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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 \( \subseteq \). ... |
I am going ahead with asking what might appear as a debugging question. But,I am looking for something conceptual that I might have missed, and this question is somewhat related to my previous question: NVE MD simulation of inert gas: Problem maintaining equilibrium, although a different issue now. If the moderators de... |
The key to this question is to note that gunpowder doesn't technically explode -- it deflagrates. It doesn't have a super-sonic explosion, but rather a sub-sonic burn. To get the powerful kick needed to project a rifle or handgun bullet, we rely on the fact that gunpowder burns faster in a confined space. The tighter t... |
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To send content items to your Kindle, first ensure no-rep... |
Basically 2 strings, $a>b$, which go into the first box and do division to output $b,r$ such that $a = bq + r$ and $r<b$, then you have to check for $r=0$ which returns $b$ if we are done, otherwise inputs $r,q$ into the division box..
There was a guy at my university who was convinced he had proven the Collatz Conject... |
Rich Trigonometry concepts, Compound angles
Trigonometry first established relationships between the angle and side measurements of a right angled triangle by defining trigonometric functions and thus extended the reach of mathematics wonderfully. Like any other branch of mathematics, from the basic trigonometric funct... |
Dimensionality reduction is used to remove irrelevant and redundant features.
When the number of features in a dataset is bigger than the number of examples, then the probability density function of the dataset becomes difficult to calculate.
For example, if we model a dataset \(S = \{x^{(i)}\}_{i=1}^m,\ x \in R^{n}\) ... |
I'll provide a description of $(\alpha)^{\mathfrak{A}}$ in the case of countable $\mathfrak{A}$. I base my answer on observations by Emil Jeřábek (see discussion below the initial question), but of course any mistakes here are due to me.
From Cantor's normal form theorem it is easy to conclude that each ordinal $\alpha... |
Mathtex Questions answered by this recipe Can PmWiki be used to display long mathematical sequences, logical demonstrations (in Fitch mode)?
This section is optional; use it to indicate the types of questions (if any) this recipe is intended to answer.
Description
MathTex replace MimeTex for those who have latex instal... |
In the laboratory, in your body, and in the outside environment, the majority of chemical reactions take place in solutions. Macroscopically a
solution is defined as a homogeneous mixture of two or more substances, that is, a mixture which appears to be uniform throughout. On the microscopic scale a solution involves t... |
Suppose that we have finite extensions $F \subset L \subset M$ and $\sigma \in Gal(M/F)$ and assume that $F \subset L$ is radical. Prove that $F \subset \sigma L$ is also radical.
Since the extension $F \subset L$ is radical, there exist $\alpha_1, \dots , \alpha_n \in \overline{F}$ such that
$i) \ L =F( \alpha_1, \dot... |
The general theme is game dynamics leading to equilibrium concepts.The plan is to deal with the following topics (all concepts will be defined, and proofs / proof outlines will be provided):(1) An integral approach to the construction of calibrated forecasts and their use for Nash equilibrium dynamics.(2) Blackwell's A... |
I am using the usual estimator for kurtosis, $$\hat{K}=\frac{\hat{\mu}_4}{\hat{\sigma}^4}$$, but I notice that even small 'outliers' in my empirical distribution, i.e. small peaks far from the center, affect it tremendously. Is there a kurtosis estimator which is more robust?
There are several. You will find an exhaust... |
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... |
Analysis of a phase field Navier-Stokes vesicle-fluid interaction model
1.
Department of Mathematics, Pennsylvania State University, University Park, PA 16802, United States
2.
Department of Mathematics, The Pennsylvania State University, University Park, PA 16802
Keywords:Weak Solution, Phase Field, Bending Elastic En... |
Degree $n$ : $45$ Transitive number $t$ : $12$ Group : $C_5\times C_9:C_3$ Parity: $1$ Primitive: No Nilpotency class: $2$ Generators: (1,8,13,20,26,31,38,45,6,10,18,23,30,35,40,2,9,15,19,25,33,39,44,5,12,16,22,29,34,42,3,7,14,21,27,32,37,43,4,11,17,24,28,36,41), (1,20,38,10,30,2,19,39,12,29,3,21,37,11,28)(4,23,42,13,3... |
Definition:Partial Derivative/Real Analysis Contents Definition
Let $U\subset\R^n$ be an open set.
Let $f : U \to \R$ be a real-valued function.
Let $a = (a_1,\ldots,a_n)^\intercal \in U$.
Let $f$ be differentiable at $a$.
Let $i\in\{1,\ldots, n\}$.
The
partial derivative of $f$ with respect to $x_i$ at $a$ is denoted ... |
I'm very confused about some contradicatory statements, and I hope someone can help me clarify this.
Let $\Gamma$ be a congruence subgroup. It is well known that modular forms of weight $k$ for $\Gamma$ can be constructed as global sections of a sheaf $\mathcal{G}_k$ on the modular curve $X(\Gamma)$. If $\Gamma$ contai... |
A well-known theorem by Martin asserts that the degrees of maximal sets are precisely the high recursively enumerable degrees, and the same is true with ‘maximal’ replaced by ‘dense simple’, ‘r-maximal’, ‘strongly hypersimple’ or ‘finitely strongly hypersimple’. Many other constructions can also be carried out in any g... |
J. PANT
Articles written in Journal of Astrophysics and Astronomy
Volume 40 Issue 2 April 2019 Article ID 0009
We report optical observations of TGSS J1054 $+$ 5832, a candidate high-redshift ($z = 4.8 \pm 2$) steep-spectrum radio galaxy, in $r$ and $i$ bands, using the faint object spectrograph and camera mounted on 3... |
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Consider a quadrilateral ABCDABCDABCD . Find the necessary and sufficient condition with proof so that there exists a point PPP in the interior of ABCDABCDABCD such that A(PAB)=A(PBC)=A(PCD)=A(PDA)A(PAB)=A(PBC)= A(PCD)= A(PDA)A(PAB)=A(PBC)=A(PCD)=A(PDA).
A( ) rep... |
Given a $2\times2$ matrix, which entries are functions in the complex plane $$\hat{A}(z)=\left(\begin{array}{cc}a(z)&b(z)\\c(z)&d(z)\end{array}\right)$$Where $a(z),b(z),c(z)$ and $d(z)$ are functions in the complex plane. I would like to obtain two new matrices, denoted as $\hat{\phi}_+(z)$ and $\hat{\phi}_-(z)$, such ... |
Definition:Derivative/Higher Derivatives/Second Derivative Definition
Hence $f'$ is defined on $I$ as the derivative of $f$.
Let $\xi \in I$ be a point in $I$.
Let $f'$ be differentiable at the point $\xi$.
Then the
second derivative $\map {f''} \xi$ is defined as: $\displaystyle f'' := \lim_{x \mathop \to \xi} \dfrac ... |
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... |
Edit. As the OP points out, for his purpose it suffices to take the zero locus of a single (nonzero) partial derivative. So the OP produces a proper closed subset of $V$ containing the singular locus and having degree bounded by $(\text{deg}(V)-1)\text{deg}(V)$. Although this is not what the OP asks, there are cases wh... |
The Ramanujan Summation of some infinite sums is consistent with a couple of sets of values of the Riemann zeta function. We have, for instance, $$\zeta(-2n)=\sum_{n=1}^{\infty} n^{2k} = 0 (\mathfrak{R}) $$ (for non-negative integer $k$) and $$\zeta(-(2n+1))=-\frac{B_{2k}}{2k} (\mathfrak{R})$$ (again, $k \in \mathbb{N}... |
I was trying to solve a differential equation that I defined to study the dynamics of a system. Meanwhile, I encounter integration. The integration is shown in the image below. I tried some solutions but I am failed to get a solution. In one solution, I took "x" common from the denominator terms...
For the diagramIn sc... |
I am a fan of good documentation—I feel it's the most undervalued component of many projects but I haven't been able to develop a reliable process to:
Collect information Format it Keep it up to date
This is my attempt to come up with that process.
vim
I want to edit my documentation in vim. I like it because it's an e... |
Degree $n$ : $44$ Transitive number $t$ : $50$ Parity: $1$ Primitive: No Nilpotency class: $-1$ (not nilpotent) Generators: (1,32,15,27,8,23,22,41,14,37,5,34,20,29,12,26,3,44,17,39,10,35)(2,31,16,28,7,24,21,42,13,38,6,33,19,30,11,25,4,43,18,40,9,36), (1,21)(2,22)(3,19)(4,20)(5,18)(6,17)(7,15)(8,16)(9,14)(10,13)(11,12)(... |
I was reading the following book: http://neuralnetworksanddeeplearning.com/chap2.html
and towards the end of equation 29, there is a paragraph that explains this:
However I am unsure how the equation below is derived:
Artificial Intelligence Stack Exchange is a question and answer site for people interested in conceptu... |
Lephenixnoir af424d1baa update documentation after writing the wiki 3ヶ月前 config 4ヶ月前 include/TeX 3ヶ月前 src 3ヶ月前 .gitignore 3ヶ月前 Makefile 4ヶ月前 README.md 3ヶ月前 TODO.md 3ヶ月前 configure 3ヶ月前 font5x7.bmp 4ヶ月前 font8x9.bmp 4ヶ月前 font10x12.bmp 4ヶ月前
This library is a customizable 2D math rendering tool for calculators. It can be us... |
Completeness Theorem for Semantic Tableaus Theorem
Let $\mathbf A$ be a WFF of propositional logic.
Let $\mathbf A$ be unsatisfiable for boolean interpretations.
Proof
The proof proceeds by contradiction.
This claim is proved by inductively establishing the following claim for all nodes $t$ of $T$: Inductively suppose ... |
Let $q$ be a prime power and let $m$ be a positive integer coprime to $q$. Further, let $E_1(\mathbb F_q)$ and $E_2(\mathbb F_q)$ be two isogenous supersingular elliptic curves over a finite field $\mathbb F_q$ such that
$$E_i(\mathbb F_q)[m] \cong \mathbb Z/m\mathbb Z \times \mathbb Z/m\mathbb Z$$
for $i = 1, 2$. Supp... |
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1. The Genomes OnLine Database (GOLD) v.4: status of genomic and metagenomic projects and their associated metadata
Nucleic Acids Research, ISSN 0305-1048, 1/2012, Volume... |
Tutor profile: Ikechukwu "Daniel" A. Questions Subject: Pre-Calculus
Find the quotient of $$\frac{2i+3}{7-6i}$$ and simplify. Then, find the exact modulus of the result.
Multiply both the numerator and denominator by the conjugate of the denominator $$\frac{2i+3}{7-6i} *\frac{7+6i}{7+6i} = \frac{(2i+3)(7+6i)}{85} = \fr... |
Let $k$ be a $p$-adic field, $G$ a connected reductive group over $k$ with minimal parabolic $P_0$ containing a maximal split torus $A_0$. Let $W = N_G(A_0)(k)/Z_G(A_0)(k)$ be the Weyl group, and $S \subset W$ the simple reflections from $P_0$.
For $\theta, \Omega \subset S$, we have the standard parabolic subgroups $P... |
I need to numerically determine the convergence order of Euler's method for various step-sizes. I am unsure how to go about doing this.
Here is the question:
Problem statement: $\frac{dy}{dt}=\alpha t^{\alpha - 1}, y(0)=0$, where $\alpha > 0$. Use Euler's method to solve the initial value problem for $\alpha = 2.5,1,5,... |
(19 intermediate revisions by 5 users not shown) Line 1: Line 1: − Stoke's Theorem is a generalization of the [[Fundamental Theorem of Calculus]] , which states that if ''M'' is an oriented piece-wise smooth [[manifold]] of [[dimension]] k and <math>\omega</math> is a smooth (''k''−1)-form with compact support on ''M''... |
Bulletin of the American Physical Society 65th Annual Meeting of the APS Division of Fluid Dynamics Volume 57, Number 17 Sunday–Tuesday, November 18–20, 2012; San Diego, California
Session M27: Boundary-Layer Instability II Hide Abstracts Chair: Jill Klentzman, University of Arizona
Room:
31C
Tuesday, November 20, 2012... |
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Hello friends, We have to find the last two digits of 1×3×5×7×9....×991\times3\times5\times7\times9....\times991×3×5×7×9....×99, I did and came out with 25.But I want to verify.
Note by Kishan K 6 years, 3 months ago
Easy Math Editor
This discussion board is a pl... |
It's hard to say just from the sheet music; not having an actual keyboard here. The first line seems difficult, I would guess that second and third are playable. But you would have to ask somebody more experienced.
Having a few experienced users here, do you think that limsup could be an useful tag? I think there are a... |
The cornerstone of the argument is the following:
If the cycle attack works, then you can factor $n$ (see details below). The attacker can choose $e$. I.e., when trying to factor $n$, the attacker is not constrained to use the specific $e$ which you selected for your public key; he can invent his own $e$, since he will... |
Definition:Lower Sum Definition
Let $\left[{a \,.\,.\, b}\right]$ be a closed real interval.
Let $P = \left\{{x_0, x_1, x_2, \ldots, x_n}\right\}$ be a finite subdivision of $\left[{a \,.\,.\, b}\right]$. Then: $\displaystyle L^{\left({f}\right)} \left({P}\right) = \sum_{\nu \mathop = 1}^n m_\nu^{\left({f}\right)} \lef... |
I have been looking for (linear) Extension Operators for Slobodeckii spaces $W^{s,p}(\Omega)$ where $s>1$ and $\Omega \subset\mathbb{R}^N$ is a sufficiently smooth domain, where the influence of $\partial \Omega$ on the constants which define the continuity of this operator are given.
Indeed, by considering $E:W^{s,p}(... |
Are two signals are the same if their
auto-convolution functions are the same?
Almost. Look at the autoconvolution in the frequency domain where the autoconvolution of $x$ (with itself) gives us $(X(f))^2$ in the frequency domain while the autoconvolution of $-x$ (with itself) gives us $(-X(f))^2 = (X(f))^2$. So, given... |
A neural network is a non-linear classifier (separator is not a linear function). It can also be used for regression.
A Shallow neural network is a one hidden layer neural network.
A Vanilla neural network is a regular neural network having layers that do not form cycles.
TensorFlow Playground is an interactive web int... |
Counter-question: why should every type be inhabited by a term? You could not have the Curry-Howard correspondence between typing systems and logic if every type was inhabited.
Concrete answer: I don't have Pierce's book handy, but I think you are talking about the system $\lambda\underline{\omega}$ in Barendregt's $\l... |
Dini criterion for the convergence of Fourier series
A criterion first proved by Dini for the convergence of Fourier series in [Di].
TheoremConsider a summable $2\pi$ periodic function $f$ and a point $x\in \mathbb R$. If thereis a number $S$ and a $\delta>0$ such that\begin{equation}\label{e:Dini}\int_0^\delta |f(x+u)... |
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... |
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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 ... |
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 ... |
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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 \( \subseteq \). ... |
I recently gave a talk on Schubert calculus in the Student Algebraic Geometry Seminar at UC Berkeley. As a combinatorialist, this is a branch of enumerative geometry that particularly strikes my fancy. I also made a handout for the talk called “Combinatorics for Algebraic Geometers,” and I thought I’d post it here in b... |
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 ... |
I recently gave a talk on Schubert calculus in the Student Algebraic Geometry Seminar at UC Berkeley. As a combinatorialist, this is a branch of enumerative geometry that particularly strikes my fancy. I also made a handout for the talk called “Combinatorics for Algebraic Geometers,” and I thought I’d post it here in b... |
I have a function
fthat I want to restrict to a certain sub-domain of the domain it has been originally defined for. Usually, in mathematics this is illustrated by a vertical bar followed by the restricted set in the lower right of the function symbol. E.g. usually I write
f_{\mid A}
which means
f restricted to the set... |
Journal of Symbolic Logic J. Symbolic Logic Volume 58, Issue 1 (1993), 249-290. On Strong Provability Predicates and the Associated Modal Logics Abstract
PA is Peano Arithmetic. $\mathrm{Pr}(x)$ is the usual $\Sigma_1$-formula representing provability in PA. A strong provability predicate is a formula which has the sam... |
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... |
Vague question:Is there a criterion to deduce that a morphism between algebraic stacks is finite based on the local deformation functors?
For sure this is not enough, so let me be more specific.
Suppose that $f: X \to Y$ is a morphism of algebraic stacks. Let us assume in addition that the diagonal $\Delta_f : X \to X ... |
Defining parameters
Level: \( N \) = \( 3600 = 2^{4} \cdot 3^{2} \cdot 5^{2} \) Weight: \( k \) = \( 1 \) Character orbit: \([\chi]\) = 3600.ec (of order \(20\) and degree \(8\)) Character conductor: \(\operatorname{cond}(\chi)\) = \( 400 \) Character field: \(\Q(\zeta_{20})\) Newforms: \( 0 \) Sturm bound: \(720\) Tra... |
Abstract
We prove two results. (1) There is an absolute constant $D$ such that for any finite quasisimple group $S$, given $2D$ arbitrary automorphisms of $S$, every element of $S$ is equal to a product of $D$ ‘twisted commutators’ defined by the given automorphisms.
(2) Given a natural number $q$, there exist $C=C(q)$... |
How to find the equations of the lines that make up the ruled surface z= 2xy? There are a lot of lines and solving this seems non-obvious. I imagine the first thing to know is the equation of a line in 3d. What is the equation for a 3D line?
The points $\;M=\Bigl(x,\dfrac 2x, 4\Bigr)$ and $\;N=\Bigl(x,-\dfrac 2x, -4\Bi... |
The question
I consider the Laplacian $\Delta = \partial_1^2 + \partial_2^2 + \partial_3^2$ in $\mathbb{R}^3$. By the "standard" fundamental solution of the Laplacian, I mean the function
$$ \displaystyle E(x) = C|x|^{-1} $$
where $C$ is some normalization constant.
I would like to know if one can construct a fundament... |
How to find multiple roots?
find_root is finding only "one" root, when there are many in a given range? Very simple question. For ex: sin(x)=cos(pi/2+x) may have multiple solutions in the selected range.
find_root is finding only "one" root, when there are many in a given range? Very simple question. For ex: sin(x)=cos... |
Aprahamian, Mary and Higham, Nicholas J. (2013)
The Matrix Unwinding Function, with an Application to Computing the Matrix Exponential. [MIMS Preprint]
PDF
paper.pdf
Download (412kB)
Abstract
A new matrix function corresponding to the scalar unwinding number of Corless, Hare, and Jeffrey is introduced. This matrix unwi... |
GR8677 #94
Problem
Electromagnetism}LR Circuit
Once the switch S is closed, although the initial current through the inductor is 0, the change in current through it is maximal. Recalling that , one realizes that the voltage across must be non-zero at the start. Thus, plots (C), (D), and (E) are eliminated.
Now, one mus... |
Abstract
Consider a system of $N$ bosons in three dimensions interacting via a repulsive short range pair potential $N^2V(N(x_i-x_j))$, where $\mathbf{x}=(x_1, \ldots, x_N)$ denotes the positions of the particles. Let $H_N$ denote the Hamiltonian of the system and let $\psi_{N,t}$ be the solution to the Schrödinger equ... |
Fractions on a Binary Tree II
We have already discussed an instance of a binary tree related to the Stern-Brocot tree. A fraction $\frac{a}{b}$ on the tree served a parent to two other fractions: $\displaystyle\frac{a}{a + b}$ and $\displaystyle\frac{b}{a + b}.$ At the time we only considered the case where $a \lt b.$ ... |
We continued discussing recursion. We also discussed memoization and demonstrated it.
from IPython.core.interactiveshell import InteractiveShellInteractiveShell.ast_node_interactivity = "all"
A bus driver needs to give an exact change and she has coins of limited types. She has infinite coins of each type. Given the am... |
GR8677 #96
Comments
casseverhart13 2019-08-12 07:04:10 I’d been just browsing every now and then and also got to learn to read this problem. power washing GRE0717 2015-10-20 21:28:08 I couldn\'t figure why the odd terms would give zero coef cause n=1 ,3, 5,... for square well are even functions. The question had n=0 as... |
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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-... |
In Higher Algebra Proposition 5.4.4.10
1, Lurie proves that for a coCartesian fibration of $\infty$-operads $q:\mathscr{C}^\otimes\to\mathscr{O}^\otimes$, where $\mathscr{O}^\otimes$, when viewed as an $\infty$-category, is pointed and $\mathscr{C}$ is a stable $\mathscr{O}$-monoidal $\infty$-category under the coCarte... |
Linear Algebra
A matrix is a 2-D array of numbers.
A tensor is a n-D array of numbers.
Matrices are associative but not commutative.
Not all square matrices have inverse. A matrix that is not invertible is called Singular or Degenerative.
A matrix is “singular” if any of the following are true:
-Any row or column conta... |
My setup is similar to Emrakul's, but since the OP asked for patterns, I will explore what Emrakul left as an exercise. And while I'll mostly discuss the same tips as in Xynariz's answer, his approach does not consider carry digits generally, which can miss possible solutions.
Like in Sudoku, there are quite a few patt... |
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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 \( \subseteq \). ... |
Probabilist often work on Polish spaces. Does somebody know an ("non-exotic") example, for which it is not possible to work on a Polish space, but instead one has to work on a general measurable space? By non-exotic example I mean something like a stochastic process, which is really used in applications, and cannot be ... |
First some setup:
Definition 1.9A graph$\Gamma$ consists of a set $V(\Gamma)$ of vertices and a set $E(\Gamma)$ of edges, each edge being associated to an unordered pair of vertices by a function "Ends": $\text{ENDS}(e) = \{v,w\}$ where $v,w \in V$. In this case we call $v$ and $w$ the ends of the edge $e$ and we also ... |
GR0177 #50
Problem This problem is still being typed.
Wave Phenomena}Sound
Since the wavelength of the wave does not change, as the pipe presumably stays approximately the same length, only the frequency varies. If the speed of sound changes, then the frequency changes. If the speed of sound is lower than usual, then t... |
This is claimed in a Wikipedia Article:
If two representations (of a $C^*$-algebra $A$) $\rho$ and $\sigma$, on Hilbert spaces $H$ and $G$ respectively, are each unitarily equivalent to a subrepresentation of the other, then they are unitarily equivalent.
I don't really follow the proof given. Indeed, what bothers me i... |
This shows you the differences between two versions of the page.
Both sides previous revision Previous revision numerical-shadow [2018/05/22 14:43]
plewandowska [Other names]
numerical-shadow [2018/10/08 08:50] (current)
plewandowska [Definition]
Line 3: Line 3: ===== Definition ===== ===== Definition ===== - For any s... |
It's hard to say just from the sheet music; not having an actual keyboard here. The first line seems difficult, I would guess that second and third are playable. But you would have to ask somebody more experienced.
Having a few experienced users here, do you think that limsup could be an useful tag? I think there are a... |
Set between Connected Set and Closure is Connected Theorem
Let $T$ be a topological space.
Let $H$ be a connected set of $T$.
Let $H \subseteq K \subseteq H^-$, where $H^-$ denotes the closure of $H$. Then $K$ is connected.
Let $T$ be a topological space.
Let $H$ be a connected set of $T$.
Let $H^-$ denote the closure ... |
Gamma-function $\Gamma$-function
2010 Mathematics Subject Classification:
Primary: 33B15 Secondary: 33B2033D05 [MSN][ZBL]$\newcommand{\abs}[1]{\left|#1\right|}\newcommand{\Re}{\mathop{\mathrm{Re}}}\newcommand{\Im}{\mathop{\mathrm{Im}}}$
A transcendental function $\Gamma(z)$ that extends the values of the factorial $z!$... |
An Experimental Study of the Decay $$D^0 \to K^- K^- K^+ \pi^+$$ Abstract
Using data from the E791 experiment at Fermi National Accelerator Laboratory (Fermilab), we have studied the Cabibbo favored, but phase space suppressed decay $$D^0 \to K^-K^- K^+ \pi^+$$ with the normalization channel $$D^0 \to K^- \pi^- \pi^+ \... |
I’ll be flying to Nebraska tomorrow to teach at the Math Olympiad Summer Program. One of my more advanced classes will be on projective geometry and how it can help us understand Euclidean geometry. I thought I would share the introduction from my handout, since it is an attempt to demonstrate one of the many reasons p... |
GR0177 #56
Problem This problem is still being typed.
Mechanics}Fluid Statics
The physical equation required is the buoyancy equation or Archimedes' Principal. The buoyant force is given by, . refers to the density of the fluid that buoy's the object. In this case, is just the density of air (not Helium).
The buoyant f... |
Answer
(a) The simplest way to find 10% of a number is to move the decimal one place to the left. (b) 10% of 50 is 5. 10% x 50 = $\frac{10}{100}\times50 = \frac{1}{10}\times50 = 50\div10 = 5$
Work Step by Step
(a) The simplest way to find 10% of a number is to move the decimal one place to the left. (b) 10% of 50 is 5.... |
202 35 Summary What happens to invariant mass of an object when it gets closer or further from a gravitational body?
In Special Relativity, you learn that invariant mass is computed by taking the difference between energy squared and momentum squared. (For simplicity, I'm saying c = 1).
[tex] m^2 = E^2 - \vec{p}^2 [/te... |
I've been reading Chen's original works on iterated integrals and in order to consider differential forms on the path space $PM$ of a smooth manifold $M$ he gives $PM$ the following "differentiable space" structure:
Let $N$ be a smooth manifold. A continuous map $\alpha: N \to PM$ (where $PM$ has the compact open topol... |
I have solution that can guarantee the end goal being reached in a maximum of
four five steps. (Many thanks for @dmg and @Taemyr for their comments to fix this solution.) The trick is to:
Reduce the cups into the following configuration:
$\begin{bmatrix} \circ & \bullet \\ \bullet & \circ \end{bmatrix} $
where turning ... |
Three-body closed chain of interactive (an)harmonic oscillators and the algebra $sl(4)$
Alexander TURBINER, Willard MILLER JR, Adrian ESCOBAR-RUIZ
- 2019-10-07 (P/19/13)
In this work we study 2- and 3-body oscillators with quadratic and sextic pairwise potentials which depend on relative {\it distances}, $|{\bf r}_i - ... |
Some means inequalities for positive operators in Hilbert spaces 1k Downloads Abstract
In this paper, we obtain two refinements of the ordering relations among Heinz means with different parameters via the Taylor series of some hyperbolic functions and by the way, we derive new generalizations of Heinz operator inequal... |
You are here News
Recent result from PandaX-II was published on Physical Review Letter (Phys. Rev. Lett. 119, 181302, "Editor's Suggestion") on October 30, 2017, back-to-back with the first result from XENON1T experiment. The papers are highlighted by a Physics "Viewpoint" commentary by Dan Hooper from FNAL and Univ. o... |
Since it was getting boring to always do OOP Languages I decided to dabble in the functional realm of programming.
For that I chose the narrowly missed community-challenge by Edward: Resistor Mania, since it really is a quick-to solve using recursive and functional style.
Challenge description:
In electronics, two resi... |
I have a question that seems to not been answered directly, i tried using the
empheq package to make boxes around equation (in the align environment ) and it works, but i want a wide box which occupies the hole textwidth and includes the equation number.
Here is an example code:
\documentclass[]{article} \usepackage{am... |
Kimi and Jordan Task
Kimi and Jordan are each working during the summer to earn money in addition to their weekly allowance. Kimi earns \$9 per hour at her job, and her allowance is \$8 per week. Jordan earns \$7.50 per hour, and his allowance is \$16 per week.
Jordan wonders who will have more income in a week if they... |
Here is a closely related pair of examples from operator theory, von Neumann's inequality and the theory of unitary dilations of contractions on Hilbert space, where things work for 1 or 2 variables but not for 3 or more.
In one variable, von Neumann's inequality says that if $T$ is an operator on a (complex) Hilbert s... |
Abstract
Let $G={\bf SL}l(n,\Bbb{R})$ with $n\geq 6$. We construct examples of lattices $\Gamma \subset G$, subgroups $A$ of the diagonal group $D$ and points $x\in G/\Gamma$ such that the closure of the orbit $Ax$ is not homogeneous and such that the action of $A$ does not factor through the action of a one-parameter ... |
Best Compromise
There is a saying “a good compromise makes no one happy”. As distressing as that may be, I guess most people still think it is a good idea to seek the best agreement. The problem though, is to define the measure in which the word “best” gets a meaning. Let us consider $n$ people, each with a firm belief... |
Banach Journal of Mathematical Analysis Banach J. Math. Anal. Volume 8, Number 1 (2014), 55-63. On the essential spectrum of the sum of self-adjoint operators and the closedness of the sum of operator ranges Abstract
Let $\mathcal{H}$ be a complex Hilbert space, and $A_1,\ldots,A_N$ be bounded self-adjoint operators in... |
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