin{array}{cccc}\gamma & 0 & -\gamma\beta &0\\0&1&0&0\\-\gamma\... |
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. ... |
The best model is not always the most complicated. Sometimes including variables that are not evidently important can actually reduce the accuracy of predictions. In this section we discuss model selection strategies, which will help us eliminate variables from the model that are found to be less important.
In practice... |
Learning Objectives
Identify a conic in polar form. Graph the polar equations of conics. Define conics in terms of a focus and a directrix.
Most of us are familiar with orbital motion, such as the motion of a planet around the sun or an electron around an atomic nucleus. Within the planetary system, orbits of planets, a... |
Hints will display for most wrong answers; explanations for most right answers. You can attempt a question multiple times; it will only be scored correct if you get it right the first time.
I used the official objectives and sample test to construct these questions, but cannot promise that they accurately reflect what’... |
I have a question regarding the physical significance of the canonical energy momentum tensor $T_\nu ^\mu$ in the context of classical field theory. It is defined as
$T_\nu ^\mu = \frac{\partial \mathcal{L}}{\partial ( \partial_\mu \Phi^I)} \partial_\nu \Phi^I - \delta_\nu ^\mu \mathcal{L} $, where $\Phi^I$ is the set ... |
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