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There is the instantaneous force between the mass and the scales, and then there's the reading of the scales. Factors influencing both of these depend on many unknown factors - so here are just some general thoughts.
First, if you drop a mass $M$ from height $h$ onto scales with mass $m$, and the two will then move as ... |
Need help solving the problem $\tan(\tan^{-1}(\frac{2}{5}))$ using inverse functions without the use of a calculator, I have no idea how to use $\frac{2}{5}$ as I am only familiar with numbers on the unit circle.
Think about what the inverse tangent function is.
In English:
$\tan^{-1} x$ takes an input number $x$ and r... |
In the following, $x$ runs in the interval $J=[-1,1]$.We introduce the functions of $x\in J$$$\begin{aligned}A(x) &= \sqrt{58-42 x}\ ,\\B(x) &= \sqrt{149-140\sqrt{ 1-x^2}}\ .\\&\qquad\text{Then we have }\\10^2(58-A^2)^2 + 3^2(149-B^2)^2 &= 420^2\ .\end{aligned}$$So we can formulate an equivalent problem:
Minimize $a+b$... |
I try to calculate the gradient of a function and the divergence of a vector field in spherical coordinates. Nothing special so far, but a formula that I learned in a general relativity lecture creates confusion.
First of all consider a vector field $f$ and a function $h$ on $\mathbb R^3$. Of course in spherical coordi... |
Say I have a rational number, $n$, that approximates an irrational number of the form:
$$n \approx {a+\sqrt b \over c}$$
in terms of being irrational.
What is a good way of finding the unknown integer constants $a$, $b$, and $c$?
Ex: $n = {33385282\over 20633239} \approx 1.618034 \approx \phi \approx {1 + \sqrt 5 \over... |
When we learn quantum mechanics, we are told that the only way to extract information from a system is to conduct measurements. We are told that if two observables commute then performing one measurement does not affect the outcome of the other.
This is how we are told measurements work: if $a$ is an eigenvalue of $\ha... |
Hello, I am curious if I have this correct and if it has a name.A thin walled cylinder is spinning on its axis along its length in a closed system. It begins to draw itself in converting its invariant mass to kinetic energy. In polar coordinates ##E=\gamma_\theta m c^2, L=\gamma_\theta m...
So the universe is expanding... |
Most often, the $S$-matrix is defined as an operator between asymptotic initial and final Hilbert spaces for a
time-dependent scattering process, i.e. between $t\to-\infty$ and $t\to\infty$. There unitarity encodes conservation of probabilities over time. On the other hand, the book that OP mentions, Ref. 1, talks abou... |
An obstacle problem for Tug-of-War games
1.
Department of Mathematics, University of Pittsburgh, Pittsburgh, Pennsylvania 15260, United States
2.
Departamento de Análisis Matemático, Universidad de Alicante, Ap 99, 03080, Alicante, Spain
3.
Department of Mathematics, Dartmouth College, Hanover, NH 03755, United States
... |
I recently read Khinchin's derivation of Liouville's theorem. I was able to follow the math for the most part, however I was hoping for an intuitive understanding about why the form of the measure on an energy surface in phase space is different than the form of the measure on the whole phase space
If we have an $N$-di... |
Note that $n$ is really the momentum in the $\sigma$ direction so it has the units of the world sheet mass. The exponent $-n\epsilon$ in the regulator has to be dimensionless so $\epsilon$ has the units of the world sheet distance.
Consequently, the removed term $1/\epsilon^2$ has the units of the squared world sheet m... |
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... |
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Production of light nuclei and anti-nuclei in $pp$ and Pb-Pb collisions at energies available at the CERN Large Hadron Collider
(American Physical Society, 2016-02)
The production of (anti-)deuteron and (anti-)$^{3}$He nuclei in Pb-Pb collisions at $\sqrt{s_{\rm NN}}$ = 2.76 TeV has ... |
Can I be a pedant and say that if the question states that $\langle \alpha \vert A \vert \alpha \rangle = 0$ for every vector $\lvert \alpha \rangle$, that means that $A$ is everywhere defined, so there are no domain issues?
Gravitational optics is very different from quantum optics, if by the latter you mean the quant... |
If the computer starts in the middle of the stream, it has no way to know—it will be completely confused.Fortunately, that's not how the protocol works. The computer and terminal have to sync up before they can communicate. There are a few different ways of doing that, but once they're in sync (which includes agreeing ... |
I) There are already several good answers. OP is asking about the momentum of the non-relativistic string with only transverse displacements, whose Lagrangian density usually is given as
$$ {\cal L}_T ~:=~\frac{\rho}{2} \dot{\eta}^2 - \frac{\tau}{2} \eta^{\prime 2} \tag{1}$$
in textbooks.
II) Let us fix notation: $\rho... |
Schedule of the International Workshop on Logic and Algorithms in Group Theory Monday, October 22
10:15 - 10:50 Registration & Welcome coffee 10:50 - 11:00 Opening remarks 11:00 - 12:00 Alex Lubotzky: First order rigidity of high-rank arithmetic groups 12:00 - 14:00 Lunch break 14:00 - 15:00 Zlil Sela: Basic conjecture... |
Let $f$ be defined for $x \in \mathbb{R}$ by $$ f\left(x\right)=2\text{arctan}\left(e^x\right)-\frac{\pi}{2} $$ I've shown that $f$ is odd and satisfies for $x \in \mathbb{R}$ $$f'\left(x\right)=\cos\left(f\left(x\right)\right)$$ To prove it, i've used that $$ \cos\left(f\left(x\right)\right)=2\sin\left(\text{arctan}\l... |
Distance, or farness, is a numerical description of how far apart objects are. In physics or everyday usage, distance may refer to a physical length, or an estimation based on other criteria (e.g. "two counties over"). In mathematics, a distance function or metric is a generalization of the concept of physical distance... |
Averaging the above two results.
PRESENTED IN PREPRINT ON FIG 3.
Statistical errors only.
WITH OMEGA/RHO DECAY PARAMETRIZATION.
WITH OMEGA/A1 DECAY PARAMETRIZATION.
Data read from graph.
Data read from graph.
Data read from graph.
Statistical errors only.
Statistical errors only.. An entry 0.00 indicates a statistical ... |
The problem
Find where does the following series converge and where does it converge absolutely $\sum_n \dfrac{(-4+4\sqrt3i)^n}{n} \dfrac{1}{(z+3)^{6n}}$.
My attempt.I first took the following substitution $w=\dfrac{1}{(z+3)^6}$, so I'm left with the following power series $\sum_n \dfrac{(-4+4\sqrt3i)^n}{n} w^n $ which... |
M3: Introductory Calculus - Material for the year 2019-2020
16 lectures
These lectures are designed to give students a gentle introduction to applied mathematics in their first term at Oxford, allowing time for both students and tutors to work on developing and polishing the skills necessary for the course. It will hav... |
Let $X_1,X_2,...$ a sequence of random variables identically distributed following a Pareto distribution of parameter $\alpha>0$ such that $P(X_1>x)=x^{-\alpha}$ for $x\geqslant 1$. Show that for a sequence of constants $c_1,c_2,...$ we have:
$\limsup\frac{\log(X_n)}{c_n}=\frac{1}{\alpha}$ almost surely.
I thought of t... |
Frequent Links ISO 217
It has been suggested that this article be merged into Paper_size. (Discuss) Proposed since October 2014.
The
ISO 217:1995 standard defines the RA and SRA paper formats.
These paper series are untrimmed raw paper. RA stands for “raw format A” and SRA stands for “supplementary raw format A”. The R... |
Separable Differential Equations
A first order differential equation is \( \textcolor{blue}{\mbox{separable}} \) if it can be written as
\begin{equation} \label{eq:3.5.1}
h(y)y' = g(x), \end{equation}
where the left side is a product of \(y'\) and a function of \(y\) and the right side is a function of \(x\). Rewriting... |
To define characteristic classes in smooth vector bundles $E\longrightarrow M$ there is a more or less standard procedure: to choose a connection $\nabla$ and to derive the curvature $\Omega$, which is an $End(E)$-valued 2-form. In each chart $U_\alpha$, $\Omega$ may be described by a $r\times r$ matrix ($r$ rank of $E... |
The question title says it all: We know that in general, specifying the short rate $r(t)$ does
not specify the bond prices $P(t, T)$. So how can a model for short rates—for example the Vasicek model—be powerful enough to price interest rate derivatives?
The question title says it all: We know that in general, specifyin... |
The more radicals prefer Oristano and its surroundings, because if the frequent mistral wind in Capo Mannu rages, you can jump the biggest waves of the Mediterranean (3-5 meters) with the wind perfectly at the side, or to be a little more comfortable logistically
The great variety of the landscape, the changeable scena... |
Current browse context:
physics.atom-ph
Change to browse by: References & Citations Bookmark(what is this?) Physics > Atomic Physics Title: Terahertz-driven phase transition applied as a room-temperature terahertz detector
(Submitted on 1 Sep 2017)
Abstract: There are few demonstrated examples of phase transitions that... |
I think the author of this problem forgot to add units to $K_c$ since it's
not a dimensionless entity:
$$K_c = \frac{[\ce{NO}]^2}{[\ce{N2O}][\ce{O2}]^{0.5}}$$
and should be $K_c = \pu{1.7e-13 mol^{0.5} L^{-0.5}}$. In general
$$[K_c] = \mathrm{dim}(c)^{Δn}$$
where square brackets denote the dimensions of the quantity $K... |
In Exercises [exer:7.4.1} –[exer:7.4.18} find the general solution of the given Euler equation on \((0,\infty)\).
[exer:7.4.1] \(x^2y''+7xy'+8y=0\)
[exer:7.4.2] \(x^2y''-7xy'+7y=0\)
[exer:7.4.3] \(x^2y''-xy'+y=0\)
[exer:7.4.4] \(x^2y''+5xy'+4y=0\)
[exer:7.4.5] \(x^2y''+xy'+y=0\)
[exer:7.4.6] \(x^2y''-3xy'+13y=0\)
[exer... |
How do I
1 show that $M=[0,3]\subset \mathbb{R}$ is a manifold with boundary?
2 find a $C^2$ partition of unity for the open cover $M=[0,2)\cup(1,3]$? 3 show that $\omega=(x-2)dx$ is/is not an orientation on $M$?
What I know:
Let $M$ be a manifold in vector space $V$. Then it is covered by coordinate patches $f:A\right... |
In the answers to this question, it is said that
The de-icing system on most turbine aircraft (including MD-82 involved in that accident) uses bleed air from the engines, that is it extracts some air from behind the (low pressure stage of the) compressor. This air is therefore not ejected from the nozzle and not produc... |
Can n! be a perfect square when n is an integer greater than 1? (But is it possible, to prove without Bertrand's postulate. Because bertrands postulate is quite a strong result.)
Assume, $n\geq 4$. By Bertrand's postulate there is a prime, let's call it $p$ such that $\frac{n}{2}<p<n$ . Suppose, $p^2$ divides $n$. Then... |
Suppose I wanted to travel to one of the recently discovered potentially Earth-like planets such as Kepler 186f that is 490 light years away. Assuming I had a powerful rocket and enough fuel, how long would it take me?
Start by considering what is seen by the people watching you from the Earth. Nothing can travel faste... |
Optimality conditions for $ E $-differentiable vector optimization problems with the multiple interval-valued objective function
1.
Faculty of Mathematics and Computer Science University of Łódź, Banacha 22, 90-238 Łódź, Poland
2.
Department of Mathematics, Hadhramout University, P.O. BOX : (50511-50512), Al-Mahrah, Ye... |
Suppose $f_1,f_2,\ldots $ is a sequence of convex functions that converges to a continuous convex $f$. Let $x_1^*,x_2^*$ be their respective (not necessarily unique) minima, and let y be a minima of $f$ (once again need not be unique). Can we prove that there exists a version of $x_1^*,x_2^*,\ldots$ such that $x_n^*\ri... |
Finding the phase response of a biquad at a specific frequency is simple. Recall the transfer function of a biquad:
$$H(z) = \frac{b_0 + b_1z^{-1} + b_2z^{-2}}{a_0 + a_1z^{-1} + a_2z^{-2}}$$
The frequency response of a system can be calculated by letting $z = e^{j\omega}$, where $\omega$ is a normalized frequency in th... |
77 11 Homework Statement A pendulum is made up of a light rigid beam of length 𝐿=0.50m and two point masses. The beam is attached to a fixed point at one end. One of the masses is of mass 𝑀=2.0kg and is attached to the beam at the opposite end to this fixed point. The other mass is of mass 𝑚=0.80kg and is attached t... |
Connell D’Souza our co-blogger has worked with a team that develops robotic boats. The outcome is clearly impressive.
—
For today’s post, I would like to introduce you to Alejandro Gonzalez. Alex is a member of the RoboBoat team – VantTec of Tecnológico de Monterrey in Monterrey, Mexico. I met Alex at RoboBoat 2018 whe... |
In this simple note http://arxiv.org/abs/0907.1813 (to appear in Colloq. Math.), Rossi and I proved a characterization in terms of "inversion of Riesz representation theorem".
Here is the result: let $X$ be a normed space and recall Birkhoff-James ortogonality: $x\in X$ is orthogonal to $y\in X$ iff for all scalars $\l... |
I am using JHEP class for my physics thesis, but everything written in math environment becomes automatically in bold font. I have tried with different compilers like: TeXworks and TeXmaker. I even send the tex file to my mentor who compiled it on an apple computer and then it works just fine, no bold font.
So the prob... |
I have two identical fermions in an infinite potential well. They are non-interacting. How should I show that the first excited state is four-fold degenerate? Is the wavefunction just the superposition of the wavefunction of each fermion?
In the ground state, both electrons are in the state with the lowest value of "n"... |
Research Open Access Published: Existence and regularity of time-dependent global attractors for the nonclassical reaction-diffusion equations with lower forcing term Boundary Value Problems volume 2016, Article number: 10 (2016) Article metrics
1027 Accesses
Abstract
Based on the notation of time-dependent attractors,... |
Just like other systems, the Microwave systems consists of many Microwave components, mainly with source at one end and load at the other, which are all connected with waveguides or coaxial cable or transmission line systems.
Following are the properties of waveguides.
Consider a waveguide having 4 ports. If the power ... |
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... |
I would like to derive the Fourier transform of $f(x)=\ln(x^2+a^2)$, where $a\in \mathbb{R}^+$ by making use of the properties:
\begin{equation} \mathcal{F}[f'(x)]=(ik)\hat{f}(k)\\ \mathcal{F}[-ixf(x)]=\hat{f}'(k) \end{equation} For the Fourier transform I use the definition given by:
\begin{equation} \hat{f}(k)=\frac{... |
Maass forms of levels 1 to 10 with $0 \leq R\leq 10$
The horizontal axis is the spectral parameter $R$ with the Laplace eigenvaluesatisying $\lambda=1/4+R^2$. The vertical axis is the level $N$. Each pointcorresponds to a Maass form of weight 0 and trivial character on $\Gamma_0(N)$with the color showing whether the sy... |
Given two groups $G_1$ and $G_2$ with operations $*_1$ and $*_2$, the direct product of sets $G_1\times G_2$ is a group under the operation \[ (a_1, a_2)*(b_1, b_2) = (a_1*_1 b_1, a_2 *_2 b_2). \] This has normal subgroups \[ H_1=\{(a,e_2) \mid a \in G_1\}\cong G_1\] and \[ H_2=\{(e_1,a) \mid a \in G_2\}\cong G_2\] suc... |
I wrote the following proof. I used the following code and it resulted in the following output:
\begin{proof}\[S_n = \frac{a(1-r^n)}{1-r}\]\begin{align*} \lim _{n\to \infty} S_n &= \lim _{n\to \infty} \frac{a(1-r^n)}{1-r}\\ &= \lim _{n\to \infty} \frac {a}{1-r} - \lim _{n\to \infty} \frac{ar^n}{1-r}\\ &= \lim _{n\to \i... |
Convert between Percent, Fractions and Decimals 03:41 minutes Get your free trial content now! Video Transcript Transcript Convert between Percent, Fractions and Decimals
This is Toni. He's the owner of "Toni's 100% Pizza," which is famous for its delicious, customized pizzas. At the moment, he's taking a customer's or... |
Illinois Journal of Mathematics Illinois J. Math. Volume 48, Number 3 (2004), 965-976. On the structure of the set of semidualizing complexes Abstract
We study the structure of the set of semidualizing complexes over a local ring. In particular, we prove that for a pair of semidualizing complexes $X_1$ and $X_2$ such t... |
I have come across this question that asks to find Fourier series coefficients of the following signal. $$1+\sin (\omega_0 t) + \cos (\omega_0 t) + \cos (2\omega_0 t + \pi / 4) $$
In my intuition, the signal is already in Fourier series form, and the question asks just to find the trigonometric Fourier coefficients.
I ... |
In Wikipedia's ideal gas article there is a derivation for the thermodynamic entropy that results in $$S = Nk\ln\left[\frac{V}{N} \left(\frac{U}{\hat{c}_V Nk}\right)^{\hat{c}_V} \frac{1}{\Phi}\right],$$ and the article states:
[...] $\Phi$ may vary for different gases, but will be independent of the thermodynamic state... |
PACM, Princeton University
Abstract: We consider a learning problem in statistical physics: given an ensemble \rho(x)=e^{-\beta H(x)}/Z and a coarse-graining procedure y=y(x) that maps x to a reduced set of variables y, we need to model the free energy surface F(y) = - (1/\beta) \log \int dx\rho(x)\delta(y-y(x)). This ... |
That the moment of inertia about an axis passing through the CM is minimized, with respect to any other parallel axes, is a consequence of the quadratic (squared) dependence of the moment of inertia on distance. In other words, the ${r^2}$ term in ${I=mr^2}$ makes it so that masses at farther distances are preferential... |
Just doing some revision for ODEs and came across this problem. Find the general solution to $$u''+4u=0.$$
So far I've applied the characteristic polynomial: $$\begin{array}{r c l} \lambda^2 +4 & = & 0 \\ \lambda^2 & = & -4 \\ \lambda & = & i\sqrt{4} \\ \lambda & = & 2i, -2i. \\ \end{array}$$
So the general solution sh... |
Hi I am trying to evaluate the integral $$ \mathcal{I}(\omega)=\int_{-\infty}^\infty J^3_0(x) e^{i\omega x}\mathrm dx $$ analytically. We can also write $$ \mathcal{I}(\omega)=\mathcal{FT}\big(J^3_0(x)\big) $$ which is the Fourier Transform of the cube of Bessel function. The Bessel function $J_0$ is given by $$ J_0(x)... |
This is a crosspost from MSE. It's been up there for a few weeks now. A 200 rep bounty yielded no results (or even comments). I'm hoping someone here has some helpful ideas. See this post for the original.
Consider $U$ a nice compact region in $\mathbb{C}$ with boundary $\Gamma$. Let $S_1$ b the ideal of trace class op... |
Difference between revisions of "Probability Seminar"
(→Thursday, May 7, TBA)
(→Thursday, April 16, Scott Hottovy, UW-Madison)
Line 161: Line 161:
Title: '''An SDE approximation for stochastic differential delay equations with colored state-dependent noise'''
Title: '''An SDE approximation for stochastic differential d... |
Research Open Access Published: Monotone positive solution of a fourth-order BVP with integral boundary conditions Boundary Value Problems volume 2015, Article number: 172 (2015) Article metrics
1027 Accesses
2 Citations
Abstract
In this paper, we investigate the existence of concave and monotone positive solutions for... |
THE BROKEN LINK BETWEEN SUPPLY AND DEMAND CREATES CHAOTIC TURBULENCE (+controls)
The existing global capitalistic growth paradigm is totally flawed
Growth in supply and productivity is a summation of variables as is demand ... when the link between them is broken by catastrophic failure in a component the creation of u... |
I am trying to derive the differential of the product of two processes, but I got stuck. This is what I have until now:
We have the following two stochastic processes: $dX_t= \mu_t dt +\sigma_t dW_t$ and $dY_t = \eta_t dt + \vartheta_t d \bar{W}_t$, with the correlation between the two Brownian motions equal to $\rho$,... |
Previous
Important principles and relationships in Life Sciences
Next
Mathematical skills in Life Sciences
Presenting data (ESG3H) Biological drawings and diagrams (ESG3J)
Drawings and diagrams are an essential part of communication in science, and especially Life Sciences. Remember it is not an artwork or sketch! But ... |
Research Open Access Published: New periodic solutions with a prescribed energy for a class of Hamiltonian systems Boundary Value Problems volume 2017, Article number: 30 (2017) Article metrics
614 Accesses
1 Citations
0 Altmetric
Abstract
We consider a class of second order Hamiltonian systems with a \(C^{2}\) potenti... |
First, let's speak about perceptrons in general:
their
input $X_0$ is a $K$-dimensional vector. So if you want to use $(P_{bid}(t),P_{ask}(t), Q_{bid}(t),Q_{ask}(t))$, it would mean that without any effort (but later we will see that is would be better to do some efforts, as usual):$$X_0(t)=(P_{bid}(t),P_{ask}(t), Q_{b... |
Apparently, we can solve an MDP (that is, we can find the optimal policy for a given MDP) using a linear programming formulation. What's the basic idea behind this approach? I think you should start by explaining the basic idea behind a linear programming formulation and which algorithms can be used to solve such const... |
$\int_0^\infty \frac{m^{x+1}e^{-2m}}{\Gamma(x+1)\Gamma(2)}dm =\frac{\Gamma(x+2)\frac{1}{2}^{x+2}}{\Gamma(x+1)\Gamma(2)}$
How does the left side equal the right side? I understand that the gamma function is $\Gamma(z) = \int_0^\infty t^{z-1} e^{-t} dt$
and that $\Gamma(x+2) = \int_0^\infty m^{x+2-1} e^{-m} dm$
However I... |
102 5 Homework Statement Figure (See below) shows a valve separating a reservoir from a water tank. If this valve is opened, what is the maximum height above point B attained by the water stream coming out of the right side of the tank? Assume h = 10.0 m, L = 2.00 m, and ## \Theta ## = 30.0°, and assume the cross-secti... |
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... |
Is there a canonical regression approach for predicting the ranks of a response?
I'd like to fit a regression to a dataset where the response is highly non-normal with very large outliers. There are about 10 predictors. I haven't had much success with transformations (the best has been adding a constant and then loggin... |
Central Board of Secondary Education (CBSE) is responsible for conducting an examination of the school affiliated to the central board. It is of prime importance for the students to excel in the field of education for their brightening future. Maths requires proper understanding and skills rather than just memorizing t... |
You are effectivelly talking about the Renormalization group in quantum field theory, the paradigmatic self-similar system underlying the whole of nature--with ultimate (subsequent) dramatic consequences in the strong interactions.
Specifically, in 1954, Gell-Mann and Low introduced their eponymous RG equation for QED,... |
The rather anti-climatic answer to "
Does anyone know why this is?" is that simply nobody cares enough to implement a non-negative ridge regression routine. One of the main reasons is that people have already started implementing non-negative elastic net routines (for example here and here). Elastic net includes ridge ... |
This question already has an answer here:
I'm having trouble finding a way to express this fraction with the amsmath package.
The result I'm getting isn't quite nice. Are there alternative ways to write this fraction?
\documentclass[10pt,norsk, fleqn]{extarticle} \usepackage[a4paper, margin=1.2cm,includeheadfoot]{geome... |
\usepackage{hyperref}
\usepackage[ocgcolorlinks]{ocgx2}[2017/03/30]
Package
, as of version
ocgx2
0.24, re-implements the option of
ocgcolorlinks
, based on B. Lerner's code with some refinements:
hyperref
Besides OCG colour links that wrap around line breaks, also wrapping at
page breaks and nested hyperlinks are supp... |
EDIT: Actually, one can indeed change the alignment of
array in LyX by GUI means, Besides, I learnt that
array is a bad way of doing what I describe in the "Background" below and I should use
alignat. However, I think this question is relevant nevertheless, because there might be cases one wants to include own commands... |
Inverse scattering on conformally compact manifolds
1.
Department of Mathematics, Purdue University, 150 N. University Street, West Lafayette, IN 47907-2067, United States
2(y) at the boundary and $V\in C^\infty(X)$ not vanishing at the boundary. We prove that the scattering matrices at two fixed energies $\lambda_1,$ ... |
2018-12-08
We begin with Adam Tooze laying out the issues:
Adam Tooze: Italy: How Does the E.U. Think This Is Going to End?: "Over the past 10 years, Italy’s gross domestic product per capita has fallen... unique among large advanced economies...
...More than 32 percent of Italy’s young people are unemployed. The gloom... |
Let $X$ be a connected space. According to Getzler BV-algebras and two-dimensional topologcial field theories , page 271, we have and isomorphism
$ H_*(\Omega^2\Sigma^2X) \cong {\cal G}( \widetilde{H}_* X ) $
where ${\cal G}( V)$ means the free Gerstenhaber (Getzler calls it "braid") algebra over the graded space $V$ a... |
<< ToK
ToK Warszawa meeting - Rough Notes Thu 15 Feb 2007 These are just rough notes - feel free to correct them, add links, etc. Hector Rubinstein - stockholm - magnetic fields
Magnetic fields on kpc scales exist. They may exist on intergalacticscales - it's unclear whether or not their origin is primordial.
CMB - Pla... |
The primitive classes are the highest weight vectors.
Hard Lefschetz says that the operator $L$ (which algebraic geometers know as intersecting with a hyperplane) is the "lowering operator" $\rho(F)$ in a representation $\rho \colon \mathfrak{sl}_2(\mathbb{C})\to End (H^\ast(X;\mathbb{C}))$. The raising operator $\rho(... |
Recovering two Lamé kernels in a viscoelastic system
1.
Dipartimento di Matematica “F. Enriques”, Universitá di Milano, via C. Saldini 50, 20133 Milano, Italy
2.
Sobolev Institute of Mathematics, Siberian branch of Russian Academy of Sciences, Acad. Koptyug prosp., 4, Novosibirsk, 630090, Russian Federation
sametempora... |
Overview A negative-temperature coefficient (NTC) thermistor can be used as a temperature sensor. A NTC thermistor is a resistor which has a non-linear change in resistance in a response to a change in temperature. It is a passive sensor. NTCs vs RTDs
A NTC differs from a
resistive temperature detector (RTD) in the mat... |
Part of the order contained two 10uF electrolytic capacitors but at different ratings, one at 1000V and one at 630V (for what it's worth, the voltage I'm working with here is ~440V).
If you're sure both have 440V on them, you can use 600V for both, it's likely to be cheaper. I wonder why the original was rated at 1kV.
... |
Geometry is a branch of mathematics that concerned with questions of shape, size, the relative position of figures, and the properties of space.Geometry Formulas are used to calculate the length, perimeter, area and volume of different geometric figures and shapes. They are also used to calculate the arc length, radius... |
Maxwell's Equations are usually written as:
$$\vec{\nabla}\cdot\vec{E}=\rho/\epsilon_0,$$
$$\vec{\nabla}\cdot\vec{B}=0,$$
$$\vec{\nabla}\times \vec{E}=-\frac{\partial \vec{B}}{\partial t},$$
$$\vec{\nabla}\times \vec{B}=\mu_0\left(\vec{J}+\epsilon_0\frac{\partial \vec{E}}{\partial t}\right).$$
But the last two might be... |
Research Open Access Published: Blow-up and nonexistence of solutions of some semilinear degenerate parabolic equations Boundary Value Problems volume 2015, Article number: 157 (2015) Article metrics
1050 Accesses
2 Citations
Abstract
In this paper we study a class of semilinear degenerate parabolic equations arising i... |
Research Open Access Published: Global existence and blow-up to the solutions of a singular porous medium equation with critical initial energy Boundary Value Problems volume 2016, Article number: 80 (2016) Article metrics
855 Accesses
1 Citations
Abstract
This paper is devoted to the study of a singular porous medium ... |
Thanks to WillJagy for the helpful comments. The wolfram article on this is nice. Particularly, formula (37) of that article is pretty impressive in light of how complicated this gets in the case $n=3$. For this case check out the MO post for a summary and then this Bateman paper for the whole story.
The piece by Ono i... |
90 6 Homework Statement Two bodies of equal mass are connected by an ideal rope and are inside a room which can accelerate vertically. The second body is attached to a spring of constant ##200 \frac{N}{m}##. Find the deformation of the spring when A) the room moves with constant velocity B) the room is accelerating upw... |
I'm learning (or at least
trying to learn) about electrochemistry, but a major obstacle to that, is that different books I refer use different terms for the same symbols. So in a last ditch attempt to clear stuff up, I've resorted to Chem.SE.
So here's what I intend to do; I'll list out everything I think I've understo... |
Abstract (englisch):
In this thesis, we investigate the Cauchy problem for the quasilinear stochastic evolution equation
\begin{equation*}
\begin{cases}
u(t)=[{-}A(u(t))u(t)+f(t)]\operatorname{dt}+B(u(t))dW(t),\quad t\in [0,T],\\
u(0)=u_0
\end{cases}
\end{equation*}
in a Banach space $ X. $
In the first part of the the... |
Luckily for us, a really smart guy named Josiah Willard Gibbs figured out how these two tendencies work together back in the late 1800's. As a result, in chemical thermodynamics we now have a state function called the Gibbs Free Energy that describes what is called the thermodynamic potential of a system at constant pr... |
I'm trying to rotate the
\vDash symbol from
amssymb:
\documentclass{article}\usepackage{graphicx}\usepackage{amssymb}\newcommand{\vDashR}{\rotatebox[origin=c]{180}{\ensuremath\vDash}}\begin{document}$\Sigma\vDash\vDashR\Gamma$\end{document}
The rotation comes from here.
With Detexify, I find no predefined symbol.
My pr... |
What's the exact value of $\lim\limits_{n\rightarrow \infty}\frac{e^n}{\sum\limits_{i=0}^{i=n}\frac{n^i}{i!}}$?
p.s. I suppose it may be 2, but I cannot prove it.
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What's the exact... |
Senior Member
Join Date: Oct 2017
Location: Glasgow
Posts: 474
Cooling tower models
As mentioned in another thread, here's some research I've been doing on cooling towers which might come in handy when working out evaporation ratess. The method below uses the effectiveness of a counterflow heat exchanger; for a more st... |
2018-09-02 17:21
Measurement of $P_T$-weighted Sivers asymmetries in leptoproduction of hadrons / COMPASS Collaboration The transverse spin asymmetries measured in semi-inclusive leptoproduction of hadrons, when weighted with the hadron transverse momentum $P_T$, allow for the extraction of important transverse-momentu... |
For a matroid M of rank r on n elements, let b(M) denote the fraction of bases of M among the subsets of the ground set with cardinality r. We show that $$\Omega \left( {1/n} \right) \leqslant 1 - b\left( M \right) \leqslant O\left( {\log {{\left( n \right)}^3}/n} \right)a\;sn \to \infty $$ Ω ( 1 / n ) ≤ 1 − b ( M ) ≤ ... |
Here is a beautiful result from numerical analysis. Given any nonsingular $n\times n$ system of linear equations $Ax=b$, an optimal Krylov subspace method like GMRES must necessarily terminate with the exact solution $x=A^{-1}b$ in no more than $n$ iterations (assuming exact arithmetic).
The Cayley-Hamilton theorem pro... |
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