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How to Calculate the Statical or First Moment of Area of Beam Sections
The statical or first moment of area (Q) simply measures the distribution of a beam sections’s area relative to an axis. It is calculated by taking the summation of all areas, multiplied by its distance from a particular axis (Area by Distance).
In ... |
Let $S$ be a finite set of integers (this set contains about 200000 elements). Let $T \subset S$ be a particular subset of $S$ called
target. $S$ keeps growing. So does $T$. Each new element of $S$ might or might not be in $T$.
No (known, or practical) algorithm can determine if an element $s \in S$ is in the
target se... |
I have a problem verifying the following equation (in three dimensions)
$$\epsilon_{abc} e^a\wedge R^{bc}=\sqrt{|g|}Rd^3 x$$
where $R$ is the Ricci scalar and $R^{bc}$ is the Ricci curvature
Attempt at a solution:
$$\epsilon_{abc} e^a\wedge R^{bc}=\epsilon_{abc} e_\mu^ae_\alpha^be_\beta^c R^{\alpha\beta}_{\nu\rho} dx^\... |
I have a time series that has been measured after convolution with a moving average filter. Knowing the parameters of the moving average filter, is it possible to reconstruct/constrain the values of ...
I have 2 oversampling ADC's running parallelly, each to process data in a specific range of the input as shown below:... |
Since moving to a Mac a bit over a year ago, I've had only a few reasons to look back (the business with the HP LJ1022 printer being one of them). I'm now rather close to the end of my tether, and the reason is fonts.
As an academic and a computer scientist, I end up writing quite a lot of papers and presentations with... |
Expanding on
physicsphile's answer, there is an alternative way of computing the expectation value of $f(q)$, and that is to sum the possible values of $f(q)$ weighted by their respective probabilities as follows.
If $f(q)$ represents a physical dynamical variable, then it is a Hermitian (self-adjoint) operator and can... |
I am trying to intuitively understand why equation $Q=CV$ should work. I can understand why $V$ should be proportional to $Q$ but not why $Q$ should be proportional to $V$. In the end, $C$ is constant so $\frac{1}{C}$ will be a constant too. So the equation should work. But intuitively I am not able to understand
A cap... |
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J/Ψ production and nuclear effects in p-Pb collisions at √sNN=5.02 TeV
(Springer, 2014-02)
Inclusive J/ψ production has been studied with the ALICE detector in p-Pb collisions at the nucleon–nucleon center of mass energy √sNN = 5.02TeV at the CERN LHC. The measurement is performed in... |
Generalized Truth Functions
Logic is all about choices. An idea is true or false, a student is present or absent, a switch is on or off. All the truth tables and specialized language of propositional calculus is geared to exploring these choices and their consequences.
In this section I will layout basic concepts and u... |
Truth Function Algebra
Algebra is all about keeping a predicate true while rearranging the variables that define its shape. Identities introduce new or repeats of existing variables, commutativity switches the location of variables, and associativity changes what functions variables are in.
This section will explore th... |
I got this problem:
Prove that if $f:[a,b]\to[a,b]$ is a nondecreasing function then $\exists x_0\in[a,b]$ such that $f(x_0)=x_0$ (i.e. $f$ has a fixed point).
(Hint: set $A=\{x\in[a,b]|x\leq f(x)\}$ and show that $x_0=\sup f([a,b])$ exist and that $f(x_0)=x_0$)
I tried to show that $A\neq\emptyset$ by supposing that $... |
It is not quite true that we don't obtain any useful information. The relativistic particle action is indeed$$ S = -m_0c^2 \int dt_{\rm proper} $$ When you substitute your correct formula for $dt_{\rm proper}$ and Taylor expand the Lorentz factor in it, the integral has the factor of $dt_{\rm coordinate}(1-v^2/c^2+\dot... |
Ex.5.3 Q1 Arithmetic progressions Solutions - NCERT Maths Class 10 Question
Find the sum of the following APs.
(i) \(2, 7, 12 ,\,\dots,\) to \(10\) terms.
(ii) \(- 37, - 33, - 29,\,\dots, \)to \(12\) terms
(iii) \(0.6, 1.7, 2.8 ,\,\dots,\) to \(100\) terms
(iv) \(\begin{align}\frac{1}{{15}},\frac{1}{{12}},\frac{1}{{10}... |
2018-09-11 04:29
Proprieties of FBK UFSDs after neutron and proton irradiation up to $6*10^{15}$ neq/cm$^2$ / Mazza, S.M. (UC, Santa Cruz, Inst. Part. Phys.) ; Estrada, E. (UC, Santa Cruz, Inst. Part. Phys.) ; Galloway, Z. (UC, Santa Cruz, Inst. Part. Phys.) ; Gee, C. (UC, Santa Cruz, Inst. Part. Phys.) ; Goto, A. (UC,... |
The rest of these docs assume that you’re familiar with the basics of Clojure, and have a working copy of Leiningen (version >= 2) installed. If you’re not yet familiar with Leiningen then you should head over to the Leiningen website and get it installed first. It’s a really nice tool that makes things very easy!
Gori... |
Given a planar graph G with $N$ nodes, 4 colors are enough to color each node, so that adjacent nodes have different colors.
Let $k > 4$. Is there an algorithm to color the nodes with $k$ colors, so that the colors are distributed the most equally possible?
In other words:
Let's call $c_1, ..., c_k$ the colors. We defi... |
Before we can even think of trying to derive it from the Schwarzschild metric, why not first have a go at it with
Newton's law of universal gravitation in its full form, that is, using classical mechanics to its fullest extend before we pull in modern physics? I'd think one is rather hastily skipping a step here ... Th... |
I am trying to optimize this cost function by using Gauss-Newton method. $$f = \sum_{i = 1}^n Tr{(Z^TZ)}$$ where $Z$ is a $4\times4$ matrix and it is a function of real vector $\vec{a}\in\mathbb{R}^5$. And because I am using Gauss-Newton approach, I define $g \in\mathbb{R}^{n}$ to be $\sqrt{Tr(Z^T_iZ_i)} = \sqrt{p_i}$,... |
Edit: My original post assumed $p$-arity rather than $p$-regularity. If the $p$ child trees of the root, rather than being (infinite) trees similar to the $p$-regular parent, are of $(p-1)$-arity, then the recursion given needs to be adapted accordingly.
Note however this previous Question and Answer, which appears to ... |
Benney-Luke equations: a reduced water wave model¶
The work is based on the article “Variational water wave modelling: from continuum to experiment” by Onno Bokhove and Anna Kalogirou [BK16]. The authors gratefully acknowledge funding from EPSRC grant no. EP/L025388/1 with a link to the Dutch Technology Foundation STW ... |
I'm familiar with using the Calculus of variations to find the condition for which first order variations of a functional wrt a function are zero:
We start with a functional $J[x]= \int_{t_f}^{t_i}L(x(t),\dot x(t),t)dt$, where $t_i, t_f$ are constants and $\dot x(t)= dx/dt$
If $J[f]$ is stationary at $f$, we add to $f$... |
Given a two positive matrices $A,B$. For simplicity, let's assume that $Tr A=Tr B=1$. Assume that $\|A-B\|_1\leq\varepsilon$, for some small $\varepsilon>0$, where $\|\cdot\|_1$ is the $l_1$-norm, namely the sum of all its singular values.
My question is whether there is a generic transformation to move $A$ to $B$ for ... |
...no strings attached... In recent years, I got used to the fact that Sean Carroll is confused about some very basic physics – the postulates of quantum mechanics as well as thermodynamics (and the very basic insight due to Boltzmann and others that its laws are microscopically explained by statistical physics and not... |
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J/Ψ production and nuclear effects in p-Pb collisions at √sNN=5.02 TeV
(Springer, 2014-02)
Inclusive J/ψ production has been studied with the ALICE detector in p-Pb collisions at the nucleon–nucleon center of mass energy √sNN = 5.02TeV at the CERN LHC. The measurement is performed in... |
Difference between revisions of "De Bruijn-Newman constant"
(→t=0)
(→Bibliography)
Line 110: Line 110:
* [N1976] C. M. Newman, Fourier transforms with only real zeroes, Proc. Amer. Math. Soc. 61 (1976), 246–251.
* [N1976] C. M. Newman, Fourier transforms with only real zeroes, Proc. Amer. Math. Soc. 61 (1976), 246–251.... |
Consider two states of the type $|\alpha,\xi \rangle = \hat{D}(\alpha) \hat{S}(\xi) |0\rangle$, where $D$ and $S$ are the displacement and squeeze operators, respectively, and $|0\rangle$ is a 1D harmonic oscillator vacuum state.
My question is: Is there a closed formula for $\langle \alpha, \xi | \beta, \eta \rangle$?... |
Ex.7.2 Q10 Coordinate Geometry Solution - NCERT Maths Class 10 Question
Find the area of a rhombus if its vertices are \((3, 0)\), \((4, 5)\), \((-1, 4)\) and \((-2, -1)\) taken in order.
[Hint: Area of a rhombus \(=\) (product of its diagonals)]
Text Solution Reasoning:
A rhombus has all sides of equal length and oppo... |
To open the application about the topic, open the following post: Interactive demonstration of intensity transforms
Image processing often requires transforming the intensity values for example to turn the image easier to process or to highlight certain objects. In this post an effective way of some simple transforms a... |
One slopiness that many teachers are guilty of is teaching this misleading thing:
The position operator $\hat{x}$ has eigenvectors $|x_0\rangle$ that obey
$$\hat{x} |x_0\rangle = x_0|x_0\rangle$$
and are represented by distributions on domain of $x$: $\delta(x-x_0)$ for different $x_0$. (WRONG)
The incorrect prediction... |
Say a deck of cards is dealt out equally to four players (each player receives 13 cards).
A friend of mine said he believed that if one player is dealt four-of-a-kind (for instance), then the likelihood of another player having four-of-a-kind is increased - compared to if no other players had received a four-of-a-kind.... |
OpenCV 3.3.0
Open Source Computer Vision
In this chapter,
As an OpenCV enthusiast, the most important thing about the ORB is that it came from "OpenCV Labs". This algorithm was brought up by Ethan Rublee, Vincent Rabaud, Kurt Konolige and Gary R. Bradski in their paper
ORB: An efficient alternative to SIFT or SURF in 2... |
Trisect sides of a quadrilateral and connect the points to have nine quadrilaterals, as can be seen in the figure. Prove that the middle quadrilateral area is one ninth of the whole area.
Consider all occurring points as vectors, as in @Calvin Lin's answer, and write $\mu$ for ${1\over3}$. Then $$p=(1-\mu)a+\mu b,\quad... |
In my talk at 2018 Chinese Mathematical Logic Conference, I asked if \((V,\subset,P)\) is epsilon-complete, namely if the membership relation can be recovered in the reduct. Professor Joseph S. Miller approached to me during the dinner and pointed out that it is epsilon-complete. Let me explain how.
Theorem
Let \((V,\i... |
The first hep-th paper today is
heterotic \(E_8\times E_8\) strings on Calabi-Yau three-folds, string theorists' oldest promising horse heterotic Hořava-Witten M-theory limit with the same gauge group, on Calabi-Yaus times a line interval type IIB flux vacua – almost equivalently, F-theory on Calabi-Yau four-folds – wi... |
This shows you the differences between two versions of the page.
— epimorphisms_are_surjective [2010/08/20 20:37] (current)
jipsen created
Line 1: Line 1: + =====Epimorphisms are surjective===== + + A morphism $h$ in a category is an \emph{epimorphism} if it is right-cancellative, i.e. for all + morphisms $f$, $g$ in t... |
2019-09-04 12:06
Soft QCD and Central Exclusive Production at LHCb / Kucharczyk, Marcin (Polish Academy of Sciences (PL)) The LHCb detector, owing to its unique acceptance coverage $(2 < \eta < 5)$ and a precise track and vertex reconstruction, is a universal tool allowing the study of various aspects of electroweak an... |
Basically 2 strings, $a>b$, which go into the first box and do division to output $b,r$ such that $a = bq + r$ and $r<b$, then you have to check for $r=0$ which returns $b$ if we are done, otherwise inputs $r,q$ into the division box..
There was a guy at my university who was convinced he had proven the Collatz Conject... |
The first equation actually contains the definition of the standard equilibrium constant:$$K^\circ = \exp\left\{\frac{−\Delta_r G^\circ}{R T}\right\}$$With this definition the equilibrium constant is dimensionless.
Under standard conditions the van't Hoff equation is$$\frac{\mathrm{d} \ln K^\circ}{\mathrm{d}T} = \frac{... |
One disadvantage of the fact that you have posted 5 identical answers (1, 2, 3, 4, 5) is that if other users have some comments about the website you created, they will post them in all these place. If you have some place online where you would like to receive feedback, you should probably also add link to that. — Mart... |
where the left part of the equal is the circuit representation of the Toffoli gate where the first two lines are the control qubits and the third one is the target. On the right side we have the CNOT gate whose matrix representation is
$$ CNOT=\left(\begin{array}{cccc} 1 & 0 & 0 & 0\\ 0 & 1 & 0 & 0\\ 0 & 0 & 0 & 1\\ 0 ... |
For an FIR filter, with symmetrical tap values $h[N-1-n]=h[n]$,
why is the group delay $\frac{N-1}{2} T$ (where $N$ is the number of taps of the FIR filter and $T$ is the sampling time)? Why is linear phase so important for the filter response?
Signal Processing Stack Exchange is a question and answer site for practiti... |
I would like to calculate an observable's expectation value of a state, the ground state, or time evolution of a finite system with $N$ spins under an Hamiltonian $H$.
For the sake of discussion assume $N=16$ so we can use IBM QC.
How to translate a given Hamiltonian into Quantum logic gates in order to simulate the sy... |
Say there is a population of mass 1 in which individuals can choose one of two traits (1 and 2). The population share with trait 1 at time $t+1$, $$p_{t+1}=\frac{1}{1+e^{-\beta\left(u_1-u_2+J(2p_t-1)\right)}}$$ for constants $u_1,u_2,\beta,J$, with $u_1>u_2$. I can't calculate them analytically, but it can be shown tha... |
As described in the Rich Output tutorial, the IPython display system can display rich representations of objects in the following formats:
This Notebook shows how you can add custom display logic to your own classes, so that they can be displayed using these rich representations. There are two ways of accomplishing thi... |
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How To Fix Error In The Midpoint Rule
If you have Error In The Midpoint Rule then we strongly recommend that you
.download and run this (Error In The Midpoint Rule) repair tool
Symptoms & Summary
Error In The Midpoint Rule and other critical errors can occur whe... |
It is demonstrated that the square trace of the electromagnetic tensor is nothing and it is valid: $$ \mathrm{Tr}\,{F}^2_{\mu\nu}=\frac{2}{c^{2}}(E^2-c^2B^2). $$ Proof: $F_{\mu\nu}=-F_{\nu\mu}$, hence $$ \mathrm{Tr}\,{F}^2_{\mu\nu}=\sum_{\mu}\left(F^{2}\right)_{\mu\mu}=-\sum_{\mu\nu}F_{\mu\nu}F_{\nu\mu}=-\sum_{\mu\nu}F... |
I'm trying to better understand the causes for the equation of time by deriving an approximation from first principles.
My naive approach, $EOT_{NAIVE}$, is to take the difference between the right ascension of the mean sun, $\alpha_M(t)$, and the right ascension of the "real" sun $$EOT_{NAIVE}(t)=\langle\dot{\alpha }\... |
Help:Wikitext examples For basic information see Help:Editing. Contents Basic text formatting[edit]
You can format the page using Wikitext special characters.
What it looks like What you type
You can
3 apostrophes will
(Using 4 apostrophes doesn't do anythingspecial --
You can ''italicize'' text by putting 2 apostrophe... |
I just read the topic about Ergodicity but I have ambiguity about its meaning (by intuition). What does mean: (for mean) Statistical average = Time average. Could you please explain it in detail. Thanks.
If you sample a random process for a specific t, you will get one realization of a random variable. For another t, y... |
I really can't figure out how to do this at all. I've been trying to show this for nearly 4 hours now. I've tried working from $\tanh(z)=\frac{\sinh(z)}{\cosh(z)}$ and expanding the top and bottom, but that just becomes a mess that, after trying so hard to put into the desired form, didn't work. I also tried working fr... |
Ex.14.1 Q1 Statistics Solution - NCERT Maths Class 10 Question
A survey was conducted by a group of students as a part of their environment awareness programme, in which they collected the following data regarding the number of plants in \(20\) houses in a locality. Find the mean number of plants per house.
Number of p... |
Electronic Journal of Probability Electron. J. Probab. Volume 22 (2017), paper no. 99, 23 pp. Harmonic moments and large deviations for a supercritical branching process in a random environment Abstract
Let $(Z_n)_{n\geq 0}$ be a supercritical branching process in an independent and identically distributed random envir... |
I assume from your solution that your time series closely fits a sine wave. The method you are using is quite good if you restrict yourself to the set of data which is near the peaks.
The more standard way is to find a best fit sinusoid using linear algebra techniques. You have stated the period, so you know the freque... |
There are a few things that confuse me by your comments and question. Instead of "I would like to find the posterior density of the parameters
conduct Gibbs sampling" I assume you mean that you would like to conduct Gibbs sampling in order to sample from $p(x_{1:t},\theta|y_{1:t})$ and thereby have draws from $p(\theta... |
Lecture: HGX205, M 18:30-21
Section: HGW2403, F 18:30-20 Exercise 01 Prove that \(\neg\Box(\Diamond\varphi\wedge\Diamond\neg\varphi)\) is equivalent to \(\Box\Diamond\varphi\rightarrow\Diamond\Box\varphi\). What you have assumed? Define strategyand winning strategyfor modal evaluation games. Prove Key Lemma: \(M,s\vDas... |
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J/Ψ production and nuclear effects in p-Pb collisions at √sNN=5.02 TeV
(Springer, 2014-02)
Inclusive J/ψ production has been studied with the ALICE detector in p-Pb collisions at the nucleon–nucleon center of mass energy √sNN = 5.02TeV at the CERN LHC. The measurement is performed i... |
According to me, $\ce{Fe^{2+}}$ should be a better reducing agent because $\ce{Fe^2+}$ - after being oxidized - will attain a stable $\ce{d^5}$ configuration, whereas $\ce{Cr^2+}$ will attain a $\ce{d^3}$ configuration. I think the half filled $\ce{d^5}$ configuration is more stable than the $\ce{d^3}$ configuration. W... |
Proof:
a, f has a limit everywhere, and it is $0$.
It is enough, to show it on $(-1,1)$. Let us have an arbitary $a \in (-1,1)$.
First, we need, that for every $\epsilon > 0$, such $\delta$ exists, that if $|x-a| < \delta$, then $|f(x)-0| < \epsilon$. Let us have $N > \frac{1}{\epsilon}$, then $|f(x)-0|=|f(x)| \le \fra... |
Let $X(f)$ denote the Fourier transform of $x(t)$ where$$\begin{align*}X(f) &= \int_{-\infty}^{\infty} x(t) \exp(-j2\pi ft) \mathrm dt\\x(t) &= \int_{-\infty}^{\infty} X(f) \exp(+j2\pi ft) \mathrm df\end{align*}$$which I will denote via $x(t) \leftrightarrow X(f)$.The following transform pairs will be needed in what fo... |
Preprints (rote Reihe) des Fachbereich Mathematik Refine Keywords Brownian motion (2) (remove)
303
We show that the intersection local times \(\mu_p\) on the intersection of \(p\) independent planar Brownian paths have an average density of order three with respect to the gauge function \(r^2\pi\cdot (log(1/r)/\pi)^p\)... |
Your reasoning is correct, but you need to go a little further to deduce the answer.
The question does not say but we must assume that the mean position O is the same for P and Q. The phase difference between them remains the same, but the separation changes.
Suppose that, at some instant, P and Q are moving in the sam... |
The cost of boundary controllability for a parabolic equation with inverse square potential
Institut de Mathématiques de Toulouse, UMR CNRS 5219, Université Paul Sabatier Toulouse Ⅲ, 118 route de Narbonne, 31 062 Toulouse Cedex 4, France
$ 1-D $
$ u_t -u_{xx} - \frac{\mu}{x^2} u = 0, \qquad x\in (0,1), \ t \in (0,T), $... |
I am struggling with proving this question
Show that if $a_n \leq x$ for all $n \geq 1$, then (the formal limit when n goes to infinity) $\lim_{n\rightarrow \infty} a_n \leq x$.
I am assuming by contradiction that $\lim_{n \rightarrow \infty}a_n > x$.
Then there exists a rational $q$ between them s.t $x < q < \lim_{n \... |
Several recent hep-ph papers studied grand unification without supersymmetry, an approach that seems intriguing to a whole group of researchers. Grand unification theories (GUT) work nicely with supersymmetry (SUSY) – it's the supersymmetric version of the \(SU(5)\) and larger models that achieves the accurate unificat... |
Main Page The Problem
Let [math][3]^n[/math] be the set of all length [math]n[/math] strings over the alphabet [math]1, 2, 3[/math]. A
combinatorial line is a set of three points in [math][3]^n[/math], formed by taking a string with one or more wildcards [math]x[/math] in it, e.g., [math]112x1xx3\ldots[/math], and repl... |
Steady-state continuity equation on an extruded mesh¶
This demo showcases the use of extruded meshes, including the new regions of integration and the construction of sophisticated finite element spaces.
We now consider the equation
in a domain \(\Omega\), where \(\vec{u}\) is a prescribed vector field, and \(q\) is an... |
Main Page Contents The Problem
Let [math][3]^n[/math] be the set of all length [math]n[/math] strings over the alphabet [math]1, 2, 3[/math]. A
combinatorial line is a set of three points in [math][3]^n[/math], formed by taking a string with one or more wildcards [math]x[/math] in it, e.g., [math]112x1xx3\ldots[/math],... |
My homework problem reads:
Consider a free particle in one dimension. Write an expression for the wavefunction $\psi(x, t)$ given an initial state $\psi_0(x) = Ae^{-ax^2}$ at $t = 0$, where $A$ is a normalization constant (that you do not need to calculate).
This is my attempt:
$\begin{align} \left<p|\psi_0\right> &= \... |
This is a tricky question because it asks about the meaning of words. People use the word "particle" to refer to various, not always well defined, notions in physics.
In the end, I think the simplest and more correct single way to categorize the terms is to interpret "particle" as "excitation of a field". For example, ... |
I don't think it's the case that all $n>0$ terms vanish, because the mode expansion of $\phi$ has a zero mode $\phi_0$. Its expansion is
\begin{equation}\phi \left(z,\bar{z}\right) = \phi_0 - i\pi_0 \log\left(z\bar{z}\right) +i \sum_{n\neq 0} \frac{1}{n} \left(a_n z^{-n} + \bar{a}_n \bar{z}^{-n}\right)\end{equation}
Co... |
The $x$ component of vector $A$ is 25.0 m and the $y$ component is 40.0 m.
(a) What is the magnitude of $A$?
(b) What is the angle between the direction of $A$ and the positive direction of x?
For (b) I tried using the formula $\tan \theta = \frac{a_y}{a_x} = \frac{40}{-25} = -1.6$, thus $\arctan(-1.6)=58$ degrees whic... |
This is probably more of a model specification question than a technical question about PyMC3 itself, but I’m hoping someone here can help. Basically, multi-group logistic ANOVA in PyMC3 is giving different results than other Bayesian models and frequentist methods, and I’d like to figure out why.
I’m providing as much... |
I want to design a filter with a custom phase delay related to frequency. As frequency increases, phase delay should increase.
The time delay as a function of frequency can be expressed as: $t_d = \frac{L}{C_{ph}} - \frac{1}{f}$
$L$ and $C_{ph}$ are constants of $0.0017$ and $2628$ respectively.
The range of $f$ is $50... |
Communications in Mathematical Analysis Commun. Math. Anal. Volume 17, Number 2 (2014), 131-150. Commutators of Convolution Type Operators with Piecewise Quasicontinuous Data Abstract
Applying the theory of Calderon-Zygmund operators, we study the compactness of the commutators $[aI,W^0(b)]$ of multiplication operators... |
I keep reading about the Unification Algorithm.
What is it and why is so important to Inference Engines? Why is it so important to Computer Science?
Computer Science Stack Exchange is a question and answer site for students, researchers and practitioners of computer science. It only takes a minute to sign up.Sign up to... |
Mixed formulation for the Poisson equation¶
We’re considering the Poisson equation \(\nabla^2 u = -f\) using a mixed formulation on two coupled fields. We start by introducing the negative flux \(\sigma = \nabla u\) as an auxiliary vector-valued variable. This leaves us with the PDE on a unit square \(\Omega = [0,1] \t... |
For a configuration manifold $M$ we expect there to be a bracket on $\mathcal C^\infty (T^*M)$ endowing the space with a Lie algebra structure. Here we assume that $T^*M$ is also equipped with a non-degenerate symplectic 2-form $\omega_H$ and that the bracket can be written $\omega_H(X_f,X_g)$ for two Hamiltonian vecto... |
Despite the comments to the contrary, this circuit does have a steady state solution since the voltage source produces 20V for \$t \ge 0\$.
My best guess is that because there is a parallel branch which by KCL
should equal 100ix and would be zero because of the open circuit
provided by the capacitor.
That's correct. Th... |
Given a DeSitter-space metric from the line element:
$$ ds^2=\left(1-\frac{r^2}{R^2}\right)dt^2-\left(1-\frac{r^2}{R^2}\right)^{-1}dr^2-r^2d\Omega^2 $$
Where $R=\sqrt{\frac{3}{\Lambda}}$, and $\Lambda$ is a positive cosmological constant, I am trying to derive the equations for radial null geodesics. I derived the geod... |
Publications Influence
Claim Your Author Page
Ensure your research is discoverable on Semantic Scholar. Claiming your author page allows you to personalize the information displayed and manage publications.
We find the sum of series of the form $$\sum\limits_{i = 1}^\infty {\frac{{f(i)}}{{{i^r}}}} $$ for some special f... |
This is the question as posed to the DSP folks. Electrical engineers like to use particular definitions of the Fourier Transform (using Hz, rather than angular frequency) and the sinc function.
Out of consideration to you kind folks, I will try to eliminate a few symbols, like I will, without loss of generality, set th... |
Baire's lemma says :
Let $X$ a complete metric space. Let $(X_n)_n$ a sequence of closed subset. Suppose $Int(X_n)=\emptyset$ for all $n$. Then $Int(\bigcup_{n\in\mathbb N}X_n)=\emptyset$.
And here an equivalent form :
Let $X$ a non-empty complete metric space. Let $(X_n)_n$ a sequence of closed set s.t. $\bigcup_{n=1}... |
I am having trouble
understanding my problem and what to calculate
I have been given the subspace $U=\{x=$$ \begin{vmatrix} x_1\\ x_2\\ x_3\\ \end{vmatrix} \in F^3 | x_1 + x_2 + x_3 = 0\} \subset F^3 $
and the linear transformation $f: U \rightarrow F^2 $ $f\begin{vmatrix} x_1\\ x_2\\ x_3\\ \end{vmatrix} =\begin{vmatri... |
Liouville theorems for stable weak solutions of elliptic problems involving Grushin operator
Division of Computational Mathematics and Engineering, Institute for Computational Science, Ton Duc Thang University, Ho Chi Minh City, Vietnam, Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City,... |
This shows you the differences between two versions of the page.
kleene_algebras [2010/07/29 18:30]
127.0.0.1 external edit
kleene_algebras [2010/09/04 17:00] (current)
jipsen
Line 16: Line 16: ==Morphisms== ==Morphisms== Let $\mathbf{A}$ and $\mathbf{B}$ be Kleene algebras. Let $\mathbf{A}$ and $\mathbf{B}$ be Kleene ... |
Healy, MW, Darnley, MJ, Copperwheat, CM, Filippenko, AV, Henze, M, Hestenes, JC, James, PA, Page, KL, Williams, SC and Zheng, W (2019)
AT 2017fvz: a nova in the dwarf irregular galaxy NGC 6822. Monthly Notices of the Royal Astronomical Society, 486 (3). pp. 4334-4347. ISSN 0035-8711
Text
AT 2017fvz a nova in the dwarf ... |
Context, I have a geometric algorithm that is sensitive to collinear points and receives as input a list of points in 2D generated randomly. Suppose that I have a Boolean function nonCollinear(x,y,z) that given three points returns true if they are non collinear and false otherwise. Is there an efficient algorithm to g... |
If we convolve 2 signals we get a third signal. What does this third signal represent in relation to the input signals?
There's not particularly any "physical" meaning to the convolution operation. The main use of convolution in engineering is in describing the output of a linear, time-invariant (LTI) system. The input... |
I'm trying to get the AdS solution to the circular wilson loop. The standard AdS metric is:
$ds^2 = \frac{L^2}{z^2}(\eta_{\mu \nu} dx^{\mu} dx^{\nu} + dz^2)$
If I take the circle of radius R at the x1,x2 plane I can choose polar coordinates:
$x_1 = R cos(\theta)$, $x_2 = R sin(\theta)$
$ds^2 = \frac{L^2}{z^2}(-dt^2 + d... |
Method of sub-super solutions for fractional elliptic equations
1.
School of Mathematics, Hunan University, Changsha 410082, Hunan, China
2.
School of Mathematics and Applied Statistics, University of Wollongong, Wollongong, 2522, NSW, Australia
3.
School of Mathematics(Zhuhai), Sun Yat-sen University, Zhuhai 519082, G... |
I am working on a problem, which would possibly relate the Fourier transform/series with the jump singularities of the function where the function itself or one of its derivatives jump. ((some kind of logarthmic blow ups too, possibly as a corollary).
Consider a BV function $f(t)$ in $L^2(\mathbb{R})$ such that $f(t) =... |
There are proofs that treat the cases of real and non-real $\chi$ on an equal footing. One proof is in Serre's Course in Arithmetic, which the answers by Pete and David are basically about. That method is using the (hidden) fact that the zeta-function of the $m$-th cyclotomic field has a simple pole at $s = 1$, just li... |
Given a field $k$. We denote $A_{mn}=k[\{X_{ij}\}_{1\le i\le m,1\le j\le n}]$ a polynomial ring of $mn$ variables. Given $m,n,r>0$, we have a natural homomorphism $\phi\colon A_{mn}\to A_{mr}\otimes_kA_{rn}$ induced by matrix multiplication: $Z_{ij}\mapsto\sum_{l=1}^rX_{il}Y_{lj}$. Let $I\subseteq A=A_{mn}$ be the idea... |
Optimization problems arising in intelligent systems are similar to those studied in other fields (such as operations research, control, and computational physics), but they have some prominent features that set them apart, and which are not addressed by classic optimization methods. Numerical optimization is a domain ... |
This one can be done with "residue at infinity" calculation. This method is shown in the Example VI of http://en.wikipedia.org/wiki/Methods_of_contour_integration .
First, we use $z^z = \exp ( z \log z )$ where $\log z$ is defined for $-\pi\leq \arg z < \pi$.
For $(1-z)^{1-z} = \exp ( (1-z)\log (1-z) )$, we use $\log (... |
Ok, here is how I see these issues now after taking a bit more time to think about them:
In the first paper it is said that the Euler equations emerge as the infinite Reynolds number limit of the Navier Stokes equation which means that according to the definition of the Reynolds number
$$ RE = \frac{V L}{\nu} $$
the mo... |
Ex.12.1 Q4 Areas Related to Circles Solution - NCERT Maths Class 10 Question
The wheels of a car are of diameter \(80\, \rm{cm}\) each. How many complete revolutions does each wheel make in \(10\) minutes when the car is traveling at a speed of \(66\, \rm{km}\) per hour?
Text Solution What is known?
Diameter of the whe... |
When someone says a real valued function $f(x)$ on $\mathbb{R}$ is finite, does it mean that $|f(x)| \leq M$ for all $x \in \mathbb{R}$ with some $M$ independent of $x$?
I am not familiar with the term
finite in this context. One possible definition would be this.
A function $f: A \to B$ is finite if and only if $f(A) ... |
Shinichi Mochizuki of Kyoto divided the steps needed to prove the 1985 conjecture by Oesterlé and Masser into four papers listed at the bottom of the Nature article above.
Up to a few exceptions to be proved separately, a strengthening of Fermat's Last Theorem Four days ago, Nature described a potentially exciting deve... |
Electronic Journal of Probability Electron. J. Probab. Volume 23 (2018), paper no. 6, 48 pp. Pinning of a renewal on a quenched renewal Abstract
We introduce the pinning model on a quenched renewal, which is an instance of a (strongly correlated) disordered pinning model. The potential takes value 1 at the renewal time... |
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