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The Product of a Subgroup and a Normal Subgroup is a Subgroup
Problem 448
Let $G$ be a group. Let $H$ be a subgroup of $G$ and let $N$ be a normal subgroup of $G$.The product of $H$ and $N$ is defined to be the subset\[H\cdot N=\{hn\in G\mid h \in H, n\in N\}.\]Prove that the product $H\cdot N$ is a subgroup of $G$.
A ... |
(a) Prove that the column vectors of every $3\times 5$ matrix $A$ are linearly dependent.
Note that the column vectors of the matrix $A$ are linearly dependent if the matrix equation\[A\mathbf{x}=\mathbf{0}\]has a nonzero solution $\mathbf{x}\in \R^5$.
The equation is equivalent to a $3\times 5$ homogeneous system.As t... |
Infinite many positive solutions for nonlinear first-order BVPs with integral boundary conditions on time scales Abstract
In this paper, we investigate the existence of infinite many positive solutions for the nonlinear
first-order BVP with integral boundary conditions $$ \cases x^{\Delta}(t)+p(t)x^{\sigma}(t)=f(t,x^{\... |
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Revision as of 22:01, 8 November 2016 Contents 1 Fall 2016 2 Spring 2017 3 Fall ... |
NTS ABSTRACTSpring2019
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Contents Jan 25
Asif Ali Zaman A log-free zero density estimate for Rankin-Selberg $L$-functions and applications Abstract:We discuss a log-free zero density estimate for Rankin-Selberg $L$-functions of the form $L(s,\pi\times\pi_0)$, where $\pi$ varies in a given set of cusp forms ... |
Collisional Frequency is the average rate in which two reactants collide for a given system and is used to express the average number of collisions per unit of time in a defined system.
Background and Overview
To fully understand how the collisional frequency equation is derived, consider a simple system (a jar full of... |
Is it true that the cardinality of every maximal linearly independent subset of a finitely generated free module $A^{n}$ is equal to $n$ (not just at most $n$, but in fact $n$)? Here $A$ is a nonzero commutative ring. I know that it's true if $A$ is Noetherian or integral domain. I thought it was not true in general bu... |
The answer is yes. Suppose we have a factorization $Q = A\cdot B$.
One easy observation is that $A$ and $B$ must be disjoint (since for $w\in A\cap B$ we get $w^2\in Q$). In particular, only one of $A,B$ can contain $\epsilon$. We can assume wlog (since the other case is completely symmetric) that $\epsilon\in B$. Then... |
This question is coming from the fact that all the counter examples for which second order stochastical domination holds but first oder stochastical domination fails do not accept increasing likelihood ratio condition.
From this, a natural question is: If second order stochastical domination together with increasing li... |
(a) Prove that the additive group $\Q=(\Q, +)$ is not finitely generated.
Seeking a contradiction assume that the group $\Q=(\Q, +)$ is finitely generated and let $r_1, \dots, r_n$ be nonzero generators of $\Q$.Express the generators as fractions\[r_i=\frac{a_i}{b_i},\]where $a_i, b_i$ are integers.
Then every rational... |
I know I promised a post on regression, but then I realized I only have a shallow understanding of Boosting and AdaBoost. So I biked to the nearest public library, when to the index cards, search for ‘Boost’ and after perusing through hundreds of self-help books, I found the greatest resource on AdaBoost: “How to Boost... |
Emil Stoyanov's New Year's Problem What Is This About? Source
Problem
In $\Delta ABC,\,$ $M\in BC,\,$ $N\in AC;\,$ $K=AM\cap BN;\,$ the circumcircles $(AKN)\,$ and $(BKM)$ intersect a the orthocenter $H\,$ of $\Delta ABC.$
Prove $AM=BN.$
Solution 1
Let $AD\,$ and $BE\,$ be two altitudes in $\Delta ABC.\,$ Since $\Delta... |
An $n\times n$ matrix $A$ is said to be singular if there exists a nonzero vector $\mathbf{v}$ such that $A\mathbf{v}=\mathbf{0}$.
Otherwise, we say that $A$ is a nonsingular matrix.
Proof.
Let $\mathbf{v}=\begin{bmatrix}1 \\1 \\\vdots \\1\end{bmatrix}$ be the $n$-dimensional vector all of whose entries are $1$.Then we... |
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math.SP
Change to browse by: References & Citations Bookmark(what is this?) Mathematics > Spectral Theory Title: Example of periodic Neumann waveguide with gap in spectrum
(Submitted on 25 May 2016)
Abstract: In this note we investigate spectral properties of a periodic waveguide $\Omega^\vareps... |
NTS ABSTRACTSpring2019
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Contents Jan 23
Yunqing Tang Reductions of abelian surfaces over global function fields For a non-isotrivial ordinary abelian surface $A$ over a global function field, under mild assumptions, we prove that there are infinitely many places modulo which $A$ is geometrically isogenous ... |
Express a Hermitian Matrix as a Sum of Real Symmetric Matrix and a Real Skew-Symmetric Matrix
Problem 405
Recall that a complex matrix is called Hermitian if $A^*=A$, where $A^*=\bar{A}^{\trans}$.Prove that every Hermitian matrix $A$ can be written as the sum\[A=B+iC,\]where $B$ is a real symmetric matrix and $C$ is a ... |
Triple
Time Limit: 12000/6000 MS (Java/Others)
Memory Limit: 65536/65536 K (Java/Others)
Description
Given the finite
multi-set $A$ of $n$ pairs of integers, an another finite multi-set $B$ of $m$ triples of integers, we define the product of $A$ and $B$ as a multi-set $C =A * B \\ = \{\langle a,c,d\rangle \mid \langle... |
Introduction to Semiconductors
concept
Our study of analog circuits will be built on our understanding of semiconductor physics. Semiconductors (metals which are somewhere between copper wire and a brick wall in terms of resistance) allow for some very clever devices to be built that work in strange, nonlinear ways and... |
Consider the Koch curve $G \subseteq \mathbb{R}^2$. Clearly $G$ is the invariant set (IS) of the iterated function system (IFS) $\lbrace \phi_1, \phi_2, \phi_3, \phi_4 \rbrace$. Where (not wanting to jump between $\mathbb{R}^2$ and $\mathbb{C}$ but doing so for ease):
$\phi_1(x) = \frac{1}{3} x$, $\phi_2(x) = \frac{1}{... |
2018-08-25 06:58
Recent developments of the CERN RD50 collaboration / Menichelli, David (U. Florence (main) ; INFN, Florence)/CERN RD50 The objective of the RD50 collaboration is to develop radiation hard semiconductor detectors for very high luminosity colliders, particularly to face the requirements of the possible u... |
Math/Display
< Math >
Contents Display Math
The famous result (once more) is given by \startformula c^2 = a^2 + b^2. \stopformula
This, when typeset, produces the following:
Numbering Formulae
The famous result (once more) is given by \placeformula \startformula c^2 = a^2 + b^2. \stopformula
This, when typeset, produce... |
We've been talking about the Miller-Rabin randomized primality test, which is one of the easiest to implement and most effective tests that, given a number, will either prove it to be composite or state that it is most likely prime. As good as it is for practical applications, the Miller-Rabin test leaves something to ... |
(This is basically an extension of $\pi$ Day puzzle one to twenty)
$\tau$ is greater than $\pi$ and $\tau>\pi$.
Create the numbers from $1$ to $20$ using only:
Tau ($\tau$, equivalent to $2\pi$) Basic arithmetic operations ($+-\times\div$) Square roots ($\sqrt{x}$ or $\sqrt[2]{x}$) Exponentiation ($x^y$) Negative tau (... |
Define $\tilde{\phi}([g])=\phi(g)$ and show that this is well-defined.
Show that $\tilde{\phi}$ is a homomorphism.
Show that $\tilde{\phi}$ is injective.
Proof.
Define the map $\tilde{\phi}: G/\ker{\phi} \to G’$ by sending $[g]$ to $\phi(g)$. Here $[g]$ is the element of $G/\ker{\phi}$ represented by $g\in G$.
We need ... |
With which notation do you feel uncomfortable?
closed as not constructive by Loop Space, Chris Schommer-Pries, Qiaochu Yuan, Scott Morrison♦ Mar 19 '10 at 6:10
As it currently stands, this question is not a good fit for our Q&A format. We expect answers to be supported by facts, references, or expertise, but this quest... |
An $n\times n$ matrix is invertible if and only if its rank is $n$.The rank of a matrix is the number of nonzero rows of a (reduced) row echelon form matrix that is row equivalent to the given matrix.
Solution.
We compute the rank of the matrix $A$.Applying elementary row operations, we obtain\begin{align*}\begin{bmatr... |
Keeping Track of Element Order in Multiphysics Models
Whenever you are building a finite element model in COMSOL Multiphysics, you should be aware of the element order that is being used. This is particularly important for multiphysics models as there are some distinct benefits to using different element orders for dif... |
S Muralithar
Articles written in Pramana – Journal of Physics
Volume 55 Issue 3 September 2000 pp L471-L478 Rapid Communication
Excited states of
63Cu were populated via the $^{52}{\rm Cr} + {}^{16}{\rm O}$ (65 MeV) reaction using the gamma detector array equipped with charged particle detector array for reaction chann... |
Fractal Weyl bounds and Hecke triangle groups
1.
Laboratoire de Mathématiques D'avignon, Université d'Avignon, 301 rue Baruch de Spinoza, 84916 Avignon Cedex, France
2.
University of Bremen, Department 3 - Mathematics, Bibliothekstr. 5, 28359 Bremen, Germany
3.
Institute for Mathematics, University of Jena, Ernst-Abbe-... |
A particle moves along the x-axis so that at time t its position is given by $x(t) = t^3-6t^2+9t+11$ during what time intervals is the particle moving to the left? so I know that we need the velocity for that and we can get that after taking the derivative but I don't know what to do after that the velocity would than ... |
Group of Invertible Matrices Over a Finite Field and its Stabilizer Problem 108
Let $\F_p$ be the finite field of $p$ elements, where $p$ is a prime number.
Let $G_n=\GL_n(\F_p)$ be the group of $n\times n$ invertible matrices with entries in the field $\F_p$. As usual in linear algebra, we may regard the elements of $... |
April 23rd, 2016, 05:13 AM
# 11
Banned Camp
Joined: Dec 2012
Posts: 1,028
Thanks: 24
Luckily my last post was blown away for an unknown reason....
The point is show that a proportional condition on $Y$ (here Delta/Delta=1) on a curve $Y=X^2$, that has a first linear derivate can again "generate" a proportional conditio... |
Another reason for the popularity of statistical significance testing is probably that complicated mathematical procedures lend an air of scientific objectivity to conclusions.
—Ronald P. Carver
Significance testing is all about whether the outcome would be too much of a coincidence for the hypothesis to be true. But h... |
True or False Problems of Vector Spaces and Linear TransformationsThese are True or False problems.For each of the following statements, determine if it contains a wrong information or not.Let $A$ be a $5\times 3$ matrix. Then the range of $A$ is a subspace in $\R^3$.The function $f(x)=x^2+1$ is not in the vector space... |
Find a Matrix so that a Given Subset is the Null Space of the Matrix, hence it’s a Subspace Problem 252
Let $W$ be the subset of $\R^3$ defined by
\[W=\left \{ \mathbf{x}=\begin{bmatrix} x_1 \\ x_2 \\ x_3 \end{bmatrix}\in \R^3 \quad \middle| \quad 5x_1-2x_2+x_3=0 \right \}.\] Exhibit a $1\times 3$ matrix $A$ such that ... |
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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... |
Application of Field Extension to Linear Combination Problem 335
Consider the cubic polynomial $f(x)=x^3-x+1$ in $\Q[x]$.
Let $\alpha$ be any real root of $f(x)$. Then prove that $\sqrt{2}$ can not be written as a linear combination of $1, \alpha, \alpha^2$ with coefficients in $\Q$. Proof.
We first prove that the poly... |
I was hoping someone might be able to offer some advice on placing knots for restricted cubic splines. In brief, I am helping a team of clinicians who want to predict which patients require a specialist team to meet them when they arrive (via ambulance) at the hospital. The outcome is severe trauma or not (assessed pos... |
I have a LP problem with n decision variables, \(x_1, \ldots, x_n\), and one of the constraints is
\[\max(x_1, \ldots, x_n) = c\]
where \(c\) is a constant and \(max\) is the max function (i.e., it returns the highest of the parameters \(x_1, \ldots,x_n\)).
Is there a way to cope with this constraint, transforming it i... |
Let $n$ be a positive integer.Since $G/N$ is a cyclic group, let $g$ be a generator of $G/N$.So we have $G/N=\langle g\rangle$.Then $\langle g^n \rangle$ is a subgroup of $G/N$ of index $n$.
By the fourth isomorphism theorem, every subgroup of $G/N$ is of the form $H/N$ for some subgroup $H$ of $G$ containing $N$.Thus ... |
I have an output signal $y$ which is an input signal $x$ convolved $\star$ with an impulse response function $h$ with some added noise $n$ :
$$y(t) = h(t) \star x(t) + n(t)$$
I know the input signal $x$ and output signal $y$ and would like to calculate $h$ the impulse response function. I found that deconvolution is no... |
N Nimai Singh
Articles written in Pramana – Journal of Physics
Volume 60 Issue 2 February 2003 pp 405-409
Raj Gandhi Kamales Kar S Uma Sankar Abhijit Bandyopadhyay Rahul Basu Pijushpani Bhattacharjee Biswajoy Brahmachari Debrupa Chakraborti M Chaudhury J Chaudhury Sandhya Choubey E J Chun Atri Desmukhya Anindya Datta G... |
I programmed one. Simple, i know, but it does the job
Let me know what you guys think of it.
EDIT: Download Math Tool 3.5 here
Last edited by janvdl; Jan 11th 2008 at 05:50 AM.
Reason: 3.5 Released
Follow Math Help Forum on Facebook and Google+
Originally Posted by janvdl I programmed one. Simple, i know, but it does t... |
1. Linear combination
If a vector can be expressed as a
linear combination of other vectors, they are said to be linearly dependent. Example I
We’d like to know if one vector in Figure 6.1 depends upon the others, as the following :
We have thus :
Let’s factorize the right hand-side of $(2)$ :
Let’s proceed with the ma... |
For Bayesians, probabilities are beliefs. When I say it’ll probably rain today, I’m telling you something about my personal level of confidence in rain today. I’m saying I’m more than \(50\%\) confident it’ll rain.
But how can we quantify something as personal and elusive as a level of confidence? Bayesians answer this... |
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Higher harmonic flow coefficients of identified hadrons in Pb-Pb collisions at $\sqrt{s_{\rm NN}}$ = 2.76 TeV
(Springer, 2016-09)
The elliptic, triangular, quadrangular and pentagonal anisotropic flow coefficients for $\pi^{\pm}$, $\mathrm{K}^{\pm}$ and p+$\overline{\mathrm{p}}$ in Pb-... |
Solving Laplace Equation having boundary conditions
Hello,
Please watch this video https://youtu.be/_cPU-nf9owk and tell me whether $A)C_{n,m}=\frac {16V_0}{\pi^2 mn\cosh{\bigg(\sqrt{(\frac{n\pi}{a})^2+ (\frac{n\pi}{a})^2}}\bigg)}$ or $B)C_{n,m}=\frac {16V_0}{\pi^2 mn\cosh{\bigg(\sqrt{(\frac{n\pi}{a})^2+ (\frac{n\pi}{a... |
A question that pops up for many DSP-ers working with IIR and FIR filters, I think, is how to look at a filter’s frequency and phase response. For many, maybe they’ve calculated filter coefficients with something like the biquad calculator on this site, or maybe they’ve used a MATLAB, Octave, Python (with the scipy lib... |
A particle moves along the x-axis so that at time t its position is given by $x(t) = t^3-6t^2+9t+11$ during what time intervals is the particle moving to the left? so I know that we need the velocity for that and we can get that after taking the derivative but I don't know what to do after that the velocity would than ... |
Nullspace
Let A be a mxn matrix. The nullspace is therefore the set of vectors $\vec{x}$ such that $A\vec{x} = \vec{0}$
Nul(A)
A = $\begin{bmatrix} 1&0&1\\2&-1&1\end{bmatrix}$
Is $b = \begin{bmatrix} 2\\-2 \end{bmatrix} \in$ Nul(A)
NO! $A*b \neq \vec{0}$. Actually, we cannot even perform the operation. It can therefore... |
I know I promised a post on regression, but then I realized I only have a shallow understanding of Boosting and AdaBoost. So I biked to the nearest public library, when to the index cards, search for ‘Boost’ and after perusing through hundreds of self-help books, I found the greatest resource on AdaBoost: “How to Boost... |
I’m extremely agitated today. I dunno why. Maybe because there was some convulsion in the peaceful tidings of the house I live in, or the fact that I’m kinda hungry at the moment. Anyways, I don’t have time for chitchat. Let’s get to the studying.
The following is taken from
Foundations of Machine Learning by Rostamyar... |
If you look at the little network diagram below, you’ll probably agree that $P$ is the most “central” node in some intuitive sense.
This post is about using a belief’s centrality in the web of belief to give a coherentist account of its justification. The more central a belief is, the more justified it is.
But how do w... |
Thanks for all the answers. I realize that I had a big mistake. I did not figure out the distribution of the pseudo-random sequences.
I try to use PRGs or PRFs to define the pseudo-random sequences. If there is a formal one, please tell me.
Of course, the pseudo-random sequence and the truly random sequence are indisti... |
($M(n)$ is "the time required to perform precision$n$multiplication.") $\:$ By page 10 of this paper,
a precision-$n$ approximation to $\pi$ can be computed in time $\;\; O\Big(\hspace{-0.04 in}M(n)\hspace{-0.02 in}\cdot \hspace{-0.02 in}\log(n)\hspace{-0.04 in}\Big) \;\;\;$. By the very end of this paper, one can find... |
Hi, Can someone provide me some self reading material for Condensed matter theory? I've done QFT previously for which I could happily read Peskin supplemented with David Tong. Can you please suggest some references along those lines? Thanks
@skullpatrol The second one was in my MSc and covered considerably less than my... |
The Annals of Probability Ann. Probab. Volume 22, Number 2 (1994), 833-853. Ergodic Theorems for Infinite Systems of Locally Interacting Diffusions Abstract
Let $x(t) = \{x_i(t), i \in \mathbb{Z}^d\}$ be the solution of the system of stochastic differential equations $dx_i(t) = \bigg(\sum_{j\in\mathbb{Z}^d}a(i,j)x_j(t)... |
I am going to assume that by constant, you really mean constant as opposed to instantaneous. In other words, we are still bound by the speed of light propagation delay. We are also bound by the laws of orbital mechanics as currently understood.
Since you use "planets" plural, I take it that humanity has colonies on mul... |
Imagine you’re going to flip a fair coin twice. You could get two heads, two tails, or one of each. How probable is each outcome?
It’s tempting to say they’re equally probable, \(1/3\) each. But actually the first two are only \(1/4\) likely, while the last is \(1/2\) likely. Why?
There are actually four possible outco... |
Let $N$ be a type ${\rm II}$ factor, with trace $\tau$. Consider its fundamental group$$ \mathcal{F}(N)= \{ \tau(p)/\tau(q) \ | \ p,q \text{ non-zero finite projections in } N \text{ and } pNp \simeq qNq \}. $$
Let $\alpha$ be a free ergodic measure preserving action of a countable ICC group $\Gamma$ on a $\sigma$-fini... |
A particle moves along the x-axis so that at time t its position is given by $x(t) = t^3-6t^2+9t+11$ during what time intervals is the particle moving to the left? so I know that we need the velocity for that and we can get that after taking the derivative but I don't know what to do after that the velocity would than ... |
Miloslav Znojil
For non-Hermitian equilateral q-pointed star-shaped quantum graphs of paper I [Can. J. Phys. 90, 1287 (2012), arXiv 1205.5211] we show that due to certain dynamical aspects of the model as controlled by the external, rotation-symmetric complex Robin boundary conditions, the spectrum is obtainable in a c... |
The Blum-Blum-Shub generator is a deterministic Pseudo-Random Bit Generator with security reducible to that of integer factorization.
Setup: Secretly chose random primes $P$, $Q$, with $P\equiv Q\equiv 3\pmod4$, and compute $N=P\cdot Q$. Secretly chose a random seed $x_0$ in $[1\dots n-1]$ with $\gcd(x_0,N)=1$.
Use: To... |
A Relation of Nonzero Row Vectors and Column Vectors
Problem 406
Let $A$ be an $n\times n$ matrix. Suppose that $\mathbf{y}$ is a nonzero row vector such that\[\mathbf{y}A=\mathbf{y}.\](Here a row vector means a $1\times n$ matrix.)Prove that there is a nonzero column vector $\mathbf{x}$ such that\[A\mathbf{x}=\mathbf{... |
A particle moves along the x-axis so that at time t its position is given by $x(t) = t^3-6t^2+9t+11$ during what time intervals is the particle moving to the left? so I know that we need the velocity for that and we can get that after taking the derivative but I don't know what to do after that the velocity would than ... |
$L^q$-Extensions of $L^p$-spaces by fractional diffusion equations
1.
Department of Mathematics and Department of Computer Science, Georgetown University, Washington D.C. 20057
2.
Department of Mathematics and Statistics, Memorial University of Newfoundland, St. John's, NL A1C 5S7, Canada
Mathematics Subject Classifica... |
Let $x$ be an element in $F$. We want to show that there exists $a, b\in F$ such that\[x=a^2+b^2.\]
Since $F$ is a finite field, the characteristic $p$ of the field $F$ is a prime number.
If $p=2$, then the map $\phi:F\to F$ defined by $\phi(a)=a^2$ is a field homomorphism, hence it is an endomorphism since $F$ is fini... |
This article is all about the basics of probability. There are two interpretations of a probability, but the difference only matters when we will consider inference.
Frequency The degree of belief Axioms of Probability
A function \(P\) which assigns a value \(P(A)\) to every event \(A\) is a
probability measure or prob... |
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Discrete & Continuous Dynamical Systems - A
April 2007 , Volume 17 , Issue 2
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Abstract:
This special issue of DCDS is dedicated to Carlos Gutierrez and Marco Antonio Teixeira, on the occasion of their 60th birthday.
Born in Peru, C. Gutier... |
Formula Constrained Optimization
For example, a quarter-wave stack with
pairs and QWOT thicknesses equal to m and a can be represented as b
We can consider some set of possible values for integers
, and for every possible combination of m and n OptiLayer will try to find optimal values of continuous parameters m and a ... |
Expectation Maximization Last updated on 02-15-2018. Table of Contents Introduction: Density estimation Jensen Inequality EM Algorithm Formalization Towards deeper understanding of EM: Evidence Lower Bound (ELBO) Applying EM on Gaussian Mixtures Real example
Note: All the materials below are based on the excellent lect... |
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Most kings together in a game
⛀ L. Camara ⛂ M. Jaggoe ⚐ Drawn Game
1985-02-22 World Championship Youth 1985
A game with 5 against 2 kings is more common. It's a difficult endgame; the player with the 5 kings has a winning position, but some players don't know how. One example: ... |
The risk-neutral measure $\mathbb{Q}$ is a mathematical construct which stems from the
law of one price, also known as the principle of no riskless arbitrage and which you may already have heard of in the following terms: "there is no free lunch in financial markets".
This law is at the heart of securities'
relative va... |
As others have pointed it out, it's difficult to know what he meant. Remember that he was reporting on something he had been told which he probably hadn't fully comprehended at the time, or of which he had only an inaccurate recollection at the time of writing.
This answer is the configuration that came to my mind as h... |
Given that $\sin\theta = \dfrac{1}{2}$ and that $\cos\theta = -\dfrac{\sqrt{3}}{2}$ and $0^\circ \leq \theta \leq 360^\circ$, find the value of $\theta$.
Since $\sin\theta > 0$ and $\cos\theta < 0$, you have correctly concluded that $\theta$ is a second-quadrant angle. You also took the inverse cosine of $-\dfrac{\sqrt... |
I was reading the following notes on tensor products: http://www.math.uconn.edu/~kconrad/blurbs/linmultialg/tensorprod.pdf
At some point (p. 39) there is the following example
In the last paragraph, he says that using exterior powers it can be proved that if $I\oplus I\simeq S^2$ as $S$-module, then $I\otimes_S I\simeq... |
Part a) of this is fine, but I'm really stuck on part b) and I have a test on this in an hours time, does anyone have any hints?
closed as off-topic by Toby Mak, Dietrich Burde, воитель, mrtaurho, Yanior Weg Aug 12 at 19:32
This question appears to be off-topic. The users who voted to close gave this specific reason:
"... |
Goldbach's Theorem Theorem
Let $F_m$ and $F_n$ be Fermat numbers such that $m \ne n$.
Then $F_m$ and $F_n$ are coprime.
Without loss of generality, suppose that $m > n$.
Then $m = n + k$ for some $k \in \Z_{>0}$.
\(\displaystyle F_m - 1\) \(\equiv\) \(\displaystyle -1\) \(\displaystyle \pmod p\) as $p \divides F_m$ \(\... |
Consider a $C^k$, $k\ge 2$, Lorentzian manifold $(M,g)$ and let $\Box$ be the usual wave operator $\nabla^a\nabla_a$. Given $p\in M$, $s\in\Bbb R,$ and $v\in T_pM$, can we find a neighborhood $U$ of $p$ and $u\in C^k(U)$ such that $\Box u=0$, $u(p)=s$ and $\mathrm{grad}\, u(p)=v$?
The tog is a measure of thermal resist... |
That's a
great question! What you are asking about is one of the missing links between classical and quantum gravity.
On their own, the Einstein equations, $ G_{\mu\nu} = 8 \pi G T_{\mu\nu}$, are local field equations and do not contain any topological information. At the level of the action principle,
$$ S_{\mathrm{eh... |
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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 i... |
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Now showing items 1-10 of 165
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 i... |
amp-mathml
Displays a MathML formula.
Required Script
<script async custom-element="amp-mathml" src="https://cdn.ampproject.org/v0/amp-mathml-0.1.js"></script>
Supported Layouts container Examples amp-mathml.amp.html Behavior
This extension creates an iframe and renders a MathML formula.
Example: The Quadratic Formula ... |
Suppose that $A$ and $B$ are DFAs. We know that there is some DFA $M$ such that $L(M) = L(A) \bigtriangleup L(B)$, the symmetric difference. Also, we can construct this $M$ by some Turing machine $N$. But can we ensure that $N$ has the following form?
$N$ consists of (i) a read-only input tape, (ii) a work tape that is... |
Let us denote $X^\top X$ by $A$. By construction, it is a $n\times n$ square symmetric positive semi-definite matrix, i.e. it has an eigenvalue decomposition $A=V\Lambda V^\top$, where $V$ is the matrix of eigenvectors (each column is an eigenvector) and $\Lambda$ is a diagonal matrix of non-negative eigenvalues $\lamb... |
Using usual notation we have,
$SDP(G) \geq OPT(G) \geq Alg_{GW}(G) \geq \alpha_{GW} SDP(G) \geq \alpha_{GW} OPT(G)$
where we mean,
$SDP(G)$ = The maximum value that the SDP finds of the objective function $\sum_{(u,v) \in E} w_{uv}( 1-\vec{y_u}.\vec{y_v})/2$ (one unit vector $\vec{y_v}$ in $\mathbb{R}^d$ for each verte... |
Pole (of a function)
$ \newcommand{\abs}[1]{\left| #1 \right|} \newcommand{\set}[1]{\left\{ #1 \right\}} $
An isolated singular point $a$ of single-valued character of an analytic function $f(z)$ of the complex variable $z$ for which $\abs{f(z)}$ increases without bound when $z$ approaches $a$: $\lim_{z\rightarrow a} f... |
I came across John Duffield Quantum Computing SE via this hot question. I was curious to see an account with 1 reputation and a question with hundreds of upvotes.It turned out that the reason why he has so little reputation despite a massively popular question is that he was suspended.May I ...
@Nelimee Do we need to m... |
Primary groups and pure subgroups.
Hi: Let G be a p-primary group that is not divisible. Assume there is $x \in G[p]$ that is divisible by $p^k$ but not by $p^{k+1}$ and let $x= p^k y$. I must prove that $<y> \cap nG \subset n<y>$. $p^{k+1}y= px= 0$. In case $(n,p)=1$, there is $b \in <y>$ such that $y=nb$ and then $sy... |
Geometrical Optics 101: Paraxial Ray Tracing Calculations
Ray tracing is the primary method used by optical engineers to determine optical system performance. Ray tracing is the act of manually tracing a ray of light through a system by calculating the angle of refraction/reflection at each surface. This method is extr... |
Huge cardinal Huge cardinals (and their variants) were introduced by Kenneth Kunen in 1972 as a very large cardinal axiom. Kenneth Kunen first used them to prove that the consistency of the existence of a huge cardinal implies the consistency of $\text{ZFC}$+"there is a $\omega_2$-saturated $\sigma$-ideal on $\omega_1$... |
$\ce{NH3}$ is a weak base so I would have expected $\ce{NH4+}$ to be a strong acid. I can't find a good explanation anywhere and am very confused. Since only a small proportion of $\ce{NH3}$ molecules turn into $\ce{NH4+}$ molecules, I would have expected a large amount of $\ce{NH4+}$ molecules to become $\ce{NH3}$ mol... |
I want to calculate the kinetic energy of a disk (radius $R$ and mass $M$) rolling without slipping in horizontal plane, but with center of mass displaced a distance $r$ from the geometrical center.
I have no problem with the translational part (center of mass), but when dealing with the rotational $\dfrac{1}{2}I\dot{\... |
I think it'd be nice to have a whole set of possible messages, each associated with some equation which has zero on the right hand side. It'd look something like this:
"404; Did you just [insert operation that yields zero*]? Because there's nothing here! (Insert relevant equation**)"
*Examples; (**Corresponding equatio... |
Developing flow From Thermal-FluidsPedia
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Similar analysis and conclusions can be made with the Schmidt number, Sc, relative to mass transfer problems concerning the entrance effects due to mass diffusion. If one needs to get detailed information concerning the hydrodynamic, thermal or concentration entr... |
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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 ... |
I am preparing for an exam and am stuck on the following problem :
Let $G$ be a group of order $2555 = 5 \cdot 7 \cdot 73$, show that $G$ is cyclic.
It is not hard to show that the Sylow-73 subgroup is normal in $G$ and that at either the Sylow-5 or the Sylow-7 subgroup is normal. My thought was to prove that both the ... |
Numerical Solution of the KdV Contents Introduction
We present here a method to solve the KdV equation numerically. There are many different methods to solve the KdV and we use here a spectral method which has been found to work well. Spectral methods work by using the Fourier transform (or some varient of it) to calcu... |
Measure algebra (measure theory)
$\newcommand{\A}{\mathcal A}\newcommand{\B}{\mathcal B} $A
measure algebra is a pair $(\B,\mu)$ where $\B$ is a Boolean σ-algebra and $\mu$ is a (strictly) positive measure on $\B$. The (strict) positivity means $\mu(x)\ge0$ and $\mu(x)=0\iff x=\bszero_{\B}$ for all $x\in\B$. However, a... |
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... |
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