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If you take the square root of the perimeter of a triangle and double it, you get the area of the triangle. The sides have integer lengths which are mutually different from each other. What are the lengths of its sides?
Let the side lengths of the triangle be $a,b,c$, and let $P = a+b+c$.
By Heron's formula, $$A = \sqr... |
First of all, the axiom of countable choice says that given a countable family of non-empty sets, you can choose from each set
simultaneously. If you want to choose from one, then from another, then from another, and so on you need a strictly stronger form of choice called Dependent Choice, abbreviated as $\sf DC$.
To ... |
While trying to solve the exercise below, I came up with a wrong conclusion, but I can't see why it's wrong. Also I'm accepting suggestions to get the right solution. This is the problem 17 from chapter 10 of Rudin's Functional Analysis.
Let $A$ be a Banach algebra. Suppose that the spectrum of $x\in A$ is not connecte... |
In this scenario, the "joint dynamics" are trivially computed since the option value is a known deterministic function of stock price. For example, the mean of the option value for time $\tau$ is$$\mu_O = \int_0^\infty BSM( S_\tau ) p(S_\tau) dS_\tau$$which is best computed using quadrature as available in standard num... |
I understand how to derive the black scholes solution if $dS_t$ = $\mu S_tdt$ + $\sigma S_tdW_t$ and r is constant. The solution is c(t, x) = $xN(d_{+}(T - t), x))$ - K$e^{-r(T - t)}N(d\_(T - t), x))$ where $d_{+}(\tau, x)$ = $\frac{1}{\sigma\sqrt{\tau}}$ * $[log\frac{x}{K} + (r + \frac{1}{2}\sigma^2)\tau]$, $d\_(\tau,... |
I mean the basic principle is,
you're right, this setup is described by the math of classical electrical circuits as one which should drive an infinite current, and if you only have one charge to move then an infinite current necessitates it moving with infinite speed. If you do not give it a way to lose energy then it... |
In Blake 1986 'Mechanics of Flow-Induced Sound and Vibration V1: General Concepts', pg. 148 the author provides a helpful equation for the pressure radiated by organ pipes when the cavity is small compared to a wavelength, i.e., $\lambda_0 \gg$ cavity dimensions. (
Note this is the usual approximation for organ pipes, ... |
Suppose $Y_1,\dots,Y_n\mid\mu,\sigma^2 \sim \text{ iid } N(\mu,\sigma^2)$ and suppose the priors $\mu \mid \sigma^2 \sim N(\mu_0, \sigma^2 / \kappa_0)$ and $1/\sigma^2 \sim \text{gamma}(\nu_0/2, \nu_0 \sigma_0^2 / 2)$ are placed on the unknown parameters. Then \begin{align*} p(\sigma^2 \mid y_1,\dots,y_n) &\propto p(\s... |
In signal processing, cross-correlation is a measure of similarity of two waveforms as a function of a time-lag applied to one of them. This is also known as a sliding dot product or sliding inner-product. It is commonly used for searching a long signal for a shorter, known feature. It has applications in pattern recog... |
I was reading some stuff earlier today, and I wasn't sure how they changed the exponentials to trigs in this expression:
$$C_1x^{-1/4}\exp\left(\frac{2}{3}ix^{3/2}\right)+C_2x^{-1/4}\exp\left(-\frac{2}{3}ix^{3/2}\right)$$
$=$
$$A_1x^{-1/4}\sin\left(\frac{2}{3}x^{3/2}\right)+A_2x^{-1/4}\cos\left(\frac{2}{3}x^{3/2}\right... |
A note on a superlinear and periodic elliptic system in the whole space
1.
Department of Mathematics, Yunnan Normal University, Kunming 650092 Yunnanage, China
2.
Office of Adult Education, Simao Teacher's College, Simao 665000 Yunnan, China
3.
Department of Mathematics, Yunnan Normal University, Kunming 650092 Yunnan
... |
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... |
Rather than answer the question numerically I have outlined the four different cases,
reversible / irreversible and isothermal / adiabatic.
In adiabatic changes no energy is transferred to the system, that is the heat absorbed or released to the surroundings is zero. A vacuum (Dewar) flask realises a good approximation... |
Adelman's theorem relativizes, i.e. for every oracle $O$ we have $\mathsf{BPP^O\subseteq P/Poly^O}$. To see why you have to go over the proof of Adelman's theorem. The proof goes through showing that given a probabilistic machine with exponentially low error probability, there exists a sequence of coin tosses which pro... |
Preprints (rote Reihe) des Fachbereich Mathematik Refine Year of publication 1996 (22) (remove)
293
Tangent measure distributions were introduced by Bandt and Graf as a means to describe the local geometry of self-similar sets generated by iteration of contractive similitudes. In this paper we study the tangent measure... |
To touch upon a paper published when you look at the interactive journal that is scientific Model developing (GMD) or perhaps in its conversation forum Geoscientific Model Development Discussions (GMDD), please select among the after two choices:
If you want to submit an interactive comment (brief remark, referee remar... |
Feynman-Kac for SPDEs with multiplicative noise
One application of the celebrated Feynman-Kac formula in probability theory gives a stochastic representation of solutions to Cauchy problems. Following the basic idea of the proof, the formula is first derived for terminal value problems of type \[ -\frac{\partial}{\part... |
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Even × Even = Even Even ÷ Even = Even ? \begin{aligned} \text{ Even } \times \text{ Even } &=& \text{ Even } \\\text{ Even } \div \text{ Even } &=& \text{ Even }?\end{aligned} Even × Even Even ÷ Even == Even Even ?
It is true that the product of two even numbers ... |
Plastids
Category : 11th Class
Plastids are semiautonomous organelles having DNA, RNA, Ribosomes and double membrane envelope. These are largest cell organelles in plant cell.
History
(1) Haeckel (1865) discovered plastid, but the term was first time used by Schimper (1883)
.
(2) A well organised system of grana and st... |
Relative Velocity:
We encounter occasions where one or more objects move in a frame which is non-stationary with respect to another observer. For example, a boat crosses a river that is flowing at some rate or an airplane encountering wind during its motion. In all such instances, in order to describe the complete moti... |
In a paper by Joos and Zeh, Z Phys B 59 (1985) 223, they say:This 'coming into being of classical properties' appears related to what Heisenberg may have meant by his famous remark [7]: 'Die "Bahn" entsteht erst dadurch, dass wir sie beobachten.'Google Translate says this means something ...
@EmilioPisanty Tough call. ... |
This is an excellent series of questions, so I will have a go at part of it! I will start with an example from Verdeyen’s book (J. T. Verdeyen, Laser Electronics, Prentice-Hall, Inc., Englewood Cliffs, NJ, ©1981, Chapter 14). Assume $\lambda$ = 500 nm, quantum efficiency = 0.15, photomultiplier (PMT) gain = 1.68x$10^7$... |
Do we take gravity = 9.8 m/s² for all heights when solving problems?
No, the value $9.8\frac{\mathrm{m}}{\mathrm{s}^2}$ is an approximation that is only valid at or near the Earth's surface. You can go a few miles up or down and it'll still be good enough, but once you get any significant distance away from the surface... |
During a discussion with my professor, he asked me about relativistic resistance transformation. Firstly I started with the formula $R=\frac{\rho L}{s}$, where $\rho$ is electric resistivity. So if some resistor moves with relativistic speed its length contracts. And this means that its resistance changes like its leng... |
There is a problem in checking whether the homography is OK.
The algorithm for checking correct homographies may interest someone, so I will write it down here:
1) Create a quadrilateral $ABDC$ with vertex coordinates (in homogenous coordinates):
$$\begin{eqnarray} A:& (-w/2,-h/2, 1.0) \\ B:& (w/2,-h/2, 1.0) \\ C:& (-w... |
In what follows, we have a level $N \geq 3$, and the modular curve $X(N)$, and the invertible sheaf $\omega$ on $X(N)$ such that the global sections of $\omega^{\otimes k}$ correspond to modular forms of weight $k$ and level $N$.
In this letter, Serre looks at an exact sequence of sheaves:
$0 \rightarrow \omega^{k - p ... |
In this question it is shown that being able to compute reciprocals (together with sums and differences) is enough to do do multiplication in a field of characteristic $\ne 2$. That made me wonder:
Can we formulate a set of field axioms that are based on the reciprocal function rather than a multiplication operation? S... |
If we arbitrarily choose a point from each orthant in $\mathbb{R}^n$, that is we choose $2^n$ points in total, how do we prove that 0 is in the convex hull of these $2^n$ points? It seems obvious, but when I sit down and start thinking about it, I couldn't definitely find a set of $\lambda_i, i = 1,2,\cdots,2^n$ such t... |
Extraordinary claims require extraordinary proofs which really is the reason why this sorts of discussion is important. Similarly, sometimes, you are so blinded to some sorts of a truth and are faced with something so different that you can misread entirely what is being said. If you read this morning's entry, you migh... |
I would appreciate if somebody could run this over and see if it works out? any suggestions or pointers would be appreciated. I denote the standard eta function $\eta$ by $\zeta^{*}$. I have not used big O notation and just used general well behaved functions. I do not wish to express the full error term, but instead ,... |
What I want to achieve
The framework ROOT can create 2D histogram plots with colored boxes indicating count rate that looks something like:
My question is really only:
can I produce this kind of 2D histogram through PGFPlots? The rest of this post describes my current findings and attempts.
As of writing quite recently... |
Spectral internal transmittance τ
i (λ) is the ratio of the light intensities at the outlet Φ out (λ) and inlet Φ in (λ) of the flow cell.
$\tau_{i} \left( \lambda \right) = \frac{\phi_{\text{out}} \left( \lambda \right) }{\phi_{\text{in}} \left( \lambda \right) }$
Fig. 51: Internal spectral transmittance
Unlike the tr... |
One disadvantage of the fact that you have posted 5 identical answers (1, 2, 3, 4, 5) is that if other users have some comments about the website you created, they will post them in all these place. If you have some place online where you would like to receive feedback, you should probably also add link to that. — Mart... |
Research talks;Number Theory
For a non-principal Dirichlet character $\chi$ modulo $q$, the classical Pólya-Vinogradov inequality asserts that
$M (\chi) := \underset{x}{max}$$| \sum_{n \leq x}$$\chi(n)| = O (\sqrt{q} log$ $q)$. This was improved to $\sqrt{q} log$ $log$ $q$ by Montgomery and Vaughan, assuming the Genera... |
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2.Prove that no number in this sequence 11,111,1111,11111,........... is a perfect square 2. \text{Prove that no number in this sequence } 11,111,1111,11111,........... \\ \text{ is a perfect square} 2.Prove that no number in this sequence 11,111,1111,11111,........ |
Here is one definition of the proportional odds model: $$\frac{S(t;{\bf Z})}{1-S(t;{\bf Z})}=e^{-{\bf Z}^T\pmb{\beta}}\frac{S_0(t;{\bf Z})}{1-S_0(t;{\bf Z})},$$ where ${\bf Z}$ = covariates, $\pmb{\beta}$ = regression coefficients, $T$ = survival time, $S(\cdot)$ = survival function, $S_0(\cdot)$ = baseline survival fu... |
In David Chandler's 'intro to statistical mechanics' he states that for an ideal gas at high-temperature
$$ \langle n_j\rangle=\langle N\rangle\frac{e^{-\beta \epsilon_j}}{\sum e^{-\beta \epsilon_j}} $$
Which I can believe from intuition, but he losses me on the derivation.
Starting with the general form for the occupa... |
I am thinking I can't be the only one encountering this. I am trying to do maximum likelihood estimation on a probit model, i.e. trying to find the most optimal fit for three parameters in my case through the following equation:
$$l\left(\beta; y, X\right) = \sum_{i=1}^N \left[y_i \ln\left(F\left(x_i \beta\right)\right... |
We use the notation $\chi_{q}(n,\cdot)$ to identify Dirichlet characters $\Z\to \C$, where $q$ is the modulus, and $n$ is the index, a positive integer coprime to $q$ that identifies a Dirichlet character of modulus $q$ as described below. The LMFDB label $\texttt{q.n}$, with $1\le n < \max(q,2)$ uniquely identifies $\... |
If we have some reaction $\ce{A(aq) + B(aq) -> AB(aq)}$ and right now we have less $\ce{A}$ and $\ce{B}$ then we would have at equilibrium, is there ever a time where the amount of $\ce{A}$ and $\ce{B}$ would overshoot the equilibrium of $\ce{A}$ and $\ce{B}$ if the reaction proceeded without any new sources of energy ... |
If I write FourierSinSeries[x, x, 10]
Mathematica will output the first 10 terms of the Fourier Sine Series f(x) = x defined for 0 < x < Pi.
How do I output the the Fourier Sine Series for a different domain, say 0 < x < 2 Pi?
Mathematica Stack Exchange is a question and answer site for users of Wolfram Mathematica. It... |
I think you need the Nernst equation. This is something we were just introduced to today in my class, so I’m not so sure about the notation you’re using in your question at the top, but you should be able to correct my answer to fit your needs if you understand the equation I’m about to implement.
$$E_\text{cell} = E^\... |
Title Topological "observables" in semiclassical field theories Publication Type Journal Article Year of Publication 1992 Authors Nolasco, M, Reina, C Journal Phys. Lett. B 297 (1992) 82-88 Abstract
We give a geometrical set up for the semiclassical approximation to euclidean field theories having families of minima (i... |
Markov's principle is a statement of constructive arithmetic that allows classical reasoning on formulas of the shape $\exists x P$ when $P$ is a recursive predicate: $\neg \neg \exists x P \to \exists x P$
Its formulation is well known in the context of arithmetic, and it is well known that adding it to Heyting Arithm... |
In this tutorial you will learn how to set up and execute Purpose:
calculations of the magneto-optical Kerr effect (
exciting
). As an example, we calculate the
MOKE
spectrum for ferromagnetic fcc-Ni.
MOKE 0. Define relevant environment variables and download scripts Read the following paragraphs before starting with t... |
(I will not be surprised if this problem has been solved and/or has a trivial solution – I just do not know the right terminology to google for it.)
So the problem is as follows. I have an $m \times n$ matrix consisting of zeroes and ones. I treat the rows $\mathbf r_1, \mathbf r_2, \dotsc, \mathbf r_m$ of the matrix a... |
I hope you can help me and this is the right forum to ask.
In the process of building and programming my own Quadcopter, I encountered the term Euler angles. I took some time to understand them and then wondered why they are used in multicopter systems.
In my understanding Euler angles are used to rotate a point or vec... |
Is there a known expression for the eigenvalue distribution of a matrix of the form
$$\sum\limits_{i=1}^n k_ia_ia_i^T$$
where $a_i \in \mathcal{R}^m$, with $n > m$, $a_i \sim \mathcal{N}(0,\Sigma)$ and $k_i > 0$? For simplicity we can consider the case $\Sigma = \text{I}_d$. (Equivalently, the expression is $\sum\limit... |
I've already posted an answer on this thread, but I found another example I'd like to describe separately. Let $r > 0$ and consider the following problem, coming from compound interest or as one definition of $e^r$:
Show that $f(n) = (1 + \frac{r}{n})^n$ increases with $n$.
One generalize the problem strategy is to all... |
We know that there are Whitehead theorem for homotopy and homology theory.
Is there the Whitehead theorem for cohomology theory for 1-connected CW complexes?
MathOverflow is a question and answer site for professional mathematicians. It only takes a minute to sign up.Sign up to join this community
We know that there ar... |
I am referring to the following three reactions. Two of these reactions are imaginary ($\ce{M}$ and $\ce{X}$ are imaginary).
$$\begin{alignat}{3} \ce{X- + 2e- \;&<=> X^3-} \qquad &&E^\circ_{\ce{X^3-}/\ce{X-}}=0.9\ \mathrm{V}\qquad &&&\text{(a)}\\ \ce{2H+ + MO^2+ + e- \;&<=> M^3+ + H2O} \qquad &&E^\circ_{\ce{MO^2+}/\ce{... |
F-test is named after the more prominent analyst R.A. Fisher. F-test is utilized to test whether the two autonomous appraisals of populace change contrast altogether or whether the two examples may be viewed as drawn from the typical populace having the same difference. For doing the test, we calculate F-statistic is d... |
Current browse context:
gr-qc
Change to browse by: Bookmark(what is this?) General Relativity and Quantum Cosmology Title: Generators of local gauge transformations in the covariant canonical formalism of fields
(Submitted on 15 Sep 2019)
Abstract: We investigate generators of local gauge transformations in the covaria... |
It is often explained, that the rule of thumb for exercising American options is to check when the benefit from the interest rate (sell the stock earlier, get the cash, put in the bank) is higher than the time value of the option. This is all clear in the positive interest rate environment, but the question is then - w... |
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... |
This problem can be expressed as the original Merton's portfolio problem.
Consider wealth process defined by SDE
$$d X _ { t } = \frac { X _ { t } \alpha _ { t } } { S _ { t } } d S _ { t } + \frac { X _ { t } \left( 1 - \alpha _ { t } \right) } { S _ { t } ^ { 0 } } d S _ { t } ^ { 0 }$$
where $\alpha_t$ is proportion... |
Extraordinary claims require extraordinary proofs which really is the reason why this sorts of discussion is important. Similarly, sometimes, you are so blinded to some sorts of a truth and are faced with something so different that you can misread entirely what is being said. If you read this morning's entry, you migh... |
Prajapati, Ravindra S and Sirajuddin, Minhajuddin and Durani, Venuka and Sreeramulu, Sridhar and Varadarajan, Raghavan (2006)
Contribution of Cation-\pi Interactions to Protein Stability. In: Biochemistry, 45 (50). pp. 15000-15010.
PDF
Contribution_of_Cation-.pdf
Restricted to Registered users only
Download (500kB) | R... |
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... |
Let the stochastic process $\{X_t \}_{t \in \mathbb{N}}$ be defined as $$X_t = \sum_{i = 0}^{\infty} \phi^i W_{i-t} $$
where $\phi \in \mathbb{R}$ and the $W_i$ are white noise with $ W_i\sim N(0, \sigma) \forall i \in \mathbb{Z}$. It is well known in econometric theory that these kind of processes are solutions to aut... |
Just in view of the
double universal covering provided by $SU(2)$, $SO(3)$ must a quotient of $SU(2)$ with respect to a central discrete normal subgroup with two elements. This is consequence of a general property of universal covering Lie groups:
If $\pi: \tilde{G} \to G$ is the universal covering Lie-group homomorphi... |
Quadratic Equations / Functions Learn easily with Video Lessons and Interactive Practice Problems Introduction Quadratic functions are easy to recognize. The polynomial expression known as a quadratic contains a variable that is squared making it a 2nd degree equation, and the graph is U-shaped. Quadratic expressions t... |
I'm right now learning about Monodromy from self-studying Rick Miranda's fantastic book "Algebraic Curves and Riemann surfaces". Today, I read about monodromy, and the monodromy representation of a holomorphic map between compact Riemann surfaces. I understand that we start by having a holomorphic map $F:X \rightarrow ... |
One way of understanding why the muon decay $$\mu^-\to e^-+\bar{\nu}_e+\nu_\mu\tag{1}$$ is a
Charged Current (CC) process is to write the intermediate step through which the decay (1) proceeds i.e., $$\mu^-\to \nu_\mu+\color{red}{W^-}\to \nu_\mu+\color{red}{e^-+\bar{\nu}_e}.\tag{2}$$ Now the intermediate step explains ... |
Let $k$ be a field. What is an explicit power series $f \in k[[t]]$ that is transcendental over $k[t]$?
I am looking for elementary example (so there should be a proof of transcendence that does not use any big machinery).
MathOverflow is a question and answer site for professional mathematicians. It only takes a minut... |
Get your free trial content now! Video Transcript Transcript Percent Change
Xenia is really into social media. Hoping to increase the number of people following her on VidPicStar, she plans to test out different kinds of content – to learn what people really want to see.
First, she posts a really funny video she took a... |
CIE 1931 xy chromaticity diagram
showing the gamut
of the sRGB color space and location of the primaries. The D65 white point
is shown in the center. The Planckian locus
is shown with color temperatures labeled in kelvin
. The outer curved boundary is the spectral (or monochromatic) locus, with wavelengths shown in nan... |
Suppose that we have a time-homogeneous discrete-time Markov chain $(X_n)$. We want to estimate the transition probabilities $p_{ij} = \mathbb{P}[X_{n+1} = j \mid X_n = i]$.
In the case when we have full information, e.g. we observe $(X_1, X_2, \ldots, X_N)$, the maximum likelihood estimator is $$ \hat{p}_{ij} = \frac{... |
(1) is true if $char(k)=0$. This follows from a combination of results. First of all, it is true over any field that the spectrum $MGL$ is connective, which means that
$$MGL^{p,q}(X)=0$$
if $p>q+dim(X)$, $X\in Sm/k$ [1, Cor. 2.9]. (Slightly more is true: for any $p\geq q+dim(X)$, the orientation map $MGL\to H\mathbb{Z}... |
I have a question concerning fermions in curved space-time.
Please read it to the end before suggesting the spin-connection and vierbein-based approach.
I heard that there is a special way of thinking about spin-1/2 particles (Dirac fermions) in flat space-time: the spinor field $\psi(x)$ is considered a (Grassmanian) ... |
How fast would you throw an object that it never came back down? This is where escape speed comes into the picture. It is the minimum speed required to escape a planet’s gravitational pull.
A spacecraft leaving the surface of the earth should be going at a speed of about 11 kilometres (7 miles) per second to enter the ... |
Sep 30th 2019, 05:59 AM
# 2
Senior Member
Join Date: Oct 2017
Location: Glasgow
Posts: 474
There's no need to introduce work done here. The potential is related to the electric field strength by:
$\displaystyle \vec{E} = - \nabla V$
Assuming the scalar field $\displaystyle V(x,y,z) = c_0 c_1 x^3 + x - 25 yz^4$, we can ... |
Research Open Access Published: Exponential decay rate for a quasilinear von Karman equation of memory type with acoustic boundary conditions Boundary Value Problems volume 2015, Article number: 122 (2015) Article metrics
1143 Accesses
5 Citations
Abstract
In this paper, we show the exponential decay result of the quas... |
Lets say you are given a distribution function $f(p)$ and you want to define a temperature, $T_f$, for this distribution. (I assume $\mu = 0$.)
It is then natural to define a temperature the following way: \begin{equation} T_f \equiv \frac{ \int d^3p \ G(p) f(p)}{\int d^3p \ f(p)}, \end{equation} where $G(p)$ is define... |
Suppose we have a $U$ shaped hollow tube consisting of three parts as : $T_{v1}$, $T_{v2}$, and $T_{h}$ , representing two vertical tubes and one horizontal tube respectively. The configuration is kept fixed as such so that the horizontal tube acts as a base. Let $T_{v1}$ have a cross-sectional area $A$ and $T_{v2}$ ha... |
Annals of Mathematical Statistics
Опубликовано на портале: 31-03-2004
Theodore W. Anderson, Donald A. DarlingAnnals of Mathematical Statistics. 1952. Vol. 23. No. 2. P. 193-212.
The statistical problem treated is that of testing the hypothesis that $n$ independent, identically distributed random variables have a specif... |
Hex 1.0
Hydrogen-electron collision solver
#include <tuple>
#include "arrays.h"
#include "input.h"
#include "matrix.h"
#include "radial.h"
#include "parallel.h"
#include "opencl.h"
class PreconditionerBase Preconditioner template. More... class NoPreconditioner Solution driver without actual preconditioner. More... cla... |
I'm currently taking a convex optimization class and we're using the textbook by Boyd & Vandenberghe. I was solving an exercise problem when I came across a question (for anybody curious the problem is Exercise 9.1). I have two questions in total regarding the same problem. One about a detail within the problem and one... |
Simplify result of this definite integral
It is well known that for $n\in\mathbb{N}$ and $n>0$ (an maybe even for more than these restrictions): $$I_n = \int_0^\infty\frac{x^n}{e^x-1}dx = \zeta(n+1)n!$$ which, analytically can be shown easily by expanding $1/(1-e^{-x})$ into a geometric series, which leads to trivial i... |
I just started having a look at 2 Higgs Doublet Models (2HDM) and came across this:
The general idea seems pretty simple. Introduce a second Higgs doublet that acquires a vev.
The general Yukawa interaction term (ignoring leptons) for both doublets $\Phi^1$ and $\Phi^2$ then looks like: $$ \mathcal{L}_Y = Y_{ij}^{U1}\o... |
Lets start by writing the definition of the equilibrium constant, for some general reaction:
$$\sum_i^{n_\text{reac}} a_iA_i = \sum_j^{n_\text{prod}}b_jB_j$$
The above is a general reaction, where $a_i$ and $b_j$ is the stoichiometry and $A_i$ and $B_i$ is the
molecules. For this reaction we can write the equilibrium c... |
Thank you for using the timer!We noticed you are actually not timing your practice. Click the START button first next time you use the timer.There are many benefits to timing your practice, including:
Does GMAT RC seem like an uphill battle? e-GMAT is conducting a free webinar to help you learn reading strategies that ... |
In this article on recurrent neural networks by Razvan Pascanu, $\mathbf x_t$ is the state at time $t;$ $\mathbf u_t$ the input at time $t$; and $\mathcal E$ is the cost function:
A proof is given of the fact that if the absolute value of the main eigenvalue of the matrix of recurrent weights is $\rho < 1$ then the van... |
Often big datasets and high dimensionality go hand in hand. Sometimes the dimensionality is so high that storage of the full MCMC chain in memory becomes an issue. There are a number of ways around this, including: calculating the Monte Carlo estimate on the fly; reducing the dimensionality of the chain using a test fu... |
I am looking for a full account of the relationship between the various versions of Floer theory on a symplectic manifold $M$. If we take the usual Floer equation (Hamiltonian version) \begin{equation*} \frac{\partial u}{\partial s} + J \left( \frac{\partial u}{\partial t} - X_H(u) \right) = 0 \ , \end{equation*} there... |
The issue stems to an unfortunate coincidence for small values of $n$, namely that the Rankin-Selberg $L$-function is, in some sense, "close to" being the Dirichlet series you write when both $F$ and $G$ have degree $1$ or $2$ Euler factors. But for $n \geq 3$, this is no longer the case.
The Rankin-Selberg product $\p... |
The computation requires two processes:
row operations of the type used in Gaussian elimination (with some restrictions because we require that the integer equivalence class be preserved) and the corresponding column operations, the Euclidean algorithm for finding the greatest common divisor of two integers.
Specifical... |
Let $A$ be a finite dimensional $\mathrm{C}^*$-algebra.
We have the usual absolute value:
$$|a|:=\sqrt{a^*a},$$
and the cone of positive elements:
$$A^+:=\{a\in A:\exists \,b\in A, a=b^*b\}.$$
An operator $T\in B(A)$ is said to be positive if $T(A^+)\subset A^+$.
Does it hold that $|Tf|=T|f|$ for positive $T$?.
Context... |
The Hamiltonian for a relativistic charged particle moving in a static electromagnetic field is the well known: $$H=c\sqrt{\left(\mathbf{P}-q\mathbf{A}\right)^{2}+m^{2}c^{2}}+q\phi$$ where,\begin{align*} \mathbf{B} & =\nabla\times\mathbf{A},\\ \mathbf{E} & =-\nabla\phi. \end{align*} Now let's suppose that one wants to ... |
The model here is the binomial option pricing model, so the second term in the brackets represents the expected future value of the option (under riskneutral probabilities).The aim of the option holder is always to maximize the value of his option. He can at any point sell the option at the fair market price $E(V_{n+1}... |
Title Renormalization for Autonomous Nearly Incompressible BV Vector Fields in Two Dimensions Publication Type Journal Article Year of Publication 2016 Authors Bianchini, S, Bonicatto, P, Gusev, NA Journal SIAM Journal on Mathematical Analysis Volume 48 Pagination 1-33 Abstract
Given a bounded autonomous vector field $... |
2019-09-27 09:59
Higgs boson pair production at colliders: status and perspectives / Di Micco, Biagio (Universita e INFN Roma Tre (IT)) ; Gouzevitch, Maxime (Centre National de la Recherche Scientifique (FR)) ; Mazzitelli, Javier (University of Zurich) ; Vernieri, Caterina (SLAC National Accelerator Laboratory (US)) ; ... |
What is the motivation for including the compactness and semi-simplicity assumptions on the groups that one gauges to obtain Yang-Mills theories? I'd think that these hypotheses lead to physically "nice" theories in some way, but I've never, even from a computational perspective. really given these assumptions much tho... |
In probability theory and statistics, the coefficient of variation (CV), also known as relative standard deviation (RSD), is a standardized measure of dispersion of a probability distribution or frequency distribution.
Relative Standard Deviation, RSD is defined and given by the following probability function:
${100 \t... |
Standard busy beaver function draws attention to final count of nonzero symbols on tape. We could instead look at largest amount of nonzero symbols appearing on tape at
any point of computation. This function's lower bound would be $\Sigma(n)$ and upper bound would be $S(n)$ (max shifts function). Was there made any re... |
This depends, of course, on the underlying probability space, most notably the filtration. In general, there are plenty of progressive processes which are not predictable, and this should be fairly standard material. If one works with the raw (un-augmented) filtration on the canonical path space of continuous functions... |
There is no shortage of idiots and assholes in this world. I see them everyday in my mail inbox. The rich Nigerian widow, Idi Amin’s grandson, Gaddafi’s daughter-in-law, Saddam Husain’s son-in-law, are all looking for a “reliable” partner in their business adventures and seek my help in this matter. Of course, they pro... |
I know that a linear operator is bounded if and only if it is continuous. But what about a bounded linear functional? Is this just a special case of a linear operator, and hence it is also bounded if and only if it is continuous?
But if that is the case, it would seem to make the definition of the weak topology redunda... |
To give a little bit more detail on 0-0-0's answer: Let $V$ be an $\mathbb{F}$-vector space of finite dimension.
We first prove the following theorem:
Theorem: Let $\phi\in\mathsf{Hom}(V,V)$, $U\subseteq V$ invariant under $\phi$. Let $\phi|_U:U\to U$ be the restriction of $\phi$ to $U$. Then $q_{\phi|_U}$ divides $q_\... |
Let $F$ be a Maass cusp form for $\mathrm{SL}(3,\mathbb{Z})$ (level 1 trivial character).
Let $g$ be a Maass cusp form for $\Gamma_0(N)$ with character $\chi$ mod $N$. For convenience, you may assume $\chi$ is primitive mod $N$. You may also take $g$ to be an Eisenstein series $E(z,s,\chi)=\sum_{\gamma\in \Gamma_\infty... |
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