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Damping in Structural Dynamics: Theory and Sources
If you strike a bowl made of glass or metal, you hear a tone with an intensity that decays with time. In a world without damping, the tone would linger forever. In reality, there are several physical processes through which the kinetic and elastic energy in the bowl di... |
№ 9
All Issues Derech V. D.
↓ Abstract
Ukr. Mat. Zh. - 2018. - 70, № 8. - pp. 1072-1084
Let $S$ be a finite semigroup. By $\mathrm{S}\mathrm{u}\mathrm{b}(S)$ we denote the lattice of all its subsemigroups. If $A \in \mathrm{S}\mathrm{u}\mathrm{b}(S)$, then by $h(A)$ we denote the height of the subsemigroup $A$ in the l... |
Difference between revisions of "Group cohomology of elementary abelian group of prime-square order"
(Created page with "Suppose <math>p</math> is a prime number. We are interested in the elementary abelian group of prime-square order <math>E_{p^2} = (\mathbb{Z}/p\mathbb{Z})^2 = \mathbb{Z}/...")
(→Over the integers)
(3... |
Difference between revisions of "Group cohomology of elementary abelian group of prime-square order"
(→Over the integers)
(→Over the integers)
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Suppose <math>p</math> is a [[prime number]]. We are interested in the [[elementary abelian grou... |
I’m frequently told that probabilities are the limit of relative frequencies for an infinite number of repetitions. It sounds nice: it defines a difficult concept – probabilities – in terms of a simple one – frequencies – and even gives us a way to measure probabilities, if we fudge the “infinite” part a bit. The probl... |
Catherine Therese J. Quiñones
The virial theorem is a general theorem relating the potential energy (V) and the kinetic energy (T) in a bound system. A simple physical example is a small object orbiting around another object bound by a force as in the case of a hydrogen atom. The average kinetic energy and potential en... |
Let $X_n(\Bbb{Z})$ be the simplicial complex whose vertex set is $\Bbb{Z}$ and such that the vertices $v_0,...,v_k$ span a $k$-simplex if and only if $|v_i-v_j| \le n$ for every $i,j$. Prove that $X_n(\Bbb{Z})$ is $n$-dimensional...
no kidding, my maths is foundations (basic logic but not pedantic), calc 1 which I'm pr... |
A solution is defined as a homogeneous mixture of two or more components existing in a single phase. In this description, the focus will be on liquid solutions because within the realm of biology and chemistry, liquid solutions play an important role in multiple processes. Without the existence of solutions, a cell wou... |
Creating Symbolic Links
The function
CreateSymbolicLink allows you to create symbolic links using either an absolute or relative path.
Symbolic links can either be absolute or relative links. Absolute links are links that specify each portion of the path name; relative links are determined relative to where relative–li... |
This post is quite
smaller than previous ones as it just states the optimization techniques required to train a neural network. I thought of including a example but many resources are available free online and therefore it is not necessary to reinvent the wheel. So coming straight to the point, Optimization techniques ... |
The
moment magnitude scale was introduced in 1979 by Thomas C. Hanks and Hiroo Kanamori as a successor to the Richter scale and is used by seismologists to compare the energy released by earthquakes. [1] The moment magnitude $ M_\mathrm{w} $ is a dimensionless number defined by $ M_\mathrm{w} = {2 \over 3}\left(\log_{1... |
Berry-Esseen's Central Limit Theorem for Non-causal Linear Processes in Hilbert Space
Berry-Esseen's Central Limit Theorem for Non-causal Linear Processes in Hilbert Space
Abstract
Let $H$ be a real separable Hilbert space and $(a_k)_{k\in\mathbb{Z}}$ a sequence of bounded linear operators from $H$ to $H$. We consider ... |
Current browse context:
math.PR
Change to browse by: References & Citations Bookmark(what is this?) Mathematics > Probability Title: Projections of planar Mandelbrot measures
(Submitted on 30 May 2016)
Abstract: Let $\mu$ be a planar Mandelbrot measure and $\pi_*\mu$ its orthogonal projection on one of the main axes. W... |
Nowadays we can associate to a topological space $X$ a category called the fundamental (or Poincare) $\infty$-groupoid given by taking $Sing(X)$.
There are many different categories that one can associate to a space $X$. For example, one could build the small category whose object set is the set of points with only the... |
With \(U\), \(A\), \(H\) and \(G\) in hand we have potentials as a functions of whichever variable pair we want: \(S\) and \(V\), to \(T\) and \(P\). Additional Legendre transforms will provide us with further potentials in case we have other variables (such as surface area \(A\), length \(L\), magnetic moment \(M\), e... |
Update, trying to explain this in a better way:
I mean how to find the result without a calculator.
Base 2 Log 16 = 4: simple to figure out: 2 . 2 . 2 . 2
what about
Base 2 Log 18 = ??
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It ... |
It’s been a while, so let’s include a recap : a (transitive) permutation representation of the modular group $\Gamma = PSL_2(\mathbb{Z}) $ is determined by the conjugacy class of a cofinite subgroup $\Lambda \subset \Gamma $, or equivalently, to a dessin d’enfant. We have introduced a
quiver (aka an oriented graph) whi... |
This vignette illustrates the basic functionality of the
package by simulating a few stochastic processes and estimating their parameters from regularly spaced data. SuperGauss
A one-dimensional fractional Brownian motion (fBM) \(X_t = X(t)\) is a continuous Gaussian process with \(E[X_t] = 0\) and \(\mathrm{cov}(X_t, ... |
The Monster is the largest of the 26 sporadic simple groups and has order
808 017 424 794 512 875 886 459 904 961 710 757 005 754 368 000 000 000
= 2^46 3^20 5^9 7^6 11^2 13^3 17 19 23 29 31 41 47 59 71.
It is not so much the size of its order that makes it hard to do actual calculations in the monster, but rather the ... |
I am reading a book and I'm trying to understand the concept of quasi Fermi levels.
For example,
A steady state of Electron Hole pairs are created at the rate of $10^{13}$ cm$^{-3}$$10^{13}\ \mathrm{cm}^{-3}$ per $\mu s$$\mu$s in a sample of Siliconsilicon.
The equilibrium concentration of electrons in the sample is $n... |
The angle between two radii of a circle is known as the central angle of the circle. The two points of the circle, where the radii intersects in the circle (Note – The other end of the radii meets at the center of the circle), forms a segment of the Circle called the Arc Length.
Formula to Find the Central Angle of a C... |
№ 9
All Issues Romanyuk A. S. Estimates of some approximating characteristics of the classes of periodic functions of one and many variables
Ukr. Mat. Zh. - 2019. - 71, № 8. - pp. 1102-1115
UDC 517.5
We obtain the exact-order estimates for some approximating characteristics of the classes $\mathbb{W}^{\boldsymbol{r}}_{... |
It’s been a while, so let’s include a recap : a (transitive) permutation representation of the modular group $\Gamma = PSL_2(\mathbb{Z}) $ is determined by the conjugacy class of a cofinite subgroup $\Lambda \subset \Gamma $, or equivalently, to a dessin d’enfant. We have introduced a
quiver (aka an oriented graph) whi... |
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Now showing items 1-1 of 1
Production of charged pions, kaons and protons at large transverse momenta in pp and Pb-Pb collisions at $\sqrt{s_{NN}}$ = 2.76 TeV
(Elsevier, 2014-09)
Transverse momentum spectra of $\pi^{\pm}, K^{\pm}$ and $p(\bar{p})$ up to $p_T$ = 20 GeV/c at mid-rapidity, |y| $\le$ 0.8, in pp and ... |
The usual argument to show that the group of all orientation-preserving symmetries of the Klein quartic is the simple group $L_2(7)$ of order $168$ goes like this:
There are two families of $7$ truncated cubes on the Klein quartic. The triangles of one of the seven truncated cubes in the first family have as center the... |
Consider two systems (1 and 2) in thermal contact such that
\(N_2\) \(\gg\) \(N_1\) \(E_2\) \(\gg E_1\) \(N\) \(N_1 + N_2; E = E_1 + E_2 \) \(\text {dim} (x_1)\) \(\gg\) \(\text {dim} (x_2) \) and the total Hamiltonian is just \(H (x) = H_1 (x_1) + H_2 (x_2) \)
Since system 2 is infinitely large compared to system 1, i... |
I am reading this paper entitled "Quantum algorithm for linear systems of equations" and am trying to understand a portion of the algorithm described on page 2 and in more detail in the appendix starting at the bottom of page 10 (section 3. Phase Estimation calculations).
Suppose we have a hermitian matrix $A$ of dimen... |
Exploring Vecten's Wreaths with Linear Algebra Introduction
What follows is Long Huynh Huu's development of a result by Hirotaka Ebisui and Thanos Kalogerakis, reported elsewhere earlier.
The problem deals with an extension of Vecten's construction of squares on the sides of a triangle and then adding another layer of ... |
I thought I was done writing about this topic, but it just keeps coming back. The internet just cannot seem to leave this sort of problem alone:
I don't know what it is about expressions of the form \(a\div b(c+d)\) that fascinates us as a species, but fascinate it does. I've written about this before (as well as why "... |
In many cases, the symmetry of a molecule provides a great deal of information about its quantum states, even without a detailed solution of the Schrödinger equation. A geometrical transformation which turns a molecule into an indistinguishable copy of itself is called a
symmetry operation. A symmetry operation can con... |
I am trying to prove the following Lemma, which seems intuitive, but I still have doubts:
Lemma
Given a Brownian motion $\{W_t,\mathcal F_t:0\le t \le1\}$, two bounded processes, $\mu$ and $\sigma$, with $\sigma$ continuous and $\sigma_0\neq 0$, such that the integral
$$ X_t=\int_0^t \sigma_t dW_t + \int_0^t \mu_t dt$$... |
When a manufacturer lists a chemical as ACS Reagent Grade, they must demonstrate that it conforms to specifications set by the American Chemical Society (ACS). For example, the ACS specifications for NaBr require that the concentration of iron be ≤5 ppm. To verify that a production lot meets this standard, the manufact... |
In part V we saw how a statement Alice would like to prove to Bob can be converted into an equivalent form in the “language of polynomials” called a Quadratic Arithmetic Program (QAP).
In this part, we show how Alice can send a very short proof to Bob showing she has a satisfying assignment to a QAP. We will use the Pi... |
Jogesh C Pati
Articles written in Pramana – Journal of Physics
Volume 60 Issue 2 February 2003 pp 291-336
It is noted that a set of facts points to the relevance in four dimensions of conventional supersymmetric unification based on minimally a string-unified
2( τ), suggested by SuperK), (v) the intricate pattern of th... |
1. Introduction
Percentages is applied in several chapters in math (including Profit & Loss, Interest & Growth, Ratio & Proportion). Quite a few Data Interpretation questions include percentage in some form.
%
is the symbol used to denote percentage. For instance, $40$ percent is written as 40%.
The value of this symbo... |
Difference between revisions of "Learn more about it"
Line 246: Line 246:
* Internally WIKI converts the spaces between words into underscores.
* Internally WIKI converts the spaces between words into underscores.
*First letter of target is automatically capitalized.
*First letter of target is automatically capitalized... |
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Now showing items 1-1 of 1
Production of charged pions, kaons and protons at large transverse momenta in pp and Pb-Pb collisions at $\sqrt{s_{NN}}$ = 2.76 TeV
(Elsevier, 2014-09)
Transverse momentum spectra of $\pi^{\pm}, K^{\pm}$ and $p(\bar{p})$ up to $p_T$ = 20 GeV/c at mid-rapidity, |y| $\le$ 0.8, in pp and ... |
Let $X_n(\Bbb{Z})$ be the simplicial complex whose vertex set is $\Bbb{Z}$ and such that the vertices $v_0,...,v_k$ span a $k$-simplex if and only if $|v_i-v_j| \le n$ for every $i,j$. Prove that $X_n(\Bbb{Z})$ is $n$-dimensional...
no kidding, my maths is foundations (basic logic but not pedantic), calc 1 which I'm pr... |
Let $X_n(\Bbb{Z})$ be the simplicial complex whose vertex set is $\Bbb{Z}$ and such that the vertices $v_0,...,v_k$ span a $k$-simplex if and only if $|v_i-v_j| \le n$ for every $i,j$. Prove that $X_n(\Bbb{Z})$ is $n$-dimensional...
no kidding, my maths is foundations (basic logic but not pedantic), calc 1 which I'm pr... |
Difference between revisions of "Robot Dynamics and Control"
(→Chapter Summary)
Line 89: Line 89:
tracked without solving the inverse kinematics problem. Stability of
tracked without solving the inverse kinematics problem. Stability of
these controllers can be verified using Lyapunov stability.
these controllers can be... |
I would like to do the integral
$$I=\int_0^{2\pi}d\phi\frac{\ln(e^{i\phi}+e^{-i\phi}-\frac{5}{2})}{e^{i\phi}+e^{-i\phi}-\frac{5}{2}}.$$
Numerically, we readily find that it has a specific finite value:
fun = -(5/2) + E^(-I \[Phi]) + E^(I \[Phi]);NIntegrate[ Log[fun]/fun, {\[Phi], 0, 2 \[Pi]}]
-0.493368 - 13.1595 I
Now,... |
Part 3 in the quest for the hydrogen molecule
Last time we talked about how the position and velocity of a particle are not independent properties. In fact, they are totally dependent! Unfortunately this is sometimes explained as that they can not be independently ‘measured’ or that there is ‘uncertainty’. That is abso... |
In physics, a
wave vector (also spelled wavevector) is a vector which helps describe a wave. Like any vector, it has a magnitude and direction, both of which are important: Its magnitude is either the wavenumber or angular wavenumber of the wave (inversely proportional to the wavelength), and its direction is ordinaril... |
Show that for each prime number $p$ different from $2$ and $5$, there exist some number $1111\cdots 1111$ all made by ones that is a multiple of $p$
For instance, $3$ divides $111$ and $7$ divides $111111$
Consider the number $\dfrac{1}{p}$. Since $p$ is not $2$ or $5$, its decimal representation is a pure periodic dec... |
The typical characterization of points constructible by compass and straightedge is the following:
Let $S\subseteq\mathbb{C}$ with $0,1\in S$, $K_0 = \mathbb{Q}(S\cup \bar{S})$ and $a\in\mathbb{C}$. Then $a$ is constructible from $S$ by compass and straightedge if and only if there is a tower of quadratic field extensi... |
Could you please help me to solve this?
http://i.imgur.com/o5CLFI7.jpg
Could you please help me to solve these inequations..? I have many more and won't be able to solve them all :eek::eek:.. I need help.
If there are specific questions you have regarding specific problems we can possibly help.
We don't do your homewor... |
The
Isomorphism Conjecture of Berman and Hartmanis states that all $NP$-complete sets are polynomial time isomorphic to each other. This means that $NP$-complete problems are efficiently reducible to each other via polynomial time computable and invertible bijections. The conjecture implies $P\neq NP$.
The isomorphism ... |
Definition:Real Interval/Notation Contents Definition
An arbitrary interval is frequently denoted $\mathbb I$, although some sources use just $I$. Others use $\mathbf I$.
\(\displaystyle \openint a b\) \(:=\) \(\displaystyle \set {x \in \R: a < x < b}\) Open Real Interval \(\displaystyle \hointr a b\) \(:=\) \(\display... |
A simple way to understand an ionization constant is to think of it in a clear-cut way: To what degree will a substance produce ions in water? In other words, to what extent will ions be formed?
Introduction
Water has a very low concentration of ions that are detectable. Water undergoes self-ionization, where two water... |
From the last lecture, we saw that Liouville's equation could be cast in the form
\[ \frac {\partial f}{\partial t} + \nabla _x \cdot \dot {x} f = 0 \]
The Liouville equation is the foundation on which statistical mechanics rests. It will now be cast in a form that will be suggestive of a more general structure that ha... |
A
vector-valued function, also referred to as a vector function, is a mathematical function of one or more variables whose range is a set of multidimensional vectors or infinite-dimensional vectors. The input of a vector-valued function could be a scalar or a vector. The dimension of the domain is not defined by the di... |
I'm looking at Example VII.3.3.3 (p.193, 2nd ed.) of Silverman's
The Arithmetic of Elliptic Curves. We have the elliptic curve $E:y^2=x^3+x$, with discriminant $\Delta=-64$, so there is good reduction for all primes $p\geq 3$. It is noted that $(0,0)$ is a point of order two in $E(\mathbb{Q})$, and that $$\tilde{E}(\ma... |
Definition:Ultrafilter on Set Contents Definition
Let $S$ be a set.
Let $\mathcal F \subseteq \powerset S$ be a filter on $S$.
Then $\mathcal F$ is an ultrafilter (on $S$) if and only if:
or equivalently, if and only if:
whenever $\mathcal G$ is a filter on $S$ and $\mathcal F \subseteq \mathcal G$ holds, then $\mathca... |
Let $X_n(\Bbb{Z})$ be the simplicial complex whose vertex set is $\Bbb{Z}$ and such that the vertices $v_0,...,v_k$ span a $k$-simplex if and only if $|v_i-v_j| \le n$ for every $i,j$. Prove that $X_n(\Bbb{Z})$ is $n$-dimensional...
no kidding, my maths is foundations (basic logic but not pedantic), calc 1 which I'm pr... |
The universal-NOT gate in quantum computing is an operation which maps every point on the Bloch sphere to its antipodal point (see Buzek et al, Phys. Rev. A 60, R2626–R2629). In general, a single qubit quantum state, $|\phi\rangle = \alpha |0\rangle + \beta | 1 \rangle$ will be mapped to $\beta^* |0\rangle - \alpha^*| ... |
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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-... |
Conway’s orbifold notation gives a uniform notation for all discrete groups of isometries of the sphere, the Euclidian plane as well as the hyperbolic plane.
This includes the groups of symmetries of Escher’s Circle Limit drawings. Here’s Circle Limit III
And ‘Angels and Devils’ aka Circle Limit IV:
If one crawls along... |
When considering a bilattice you need to distinguish two type of sites.
A B A B
-------o-------o---------------o-------o----
|<--a-->|<------b------>|
For instance you can denote the two kind of sites with letters $A$ and $B$ as it is shown above. Then you have now two different creation and destruction operators . $c_... |
The problem is: $\sum_{n=1}^{\infty} \frac{1}{n(n+3)}$
The first thing I did was use the divergence test which didn't help since the result of the limit was 0.
If I multiply it through, the result is $\sum_{n=1}^{\infty} \frac{1}{n^2+3n}$
I'm wondering if I can consider this as a p-series and simply use the largest pow... |
This is a bit of fun geometry that doesn’t have much to do with what’s going on in class, but does reflect on mathematical thinking.
An article promoting the use of technology in the classroom began: “Draw a perfect circle. Now bisect that with a 45-degree angle, the perfect slice of geometric pizza. Now, using your dr... |
Covariance
Covariance measures the extent to which two variables, say x and y, move together. A positive covariance means that the variables move in tandem and a negative value indicates that the variables have an inverse relationship. While covariance can indicate the direction of relation, the correlation coefficient... |
Construct sequence of continuous functions $f_n:[0,1] \to \mathbb{R} $ such that $\displaystyle \lim _{n \to \infty} f_n(x)=0$ implies that $\displaystyle \lim_{n \to \infty} \int _0 ^ 1 f_n(x) dx = +\infty$
$$f_n(x) = \begin{cases} 6n^3x(1-nx), & 0\le x\le \frac 1n \\ 0, & \frac 1n<x\le 1 \end{cases}$$
If you dislike ... |
Event detail Probabilistic Operator Algebra Seminar: An Elementary Approach to Free Gibbs States with Convex Potentials
Seminar | January 28 | 2-4 p.m. | 736 Evans Hall
David Andrew Jekel, UCLA
We present an alternative approach to the theory of free Gibbs states with convex potentials. Instead of solving SDE's, we com... |
The Fibonacci sequence is defined to be $u_1=1$, $u_2=1$, and $u_n=u_{n-1}+u_{n-2}$ for $n\ge 3$. Note that $u_2=1$ is a definition, and we may have just as well set $u_2=\pi$ or any other number. Since $u_2$ shares no relation to $u_1$ (without considering any other $u_k$), we can't use induction to go from the case $... |
I recently read the article Nonce-Based Symmetric Encryption by Rogaway, where he presents two different notions of indistinguishability, which he calls
ind$ and ind, respectively. Here's the definitions of these to notions:
First, let $A^g$ be an algorithm with access to an oracle $g$, and let $\Pi = (\mathcal{E},\mat... |
The risk of collision is only theoretical; it will not happen in practice. Time spent worrying about such a risk of collision is time wasted. Consider that even if you have $2^{90}$ 1MB blocks (that's a billion of billions of billions of blocks -- stored on 1TB hard disks, the disks would make a pile as large of the US... |
User:Dfeuer/Open Set may not be Open Ball
[{WIP|not there yet}}
Theorem Proof
Let $x, y, z \in A$ be $3$ distinct points in $M$ such that
$d \left({x, y}\right) \le d \left({y,z}\right)$ $d \left({x, z}\right) \le d \left({y,z}\right)$
Let $r = \dfrac {\min\left\{{d \left({x,y}\right), d \left({x,z}\right)\right\}} \mi... |
ä is in the extended latin block and n is in the basic latin block so there is a transition there, but you would have hoped \setTransitionsForLatin would have not inserted any code at that point as both those blocks are listed as part of the latin block, but apparently not.... — David Carlisle12 secs ago
@egreg you are... |
Computing Variational Derivatives
Allow me to start with a definition. Given a function $u = u(x)$, a function $L$ of $x, u$, and all derivatives of $u$; and
$I = \int L(x,u,u_x u_{xx}, \ldots)dx$
the
variational derivative of $I$ is defined as
$\frac{\delta I}{\delta u} := \frac{\partial L}{\partial u} - \frac{d}{dx} ... |
Analytic results for the linear stability of the equilibrium point in Robe's restricted elliptic three-body problem
1.
Department of Mathematics, Zhejiang University, Hangzhou 310027, Zhejiang, China
2.
School of Mathematics and Statistics, Northeastern University at Qinhuangdao, Qinhuangdao 066004, Hebei, China
We stu... |
Markdown example Welcome to Markdown!
Hey! I’m your first Markdown document in
StackEdit 1. Don’t delete me, I’m very helpful! I can be recovered anyway in the Utils tab of the Settings dialog. Documents
StackEdit stores your documents in your browser, which means all your documents are automatically saved locally and ... |
The bonding of alkali cations to water, to EDTA, and to crown ethers is , at least based upon QTAIM analysis$^{[1]}$ of representative systems. strictly electrostatic in all three cases
For this analysis, I ran gas-phase quantum chemical optimizations on $[\ce{Li}(\text{12-crown-4})]^+$, $[\ce{Na}(\text{EDTA})]^{3-}$, ... |
Determinant with Rows Transposed Theorem Proof
Let $\mathbf A = \sqbrk a_n$ be a square matrix of order $n$.
Let $\map det {\mathbf A}$ be the determinant of $\mathbf A$.
Let $1 \le r < s \le n$.
From Parity of K-Cycle, $\map \sgn \rho = -1$.
Let $\mathbf A' = \sqbrk {a'}_n$ be $\mathbf A$ with rows $r$ and $s$ transpo... |
First note that your formula can be interpreted as the nth term of a sequence:
$$\{n(2n+1)(2n-1)/3\}=1,10,35,84,165,...$$
You claim that your nth term formula gives the summation (more properly, the partial sums) of all squares of odd numbers, up to $n$. This implies that term $n=3$, for example, is the sum of the firs... |
I need some sharped and advanced advices for the following issue ...
Model and its assumptions
I'm working on the methodology of a two-way error component model. Here is the model: $y_{jis} = x_{jis} \beta + \upsilon_{jis}$. $j$ refers to school, $i$ refers to individual and $s$ to tested area/topic (mathematics or eng... |
This answer describes a realistic problem where a natural consistent estimator is dominated (outperformed for all possible parameter values for all sample sizes) by an inconsistent estimator. It is motivated by the idea that consistency is best suited for quadratic losses, so using a loss departing strongly from that (... |
Bifurcation and multiplicity results for a class of $n\times n$ $p$-Laplacian system
1.
Department of Mathematics, Indian Institute of Technology Madras, Chennai-600036, India
2.
Department of Mathematics and Statistics, University of North Carolina at Greensboro, Greensboro, NC 27412, USA
3.
Department of Mathematics,... |
Why Yitang Zhang's proof is probably far less fundamental than the claim
Yitang Zhang worked at Subway before he would land a mathematics job. And when he did, he wasn't publishing almost anything for years before he would offer a proof of something rather important weeks ago. That turned the name of the popular math i... |
Hint $\ $ By $ $ Vieta, $\,\ x^2 -\frac{10}3 x - 67\, =\, (x-a)(x-b)\iff \ \color{#0a0}{a+b} = 10/3,\ \color{#c00}{ab} = -67$
$(a-b)^2$ is
symmetric in $\,a,b\,$ so by FTSP it can be written as a polynomial in $\,\color{#0a0}{a+b},\ \color{#c00}{ab}$
Indeed, applying Gauss's Algorithm we find that $\, (a-b)^2 = (\color... |
I am faced with the following problem:
Given $C = \{B,C,D,F\}$ and $V = \{A, E, I, O, U\}$ find the number of 9-letter words with elements from $C$ and $V$ such that no two vowels (elements of V) are adjacent.
Following this answer about a very similar question I get that I should express the problem as a double recurr... |
A $\sigma$-algebra is an algebraic structure (specifically, a Boolean algebra with a countably infinite operation of countable supremum (satisfying the axiom that it's the supremum of its arguments)),
together with a representation of its elements as sets, making the operations the real set operations.
When forming the... |
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 $\omega_1$... |
SONIC FORMS Brand new Dynamic Synthesis album is here: Sonic environments for public and private spaces Roland Kuit - KYMA
Dynamic synthesis is used to create information streams.
Lissajous orbits on van der Pol oscillator.
A system of parametric equations: {\displaystyle x=A\sin(at+\delta ),\quad y=B\sin(bt),} x=A\sin... |
→ → → → Browse Dissertations and Theses - Mathematics by Title
Now showing items 469-488 of 1147
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(2001)The approach to the ideal membership problem for Z [X] followed here is based on some properties (such as Weierstrass Division) of the ring Z p〈X〉 of restricted power series with coefficients ... |
How do you find the square root of an irrational numbers? Irrational numbers arise in many circumstances in mathematics. Examples include the following: The hypotenuse of a right triangle with base sides of length 1 has length \( \sqrt{2}\), which is irrational.... The difference between rational and irrational numbers... |
Monopoly Power
Monopoly power (also called market power) refers to a firm’s ability to charge a price higher than its marginal cost. Monopoly power typically exists where the there is low elasticity of demand and significant barriers to entry.
Why is it that a firm in perfect competition is a price-taker while a monopo... |
I never know what is meant by Chevalley's theorem, everyone has its own version. The version I know is
EGA IV 1 théorème 1.8.4 (that I will call main theorem) : if the morphism of schmes $f : X \to Y$ is locally of finite presentation then for if $Z$ is a locally constructible subset of $Y$, the subset $f(Z)$ is locall... |
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Now showing items 1-9 of 9
Production of $K*(892)^0$ and $\phi$(1020) in pp collisions at $\sqrt{s}$ =7 TeV
(Springer, 2012-10)
The production of K*(892)$^0$ and $\phi$(1020) in pp collisions at $\sqrt{s}$=7 TeV was measured by the ALICE experiment at the LHC. The yields and the transverse momentum spectra $d^2 ... |
Yesterday, I came across an interesting post by Allison at Infinigons. She reminds us that we must remain fearless in the face of difficult problems, and attempt to do
something, rather than give problems a cursory once-over, then run to Google. It is worth reading her post for the details.
The example she gives is a f... |
Can somebody explain in a simple way why, talking about representations $$3\otimes3\otimes3=1\oplus8\oplus8\oplus10~?$$
Here $3$ and $\bar{3}$ are the fundamental and anti-fundamental of $SU(3)$, in this case.
Physics Stack Exchange is a question and answer site for active researchers, academics and students of physics... |
If $\omega=\frac{\sqrt{2}}{2}+i \frac{\sqrt{2}}{2}$, then $\omega$ is an 8th root of unity. And I know $\omega,\omega^3,\omega^5$,and $\omega^7$ are furthermore primitive 8th roots of unity in $\mathbb{C}$. But what happens when we change $\mathbb{C}$ to $\mathbb{Z}/17\mathbb{Z}$ (integers mod 17)? How can I find the p... |
A trick that is standard in my little world is this: the matrix$$M = \left(\begin{array}{rr}-2 & -4 \\4 & 6\end{array}\right)$$has trace $4$ and determinant $4.$ The characteristic roots satisfy $\lambda^2 - 4 \lambda + 4 = 0.$ The Cayley-Hamilton Theorem (if this is not familiar, see the ADDENDUM) says that$$ a_{n+2} ... |
This is not homework. Problem 3-38 reads:
Let $A_{n}$ be a closed set contained in $(n,n+1)$. Suppose that $f:\mathbb{R}\rightarrow \mathbb{R}$ satisfies $\int_{A_{n}}f=(-1)^{n}/n$ and $f(x)=0$ for $x\notin$ any $A_{n}$. Find two partitions of unity $\Phi$ and $\Psi$ such that $\sum_{\phi\in\Phi}\int_{\mathbb{R}}\phi\c... |
I am reading the following paper: https://arxiv.org/pdf/math/0211450.pdf (p.10).
My question is the part with red line. Why taking square of $n_i$?
I read the following article: Inequivalent representations of a finite group, which says $$\deg \chi=\sum_{i=1}^k n_i\deg\chi_i$$ where $\chi_i$ is the character of the rep... |
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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... |
Composition series composition series
A composition sequence is a finite subset $\{a_0,\ldots,a_n\}$ of a partially ordered set with least element $0$ and greatest element $1$ such that\[0 = a_0 < a_1 < \cdots < a_n = 1\]and all the intervals $[a_i,a_{i+1}]$ are simple (elementary) (cf. Elementary interval). One can al... |
Difference between revisions of "Talk:Absolute continuity"
From Encyclopedia of Mathematics
(Created page with "I moved some portions of the old article in Signed measure. I have not had the time to add all Mathscinet and Zentralblatt references. ~~~~")
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I moved some portions of the old article in [[Sign... |
Equivalence of Well-Ordering Principle and Induction/Proof/WOP implies PFI Theorem That is:
implies:
Principle of Finite Induction: Given a subset $S \subseteq \N$ of the natural numbers which has these properties: $0 \in S$ $n \in S \implies n + 1 \in S$ then $S = \N$. Proof
To save space, we will refer to:
We assume ... |
This question already has an answer here:
Real Analysis Prove that 2/π ≤(sinx)/x ≤ 1 for all |x|≤ π/2 ? Just need the 2/π greater than part.
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Refine Year of publication 1998 (21) (remove) Document Type Article (21) (remove) Keywords
We prove that there exists a positive \(\alpha\) such thatfor any integer \(\mbox{$d\ge 3$}\) and any topological types \(\mbox{$S_1,\dots,S_n$}\) of plane curve singularities, satisfying \(\mbox{$\mu(S_1)+\dots+\mu(S_n)\le\alpha... |
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