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You know the geometric series
$$\sum_{n=0}^{\infty}r^n=\frac{1}{1-r},\quad |r|<1\tag{1}$$
Due to convergence of (1) (for $|r|<1$) you can take the derivative with respect to $r$ by taking the element-wise derivatives of the left-hand side. Equating the derivatives of both sides of (1) gives
$$\sum_{n=0}^{\infty}nr^{n-1... |
Answer
$$x=.13,2.37$$
Work Step by Step
Using the quadratic formula, we obtain: $$x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$$ $$x=\frac{40\pm \sqrt{(-40)^2-4(16)(5)}}{2(5)}$$ $$x=.13,2.37$$
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Background: I have seen lots of people asking whether multiplication and pseudo-random sequences can be approximated by a NN without providing whether the inputs and outputs are bounded or not, and people have answered it (lot of upvotes) based on conventional NN knowledge. without taking into consideration the aforeme... |
I was waiting in line at my local bank recently and spotted an urn filled with coins on a table in the corner of the lobby. When I got to the head of the line, I inquired about it and the clerk told me the urn was part of a contest among some of the bank employees. The objective of the contest was to guess the average ... |
40th SSC CGL level Question Set, topic Trigonometry 4
This is the 40th question set for the 10 practice problem exercise for SSC CGL exam and 4th on topic Trigonometry.
We repeat the method of taking the test. It is important to follow result bearing methods even in practice test environment.
Method of taking the test ... |
To cap off this post with a mathematical gemstone, below is the full computation of the automorphism group of the graded noncommutative ring mentioned on the previous page.
Any automorphism of the noncommutative $\mathbb{C}$-algebra $$R_q:=\mathbb{C}\langle x,y\rangle/(xy-qyx)$$ that preserves the grading by degree can... |
To cap off this post with a mathematical gemstone, below is the full computation of the automorphism group of the graded noncommutative ring mentioned on the previous page.
Any automorphism of the noncommutative $\mathbb{C}$-algebra $$R_q:=\mathbb{C}\langle x,y\rangle/(xy-qyx)$$ that preserves the grading by degree can... |
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We've seen that classical logic is closely connected to the logic of subsets. For any set \( X \) we get a poset \( P(X) \), the
power set of \(X\), whose elements are subsets of \(X\), with the partial order being \( \subseteq \). ... |
Comments to the question contain several contributions to alternative approaches by Uri Bader. Since the latter seems to be reluctant to collect them into an answer, I decided to do the part I understand.
Approach 1.
Suppose given $P$ with top and bottom; then removing top and bottom from $P\times\{1,...,n\}$ is the un... |
Let $R$ be a ring with identity (not necessarily commutative) and $R[x]$ be a ring of polynomials over $R$. We say that a ring $S$ is an
extension of $R$ if there is a subring $\tilde{R}$ in $S$ isomorphic to $R$.Let $S$ be an extension of $R$, and $$\phi: R\to \tilde{R}\subset S$$be a ring isomorphism.We say that a po... |
Hi, I’m Maria and I’m a $q$-analog addict. The theory of $q$-analogs is a little-known gem, and in this series of posts I’ll explain why they’re so awesome and addictive!
So what is a $q$-analog? It is one of those rare mathematical terms whose definition doesn’t really capture what it is about, but let’s start with th... |
I need some help with understanding a part of this proof and also writing it up correctly. Given $a_n\geq a_{n+1}\geq b_{n+1} \geq b_n$ with $a_1=a$ and $b_1=b$. I am also given that $$a_{n+1}=\frac{a_n+b_n}{2}$$ and $$b_{n+1}=\sqrt{a_nb_n}$$ I need to show that sequences ${a_n}$ and ${b_n}$ converges and that ${a_n}$ ... |
$\frac{1-(-$\frac{1}{2}^t$) }{$\frac{3}{2}$}$
For some reason it gives me an error, something about a
Missing \endgroup, be warned I'm new to Latex.
TeX - LaTeX Stack Exchange is a question and answer site for users of TeX, LaTeX, ConTeXt, and related typesetting systems. It only takes a minute to sign up.Sign up to jo... |
Let $X_1,\dots,X_n$ be complete vector fields on $\mathbb R^n$ and suppose that $(X_1(p),\dots,X_n(p))$ is a basis for all $p \in \mathbb R^n$.
Question: Is it possible to choose a cube $C$ around the origin of $\mathbb R^n$ such that there is for every $p \in C$ a piecewise smooth curve $\alpha \subset C$ which connec... |
Defining parameters
Level: \( N \) = \( 3600 = 2^{4} \cdot 3^{2} \cdot 5^{2} \) Weight: \( k \) = \( 1 \) Character orbit: \([\chi]\) = 3600.fq (of order \(60\) and degree \(16\)) Character conductor: \(\operatorname{cond}(\chi)\) = \( 3600 \) Character field: \(\Q(\zeta_{60})\) Newforms: \( 0 \) Sturm bound: \(720\) T... |
Reliance on mechanical procedures in solving problems
Often we find at high school level, math problems solved in a long series of steps. Especially this we find in case of problems of the type,
Prove that, "Some expression " = "Some other expression".
In school math terminology, the "Some expression" is called
LHS (sh... |
I am currently working on a physics problem that turns into a non-linear boundary value problem. I need an efficient numerical solver that I could run on my laptop with i5 dual core CPU. I am discretizing my 15 equations on an N x N x N cubic grid using fourth order finite difference derivatives. I am interested in usi... |
Family Size Problem 1
Consider a couple beginning a family; in the interest of promoting a diverse family, they decide to have children until they have both sexes. How many children can they expect to have?
Hint
We have already solved a very similar problem estimating the number of (Bernoulli) trials until the first su... |
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Production of light nuclei and anti-nuclei in $pp$ and Pb-Pb collisions at energies available at the CERN Large Hadron Collider
(American Physical Society, 2016-02)
The production of (anti-)deuteron and (anti-)$^{3}$He nuclei in Pb-Pb collisions at $\sqrt{s_{\rm NN}}$ = 2.76 TeV has ... |
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We've seen that classical logic is closely connected to the logic of subsets. For any set \( X \) we get a poset \( P(X) \), the
power set of \(X\), whose elements are subsets of \(X\), with the partial order being \( \subseteq \). ... |
Proving uniqueness
You can prove that the elements are unique in $O(m)$ time and space by pre-sorting them and then giving a zero-knowledge proof that they are in sorted order. Details follow.
Assume the elements of $\Sigma$ are integers in the range $[0,K-1]$, where $K$ is a constant chosen in advance and made public.... |
Gradient blowup rate for a semilinear parabolic equation
1.
College of Science, Xi’an Jiaotong University, Xi’an, 710049, China
2.
Department of Mathematics, University of Notre Dame, Notre Dame, Indiana 46556
xx$ +x^m |u_x|^p, p> 0, m\geq 0$, for which the spatial derivative of solutions becomes unbounded in finite ti... |
Background:
I notice that there is quite a bit of similarity between the standard heat equation and the energy equation (from the navier stokes equations). The heat equation is given as
$$\frac{\partial\left(\rho h\right)}{\partial t} + \nabla\cdot\left(u\rho h \right) - \nabla\cdot\left(k\nabla T \right)=0$$
with $\rh... |
shortest path between 2 points
This spec goes into the cost function design.
maintain a minimum distance to obstacles
Given 2D occupancy grid, threshold probability values to get occupied/free cell representation of the environment. Then, expand each obstacle cell by given minimum distance value. Once done, this spec g... |
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D-meson nuclear modification factor and elliptic flow measurements in Pb–Pb collisions at $\sqrt {s_{NN}}$ = 5.02TeV with ALICE at the LHC
(Elsevier, 2017-11)
ALICE measured the nuclear modification factor ($R_{AA}$) and elliptic flow ($\nu_{2}$) of D mesons ($D^{0}$, $D^{+}$, $D^{⁎+}$... |
I've asked some other questions before about Rijndael's S-boxes, and step by step I'm coming to an understanding; but those steps often guide me to new questions.
I did some lines of code to understand how these S-boxes work implementing $S(z) = f(g(z))$ where $g(z)$ is the transformation by multiplicative inverse in a... |
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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 ... |
, EURASIP Journal on Advances in Signal Processing (2008), Article ID 258184.[21] SOUSA. R.—FERREIRA, A.—ALKU, P. : The Harmonic and Noise Information of the Glottal Pulses, Speech, Biomedical Signal Processing and Control 10 (2014), 137–143.[22] LECLERC, I.—DAJANI, H. R.—GIGUERE, C. : Differences in Shimmer Across For... |
To extend Müller's answer,
Should the microphones be placed in separate tubes in order to improve separation?
No, you are trying to identify the direction of the source, adding tubes will only make the sound bounce inside the tube which is definitely not wanted. If only one tube hears the sound due to no reflections ar... |
Answer
$R-factor = 25 \frac{^{\circ} F ft^2 h}{Btu}$
Work Step by Step
We find: $R-factor= \frac{ \Delta T}{ H}$ We plug in the given values: $ R-factor = \frac{1}{.040}$ We find: $R-factor = 25 \frac{^{\circ} F ft^2 h}{Btu}$
You can help us out by revising, improving and updating this answer.Update this answer
After y... |
Sperner.tex
\section{Sperner's theorem} \label{sec:sperner}
The first nontrivial case of Szemer\'edi's theorem is the case of arithmetic progressions of length $3$. However, for the density Hales--Jewett theorem even the case $k=2$ is interesting. DHJ($2$) follows from a basic result in extremal combinatorics: Sperner'... |
A useful "abstract nonsense" construction in ergodic theory takes a measure-preserving transformation$T$ of a probability space $(X,\mathcal B,\mu)$ and extends it to an
invertible measure-preserving transformation $\bar T$ of a probability space $(\bar X,\bar{\mathcal B},\bar\mu)$.
One description of this is in Omri S... |
What is the difference between cointegration and the vector error correction model (VECM)? I applied cointegration test and found long run association between variables, so should I apply VECM?
Cointegration is a phenomenon that may be exhibited by a group of integrated time series; being cointegrated is a feature that... |
I found in the book of Murphy, C*- Algebras and Operator Theory, the Theorem 7.1.2 :
Let A be an unital C* algebra, the semi group $V(A)$ of equivalent projections (under Murray Von Neumann equivalence) in $M_∞(A)$ is cancellative.
For the proof he proceeds as follow :
take some projection $p, q, r$ such that $[p] \opl... |
Revista Matemática Iberoamericana
Full-Text PDF (643 KB) | Metadata | Table of Contents | RMI summary
Volume 29, Issue 1, 2013, pp. 237–292 DOI: 10.4171/RMI/719
Published online: 2013-01-14
Real-variable characterizations of Orlicz–Hardy spaces on strongly Lipschitz domains of $\mathbb{R}^n$Dachun Yang
[1]and Sibei Yan... |
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Production of light nuclei and anti-nuclei in $pp$ and Pb-Pb collisions at energies available at the CERN Large Hadron Collider
(American Physical Society, 2016-02)
The production of (anti-)deuteron and (anti-)$^{3}$He nuclei in Pb-Pb collisions at $\sqrt{s_{\rm NN}}$ = 2.76 TeV has ... |
ISSN:
1556-1801
eISSN:
1556-181X
All Issues
Networks & Heterogeneous Media
June 2006 , Volume 1 , Issue 2
Select all articles
Export/Reference:
Abstract:
This work is concerned with some aspects of the social life of the amoebae
Dictyostelium discoideum(Dd). In particular, we shall focus on the early stages of the star... |
also, if you are in the US, the next time anything important publishing-related comes up, you can let your representatives know that you care about this and that you think the existing situation is appalling
@heather well, there's a spectrum
so, there's things like New Journal of Physics and Physical Review X
which are... |
Integral Multiple of an Algebraic Number Theorem
Let $K$ be a number field and $\alpha \in K$.
Then there exists a positive $n \in \Z$ such that $n \alpha \in \mathcal O_K$. In this context, $ \mathcal O_K$ denotes the algebraic integers in $K$. Proof
If $\alpha = 0$ then any integer works and the proof is finished.
Le... |
Actually, the motivation for introducing dependent types goes in the opposite direction! Curry had noticed that there was a direct correspondence between typed terms in the $SK$ calculus and proofs in (minimal implicational)
propositional logic, but there was no programing language known to correspond in such a way to ... |
According to many references [1,2], the time-varying "impulse response" can compute wireless channel output $y(t)$ at time $t$ using the following expression: $$ y(t) = \int h(\tau, t) x(t - \tau) d\tau $$
In both references, they state that this represents the response of the channel at time $t$ to an impulse applied ... |
Taking a slant on xnor's idea, consider the velocity of any ant towards $O$. I'll use the standard figures for the internal angle of a regular pentagon and the radius of a circumscribed circle from wikipedia.Name the vertices $A,B,C,D,E$ starting at the top and working clockwise, and let $\theta = \angle OAB$.
By symme... |
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* (e) $H>0,\; q=0$: expanding, zero deceleration
* (e) $H>0,\; q=0$: expanding, zero deceleration
* (f) $H<0,\; q=0$: contracting, zero deceleration
* (f) $H<0,\; q=0$: contracting, zero deceleration
−
* (g) $H=0,\; q=0$ : static.</p>
+
* (g) $H=0,\; q=0$ : static
+
.</p>
</div>
</div>
</div></div>
</... |
One intuitive way to understand a DAE is to interpret it as a dynamical system which can be controlled by some input signals, whose output signals have to satisfy some (equational) constraints. For a typical multibody system, the input signals are the forces perpendicular to the constraints, the output signals are the ... |
983 173
I'll take on problem 1, though I'm only somewhat familiar with its subject matter.
(a) This is presumably for finding the primitive polynomials in GF8. These are cubic polynomials with coefficients in GF2 that cannot be expressed as products of corresponding polynomials for GF4 and GF2. I will use x as an undet... |
For $t \in \mathbb{R}$ define $$ F(t) = \sum_{n=1}^{[t]} \frac{(-1)^{(n-1)}}{n^{\frac12 + it}}$$
Let $\operatorname{Arg}(t)$ be $\operatorname{atan2}(\Im t , \Re t)$ - basically this is $\arctan$, but the sign depends on the quadrant.
Observation $\operatorname{Arg}(F(t))$ jumps (usually from negativeto positive) very ... |
Rich trigonometry concept of Friendly Function Pair enables elegant solution
In
, we have explained how rich problem solving trigonometry concepts are derived from basic concepts for solving problems faster. In this session we will highlight Basic and Rich Trigonometry concepts and applications how the rich trigonometr... |
2018-09-11 04:29
Proprieties of FBK UFSDs after neutron and proton irradiation up to $6*10^{15}$ neq/cm$^2$ / Mazza, S.M. (UC, Santa Cruz, Inst. Part. Phys.) ; Estrada, E. (UC, Santa Cruz, Inst. Part. Phys.) ; Galloway, Z. (UC, Santa Cruz, Inst. Part. Phys.) ; Gee, C. (UC, Santa Cruz, Inst. Part. Phys.) ; Goto, A. (UC,... |
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We've seen that classical logic is closely connected to the logic of subsets. For any set \( X \) we get a poset \( P(X) \), the
power set of \(X\), whose elements are subsets of \(X\), with the partial order being \( \subseteq \). ... |
Triangle from Inradius, Circumradius, Side or Angle
Given circle $C(O,R)$ with center $O$ and radius $R,$ we'll be looking into the problem of constructing $\Delta ABC$ inscribed into $C(O,R)$ and having inradius $r.$ Assuming $R\gt 2r,$ the triangle exists and is unique, provided either one of the angles or one of the... |
Difference between revisions of "Permanent"
(LaTeX part)
(LaTeX)
Line 1: Line 1: −
{{TEX|
+
{{TEX|}}
''of an $m \times n$-matrix $A = \left\Vert a_{ij} \right\Vert$''
''of an $m \times n$-matrix $A = \left\Vert a_{ij} \right\Vert$''
Line 48: Line 48:
Upper bounds for permanents:
Upper bounds for permanents:
−
1) For a
... |
4 0
Limit of an integral
1. Homework Statement Evaluate: the limit as n goes to [tex]\infty[/tex] of [tex]\int^{1}_{0} (n^{3/2}x^{5/4})/(1+n^{2}x^{2})dx[/tex] dx is the lebesgue measure 2. Homework Equations I thought I could use the monotone convergence theorem or the dominated convergence theorem neither work. 3. The... |
Title
On the preservation of certain properties of functions under composition
Date of Award
1994
Degree Type
Dissertation
Degree Name
Doctor of Philosophy (PhD)
Department
Mathematics
Advisor(s)
Daniel Waterman
Keywords
homeomorphisms, convex functions, fourier series
Subject Categories
Number Theory | Partial Differe... |
Assume we have two series of indepedent success-failure observations, e.g. coin tosses $$ \boldsymbol x_1 \in \{H,T\}^{n_1} \\ \boldsymbol x_2 \in \{H,T\}^{n_2} $$
Also, let $k_i$ be the number of heads (=successes) in $\boldsymbol x_i$.
Now, I want to assume the observations are generated by two random variables $X_i$... |
How to find the number of all the positive integral solutions and the solutions itselves of $$5x+7y=100?$$
Please 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 sign up.Sign up to join this community... |
The Christoffel symbols are a measure of the first derivatives of the metric tensor. In particular, they will be zero if all derivatives are zero. In a euclidean space this will alway be the cas-e, not only in 2 dimensions!
For another coordinate system you can either use the definition (e.g. from wikipedia), which can... |
How can I show using properties of determinants that:
$$\det\begin{pmatrix} (b+c)^2 & a^2 & a^2 \\ b^2 & (c+a)^2 & b^2 \\ c^2 & c^2 & (a+b)^2 \\ \end{pmatrix} = 2abc(a+b+c)^3$$
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It only tak... |
A few years ago I read this piece about meat purveyor Pat LaFrieda and since then I’ve wanted to visit one of his restaurants. While at LaGuardia Airport awaiting a flight, all outbound flights from the airport were delayed due to inclement weather and only one outbound runway was operational. This was fortuitous—the h... |
Rocky Mountain Journal of Mathematics Rocky Mountain J. Math. Volume 44, Number 3 (2014), 717-731. Associate elements in commutative rings Abstract
Let $R$ be a commutative ring with identity. For $a,b\in R$, define $a$ and $b$ to be \textit{associates}, denoted $a\sim b$, if $a\mid b$ and $b\mid a$, so $a=rb$ and $b=s... |
I asked this in the Ethereum StackExchange yesterday but I figured it would be more appropriate to ask it here.
I am looking into implementing some operations for the BLS signature scheme in Solidity, using the new precompiled contracts for pairing operations released with Ethereum Byzantium, but I am not sure whether ... |
Let $\Omega$ be an open bounded subset of $\mathbb R^N$.
Let $u_0 \in L^\infty(\Omega)$ and $f \in L^\infty((0,T)\times\Omega).$
Consider the following boundary value problem for the heat equation: $$ \begin{cases} u_t - \Delta u = f \\ u|_{\partial\Omega} = 0\\ u(0) = u_0 \end{cases} $$
Questions:
Let $k \ge 2$. Assum... |
Examples of Functions
In a compact form a
function is a well defined unidirectional dependency, a concept of which I shall provide several examples. Functions that are not numeric
The set of fingerprints is uniquely defined for every person. That is to say, there is a function (call it $f)$ from the set of people to th... |
Dependency Parsing Unlabled Dependency Parses root is a special root symbol Each dependency is a pair (h, m) where h is the index of a head word, m is the index of a modifier word. In the figures, we represent a dependency (h, m) by a directed edge from h to m Dependencies in the above example are (0, 2), (2, 1), (2, 4... |
We are given that the number $b_i$ announced by girl $i$ is the average of the numbers $x_{i^+}$ and $x_{i^-}$ chosen by the neighboring girls $i^+$ and $i^-$:
$$2 b_i = x_{i^+} + x_{i^-},$$
where
$$\begin{array}{rcl}i^+ & = & i + 1 - \left\lfloor \frac{i}{N} \right\rfloor N, \\i^- & = & i - 1 + \left\lfloor \frac{N + ... |
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Measurement of electrons from beauty hadron decays in pp collisions at root √s=7 TeV
(Elsevier, 2013-04-10)
The production cross section of electrons from semileptonic decays of beauty hadrons was measured at mid-rapidity (|y| < 0.8) in the transverse momentum range 1 < pT <8 GeV/c w... |
My model is the following: I have a 1D-lattice with L sites. Each site can be occupied by either one or zero atoms. The Hamiltonian looks as follows: $$H = T\sum(b^\dagger_i b_{i+1} + h.c.) + V\sum n_i n_{i+1}$$
My question is now of a rather basic quantum mechanical nature. I want to make sure what I'm doing is right ... |
XGBoost mostly combines a huge number of regression trees with a small learning rate. In this situation, trees added early are significant and trees added late are unimportant.
Vinayak and Gilad-Bachrach proposed a new method to add dropout techniques from the deep neural net community to boosted trees, and reported be... |
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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... |
Possible Duplicate: Cardinality of the permutations of an infinite set
Why does the symmetric group on an infinite set X have the cardinality of the power set ${\cal P}(X)$?
MathOverflow is a question and answer site for professional mathematicians. It only takes a minute to sign up.Sign up to join this community
Possi... |
Journal of Symbolic Logic J. Symbolic Logic Volume 60, Issue 1 (1995), 178-190. The Equivalence of NF-Style Set Theories with "Tangled" Theories; The Construction of $\omega$-Models of Predicative NF (and more) Abstract
An $\omega$-model (a model in which all natural numbers are standard) of the predicative fragment of... |
Abstract
The Deligne groupoid is a functor from nilpotent differential graded Lie algebras concentrated in positive degrees to groupoids; in the special case of Lie algebras over a field of characteristic zero, it gives the associated simply connected Lie group. We generalize the Deligne groupoid to a functor $\gamma$ ... |
It is known (as a slogan) that the "existential fragment of second-order logic (ESO) is compact".
My first question is:
(1) Is ESO compact for:
(a) uncountable languages
(b) languages with constants or just for relational vocabularies?
The possible answers are obviously:
ESO is compact only for countable languages (wit... |
I’ve been doing a lot of reading on confidence interval theory. Some of the reading is more interesting than others. There is one passage from Neyman’s (1952) book “Lectures and Conferences on Mathematical Statistics and Probability” (available here) that stands above the rest in terms of clarity, style, and humor. I h... |
Beyoncé’s record,
4, was officially released this week, despite having been out and about on the Internet for quite a while. On that album is a song titled “1+1,” the number Bey performed so astonishingly well in her dressing room (and then later on American Idol). Because thinking about song titles is part of how we p... |
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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... |
On a case-by-case basis, it is possible to typeset text within math mode using
\textrm{...} or
\mathrm{...}, the latter being used predominantly for typesetting units or symbols and not pure text (since it gobbles spaces that are not escaped).
\mbox{...} is another alternative to
\textrm{...}, since it resets its conte... |
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GR8677 #19
Problem
Quantum Mechanics}Bohr Theory
Recall the Rydberg energy. QED
Comments
casseverhart13 2019-10-01 03:22:05 Good Examine and fascinating. Thanks. www.trustytreeservice.com ernest21 2019-08-10 03:09:33 Instead of doing the long division by hand, you could just say that gamma is less than 2. Solving the i... |
This is a continuation of Part 1 of this series of posts on $q$-analogs. Counting by $q$’s
Another important area in which $q$-analogs come up is in combinatorics. In this context, $q$ is a formal variable, and the $q$-analog is a generating function in $q$, but viewed in a different light than usual generating functio... |
Let $F_0 \subset F_1 \subset F_2 \subset \cdots$ and $K_0 \subset K_1 \subset K_2 \subset \cdots$ be two towers of fields. Also, let $F = \cup_{i=0}^\infty F_i$ and $K = \cup_{i=0}^\infty K_i$.
Now suppose for each $i$ we have injective homomorphisms from $F_i$ to $K_{\sigma(i)}$ and from $K_i$ to $F_{\mu(i)}$ where $i... |
I would like to solve 3D transient incompressible Navier-Stokes with FEM, Newton method, Schur-based preconditioner, Lagrangean P2/P1 elements (no stabilization), in a rigid pipe discretized with tetrahedrons.
The fluid is initially at rest, I impose constant inlet and outlet pressure boundary conditions (and therefore... |
Difference between revisions of "Main Page"
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Line 30: Line 30:
Prove that for any <math>c>0</math> there is a <math>d</math>, such that any c-dense subset of the Cartesian product of an IP_d set (it is a two dimensional pointset) has a corner.
Prove that for any <math>c>0</math> there is a <math>d<... |
Let $\mathcal{O}_0$ be the principal block of the BGG category $\mathcal{O}$ for a finite dimensional simple Lie algebra over $\mathbb{C}$. For an element $w$ in the Weyl group $W$, let $\Delta_w$ denote the Verma module with highest weight $w_0w^{-1}\cdot 0$, where $w_0\in W$ is the longest element, and $\cdot$' denot... |
In this MathStackExchange post the question in the title was asked without much outcome, I feel.
Edit: As Douglas Zare kindly observes, there is one more answer in MathStackExchange now.
I am not used to basic Probability, and I am trying to prepare a class that I need to teach this year. I feel I am unable to motivate... |
The polynomial Freiman-Ruzsa conjecture states that there exists $k > 0$, such that for all $\epsilon > 0$, and for all large $n$ and all functions $ f: \mathbb{F}_2^n \mapsto\mathbb{F}_2^n$, the following holds. If
$$Pr_{x, x' \in \mathbb{F}_2^n} [f(x) + f(x') = f(x+x')] \geq \epsilon \;,$$ then there is a matrix $M \... |
uses two matrices $A$ and $B$ and calculates the product $AB$. It is an online math tool specially programmed to perform multiplication operation between the two matrices $A$ and $B$. The matrix multiplication is not commutative operation. In the matrix multiplication $AB$, the number of columns in matrix $A$ must be e... |
What is the step by step numerical approach to calculate the pseudo-inverse of a matrix with
M rows and N columns, using LU decomposition?
So far, I have found this, but it uses singular value decomposition.
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals... |
Abstract
Let $\pi$ be an $\mathrm{SL}(3,\mathbb Z)$ Hecke-Maass cusp form satisfying the Ramanujan conjecture and the Selberg-Ramanujan conjecture, and let $\chi$ be a primitive Dirichlet character modulo $M$, which we assume to be prime for simplicity. We will prove that there is a computable absolute constant $\delta... |
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I'm not sure this is the right thread to post my problem :
I'm trying to define a
[itex]x(\theta, \phi) = \sin^3{\theta} \; \cos{\phi},[/itex] [itex]y(\theta, \phi) = \sin^3{\theta} \; \sin{\phi},[/itex] [itex]z(\theta) = \sin^2{\theta} \; \cos{\theta}.[/itex]
The surface element is this :
[itex]dS(\theta, \phi) =... |
Alright, I have this group $\langle x_i, i\in\mathbb{Z}\mid x_i^2=x_{i-1}x_{i+1}\rangle$ and I'm trying to determine whether $x_ix_j=x_jx_i$ or not. I'm unsure there is enough information to decide this, to be honest.
Nah, I have a pretty garbage question. Let me spell it out.
I have a fiber bundle $p : E \to M$ where ... |
A recursive algorithm and a series expansion related to the homogeneous Boltzmann equation for hard potentials with angular cutoff
Sorbonne Université, CNRS, LPSM, UMR 8001, F-75005 Paris, France
We consider the spatially homogeneous Boltzmann equation for hard potentials with angular cutoff. This equation has a unique... |
A forum where anything goes. Introduce yourselves to other members of the forums, discuss how your name evolves when written out in the Game of Life, or just tell us how you found it. This is the forum for "non-academic" content.
A for awesome Posts: 1901 Joined: September 13th, 2014, 5:36 pm Location: 0x-1 Contact: vi... |
Sixteenth SSC CGL level Question Set on Trigonometry
This is the sixteenth Question set of 10 practice problem exercise for SSC CGL exam on topic Trigonometry. Students should complete this question set in prescribed time first and then only refer to the solution set.
We found from our analysis of the Trigonometry prob... |
Cyclic asymptotic behaviour of a population reproducing by fission into two equal parts
1.
Laboratoire de Géodésie, IGN-LAREG, Bâtiment Lamarck A et B, 35 rue Hélène Brion, 75013 Paris, France
2.
Sorbonne Universités, Inria, UPMC Univ Paris 06, Mamba project-team, Laboratoire Jacques-Louis Lions, Paris, France
3.
Wolfg... |
\begin{align} u'' &+ \Gamma^0_{00}(u')^2 + 2\Gamma^0_{01}u'v' + \Gamma^0_{11}(v')^2 = 0,\\ v'' &+ \Gamma^1_{00}(u')^2 + 2\Gamma^1_{01}u'v' + \Gamma^1_{11}(v')^2 = 0, \end{align} where $\Gamma^m_{ij}(u(s),v(s))$ is the Christoffel symbol of second kind. The geodesic solution $u = u(s),v = v(s)$ is a curve defined for th... |
Sixteenth SSC CGL level Solution Set, topic Trigonometry
This is the sixteenth solution set of 10 practice problem exercise for SSC CGL exam on topic Trigonometry. Students should complete the corresponding question set in prescribed time first and then only refer to the solution set.
We found from our analysis of the ... |
(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... |
The orthogonal group, consisting of all proper and improper rotations, is generated by reflections. Every proper rotation is the composition of two reflections, a special case of the Cartan–Dieudonné theorem.
Yeah it does seem unreasonable to expect a finite presentation
Let (V, b) be an n-dimensional, non-degenerate s... |
There are 21 elements with only one isotope, so all their atoms have identical masses. All other elements have two or more isotopes, so their atoms have at least two different masses. But all elements obey the law of definite proportions when they combine with other elements, so they
behave as if they had just one kind... |
How to Design a Linear Cover Time Random Walk on a Finite Graph Abstract
A random walk on a finite graph
G = ( V, E) is random token circulation on vertices of G. A token on a vertex in V moves to one of its adjacent vertices according to a transition probability matrix P. It is known that both of the hitting time and ... |
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