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Find All 3 by 3 Reduced Row Echelon Form Matrices of Rank 1 and 2(a) Find all $3 \times 3$ matrices which are in reduced row echelon form and have rank 1.(b) Find all such matrices with rank 2.Solution.(a) Find all $3 \times 3$ matrices which are in reduced row echelon form and have rank 1.First we look at the rank 1 c... |
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Petri net
Definition from Dictionary, a free dictionary
Teach only love for that is what you are.A Course In Miracles
EnglishWikipedia Noun
Singular
Plural
Petri net({{{1}}}) One of several mathematical representations of discrete distributed systems, a 5-tuple <math>(S,T,F... |
Suppose $f=f(x)=f(x_1,\cdots,x_n)$ is a homogeneous polynomial of degree $n$ in the ring $k[x_1,\cdots,x_n]$, with $k$ a field. Denote by $H_f$ the hypersurface given by $f=0$. Suppose that for every smooth point $z$ of $H_f$, $f(x)$ is divisible by the linear form $f_x(x,z) = \sum_{i=1}^n x_i \frac{\partial f(\xi)}{\p... |
I am studying literature on the nonlinear Schroedinger equation. More generally, I am wondering how to tackle an equation of motion such as
$\bigl(i\partial_t-\Delta\bigr)\psi(\vec{x},t)+V(\vec{x},t)=0$
where the potential is of the form
$V(\vec{x},t)=\int d\vec{x}_1...d\vec{x}_n~ \psi(\vec{x}-\vec{x}_1,t)...\psi(\vec{... |
I was wondering if it feasible to think of the Polyakov action as a generalisation of the point-particle action $$ S_0 = \frac{1}{2}\int d\tau(\eta^{-1}\dot{X}^\mu\dot{X}_\mu - \eta m^2) $$ by considering the Lagrangian $$ L_0(\tau) = \frac{1}{2}(\eta^{-1}(\tau)\dot{X}^\mu(\tau)\dot{X}_\mu(\tau) - \eta(\tau) m^2) $$ as... |
Let's say we have two modes, with the following labeling of occupation number states:
$ \lvert \Psi \rangle = \begin{pmatrix} 0,0 \\ 0,1 \\ 1,0 \\ 1,1 \end{pmatrix} $
An example of (what I assume to be) fermionic creation operators for the two modes is
$\hat a_1^\dagger = \begin{pmatrix} 0 & 0 & 0 & 0 \\ -1 & 0 & 0 & 0... |
I suggest to create a tag synonym analysis-and-odes $\to$ ca.classical-analysis-and-odes. The tag analysis-and-odes has only five questions and empty tag info - so it does not seem to have any distinction from ca.classical-analysis-and-odes. Four of the five questions in this tag were asked by t...
I'd like to propose ... |
Is there a standard or common way to write scientific notation in different bases that doesn't require repeating the base in both the coefficient and the exponent base?
For example, this notation is correct, but is quite verbose:
Implicit base 10: $100 \cdot \tau = 6.283 \times 10^2$ Explicit base 10: $100 \cdot \tau =... |
Limit Divergence Criteria
Recall from The Sequential Criterion for a Limit of a Function page, that for a function $f : A \to \mathbb{R}$ and for $c$ being a cluster point of $A$, then $\lim_{x \to c} f(x) = L$ if and only if for all sequences $(a_n)$ from $A$ for which $\lim_{n \to \infty} a_n = c$ we also have that $... |
Goal First Optimization This is most definitely not my invention. I merely implemented my interpretation of the work of Jelena Vuckovic and her students. I found it incredibly fascinating and a fundamentally different design paradigm from what I had seen in the half-dozen solvers I've used over the years.
In contrast, ... |
From Newton’s law, we know that the time rate change of the momentum of a particle is equal to the net force acting on the particle and is in the direction of that force.\(F_{net} = \frac{dp}{dt}\)
This clearly makes us understand that linear momentum can be changed only by a net external force. If there is no net exte... |
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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 ... |
Search
Now showing items 1-1 of 1
Production of charged pions, kaons and protons at large transverse momenta in pp and Pb-Pb collisions at $\sqrt{s_{NN}}$ = 2.76 TeV
(Elsevier, 2014-09)
Transverse momentum spectra of $\pi^{\pm}, K^{\pm}$ and $p(\bar{p})$ up to $p_T$ = 20 GeV/c at mid-rapidity, |y| $\le$ 0.8, in pp and ... |
Probability Seminar Spring 2019 Thursdays in 901 Van Vleck Hall at 2:25 PM, unless otherwise noted. We usually end for questions at 3:15 PM.
If you would like to sign up for the email list to receive seminar announcements then please send an email to join-probsem@lists.wisc.edu
January 31, Oanh Nguyen, Princeton
Title:... |
This question already has an answer here:
Choosing between $z$-test and $t$-test 2 answers
Suppose we have that $X_1, \ldots, X_n \sim N(\mu, \sigma^2)$ where $\sigma^2$ is known. If we wanted to test the hypothesis of:
$$ H_0: \mu = \mu_0 \ \ \text{and} \ \ H_1: \mu \neq \mu_0 $$
a lot of books just jump directly to u... |
Consider the transverse-field Ising chain (TFIC) in a transverse-field $B$:
$$H_{TFIC}(B)\equiv -\sum_{j=1}^{N-1} \sigma^x_j\sigma^x_{j+1}+B\sum_{j=1}^N \sigma^z$$
At $B=0$, we have the classical Ising chain, and so there is a set of groundstates for this system with zero entanglement, namely the all-up and all-down st... |
The Annals of Probability Ann. Probab. Volume 8, Number 1 (1980), 115-130. De Finetti's Theorem for Markov Chains Abstract
Let $Z = (Z_0, Z_1, \cdots)$ be a sequence of random variables taking values in a countable state space $I$. We use a generalization of exchangeability called partial exchangeability. $Z$ is partia... |
Suppose there are $n$ data values $x_1<x_2<\ldots<x_{n-1}<x_n$，and I've found a partition number $k$, such that$$\left|\frac{1}{k}\sum_{i=1}^k(x_i-\hat{\mu_k})^2-\frac{1}{n-k}\sum_{j=k+1}^n(x_j-\hat{\mu}_{n-k})^2\right|$$is minimal. Here $\hat{\mu}_k$ is the mean of the first $k$ values, and $\hat{\mu}_{n-k}$ is the me... |
Row Echelon Form of a Matrix
If we have a matrix $A$ that represents a system of linear equations, we can reduce $A$ to what is known as
Row Echelon Form (often times abbreviated as REF) in order to solve the system. We must first look at the definition for a matrix to be in this form.
Definition: Let $A$ be an $m \tim... |
Recall that an offset is just a predictor variable whose coefficient is fixed at 1. So, using the standard setup for a Poisson regression with a log link, we have:$$\log \mathrm{E}(Y) = \beta' \mathrm{X} + \log \mathcal{E}$$where $\mathcal{E}$ is the offset/exposure variable. This can be rewritten as$$\log \mathrm{E}(Y... |
The values used will often be OK.
A larger than usual motor inductance may cause problems.
The snubber's job is to protect the switch contacts from inductive turnoff transients from the motor. Stopping the transient at source (across the motor) or at destination (across the contacts) both work. Arguably, having it at t... |
I am curious to find the energies of Dirac delta potential inside the ISW (walls at $x=0,L$) $$ H = -\frac{\hbar^2}{2m} \frac{\partial^2}{\partial x^2} + V_0\delta(x-L/2) $$
using Wilson-Sommerfeld Quantization (WSQ),
so I looked at this integral (Here, $p_1=\sqrt{2 m E}, p_2=\sqrt{2 m (E- V_0\delta(x-L/2))}~$) $$\oint... |
@JosephWright Well, we still need table notes etc. But just being able to selectably switch off parts of the parsing one does not need... For example, if a user specifies format 2.4, does the parser even need to look for e syntax, or ()'s?
@daleif What I am doing to speed things up is to store the data in a dedicated f... |
Limiting behavior of trajectory attractors of perturbed reaction-diffusion equations
Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing 211106, China
In this paper, we study the relations between the long-time dynamical behavior of the perturbed reaction-diffusion equations and the e... |
Though the underlying concepts that are required to build and train a neural network are
difficult, It is very easy to implement it in code. So in this post, let’s Code a neural network by hand Use to build a neural network keras
Firstly let’s see how can we build our own neural network with just raw python code. For t... |
Synchronization for stochastic differential equations with nonlinear multiplicative noise in the mean square sense
School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan, Hubei 430074, China
We provide a more clear technique to deal with general synchronization problems for SDEs, whe... |
Intro:
This has been a long coming, endless traps have been setting the math evolutionary progress back throughout time, and you, Physics and Math people have been forced to use simple text equation display techniques to show complex math. Well, be that no longer, as i am about to introduce you to the world that no lon... |
Change of Variables in Double Integrals
Recall from the Evaluating Double Integrals in Polar Coordinates page that if the region $D = \{ (r, \theta) : h_1(\theta) ≤ r ≤ h_2(\theta), \alpha ≤ \theta ≤ \beta \}$ then:(1)
What we have really done is defined a transformation in using these substitution to make evaluating c... |
An equity has a value of 100 Euros, and pay a dividend of 5 Euros in 6 months. The interest rate of 6 months is 5% and the interest rate for 1 year is 6%. I would like to compute the value of the price of this equity after 1 year ?
We consider the forward value, which can be employed to estimate the equity value.
Let $... |
The Infona portal uses cookies, i.e. strings of text saved by a browser on the user's device. The portal can access those files and use them to remember the user's data, such as their chosen settings (screen view, interface language, etc.), or their login data. By using the Infona portal the user accepts automatic savi... |
The Annals of Statistics Ann. Statist. Volume 24, Number 6 (1996), 2350-2383. Heuristics of instability and stabilization in model selection Abstract
In model selection, usually a "best" predictor is chosen from a collection ${\hat{\mu}(\cdot, s)}$ of predictors where $\hat{\mu}(\cdot, s)$ is the minimum least-squares ... |
The radio spectrum is a very precious resource like real estate and must be utilized judiciously. Pulse shaping filters control the spectral leakage of the transmitted signal in a wireless channel due to the strict restrictions to comply with a spectral mask. This is even more important for the upcoming 5G wireless sys... |
I think you're either misusing the word "renormalizable" or using it in a very old-fashioned way. Perturbative quantum gravity is renormalizable at all loop orders in the sense that divergences can be removed by the addition of local counterterms. Like all EFTs for which the leading interaction is irrelevant (in this c... |
Coverings of a Subset in Euclidean Space
Definition: Let $S \subseteq \mathbb{R}^n$. A Covering of $S$ is a collection of subsets of $\mathbb{R}^n$, $\mathcal F$, such that $\displaystyle{S \subseteq \bigcup_{A \in \mathcal F} A}$. If $\mathcal F$ is a collection of open sets, then $\mathcal F$ is called an Open Coveri... |
Double Series of Real Numbers and Cauchy Products Review
Table of Contents
Double Series of Real Numbers and Cauchy Products Review
We will now review some of the recent material regarding double series of real numbers and Cauchy products.
On the Double Series of Real Numberswe said that if $(a_{mn})_{m,n=1}^{\infty}$ ... |
Moscow-Beijing topology seminar 报告人简介 2019-10-30
Title: Stringc structures
and modular invariants
Speaker: 黄瑞芝 Huang Ruizhi （中科院）
Abstract: Spin structure and
its higher analogies play important roles in index theory and mathematical
physics. In particular, Witten genera for String manifolds have nice geometric
implica... |
Weighted elliptic estimates for a mixed boundary system related to the Dirichlet-Neumann operator on a corner domain
School of Mathematics, Sun Yat-sen University, No.135 Xingangxi Road, Haizhu District, Guangzhou 510275, China
Based on the $ H^2 $ existence of the solution, we investigate weighted estimates for a mixe... |
Infinitely many segregated solutions for coupled nonlinear Schrödinger systems
Department of Mathematics, Zhejiang Normal University, Jinhua 321004, China
$ \left\{\begin{array}{ll} -\Delta u+(1+\delta a(x))u = \mu_1 u^3+\beta uv^2 &\mbox{in }\mathbb{R}^3,\\ -\Delta v+(1+\delta b(x))v = \mu_2 v^3+\beta u^2v &\mbox{in }... |
Standing waves for Schrödinger-Poisson system with general nonlinearity
1.
School of Mathematics and Statistics, Central South University, Changsha, 410083 Hunan, China
2.
School of Mathematics and Statistics, Hunan University of Technology and Business, Changsha, 410205 Hunan, China
$ \begin{eqnarray*} \left\{ \begin{... |
Probability Seminar Spring 2019 Thursdays in 901 Van Vleck Hall at 2:25 PM, unless otherwise noted. We usually end for questions at 3:15 PM.
If you would like to sign up for the email list to receive seminar announcements then please send an email to join-probsem@lists.wisc.edu
January 31, Oanh Nguyen, Princeton
Title:... |
It may be helpful to note that the event of interest can be modeled using a discrete random variable $X$: $X = i$ if $i$ of three dices result in the same number, $i = 0, 2, 3$. You are interested in determining $P[X = 2]$ (or perhaps $P[X = 2] + P[X = 3]$).
Taking $P[X = 2]$ for example, it can be computed as follows:... |
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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... |
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Search for new resonances in $W\gamma$ and $Z\gamma$ Final States in $pp$ Collisions at $\sqrt{s}=8\,\mathrm{TeV}$ with the ATLAS Detector
(Elsevier, 2014-11-10)
This letter presents a search for new resonances decaying to final states with a vector boson produced in association with a... |
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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 ... |
I post this answer to check my understanding.
Imagine a wavefunction in 1 dimensions with a known energy and momentum it's wavefunction will be:
$$\Psi(x, t) = e^{i(kx-\omega t)} = e^{i(px-E t)/\hbar}$$
With some calculus and algebra you can derive the momentum operator and get this:
$$-i\hbar \partial_x \Psi = p \Psi$... |
what important elements can relate to electrical resistance when considering about the resistance effect and force? i find some equations may be concerned,like the Ohm's law,R=V/I.V is voltage and I is currents.Also R=gL/A g is resistivity and L is length, A is cross section also how to measure the resistance in experi... |
Let
$$1 \longrightarrow K \longrightarrow G \longrightarrow Q \longrightarrow 1$$
be a short exact sequence of groups and let $M$ be a $\mathbb{Z}[G]$-module. The Hochschild--Serre spectral sequence in homology is of the form
$$E^2_{pq} = H_p(Q;H_q(K;M)) \Longrightarrow H_{p+q}(G;M).$$
All the sources I've consulted co... |
This harmonic oscillator suffers damping. Why is that? I don't
understand the mechanism of this damping.
The electron pair is an oscillating electric dipole, so it radiates energy according to the Larmor formula ${dE \over dt}\sim-|\ddot P|^2$ ($P$ is the magnitude of the polarisation). The total energy of the oscillat... |
panel-qtet.Rmd
The goal is to estimate the Quantile Treatment Effect on the Treated (QTET) which is given by
\[ F^{-1}_{Y_{1t}|D=1}(\tau) - F^{-1}_{Y_{0t}|D=1}(\tau) \]
for \(\tau \in (0,1)\) and where \(Y_{1t}\) are treated potential outcomes in period \(t\), \(Y_{0t}\) are untreated potential outcomes in period \(t\)... |
From Jacod and Shiryaev's Limit Theorems for Stochastic Processes, we get the following definitions.
Definitions: A process with independent increments (abbreviated PII) $X = (X_t)_{t \geq 0}$ on a stochastic basis $(\Omega, \mathcal{F}, \mathbb{F} = (\mathcal{F}_t)_{t \geq 0}, \mathbb{P})$ is a càdlàg adapted real-val... |
To directly answer the question: Simplex noise is patented, whereas Perlin noise is not. Other than that, Simplex noise has many advantages that are already mentioned in your question, and apart from the slightly increased implementation difficulty, it is the better algorithm of the two.I believe the reason why many pe... |
I have found a definition of phase margin of amplifier system from Texas Instruments application report. This definition looks like this:$$\phi = tan^{-1} (A \beta)$$where \$ A\$ is amplifiers open-loop gain (aka direct gain) and \$ \beta \$ is feedback return signal ratio - or \$ A \beta \$ known as
loop gain. Now, \$... |
Let $E$ be a set of finite outer measure and $F$ a collection of closed, bounded intervals that cover $E$ in the sense of Vitali. Show that there is a countable disjoint collection {${I_k}$}$_{k=1}^\infty$ of intervals in $F$ for which
$m$*$[E$~$\bigcup_{k=1}^{\infty}I_k] = 0$.
This is the same as the Vitali Covering L... |
The following is quoted from the Mathematical Reviews.
MR0544896 (80j:12002) Reviewed
Bhaskaran, M. Construction of genus field and some applications. J. Number Theory 11 (1979), no. 4, 488–497. 12A35 (12A65)
Let $k$ be a finite algebraic number field and $K$ its Hilbert class field, i.e., $K/k$ is maximally abelian su... |
The term divergence means a function $D$, which, given two probability distributions $P,Q$, assigns a non-negative real number $D(P,Q)$ such that $D(P,Q) = 0$ iff $P(x)=Q(x) \forall x$.
The relative entropy (or the Kullback-Leibler divergence) $$D_f(P,Q) = \sum_x P(x)\log\left(\frac{P(x)}{Q(x)}\right)$$ is a classical ... |
This is not a complete answer so far, I will come back completing it when time. Using results and notation from What is the moment generating function of the generalized (multivariate) chi-square distribution?, we can write$$ \| Y \|^2 = Y^T Y$$which we can write as a sum of $n$ independent scaled chisquare random vari... |
Partial Derivatives Examples 1
We will now look at some more examples of computing partial derivatives for functions of several variables. Be sure to review the Partial Derivatives page before hand! More examples can be found on the Partial Derivatives Examples 2 page.
Before we look at the following examples, it will ... |
In 2-space, a line can algebraically be expressed by simply knowing a point that the line goes through and its slope. This can be expressed in the form $y - y_0 = m(x - x_0)$. In 3-space, a plane can be represented differently. We will still need some point that lies on the plane in 3-space, however, we will now use a ... |
Recently I have seen that the Einstein-Hilbert action (eventually with the Gibbon-Hawkings boundary term) is not all in the description of spacetime. There can exist also various additional terms in the action that give information about the topology of the spacetime manifold. These terms are:
- A Pontryagin term ($S_{... |
In asset allocation, you usually send reports to your clients where you will report the volatility of its portfolio. Assuming you only have monthly returns, you will compute volatility over a considered period of $n$ months with the classic sample volatility estimate:
$$\sigma_s=\sqrt{\frac{1}{n-1} \sum_{i=1}^n (x_i-\b... |
Define a group homomorphism $\psi: G\to \Aut(N)$ by $\psi(g)(n)=gng^{-1}$ for all $g\in G$ and $n\in N$.We need to check:
The map $\psi(g)$ is an automorphism of $N$ for each $g\in G$.
The map $\psi$ is in fact a group homomorphism from $G$ to $\Aut(N)$.
The assumption that the orders of groups $G/N$ and $\Aut(N)$ are ... |
Metric Spaces Review
Metric Spaces Review
We will now review some of the definitions of a metric and a metric space and review some examples of metric spaces that we saw recently.
On the Metric Spacespage we first defined a special type of function on a set $M$ known as a Metricwhich is a function $d : M \times M \to [... |
Partial Derivatives Examples 2
We will now look at even more examples of computing partial derivatives for functions of several variables. Be sure to review the Partial Derivatives page beforehand! More examples can be found on the Partial Derivatives Examples 1 page.
Before we look at the following examples, it will b... |
Quotient Normed Linear Spaces
Let $(X, \| \cdot \|_X)$ be a normed linear space and let $M$ be a linear subspace of $X$. We ultimately want to turn $X / M$ into a normed linear space where:(1)
Where $x + M = \{ x + m : m \in M \}$.
We define addition of $x + M, y + M \in X/M$ by:(2)
And for all $\alpha \in \mathbb{R}$ ... |
This reduction is for average constrained CSMC to importance weighted binary classification. It is nearly identical to the filter tree reduction of unconstrained CSMC, with the addition that infeasible choices automatically lose any tournament they enter (if both entrants are infeasible, one is chosen arbitrarily). Bec... |
We first claim that there is a unique Sylow $11$-subgroup of $G$.Let $n_{11}$ be the number of Sylow $11$-subgroups in $G$.
By Sylow’s theorem, we know that\begin{align*}&n_{11}\equiv 1 \pmod{11}\\&n_{11}|21.\end{align*}By the first condition, $n_{11}=1, 12, 23 \cdots$ and only $n_{11}=1$ divides $21$.Thus, we have $n_... |
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Production of $K*(892)^0$ and $\phi$(1020) in pp collisions at $\sqrt{s}$ =7 TeV
(Springer, 2012-10)
The production of K*(892)$^0$ and $\phi$(1020) in pp collisions at $\sqrt{s}$=7 TeV was measured by the ALICE experiment at the LHC. The yields and the transverse momentum spectra $d^2 ... |
We all know it does mean revert. The question is why. What's making volatility mean-revert? Is it some sort of cyclical behaviour of option traders? The way it's calculated? Why?
Volatility is mean reverting if the underlying security doesn't drop to zero.
If the security has some underlying "value" then its price is c... |
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Production of Σ(1385)± and Ξ(1530)0 in proton–proton collisions at √s = 7 TeV
(Springer, 2015-01-10)
The production of the strange and double-strange baryon resonances ((1385)±, Ξ(1530)0) has been measured at mid-rapidity (|y|< 0.5) in proton–proton collisions at √s = 7 TeV with the ... |
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Now showing items 1-5 of 5
Measurement of electrons from beauty hadron decays in pp collisions at root √s=7 TeV
(Elsevier, 2013-04-10)
The production cross section of electrons from semileptonic decays of beauty hadrons was measured at mid-rapidity (|y| < 0.8) in the transverse momentum range 1 < pT <8 GeV/c wit... |
Unit Tangent Vectors to a Space Curve
Recall from the Derivatives of Vector-Valued Functions page that if $\vec{r}(t) = (x(t), y(t), z(t))$ is a vector-valued function defined for $t$ an the interval $I = [a, b]$ and is differentiable, then the derivative $\vec{r'}(t)$ gives us the tangent vector corresponding to each ... |
Consider the following Lagrangian for a massive vector field $A_{\mu}$ in Euclidean space time: $$\mathcal L = \frac{1}{4} F^{\alpha \beta}F_{\alpha \beta} + \frac{1}{2}m^2 A^{\alpha}A_{\alpha}$$ where $F_{\alpha \beta} = \partial_{\alpha}A_{\beta} - \partial_{\beta}A_{\alpha}$ which means $$\mathcal L = \frac{1}{4} (\... |
The expected boson occupation for a state with energy $\epsilon_j$ is given by
$$\langle n_j \rangle = \frac{1}{e^{\beta (\epsilon_j - \mu)}-1} = \frac{1}{z^{-1}e^{\beta\epsilon_j}-1} = \frac{z}{e^{\beta \epsilon_j}-z}$$
Here $\beta = \frac{1}{kT}$ and I have defined the fugacity $z=e^{\beta\mu}$ where $\mu$ is the che... |
We give two proofs. The first one uses Bays’ theorem and the second one simply uses the definition of the conditional probability.
Solution 1.
Let $E$ be the event that the first coin lands heads. Let $F$ be the event that at least one of two coins lands heads.By Bayes’ rule, the required probability can be calculated ... |
The Kernel of a Group Homomorphism
The Kernel of a Group Homomorphism
Definition: Let $(G, \cdot)$ and $(H, *)$ be two groups and let $f : G \to H$ be a group homomorphism. Let $e_2$ be the identity of $H$. Then the Kernel of $f$ is defined as the subgroup (of $G$) denoted $\mathrm{ker} (f) = f^{-1} ( \{ e_2 \} ) = \{ ... |
Sec 3.1 Introduction Equivalence Principle:
\(\quad\)
At every space-time point with arbitrary gravitational fields, there exists local(Inertial) frame with respect to which the laws of physics in a sufficiently small region takes the same form as in Mincowski space-time with no gravitational field. Sec 3.2 Motion in a... |
Functions that are Not Binary Operations
Recall from the Unary and Binary Operations on Sets page that if $S$ is a set then a function $f : S \times S \to S$ is said to be a binary operation and we must be specific in having that:
Each pair $(x, y) \in S \times S$ is mapped into $S$. $f(x, y)$ is defined. Each pair $(x... |
when you have a chiral superfield in the adjoint representation in your theory (i.e the Higgs $\Sigma_{24}$ in $SU(5)$), you can write it as a $5\times5$ Matrix: $(\Sigma_{24})_i^j=\Sigma^a (t^a)_i^j$ (sum over a), where the $t^a$ are the generatorns of the $SU(5)$.
My question is: is it possible that the $\Sigma_a$ ar... |
The goal is to remove the white line after the
1. in the second
enumerate in the picture, so it will look like the first
enumerate.
I don't like the first
enumerate because it uses inline math, needs the white line in the code to make a new paragraph, and uses
\displaystyle which I think is not the way to go: it feels ... |
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Measurement of electrons from beauty hadron decays in pp collisions at root √s=7 TeV
(Elsevier, 2013-04-10)
The production cross section of electrons from semileptonic decays of beauty hadrons was measured at mid-rapidity (|y| < 0.8) in the transverse momentum range 1 < pT <8 GeV/c wit... |
Upper and lower time decay bounds for solutions of dissipative nonlinear Schrödinger equations
1.
Department of Mathematics, Graduate School of Science, Osaka University, Osaka, Toyonaka 560-0043, Japan
2.
Department of Mathematics, College of Science, Yanbian University, No. 977 Gongyuan Road, Yanji City, Jilin Provin... |
It seems in the literature that there is a certain notion of a “macroscopic wavefunction” associated with a Bose-Einstein system (see this PSE answer) which exhibits a global $U(1)$-phase symmetry. After the BEC phase transition, this symmetry is supposedly broken corresponding to the sudden vanishing of the chemical p... |
Okay, so, in the traditional Bernoulli Urn problem, we have an urn with a number N, possibly infinite, of coloured balls, and there are k possible colours. That one I grok.
However, what if I don't actually
know what k is? That is, what if I have an urn with N balls and an unknown but finite and strictly positive numbe... |
Please reference this paper for notation in this question.
I'm trying to understand two claims made in the above paper (they may be related). First, in the construction of $\mathcal{H}_\lambda$ on page 4, we start with the usual irreducible representation $V_\lambda$ of the semisimple Lie algebra $\mathfrak{g}$, declar... |
In This MO question, Werner said that Hecke operator "changes" characters. I'm looking for any explicit theory of this kind, about Hecke operator with characters.
Actually, there are somewhat explicit example I found, for $\Gamma_{0}(4)$. Define $\chi:\Gamma_{0}(4)\to \mathbb{C}^{\times}$ as $\chi(T)=\chi(R)=e^{2\pi i/... |
Thompson, 1987, doesn't address this directly, but did consider an algorithm for specific configurations of the probabilities. He was looking for the worst case scenario when the bounds of error were not constant, and suggested a search over many configurations.
Here is my modification of Thompson's algorithm. This ver... |
I wish to plot the function $f(x)=\sin(\omega x).$ One property of this function is that it is periodic in $x$ with period $\frac{2 \pi}{\omega}$.
I wish to plot $f(x)$ in the region $x\in (-\frac{2\pi}{\omega},\frac{2\pi}{\omega})$, with ticks on $$-\frac{2\pi}{\omega},-\frac{3}{2}\frac{\pi}{\omega},-\frac{\pi}{\omega... |
Difference between revisions of "SageMath"
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== Installation ==
== Installation ==
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|the []
* {{Pkg|sagemath}} contains the command-line version;
* {{Pkg|sagemath}} contains the ... |
SM + W' and Z' at NLO in QCD Contact Authors
Benjamin Fuks
LPTHE - CNRS - UPMC (Paris VI) fuks AT lpthe.jussieu.fr
Richard Ruiz
Universite Catholique de Louvain (CP3) richard.ruiz AT uclouvain.be Model Description
This effective model extends the Standard Model (SM) field content by introducing the massive vector field... |
The offset tree is a reduction from cost-sensitive multiclass classification (CSMC) with partial feedback to binary classification. It is designed for when there is a single decision amongst a fixed set of classes (like vanilla CSMC) and historical data where only the value of the decision chosen has been revealed (unl... |
Motivation: As is stated in the former post, a left ideal $I$ of a maximal order $\mathcal{O}$ in a quaternion algebra ramified at $p$ ($p$ is a prime) and $\infty$ can be used to construct modular form $\theta_I$ of weight 2 with Fricke eigenvalue $-1:$
$$\theta_I(\tau)=\sum_{x\in I}e^{2\pi i\tau\frac{N(x)}{N(I)}}$$ O... |
In the standard GARCH(1,1) model with normal innovations
$\sigma^2_t=\omega+\alpha\epsilon^2_{t-1}+\beta\sigma^2_{t-1} $
the likelihood of $m$ observations occurring in the order in which they are observed is
$\sum_{t=1}^m\left[-\ln(\sigma^2_{t})-{\left(\frac{\epsilon^2_{t}}{\sigma^2_{t}}\right)}\right] $
This expressi... |
Say we've previously used a neural network or some other classifier C with $N$ training samples $I:=\{I_1,...I_N\}$ (that has a sequence or context, but is ignored by C) the, belonging to $K$ classes. Assume, for some reason (probably some training problem or declaring classes), C is confused and doesn't perform well. ... |
Let $(T_t)$ be a strongly continuous semigroup of positive operators on $C(K)$, where $K$ is a compact space. Assume also that $T_t1 =1 $ for every $t\geq 0$. (This is also called a Feller Semigroup.)
Since $K$ is compact we know that there exists a probability measure $\mu$ on $K$ satisfying $\mu T^*_t = \mu $ for eve... |
Well there are problems in your question and analysis. First off, there have been a few SE questions recently about this "Keplerian" treatment of dark matter. The shell theorem, that the gravitational field is the equivalent of that due to the mass inside radius $r$, and that exterior masses can be ignored is
only true... |
The following is another solution that uses "analytic geometry," at a lower level of technical sophistication. The downside is that the equations look uglier and less structured than they could be.
We will use the not very hard to prove fact that if a line has equation $ax+by+c=0$,then the perpendicular distance from $... |
Table of Contents
Basic Theorems on the Composition of Two Functions
Recall from The Composition of Two Functions page that if $f : A \to B$ and $g : B \to C$ are functions then the composition of $f$ and $g$ is the function $g \circ f : A \to C$ defined for all $x \in A$ by $(g \circ f)(x) = g(f(x))$.
On that page, we... |
A bijective ring homomorphism is called an isomorphism.
If there is an isomorphism from $R$ to $S$, then we say that rings $R$ and $S$ are isomorphic (as rings).
Proof.
Suppose that the rings are isomorphic. Then we have a ring isomorphism\[f:2\Z \to 3\Z.\]Let us put $f(2)=3a$ for some integer $a$. Then we compute $f(4... |
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What is the slope of the curve 8x2+5y2=r2 8x^2 + 5y^2 = r^28x2+5y2=r2 (where r≠0)r \neq 0)r=0) at a point (x1,y1) (x_{1}, y_{1}) (x1,y1) that lies on the curve?
What is the slope of the tangent line of the curve x2=y2 x^2 = y^2 x2=y2 at the point (15,−15)? (15, -... |
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