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Please excuse the longish question, it just needs some explanation to get down to the actual problem. Those familiar with the mentioned algorithms probably could jump directly to the first simplex tablau.
To solve least absolute deviation problems (a.k.a $L_1$-optimization), the Barrodale-Roberts-algorithm is a special... |
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Production of $K*(892)^0$ and $\phi$(1020) in pp collisions at $\sqrt{s}$ =7 TeV
(Springer, 2012-10)
The production of K*(892)$^0$ and $\phi$(1020) in pp collisions at $\sqrt{s}$=7 TeV was measured by the ALICE experiment at the LHC. The yields and the transverse momentum spectra $d^2 ... |
You surely know about the Brahmagupta–Fibonacci identity,
$$(a_1^2 + b_1^2)(a_2^2 + b_2^2) = (a_1a_2 \pm b_1b_2)^2 + (a_1b_2 \mp a_2b_1)^2$$
which tells us that the product of two numbers, each of which is the sum of two squares, is itself a sum of two squares. That is to say, the set of all sums of two squares is clos... |
There's a little bit of calculation you need to do here to make sure Cauchy's Residue Theorem is applicable here (you need to make sure that certain integrals are bounded etc) but this is a sketch:
Let
$$f(z) = \frac {\pi} {(1+z^2)\tan(\pi z)}$$
Then $f$ has simple poles $\forall n \in \mathbb{Z}$ and also at $\pm i$.
... |
As is well-known (see here for a M.O. question) all Kahler manifolds are $spin^c$. I would like to ask which are in fact $spin$.
Taking my motivation from the case of complex projective space, I make the following (naive) conjecture:
Conjecture: A compact $2n$-dimensional Kahler manifold $M$ is spin, if there exists a ... |
I think that no. For example, Let $x=\{1,2,3\}$ and $z=\{1,2,3,4\}$. So, $\{\{1,2,3\}\}=\{\{1,2,3,4\}\}$. Yet, $x\neq z$.
Can you explain?
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It only takes a minute to sign up.Sign up to join... |
Let $X_1,X_2,X_3$ be three discrete (integer and non-negative valued) random variables with local probabilities $a_k:=\mathbb{P}(X_1=k)$, $b_k:=\mathbb{P}(X_2=k)$, $c_k:=\mathbb{P}(X_3=k)$ and $s_k:=\mathbb{P}(X_1+X_2+X_3=k)$, $k=0,1,2,\dots$
Let us define two recurrent sequences. The first $(\alpha_n)$ by $$\alpha_0:=... |
Is it true that the cardinality of every maximal linearly independent subset of a finitely generated free module $A^{n}$ is equal to $n$ (not just at most $n$, but in fact $n$)? Here $A$ is a nonzero commutative ring. I know that it's true if $A$ is Noetherian or integral domain. I thought it was not true in general bu... |
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Hi I'm stuck on an integration problem where I need to use the method of cylindrical shells to calculate a volume.
Q. Using the method of cylindrical shells, find the volume generated when the area bounded by the curve y = x^2 - 3 and the line y = 2x is revolved about the line x = 7.
The main thing that I'm havin... |
Elementary number theory¶ Taking modular powers¶
How do I compute modular powers in Sage?
To compute \(51^{2006} \pmod{97}\) in Sage, type
sage: R = Integers(97)sage: a = R(51)sage: a^200612
Instead of
R = Integers(97) you can also type
R = IntegerModRing(97). Another option is to use the interfacewith GMP:
sage: 51.po... |
Of course you can restore the original equation from dispersion relation, at least sometimes. But I think your equations of $k = -i\nabla$ is not correct, because $k$ is a number the other is an operator, you cannot put = between them. Be careful when you abuse the notation and know what you are doing.
But you are on t... |
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Production of light nuclei and anti-nuclei in $pp$ and Pb-Pb collisions at energies available at the CERN Large Hadron Collider
(American Physical Society, 2016-02)
The production of (anti-)deuteron and (anti-)$^{3}$He nuclei in Pb-Pb collisions at $\sqrt{s_{\rm NN}}$ = 2.76 TeV has ... |
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What was your best troll you did in math?
Note by Sharky Kesa 5 years, 1 month ago
Easy Math Editor
This discussion board is a place to discuss our Daily Challenges and the math and science related to those challenges. Explanations are more than just a solution —... |
Consider a $2\times 2$ block matrix and a linear system of equations associated to it:
\begin{equation} \begin{pmatrix} - A & B \\ B^t & C \end{pmatrix} \begin{pmatrix} x \\ y \end{pmatrix} = \begin{pmatrix} \phi \\ \psi \end{pmatrix} \end{equation}
Assume that $A$ and $C$ are symmetric, and symmetric positive semi-def... |
Hessian Valuations Speaker(s):Monika Ludwig (Technische Universität Wien) Location:MSRI: Simons Auditorium Tags/Keywords
Valuation
convex function
intrinsic volume
Primary Mathematics Subject Classification Secondary Mathematics Subject ClassificationNo Secondary AMS MSC 11-Ludwig
Different approaches to introduce intr... |
Given a Hopf-algebra $H$ (over a commutative ring), it is a classical fact that its category of (left) modules is monoidal, even if $H$ is not commutative. Given two left modules $M$ and $N$, we can form a new left module structure on $M\otimes N$ via the structure map $$H\otimes M\otimes N\overset{\Delta\otimes 1\otim... |
I have some hints for you and I suggest you work from there. I might have made errors as well. If you need more help or find an error, leave a comment.
First we write the probability mass function for a having the result $N$ on a single die:
$$prob(N_i)=1/6,\, \text{with }N=1,2,3,4,5,6$$
This is a Discrete Uniform Dist... |
In physics,
coherence length is the propagation distance over which a coherent wave (e.g. an electromagnetic wave) maintains a specified degree of coherence. Wave interference is strong when the paths taken by all of the interfering waves differ by less than the coherence length. A wave with a longer coherence length i... |
Before I start, I'll admit that I've criticized the question based on its improbability; however, I've been persuaded otherwise. I'm going to try to do the calculations based on completely different formulas than I think have been used; I hope you'll stay with me as I work it out.
Let's imagine that Lucifer becomes a m... |
An
antichain in a DAG $(V, E)$ is a subset $A \subseteq V$ of vertices that are pairwise unreachable, namely, there are no $v \neq v' \in A$ such that $v$ is reachable from $v'$ in $E$. From Dilworth's theorem in partial order theory, it is known that if DAG has no antichain of size $k \in \mathbb{N}$, then it can be d... |
Arkiv för Matematik Ark. Mat. Volume 38, Number 1 (2000), 21-36. Vector-valued Hardy inequalities and B-convexity Abstract
Inequalities of the form$\sum\nolimits_{k = 0}^\infty {|\hat f(m_k )|/(k + 1) \leqslant C||f||_1 } $ for all
f∈ H 1, where { m } are special subsequences of natural numbers, are investigated in the... |
Here is a summary of what is known about approximability of $k$-CSP over a domain of size $q$:
The best known approximation algorithms for the problem give an $\Omega(q \max(k, \log q)/q^k)$ approximation [MM14 and MNT16]. For $k = \Omega(q)$, there is a matching hardness of $O(kq/q^k)$ by Håstad (UGC-hardness) and Cha... |
What happens to all of the electrons and protons in the material of a neutron star?
Could there ever be an electron star or a proton star?
If a dense, spherical star were made of uniformly charged matter, there'd be an attractive gravitational force and a repulsive electrical force. These would balance for a very small... |
The Annals of Probability Ann. Probab. Volume 27, Number 3 (1999), 1283-1303. Integrated Brownian Motion, Conditioned to be Positive Abstract
We study the two-dimensional process of integrated Brownian motion and Brownian motion, where integrated Brownian motion is conditioned to be positive. The transition density of ... |
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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... |
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Measurement of electrons from beauty hadron decays in pp collisions at root √s=7 TeV
(Elsevier, 2013-04-10)
The production cross section of electrons from semileptonic decays of beauty hadrons was measured at mid-rapidity (|y| < 0.8) in the transverse momentum range 1 < pT <8 GeV/c wit... |
By Murray Bourne, 22 Mar 2007
Last week was "Pi Day".
Google trends shows there is a periodic peak in search trends for pi on that day each year.
My post on pi was one of them.
There was a surge in 2013, after the movie "Life of Pi" was released.
See the 1 Comment below.
Posted in Mathematics category - 22 Mar 2007 [Pe... |
LLVM optimizes power sums, such as
int sum(int count) { int result = 0; for (int j = 0; j < count; ++j) result += j*j; return result; }to code that calculates the result without a loop (godbolt) sum(int): test edi, edi jle .LBB0_1 lea eax, [rdi - 1] lea ecx, [rdi - 2] imul rcx, rax lea eax, [rdi - 3] imul rax, rcx shr ... |
The Krylov-Bogolioubov theorem is a fundamental result in the ergodic theory of dynamical systems which is typically stated as follows: if $T$ is a continuous transformation of a nonempty compact metric space $X$, then there exists a Borel probability measure $\mu$ on $X$ which is invariant under $T$ in the sense that ... |
This question is largely about definitions of PCA/FA, so opinions might differ. My opinion is that PCA+varimax should not be called either PCA or FA, bur rather explicitly referred to e.g. as "varimax-rotated PCA".
I should add that this is quite a confusing topic. In this answer I want to explain what a rotation actua... |
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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... |
We say that a multilinear polynomial $P(x_1,\ldots,x_n)$ in $n$ commuting variables over $\mathbb{R}$ has
zero trace if$$ \frac{d}{dt} P(t,\ldots,t) = 0. $$Equivalently,$$ \left(\sum_{i=1}^n \frac{\partial}{\partial x_i}\right) P = 0. $$(Suggestions for a better name are welcome.)
Such functions come up, for example, w... |
I watched a YouTube movie about Reaction Engines development of the Sabre engine which main feature is cooling intake air. However, I cannot find an overview of the temperature of intake air at different airspeed levels. I am looking for an overview based on speed of sound levels and the increase on intake air temperat... |
Given a field $F$, can you necessarily construct a field extension $E \supset F$ such that $\operatorname{Gal}(E/F) = S_n\,$?
We will prove that there exists a finite Galois extension $K/\mathbb{Q}$ such that $S_n$ = $Gal(K/\mathbb{Q})$ for every integer $n \geq 1$.We will follow mostly van der Waerden's book on algebr... |
For which values of $z$ does $$\sum_{n=1}^\infty \frac{\tan(nz)}{n^2}$$ converge? For which values of $z$ is the limiting function analytic?
One can show, as in this answer, that $$\left|\frac{e^{inz}-e^{-inz}}{e^{inz}+e^{-inz}}\right|$$ is bounded as $n\to \infty$, so long as $\text{Im}(z)\neq 0$. But the article abov... |
rencsee wrote:
What is the remainder when the positive integer x is divided by 9?
(1) x + 34 is a multiple of 18 (2) x is a multiple of 11
\(\left\{ \matrix{
\,\,1\, \le \,x = 9Q + r\,\,,\,\,Q \ge 0\,\,{\mathop{\rm int}} \hfill \cr
\,\,0 \le r \le 8\,\,{\mathop{\rm int}} \,\,\,\,\, \Rightarrow \,\,\, - 2\,\, \le r - 2\... |
Let $\mathcal{C}$ be a small category and $\Sigma$ a collection of morphisms in $\mathcal{C}$. Denote by $F_\Sigma:\mathcal{C} \to \mathcal{C}[\Sigma^{-1}]$ the usual quotient functor from $\mathcal{C}$ to its localization about $\Sigma$.
Are there conditions on $\Sigma$ which guarantee that $F_\Sigma$ induces a homoto... |
Existing algorithms for solving ODEs handle functions $\frac{dy}{dt} = f(y, t)$, where $y \in \mathbb R^n$. But in many physical systems, the differential equation is autonomous, so $\frac{dy}{dt} = f(y)$, $y \in \mathbb R^n$, with the $t$ left out. With this simplifying assumption, what improvements can be seen in exi... |
There's several issues here.
(1) Is a given incidence correspondence actually a closed variety?
(2) What are explicit equations for the correspondence in the product of the relevant spaces?
(3) What are geometric properties of the incidence correspondence?
Most often, questions (1) and (3) are studied and little attent... |
№ 9
All Issues Petrenko S. M.
Ukr. Mat. Zh. - 2016. - 68, № 1. - pp. 64-77
The notion of conflict system is introduced in terms of couples of probability measures. We construct several models of conflict systems and show that every trajectory with initial state given by a couple of measures $\mu, \nu$ converges to an e... |
The Rudin-Shapiro sequence (also known as the Golay-Rudin-Shapiro sequence) is defined as follows.
Let $a_n = \sum \epsilon_i\epsilon_{i+1}$ where $\epsilon_1,\epsilon_2,\dots$ are the digits in the binary expansion of $n$. $WS(n)$, the $n$th term of the Rudin Shapiro sequence is defined by $$WS(n)=(-1)^{a_n}.$$
Questi... |
trying to determine if the series is conditionally convergent or divergent. $$\sum_{n = 1}^\infty \frac{2^{n^{2}}}{n!}$$ with n! i tried the ratio test on the series $$\frac{2^{(n+1)^{2}}}{(n+1)!} * \frac{n!}{2^{n^{2}}} = \frac{2^{2n+1}}{(n+1)} $$ which is > 1 as $n\to \infty$ and is overall divergent ? not sure if I a... |
Just for fun, here's a purely abstract way of seeing neither of these can happen:
The functors you wrote down both preserve weak equivalences, so are morphisms of relative categories, and induce adjunctions of the associated $\left(\infty,1\right)$-categories, which are $\infty$-groupoids and $1$-groupoids (which is ac... |
User:Jan A. Sanders/An introduction to Lie algebra cohomology/Lecture 2 Central extensions
The definition of projective is important when \(R\) is not \(\mathbb{R}\ ,\) \(\mathbb{C}\) or in general a field of characteristic zero, or when the dimension of the Lie algebra is not finite, otherwise it can be skipped.
defin... |
The state of a qubit, or of a collection of qubits, is given by a state vector. However, most people would say that the
output of a quantum computer is in fact the result of a measurement, which transforms the state into one which indicates a single outcome.
There are many ways to approach this, but the simplest one to... |
Yes, and no. There is a "categorically comprehensive" reason for this trace map to exist, but not necessarily to construct it. And to prove that this reason is valid, one does require categorical machinery. The elevator speech answer is:
THH is an algebra in some symmetric monoidal category. K is the unit in this symme... |
For the heat equation
\begin{equation} u_t(t,x) = \nu u_{xx}(t,x) \end{equation}
for $x \in [0,1]$ with boundary conditions $u(t,0) = u(t,1) = 0$ and initial value $u(0,x) = u_0(x)$ it is easy to show that the "energy" defined as
\begin{equation} E(t) = \frac{1}{2} \int_{0}^{1} u^2(t,x)~dx \end{equation}
decays over ti... |
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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... |
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,... |
Without a lot of expensive equipment the best you can do is make a rough estimate. By incorrectly assuming that the light that you see describes the black body temperature of the object, by assuming that the system is in thermal equilibrium with itself and that the temperature within the system is spatially and tempora... |
Many believe that $\mathsf{BPP} = \mathsf{P} \subseteq \mathsf{NP}$. However we only know that $\mathsf{BPP}$ is in the second level of polynomial hierarchy, i.e. $\mathsf{BPP}\subseteq \Sigma^ \mathsf{P}_2 \cap \Pi^ \mathsf{P}_2$. A step towards showing $\mathsf{BPP} = \mathsf{P}$ is to first bring it down to the firs... |
To evaluate detection performance, we plot the
miss-rate $mr(c) = \frac{fn(c)}{tp(c) + fn(c)}$ against the number of false positives per image $fppi(c)=\frac{fp(c)}{\text{#img}}$ in log-log plots. $tp(c)$ is the number of true positives, $fp(c)$ is the number of false positives, and $fn(c)$ is the number of false negat... |
Given that $p$ is a Mersenne prime, it is easy to check that ${\rm gcd}(p+1,p^{2}+1) = {\rm gcd}(p+1,p^{4}+1)= {\rm gcd}(p^{2}+1,p^{4}+1) = 2$, and we recall that $p+1$ is a power of $2$. Let $G$ be a solvable group of order $p^{4}(p+1)(p^{2}+1)(p^{4}+1)$. Suppose that $G$ has an irreducible character of degree $p^{4}$... |
I've known about Noether's theorem for some time and reading some things about it recently I've realised I haven't completely understood it. In that case I've been trying to understand a more rigorous approach to it as presented in Spivak's Mechanics book.
There Spivak first derives a corollary from the derivation of t... |
Consider the sphere of unit radius centered at $(0,0,1)$,and the cone of equation $z^2=x^2+y^2.$ Find the volume above the cone and inside the sphere.
The equation of the sphere is $$1 \leq x^2+y^2+(z-1)^2=x^2+y^2+z^2-2z+1$$
Using spherical coordinates this gives $$1 \leq \rho ^2\sin^2\varphi \cos^2\theta + \rho^2\sin^... |
Suppose we have a $k$-dimensional subspace $V$ in $\mathbb{R}^n$ given by a basis $\{v_1,\cdots,v_k\in \mathbb{R}^n\}$, find an index set $I\subset [n]$ with $|I|=m$ where $k\le m\le n$, such that $$\max_{v\in V}\frac{||v||_2}{||v_I||_2}$$ is minimum, where $v_I\in \mathbb{R}^m$ is the projection of $v$ to the coordina... |
$$ \min \delta CVaR - (1-\delta) \sum_i^{n} \mu_i x_i \\ \sum x_i = \sum x^{old}_i \\ Losses(s) = \sum x_i - \sum_i^{n} (R(s,i))x_i \\ VaRDev(s) = Losses(s) - VaR \\ CVaR = VaR + \frac{\sum_s^{} p_s VaRDev(s)}{1-\alpha} $$
The Markowitz style Mean-cVaR portfolio is stated above. It Appears in
by Zenios. $x^{old}$ is ex... |
Let $\Delta ABC$ be our triangle and $KLMN$ be our rectangle.
There are three cases:
1) $KN\subset AC$;
2) $KN\subset AB$ and
3) $KN\subset BC$.
In the first case let $L\in AB$ and $M\in BC$.
By the Heron's formula $$S_{\Delta ABC}=\frac{1}{4}\sqrt{2(5^28^2+5^2(\sqrt{41})^2+8^2(\sqrt{41})^2)-5^4-(\sqrt{41})^4-8^4}=16.$... |
Superfunctions Contents Covers
The back cover suggests short abstract of the Book and few notes about the Author.
About the topic
Assume some given holomorphic function \(T\). The superfunction is holomorphic solution F of equation \(T(F(z))=F(z+1)\)
The Abel function (or abelfunction) is the inverse of superfunction, ... |
User:Jan A. Sanders/An introduction to Lie algebra cohomology/Lecture 8 The trace and Killing form
Let \( R\) be \(\mathbb{C}\) and \(\dim_\mathbb{C}\mathfrak{a}<\infty\ .\) Then define \(K_\mathfrak{a}\in C^2(\mathfrak{g},\mathbb{C})\) by\[ K_\mathfrak{a}(x,y)=\mathrm{tr}(d_1(x) d_1(y))\]In the case \(\mathfrak{a}=\ma... |
2019-10-14 17:21
Performance of VELO clustering and VELO pattern recognition on FPGA/LHCb Collaboration This document contains plots and tables showing the performance obtained on VELO clustering and VELO pattern recognition using algorithms implementable on FPGA. The data used are simulated with LHCb Upgrade condition... |
Unfoldings
James Murdock (2006), Scholarpedia, 1(12):1904. doi:10.4249/scholarpedia.1904 revision #91898 [link to/cite this article]
Contents Introduction
A mathematical model of a real-world problem is usually based onidealized assumptions. If the model proves inadequate, it can beimproved by adding small terms that w... |
Some of its key features are Non-orthogonal tight-binding with a minimal sp (d,f…) basis Self-consistent and spin polarized calculations Standard DFT-like properties including thermodynamic and electrical levels, vibrational modes/intensities/Raman cross-sections, … LDA+U like corrections for strongly correlated electr... |
I read the Devinatz-Hopkins-Smith proof of the nilpotence conjectures last year, and while I followed along sentence to sentence I don't think I understood much of the motivating reasons for why what they did was a sensible mode of proof. I intend to go back and figure some of these conceptual pieces out; this question... |
Say I am measuring a quantity $x$ in physical system whose true value is approximately sinusoidal in time. I have an instrument to sample this quantity, for which the manufacturer gives an accuracy spec. Can I use this accuracy spec $(\Delta x?)$ to compute the uncertainty of the sample mean $\bar{x}$ of the quantity b... |
This question is from HRW's Fundamentals of Physics. It goes:
A tall, cylindrical chimney falls over when its base is ruptured. Treat the chimney as a thin rod of length $55.0\;m$. At the instant it makes an angle of $35.0^\circ$ with the vertical as it falls, what is the radial acceleration of the top?
What I did is t... |
Let $a_n>0$ and $b_n>0$ be two strictly declining sequences such that the series $$\sum_{n=1}^\infty \frac{a_n}{b_n}$$ is convergent. For $\sigma>0$ define $$f^N(\sigma) = \sum_{n=1}^N \frac{a_n}{b_n + \sigma/N}$$ Is it generally true that $\lim_{N \to \infty} f^N(\sigma)$ is independent of $\sigma$ or are there counte... |
I imagine you'll get many answers to your question- here is my humble attempt.
From the Mathematical point of view, the first thing I always remember is to think of equations and formulas as part of the sentence- they are not separate objects that stand alone on the page From the typesetting point of view, it's always ... |
1,062 6
Quick question, what is the approach to this problem?
Keep in mind I am supposed to use the Fundamental Theorem of Line Integrals.
[tex]\int_{C} 2ydx + 2xdy [/tex]
Where C is the line segment from (0,0) to (4,4).
Unless I am missing something I need to make that into the form of [tex]\vec{F} \cdot \vec_d{R}[/te... |
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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... |
Linear codes and ciphers¶ Codes¶
A linear code of length \(n\) is a finite dimensional subspace of \(GF(q)^n\). Sage can compute with linear error-correcting codes to a limited extent. It basically has some wrappers to GAP and GUAVA commands. GUAVA 2.8 is not included with Sage 4.0’s install of GAP but can be installed... |
If $A$ is a ($\mathbb Z$-)graded algebra, we can define its Hochschild cohomology in the usual way, via the standard complex of $A$-bimodules:
$$C_*(A)=\cdots\rightarrow A\otimes A\otimes A\rightarrow A\otimes A.$$
Since $A$ is graded, then so is the envelopìng algebra $A^{op}\otimes A$, therefore there is a ($\mathbb ... |
Suppose I had a ray of unpolarized light, and I was sitting inside the beam and looking at the electric fields oscillating, then , if I am looking at a point how would the oscillations look like? I cannot seem to understand it.
I guess you have this image in mind:
This hods just for a single photon, or elementary packe... |
I am dealing with a highly nonlinear system of two PDEs. I already have a code to solve the system in case of Dirichlet boundary conditions. The explicit system is:
$$ \begin{eqnarray*} \partial_{t}u & = & D_{11}\partial_{x}^{2}u+\partial_{x}D_{11}\cdot\partial_{x}u+D_{12}\partial_{x}^{2}v+\partial_{x}D_{12}\cdot\parti... |
In a paper by Joos and Zeh, Z Phys B 59 (1985) 223, they say:This 'coming into being of classical properties' appears related to what Heisenberg may have meant by his famous remark [7]: 'Die "Bahn" entsteht erst dadurch, dass wir sie beobachten.'Google Translate says this means something ...
@EmilioPisanty Tough call. ... |
Geometry and Topology Seminar Contents Fall 2016
date speaker title host(s) September 9 Bing Wang (UW Madison) "The extension problem of the mean curvature flow" (Local) September 16 Ben Weinkove (Northwestern University) "Gauduchon metrics with prescribed volume form" Lu Wang September 23 Jiyuan Han (UW Madison) "Defo... |
To evaluate detection performance, we plot the
miss-rate $mr(c) = \frac{fn(c)}{tp(c) + fn(c)}$ against the number of false positives per image $fppi(c)=\frac{fp(c)}{\text{#img}}$ in log-log plots. $tp(c)$ is the number of true positives, $fp(c)$ is the number of false positives, and $fn(c)$ is the number of false negat... |
How can we prove that the inverse of an upper (lower) triangular matrix is upper (lower) triangular?
Another method is as follows. An invertible upper triangular matrix has the form $A=D(I+N)$ where $D$ is diagonal (with the same diagonal entries as $A$) and $N$ is upper triangular with zero diagonal. Then $N^n=0$ wher... |
One can explore things visually/experimentally and make good discoveries, Theory is needed to justify them. Here, however, are more experiments and speculation. This is somewhat the same thing looked at in different ways, but I think each adds something.
We see that if the (real) coefficients of $p(x)=\sum_0^n a_ix^i$ ... |
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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 "Dev:Bline Speed"
m (→Bline's parameter's "speed")
Line 1: Line 1:
== Bline's parameter's "speed" ==
== Bline's parameter's "speed" ==
−
If you have played enough with Blines, "
+
If you have played enough with Blines, "Vertex" and "Tangent" converts you perhaps have noticed that a chang... |
Please note: this question was posted first (September 4) in math.stackeschange.com and then (September 16) in stats.stackeschange.com. It got no answers in neither of those sites.
Let the regularized incomplete beta and gamma functions be defined as usual: \begin{equation} I_p(z,w) = \frac a {B(z,w)} \int_0^p t^{z-1} ... |
OP mistakenly believes the relationship between these two functions is due to the number of samples (i.e. single vs all). However, the actual difference is simply how we select our training labels.
In the case of binary classification we may assign the labels $y=\pm1$ or $y=0,1$.
As it has already been stated, the logi... |
Series
Series refers to the infinite sum, that is defined as limit of sum, is it converges, and as way to get the asymptotic approximations, if diverge.
Example 1
Sometimes, the results of application of the Series operator are difficult to interpret. One example squared result of function HankelH0 of square root of pa... |
As per Ohms law , V = IR OR I = V/ R
So if I set R to 0 , then V should be equal to I ?
However when I connect 9 Volt battery poles to each other with multimeter in between the reading says 0.2 A.
Electrical Engineering Stack Exchange is a question and answer site for electronics and electrical engineering professional... |
I am learning EE, and about complex frequencies, but what is its physical meaning? What is it used for? Why is it? And only happen in the laplace transform?
closed as too broad by gented, The Photon, ZeroTheHero, Jon Custer, SRS Mar 19 at 17:15
Please edit the question to limit it to a specific problem with enough deta... |
Let $C_1$ be our $\color{blue}{\text{blue circle}}$, and $C_2$ our $\color{darkorange}{\text{orange circle}}$ with the following coordinates. Note that $C_2$ lies at $(0,R)$ which is an important detail for this problem.
Our two circles' equations are
$\begin{eqnarray}C_1&:& x^2+y^2 &= R^2 \tag{1}\\C_2&:& (x-R)^2+y^2 &... |
That post has a more generalized form of a metric I occasionally see $d(x,y) = \frac{|x-y|}{1+|x-y|}$. When would using this metric be useful exactly? It occasionally comes up when I study analysis, but I don't know why, I don't know what people use it for or what benefit it could ever bring over the standard metric. I... |
I've studied that the spin space of an electron is a two-dimensions Hilbert space. A possible representation of this space can be constructed defining:$$\chi_+ = \begin{pmatrix}1 \\ 0 \end{pmatrix} \quad \chi_- = \begin{pmatrix}0 \\ 1 \end{pmatrix} $$
With this base the spin operators became: $$ \hat{S}_n = \frac{\hbar... |
Liouville Numbers are Irrational Theorem Proof
Let $x$ be a Liouville number.
$x = \dfrac a b$
with $a, b \in \Z$ and $b > 0$.
By definition of a Liouville number, for all $n \in \N$, there exist $p,q \in \Z$ (which may depend on $n$) with $q > 1$ such that:
$0 < \left \lvert x - \dfrac p q \right \rvert < \dfrac 1 {q^... |
I have some doubts related to some of the optical flow implementations.
How to compute angular error for optical flow algorithms? I know the formula for computing, $\theta=\arccos(\vec{v}_c\cdot\vec{v}_e)$
I have the computed flow field $\vec{v}_c$. How to get the exact flow field $\vec{v}_e$, ie the actual movement of... |
Superfluids passing an obstacle and vortex nucleation
1.
Courant Institute of Mathematical Sciences, 251 Mercer Street, New York, NY. 10012, USA
2.
Department of Mathematics, University of British Columbia, Vancouver BC V6T 1Z2, Canada
$ \epsilon^2 \Delta u+ u(1-|u|^2) = 0 \ \mbox{in} \ {\mathbb R}^d \backslash \Omega,... |
Another way to see that the difficulty there is the each appearance of "provable" in quotes refers to the formal Pvbl relation, which only resembles the real provability relation in certain respects.
In particular, there are consistent theories $T$ that extend PA such that $T \vdash \text{Pvbl}_T(\phi)$ for
every formu... |
You are mixing up two different quantities (entropy of reaction, and molar entropies of the two gases involved in the reaction) and
either your text book is in error, or you have misread it somehow. For that reaction, as written, the formation of ozone from oxygen,$\Delta G$ is positive and $\Delta S$ is negative (the ... |
For an undirected graph $G$, let us denote $\gamma(G)$ the chromatic number of $G$. Let us define for positive integer $n$, the language $$ L_n = \{\langle G\rangle : \gamma(G) = n\}. $$ This is the language of undirected graphs with chromatic number $n$. I think $L_n \in \mathrm{P}^{\mathrm{NP}}$, for any $n$.
My argu... |
Day Date Topic Text Exercise 50 Thurs Nov 15 Radian Measure pg 320 1aceg, 2aceg, 3bc, 4bc, 5, 7ab, 8ab, 9ac, 11, 12, 13
Challenge: 10, 16*
*the answer for 16 should be about 86.81 radians per second
51 Fri Nov 16 PD DAY 52 Mon Nov 19 Radian Measure and Angles on the Plane pg 330 2ab, 3, 5acdf, 6cdef, 7ad, 11, 13, 15, 1... |
How great would it be if you were able to perfectly characterize melodies in mathematical terms? You could populate an abstract "melodyspace" with your own melodies and find similar or totally different ones.
Lets reduce the complexity right away and consider only pitch and note length. These two quantities offer plent... |
As you know, the peak AC input signal for delivering any particular power into any particular speaker load is:
$$V_\text{P}=\sqrt{2\:R\:P}$$
In your case, with \$1\:\text{W}\$ and \$R_\text{SPKR}=4\:\Omega\$, this works out to \$V_\text{P}=2.83\:\text{V}\$ and \$I_\text{P}=710\:\text{mA}\$.
Also, your capacitor needs t... |
I suspect your text is taking $$\hat x=x\times \;,\qquad \text{ and } \qquad \hat p_x=\frac {\hbar}i\frac d{dx},$$as postulates (it only holds in the Schrödinger Picture and with the Position Representation). And what it is saying is that it expects you to take any other observable $O$ and write it as a function of $t$... |
I) One problem is that the momentum operator $\hat{p}$ is an unbounded operator, which means that it is only defined on a domain $D(\hat{p}) \subsetneq {\cal H}$ of the Hilbert space ${\cal H}=L^2(\mathbb{R})$.
When we apply the differentiation operator $\hat{p}=\frac{\hbar}{i}\frac{d}{dx}$ to OP's wave function
$$\tag... |
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