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From
Online Computation and Competitive AnalysisBy Allan Borodin, Ran El-Yaniv, to prove that an online algorithm $\text{ALG}$ is $c$-competitive for a minimization problem (i.e., there exists a constant $\alpha$ such that $\text{ALG}(I)\leq c\cdot \text{OPT}(I) +\alpha,$), it is sufficient to find a potential function... |
Journal of Symplectic Geometry J. Symplectic Geom. Volume 10, Number 4 (2012), 601-653. On the growth rate of Leaf-Wise intersections Abstract
We define a new variant of Rabinowitz Floer homology that is particularly well suited to studying the growth rate of leaf-wise intersections. We prove that for closed manifolds ... |
I am trying to reproduce the results from a paper in Mathematica. This task involves $K$ double integrals of the form
$$\int f(x,y)g(x)dx,$$
where $f(x,y)$ is a bivariate normal density with mean $(-4.08, -3.41)$ and diagonal covariance matrix with diagonal $(1/10,1/21)$, and $g(x)$ is a normal density with mean $\beta... |
Consider $\sum_{n=1}^{\infty}nx^n\sin(nx)$. Find $R > 0$ such that the series is convergent for all $x\in(-R,R)$. Calculate the sum of the series.
I could find the radius of convergence is $R=1$, hence for any $x\in (-1,1)$ the series is continuous and convergent, However, I have some problem in finding the exact sum o... |
I am working with
lmer in R and am unsure on the assumptions on the variance-covariance matrix for the random effects in a mixed effects model.
If I have a 2 factor model, say of the form (in mixed effects R language):
Y ~ x + (1|factor1) + (variable1|factor1) + (1|factor2) + (variable1|factor2)
I know that in the unde... |
This is the mail archive of the
cygwin@cygwin.commailing list for the Cygwin project.
Re: Writing mathematical formulas From: Igor Pechtchanski <pechtcha at cs dot nyu dot edu> To: Alex Vinokur <alexvn at connect dot to> Cc: Randall R Schulz <rschulz at sonic dot net>, <cygwin at cygwin dot com> Date: Sun, 25 May 2003 ... |
In this paper, the first discussion (
Universal latent variable representation by C. Andrieu, A. Doucet and A. Lee) authors state that
Sampling exactly $Y \sim f(y|\theta)$ on a computer most often means that $Y=\phi(\theta,U)$ where $U$ is a random vector of probability distribution $D(\cdot)$ and $\phi(\cdot,\cdot)$ ... |
Is there a formal mathematical proof that the solution to the German Tank Problem is a function of
only the parameters k (number of observed samples) and m (maximum value among observed samples)? In other words, can one prove that the solution is independent of the other sample values besides the maximum value?
Is ther... |
Does the OLS (ordinary least squares) method of regression consider only one sample value in calculating the sample regression function (SRF)? If not, then how is the SRF created when there is more than one observation per $X_{i}$?
It is not very clear what you're asking, but if the model is of the form
$$ y_i = \beta_... |
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But the really cool part is this: given preorders \(X\) and \(Y\), we can get a feasibility relation \(\Phi : X \nrightarrow Y\) either from a monotone function \(f : X \to Y\) or from a monotone function \(g: Y \to X\). So, feasibi... |
Differentiability of a function:
Differentiability applies to a function whose derivative exists at each point in its domain.
Actually, differentiability at a point is defined as: suppose f is a real function and c is a point in its domain. The derivative of f at c is defined by
\(\lim\limits_{h \to 0} \frac{f(x+h) – f... |
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We've been having fun with databases using categories and functors. To go any further we need 'natural transformations'. These are one of the most important aspects of category theory. They give it a special flavor different from al... |
The answer is yes, it is always a submersion. First of all, $\pi:=\pi_M$ is clearly surjective. Also, for any point $s'\in S'$ lying over some $p'\in M'$, the tangent space at $s'$ maps surjectively onto the tangent space at $p'$ (since $\pi':=\pi_{M'}$ is a submersion.) Take then a point $p\in M$ and a vector $v\in T_... |
This is just an elaboration on Brendan McKay's beautiful answer, but too long for a comment. The crucial idea is to simplify the problem by generalising it, introducing a maximisation on the indices of the sum, detached from the original planar graph $G$.
For $x = (x_1, \ldots, x_n) \in \mathbb{R}_{\geq 0}^n$ and a mul... |
I have a
markov chain with $Q(u,v)$ as transition probability matrix and $\pi(u)$ as stationary distribution defined on state space $\Omega$. The dimension of matrix $Q$ is $nxn$ and vector $\pi$ is $1xn$.
I need to construct a
vorticity matrix $\Gamma (u,v)$ of dimension $nxn$ which has below properties
$\Gamma$ is sk... |
Courtesy of the OpenCV 2.3 GPU code comes a neat snippet of code for using a template parameter for reading RGB or BGR ordered components when dealing with RGB triplets.
The Code template <int blueIndex> float rgb2grey(const float *src) { return 0.114f*src[blueIndex^2] + 0.587f*src[1] + 0.299f*src[blueIndex]; }
Then to... |
Here is the standard way to prove the result.
First note that there is a non-zero $\mathcal C^\infty$ function $\theta\geq 0$ on $\mathbb R$ which is supported on $[0,1]$.
From this, it follows that for any $\varepsilon >0$, there is a non-negative $\mathcal C^\infty$ function $\phi_\varepsilon$ on $\mathbb R^n$ which ... |
Seeing that in the Chomsky Hierarchy Type 3 languages can be recognised by a DFA (which has no stacks), Type 2 by a DFA with one stack (i.e. a push-down automaton) and Type 0 by a DFA with two stacks (i.e. with one queue, i.e. with a tape, i.e. by a Turing Machine), how do Type 1 languages fit in...
Considering this ps... |
Suppose you observe the historical returns of \(p\) different fund managers, and wish to test whether any of them have superior Signal-Noise ratio (SNR)compared to the others. The first test you might perform is the test of pairwise equality of all SNRs.This test relies on the multivariate delta method and central limi... |
The $\mathbb{Z_5}$-vector space $\mathfrak{B}$ 3 over the field $(\mathbb{Z_5}, +, .)$ $\mathfrak{B}$ 3over the field $(\mathbb{Z_5}, +, .)$ 1. BackgroundThis is a formal introduction to the genetic code $\mathbb{Z_5}$-vector space $\mathfrak{B}^3$ over the field $(\mathbb{Z_5}, +, .)$. This mathematical model is defin... |
Frequently, 19th century physicists—e.g., Helmholtz or Maxwell—did not use modern-day vector notation, which Gibbs contributed in large part to.
For example, Helmholtz in his famous paper on the conservation of energy writes
$$X=m\frac{du}{dt},\hspace{1em}Y=m\frac{dv}{dt},\hspace{1em}Z=m\frac{dw}{dt},$$
where $X,Y,Z$ a... |
Yes, an instanton is a classical solution to the Euclidean equations of motion with finite action. Its topological charge is given by $k = \frac{1}{8\pi}\int \mathrm{tr}(F\wedge F)$ which is the integral of the divergence of the Chern-Simons current.
There are many different instantons possible. A generic instanton for... |
The above graph is pulled from the book "Automatic Control Systems" by Kuo.
The subject loop transfer function is $$L(s)=\frac{K}{s(1+T_1s)}$$ or $$L(j\omega)=\frac{-jK(1-jT_1\omega)}{\omega(1+T_1^2\omega^2)}$$ or $$L(j\omega)=\frac{K(-j-T_1\omega)}{\omega(1+T_1^2\omega^2)}$$
Hence the phase equation should be $$tan(\t... |
This question already has an answer here:
Prove, that set $\{f \in \mathbb{N^N} \: | \:f \: $is strictly increasing $\}$ has the same cardinality as $\mathbb R$.
My attempts:
The beginning of this task was quite easy, but then I got stuck on constructing an injection between a set of function (let's call it $X$) and $\... |
Note this is a hard problem, which depends on so many factors. Ergo giving complete answers which go through all the possibilities is a bit hard. For instance, the case changes dramatically depending on where you attach the pinpoint on Earth(i.e. north pole or equator) or whether Moon is in its apogee or perigee or som... |
As stated, $\log (n) = O (2^n)$ is trivially true.
All that it says is that $\log n$, in the end, grows no faster than $2^n$. For $2^n$, you can substitute $n$, $\sqrt n$, indeed any root of $n$.
However carelessly stated, I think this really refers to the following:
To represent a number of size $2^n$, you need $n$ bi... |
@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... |
This question already has an answer here:
Can anyone help me on how to prove that sin(x)/x is not Lebesgue Integrable in [1,+00], Thanks in advance.
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It only takes a minute to sign up.Sign ... |
In order to become the very best Pokenom trainer, Bash is studying Pokenom’s evolutions.
Each Pokenom has a combat power ($CP$), indicating how strong the Pokenom is. After certain amount of training, a Pokenom can evolve, and the evolved Pokenom will have higher $CP$. A Pokenom can evolve multiple times. There is no k... |
I am trying to solve the question 6.12 in Arora-Barak (Computational Complexity: A modern approach). The question asks you to show that the $\mathsf{PATH}$ problem (decide whether a graph $G$ has a path from a given node $s$ to another given node $t$) which is complete for $\mathbf{NL}$ is also contained in $\mathbf{NC... |
Serial of year 28
You can find the serial also in the yearbook.
We are sorry, this serial has not been translated. Text of serial Tasks (6 points)1. Series 28. Year - S. Unsure
Write down the equations for a throw in a homogeneous gravitational field (you don't need to prove them but you need to know how to use them). ... |
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... |
The distance $d_K^H(x,y)$ between two points on the hyperboloid $H_K$ with curvature $K<0$ can be emulated on the distance $d_{-1}(x,y)$ of the hyperboloid $H_{-1}$ of curvature ($K=-1$) as follows: $$ d_K^H(x,y)=R\cdot d_{-1}^H(x/R,y/R) $$ where $R$ is the radius and is related to the curvature as follows: $R=\frac{1}... |
I feel like this question might be marked as duplicate because I see many similar incurring in that fate but I'll try anyway. I would say I did not find anything similar.
I have been thought a procedure to find conugate prior distributions that is based on sufficient statistics. The idea is to compute the likelihood of... |
Basically 2 strings, $a>b$, which go into the first box and do division to output $b,r$ such that $a = bq + r$ and $r<b$, then you have to check for $r=0$ which returns $b$ if we are done, otherwise inputs $r,q$ into the division box..
There was a guy at my university who was convinced he had proven the Collatz Conject... |
Thank you for using the timer!We noticed you are actually not timing your practice. Click the START button first next time you use the timer.There are many benefits to timing your practice, including:
Does GMAT RC seem like an uphill battle? e-GMAT is conducting a free webinar to help you learn reading strategies that ... |
I have been helping undergrads in an introduction to linear algebra course. When solving some exercise consisting in showing that a map is linear some get lazy after proving that it is closed under addition and do not prove the closure under scalar multiplication. I wanted to confront them with an example of a map clos... |
Apart from the formal result about
#P-hardness, there's something worth touching on, about the nature of strong simulation itself. I'll comment first on strong simulation, and then specifically on the quantum case. 1. Strong simulation even of classical randomised computation is hard
Strong simulation is a very powerfu... |
As yet I don't know how to prove this, but a formula that seems to work is
$$\displaystyle p=2\left(n-2^{\bmod\left(\frac{(\log(n)-0.001)}{\log(2)}\right)\right)-1.$$
The logs are to base 10 and mod (I hope, otherwise I need to find another operator,) delivers the integer part of the expression within the brackets.
p i... |
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... |
Is it true to say that $\Sigma^* \cdot$ {$a^nb^n: n>=0$} = $\Sigma^*$
Becuase if we take $\Sigma^*$ and concatenate it to {$a^nb^n: n>=0$} we don't get any "new" words than those we had in $\Sigma^*$ in the first place.
Computer Science Stack Exchange is a question and answer site for students, researchers and practiti... |
Each team plays $4$ games.
$P(\text{a team wins all its games}) = {5\choose{1}}\cdot{1\over{2}}^4$
$P(\text{a team loses all its games}) = {5\choose{1}}\cdot{1\over{2}}^4$
$P(\text{a team wins all its games and any remaining team loses all its games}) = {5\choose{1}} \cdot {4\choose{1}} \cdot {1\over2}^7$
$P(\text{at l... |
This is true for finite-dimensional spaces: the diagonal operators on a finite dimensional complex vector space
form contain a dense open set and the nondiagonalizable operators have measure 0.
To be precise, let $T$ be an operator on a complex Banach space $X$ which is not finite-dimensional. For each $\lambda \in \ma... |
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Now showing items 31-40 of 167
Transverse sphericity of primary charged particles in minimum bias proton-proton collisions at $\sqrt{s}$=0.9, 2.76 and 7 TeV
(Springer, 2012-09)
Measurements of the sphericity of primary charged particles in minimum bias proton--proton collisions at $\sqrt{s}$=0.9, 2.76 and 7 TeV ... |
Abbreviation:
AbLGrp
An
(or abelian $\ell $ abelian lattice-ordered group ) is a lattice-ordered group $\mathbf{L}=\langle L, \vee, \wedge, \cdot, ^{-1}, e\rangle$ such that -group
$\cdot$ is commutative: $x\cdot y=y\cdot x$
Let $\mathbf{L}$ and $\mathbf{M}$ be $\ell$-groups. A morphism from $\mathbf{L}$ to $\mathbf{M}... |
I am reading MWG's explanation in Chapter 3 when showing continuous preference relation implies the existence of continuous utility function.
First, the authors show $u(.)$ is continuous by using the definition that the image under $u(.)$ of a convergent sequence is convergent. Consider a sequences $x_n\rightarrow x$. ... |
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Now let's look at a mathematical approach to resource theories. As I've mentioned, resource theories let us tackle questions like these:
Our first approach will only tackle question 1. Given \(y\), we will only ask
is it possible to... |
What is the assumption for Boltzmann H-theorem? One can derive it just from the unitarity of quantum mechanics, so this should be generally true, does it imply a closed system will always thermalize eventually? Does it apply for many-body localized states?
I would like to share my thoughts and questions on the issue. T... |
Principle of Recursive Definition Contents Theorem
Let $\N$ be the natural numbers.
Let $T$ be a set.
Let $a \in T$.
Let $g: T \to T$ be a mapping.
$\forall x \in \N: f \left({x}\right) = \begin{cases} a & : x = 0 \\ g \left({f \left({n}\right)}\right) & : x = n + 1 \end{cases}$
Let $p \in \N$.
Let $p^\geq$ be the uppe... |
Faddeeva Package From AbInitio
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Line 25: Line 25: :<math>\mathrm{erf}(x) = 1 - \mathrm{erfc}(x) = \begin{cases} 1 - e^{-x^2} w(ix) & ... |
Abbreviation:
QtGrpd
A
is a groupoid $\mathbf{A}=\langle A,\cdot\rangle$ such that quasitrivial groupoid
$\cdot$ is
: $x\cdot y=x\text{ or }x\cdot y=y$ quasitrivial
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.
It is ... |
Just including my answers here for my own sake, I tried to skip other people's answers until writing this.
> Puzzle 18. Does f! always have a left adjoint? If so, describe it. If not, give an example where it doesn't, and some conditions under which it does have a left adjoint.
> Puzzle 19. Does f! always have a right ... |
Where the graph of the tangent function increases, the graph of the cotangent function decreases. Click to search:. Therefore, the LCD can be seen as a periodicity multiplier. If we look at any larger interval, we will see that the characteristics of the graph repeat. Use the reciprocal relationship of the cosine and s... |
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'm learning how to control a double integrator with $H_\infty$.
my model is simply
$ \dot{r} = v $
$ \dot{v} = F/m $
$ r(t_0) = 0$ m, $v(t_0) = 0 $ m/s, $m = 1000 $ kg
so I want to be able to track a step command. I have noise on measurements of position, velocity and force, assumed with a noise having a std of 0.02 m... |
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physics.atom-ph
Change to browse by: References & Citations Bookmark(what is this?) Physics > Atomic Physics Title: Transition from electromagnetically induced transparency to Autler-Townes splitting in cold cesium atoms
(Submitted on 1 Sep 2017)
Abstract: Electromagnetically induced transparenc... |
Also, read Matrix Formulas Determinant Formulas Set Theory Mean Median Mode Formula:
Nowadays, you must be aware of the use of data through statistics almost everywhere. Take an example of cricket match. While watching the match you see several graphical representations of different types of data such as sixes per over... |
How do I prove that if $A\in\mathbb C^{n\times n}$ is a matrix then it is irreducible if and only if its associated graph (defined as at Graph of a matrix) is strongly connected?
Update:
Seeing as no-one answered for over a week, I tried to do it by myself.
The first thing I did was try to show column or row permutatio... |
Fix an algebraically closed field $k$ (arbitrary characteristic), all schemes will be of finite type over $k$.
(Property *): I'm interested in (classes of) examples of schemes $X$ (irreducible, of dimension $n$) so that any morphism of schemes $\phi: X \rightarrow Y$ with $\dim Y < n$ is constant.
There are two example... |
2019-09-20 08:41
Search for the $^{73}\mathrm{Ga}$ ground-state doublet splitting in the $\beta$ decay of $^{73}\mathrm{Zn}$ / Vedia, V (UCM, Madrid, Dept. Phys.) ; Paziy, V (UCM, Madrid, Dept. Phys.) ; Fraile, L M (UCM, Madrid, Dept. Phys.) ; Mach, H (UCM, Madrid, Dept. Phys. ; NCBJ, Swierk) ; Walters, W B (Maryland U... |
Refine Language English (6) (remove)
If \(A\) generates a bounded cosine function on a Banach space \(X\) then the negative square root \(B\) of \(A\) generates a holomorphic semigroup, and this semigroup is the conjugate potential transform of the cosine function. This connection is studied in detail, and it is used f... |
I am reading Katz' book
Enumerative Geometry and String Theory. I have a few questions regarding the moduli space of degree $d$ genus $0$ stable maps into $\mathbb P^n$, denoted $\overline{M}(\mathbb{P}^n, d)$. First let me paraphrase some definitions in the book (given between p.32-37) to the best of my understanding ... |
Abbreviation:
NRng$_1$
A
is a structure $\mathbf{N}=\langle N,+,-,0,\cdot,1\rangle $ of type $\langle 2,1,0,2,0\rangle $ such that near-ring with identity
$\langle N,+,-,0,\cdot\rangle $ is a near-rings
$1$ is a
: $x\cdot 1=x\mbox{and}1\cdot x=x$ multiplicative identity
Let $\mathbf{M}$ and $\mathbf{N}$ be near-rings w... |
Consider the "compacted" formula (as also used in the "Syracuse"-version of the Collatz), defining one "step" beginning on $a$ going to $b$ (both odd $\ge 1$):$$ b = {3a+1\over 2^A } \tag 1$$ where $A$ contains the number of halving-steps.
Now to have a (very) simple cycle of just one step we must have:$$ a = {3a+1\ove... |
Assume that $\phi:\mathbb{R}^n\rightarrow \mathbb{R}^n$ is a smooth vector field, and assume that we can find vectors $y_k,x_k$ ($k$ positive integer) such that $(\phi(x_k)-\phi(y_k),x_k-y_k)\geq k \mid y_k-x_k\mid^2$, where $(,)$ is the usual scalar product. Why does this condition contradict the fact that $\phi$ is L... |
Suppose $f$ is an entire function on $\mathbb{C}^n$ that satisfies for every $\epsilon>0$ a growth-condition $$|f(z)|\leq C_{\epsilon}(1+|z|)^{N_{\epsilon}}e^{\epsilon | \text{Im}\,z|}$$
Show that $f$ is a polynomial. (Hint: study $\hat{f} = \mathcal{F}(f)$ the Fourier-transform).
I know I'm supposed to apply the Paley... |
Kernel of Ring Epimorphism is Ideal
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This article has been proposed for deletion. In particular:
Please assess the validity of this proposal. (discuss)
Zero extra content over the two parts in the proof Theorem
Let $\phi: \left({R_1, +_1, \circ_1}\right) \to \left({R_2, +_2, \circ_2}\ri... |
What are common cost functions used in evaluating the performance of neural networks?
Details
(feel free to skip the rest of this question, my intent here is simply to provide clarification on notation that answers may use to help them be more understandable to the general reader)
I think it would be useful to have a l... |
Let $x \in [0,1]$ denote some state (e.g. market share).Let $i \in \{1,2\}$ denote an agent (e.g. firm).Im considering a model where payoffs $F_i(x)$ are perfectly invertible in the sense that the payoff functions can be mirrored along the line $x = \frac{1}{2}$ with $F_1(x) = F_2(1-x)$. Take $F_1(x) = x$ and $F_2(x) =... |
I am just starting a course on Lie groups and I'm having some difficulty understanding some of the ideas to do with vector fields on Lie groups.Here is something that I have written out, which I
know is wrong, but can't understand why:
Let $X$ be any vector field on a Lie group $G$, so that $X\colon C^\infty(G)\to C^\i... |
Let $X$ be a Hausdorff space. Let $\mathscr{F}=\left\{f_j:X\rightarrow R\mid j\in J\right\}$ be a family of continuous real-valued functions with following property:for every $x\in X$, and every closed set $A\subset X$ with $x\notin A$, there exists $f_j\in \mathscr{F}$ with $f_j (x)>0$ and $f_j(a)=0$ for every $a\in A... |
I'm only going to address question 1 in some generality, since the infinite measure $\mu(E) = \infty$ for $\emptyset \neq E \in \Sigma$ gives a complete measure on $\Sigma$ and thus an obvious answer to question 2 (as was noted by Niels Diepeveen).
Most of the things I'm saying below can be found or extracted from Frem... |
In the mentioned context, what is meant is that, between a pair of qubits that are coupled, an XX coupling means something of the form$$X\otimes X\equiv\left(\begin{array}{cccc} 0 & 0 & 0 & 1 \\ 0 & 0 & 1 & 0 \\ 0 & 1 & 0 & 0 \\ 1 & 0 & 0 & 0 \end{array}\right),$$tensored with identity between all other qubits, where $... |
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Now showing items 1-6 of 6
Forward-backward multiplicity correlations in pp collisions at √s = 0.9, 2.76 and 7 TeV
(Springer, 2015-05-20)
The strength of forward-backward (FB) multiplicity correlations is measured by the ALICE detector in proton-proton (pp) collisions at s√ = 0.9, 2.76 and 7 TeV. The measurement... |
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... |
Each letter shown represent distinct digit...can vary from zero to nine.
$COCA$, $COLA$, $SODA$ are three concatenated numbers.
Figure these out from the following relation:
$COCA + COLA = SODA$
Puzzling Stack Exchange is a question and answer site for those who create, solve, and study puzzles. It only takes a minute ... |
The term quantum supremacy doesn't necessarily mean that one can run algorithms, as such, on a quantum computer that are impractical to run on a classical computer. It just means that a quantum computer can do something that a classical computer will find difficult to simulate.You might ask (and rightly so) what I migh... |
While this may be a fruitless pursuit of anecdotes, I still ask: what is the strangest (or most blatantly wrong (at least in the eyes of common notation)) mathematical notation you have ever seen?
closed as primarily opinion-based by Zev Chonoles, Shuchang, M Turgeon, Claude Leibovici, Paramanand Singh Mar 1 '14 at 7:0... |
In a simple pendulum system, how does the extensibility/elasticity of the string affect the time period of oscillation? Would it lead to a random or systematic error? Would the elasticity of the string result in changing lengths of the pendulum across the oscillation, hence altering the time period?
For small oscillati... |
Closed orbits of Hamiltonian systems on non-compact prescribed energy surfaces
1.
Département de Mathématiques, Faculté des Sciences de Tunis, Campus Universitaire, 2092, Tunis, Tunisia
$ \dot q = H_p (p,q),\quad \dot p=-H_q(p,q),$
such that
$H(p,q)= h,$
when the prescribed energy surface $S_h=${$(p,q)\in \mathbf R^N \... |
ISSN:
1078-0947
eISSN:
1553-5231
All Issues
Discrete & Continuous Dynamical Systems - A
February 2019 , Volume 39 , Issue 2
Select all articles
Export/Reference:
Abstract:
Let
Abstract:
We study the asymptotic behavior of a class of non-autonomous non-local fractional stochastic parabolic equation driven by multiplicat... |
Abbreviation:
Cat
A
is a structure $\mathbf{C}=\langle C,\circ,\text{dom},\text{cod}\rangle$ of type $\langle 2,1,1\rangle$ such that$C$ is a class, category
$\langle C,\circ\rangle$ is a (large) partial semigroup
dom amd cod are total unary operations on $C$ such that
$\text{dom}(x)$ is a left unit: $\text{dom}(x)\cir... |
Along the lines of Glen O's answer, this answer attempts to explain the solvability of the problem, rather than provide the answer, which has already been given. Instead of using the meta-knowledge approach, which, as Glen stated, can get hard to follow, I use the range-base approach used in Rubio's answer, and specifi... |
ISSN:
1078-0947
eISSN:
1553-5231
All Issues
Discrete & Continuous Dynamical Systems - A
April 2014 , Volume 34 , Issue 4
Special Issue on Optimal Transport and Applications
Select all articles
Export/Reference:
Abstract:
Optimal mass transportation can be traced back to Gaspard Monge's paper in 1781. There, for enginee... |
Materials in Meep From AbInitio
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Let $A$ be a non-empty subset of $\mathbb{R}$. Define the difference set to be
$A_d := \{b-a\;|\;a,b \in A \text{ and } a < b \}$
If $A$ is infinite and bounded then $\inf{A_d} = 0$.
Since $a < b$ we have $b - a > 0$. Thus zero is a lower bound for $A_d$ and $\inf(A_d) \geq 0$. I then want to show that if $\inf(A_d) = ... |
The equation I'm refering to was posed by Lagrange and states that if $S\subset \mathbb{R^3}$ is a surface with zero mean curvature, ie $H=0, \: \: \forall p \in S$ and S is given as the graph of a function $z(x,y)$ then$$(1+z_x^2)z_{yy}-2z_xz_yz_{xy}+(1+z_y^2)z_{xx}=0$$I'm looking for a proof of this. I thought I woul... |
I was reading this answer and I don't quite understand how the $\rho$ homomorphism works. The generators of the two copies of $\mathfrak{su}(2)$ in $\mathfrak{su}(2)\oplus\mathfrak{su}(2)$ are given by $N_i^+ = \frac{1}{2}(J_i+\mathrm{i}K_i)$ , $N_i^- = \frac{1}{2}(J_i-\mathrm{i}K_i)$ respectively. The $J_i$'s are the ... |
Suppose that there are a set of $n$ points $P = \{(x_1,y_1), \dots, (x_n,y_n)\}$ in 2D.
Given two coordinates $(a,b)$ and a number $r \in \mathbb{R}$, is there an algorithm with $O(|Q| + \log n)$ running time that can find the point set $Q \subseteq P$ containing those points of $P$ that are inside the circle with cent... |
I'm trying to follow the proof in Wikipedia that the PNT is equivalent to the assertion $\psi(x)\sim x$, by proving that $\psi(x)\sim\pi(x)\log x$, which it claims is a very simple proof. One direction of inequality is an actual bound, $\psi(x)\le\pi(x)\log x$, but the other inequality has a fuzz factor:
$$\psi(x) \ge ... |
Let's say I throw an object horizontally off a cliff with a fixed height, and I know the time it takes to fall. I wanted to know how far it travels, but it has an acceleration opposite the direction of initial velocity due to air resistance. Therefore, I integrated velocity with respect to time; in this case, velocity ... |
Hi, Can someone provide me some self reading material for Condensed matter theory? I've done QFT previously for which I could happily read Peskin supplemented with David Tong. Can you please suggest some references along those lines? Thanks
@skullpatrol The second one was in my MSc and covered considerably less than my... |
How to explain to a middle-school student the notion of a geometric series without any calculus (i.e. limits)? For example I want to convince my student that $$1 + \frac{1}{4} + \frac{1}{4^2} + \ldots + \frac{1}{4^n} = \frac{1 - (\frac{1}{4})^{n+1} }{ 1 - \frac{1}{4}}$$ at $n \to \infty$ gives 4/3?
The equality is equi... |
Starting from the famous infinite product $$ (1+z)^2(1-z^2)(1+z^3)^2(1-z^4)(1+z^5)^2(1-z^6)\cdots=1+2z+2z^4+2z^9+2z^{16}+\dots $$ it is easy to show by induction that $$ \prod_{k\geqslant1}\left((1-z^k)(1-z^{2k-1})^N(1+z^{2k})^{N+1}(1+z^{2k-1})^{N+3}\right)=\sum_{n=-\infty}^{+\infty}z^{n^2} $$ for any $N\geqslant0$.
Ca... |
Is it true that $(\Bbb Z_n,\cdot)$, integers modulo $n$ under multiplication, is a group if and only if $n$ is prime? If it's true, why? How can I prove it?
Note that $\mathbb{Z}_n=\mathbb{Z}/n\mathbb{Z}$ is never a group with respect to multiplication, unless $n=1$.
This is because $[0]$ is not invertible, whenever $n... |
I had the same problem a few days ago and I used the following heuristic to do it. According to my first impression it seems to work.
My specific use case was to determine a strategy in which sequence I should convert function implementations from one programming language into another so that we can execute as many tes... |
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Okay, now I've rather carefully discussed one example of \(\mathcal{V}\)-enriched profunctors, and rather sloppily discussed another. Now it's time to build the general framework that can handle both these examples.
We can define \(... |
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Today I will finally define enriched profunctors. For this we need two ways to build enriched categories.
There are lots of ways to build new categories from old, and most work for \(\mathcal{V}\)-enriched categories too
if \(\,\mat... |
Take the set of all vectors $x = (x_1, \cdots, x_n)$ that are solutions to $p_1x_1 + \cdots + p_nx_n = I > 0$. Show that this set has $n-1$ dimensions.
I have somehow managed to get myself stuck on the last part of this proof it seems. I am not using the fact that this set is a hyperplane and that hyperplanes are $n-1$... |
I am confused about the slash notation and especially taking the square of a slashed operator.
Defining $\displaystyle{\not} a \, = \, \gamma^\mu a_\mu$ we have $\,\,$ $\displaystyle{\not} a \displaystyle{\not} a = a^2 $
I tried to prove that, but I can't really doing it without assumption I didn't prove. That's my (I ... |
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