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Ms Alexandra Kiňová (23) is expecting the first Czechia's naturally born quintuplets (a package of 5 babies) on Sunday morning (tomorrow; update: they're out fine) which would mean that we match the achievement of the most fertile U.S. state – Utah – from the last week. Cool anniversary:In late January, we celebrated t... |
Quick Overview The Greatest Integer Function is also known as the Floor Function. It is written as $$f(x) = \lfloor x \rfloor$$. The value of $$\lfloor x \rfloor$$ is the largest integer that is less thanor equal to$$x$$. Definition
The Greatest Integer Function is defined as
$$\lfloor x \rfloor = \mbox{the largest int... |
Let $G$ be a finite group. For a prime number $p$, let us call $G$ an elementary $p$-group iff $\exp G=p$. I know that all elementary $2$-groups are abelian, and I also know the construction of non-abelian elementary $p$-groups of order $p^3$ for every odd prime number $p$. My question is that, can we list all the elem... |
I have an issue with an extremely elementary problem.
Consider the differential equation $y' + \cot(x) y = 1$. Obviously, one can use an integrating factor of $e^{\int \cot(x) dx} = e^{\ln(\sin(x)) } $ (the arbitrary constant would cancel out) $= \sin(x)$ to solve the differential equation, obtaining the correct answer... |
I am trying to find an easy way to compute the limit as $x \to 0$ of
$$f(x) = \frac{\sqrt{1+\tan(x)} - \sqrt{1+\sin(x)}}{x^3}$$
from first principles (i.e. without using l'Hôspital's rule).
I have gone as far as boiling down the problem to computing the limit as $x \to 0$ of
$$\frac{1 - \cos(x)}{x^2}$$
I thought about ... |
$\dfrac{\sin{A}+\cos{A}}{\sin{A}-\cos{A}} = \dfrac{5}{3}$ is the given trigonometric equation and we have to find the value of trigonometric expression $\dfrac{7\tan{A}+2}{2\tan{A}+7}$. The trigonometric expression is in terms of $\tan{A}$ but we don’t know its value. So, it’s essential to find the value of $\tan{A}$ f... |
The following LaTeX code looks pretty straightforward to me:
\begin{eqnarray*}& \lambda_l \mathbf{l}\cdot\mathbf{r} & = & \lambda_r \mathbf{l}\cdot\mathbf{r} \nonumber \\\therefore & \mathbf{l}\cdot\mathbf{r} & = & 0 \nonumber\end{eqnarray*}
but it results in the error:
! Missing $ inserted.<inserted text> $l.78 ..._l ... |
Firstly, some definitions;
Pre-image resistant: given a hash value $h$ find a message $m$ such that $h=Hash(m)$. Consider storing the hashes of passwords on the server. Eg. an attacker will try to find a valid password to your account. Second Pre-image resistant: given a message $m_1$ is should be computationally infea... |
Assume you want to find the derivative respect to X ($p \times p$) matrix of $$ \frac{\partial}{\partial X} || X - A ||_1 $$
where A is ($p \times p$) matrix.
How can I do it?
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It only take... |
The third hep-th paper in today's listings is very interesting.
OK, more seriously, they study matrix models which are clearly relevant for full-blown definitions of quantum gravity. Lots of descriptions of vacua (or superselection sectors) of quantum gravity are given by \(U(N)\) or \(SU(N)\) gauge theories in various... |
Permanent of an $m \times n$-matrix $A = \left\Vert a_{ij} \right\Vert$
The function $$ \mathrm{per}(A) = \sum_\sigma a_{1\sigma(1)}\cdots a_{m\sigma(m)} $$
where $a_{ij}$ are elements from a commutative ring and summation is over all one-to-one mappings $\sigma$ from $\{1,\ldots,m\}$ into $\{1,\ldots,n\}$. If $m=n$, t... |
Convergent Sequence is Cauchy Sequence/Normed Division Ring/Proof 1 Theorem
Let $\struct {R, \norm {\,\cdot\,}} $ be a normed division ring.
Proof
Let $\epsilon > 0$.
Then also $\dfrac \epsilon 2 > 0$.
Because $\sequence {x_n}$ converges to $l$, we have:
$\exists N: \forall n > N: \norm {x_n - l} < \dfrac \epsilon 2$
S... |
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1. Observation of a peaking structure in the J/psi phi mass spectrum from B-+/- -> J/psi phi K-+/- decays
PHYSICS LETTERS B, ISSN 0370-2693, 06/2014, Volume 734, Issue 37... |
Lord Soth
Knight of the Black Rose, image by http://jprart.deviantart.com/
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Last seen Sep 11 '14 at 21:30 Communities (9) Top network posts 58 Intuitive proofs that $\lim\limits_{n\to\infty}\left(1+\frac xn\right)^n=e^x$ 41 Is there a... |
Given: $P(x)=x^4 -4(m+2)x^2 + m^2$ has 4 real roots.
Show: the sum of the possible least 3 integer values of $m$ is zero.
This is a question asked in an entrance exam (Colégio Naval 92).
My attempt: Let $x^2=y$ to get $Q(y)=y^2 -4(m+2)y + m^2=$ and find conditions on $m$ for real roots for $Q(y)$. The discriminant woul... |
Absolutely continuous measures
A concept in measure theory (see also Absolute continuity). If $\mu$ and $\nu$ are two measures on a σ-algebra $\mathcal{B}$ of subsets of $X$, we say that $\nu$ is absolutely continuous with respect to $\mu$ if $\nu (A) =0$ for any $A\in\mathcal{B}$ such that $\mu (A) =0$. The absolute c... |
I have the following categorical data
Control Treatmentc1 285441 33296c2 40637 4187c3 737113 97433c4 34036 3993
In other words, I have 2 multinomial distributions with 4 categories each. In effect, I would like to test to determine whether or not the treatment changes the distribution of category mix (c1,c2,c3,c4).
A q... |
In signal processing, cross-correlation is a measure of similarity of two waveforms as a function of a time-lag applied to one of them. This is also known as a sliding dot product or sliding inner-product. It is commonly used for searching a long signal for a shorter, known feature. It has applications in pattern recog... |
Difference between revisions of "Absolute continuity"
m (added missing space to "vice versa", fixed upper limit in integral)
m (Lebesgue measure changed from calligraphic L to lambda, minor spacinx fixes)
Line 7: Line 7:
====Absolute continuity of the Lebesgue integral====
====Absolute continuity of the Lebesgue integr... |
Cristian Rivera
Articles written in Pramana – Journal of Physics
Volume 73 Issue 6 December 2009 pp 961-968
We propose to substitute Newton’s constant $G_{N}$ for another constant $G_{2}$, as if the gravitational force would fall off with the $1/r$ law, instead of the $1/r^{2}$; so we describe a system of natural units... |
This question already has an answer here:
Let $(X,\tau)$ be a topological space. Consider $X^2$ with the product topology. Show that $X$ is Hausdorff iff the diagonal $D = \{(x,y) \in X^2 \mid x=y\}$ is a closed subset of $X^2$.
Mathematics Stack Exchange is a question and answer site for people studying math at any le... |
The question was asked by xport in the comments to Mike's solution as to whether this solution is unique.
There are no doubt many ways to case bash an answer to this, and here is one, proving thatMike's solution is indeed unique.
Let $x_i$ be the number of times the digit $ i $ appears on the paper, then we must have
$... |
A topological space $X$ is said to be
star compact if whenever $\mathscr{U}$ is an open cover of $X$, there is a compact subspace $K$ of $X$ such that $X = \mathrm{st}(K,\mathscr{U}),$ where$\mathrm{st}(K, \mathscr{U})= \bigcup \{ U \in \mathscr{U}: U \cap K \neq \emptyset \}.$
We recursively define $\mathrm{st}^n$ for... |
I outlined a proof by Bjorn Poonen at http://www.artofproblemsolving.com/Forum/viewtopic.php?p=2450856#p2450856 . As Nils Matthes has noticed, computing the kernel is not necessary to solve Hartshorne's problem, though (in my opinion) it is more interesting than the problem itself.
$\newcommand{\kk}{\mathbb{k}}$$\newco... |
Brachistochrone is Cycloid/Proof 2 Theorem Proof $v = \dfrac {\d s} {\d t}$
where $\d s$ is an infinitesimal arc length element.
$\d s = \sqrt{1 + y'^2} \rd x$
Hence:
$v = \sqrt {1 + y'^2} \dfrac {\d x} {\d t}$ $\dfrac {m v^2} 2 + m g y = E$
where $E$ is a constant of motion.
To determine $E$ use the following initial ... |
Marginal Product of Capital
Marginal product of capital (MPK) is the incremental increase in total production that results from one unit increase in capital while keeping all other inputs constant.
Identifying the marginal product of capital is important because firms take investment decisions by comparing their margin... |
Mathematics - Functional Analysis and Mathematics - Metric Geometry
Abstract
The following strengthening of the Elton-Odell theorem on the existence of a $(1+\epsilon)-$separated sequences in the unit sphere $S_X$ of an infinite dimensional Banach space $X$ is proved: There exists an infinite subset $S\subseteq S_X$ an... |
@egreg It does this "I just need to make use of the standard hyphenation function of LaTeX, except "behind the scenes", without actually typesetting anything." (if not typesetting includes typesetting in a hidden box) it doesn't address the use case that he said he wanted that for
@JosephWright ah yes, unlike the hyphe... |
Suppose we have a tower of field extensions:
$\overline{F} \subset K \subset E \subset F$
Is it true in general that $|G(K/F)| = |G(K/E)| \cdot |G(E/F)|$?
I was able to verify some specific examples, like $\mathbb{Q}(\sqrt[3]{2}, \omega)$ for $x^3-2$ and another extension, but how could I show that this holds in genera... |
Difference between revisions of "Lower attic"
From Cantor's Attic
Line 1: Line 1:
Welcome to the lower attic, where we store the comparatively smaller notions of infinity. Roughly speaking, this is the realm of countable ordinals and their friends.
Welcome to the lower attic, where we store the comparatively smaller no... |
Problem:
I need to find the leading order term in an expansion whose leading order behavior is a priori unknown. I can of course go with Series and try different orders, say
Series[f[x],{x,x0,n}] for different $n$, however I would like to find a more elegant way. Also each calculation takes very long (almost an hour) s... |
All topologies induced by a norm over finite dimensional spaces (of the same dimension) are equivalent to the standard topology on $\mathbb R^n$ so it is very much up to you how to choose your topology, noting that $\dim V^*=\dim V$.
If you'd like, a dual vector in $V^*$ can be identified with some vector $v=(v_1, \dot... |
Here’s an interesting little problem that came across my desk this afternoon: how much time is \(10!\) seconds? Is it a duration that is best measured in seconds? days? centuries? And, perhaps more importantly, what is the best way of figuring it out? Think about it for a minute, then check below the fold for the answe... |
Equivalence of Definitions of Local Basis/Local Basis for Open Sets Implies Neighborhood Basis of Open Sets Theorem
Let $T = \struct {S, \tau}$ be a topological space.
Let $x$ be an element of $S$.
$\forall U \in \tau: x \in U \implies \exists H \in \mathcal B: H \subseteq U$ Then $\mathcal B$ satisfies: every neighbor... |
NCERT Solutions for Class 11 Chemistry Chapter 6 Chemical Thermodynamics is provided here. This topic is an extremely important topic in chemistry and is important for class 11, Class 12 and competitive exams like JEE and NEET.
Students must have a good knowledge of the topic in order to excel in the examination. We at... |
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... |
For the following reaction: $$\ce{NiO2(s) + 4 H+(aq) + 2 Ag(s) -> Ni^2+(aq) + 2H2O(l) + 2Ag+(aq)}$$ $$ E^\circ = 2.48\ \mathrm V$$
Calculate the $\mathrm{pH}$ of the solution if $E = 2.23\ \mathrm V$ and $[\ce{Ag+}] = [\ce{Ni^2+}] = 0.023\ \mathrm{mol/l}$.
My effort:
So, I know that there is the Nerst equation: $$E=E^\... |
I know I can find the orbit radius of a satellite from the equation:
$$r=\sqrt[3]{\frac{T^2GM}{4 \pi^2}}$$
but what determines the orbit period $T$? If I assume a geosynchronous orbit, would that simply mean the orbit period is the same as how long the planet takes to turn?
What is a safe orbit radius / period of a sat... |
Tool for converting complex numbers into exponential notation form and vice versa by calculating the values of the module and the main argument of the complex number.
Complex Number Exponential Form - dCode
Tag(s) : Arithmetics, Geometry
dCode is free and its tools are a valuable help in games, maths, geocaching, puzzl... |
That alternate form, I think, makes things even more confusing than the standard form.
Since the matrix involved is circulant, the affine part of the AES S-box can be represented as $$b_o = b_i \oplus (b_i \lll 1) \oplus (b_i \lll 2) \oplus (b_i \lll 3) \oplus (b_i \lll 4) \oplus 99\,,$$where $\oplus$ is xor and $\lll$... |
An under-appreciated point occurred to me while preparing for my Coursera class and to comment on Daniel Greewald, Martin Lettau and Sydney Ludvigsson's nice paper "Origin of Stock Market Fluctuations" at the last NBER EFG meeting
The answer is, it depends the horizon and the measure. 100% of the variance of
price divi... |
1of 1
Prove that \(\displaystyle{D}\) is dense on \(\displaystyle{X}\) if, and only if, for each continuous function
\(\displaystyle{f:X\longrightarrow \mathbb{R}}\) holds :
\(\displaystyle{f(x)=0\,,\forall\,x\in D\implies f=\mathbb{O}}\) .
Now assume the converse. A different definition of density in a metric space is... |
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Measurement of electrons from beauty hadron decays in pp collisions at root √s=7 TeV
(Elsevier, 2013-04-10)
The production cross section of electrons from semileptonic decays of beauty hadrons was measured at mid-rapidity (|y| < 0.8) in the transverse momentum range 1 < pT <8 GeV/c w... |
While I agree completely with poncho's answer, this other viewpoint might be useful.Specifically, I think a better comparison isn't between $\mathbb{Z}_p^*$ and $\mathbb{R}^*$, but with $\mathbb{Z}_p^*$ and $S^1$. We can view $S^1 \cong \{z\in\mathbb{C} \mid |z| = 1\}$. It's not hard to show that any $z\in S^1$ is able... |
2019-09-12 16:43
Pending/LHCb Collaboration Pending LHCB-FIGURE-2019-008.- Geneva : CERN, 10 Detaljerad journal - Similar records 2019-09-10 11:06
Smog2 Velo tracking efficiency/LHCb Collaboration LHCb fixed-target programme is facing a major upgrade (Smog2) for Run3 data taking consisting in the installation of a conf... |
I found a limits equation
$$\lim_{n \to \infty}\left(1-\frac{\lambda}{n}\right)^n=e^{-\lambda}$$
How can I get the result of $e^{-\lambda}$?
Normally, we can use
$$\lim_{x \to \infty}\left(1+\frac{n}{x}\right)^x=e^n$$
And how can I get $e^n$?
Mathematics Stack Exchange is a question and answer site for people studying ... |
Tokyo Journal of Mathematics Tokyo J. Math. Volume 36, Number 1 (2013), 269-287. On the Fourth Moment of the Epstein Zeta Functions and the Related Divisor Problem Abstract
In this paper, we study the fourth moment of the Epstein zeta function $\zeta (s;Q)$ associated to a $n\times n$ positive definite symmetric matrix... |
Arens-Fort Space is not First-Countable Theorem
Let $T = \left({S, \tau}\right)$ be the Arens-Fort space.
Then $T$ is not a first-countable space. Proof
Assume that $T$ is first-countable.
Suppose there does not exist a point $\left({n_i, m_i}\right) \in U_i$ such that $n_i > i$ and $m_i > i$.
Then:
$\forall \left({n, ... |
Module Name¶
These pages are written using reStructuredTextthat allows
emphasis, strong,
literal and many more styles.
You can add a reference [A1], include equations like:
\[V(x) = \left(\frac{1-\eta}{\sigma\sqrt{2\pi}}\right) \cdot exp\left({\frac{x^2}{2\sigma^2}}\right) + \eta \cdot \frac{\sigma}{2\pi} \cdot \frac{1... |
SCIENTIFIC PROGRAMS AND ACTIVITIES September 23, 2019
A conference of junior researchers in the areas of PDE and Dynamical Systems. will be held April 28-29 at the Fields Institute , Toronto.The goal is to encourage scientific exchange, and to create an opportunity for mathematicians in an early stage of their career t... |
So, in general, how to choose the number of terms in Taylor (Maclaurin) series to evaluate the limit?
To answer your general question about how to approach problems like these, it's useful to know the concept of
equivalence of functions. Given two functions $f$ and $g$ defined and nonzero in a neighbourhood of $a$, we ... |
I am trying to write down a formal proof.
Attempt: Firstly, we settle on the notations and considerations:
$A$, $B$, $C$ are all $m\times n$ matrices where $m$ is fixed and $n$ is arbitrary over the ground field $F$.
$e_1^r(A): \text{ multiplication of the $r^{th}$ row of A by any $0\neq c \in F$}$
$e_2^r(A): \text{ $r... |
Start with a gauge theory with Chern-Simons action
$$ S[A] = \frac{k}{4 \pi} \text{Tr} \intop_{M} \left( A \wedge dA + \frac{2}{3} A \wedge A \wedge A \right) $$
and a Wilson loop observable in the fundamental representation for a knot $K$
$$ W_K[A] = \text{Tr} \, \vec{\exp} \intop_K A^a \cdot \frac{i {\sigma^a}}{2}. $... |
I know that the both the average and worst case complexity of binary search is O(log n) and I know how to prove the worst case complexity is O(log n) using recurrence relations. But how would I go about proving that the average case complexity of binary search is O(log n)?
I think most text book will provide you a good... |
Tool to compute continued fractions. A continued fraction is the representation of a number N in a form of a series of integers (a0, a1, ..., an) such as N = (a0+1/(a1+1/(a2+1/(...1/(an))).
Continued Fractions - dCode
Tag(s) : Series
dCode is free and its tools are a valuable help in games, maths, geocaching, puzzles a... |
There are two concepts you need to know.
What is equilibrium?
Not all reactions occur until one of the reactants is consumed completely. Some of them occur until a certain point, where the system doesn't continue to evolve; rather, the concentrations of all the species remain constant in what is called a chemical equil... |
You are probably thinking about undecidable languages which are computably enumerable. Otherwise, the diagonalization technique described in answers to similar questions would have provided simple counterexamples. If you don't care about the computably enumerable part, then I would say that your question is simply a du... |
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... |
Short Version
Can I get a quantile of such an expression? \begin{equation} \sum_{k=1}^{n} A_k\exp(\mathcal{N}(t_k\mu-\sigma\sqrt{t_k}/2,\sigma))) \end{equation}
I know I can do it for one part of the summation as stated here, however I would like to know if that can be also the case for the summation.
Long Version
Let'... |
Combination Theorem for Cauchy Sequences/Product Rule Theorem
Let $\struct {R, \norm {\,\cdot\,}}$ be a normed division ring.
Let $\sequence {x_n} $, $\sequence {y_n} $ be Cauchy sequences in $R$.
Then:
$\sequence {x_n y_n}$ is a Cauchy sequence. Proof
Suppose $\norm {x_n} \le K_1$ for $n = 1, 2, 3, \ldots$.
Suppose $\... |
I want to calculate the volume of this integral by using cylindrical coordinates $$T:Z \le2-x^2-y^2, \ Z^2 \ge x^2+y^2$$ First i want to ask here i don't see the equation for the circle i mean i don't have for example $x^2+y^2=1 \ or \ x^2+y^2=2x.$ etc. So this is my first confusion and the second one i am not sure if ... |
The Annals of Probability Ann. Probab. Volume 42, Number 6 (2014), 2417-2453. On the local time of random processes in random scenery Abstract
Random walks in random scenery are processes defined by $Z_{n}:=\sum_{k=1}^{n}\xi_{X_{1}+\cdots+X_{k}}$, where basically $(X_{k},k\ge1)$ and $(\xi_{y},y\in\mathbb{Z})$ are two i... |
This question already has an answer here:
Let $$a_n=\left(1-\dfrac{1}{\sqrt2}\right)\dots \left(1-\dfrac{1}{\sqrt{n+1}}\right),n\ge1$$ Then find $\lim_{n\to \infty} a_n$.
How can I proceed? I am stuck at the first step. Please help.
Mathematics Stack Exchange is a question and answer site for people studying math at an... |
Okay, I'll give a group-theoretic answer, since that was requested, which goes most of the way to a proof. I'm assuming you mean a 3x3x3 Rubik's cube. For larger cubes, the proof is just a little bit less convenient, because these cubes don't form groups (or more precisely, the action of the group of all moves on the c... |
I am solving a question whose first item is to demonstrate the Banach Fixed Point Theorem, and the second item is as follows:
Show that for any parameter $t \in \mathbb{R}$ the system $$ \begin{cases} x = \frac{1}{2}\sin(x+y) + t - 1 \\ y = \frac{1}{2}\cos(x-y) - t + \frac{1}{2} \end{cases} $$ has a unique solution tha... |
I am attempting to solve the following CES Utility Function problem:
However, I am running into issues when I get to 3).
For 1) I have $K = \left(\frac{\omega p_1}{p_2}\right)^{\frac{1}{p+1}}$
For 2) I get $X_2^M = \frac{m}{\frac{p_1}{K}+p_2} $
For 3) I find $\lambda^* = (K^\rho + \omega)^{-\frac1p-1} \cdot \omega \cdo... |
The group completion (aka Grothendieck group) of an abelian monoid $M$ is an abelian group $G(M)$ with a homomorphism $\iota:M \to G(M)$ of monoids satisfying the following universal property: for every homomorphism $f:M \to H$ whose target is an abelian group there exists a unique homomorphism $\phi:G(M)\to H$ of grou... |
The definition of limit of a sequence I always encounterd was of the form:
DEFINITION: Limit of a Sequence: Let $\{x_n\}_{n\in\mathbb{N}}$ be some sequence of real numbers, (i.e. $x:\mathbb{N}\to\mathbb{R}$) We say that:
$lim_{n\to\infty}x_n=L$
if and only if
$\forall 0 < \epsilon \in\mathbb{R} ,\exists N\in\mathbb{N},... |
I'm quite confused by this transformation, and am trying to gain fluency in moving back and forth between these objects. I understand that a second order dyadic Cartesian tensor can be represented as the sum of rank 0, 1, and 2 irreducible spherical tensors. I also know that the crucial point of extending this process ... |
Let $\beta > 0$ and $S_{0}=0$, and let $S_{n}=\xi_{1}+\dots+\xi_{n}$,$n \geq 1$, be a random walk with i.i.d. increments $\{\xi_{n}\}$ having a common distribution
$P(\xi_{1}=-1)=1-C_{\beta}$ and $P(\xi_{1}>t)=C_{\beta}e^{-t^{\beta}}$, $t \geq 0$,
where $C_{\beta} \in (0,1)$ is s.t. $E\xi_{1}=-1/2$. Let $M= \sup_{n \ge... |
The limit of function is in terms of a variable $x$ and trigonometric function sine. In this limit problem, $x$ is used to represent a variable and represent angle of a right triangle.
$\displaystyle \lim_{x \,\to\, 0}{\dfrac{\sin{2x}+3x}{4x+\sin{6x}}}$
The function in terms of sine and variable reminds the limit of qu... |
Let $f\in L(A,\mu_x\otimes\mu_y)$ be a summable function on $A\subset X\times Y$ where $(X\times Y,\mu_x\otimes\mu_y)$ is the product of measure spaces $(X,\mu_x)$ and $(Y,\mu_y)$. Then Fubini's theorem says that $$\int_A f(x,y) d\mu_x\otimes\mu_y=\int_X\Bigg(\int_{A_x}f(x,y)d\mu_y\Bigg) d\mu_x=\int_Y\Bigg(\int_{A_y}f(... |
134 Works
A new class of languages of infinite words is introduced, called the \emph{max-regular languages}, extending the class of $\omega$-regular languages. The class has two equivalent descriptions: in terms of automata (a type of deterministic counter automaton), and in terms of logic (weak monadic second-order lo... |
Searching for just a few words should be enough to get started. If you need to make more complex queries, use the tips below to guide you.
Purchase individual online access for 1 year to this journal.
Impact Factor 2019: 0.808
The journal
Asymptotic Analysis fulfills a twofold function. It aims at publishing original m... |
You can use the so-called "binomial encoding", described in one of my answers on math.stackexchange. You have to consider, though, whether it will be worthwhile. The naive encoding takes $n \log_2 k$ bits, and the best encoding saves about $O(\log n)$ bits (the best encoding uses $\log_2 \frac{n!}{f!^k}$ bits). Plug in... |
The Classical open mapping theorem for Banach spaces tells that if $T:X \to Y$ is a continuous surjective linear map, then it is open.
I have attempted to essentially "adapt" the proof for Lie groups:
Let $G,H$ be connected Lie groups (embedded in $\mathbb R^n$, I've used second-countability and completeness so far). I... |
The cos of 30 degrees value can be derived mathematically in three methods. One of them is a trigonometric approach and other two are geometrical methods.
You must know the direct relation between the sides of a right triangle when its angle is $30$ degrees. According to properties of right triangle, the length of oppo... |
Suppose $S: K \times M \to T$ is a secure MAC. ($K$ = key space, $M$ = message space, $T = \{0,1\}^n$ = tag space.)
$S$ being secure means that no matter what messages $m_1,...,m_q$ we throw at $S$ to get back tags $t_1,...,t_q$:
$\{ (m_1,t_1),...,(m_q,t_q) \}$
we cannot subsequently find another message-tag pair $(m,t... |
Logarithmic spiral Approximate solution
The logarithmic spiral is self-similar. As a consequence of that, the tangents make the same angle with the position vector in each point of the spiral. You can use that to draw a reasonable approximation of the spiral simply by taking unit steps in the direction of the current t... |
I want to pick two papers on the arXiv today. In
Indian Association for the Cultivation of Science(I couldn't resist to write this cute name of an institution) point out that Belle-II, a Japanese B-factory experiment that began to take limited data one year ago and is already taking all the data since early 2019, may o... |
M. Oren and S. K. Nayar have proposed a reflectance model of rough diffuse surfaces and two approximate functions (We call them "full O-N" and "qualitative O-N" respectively in this article) in 1993 [link] [link] . Full O-N approximate the model very well, but it is complex and has many computationally-expensive functi... |
Principle of Finite Induction/One-Based Theorem Suppose that: $(1): \quad 1 \in S$ $(2): \quad \forall n \in \N_{>0} : n \in S \implies n + 1 \in S$ Then: $S = \N_{>0}$
Consider $\N$ defined as a naturally ordered semigroup.
The result follows directly from Principle of Mathematical Induction for Naturally Ordered Semi... |
First i transform the s-box into row matrix like if i have 4×4 s-box having 16 elements into 1×16 row matix then substitute the binary values in column . multiply the matrix by mobius trasformation matrix then tell me how to trasform the s-box which is in binary form into decimal form? Also how i calculate the non line... |
I’d like to give a simple account of what I call the hierarchy of logical expressivity for fragments of classical propositional logic. The idea is to investigate and classify the expressive power of fragments of the traditional language of propositional logic, with the five familiar logical connectives listed below, by... |
I'm trying to prove that, given $(u_n)_n \in \mathbb{C}^\mathbb{N}$ verifying $ u_{n+1}-u_n =_{n} o(\frac{1}{n})$, the following holds:
$$ \lim_{n\to\infty} \frac{u_1+...+u_n}{n} = a \in \mathbb{C} \implies \lim_{n\to\infty} u_n = a$$
It is the reciprocal to the Cesaro 'average theorem'.
An indication is given, to rewr... |
With the first week behind us, the class is starting to settle into something of a rhythm. Things are going by very quickly, but the students seem more comfortable with the homework system, and after two quizzes have a better idea about what to expect from me. And we are finally getting to the good stuff: derivatives!
... |
I have a question in which the person asking has identified that the total sum of 11 comes up more often than a sum of 12 in the rolling of three dice and this is strange as they both have the same number of possible combinations of 3 numbers that make up 11 and 12.
Clearly 11 can be made up of combinations of : (6,4,1... |
Let $ k \in \mathbb{N}$. Let $ I \subset \mathbb{R}$ be an open interval. Let $ f : I \rightarrow \mathbb{R}$ be a $k$ times continuously differentiable function with $f'(x) \not= 0 $ for all $x \in I $.
Show that:
$1)$ $f$ is injective.
2) $f(I)$ is an open interval.
3) the inverse function $ f^{-1} : f(I) \rightarrow... |
Recently the question If $\frac{d}{dx}$ is an operator, on what does it operate? was asked on mathoverflow. It seems that some users there objected to the question, apparently interpreting it as an elementary inquiry about what kind of thing is a differential operator, and on this interpretation, I would agree that the... |
The answer is that Bob and Alice each calculate $(Q_a Q_b^{-1})^{\alpha \beta}$. Alice computes the quantity $Q_a$, Bob computes $Q_b$, Alice computes $(Q_a Q_b^{-1})^\alpha$ and sends that to Bob, who can compute $c = (Q_a Q_b^{-1})^{\alpha \beta}$.
Let's step through the protocol, keeping in mind the OTR reference (a... |
Egg Drop Project
This is the classic egg drop experiment. Students try to build a structure that will prevent a raw egg from breaking when dropped from a significant height. They should think about creating a design that would reduce the amount of energy transferred from potential to kinetic energy on the egg shell. So... |
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... |
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Forward-backward multiplicity correlations in pp collisions at √s = 0.9, 2.76 and 7 TeV
(Springer, 2015-05-20)
The strength of forward-backward (FB) multiplicity correlations is measured by the ALICE detector in proton-proton (pp) collisions at s√ = 0.9, 2.76 and 7 TeV. The measurement... |
The question "why is preimage resistance needed for hash functions" is not really relevant. This is because collision resistance implies preimage resistance. Thus, it is just a fact that if you have collision resistance then you must have preimage resistance.
So, instead, I will relate to what preimage resistance is go... |
Given the ODE system
$$ \left\{ \begin{array}{l} \dot x = -2x - z \cos t, \\ \dot y = x \sin t - y, \\ \dot z = -4z + \sin^2 t. \end{array} \right. $$ I am asked to:
1) Examine stability of this system
2) Determine if the system has $2\pi$-periodic solutions.
Since we usually refer to monodromy operator in cases like t... |
Reposted from PolymathProgrammer.com, my answer to my own initial query. Generated mostly on my own after some initial help from a friend (Jason Schmurr) and my dad (Russell Gmirkin)
I believe I've solved my own inquiry. The following are functions that, when graphed in polar coordinates render lovely polygons.
In fact... |
Stochastic 3D Modeling of Three-Phase Microstructures for Predicting Transport Properties: A Case Study 143 Downloads Abstract
We compare two conceptually different stochastic microstructure models, i.e., a graph-based model and a pluri-Gaussian model, that have been introduced to model the transport properties of thre... |
I would agree with the answer key. The trick here is it's limiting molar conductivity, the molar conductivity at infinite dilution. For a neutral electrolyte compound, I was taught the notation $\Lambda ^0$, and $\lambda ^0$ was reserved for individual ions. (The $0$ superscript represents zero concentration, equivalen... |
If $Q=\operatorname{adding}(P,R)=P+R$, then $P$ can be computed from $Q$ and $R$ as $P=\operatorname{adding}(Q,-R)=Q+(-R)$ where $-R$ is easy to compute from $R$ (just change the $y$ coordinate of $R$ from $y_R$ to $p-y_R$ where $p$ is the order of the prime field). This property follows from $\operatorname{adding}$ be... |
Let $\{x,y,z\}\subset[0,+\infty)$,and $x+y+z=6$. Show that: $$xyz(x-y)(x-z)(y-z)\le 27$$
I tried AM -GM but without success. $$xyz\le\left(\dfrac{x+y+z}{3}\right)^3=8$$ maybe $$(x-y)(x-z)(y-z)\le \dfrac{27}{8}$$ it doesn't always true。
Mathematics Stack Exchange is a question and answer site for people studying math at... |
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