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I've been working with proofs involving $\limsup$ and $\liminf$, and I'm a bit confused regarding their general methodology. More specifically, I'm unsure about whether my approach to the following problem makes sense.
Problem. Let $(s_n)$ and $(t_n$) be sequences and suppose that there exists $N_0$ such that $s_n \leq... |
Contents ECE301 Fall 2008, Professor C.C. Wang Use this area to post your questions
I am trying to figure out how to compute the norm of the DT signal $ x[n]= e^{j 2 \pi n} $. According to the solutions, the answer is
$ \left| e^{j 2 \pi n} \right| = 1 $.
I don't get it. Should'nt the answer be a function of n???
Respo... |
Spring 2018, Math 171 Week 8 Exponential Distribution
Let \(X \sim \mathrm{exp}(\lambda)\).
Find the distribution of \(Y = \lceil X \rceil\)
(Answer) \(\mathrm{geometric}(1-e^{-\lambda})\)
Show that \(X\) and \(Y\) are both memoryless
Find the distribution of \(\beta X\)
(Answer) \(\mathrm{exponential}(\lambda/\beta)\)... |
Decide if the series $$\sum_{n=1}^\infty\frac{4^{n+1}}{3^{n}-2}$$ converges or diverges and, if it converges, find its sum.
Is this how you would show divergence attempt:
For $n \in [1,\infty), a_n = \frac{4^{n+1}}{3^n -2} \geq 0$
For $n \in [1,\infty), a_n = \frac{4^{n+1}}{3^n-2} \geq \frac{4^{n+1}}{3^n} = b_n$
Since ... |
Simulating Nonlinear Sound Propagation in an Acoustic Horn
When modeling acoustic devices, it’s often enough to account for linear propagation alone, even though nonlinearities are always present. However, when the signaling amplitude reaches high levels in a design, nonlinear effects become important. Engineers can in... |
I have the following partial differential equation:
I'm asked to prove that if $f\equiv 0$, then the total energy (kinetic energy + potential energy) of the system decreases with time.
What is the expression for the energy of this system? I know what the expression of energy is for parabolic or hyperbolic partial diffe... |
Here is
a reason.
The fourth of Maxwell's macroscopic equations says that$$ \nabla \times \vec{H} = \vec{J} +\frac{\partial \vec{D}}{\partial t},$$where $\vec{J}$ is the free current at a point. In general, it
is not possible to rewrite this in terms of B-field without a detailed knowledge of the microscopic behaviour ... |
Vector Cross Product
The dot product discussed in the previous section, was introduced through the requirement that arose in calculating the work done by a given force \(\vec F\) when the point of application of the force is displaced by a certain amount given by \(\vec s\) :
\[W = \vec F \cdot \vec s\]
In this section... |
Occupation Methods¶
This document explains and compares the different occupation methods availablein
ATK. We suggest these guidelines for choosing the occupationmethod, depending on the system of interest: Systems with a band-gap(semiconductors, insulators, molecules): Use either Fermi-Diracor Gaussiansmearing with a l... |
The ShiftRegister PWM Library enables usage of shift register pins as pulse-width modulated (PWM) pins. Instead of setting them to either high or low, the library lets the user set them to up to 256 PWM-levels. This post serves as a documentation page for the library and is to be extended over time.
Getting Started
In ... |
Polar or Distance Form of a Straight Line Equation \(\textbf{Art 10 :} \qquad \boxed{{\text{Polar / Distance form of a line}}}\)
Sometimes, it is very convenient to write the equation of a straight line in polar / distance form. Suppose we know that the line passes through the fixed point \(P(h,\,k)\) and is at an incl... |
Complex number
A complex number is a number of the form $z=x+iy$, where $x$ and $y$ are real numbers (cf. Real number) and $i=\def\i{\sqrt{-1}}\i$ is the so-called imaginary unit, that is, a number whose square is equal to $-1$ (in engineering literature, the notation $j=\i$ is also used): $x$ is called the real part o... |
Malonic acid is used in the manufacture of barbiturates (sleeping pills). The composition of the acid is 34.6% C, 3.9% H, and 61.5% O. What is malonic acid’s empirical formula?
Solution: Assume a sample size of 100 g to make the math easier. Thus, we will assume there is a 100 g sample of malonic acid. Now, we will cal... |
It would be extremely unlikely.
A typical bacteria is about 1 µm diameter - they come in all kinds of shapes, but let's assume a "spherical bacteria" (this is the microscopic equivalent of the spherical cow).
The drag force depends on the Reynolds number. Recall that
$$\rm{Re} = \frac{u\ell}{\nu}$$
Where $u$ is the vel... |
Huge cardinal Huge cardinals (and their variants) were introduced by Kenneth Kunen in 1972 as a very large cardinal axiom. Kenneth Kunen first used them to prove that the consistency of the existence of a huge cardinal implies the consistency of $\text{ZFC}$+"there is a $\omega_2$-saturated $\sigma$-ideal on $\omega_1$... |
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... |
The affine evaluation map is a surjective homomorphism from the quantumtoroidal ${\mathfrak {gl}}_n$ algebra ${\mathcal E}'_n(q_1,q_2,q_3)$ to thequantum affine algebra $U'_q\widehat{\mathfrak {gl}}_n$ at level $\kappa$completed with respect to the homogeneous grading, where $q_2=q^2$ and$q_3^n=\kappa^2$. We discuss ${... |
I am working thru a derivation of the group velocity formula and I get to this stage: $$y=2A\cos(x\frac{\Delta K}{2} -t\frac{\Delta \omega}{2})\sin( \bar k x-\bar \omega t)$$ Then all the derivations I have seen say that $\frac{\Delta \omega}{\Delta K} $ is the group velocity. I know mathematically why this is a veloci... |
Fit Point Process Model Involving Irregular Trend Parameters
Experimental extension to
ppm which finds optimal values of the irregular trend parameters in a point process model.
Usage
ippm(Q, …, iScore=NULL, start=list(), covfunargs=start, nlm.args=list(stepmax=1/2), silent=FALSE, warn.unused=TRUE)
Arguments Q,…
Argume... |
In mathematics, solving linear equations is one of the important topics. We can say concept of linear equations is the base of advance algebra. Many students are scared of math and this anxiety should be the first thing that needs to be fixed as soon as possible. Many times students are afraid of asking any question re... |
The average wavenumber for a ketone is about $\pu{1720 cm-1}$ and the average wavenumber for an ester is about $\pu{1740 cm-1}$. This, however, does not make sense, as the carbonyl group of an ester should have a greater single bond character than the ketone due to resonance from the adjacent oxygen atom. This greater ... |
I'm currently reading Quantum Computation and Quantum Information by Nielsen. I'm struggling to solve exercise 2.58. The problem is
Suppose we prepare a quantum system in an eigenstate $|\psi\rangle$ of some observable $M$, with corresponding eigenvalue m. What is the average observed value of $M$, and the standard dev... |
A set of linear equations with two or more variables having degree one. Before we go in details it is also recommended to have a look on other form of linear equations like linear equations with one variable and with two variables and so on. System of linear equation is one the most prominent topics in algebra. In this... |
Does anyone here understand why he set the Velocity of Center Mass = 0 here? He keeps setting the Velocity of center mass , and acceleration of center mass(on other questions) to zero which i dont comprehend why?
@amanuel2 Yes, this is a conservation of momentum question. The initial momentum is zero, and since there a... |
Why All These Stresses and Strains?
In structural mechanics you will come across a plethora of stress and strain definitions. It may be a
Second Piola-Kirchhoff Stress or a Logarithmic Strain. In this blog post we will investigate these quantities, discuss why there is a need for so many variations of stresses and stra... |
I am trying to solve the 8-puzzle using two heuristics, which are: Pieces out of place and Distance Manhattan. After consulting several websites for example see and some books, I'm with some doubts, ...
I am trying to write my own Allan Deviation calculator in Mathematica using the definition,$$\sigma(\tau)^{2}=\frac{1... |
Difference between revisions of "Lower attic"
From Cantor's Attic
Line 7: Line 7:
* [[Gamma | $\Gamma$]]
* [[Gamma | $\Gamma$]]
* [[Church-Kleene omega_1 | $\omega_1^{ck}$]]
* [[Church-Kleene omega_1 | $\omega_1^{ck}$]]
−
* [[epsilon0#
+
* [[epsilon0#| $\$]] [[epsilon0#| $\$ ]]
− +
* [[epsilon0 | $\epsilon_0$]]
* [[eps... |
Difference between revisions of "Lower attic"
From Cantor's Attic
m (removing superfluous bullet points)
Line 17: Line 17:
* the [[Feferman-Schütte]] ordinal [[Feferman-Schütte | $\Gamma_0$]]
* the [[Feferman-Schütte]] ordinal [[Feferman-Schütte | $\Gamma_0$]]
* [[epsilon naught | $\epsilon_0$]] and the hierarchy of [[... |
DFT-1/2 and DFT-PPS density functional methods for electronic structure calculations¶ Version: 2017.0
The 2017 release of QuantumATK introduces two novel density functional corrections for computing the electronic structure semiconductors and insulators: the DFT-1/2 and pseudopotential projector shift (DFT-PPS) methods... |
Spring 2018, Math 171 Week 9 Miscillaneous Poisson Process Problems
Let \(X_1, X_2, \dots\overset{\mathrm{i.i.d}}{\sim} \mathrm{exp}(\lambda)\), and let \(N(t)\) be a poisson process with rate \(\lambda\)
Show the equality \(P(\sum_{i=1}^n X_i \le t) = P(N(t) \ge n)\)
Find an analogous equality for \(P(s \le \sum_{i=1}... |
Difference between revisions of "Kunen inconsistency"
Line 43: Line 43:
Although the existence of Reinhardt cardinals has now been refuted in ZFC and GBC, the term is used in the ZF context to refer to the critical point of a nontrivial elementary embedding $j:V\to V$ of the set-theoretic universe to itself.
Although t... |
Suppose $f,\omega:{\bf R}\to{\bf R}$ are functions with $\omega(0)=0$. Suppose for some $\alpha>1$, we have $$ f(b)\leq f(a)+\omega(|b-a|)^\alpha\quad\hbox{for all } a,b\in{\bf R}\tag{*} $$ If $\omega$ is differentiable at $x=0$, show that $f\in C^\infty({\bf R})$.
The original problem is given as follows:
I think $\om... |
Neurons (Activation Functions)¶
Neurons can be attached to any layer. The neuron of each layer will affect the output in the forward pass and the gradient in the backward pass automatically unless it is an identity neuron. Layers have an identity neuron by default [1].
class
Neurons.
Identity¶
An activation function th... |
Search
Now showing items 1-6 of 6
Forward-backward multiplicity correlations in pp collisions at √s = 0.9, 2.76 and 7 TeV
(Springer, 2015-05-20)
The strength of forward-backward (FB) multiplicity correlations is measured by the ALICE detector in proton-proton (pp) collisions at s√ = 0.9, 2.76 and 7 TeV. The measurement... |
Basis Of A Three Dimensional Space
In the preceeding discussion, we talked about the basis of a plane. We can easily extend that discussion to observe that
any three non-coplanar vectors can form a basis of three dimensional space:
In other words, any vector \(\vec r\) in 3-D space can be expressed as a linear combinat... |
Medium Affects Wavelength
We have already discussed that the speed of a wave is determined by the medium, and this is true for the speed of light as well. Recall that the frequency of a wave is set by the source, so the frequency of a wave does not change as it travels into a new medium. This is true also for light wav... |
We introduce the notion of a symplectic capacity relative to a coisotropicsubmanifold of a symplectic manifold, and we construct two examples of suchcapacities through modifications of the Hofer-Zehnder capacity. As aconsequence, we obtain a non-squeezing theorem for symplectic embeddingsrelative to coisotropic constra... |
let $k$ is postive integer,and for any postive integer $n\ge 2$,
show that: $$\left[\dfrac{n}{\sqrt{3}}\right]+1>\dfrac{n^2}{\sqrt{3n^2-5}}>\dfrac{n}{\sqrt{3}}$$
where $[x]$ is the largest integer not greater than $x$
Let $q_n = \left\lfloor \frac{n}{\sqrt{3}}\right\rfloor + 1$. When $n \ge 11\sqrt{3}$, we have
$$\frac... |
$$\sum_{i=1}^n \frac1{4i-1}$$
I know I have to integrate the function but from what to find lower and upper bound.
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It only takes a minute to sign up.Sign up to join this community
It sound... |
The first question to answer: which matrices satisfy $A^2 = I$ and $\det(A) = 1$?
It suffices to note that since $A^2 - I = 0$, the minimal polynomial of $A$ must divide $x^2 - 1 = (x-1)(x + 1)$. Hence, $A$ must be diagonalizable with eigenvalues equal to $\pm 1$. Moreover, since the product of eigenvalues is equal to ... |
Your comments indicate that you are dubious about iterating operations on ordinals more than finitely many times, and very dubious about iterating them uncountably many times.
This is a fundamental point in set theory. The danger is in thinking of recursive definitions as processes which need to be carried out, in whic... |
Hi everyone I'd like to know if the following is correct and if someone knows a better way to do it.
Definition Let $x>0$ be a real, and $\alpha$ be a real number. We define the quantity $x^{\alpha}$, by the formula $\text{lim}_{n\rightarrow\infty} x^{q_n}$ where $(q_n)$ is a sequence of rationals which converges to $\... |
On a question on this site there is an explanation of the algorithm Knuth gives in
The Art Of Computer Programming to compute an approximation of $y = \log_bx$.
Now, I understand why it works; anyway, the only question arising in my mind is: how can we pre-compute a table of logarithms with arguments of the type $\frac... |
Today we will apply the ideas of the others post by a simple example. Before, we are going to answer the question of the last week.
What is exactly the $latex {h_{opt}}&fg=000000$ if we assume that
$latex \displaystyle \displaystyle f(x) = \frac{1}{\sqrt{2\pi}} \text{exp}\left(\frac{-x^2}{2}\right)? &fg=000000$
How $la... |
Bharadwaj, BVS and Chandran, LS and Das, Anita (2008)
Isoperimetric Problem and Meta-fibonacci Sequences. In: 14th Annual International Conference on Computing and Combinatorics (COCOON 2008), JUN 27-29, 2008, Dalian.
PDF
fulltext.pdf - Published Version
Restricted to Registered users only
Download (453kB) | Request a ... |
Hello one and all! Is anyone here familiar with planar prolate spheroidal coordinates? I am reading a book on dynamics and the author states If we introduce planar prolate spheroidal coordinates $(R, \sigma)$ based on the distance parameter $b$, then, in terms of the Cartesian coordinates $(x, z)$ and also of the plane... |
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... |
Given an expression
$\chi\,=\,C_{p1}\,\left[ h\,e^{- i\,p1.\,x}\,\, +\,\,h^{\dagger}\,e^{+i\,p1\,.\,x}\right]$
where $p1$ and $x$ are four-vectors; $C_{p1} = \ \frac{1}{\sqrt{(2 \pi)^3} \sqrt{2 \omega\,(p1,\ m)}}$, and $x\ .\ p1\ =\omega(p_1,m)\,t\ - {\vec p1} {\vec x}$
Please note that "$x$" and "$\chi$" are different... |
Discussion on International Mathematical Olympiad (IMO)
Here we'll talk about IMO level problems.
Rules: 1. You can post any 'math-problem' from anywhere if you are sure it has a solution. Also you should give the source.(Like book name, link or self-made) 2. If a problem remains unsolved for two days, the proposer mus... |
Thermodynamic property relations From Thermal-FluidsPedia
Line 1: Line 1:
For a single-component closed system (fixed mass), the first law of thermodynamics gives us:
For a single-component closed system (fixed mass), the first law of thermodynamics gives us:
-
<center><math>d\hat E = \delta Q - \delta W\qquad \qquad( ... |
A C*-dynamical system is said to have the ideal separation property if everyideal in the corresponding crossed product arises from an invariant ideal inthe C*-algebra. In this paper we characterize this property for unitalC*-dynamical systems over discrete groups. To every C*-dynamical system weassociate a "twisted" pa... |
Consider a real scalar field $\phi$ in a theory with a Lagrangian $$ \mathcal{L}:=-\frac{1}{2}\partial _\mu \phi \partial ^\mu \phi -V(\phi ), $$ where $$ V(\phi ):= -\mu ^2\phi ^2+\frac{\lambda}{4!}\phi ^4, $$ where both $\mu$ and $\lambda$ are positive real numbers.
We see that the potential has a couple of non-zero ... |
[OS X TeX] Missing $ inserted in a "variations" environment Ross Moore ross at ics.mq.edu.au Sun Mar 15 22:13:11 CET 2009 Hi Alain,
On 16/03/2009, at 7:56 AM, Alain Schremmer wrote:
> On Mar 15, 2009, at 4:24 PM, Peter Dyballa wrote:
>
>> discipline like you demonstrated
>
> You really ought NOT to make fun of your eld... |
The modern understanding of forces and the detailed relation of forces to motion was worked out by Newton and summarized in what has become known as “Newton's Laws of Motion” We have already spent considerable time making sense of Newton’s first and third laws, which are really part of our understanding of forces. The ... |
Introduction
The cross validation is a common technique to calibrate the binwidth histogram. They are the simplest and, sometimes, the most effective tool to describe the density of some dataset.
As usual, suppose you have a independent and identically distributed random sample $X_1, X_2, \ldots X_n$ from some unknown ... |
April 12th, 2016, 10:11 PM
# 1
Senior Member
Joined: Apr 2008
Posts: 194
Thanks: 3
How can I find the two missing solutions?
Solve tan(2x) = cot(x) for 0 x<
This is how I do it.
=
After doing some algebra, I get the equation below.
=
Next, I square root both sides and get two equations.
tan(x) = and tan(x) =
-
The refe... |
Construction of formula in Sagemath program
Let $P_k:= \mathbb{F}_2[x_1,x_2,\ldots ,x_k]$ be the polynomial algebra in $k$ variables with the degree of each $x_i$ being $1,$ regarded as a module over the mod-$2$ Steenrod algebra $\mathcal{A}.$ Here $\mathcal{A} = \langle Sq^{2^m}\,\,|\,\,m\geq 0\rangle.$
Being the coho... |
February 22nd, 2018, 03:50 PM
# 1
Senior Member
Joined: Apr 2017
From: New York
Posts: 155
Thanks: 6
Integration By Parts
Hi guys. Can somebody explain me only the last line ( in red frame). how did the last line shape just after the previous one.
I know the topic well just didn't get that algebra part of ln transforma... |
Symbols:Greek Contents
The $1$st letter of the Greek alphabet.
Minuscule: $\alpha$ Majuscule: $\Alpha$
The $\LaTeX$ code for \(\alpha\) is
\alpha .
The $\LaTeX$ code for \(\Alpha\) is
\Alpha .
The $2$nd letter of the Greek alphabet.
Minuscule: $\beta$ Majuscule: $\Beta$
The $\LaTeX$ code for \(\beta\) is
\beta .
The $\... |
New option
Wavefront/Taper analysis is implemented. The new option allows you to estimate the influence of inhomogeneities of the deposition on the spectral characteristics and on the wavefront of the reflected/transmitted wave. The option is available at Analysis -->More-->Wavefront/Taper
Phase computations include to... |
In "Entropy in Black Hole Pair Production" (arXiv:gr-qc/9306023), Strominger
et al. notes
The issue of whether (1.2) can be taken literally has bearing on the vexing question of what happens to information cast into a black hole. If one assumes that (1.2) counts all the black hole states, and that information is preser... |
Definition:Zero Vector Definition
Let $\struct {R, +_R, \times_R}$ be a ring.
Let $\struct {G, +_G}$ be an abelian group.
Let $\struct {G, +_G, \circ}_R$ be an $R$-module.
The identity of $\struct {G, +_G}$ is usually denoted $\mathbf 0$, or some variant of this, and called the zero vector.
Note that on occasion it is ... |
Authors Index,
Methods Funct. Anal. Topology
16 (2010), no. 4, 289-290
Methods Funct. Anal. Topology
16 (2010), no. 2, 112-119
In this paper we introduce the generalized continuous version of fusion frame, namely $gc$-fusion frame. Also we get some new results about Bessel mappings and perturbation in this case.
On mix... |
amp-mathml
Displays a MathML formula.
Required Script
<script async custom-element="amp-mathml" src="https://cdn.ampproject.org/v0/amp-mathml-0.1.js"></script>
Supported Layouts container Examples amp-mathml.amp.html Behavior
This extension creates an iframe and renders a MathML formula.
Example: The Quadratic Formula ... |
Authors Index,
Methods Funct. Anal. Topology
16 (2010), no. 4, 289-290
Methods Funct. Anal. Topology
16 (2010), no. 2, 112-119
In this paper we introduce the generalized continuous version of fusion frame, namely $gc$-fusion frame. Also we get some new results about Bessel mappings and perturbation in this case.
On mix... |
I’m working on a mobile application to help technician to make inspections. They have a lot of question for each task, each question is about an item inspection. When the answer is positive no additional action is required (80% of cases).
But when the answer is No, he has to identify the anomaly so I show a new page wi... |
Authors Index,
Methods Funct. Anal. Topology
16 (2010), no. 4, 289-290
Methods Funct. Anal. Topology
16 (2010), no. 2, 112-119
In this paper we introduce the generalized continuous version of fusion frame, namely $gc$-fusion frame. Also we get some new results about Bessel mappings and perturbation in this case.
On mix... |
ISSN:
1078-0947
eISSN:
1553-5231
All Issues
Discrete & Continuous Dynamical Systems - A
January 1999 , Volume 5 , Issue 1
Select all articles
Export/Reference:
Abstract:
This paper deals with various applications of two basic theorems in order- preserving systems under a group action -- monotonicity theorem and converg... |
In the course of some physics research I've been working on, a very annoying integral has appeared that I'm having difficulty evaluating numerically. Any help you could offer would be greatly appreciated. The integral to be evaluated is as follows:
$$ \int_{0}^{\infty}d\omega\int_{-\infty}^{\infty}(dk_{x})k_{x}\frac{e^... |
The voltage across an element is 12e^{-2t} V. The current entering the positive terminal of the element is 2e^{-2t} A. Find the energy absorbed by the element in 1.5 s starting from t = 0.
Solution:
The energy absorbed can be found by:
(Where W is energy absorbed, v is voltage, t is time, and i is current)
Substitute o... |
Authors Index,
Methods Funct. Anal. Topology
16 (2010), no. 4, 289-290
Methods Funct. Anal. Topology
16 (2010), no. 2, 112-119
In this paper we introduce the generalized continuous version of fusion frame, namely $gc$-fusion frame. Also we get some new results about Bessel mappings and perturbation in this case.
On mix... |
Would it be correct to characterize loop invariants as a type of tautology? I ask since the invariant must basically always be true, before the loop starts, before each iteration and after the loop terminates. I realize that there is the possibility that the invariant could become false during the body of the loop. But... |
DynamicalMatrix¶ class
DynamicalMatrix(
configuration, filename, object_id, calculator=None, repetitions=None, atomic_displacement=None, acoustic_sum_rule=None, finite_difference_method=None, constraints=None, constrain_electrodes=None, use_equivalent_bulk=None, max_interaction_range=None, force_tolerance=None, process... |
This is really just an expansion of Michael Brown's comment.
Let's say someone hands us
any two quantum systems described by Hilbert spaces $\mathcal H_1$ and $\mathcal H_2$. Then we might be curious to know how we can write down an interaction Hamiltonian for these systems. This includes, as a subcase, systems consist... |
It is generally known that 'jumps' in frequency data are difficult to estimate. In the current literature, many different techniques for estimating such jumps have been tested and often with satisfactory results. A summarizing paper about some of these techniques would be, for example, Riley, 2008.
However, all these t... |
Some Advances in Sidorenko’s Conjecture
2014/09/04 *Thursday* 4PM-5PM
Room 1409
Sidorenko’s conjecture states that for every bipartite graph \(H\) on \(\{1,\cdots,k\}\)
\begin{eqnarray*} \int \prod_{(i,j)\in E(H)} h(x_i, y_j) d\mu^{|V(H)|} \ge \left( \int h(x,y) \,d\mu^2 \right)^{|E(H)|} \end{eqnarray*} holds, where \(... |
I'm concerned with equation 2.24 of http://arxiv.org/abs/1601.00482
The superconformal hypermultiplets in this paper have a conic hyperkahler target manifold and the authors want to gauge some isometries of this manifold. Letting the isometry group be $G$ and to have an associated Lie algebra $\mathfrak{g}$ generated b... |
Evaluation of color characteristics
OptiLayer provides calculations of color properties in almost all existing color coordinate systems. You can view color coordinates in a graphical or tabular forms. Light source, detector, observer, integration step, reference white and incident angle used for color evaluation are sp... |
Question:
As the homogenous cylinder of mass
m enter the cylindrical surface, the velocity of its center is 1.5 m/s. Determine the angle {eq}\theta {/eq} at which the cylinder will come to a momentary stop. Assume that the cylinder rolls without slipping. Conservation of energy:
It states that for a body in linear or r... |
Spring 2018, Math 171 Week 10 Poisson Process Conditioning
Let \(N(t)\) be a Poisson process with rate \(\lambda\). Fix \(0 \le n\), \(s \le t\).
Compute \(\mathbb{P}(N(s)=m \mid N(t) = n)\) for \(m \le n\). Give the name and parameters of the distribution.
(Answer) Binomial(\(n,\frac{s}{t}\))
Compute \(\mathbb{E}[N(s)... |
The spectral distribution $f(\omega)$ of a stationary time series$\{Y_t\}_{t\in\mathbb{Z}}$ can be used to investigate whether or not periodicstructures are present in $\{Y_t\}_{t\in\mathbb{Z}}$, but $f(\omega)$ has somelimitations due to its dependence on the autocovariances $\gamma(h)$. Forexample, $f(\omega)$ can no... |
Learning Objectives
Given the linear kinematic equation, write the corresponding rotational kinematic equation Calculate the linear distances, velocities, and accelerations of points on a rotating system given the angular velocities and accelerations
In this section, we relate each of the rotational variables to the tr... |
Inhibitory competition plays a critical role in enabling us to focus on a few things at a time, which we can then process effectively without getting overloaded. Inhibition also ensures that those detectors that do get activated are the ones that are the most excited by a given input -- in Darwinian evolutionary terms,... |
Denote $\varSigma_1$ and $\varSigma_2$ your matrices both of dimension $p$.
Cond number:$\log(\lambda_1)-\log(\lambda_p)$ where $\lambda_1$ ($\lambda_p$) is the largest (smallest) eigenvalue of $\varSigma^*$, where $\varSigma^*$ is defined as:$\varSigma^*:=\varSigma_1^{-1/2}\varSigma_2\varSigma_1^{-1/2}$
Edit: I edited... |
The theory of quasifree quantum stochastic calculus for infinite-dimensionalnoise is developed within the framework of Hudson-Parthasarathy quantumstochastic calculus. The question of uniqueness for the covariance amplitudewith respect to which a given unitary quantum stochastic cocycle is quasifreeis addressed, and re... |
Does anyone here understand why he set the Velocity of Center Mass = 0 here? He keeps setting the Velocity of center mass , and acceleration of center mass(on other questions) to zero which i dont comprehend why?
@amanuel2 Yes, this is a conservation of momentum question. The initial momentum is zero, and since there a... |
Buckling, When Structures Suddenly Collapse
Buckling instability is a treacherous phenomenon in structural engineering, where a small increase in the load can lead to a sudden catastrophic failure. In this blog post, we will investigate some classes of buckling problems and how they can be analyzed.
What Is Buckling?
H... |
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... |
I'm given series $\sum_{n = 1}^{+\infty} \frac{(-1)^{n}}{(n+1)!}\left(1 + 2! + \cdots + n!\right)$ and I have to find whether it is convergent.
Testing for absolute convergence, we have $a_n = \frac{1}{(n+1)!} + \frac{2}{(n+1)!} + \cdots + \frac{(n-1)!}{(n+1)!} + \frac{n!}{(n+1)!}$ and since last term is $\frac{n!}{(n+... |
Magnitudes Direction Cosines And Direction Ratios Of Vectors MAGNITUDE, DIRECTION COSINES AND DIRECTION RATIOS
Consider a vector
\[\vec r = x\hat i + y\hat j + z\hat k\]
as shown in the figure below:
The magnitude or \(\vec r\) is simply the length of the diagonal of the cuboid whose sides are
x, y and z. Thus
\[\left|... |
What is Uniform Distribution
A continuous probability distribution is a
Uniform distribution and is related to the events which are equally likely to occur. It is defined by two parameters, x and y, where x = minimum value and y = maximum value. It is generally denoted by u(x,y).
OR
If the probability density function ... |
I think all the other answers do a better job at exactly replicating the original image than what I am going to share, but my main intention here is to provide some exposition and show the utility in a particular coordinate transformation that naturally results in graphics having similar properties to the original imag... |
Material objects consist of charged particles. An electromagnetic wave incident on the object exerts forces on the charged particles, in accordance with the Lorentz force. These forces do work on the particles of the object, increasing its energy, as discussed in the previous section. The energy that sunlight carries i... |
I am very confused with the meaning of Fermi sphere. I understand that it is exactly the same as the energy levels and Fermi energy in the real space and Fermi sphere is in K space but I don't know why is this important. What I have understood is the relation of Fermi sphere and real energy level is similar to that of ... |
I am self-studying models for financial economics and encountered the following problem:
I don't see how the author can conclude that $\gamma = -0.62$. Let's rearrange the second to last equation: $$\gamma - r = -4(0.19 - r)$$ as
$$r = \frac{\gamma + 0.76}{5}.$$
If $\gamma = 0.62$, then $r = 0.276.$
If $\gamma = -0.62$... |
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That's a
great question ! What you are asking about is one of the missing links between classical and quantum gravity.
On their own, the Einstein equations are local field equations:
$$ G_{\mu\nu} = 8 \pi G T_{\mu\nu} $$
and do not contain any topological information. At the level of the action principle:
$$ S_{eh} = \... |
As proved by Euler, the value of any infinite continued fraction is an irrational number. Just as every finite continued fraction is a rational number, every infinite continued fraction represents an irrational number.
We consider the class of irrational numbers of the form \(√n\), where \(√n\) is any non-square positi... |
Global existence of weak solution in a chemotaxis-fluid system with nonlinear diffusion and rotational flux
1.
School of Mathematics, Southeast University, Nanjing 210096, China
2.
Institute for Applied Mathematics, School of Mathematics, Southeast University, Nanjing 211189, China
$\begin{eqnarray*} \left\{\begin{arra... |
MLE vs. MAP Table of Contents
import numpy as npimport scipy as sp
import seaborn as snsfrom matplotlib import pyplot as plt%matplotlib inline
Motivation
While I am happily (and painfully ) learning mean field variational inference, I suddenly found that I am not 100% sure about the differences between maximum likeliho... |
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