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Lately, I have some read some papers about the hidden sector of particle physics which combines with the Standard Model through the so-called Higgs portal. Let the Lagrangian for this be composed of two simple scalar fields like this:
$L=\partial_\mu \phi_{SM} \partial_\nu \phi_{SM} +\partial_\mu \phi_H \partial_\nu \p... |
The model you describe is known as the Blum-Shub-Smale (BSS) model (also Real RAM model) and indeed used to define complexity classes.
Some interesting problems in this domain are the classes $P_R$, $NP_R$, and of course the question of whether $P_R$ = $NP_R$. By $P_R$ we mean the problem is polynomially decidable, $NP... |
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Okay, now I've rather carefully discussed one example of \(\mathcal{V}\)-enriched profunctors, and rather sloppily discussed another. Now it's time to build the general framework that can handle both these examples.
We can define \(... |
Abstract:
Using transversality and a dimension reduction argument, a result of A. Bezdek and W. Kuperberg is applied to polycylinders, showing that the optimal packing density of $\mathbb{D}^2\times \mathbb{R}^n$ equals $\pi/\sqrt{12}$ for all $n \ge 0$.
Comments and Corrigenda:
This paper was split before publication.... |
Problem A. 689. (February 2017) A. 689. Let \(\displaystyle f_1,f_2,\ldots\) be an infinite sequence of continuous \(\displaystyle \mathbb{R}\to\mathbb{R}\) functions such that for arbitrary positive integer \(\displaystyle k\) and arbitrary real numbers \(\displaystyle r>0\) and \(\displaystyle c\) there exists a numb... |
Welcome to The Riddler. Every week, I offer up a problem related to the things we hold dear around here: math, logic and probability. These problems, puzzles and riddles come from lots of top-notch puzzle folks around the world — including you! You’ll find this week’s puzzle below.
Mull it over on your commute, dissect... |
Define the quadratic variation of a semimartingale $(X_t)_{t \geq 0}$ by
$$[X,X]_t := \mathbb{P}-\lim_{n \to \infty} \sum_{j=0}^n (X_{t_j}-X_{t_{j-1}})^2$$
where $\Pi_n := \{t_0<\ldots<t_n<t\}$ is a sequence of partitions such that $|\Pi_n| \to 0$. Moreover, we set $$[X,Y]_t := \frac{1}{4} ([X+Y]_t-[X-Y]_t).$$
Using th... |
I saw a similar post at Automatic equation numbering in LyX but it didn't answer my question, so hopefully someone can help me out.
I have one of my key bindings set to:
command-sequence math-mode; math-mutate align;
I used this to insert align environments all over my document. None of these are numbered. My goal is
t... |
Current browse context:
math.PR
Change to browse by: References & Citations Bookmark(what is this?) Mathematics > Probability Title: Exceptional times for percolation under exclusion dynamics
(Submitted on 16 May 2016 (v1), last revised 28 Jun 2019 (this version, v5))
Abstract: We analyse in this paper a conservative a... |
The electronic configuration of an atom or molecule is a concept imposed by the orbital approximation. Spectroscopic transitions and other properties of atoms and molecules result from the states and not from the configurations, although it is useful to think about both the configuration and the state whenever possible... |
From the “Simple English Wikipedia”
1: The Lorentz Factoris the name of the factor by which time, length, and “relativistic mass” change for an object while that object is moving and is often written γ (gamma). This number is determined by the object’s speed in the following way: $\gamma = \frac{1}{\sqrt{1 - \frac{v^2}... |
Tangent, curve of the
The graph of the function $g=\tan x$ (Fig.a). The curve of the tangent is a periodic curve with period $T=\pi$ and asymptotes $x=(k+1/2)\pi$, $k\in\mathbf Z$. While $x$ varies from $-\pi/2$ to $+\pi/2$, $y$ grows monotonically from $-\infty$ to $+\infty$; thus, the curve of the tangent is composed... |
The assessment of nodal planes is not as trivial as it might seem at first, because they are usually not planes at all.
Orbitals can be explained in terms of symmetry operations. There are three different operations and each of them has a unique element (in cartesian coordinates):
Rotation: Axis Mirror: Plane Inversion... |
1 The Cosmic Sector
One of the outstanding achievements of the Reciprocal System of theory is the discovery of the fact that the physical universe is not limited to our familiar world of three dimensions of space and one dimension of time, the
material sector as Larson calls it. By virtue of the symmetry between the in... |
@user193319 I believe the natural extension to multigraphs is just ensuring that $\#(u,v) = \#(\sigma(u),\sigma(v))$ where $\# : V \times V \rightarrow \mathbb{N}$ counts the number of edges between $u$ and $v$ (which would be zero).
I have this exercise: Consider the ring $R$ of polynomials in $n$ variables with integ... |
Collisional Frequency is the average rate in which two reactants collide for a given system and is used to express the average number of collisions per unit of time in a defined system.
Background and Overview
To fully understand how the collisional frequency equation is derived, consider a simple system (a jar full of... |
In a 3D cartesian domain I have four points $A=(x_1,y_1,z_1)$, $B=(x_2,y_2,z_2)$, $C=(x_3,y_3,z_3)$, $D=(x_4,y_4,z_4)$, and they form a plane $ABCD$. I want to find out, if an arbitrary point $P(x,y,z)$ lies within the plane $ABCD$.
Let's say you have a
convex, non-self-intersecting quadrilateral defined by its vertice... |
My problem is mainly from this lecture notes on convex optimization here page4
Consider a s-t Minimum problem, on unweighted undirected graph $G=(V,E)$,we can formalize in following linear integer programming problem
\begin{equation*} \begin{aligned} & \underset{}{\text{minimine}} & & \sum_{u,v\in E}|x_u-x_v| \\ & \tex... |
Talk:Absolute continuity
Could I suggest using $\lambda$ rather than $\mathcal L$ for Lebesgue measure since
it is very commonly used, almost standard it would be consistent with the notation for a general measure, $\mu$ calligraphic is being used already for $\sigma$-algebras
--Jjg 12:57, 30 July 2012 (CEST)
Between m... |
Let:
$R$: The radius of the coil, $h$ the height of the coil, $n$: spiral density, ie, the number of spirals per height.
$r$: The radius of the wire, $A$: The area of the cross section of the wire.
$L$: The total size of the wiring, $N$: The amount of spirals in the coil.
$\bar R$: The overall resistance of the coil, $... |
Interested in the following function:$$ \Psi(s)=\sum_{n=2}^\infty \frac{1}{\pi(n)^s}, $$where $\pi(n)$ is the prime counting function.When $s=2$ the sum becomes the following:$$ \Psi(2)=\sum_{n=2}^\infty \frac{1}{\pi(n)^2}=1+\frac{1}{2^2}+\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{3^2}+\frac{1...
Consider a random binary str... |
The theorem states that
$$ H(P)\leq\mathrm{MinACL}(P)<H(P)+1 $$
where, $\mathrm{MinACL}$ means the minimum average code word length of a given information source, i.e. the average code word length of any Huffman coding and $H$ means the entropy of the probability distribution $P$.
Now, the problem is how to show that f... |
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We've been looking at feasibility relations, as our first example of enriched profunctors. Now let's look at another example. This combines many ideas we've discussed - but don't worry, I'll review them, and if you forget some defin... |
While the Data Preparation and Feature Engineering for Machine Learning course covers general data preparation, this course looks at preparation specific to clustering.
In clustering, you calculate the similarity between two examples by combining all the feature data for those examples into a numeric value. Combining f... |
Given an arbitrary partial order $P=(X,R)$ if for any $a,b\in X$ with $(a,b)\not\in R$ and $(b,a)\not\in R$ we define $R'=R\cup\{x\in X:(x,a)\in R\}\times \{x\in X:(b,x)\in R\}$ then I can show that $P'=(X,R')$ is an order extension of $P$ and by repeating this processes if $X$ is finite, I can then obtain all linear e... |
Consider two parallel, independent $M/M/1/1$ queues (denoted $Q_i, Q_j$) with identical arrival rate $\lambda$ and service rate $\mu$, using FCFS (First Come First Served) discipline. Note that the last $1$ in the notation $M/M/1/1$ means that the system is of finite capacity $N = 1$. In other words, for each queue sys... |
In classical mechanics we can describe the state of a system by a set of two numbers {\(\vec{R}, \vec{p}\)} where \(\vec{R}\) is the position of the object and \(\vec{p}\) is its momentum. The law of dynamics (given by Newton's second law, \(\sum{\vec{F}}=m\frac{d^2\vec{R}}{dt^2}\)) describes how the state of the objec... |
In mathematics, the
base flow of a random dynamical system is the dynamical system defined on the "noise" probability space that describes how to "fast forward" or "rewind" the noise when one wishes to change the time at which one "starts" the random dynamical system. Definition
In the definition of a random dynamical ... |
Basically 2 strings, $a>b$, which go into the first box and do division to output $b,r$ such that $a = bq + r$ and $r<b$, then you have to check for $r=0$ which returns $b$ if we are done, otherwise inputs $r,q$ into the division box..
There was a guy at my university who was convinced he had proven the Collatz Conject... |
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Okay, now I've rather carefully discussed one example of \(\mathcal{V}\)-enriched profunctors, and rather sloppily discussed another. Now it's time to build the general framework that can handle both these examples.
We can define \(... |
Consider the following problem taken from a problem booklet. My questions are:
What is displacement vector? And how to determine the direction of displacement vector at a certain point? Where is the position with zero displacement vector?
Physics Stack Exchange is a question and answer site for active researchers, acad... |
As in your question the stress was on the word
general, I have some bad news:an efficient " general solver (or a theoretical algorithm) for (...) extended Ising models, which involves an arbitrary lattice" does not exists.
Of course, one can invent algorithms that, in principle, could find the ground state. The most tr... |
e+e-</EM> Annihilation near Threshold > Top quark polarization in $e^+e^-$ annihilation into $t\bar t$is calculated for linearly polarized beams.The Green function formalism is appliedto this reaction near threshold.The Lippmann–Schwinger equations for the $S$-wave and$P$-wave Green functions are solved numerically for... |
Skills to Develop
Express products as sums. Express sums as products.
A band marches down the field creating an amazing sound that bolsters the crowd. That sound travels as a wave that can be interpreted using trigonometric functions.
Figure \(\PageIndex{1}\): The UCLA marching band (credit: Eric Chan, Flickr).
For exa... |
Let $X$ be any set. Say $\mathcal{E} \in 2^X $. Then there exists a unique smallest $\sigma-$algebra containing $\mathcal{E}$
Attempt:
Put $$ \mathcal{C} = \{ \mathcal{F} : \mathcal{F} \; \text{is a sigma algebra} \; \; and \; \; \mathcal{E} \subset \mathcal{F} \} $$
$\mathcal{C} $ is non-empty since the sigma algebra ... |
Prove that if $\liminf \left|\frac{a_{n+1}}{a_n}\right|>1$, then the series $\sum a_n$ diverges.
What I did was: let $c\geq 1$
If $\liminf \left|\frac{a_{n+1}}{a_n}\right|>c \implies \exists n_0 \in \mathbb{N}$ such that |$a_{n+1}|>|a_{n}|c\quad \forall n>n_0$.
then $|a_{n+2}|>c \cdot |a_{n+1}|>c^2\cdot |a_{n}|$ and so... |
Is the methodology to change the basis of a matrix the same as changing the basis of a vector? For example, if I had $A : \mathbb{R}^2 \to \mathbb{R}^2$ $$A=\begin{pmatrix} 3 & -5 \\ 2 & 7 \end{pmatrix}$$ in the standard basis and wanted it in the basis $v_1 = (1,3), v_2=(2,5)$. To do this, I simply multiply $A * \begi... |
I have found what I think is another bug in tikz-cd v0.9b. Take the following code:
\documentclass[11pt]{article}\usepackage{amsmath} %maths\usepackage{tikz-cd}\usetikzlibrary{arrows}\title{}\date{} \tikzset{ commutative diagrams/.cd, arrow style = tikz, diagrams={>=latex}}\begin{document}\begin{tikzpicture}[commutativ... |
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Now showing items 1-2 of 2
D-meson nuclear modification factor and elliptic flow measurements in Pb–Pb collisions at $\sqrt {s_{NN}}$ = 5.02TeV with ALICE at the LHC
(Elsevier, 2017-11)
ALICE measured the nuclear modification factor ($R_{AA}$) and elliptic flow ($\nu_{2}$) of D mesons ($D^{0}$, $D^{+}$, $D^{⁎+}$... |
Yes, it's possible to have an infinite chain.
I'm sure you're already familiar with some examples:$$ O(x) \subseteq O(x^2) \subseteq \ldots \subseteq O(x^{42}) \subseteq \ldots$$You have an infinite chain here: polynomials of growing degree. Can you go further? Sure! An exponential grows faster (asymptotically speaking... |
To send content items to your account,please confirm that you agree to abide by our usage policies.If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account.Find out more about sending content to .
To send content items to your Kindle, first ensure no-rep... |
theoratically its possible to attach the inductor with a voltage
source
Yes, in the context of ideal circuit theory, it is possible to do so without contradiction.
Let the voltage source have constant voltage across $V_S \gt 0$ and the inductor have inductance $L$. The inductor is connected to the voltage source at tim... |
Okay so we all know that one planet from the movie "Interstellar" that orbited the black hole Gargantua. How do I NOT get that? What's the minimum safe distance for a planet to be from a black hole ("safe" as in no funky relativistic time dilation and no megatsunamis)?
A black hole does not have any magic properties, i... |
Almost-periodic analytic function
An analytic function $f(s)$, $s=\sigma+i\tau$, regular in a strip $-\infty\leqslant\alpha<\sigma<\beta\leqslant+\infty$, and expandable into a series \begin{equation} \sum a_ne^{i\lambda_ns}, \end{equation}
where the $a_n$ are complex and the $\lambda_n$ are real numbers. A real number... |
Preparing NOJ
Mishka got an integer array $$$a$$$ of length $$$n$$$ as a birthday present (what a surprise!).
Mishka doesn't like this present and wants to change it somehow. He has invented an algorithm and called it "Mishka's Adjacent Replacements Algorithm". This algorithm can be represented as a sequence of steps:
... |
Consider a game in which darts are thrown at a board. The board is formed by $10$ circles with radii $20$, $40$, $60$, $80$, $100$, $120$, $140$, $160$, $180$, and $200$ (measured in millimeters), centered at the origin. Each throw is evaluated depending on where the dart hits the board. The score is $p$ points ($p \in... |
Let us have two random variables $A$ and $B$ representing lifetimes of two elements of a system, where $A$ has cdf $F_A(x)$, $A \sim Exp(\lambda_1 + \lambda_{12})$ and $B$ has cdf $F_B(y)$, $B \sim Exp(\lambda_2 + \lambda_{12})$, with joint cdf $H(x,y)$ .
Marshall-Olkin copula is defined as survival copula
$$\bar{H}(x,... |
If the sets are chosen randomly, then for the parameters you chose, the problem can be solved efficiently. In particular, the following trivial algorithm will output the correct answer with high probability: take each set of $S$, pad it by adding 10 random elements, and output the result (all sets of $S$, padded).
This... |
I'm trying to understand BRST complex in its Lagrangian incarnation i.e. in the form mostly closed to original Faddeev-Popov formulation. It looks like the most important part of that construction (proof of vanishing of higher cohomology groups) is very hard to find in the literature, at least I was not able to do so. ... |
Question: Why there is NO Charge-Parity (CP) violation from a potential Theta term in the electroweak SU(2)$_{weak,flavor}$ sector by $\theta_{electroweak} \int F \wedge F$?
(ps. an explicit calculation is required.)
Background:
We know for a non-Abelian gauge theory, the $F \wedge F $ term is nontrivial and breaks $CP... |
Inhomogeneous K-function
Estimates the inhomogeneous \(K\) function of a non-stationary point pattern.
Usage
Kinhom(X, lambda=NULL, …, r = NULL, breaks = NULL, correction=c("border", "bord.modif", "isotropic", "translate"), renormalise=TRUE, normpower=1, update=TRUE, leaveoneout=TRUE, nlarge = 1000, lambda2=NULL, recip... |
Hello guys! I was wondering if you knew some books/articles that have a good introduction to convexity in the context of variational calculus (functional analysis). I was reading Young's "calculus of variations and optimal control theory" but I'm not that far into the book and I don't know if skipping chapters is a goo... |
This is a good question. Unfortunately there are several criteria by which chemists indentify whether a process is melting or not. One of them is called the
Lindemann Criteria which says:
"Crystals are considered to melt, when the vibrational amplitude becomes half of the interatomic spacing in the crystal lattice."
Wh... |
This question already has an answer here:
I have a problem calculating the electrostatic potential energy.
I rely on these equations coming from mechanics:
\begin{equation} U_{B}-U_{A} = -W_{A \ \rightarrow \ B} (done\ by \ the \ field \ force) \end{equation}
\begin{equation} U_{B}-U_{A} = W_{A \ \rightarrow \ B} (done... |
In a book by Wise and Manohar,
Heavy Quark Physics (pg 80), they discuss the limit
\begin{equation}\lim _{\lambda\rightarrow \infty} \lambda^{\,z\,(\epsilon)}\end{equation}
where $z$ is some function of an infinitesimal parameter, $\epsilon$. Then they say "as long as $z$ depends on $\epsilon$ in a way that allows one ... |
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Now showing items 1-1 of 1
Anisotropic flow of inclusive and identified particles in Pb–Pb collisions at $\sqrt{{s}_{NN}}=$ 5.02 TeV with ALICE
(Elsevier, 2017-11)
Anisotropic flow measurements constrain the shear $(\eta/s)$ and bulk ($\zeta/s$) viscosity of the quark-gluon plasma created in heavy-ion collisions... |
Sanaris's answer is a great, succinct list of what each term in the free energy expression stands for: I'm going to concentrate on the $T\,S$ term (which you likely find the most mysterious) and hopefully give a little more physical intuition. Let's also think of a chemical or other reaction, so that we can concretely ... |
Consider the following problem, from Bjork's
Arbitrage Theory in Continuous Time:
Consider the standard Black-Scholes model. Derive the arbitrage free price process for the $T$-claim $\mathcal{X}$ where $\mathcal{X}$ is given by $\mathcal{X}=\{S(T)\}^\beta$. Here $\beta$ is a known constant.
My approach.
Let $F(t,s)$ b... |
Calculational Exercises
1. Let \(n \in \mathbb{Z}_+\) be a positive integer, let \(w_0 , w_1 ,\ldots, w_n \in \mathbb{C}\) be distinct complex numbers, and let \(z_0 , z_1 ,\ldots, z_n \in \mathbb{C}\) be any complex numbers. Then one can prove that there is a unique polynomial \(p(z)\) of degree at most \(n\) such tha... |
robot picking up plants
The end effector of these pneumatic picker-uppers consists of a shovel-shaped set of needles. The gripper takes advantage of the increased density of the plant's rootball (relative to the rest of the soil) so that compressive force is tuned just enough to hold onto the plant and not crush the ro... |
You are right in that gravity did not change during data collection. You are a victim of uncertainty, which is a very important part of experimental physics. I'm sorry in advance for the "wall of text", and I hope that this clears up some confusion.
The problem is that $1.50$ may not be
exactly $1.500000000...$. Becaus... |
Table of Contents
The nonlocal problem for the differential-operator equation of the even order with the involution Article References Ya. O. Baranetskij, P. I. Kalenyuk, L. I. Kolyasa, M. I. Kopach 109-119
On the convergence criterion for branched continued fractions with independent variables Article References R. I.... |
: There is a simple algorithm that runs in time $O(n \log n)$ and finds the inversion vector of a given array. Furthermore, there is a time lower bound of $ \Omega (n \log n) $ for any comparison-based algorithm for this problem, based on a reduction to the sorting problem. I have never read the paper Yuval Filmus refe... |
After assembling the vertical axis, all that was left was bolting on the wooden desktop and testing.
pretty computer on pretty desk
Between assembly and testing the HobbyShop staff started storing stuff on my desk...
HobbyShop staff trust my desk as a shelf.
Powersupply below. Foam cup only holds screws (no liquid don'... |
Recall that Maxwell's equations (in the absence of losses) require only that $n^2 = \epsilon\mu$. So when you take the square root, you are mathematically allowed to take either the positive or the negative square root.
Of course, then the question becomes, why would you
want to take the negative square root? Clearly, ... |
There are really two questions here: what did you do wrong, and how do you do it right? What you did wrong was mostly related to your statement of the fundamental theorem of arithmetic. You should have
$$N=\prod_{i=1}^\infty p_i^{k_i}$$
where $k_i$ are nonnegative integers, all but finitely many equal to zero (so this ... |
In 1+1D Ising model with a transverse field defined by the Hamiltonian
\begin{equation}
H(J,h)=-J\sum_i\sigma^z_i\sigma_{i+1}^z-h\sum_i\sigma_i^x
\end{equation}
There is a duality transformation which defines new Pauli operators $\mu^x_i$ and $\mu^z_i$ in a dual lattice
\begin{equation}
\mu_i^z=\prod_{j\leq i}\sigma^x_... |
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Now showing items 1-10 of 33
The ALICE Transition Radiation Detector: Construction, operation, and performance
(Elsevier, 2018-02)
The Transition Radiation Detector (TRD) was designed and built to enhance the capabilities of the ALICE detector at the Large Hadron Collider (LHC). While aimed at providing electron... |
Underpinnings of Mass Action: The Ideal Gas The Ideal Gas: The basis for "mass action" and a window into free-energy/work relations
The simplest possible multi-particle system, the ideal gas, is a surprisingly valuable tool for gaining insight into biological systems - from mass-action models to gradient-driven transpo... |
Help:Editing Math Equations using TeX This is how you edit math equations using the TeX syntax to make nice looking equations. Please use TeX when writing math. Trying to put equations directly into the text doesn't look very nice and TeX is very easy to learn.
If you already use TeX, then all you need to know is that ... |
Quenching of the E1 strength in 149Nd 64 Downloads Citations Abstract.
Lifetime measurements of excited states in
149Nd have been performed using the advanced time-delayed \( \beta\) \( \gamma\) \( \gamma\)( t) method. Half-lives of 14 excited states in 149Nd have been determined for the first time or measured with hig... |
I understand what a geodesic is, but I'm struggling to understand the meaning of the geodesic flow (as defined e.g. by
Do Carmo, Riemannian Geometry, page 63).
I can state my confusion in two different ways:
1)
Do Carmo writes:
Why does a geodesic $\gamma$ uniquely define a vector field
on an open subset? In other word... |
Let us first recall some definitions and useful formulas for a surface in $\mathbb{R}^3$ given by an immersion $F\colon U \rightarrow \mathbb{R}^3$, where $U \subset \mathbb{R}^2$ is an open set.
Denote $F_x = \frac{\partial F}{\partial{x}}$, $F_{x x} = \frac{\partial{F_x}}{\partial{x}}$, and so on.
The components of t... |
Greig Cowan Dr G A Cowan Research interests LHCb The LHCb experiment at CERN is searching for new physics through precision measurements of the properties of heavy quarks.
Quarks are the fundamental building blocks of the protons and neutrons which make up atomic nuclei. The study of heavy quarks has a long and illustr... |
1Department of Pure Mathematics, Faculty of Mathematical Sciences, University of Guilan, Iran.
2Department of Pure Mathematics, Faculty of Mathematical Sciences, University of Guilan, Iran.
Receive Date: 29 April 2015,Revise Date: 30 January 2016,Accept Date: 07 April 2016
Abstract
Let $(\Sigma_P,\sigma_P)$ be the spac... |
https://doi.org/10.1351/goldbook.B00746
The term applies to either of the equations: \[\frac{k_{\text{HA}}}{p} = G\left ( \frac{q\ K_{\text{HA}}}{p} \right )^{\alpha}\] \[\frac{k_{\text{A}}}{q} = G\left ( \frac{q\ K_{\text{HA}}}{p} \right )^{-\beta} \] (or their logarithmic forms) where \(\alpha\), \(\beta\) and \(G\) ... |
The problem is that you have not solved the question yet. What you have found is
not the friction between the boxes. It is something else. As you actually state yourself, you have instead found the maximum [static] friction. This is just the maximum possible value and not at all necessarily equal to the actual friction... |
When you write the five dimensional Kaluza-Klein metric tensor as
$$ g_{mn} = \left( \begin{array}{cc} g_{\mu\nu} & g_{\mu 5} \\ g_{5\nu} & g_{55}\\ \end{array} \right) $$
where $g_{\mu\nu}$ corresponds to the ordinary four dimensional metric and $ g_{\mu 5}$ is the ordinary four dimensional vector potetial, $g_{55}$ a... |
I think @ADG has provided a nice summary of when it is and isn't acceptable to post answers involving CAS. CAS is a lovely tool that I certainly use to check my hand-derived results and sometimes to get around tedious algebra that isn't the entire point of a problem.
However, CAS can be downright misleading, if not tho... |
CryptoDB Paper: Pairing-Friendly Elliptic Curves of Prime Order
Authors: Paulo S. L. M. Barreto Michael Naehrig Download: URL: http://eprint.iacr.org/2005/133 Search ePrint Search Google Abstract: Previously known techniques to construct pairing-friendly curves of prime or near-prime order are restricted to embedding d... |
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Re: Two semi-circles are drawn on adjacent sides of a square with side len[#permalink]
Show Tags
23 Jul 2019, 08:46
3
T... |
https://doi.org/10.1351/goldbook.H02732
The equation in the form: \[\log _{10}(\frac{k}{k_{0}}) = \rho \ \sigma \] or \[\log _{10}(\frac{K}{K_{0}}) = \rho \ \sigma \] applied to the influence of
meta- or para-substituents X on the reactivity of the @F02555@ Y in the benzene derivative m- or p-XC 6H 4Y. \(k\) or \(K\) i... |
I have multiple regression with, say 3 independent variables: $Y=B_0+B_1x_1+B_2x_2+B_3x_3$ I would like to test if $B_2+3B_3$ is significantly different from zero, i.e. $$H_0: B_2+3B_3=0$$ $$H_1: B_2+3B_3\neq 0$$ Can you please help to find appropriate way to test for significance of linear functions of two coefficient... |
Matrix Mechanics
In this lesson, we'll cover some of the fundamental principles and postulates of quantum mechanics. These principles are the foundation of quantum mechanics.
The eigenvalues are the values that you measure in an experiment: for example, the position or momentum of a particle. Because the eigenvalues ar... |
Faculty of Mathematics and Computer Science, Damghan University, Damghan, Iran.
Receive Date: 19 November 2014,Revise Date: 24 July 2015,Accept Date: 30 July 2015
Abstract
Let $A$ be a $C^{*}$ algebra, $T: A\rightarrow A$ be a linear map which satisfies the functional equation $T(x)T(y)=T^{2}(xy),\;\;T(x^{*})=T(x)^{*} ... |
I have trouble understanding the Lorentz transformation to proof the
dilation of time.
Let's use finite differences instead and, further, the entire expression for $\Delta t'$ from the Lorentz transformation
$$\Delta t' = \gamma \left(\Delta t - \frac{v}{c^2}\Delta x \right) = \frac{\Delta t - \frac{v}{c^2}\Delta x}{\s... |
Consider a $C^k$, $k\ge 2$, Lorentzian manifold $(M,g)$ and let $\Box$ be the usual wave operator $\nabla^a\nabla_a$. Given $p\in M$, $s\in\Bbb R,$ and $v\in T_pM$, can we find a neighborhood $U$ of $p$ and $u\in C^k(U)$ such that $\Box u=0$, $u(p)=s$ and $\mathrm{grad}\, u(p)=v$?
The tog is a measure of thermal resist... |
Why are axial bonds are longer than equatorial bond in case of $\mathrm{sp^3d}$ hybridization? I have done some research but I can't seem to find the answer.
You are asking for $\mathrm{sp^3d}$ hybridisation, but I do not know of a case where $\mathrm{sp^3d}$ hybridisation actually happens. Either it does not make sens... |
Direct answer to the question: yes, there are esoteric and highly impractical PLs based on $\mu$-recursive functions (think Whitespace), but no practical programming language is based on $\mu$-recursive functions due to valid reasons.
General recursive (i.e., $\mu$-recursive) functions are significantly less
expressive... |
Though less used than Nuclear Magnetic Resonance (NMR), Electron Paramagnetic Resonance (EPR) is a remarkably useful form of spectroscopy used to study molecules or atoms with an unpaired electron. It is less widely used than NMR because stable molecules often do not have unpaired electrons. However, EPR can be used an... |
Increasing the amount of installed renewable energy sources such as solar and wind is an essential step towards the decarbonization of the energy sector.
From a technical point of view, however, the stochastic nature of distributed energy resources (DER) causes operational challenges. Among them, unbalance between prod... |
Let us define the auxiliary process $\Lambda_t=e^{\kappa t}\lambda_t$. Note that:
$$ \Lambda_t = \kappa e^{\kappa t} \int_0^t(\rho_s-\lambda_s)ds+\delta e^{\kappa t}\int_0^tdN_t$$
Hence after a jump occurs at $t$:
$$ \Lambda_t=\Lambda_{t-}+\delta e^{\kappa t}$$
Therefore by Ito's lemma for jump-diffusion processes:
$$ ... |
Is there a nice closed form expression for $\mathbb{E}_{\theta' \sim Dir(\alpha)} KL (Cat(x; \theta)|| Cat(x;\theta')$, where $Dir(\alpha)$ is the Dirichlet distribution with concentration parameters $\alpha$ and $Cat(x;\theta)$ is the discrete distribution with (log-)parameters $\theta$?
It turns out I can answer this... |
On thing to keep in mind is that IR and UV divergences appear in different kinematical regimes: UV divergences are basically due to the fact that in loop integrals there are not sufficient propagators to make the integral fall off at infinity. E.g for a bubble integral
$\int d^4l \frac{1}{l^2(l-p)^2}$ will be logarithm... |
Consider again the quasilinear equation
(\(\star\)) \(a_1(x,y,u)u_x+a_2(x,y,u)u_y=a_3(x,y,u)\).
Let
$$ \Gamma:\ \ x=x_0(s),\ y=y_0(s),\ z=z_0(s), \ s_1\le s\le s_2,\ -\infty<s_1<s_2<+\infty $$ be a regular curve in \(\mathbb{R}^3\) and denote by \(\mathcal{C}\) the orthogonal projection of \(\Gamma\) onto the \((x,y)\)... |
Category:Boolean Algebras
Furthermore, these operations are required to satisfy the following axioms:
\((BA_1 \ 0)\) $:$ $S$ is closed under $\vee$, $\wedge$ and $\neg$ \((BA_1 \ 1)\) $:$ Both $\vee$ and $\wedge$ are commutative \((BA_1 \ 2)\) $:$ Both $\vee$ and $\wedge$ distribute over the other \((BA_1 \ 3)\) $:$ Bo... |
Euclidean Algorithm/Examples Contents 1 Examples of Use of Euclidean Algorithm 1.1 GCD of $341$ and $527$ 1.2 GCD of $2190$ and $465$ 1.3 GCD of $9 n + 8$ and $6 n + 5$ 1.4 Solution of $31 x \equiv 1 \pmod {56}$ 1.5 GCD of $108$ and $243$ 1.6 GCD of $132$ and $473$ 1.7 GCD of $129$ and $301$ 1.8 GCD of $156$ and $1740$... |
How to Automate Meshing in Frequency Bands for Acoustic Simulations
Think of the curved lid of an elegant grand piano. The curve corresponds to the strings’ length, which corresponds to the perception of the pitch. This visual represents an important element of acoustics: Our perception of pitch is logarithmic. This me... |
The Eyring Equation, developed by Henry Eyring in 1935, is based on transition state theory and is used to describe the relationship between reaction rate and temperature. It is similar to the Arrhenius Equation, which also describes the temperature dependence of reaction rates. However, whereas Arrhenius Equation can ... |
Exercise 1.14 of the book Rordam, Larsen and Laustsen "An introduction to K-theory for C*-algebras" asks to prove, that upper triangular matrix with elements from some C*-algebra $A$ is invertible in $M_n(A)$ iff all diagonal entries are invertible in $A$.
Trying to solve this I've found that if $a$ is invertible and $... |
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