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This is due to the mass-energy equivalence and a phenomenon called binding energy.
Forming a nucleus releases energy because the nucleons are falling into a potential energy well. Due to Einstein's mass energy equivalence this results in the mass of the new nucleus being less than that of the particles that formed it.
... |
So lets consider the following grammar
$$ \begin{align*} S &\to 0 \mid 0A \\ A &\to 1 \end{align*} $$
would the string "1" be accepted by the language or must the language start with $S$?
Computer Science Stack Exchange is a question and answer site for students, researchers and practitioners of computer science. It on... |
Note: The original answer has a flaw in "without loss of generality". The following one is based on Section 8.2.3 of the book "Computer Algorithms" (3rd edition) by Sara Baase and Allen Van Gelder.
The right part of the theorem is called the MST property.
MST Property: Let $T$ be any spanning tree. For any edge $e \not... |
I assume that you talk about the p-value on the estimated coefficient $\hat{\beta}_1$. (but the reasoning would be similar for $\hat{\beta}_0$).
The theory on linear regression tells us that, if the necessary conditions are fulfilled, then we know the distribution of that estimator namely, it is normal, it has mean equ... |
This article provides answers to the following questions, among others:
What does Pascal’s law state? What is the difference between pneumatics and hydraulics? How does a hydraulic jack work? What are the two principles used in a jack to increase the force? How is the hydraulic fluid prevented from flowing back from th... |
(2017-09-01 21:00: This answer just received a revenge downvote. Oh well...)
For every real number $t$,
$$\left|\sin t-t\right|\leqslant\tfrac16|t|^3\tag{$\ast$}$$
hence $$f(x,y)=\frac{\sin(xy)}{xy}$$ is such that, for every $(x,y)$ such that $xy\ne0$ (that is, where $f(x,y)$ exists), $$|f(x,y)-1|\leqslant\tfrac16|xy|^... |
Question: As we know, (1) the macroscopic spatial dimension of our universe is 3 dimension, and (2) gravity attracts massive objects together and the gravitational force is isotropic without directional preferences. Why do we have the spiral 2D plane-like Galaxy(galaxies), instead of spherical or elliptic-like galaxies... |
Scattering for a mass critical NLS system below the ground state with and without mass-resonance condition
1.
Department of Mathematics, Graduate School of Science, Osaka University, Toyonaka, Osaka, 560-0043, Japan
2.
Research Institute for Mathematical Sciences, Kyoto University, Kyoto, 606-8502, Japan
3.
Department ... |
Hint. If $a$ and $b$ are large enough, then $ab-a-b+1>\frac{ab}2$. Indeed; the inequality is equivalent to $(a-2)(b-2)>2$, so it suffices that $a,b\geq3$ and $\{a,b\}\neq\{3,4\}$.
Prime powers are certainly solutions, as they don't have any pair of coprime divisors $>1$. Now suppose $n$ has two nontrivial coprime divis... |
A spinor which belogs to a representation of a group $G=SO(p,q)$ is a section of a product bundle $S(M)\otimes E$, where $S(M)$ is a spin bundle over a four dimensional orientable and compact manifold $M$ and $E$ is an associated vector bundle of $P(M,G)$ in an appropriate representation. A Dirac operator $D: \Delta^+ ... |
While the language of ZFC set theory does not admit classes, this is not the case for NBG set theory. But the language of NBG does not allow quantification on symbols for classes, and it is known that NBG is conservative on ZFC for sets, meaning that every theorem concerning only sets provable in NBG is also provable i... |
I am interested in algorithms that help decide whether a
countably infinite locally finite graph is connected.
I think there is no algorithm that works for all graphs, e.g. no algorithm should work for an infinite chain with one edge removed.
I care about a specific graph $\Gamma$ whose automorphism group acts with fin... |
A cryptographic hash function $f : \{0,1\}^{*} \to \{0,1\}^n$ has three properties: (1) preimage resistance, (2) second-preimage resistance, and (3) collision resistance. Even further, these properties form a hierarchy where each property implies the one before it, i.e., a collision-resistant function is also second-pr... |
I'm trying to understand why a certain action of a Lie Group is hamiltonian.
Let $(M,g)$ be a geodesically complete Riemannian manifold. Then there exists a canonical one-form on the cotangentbundle $T^*M$ given by $\lambda_0 : T( T^*M) \to R, (v, \alpha) \mapsto \alpha(\pi_*v)$, with $\pi_*$ the derivative of the natu... |
We recall that the Lagrange Interpolation Polynomial $p_n(x)$ of a function $f\in C^n(\Omega )$ for some $\Omega \subseteq \mathbb{R}$ and $n\in \mathbb{N}$, has a pointwise error term of the form $$|p_n(x) -f(x)|= \frac{f^{(n)}(\xi (x))}{(n+1)! }\prod\limits_{j=1}^n(x-x_j) \, , $$ where $\{x_j\}\subset\Omega $ are the... |
A basic mathematical relation between any trigonometric functions is called a basic trigonometric identity. A basic trigonometric identity is usually used as a formula in mathematics. Hence, it is also called as a basic trigonometric formula.
There are four types of basic trigonometric identities in trigonometry and th... |
Advances in Differential Equations Adv. Differential Equations Volume 1, Number 6 (1996), 1075-1098. Singular boundary value problems for nonlinear elliptic equations in nonsmooth domains Abstract
Let $\Omega$ be a piecewise-regular domain in $\Bbb R^N$ and O an irregular point on its boundary $\partial \Omega$. We stu... |
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The chameleon is a hypothetical scalar particle which couples to ... |
suyash23n wrote:
The juice stall at the circus stocked just 2 brands of orange juice tetra packs. Brand A costs $1 per pack and brand B costs $1.5 per pack. Last week , brand A contributed to m% of stall’s revenue and accounted for n% of sales of juice tetra packs. Which of the following expresses m in terms of n?
(A) ... |
None of the three inequalities you’ve shown hold in general for Hermitian matrices $A$ and $B$.
To demonstrate this, we can look at the case where $A$ and $B$ are $1\times 1$ real matrices (trivially Hermitian), in which case the induced matrix norm reduces to an absolute value. Writing $A=a$ and $B=b$ for $a,b\in \mat... |
I am implementing the key exchange scheme proposed by zhang et al. on Sage. In the implementation of the scheme, they have used the two distributions $\chi_{\alpha}, \chi_{\beta}$.
How to choose $\alpha, \beta$ and what should be typical values of $\alpha\ and \ \beta$ to have 100% correctness of the scheme (that is al... |
\[\]
1. Concept Behind Inferential Statistics To begin with there are certain fundamental concepts in this section that span the section and are used throughout statistics. Often a sample is taken and the sample is a subgroup of a larger group, the population. From the sample it is desired to learn about the population... |
Let $V$ be a vector space and $T:V\rightarrow V$ a linear transformation with the property that $T(W)\subseteq W$ for every subspace $W$ of $V$. Prove that $T$ is scalar multiplication, i.e. there is an element $\lambda$ in the field of scalars such that $T(v)=\lambda v$ $\forall v\in V$.
My attempt: I gather that for ... |
Suppose I want to obtain a gate sequence representing a particular 1 qubit unitary matrix. The gate set is represented by a discrete universal set, e.g. Clifford+T gates or $\{T,H\}$ gates. A well known approach to solve the problem is to use Solovay-Kitaev (SK) algorithm. I tried this implementation for SK algorithm. ... |
The partial differential equation is a combination of the diffusion plus convective transport equations and an adsorption sink. The equation for one-dimensional solute transport model is:
$$\frac{\partial C}{\partial t} = D\frac{\partial^ 2C}{\partial^ 2x}-v\frac{\partial C}{\partial x} - \frac{\rho}{\theta} \frac{\par... |
It is well-known that the S and K combinators are Turing Complete. Are there combinators that suffice to yield (only) the primitive recursive functions?
Yes, but you have to consider typed combinators. That is, you need to give $S$ and $K$ the following type schemas: $$ \begin{array}{lcl} K & : & A \to B \to A \\ S & :... |
Gabriel Cramer was a Swiss mathematician who lived in the first half of the 18th century. In 1750 he published his method for solving sets of linear equations which is in common use today.
If we have two simultaneous equations $a_1x+b_1y=c_1$ and $a_2x+b_2y=c_2$ we could write them in matrix form like this
$\begin{bmat... |
Given some normally distributed observations $x_1,x_2,...,x_n$
$\forall i\ x_i\sim\mathcal{N}(\mu, \sigma^2)$
the ML estimator decides that the variance that maximizes the likelihood function is (see here):
$\hat{\sigma^2}=\frac{1}{n}\sum_{i=1}^{n}(x_i-\bar{x}^2)$
Now, I am trying to find the variance of this estimatio... |
In order with the explicit questions:
Yes Yes No
To answer the question I think you're attempting to ask, we can prove many things using type checking, but not everything. What does this have to do with programs? That's what the Curry-Howard correspondence tells us. The Curry-Howard correspondence is a relationship bet... |
It is well known that, given a sphere, the maximum number of identical spheres that we can pack around it is exactly 12, corresponding to a face centered cubic or hexagonal close packed lattice.
My question is: given a sphere of radius $R$, how many spheres of radius $r<R$ can we closely pack around it?
With disks, the... |
A) \[17\sqrt{3}\] units
B) \[36\]units
C) \[72\]units
D) \[48\sqrt{3}\] unitsView Solution
A) 11 cm
B) 13 cm
C) 15 cm
D) 14 cmView Solution
A) \[20\text{ }c{{m}^{2}}\]
B) \[21\text{ }c{{m}^{2}}\]
C) \[19\text{ }c{{m}^{2}}\]
D) \[18\text{ }c{{m}^{2}}\]View Solution
A) 11 m
B) 22 m
C) 15.75 m
D) 10.75 mView Solution
A) 2... |
Suppose that Alice receives a subset $S \subseteq \{1,\dots,n\}$ and Bob receives $T \subseteq \{1,\dots,n\}$. It is promised that $\lvert S \cap T \rvert = 1$. What is the randomized communication complexity of determining the common element $S \cap T$?
My interest in this is as follows. The zero-communication cost of... |
Images are essential elements in most of the scientific documents. LaTeX provides several options to handle images and make them look exactly what you need. In this article is explained how to include images in the most common formats, how to shrink, enlarge and rotate them, and how to reference them within your docume... |
This vignette describes methods to analyse all possible centrality rankings of a network at once. To do so, a partial rankings as computed from neighborhood-inclusion or, more general, positional dominance is needed. In this vignette we focus on neighborhood-inclusion but note that all considered methods are readily ap... |
SOLVED: Using Simply Beautiful Art's method, I managed to find the following upper bounds (and I numerically checked them). For all $a > 0$ and $m \in \mathbb{N}$, we have: $$\sum_{k=2m+1}^{\infty} \left(\frac{a}{\sqrt{k}}\right)^k \leq \left(1+\frac{a}{\sqrt{2}}\right)\frac{a}{\sqrt{2}}e\left[e^{\frac{a^2}{2e}} - \sum... |
The following probability question appeared in an earlier thread:
I have two children. One is a boy born on a Tuesday. What is the probability I have two boys?
The claim was that it is not actually a mathematical problem and it is only a language problem.
If one wanted to restate this problem formally the obvious way w... |
@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... |
I don't understand the different behaviour of the advection-diffusion equation when I apply different boundary conditions. My motivation is the simulation of a real physical quantity (particle density) under diffusion and advection. Particle density should be conserved in the interior unless it flows out from the edges... |
On the cohomology ring of divided powers and free ∞-loop spaces
Orateur:
Lorenzo Guerra
Dates:
Vendredi, 14 Juin, 2019 - 14:00 - 15:00
Résumé:
Given a pointed topological space $(X, \ast)$, its loop space is the space $\Omega(X, \ast)$ of continuous maps $\gamma \colon [0,1] \to X$ such that $\gamma (0) = \gamma (1) = ... |
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Production of charged pions, kaons and protons at large transverse momenta in pp and Pb-Pb collisions at $\sqrt{s_{NN}}$ = 2.76 TeV
(Elsevier, 2014-09)
Transverse momentum spectra of $\pi^{\pm}, K^{\pm}$ and $p(\bar{p})$ up to $p_T$ = 20 GeV/c at mid-rapidity, |y| $\le$ 0.8, in pp and ... |
On the optimal map in the $ 2 $-dimensional random matching problem
1.
Scuola Normale Superiore, Piazza dei Cavalieri 7, 56126 Pisa, Italy
2.
ETH, Rämistrasse 101, 8092 Zürich, Switzerland
3.
Dipartimento di Matematica, Università di Pisa, Largo Bruno Pontecorvo 5, 56127 Pisa, Italy
We show that, on a $ 2 $-dimensional... |
The entropy for the output of SHA-256 truncated to its first $128$ bits when fed a random $128$-bit input is about $127.173$ bit, down from very close to $128$ bit before truncation (see final note). The truncation does not halve the entropy, because the halves are not independent. The right line of thought is that SHA... |
Anatomy of a Short Circuit
A short circuit is an electrical fault where a conductive path (usually of low impedance) is formed between two or more conductive parts of an electrical system (e.g. phase-phase, phase-earth, phase-neutral, etc). This article looks at the nature of short circuits and tries to break down and ... |
First let us consider a Riemannian fiber bundle, i.e a fiber bundle $\pi: M\to B$ of oriented Riemannian manifolds. We denote by $T(M/B)$ the bundle of vertical tangent vectors and assume that the bundle $\pi: M\to B$ possesses the following additional structures:
a connection, that is, a choice of a splitting $TM=T_HM... |
I wouldn't have asked this question if I hadn't seen this image:
From this image it seems like there are reals that are neither rational nor irrational (dark blue), but is it so or is that illustration incorrect?
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professi... |
This paper concerns linear first-order hyperbolic systems in one space dimension of the type
$$
\partial_tu_j + a_j(x,t)\partial_xu_j + \sum\limits_{k=1}^nb_{jk}(x,t)u_k = f_j(x,t),\; x \in (0,1),\; j=1,\ldots,n,
$$
with periodicity conditions in time and reflection boundary conditions in space. We state a kind of diss... |
Actually, this is more of a general question relating to a homework problem I already did. I was given the initial wavefunction of a particle in an infinite square well:\Psi(x,0) = Ax if (0 \leq x \leq \frac{a}{2}), and =A(a-x) if (\frac{a}{2} \leq x \leq a)And of course \Psi(0,0) =...
Homework StatementProve or give a... |
I am dealing with a highly nonlinear system of two PDEs. I already have a code to solve the system in case of Dirichlet boundary conditions. The explicit system is:
$$ \begin{eqnarray*} \partial_{t}u & = & D_{11}\partial_{x}^{2}u+\partial_{x}D_{11}\cdot\partial_{x}u+D_{12}\partial_{x}^{2}v+\partial_{x}D_{12}\cdot\parti... |
An assortment of curves for fitting chemistry examples is presented in these Colby College class notes. Of particular application is the sigmoid response curve with variable "slope" for the central part of the curve:
$$ f(x) = \frac{a}{1 + e^{bx - c} } + d $$
[This is similar to the suggested
logistic function proposed... |
Consider the load balancing problem on two machines. Thus we want to distribute a set of $n$ jobs with processing times $t_1,...,t_n$ over two machines such that the makespan (maximum of the processing times of the two machines) is minimized. Professor Smart has designed an approximation algorithm
Alg for this problem,... |
The other answers here, describing oxygen toxicity are telling what can go wrong if you have too much oxygen, but they are not describing two important concepts that should appear with their descriptions. Also, there is a basic safety issue with handling pressure tanks of high oxygen fraction.An important property of b... |
I'm not sure if this is exactly what you are looking for or perhaps you already know what I am about to say.
There is a geometric notion of a twistor spinor (or conformal Killing spinor): one which is in the kernel of the Penrose operator (see below). Then one defines the twistor space as the projectivisation of the sp... |
Hey guys! I built the voltage multiplier with alternating square wave from a 555 timer as a source (which is measured 4.5V by my multimeter) but the voltage multiplier doesn't seem to work. I tried first making a voltage doubler and it showed 9V (which is correct I suppose) but when I try a quadrupler for example and t... |
$X_1,...,X_n$ are independent Poisson random variables with$ X_j $having parameter$j\lambda$.What is the fisher information contained in $(X_1,...,X_n)$ about $\lambda$? BTW,What is the likelihood function in this question? $S_n$ is the log likelihood function,is the first derivative right ?i dont know if it is correct... |
An algebraic approach to entropy plateaus in non-integer base expansions
Mathematics Department, University of North Texas, 1155 Union Cir #311430, Denton, TX 76203-5017, USA
For a positive integer $ M $ and a real base $ q\in(1, M+1] $, let $ {\mathcal{U}}_q $ denote the set of numbers having a unique expansion in bas... |
Positive ground state solutions for fractional Laplacian system with one critical exponent and one subcritical exponent
School of Mathematics and Statistics and Hubei Key Laboratory of Engineering Modeling and Scientific Computing, Huazhong University of Science and Technology, Wuhan 430074, China
$ \begin{cases} (-\De... |
Martin's comment is right on the money; in particular, the best way to get a feeling for coends is through the many examples where they appear, such as (generalized) tensor products. But from an abstract point of view, coends can be considered as universal "extranatural transformations", and the ubiquity of coends (and... |
Adjiashvili, David, Oertel, Timm and Weismantel, Robert 2015. A polyhedral Frobenius theorem with applications to integer optimization. SIAM Journal on Discrete Mathematics 29 (3) , pp. 1287-1302. 10.1137/14M0973694
PDF - Accepted Post-Print Version
Download (364kB) | Preview
Abstract
We prove a representation theorem ... |
1,764 69
Hi PF!
I am trying to solve an ODE by casting it as an operator problem, say ##K[y(x)] = \lambda M[y(x)]##, where ##y## is a trial function, ##x## is the independent variable, ##\lambda## is the eigenvalue, and ##K,M## are linear differential operators. For this particular problem, it's easier for me to work w... |
Periodic Hill¶
This tutorial will describe how to run a case from scratch. We illustrate this procedure through a relatively simple example involving incompressible laminar flow in a two-dimensional periodic hill domain. Our implementation is loosely based on the case presented by Mellen et al. [Mellen2000]. A thorough... |
The Professor has really confused me here on this one on what the
$\log 2$ mean? formula: $\text{Entropy} = \log(\text{Phrases})/\log 2$
If I understand the problem correctly, you are asking what the $\log 2$ is doing there in the denominator. This is essentially to ensure that the
base of the logarithm (whether it's $... |
I want to prove the following statement $$\forall x,y \in \mathbb R ,\ a >1 :\\ \ \ \ \ x < y \iff a^x < a^y$$
I can use all the exponentiation laws for rational numbers and I would like to prove the statement by using rational sequences $q_n \rightarrow x$ and $r_n \rightarrow y$ which converge to $x$ and $y$ for a ri... |
Given a finite sequence $\bm{a}=\langle a_i\rangle_{i=1}^n$ in $\mathbb{N}$ and a sequence $\langle x_t\rangle_{t=1}^\infty$ in $\mathbb{N}$, the Milliken–Taylor system generated by $\bm{a}$ and $\langle x_t\rangle_{t=1}^\infty$ is
\begin{multline*} \qquad \mathrm{MT}(\bm{a},\langle x_t\rangle_{t=1}^\infty)=\biggl\{\su... |
Let $F_n$ be the free group on $n$ letters.
The question is as in the title: letting $i:\text{Aut}(F_n) \hookrightarrow \text{Aut}(F_{n+1})$ be the natural injection, does there exist a homomorphism $\phi: \text{Aut}(F_{n+1}) \rightarrow \text{Aut}(F_n)$ such that $\phi \circ i = \text{id}$? My guess is "no", but I hav... |
On the existence of full dimensional KAM torus for nonlinear Schrödinger equation
1.
School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, China
2.
College of Science, The Institute of Aeronautical Engineering and Technology, Binzhou University, Binzhou 256600, China
3.
School of Mathematical... |
Event detail Harmonic Analysis Seminar: On multilinear oscillatory integral operator inequalities
Seminar | April 10 | 1:10-2 p.m. | 736 Evans Hall
Michael Christ, UCB
The title refers to inequalities of the form $\int _{[0,1]^d} \prod _{j=1}^d f_j(x_j) \,e^{i\lambda \psi (x)}\,dx = O(|\lambda |^{-\gamma } \prod _j \|f... |
You can compute the integral$$f(t) = \int_{t-1/2}^{t}\chi_{[0,1]}(u)du$$in cases, for different ranges of $t$.I think it's easier (personally) if we manipulate the rectangular pulse function instead of doing the substitution for $u$. I'm assuming that$$\chi_{[a,b]}(x) = \begin{cases} \hfill 1 \hfill & \text{ if } x\in ... |
I came up with this question when considering the field extension $\mathbb{Q}(\sqrt[\leftroot{-2}\uproot{2}4]{2})|\mathbb{Q}$. I know that the minimal polynomial of $\sqrt[\leftroot{-2}\uproot{2}4]{2}$ over $\mathbb{Q}$ is $x^4-2$ due to Eisenstein, and thus the above extension has degree 4. Now I'm trying to look at t... |
This conjecture is tested for all odd natural numbers less than $10^8$:
If $n>1$ is an odd natural number, then there are natural numbers $a,b$ such that $n=a+b$ and $a^2+b^2\in\mathbb P$.
$\mathbb P$ is the set of prime numbers.
I wish help with counterexamples, heuristics or a proof.
Addendum: For odd $n$, $159<n<50,... |
i don't have a background in Probability or Mathematics so i may be looking at a simple problem without knowing it. I have the following independent Events and their probabilities:
Event $A \rightarrow 83\%$ Event $B \rightarrow 25\%$ Event $C \rightarrow 41\%$ Event $D \rightarrow 68\%$ Event $E \rightarrow 11\%$ Even... |
Yes. Let $T$ denote the transition kernel. Suppose $\pi$ and $\nu$ are distinct stationary distributions. Let $\tau'$ be defined by $\tau'(A) = \min(\pi(A),\nu(A))$: then $\tau'$ is a finite measure. Let $p = \tau'(\mathbb{R}^+)$; since $\pi \neq \nu$, we have $p < 1$, and since the chain is irreducible, $p > 0$. Let $... |
36 7 Summary Bessel's integral form: is it e to the power of a cosine or sine?
Hello all,
This is knowledge needed to solve my take-home final exam but I just want to ask about the definition of Bessel's integrals. This is not a problem on the exam. Wikipedia says the integral is defined as: $$J_n(x) = \frac {1} {2\pi}... |
Scattering of radial data in the focusing NLS and generalized Hartree equations
Department of Mathematics & Statistics, Florida International University, Miami, FL 33199, USA
We consider the focusing nonlinear Schrödinger equation $ i u_t + \Delta u + |u|^{p-1}u = 0 $, $ p>1, $ and the generalized Hartree equation $ iv... |
@HarryGindi So the $n$-simplices of $N(D^{op})$ are $Hom_{sCat}(\mathfrak{C}[n],D^{op})$. Are you using the fact that the whole simplicial set is the mapping simplicial object between cosimplicial simplicial categories, and taking the constant cosimplicial simplicial category in the right coordinate?
I guess I'm just v... |
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πA−iln(B+C)\large \frac{\pi}{A} - i \ln {\left(B+\sqrt{C}\right)} Aπ−iln(B+C)
There is no real value for sin−1(2)\sin^{-1}(2) sin−1(2) but it has a complex one. And it is of the form as described above where, AAA, BBB and CCC are positive integers. Evaluate A+B+C... |
Dear Uncle Colin,
I'm trying to sew a traditional football in the form of a truncated icosahedron. If I want a radius of 15cm, how big do the polygons need to be?
-- Plugging In Euler Characteristic's Excessive
Hello, PIECE, and thank you for your message!
Getting an exact answer to that is a little tricky, but we can ... |
I further show that this sum distribution is impossible for any pair of dice, no matter how many faces they have, what numbers are on those faces, and what weights each face has, barring the trivial case where one die always rolls the same result.
Translate the dice weightings into generating functions
$$A(x) = \sum a_... |
The reason is that there are two ways of thinking about "points".
Let $A$ be a ring. Then, define:
A scheme-theoretic/topological point of Spec $A$ is a prime ideal of $A$. A geometric/functorial point of Spec $A$ is an equivalence class of morphisms Spec $K\rightarrow$ Spec $A$, where $K$ is a field, and two morphisms... |
In electromagnetism,
charge density is a measure of electric charge per unit volume of space, in one, two or three dimensions. More specifically: the linear, surface, or volume charge density is the amount of electric charge per unit length, surface area, or volume, respectively. The respective SI units are C·m −1, C·m... |
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... |
Preface: I am very new to Latex, and may have missed some things here.
I have a custom macro to create a horizontal line - not by my making, simply copied and pasted from the
exam package.
\newlength\linefillheight\newlength\linefillthickness\setlength\linefillheight{.25in}\setlength\linefillthickness{0.1pt}\newcommand... |
Ajay Kumar
Articles written in Proceedings – Mathematical Sciences
Volume 124 Issue 1 February 2014 pp 1-15
An Alexander dual of a multipermutohedron ideal has many combinatorial properties. The standard monomials of an Artinian quotient of such a dual correspond bijectively to some 𝜆-parking functions, and many inter... |
This article provides answers to the following questions, among others:
What is the difference between elastic and plastic deformation? What is the atomic process of deformation? In which cases must springback be considered during the deformation process? What is meant by a slip system? What is the relationship between... |
I recently came across this in a textbook (NCERT class 12 , chapter: wave optics , pg:367 , example 10.4(d)) of mine while studying the Young's double slit experiment. It says a condition for the formation of interference pattern is$$\frac{s}{S} < \frac{\lambda}{d}$$Where $s$ is the size of ...
The accepted answer is c... |
But if you don't want to have a Google account: Chrome is really good. Much faster than FF (I can't run FF on either of the laptops here) and more reliable (it restores your previous session if it crashes with 100% certainty).
And Chrome has a Personal Blocklist extension which does what you want.
: )
Of course you alr... |
If you need to include simple diagrams or figures in your document, the
picture environment may be helpful. This article describes circles, lines, and other graphic elements created with LaTeX.
Contents
Images can be "programmed" directly in your LaTeX file
\setlength{\unitlength}{1cm} \thicklines \begin{picture}(10,6)... |
Dear Uncle Colin,
I'm pretty good with quadratic inequalities and pretty good with absolute values, but when I get the two together, I get confused. For example, I struggled with the set of values satisfying $x^2 -\left| 5x-3\right| < 2 + x$. Can you help?
- Nasty Absolute Value Inequalities Ending Rongly
Hi, NAVIER, a... |
Here, the substitution isn't appropriate, because, as you see, there's no factor of $x$ in the original integrand. It would have been a better choice to substitute $y = (x^2 + 1)$ if the integral
had been $$\int x(x^2 + 1)^3\,dx$$ because then we'd have $\;dy = 2x dx\implies dx = \frac 12 dy,\;$ giving us a very nice i... |
The American Petroleum Institute, in its standard 521, outlines limits for exposure of personnel to heat radiation from flares. As hydrocarbons and hydrogen are commonly flared, and also commonly used as rocket fuel, the data is relevant. This publication is used throughout the oil industry worldwide (and therefore is ... |
In order to study the behavior of an RC circuit, I connected a resistor and a capacitor to an Arduino's I/O as shown:
The Arduino digital Output feeds the circuit with a square pulse of 2 sec duration.
(one second HIGH, one second LOW)
for a charge time of 1 sec:$$V_c = E(1-e^{-\dfrac{t}{\tau}}) = E(1-e^{-\dfrac{1}{0.8... |
Generally, one does not have a metric space embedded in some larger space where the "limits" of sequences that do not converge in $X$ may converge. So it really makes no sense to talk about "points to which the series converges but are not in $X$". As I noted in comments, if you really want to put (scare) quotes, they ... |
Probably my questions are known or evident to the experts but I'm a bit puzzled. First of all there seem to be two kinds of zeta functions that go under the name of Shintani zeta functions.
First, there are zeta functions $\zeta^{SS}$ associated with so called prehomogenous vector spaces going back to important work by... |
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*[http://en.wikipedia.org/wiki/Wikipedia:Writing_better_articles Wikipedia:Writing better articles].
*[http://en.wikipedia.org/wiki/Wikipedia:Writing_better_articles Wikipedia:Writing better articles].
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The fast signal diffusion limit in nonlinear chemotaxis systems
Institut für Mathematik, Universität Paderborn, 33098 Paderborn, Germany
$ n\geq2 $
$ \mathit{\Omega }\subset {\mathbb{R}}^n $
$ 0\not \equiv u_0\in W^{1, \infty}(\mathit{\Omega }) $
$ v_0\in W^{1, \infty}(\mathit{\Omega }) $
$ \varepsilon\in(0, 1) $
$ \be... |
I want to calculate the hamming weight of a S-Box using this formula: $\text{hw}(f) = \sum_{x=0}^{2^n-1} f(x)$. Where $f: \{0, 1\}^n \rightarrow \{0, 1\}$
My problem is that I don't know how to get the $f$-function.
I found that helpful paper: THE DESIGN OF S-BOXES. At Page 9 (18) boolean functions are described. But s... |
I see it's a very old question, but let me add my two cents. It's only an approximate solution and at times it involves some guesswork, but it turns out to be quite good. (Also, it doesn't need a computer and the math is pretty elementary.)
Let $a_n$ denote the probability of rolling total of $n$ in any number of rolls... |
What is the best way to prove the statement? I know the version of using nested intervals, but is there another way to approach the problem?
Let $X \subseteq \mathbb{R}$ be compact, and let $y \in \mathbb{R} \setminus X$. It suffices to prove $\mathbb{R} \setminus X$ is open, i.e. that $\mathbb{R} \setminus X$ contains... |
The fastest way to solve your problem instance is as outlined in the above comments.
First choose yourself a random message $m$ with $1<m<n-1$. Now compute $c\equiv m^d \pmod n$.
Try if any of the following equations holds, if an equation does hold you've found the public exponent $e$.$m \equiv c^3 \pmod n$
$m \equiv c... |
Bunuel wrote:
The height of an equilateral triangle is the side of a smaller equilateral triangle, as shown above. If the side of the large equilateral triangle is 1, what is AB?
A. 1 - √3/2
B. 0.25
C. 2 - √3
D. 1/3
E. 1 - √3/4
(The formula below we suggest you memorize. It will be used here twice.)
\({h_{eq}} = {{L\sq... |
I see often that people have troubles with the rule of product in combinatorics. I also see often that people who claim to not have troubles with it and try to explain it to the aforementioned clueless people just end up saying "it's just a formula, don't worry about where it came from and why we do it, just memorize i... |
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