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Electrochemical Impedance Spectroscopy: Experiment, Model, and App
Electrochemical impedance spectroscopy is a versatile experimental technique that provides information about an electrochemical cell’s different physical and chemical phenomena. By modeling the physical processes involved, we can constructively interpre... |
ISSN:
2156-8472
eISSN:
2156-8499 Mathematical Control & Related Fields
March 2015 , Volume 5 , Issue 1
Select all articles
Export/Reference:
Abstract:
We consider single-observed cascade systems of hyperbolic equations. We first consider the class of bounded operators that satisfy a non negativity property $(NNP)$. Wit... |
Given a probability space $(\Omega, \mathcal{F}, \mathbb{P})$, let $\{X_n: n\ge 1\}$ be sequence of square integrable random variables, i.e., $X_n \in L^2(\Omega, \mathcal{F}, \mathbb{P})$ for each $n\ge 1$. Further assume that $\mathbb{E}[X_i X_j] = 0$ whenever $i\neq j$ and $\sup_n \mathbb{E}[X_n^2] < \infty$. For ea... |
Short answer no, different margins can produce the same odd's ratio and confidence interval. Some examples to follow.
Here is a brief sketch of how to find the minimum possible N for the table. Note that as per your linked site, the standard error can be related to the cell contents by:
$$\text{SE} = \sqrt{\frac{1}{a} ... |
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Revision as of 06:01, 18 May 2006 Contents Introduction
TeX was designed for ... |
The Collatz Conjecture is well known with the sequence
$$f(n) = \begin{cases} n/2 &;\text{if } n \equiv 0 \pmod{2}\\ k\,n+1 &; \text{if } n\equiv 1 \pmod{2} \end{cases}$$
and $k=3$; the sequence converging $1$ (so called
oneness).
Is there any conjecture/theorem on whether the sequence would converge for any other valu... |
Latest (and likely final) edit: Fixing a typo, rewording the introduction
Multiples of $2$ are placed in a checkerboard fashion: This is the parity condition, and is essential if there are an even number of total lattice sites. This answer sketches a proof that it is possible to place multiples of $3$ in all rectangula... |
You can obtain the $G=KAK$ decomposition from a decomposition of the type $F=UR$. To avoid unnecessary complications, let's assume that our reductive group $G$ is a selfadjoint subgroup of $\operatorname{GL}(n,\mathbb{R})$. Then the map $g \mapsto g^{-t}$ is an involution of $G$, which is called the Cartan involution a... |
An example of methylation analysis with simulated datasets
Part 2: Potential DMPs from the methylation signal
Methylation analysis with Methyl-IT is illustrated on simulated datasets of methylated and unmethylated read counts with relatively high average of methylation levels: 0.15 and 0.286 for control and treatment g... |
THE FRAMEWORK:
Let $X_1$ be an observation from a normal random variable with mean zero and variance $\sigma^2$ and lets call the PDF $f(x)$.
I want to minimize the Kullback Liebler Information criterion between a PDF $g(x, \beta) $ of a zero mean normal random variable with variance $\beta \sigma^2$ and $f(x)$. The mi... |
I would like to show that for $t > 0$, $$\int_{1}^{\infty}\frac{3e^{yt}}{y^4}\text{ d}y$$ diverges. [This is equivalent to showing that the MGF for $Y$, with pdf $$f_{Y}(y) = \dfrac{3}{y^4}\text{, } y \in (1, \infty)$$ does not exist.]
My work:
\begin{equation*} \int_{1}^{\infty}e^{yt} \cdot \dfrac{3}{y^4}\text{ d}y = ... |
Unfortunately it is not necessary to invoke group selection to answer this question. This is one of the reasons that Dawkins likes this discussion so much - he does not believe in group selection and so the discussion in SG does not invoke group selection. ESSs are described in the book as the product of direct competi... |
Deriving the heat diffusion equation was one of the most interesting things I learned about in my undergraduate degree. The fact that you can sit in your chair and discover something about how the world works with nothing more than your brain, a pen, and some paper astonishes me.
The heat diffusion equation descrbes ho... |
@Secret et al hows this for a video game? OE Cake! fluid dynamics simulator! have been looking for something like this for yrs! just discovered it wanna try it out! anyone heard of it? anyone else wanna do some serious research on it? think it could be used to experiment with solitons=D
OE-Cake, OE-CAKE! or OE Cake is ... |
First of all, there's no reason to restrict the definition of finite additivity to finite spaces. It's just that if a finitely additive measure is defined on a finite space, then, trivially, it's countably additive.
We can extend finite additivity as you've defined it by induction. Your axiom implies that, for any $n \... |
Let us consider the surface $\mathbb{A}^{2}/\mu_{6}$ where the action is given by $$\begin{array}{ccc}\mu_{6}\times\mathbb{A}^{2} & \longrightarrow & \mathbb{A}^{2}\\(\epsilon,x_{1},x_{2}) & \longmapsto & (\epsilon^{2}x_{1},\epsilon^{4}x_{2})\end{array}$$The invariant polynomials with respect to this action are $x_{1}^... |
Difference between revisions of "Group cohomology of dihedral group:D8"
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===Over the integers===
===Over the integers===
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The first few homology groups are given below:
The first few homology groups are given below:
Revision as of 04:50, 15 January 2013
Co... |
I have some true or false questions and would like to have your help to check on it.
A). in a ring R, if $x^2=x$, $\forall x\in R$, then R is commutative For (A), when looking at $(x+y)^2$, it has $x+y=(x+y)^2=x^2+xy+yx+y^2$and then yx+xy=0, and from 2x=4x, therefore 2x=0. how this play a role here? B) In an integral d... |
If the six-pointed star is regular, then the answer is $r^2(\pi-\sqrt{3})$. If it is not, then the answer can be larger, up to a limit of $r^2\big(\pi-\frac{3}{4}\sqrt{3}\big)$.
Proof
The required area is the area of the circle ($\pi r^2$) minus the area of the star.The area of the star is the area of a large equilater... |
If a function is a combination of other functions whose derivatives are known via composition, addition, etc., the derivative can be calculated using the chain rule and the like. But even the product of integrals can't be expressed in general in terms of the integral of the products, and forget about composition! Why i... |
Tokyo Journal of Mathematics Tokyo J. Math. Volume 24, Number 1 (2001), 291-308. Lévy Processes with Negative Drift Conditioned to Stay Positive Abstract
Let $X$ be a Lévy process with negative drift starting from $x>0$, and let $\tau$ and $\tau_s$ be the first passage times to $(-\infty,0]$ and $(s,\infty)$, respectiv... |
If we have a urn with $N$ balls of two colours ($D$ red and $N-D$ black balls respectively), then probability of having $k$ red out of $n$ balls drawn
at once without replacement follows the Hypergeometric distribution:
$Pr(X = k) = \dfrac{\binom{D}{k} \binom{N - D}{n-k}}{\binom{N}{n}}$
Now assume we have some
a priori... |
Difference between revisions of "Linear representation theory of symmetric group:S5"
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==Summary==
==Summary==
+
{| class="sortable" border="1"
{| class="sortable" b... |
I am interested in computing a normalizing constant (of a Gaussian density in dimension $3$). Such normalizing constants often do not have a closed form. In dimension $2$, this normalizing constant can be computed in closed form.
The integral I would like to compute is :
$$ \int_{\mathbb{R}^{3}} e^{-(r_{1}^{2} + r_{2}^... |
For a parametric model ${\cal M} = \{p(\cdot \mid \theta, \alpha)\}$ with two parameters $\theta$ and $\alpha$ equipped with a prior distribution $\pi(\theta, \alpha)$ then the ("joint") likelihood on $(\theta, \alpha)$ after $x$ has been observed is defined by $$L(\theta, \alpha \mid x) \overset{\theta,\alpha}{\propto... |
Abbreviation:
BanSp
A
is a normed vector space $\mathbf{A}=\langle A,+,-,0,s_r (r\in F),||\cdot||\rangle$ that is Banach space : any Cauchy sequence has a limit. complete
Remark: This is a template. If you know something about this class, click on the ``Edit text of this page'' link at the bottom and fill out this page... |
@Secret et al hows this for a video game? OE Cake! fluid dynamics simulator! have been looking for something like this for yrs! just discovered it wanna try it out! anyone heard of it? anyone else wanna do some serious research on it? think it could be used to experiment with solitons=D
OE-Cake, OE-CAKE! or OE Cake is ... |
There is a lot to say here, so I will break my answer down in stages:
$(1)$. Is it possible to construct solutions to a PDE by making a sequence of a change of coordinates and then eventually write the solution in a Fourier series?
Answer:
N0
This technique might work for some
linear PDEs, but this would not work for n... |
So, I am having trouble (again) with the domain for a triple integral of a function, bounded by the paraboloid $2y^2=x$ and the $x+2y+z=4$ and $z=0$ planes
I have tried to guess the bounds for x,y and z in cartesian coordinates with no luck, and it's somewhat apparent that this needs to be done in cylindrical polar coo... |
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... |
Nonlinear Schrödinger equations on a finite interval with point dissipation
Department of Mathematics, Virginia Polytechnic Institute and State University, Blacksburg, VA USA
$ iu_t+u_{xx}+f(u) = 0 , \;\;\;\; u ( x, 0 ) = w_0 (x) $
$ x\in [0, L] $
$ L^2 $
$ u(0, t) = \beta u(L, t), \beta u_x(0, t)-u_x(L, t) = i\alpha u... |
Difference between revisions of "IX-6315 "Dawn" Electric Propulsion System"
(Fixed up electrical consumption description, minor thrust-related updates.)
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== Usage ==
== Usage ==
−
This engine has a phenomenal fuel efficiency (4200 s I<sub>sp</sub>... |
Astérisque
Volume: 341; 2012; 113 pp; Softcover
MSC: Primary 35; 37;
Print ISBN: 978-2-85629-335-5 Product Code: AST/341
Product Code: AST/341
List Price: $45.00
AMS Member Price: $36.00
A Quasi-Linear Birkhoff Normal Forms Method. Application to the Quasi-Linear Klein-Gordon Equation on \(\mathbb{S}^{1}\)Share this pa... |
To put things in context I'll first expose a straightforward method inspired by the classical evaluation of square roots (shortly : "if we know that $a^2 \le N <(a+1)^2$ then the next digit $d$ will have to verify $(10a+d)^2 \le 10^2 N <(10a+d+1)^2$. This means that we want the largest digit $d$ such that $(20a+d)d\le ... |
I was recently helping a college math student with her homework. Her teacher had offered an extra-credit question: Find two alternating series $\sum_{n=1}^\infty (-1)^{n-1}a_n$ such that $a_{n+1} \leq a_n$ for all $n$, but $\lim_{n\to\infty} a_n \neq 0$. One of the provided series should converge, and the other should ... |
I don't claim to have a full answer (yet! I hope to update this, as it's an interesting issue to try and explain well). But let me start with a few clarifying comments...
But if it really is just constructive interference of complicated states, why not just perform this interference with classical waves?
The glib answe... |
There's a 59.5125% chance of survival.
Naively, we might have thought there'd be a 55% chance of survival as 55% of the roll results are good. But the 20 is a slightly better result than the 1 is a bad one, so that pushes up the probability a bit. Let's see how.
The approach
The simplest way to tackle this is to look a... |
To Xi'an's first point: When you're talking about $\sigma$-algebras, you're asking about measurable sets, so unfortunately any answer must focus on measure theory. I'll try to build up to that gently, though.
A theory of probability admitting all subsets of uncountable sets will break mathematics
Consider this example.... |
What is the correct formula to transform AC current from a Wye connection to a Delta connection?
I am not an electrical engineer, and this is my first question on this part of StackExchange. I hope it is understandable, and a "good" question. Please let me know, what can be done better.
In the following question, I wil... |
It looks like you're new here. If you want to get involved, click one of these buttons!
Now that we've got enriched profunctors up and running, let's see how to compose them! We've already thought about it in some examples. In Lecture 58 we saw how to compose \(\mathbf{Bool}\)-enriched profunctors, also known as feasib... |
Let $\{a_n\}$ be a sequence such that
$a_n\geq 0$ for all $n$ $\{a_n\}$ is monotonically decreasing $\sum_{n=1}^\infty a_n$ converges
Is it true that as $n\rightarrow\infty$ then $$n\log n\;a_n\rightarrow 0$$
Given the hypotheses, we can show that $n a_n\rightarrow 0$ as $n\rightarrow\infty$. This follows since $$0\leq... |
I want to solve the problem: Find the curve satisfies following conditions.
Minimize the functional $J$ The coordinates of the start/end points are given Direction(tangential vector) at the start/end points are given The length of the curve is $L$
I parameterized the curve using $\theta(s)$. $s$ is the length from the ... |
Difference between revisions of "Permanent"
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The most familiar problem in the theory of permanents was van der Waerden's conjecture: The permanent of a [[doubly-stochastic matrix]] of order $n$ is bounded from below by $n!/n^n$, and this value is attained only for the matrix composed ... |
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... |
Conjugate Heat Transfer
In this blog post we will explain the concept of
conjugate heat transfer and show you some of its applications. Conjugate heat transfer corresponds with the combination of heat transfer in solids and heat transfer in fluids. In solids, conduction often dominates whereas in fluids, convection usu... |
Current browse context:
cond-mat.mtrl-sci
Change to browse by: References & Citations Bookmark(what is this?) Condensed Matter > Materials Science Title: Temperature and high fluence induced ripple rotation on Si(100) surface
(Submitted on 7 Apr 2016)
Abstract: Topography evolution of Si(100) surface due to oblique inc... |
I am doing a question on finding the Pareto efficient quantity of a public good. Instead of using the condition $\sum MRS_i = c'(G)$ where $c(G)$ denotes the cost of the public good, it asks you to find the efficient quantity by maximising the sum of the agents' utilities. Apparently this is only valid if preferences a... |
Let $n \in \mathbb{N}$ be odd. Show that: $$\Aut(\mathbb{Z}/{n\mathbb{Z}}) \cong \Aut(\mathbb{Z}/{2n\mathbb{Z}})$$
$\DeclareMathOperator{\Aut}{Aut}$ My attempt:
An automorphism $f \in \Aut(\mathbb{Z}/{n\mathbb{Z}})$ is uniquely represented by $f(1)$ since $1$ generates $\mathbb{Z}/{n\mathbb{Z}}$. $f(1)$ has to be a gen... |
On the DNA Computer Binary Code
In any finite set we can define a
, a partial order in different ways. But here, a partial order is defined in the set of four DNA bases in such a manner that a Boolean lattice structure is obtained. A Boolean lattice is an algebraic structure that captures essential properties of both s... |
This is something I have been thinking about recently, allow me to complete Mariano Suárez-Alvarez' answer.
First just an observation: "
pick any Riemannian manifold with trivial holonomy at each point: for example, a space form of curvature zero": actually you have no choice, a connection with trivial holonomy has van... |
Let A=111111 and B=142857. Find a positive integer N with six or fewer digits such that N is the multiplicative inverse of AB modulo 1,000,000.
Let A=111111 and B=142857. Find a positive integer N with six or fewer digits such that N is the multiplicative inverse of AB modulo 1,000,000.
[111,111 x 142,857] x M mod 1,00... |
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Now showing items 1-10 of 26
Kaon femtoscopy in Pb-Pb collisions at $\sqrt{s_{\rm{NN}}}$ = 2.76 TeV
(Elsevier, 2017-12-21)
We present the results of three-dimensional femtoscopic analyses for charged and neutral kaons recorded by ALICE in Pb-Pb collisions at $\sqrt{s_{\rm{NN}}}$ = 2.76 TeV. Femtoscopy is used to... |
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... |
According to the wikipedia article: http://en.wikipedia.org/wiki/Levenberg_Marquardt
--
$S(\boldsymbol\beta+\boldsymbol\delta) \approx \|\mathbf{y} - \mathbf{f}(\boldsymbol\beta) - \mathbf{J}\boldsymbol\delta\|^2$
Taking the derivative with respect to δ and setting the result to zero gives:
$(J^{T}J)\boldsymbol \delta ... |
Answer
$\theta $ lies in the First Quadrant or Quadrant-I .
Work Step by Step
The trigonometric ratios are as follows: $\sin \theta =\dfrac{y}{r} \\ \cos \theta =\dfrac{x}{r} \\ \tan \theta =\dfrac{y}{x}\\ \csc \theta =\dfrac{r}{y} \\ \sec \theta =\dfrac{r}{x} \\ \cot \theta =\dfrac{x}{y}$ where, $ r=\sqrt {x^2+y^2}$ I... |
Let's first have a look at the rectangular signal given as an example in your question. If you have a rectangle $s(t)$ in the time domain which is $1$ in the interval $[-T/2,T/2]$ and zero elsewhere, its Fourier transform is $S(f)=T\text{sinc}(Tf)$, where I use $\text{sinc}(x)=\sin(\pi x)/(\pi x)$. The value of its Fou... |
Up until a few days ago I was thinking that the following two forms of the Fisher Information are "always" equivalent: $$(1) \quad \mathcal{I(\theta)}= E_\theta [\frac{\partial \log \ell(y;\theta)}{\partial \theta} \frac{\partial \log \ell(y; \theta)}{\partial \theta'}],$$ $$(2) \quad \mathcal{I(\theta)}= E_\theta [-\f... |
Inverses for Integer Addition Theorem $\forall x \in \Z: \exists -x \in \Z: x + \paren {-x} = 0 = \paren {-x} + x$ Proof
Let us define $\eqclass {\tuple {a, b} } \boxtimes$ as in the formal definition of integers.
$\boxtimes$ is the congruence relation defined on $\N \times \N$ by:
$\tuple {x_1, y_1} \boxtimes \tuple {... |
Abbreviation:
CanMon
A
is a monoid $\mathbf{M}=\langle M, \cdot, e\rangle$ such that cancellative monoid
$\cdot $ is left cancellative: $z\cdot x=z\cdot y\Longrightarrow x=y$
$\cdot $ is right cancellative: $x\cdot z=y\cdot z\Longrightarrow x=y$
Let $\mathbf{M}$ and $\mathbf{N}$ be cancellative monoids. A morphism from... |
A while back I bought a couple of PIC16F57 (DIP) chips because they were dirt cheap. I figured someday I could use these in
something. Yes, I know, this is a horrible way to actually build something and a great way to accumulate junk. However, this time the bet paid off! Only about a year or two too late; but that’s be... |
@user193319 I believe the natural extension to multigraphs is just ensuring that $\#(u,v) = \#(\sigma(u),\sigma(v))$ where $\# : V \times V \rightarrow \mathbb{N}$ counts the number of edges between $u$ and $v$ (which would be zero).
I have this exercise: Consider the ring $R$ of polynomials in $n$ variables with integ... |
I have been trying to determine the series expansion of the beta function, but so far I haven't been successful. The two results I wish to obtain are the following:
$$ B(x,y) = \sum_{n=0}^{\infty} \frac{\binom{n-y}{n} }{x+n} $$
and \begin{equation} B(x,y) = \sum_{n=0}^{\infty} \frac{1}{n! (n+x)} \frac{\Gamma(n-y+1)}{\G... |
Let there be 3 fields $A$, $B$ and $C$.
If all elements of $A$ are algebraic over $B$ and all elements of $B$ are algebraic over $C$, prove that this implies that all elements of $A$ is algebraic over $C$.
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals i... |
This question comes from Georgi,
Lie Alegbras in Particle Physics. Consider the algebra generated by $\sigma_a\otimes1$ and $\sigma_a\otimes \eta_1$ where $\sigma_a$ and $\eta_1$ are Pauli matrices (so $a=1,2,3$). He claims this is "semisimple, but not simple". To me, that means we should look for an invariant subalgeb... |
Search
Now showing items 1-10 of 26
Kaon femtoscopy in Pb-Pb collisions at $\sqrt{s_{\rm{NN}}}$ = 2.76 TeV
(Elsevier, 2017-12-21)
We present the results of three-dimensional femtoscopic analyses for charged and neutral kaons recorded by ALICE in Pb-Pb collisions at $\sqrt{s_{\rm{NN}}}$ = 2.76 TeV. Femtoscopy is used to... |
Definition
An ordinary first order first degree differential equation is of the form
\[\frac{dy}{dx}=f(x,y)……….(1)\] which can also be written as \[Mdx+Ndy=0……….(2)\] where M and N are functions of x and y or constants. All first order first degree differential equations can’t be solved. However, in the following serie... |
2. Series 31. Year Post deadline: 27th November 2017 Upload deadline: 28th November 2017 11:59:59 PM
(3 points)1. Tooth Fairy
How big would the storage facilities of the Tooth Fairy need to be, to store all of the primary teeth of all of the children of the world? Or, in other words, how rapidly would they need to grow... |
Definition:Superfactorial Contents Definition
Let $n \in \Z_{\ge 0}$ be a positive integer.
The superfactorial of $n$ is defined as: $n\$ = \displaystyle \prod_{k \mathop = 1}^n k! = 1! \times 2! \times \cdots \times \left({n - 1}\right)! \times n!$
where $k!$ denotes the factorial of $n$.
$1, 2, 12, 288, 34 \, 560, 24... |
Abbreviation:
CLRng
A
is a lattice-ordered ring $\mathbf{A}=\langle A,\vee,\wedge,+,-,0,\cdot\rangle$ such that commutative lattice-ordered ring
$\cdot$ is
: $xy=yx$ commutative
Remark: This is a template. If you know something about this class, click on the ``Edit text of this page'' link at the bottom and fill out th... |
Consider the graph $(V,E)$ with vertex set $V=\{v_1,...,v_n\}$ and edge set $E\subset V\times V$. Further, assume that $\forall v_i\in V, (v_i,v_i)\in E$.
Assume that each vertex has an $\textit{initial value}$ (i.e. there is a function $\phi_0:V\rightarrow\mathbb{R}$). We will think of these values as changing with ti... |
Suppose $A\in R^{n\times n}$, where $R$ is a commutative ring. Let $p_i \in R$ be the coefficients of the characteristic polynomial of $A$: $\mathop{\mathrm{det}}(A-xI) = p_0 + p_1x + \dots + p_n x^n$.
I am looking for a proof that: $-\mathop{\mathrm{adj}}(A) = p_1 I + p_2 A + \dots + p_n A^{n-1}$. In the case where $\... |
I'm studying a toy theory in quantum field theory. There are two free fields: a real massive scalar field $\phi$ with mass $M$ and a complex massive scalar field $\Psi$ with mass $m$.
They are coupled by $$ \mathcal{L} \subset g \Psi \Psi^\dagger \phi $$ I'm well aware that this interaction term results in a Lagrangian... |
5. Series 31. Year Post deadline: 26th March 2018 Upload deadline: 27th March 2018 11:59:59 PM
(3 points)1. staircase on the Moon
If we once colonized the Moon, would it be appropriate to use stairs on it? Imagine the descending staircase on the Moon. The height of one stair is $h=15 \mathrm{cm}$ and it's length is $d=... |
Let's say we are given a function $f(x)$, which is not defined at the point $x_0$. How do we find linear approximation of $f$ near $x_0$? P.S. I wrote "linear" just to make things simpler, I came across this problem while trying to approximate the following function near zero: $\frac{lnx}{x*e^x}$. My problem is that to... |
6. Series 31. Year Post deadline: 7th May 2018 Upload deadline: 8th May 2018 11:59:59 PM
(3 points)1. they came apart
We have two point masses with the same mass $m$ at a distance $d$ from each other. They are located freely in space with no external gravitational forces. What's the minimum velocity we need to impart o... |
Using the definition of $m$ as an outer measure, there exist $A_i=(a_i,b_i]$ such that $A\subset \cup_i A_i$ and $\sum_i (b_i-a_i) \leq m(A) + \epsilon/2$. Let $b_i' = b_i + \epsilon 2^{-i-1}$. $G:=\cup_i (a_i,b_i')$ is an open set that contains $A$ and $m(G)\leq \sum_i (b_i'-a_i) =\epsilon/2 + \sum_i (b_i-a_i) \leq m(... |
Expectation of Shifted Geometric Distribution Theorem Then the expectation of $X$ is given by: $\expect X = \dfrac 1 p$
From the definition of expectation:
$\expect X = \displaystyle \sum_{x \mathop \in \Omega_X} x \map \Pr {X = x}$
By definition of shifted geometric distribution:
$\expect X = \displaystyle \sum_{k \ma... |
how come $π(x)π(x_p∣x)=π(x_p)π(x∣x_p)$?
This is a consequence of the form of the transition kernel for the Metropolis-Hastings algorithm:
The Markov transition kernel associated with this algorithm is$$\pi(y|x) = \rho(x,y) q(y|x) + (1-r(x)) \delta_x(y) \;,$$where $q$ denotes the density of the proposal distribution, $r... |
Mine is a tad less elegant but arguably a bit clearer and assumes only the complete basics.
0. The task
Prove that for $ \forall n \in \mathbb{N}$ it is true that $n! \leq (\frac{n+1}{2})^n $ : I. Base steps
(I need four base steps because my final inequality works for $k \ge 4$.)
$$n=0: 1 \leq (\frac{1}{2})^0 = 1 $$$$... |
The electro-weak force is known to contain a chiral anomaly that breaks $B+L$ conservation. In other words, it allows for the sum of baryons and leptons to change, but still conserves the difference between the two. This means that the standard model could have a channel for protons to decay, for example into a pion an... |
On one hand, it seems to make no sense, because of the following:
When expanded, the claim $f(n,a) \in O(n/a)$ would be
There exist $C > 0$, $n_0$, and $a_0$ such that if $n \geq n_0$ and $a \geq a_0$, then $f(n,a) \leq C \cdot n/a$.
Now, given any $\epsilon > 0$, we can find an $a_\epsilon \geq a_0$ such that $C \cdot... |
UPDATE
To make my question more precise, I'll define what I mean by an operator theory:
An
operator theoryis a theory in which the dynamical objects are operators, i.e., the equations of motion are imposed on operators.
A
wave function theory, on the other hand, is a theory in which the dynamical objects are functions ... |
This is an exercise from old exam on formal languages that I don't know how to solve:
Let $p \ge 5$ be a prime number and $L_p$ be a language of words over $\{0,1\}$ that read in binary from right (i.e. from least significant bit) give a number that gives remainder modulo $p$ from the set $\{1,2, \ldots, \frac{p-1}{2}\... |
Abbreviation:
MetSp
A
is a structure $\mathbf{X}=\langle X,d\rangle$, where $d:X\times X\to [0,infty)$ is a metric space , i.e., distance metric
points zero distance apart are identical: $d(x,y)=0\iff x=y$
$d$ is
: $d(x,y)=d(y,x)$ symmetric
the
holds: $d(x,z)\le d(x,y)+d(y,z)$ triangle inequality
Remark: This is a temp... |
The other day I was playing around in Matlab, and although I can’t remember what I set out to do I did end up making a small lossy audio compression/decompression system! It seemed like a good topic for a blog post.
The discrete cosine transformation
Before I show the code I’ll have to very briefly introduce the discre... |
See edit at the end of the question
All the references in this question refer to Quantum algorithm for solving linear systems of equations (Harrow, Hassidim & Lloyd, 2009).
HHL algorithm consists in an application of the quantum phase estimation algorithm (QPE), followed by rotations on an ancilla qubit controlled by t... |
On well-posedness of a velocity-vorticity formulation of the stationary Navier-Stokes equations with no-slip boundary conditions
1.
Department of Mathematics, University of Houston, Houston, TX, 77204, USA
2.
Department of Mathematical Sciences, Clemson University, Clemson, SC, 29634, USA
3.
Department of Mathematics, ... |
Backgrounds Proof. Suppose we have an orthogonal matrix,
$$ A = \begin{bmatrix} a & b \\ c & d \end{bmatrix} $$
we have
$$ I = A^T A = \begin{bmatrix} a^2 +c^2 & ab + cd \\ ab + cd & b^2 + d^2 \end{bmatrix} $$
thus we have the following formulas
$\Vert (a,c) \Vert_2 = 1$ $\Vert (b,d) \Vert_2 = 1$ $(a,c)(b,d)^T = 0$
So ... |
Note: Cross-posted on Physics SE.
I made some circuit to prepare a 2 qubit state, but I am having trouble understanding how to measure Bell's inequality. I know the inequality is of the form
$$|E(a,b)-E(a,b')+E(a',b)+E(a',b')| \leq 2$$
where for each $E$
$$E = \frac{N_{++} + N_{--} - N_{-+} - N_{+-}}{N_{++} + N_{--} + ... |
This question is about fitting a multivariate linear regression by maximum likelihood, under a specific parameterization of the covariance matrix, when the number of observations is smaller than the number of responses. It arises in an applied project that I'm part of.
Let $Y_i \in \mathbb R^r, i=1, \dots, n$ be indepe... |
ISSN:
1078-0947
eISSN:
1553-5231
All Issues
Discrete & Continuous Dynamical Systems - A
January 2008 , Volume 21 , Issue 1
A special issue dedicated to Edward Norman Dancer
on the occasion of his 60th birthday
Select all articles
Export/Reference:
Abstract:
Professor Edward Norman Dancer, known to his friends and colle... |
Faddeeva Package From AbInitio
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Line 24: Line 24: :<math>\mathrm{erfc}(x) = e^{-x^2} w(ix) = \begin{cases} e^{-x^2} w(ix) & \mathrm{R... |
Abbreviation:
TarskiA
A
is a structure $\mathbf{A}=\langle A,\to\rangle$ of type $\langle2\rangle$ such that $\to$ satisfies the following identities: Tarski algebra
$(x\to y)\to x=x$
$(x\to y)\to y=(y\to x)\to x$
$x\to(y\to z)=y\to(x\to z)$
Let $\mathbf{A}$ and $\mathbf{B}$ be Tarski algebras. A morphism from $\mathbf... |
I am trying to parametrize $x^2+y^2+sin(4x)+sin(4y)=4$.
I need to find a way of taking the intersections between $x^2+y^2+\sin(4x)+\sin(4y)=4$, and $\tan(nx)$. As n increases from $0\le{n}\le{2\pi}$, I can take the following in coordinate-form....
$$(n,\text{The x-intersection value})$$ $$(n,\text{The y-intersection va... |
I am studying the basics of Computation Theory and I came up with an example I can't understand.
Let's have a language $L = \{\langle M\rangle \mid L(M) = \Sigma^{\ast} \}$, so $L$ contains codes of all Turing machines which generate all the words from $\Sigma^{\ast}$. It's been said that we can reduce $H$ (the halting... |
In economics, capital refers to things that are used to produce other things.So, capital includes tangible things like a delivery truck, an office building, or a factory. These are things which often require energy to run.Hence, if a developing country has low capital per head, then it probably also has few delivery tr... |
For $s \leq t \leq T$, I want to evaluate $E\left[\exp\left(iz(W_t-W_s)+izb(s-t) + bW_T-b^2T/2 \right)|\mathcal{F_s}\right]$, where $W$ is Brownian motion on $\mathcal{F}$, and $b \in \mathbb{R}$. Clearly, $W_t -W_s $ is independent of $\mathcal{F}_s$, and $E[W_T|\mathcal{F}_s] = W_s$.
I would like to be able to write ... |
A consider a limit cone on a diagram $D: \mathbf{I} \rightarrow \mathbf{C}$:
$$ \left( L \xrightarrow{p_i} D(I) \right)_{I \in \mathbf{I}} $$
Now suppose that $L' \in \mathbf{C}$ is
some object isomorphic to $L$, and that there is some cone:
$$ \left( L' \xrightarrow{p_i'} D(I) \right)_{I \in \mathbf{I}} $$
Is it neces... |
The answer to your literal question, "Does a logical system have semantics?" is "Obviously, yes. The definition you quoted says so!" So I figure that isn't what you're actually asking.
I think the root of your misunderstanding is the word "formal". In this context, it doesn't mean "rigorous", the opposite of "hand-wavy... |
Can you explain why does the following Jacobian chain rule holds true?
$$ \\ \it J_{f \circ R}(x) = J_{f}(Rx) \circ R $$
Where, $ \ f\in C^2(\Omega; \mathbb{R} ),\ \Omega\subset\mathbb{R^2},\ and \ \it R \in SO(2) $ denotes a $2\times2$ matrix with det($\it R$) = 1 and it can be written as $\begin{pmatrix} \cos \alpha ... |
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