text stringlengths 256 16.4k |
|---|
On the optimal map in the $ 2 $-dimensional random matching problem
1.
Scuola Normale Superiore, Piazza dei Cavalieri 7, 56126 Pisa, Italy
2.
ETH, Rämistrasse 101, 8092 Zürich, Switzerland
3.
Dipartimento di Matematica, Università di Pisa, Largo Bruno Pontecorvo 5, 56127 Pisa, Italy
We show that, on a $ 2 $-dimensional... |
Total $\{k\}$-domination in special graphs
1.
University of Science and Technology of China (USTC), Hefei, China
2.
Facebook Seattle, 1101 Dexter Ave N, Seattle, WA 98109, USA
For a positive integer $k$ and a graph $G = (V,E)$, a function $f:V \to \{0,1,...,k\}$ is called a
total $\{k\}$- dominating function of $G$ if ... |
I wanted to better understand dfa. I wanted to build upon a previous question:Creating a DFA that only accepts number of a's that are multiples of 3But I wanted to go a bit further. Is there any way we can have a DFA that accepts number of a's that are multiples of 3 but does NOT have the sub...
Let $X$ be a measurable... |
I am looking for the asymptotics of the following integral
$\int_{\mathbb{R}} H_m^2(x) {\rm e}^{-2 \alpha^2 x^2} {\rm d} x = 2^{m-1/2} \alpha^{-2m -1} (1-2\alpha^2)^m \ \Gamma(m+1/2) ~ _2F_1\left(-m,m,1/2-m,\frac{\alpha^2}{2\alpha^2-1}\right)$
where $H_m$ is the $m^{\rm th}$ Hermite polynomial (orthogonal under the wei... |
High-energy neutrinos from individual blazar flares
Pre-published on: 2019 July 22
Published on: —
Abstract
Motivated by the recently reported evidence of an association between a high-energy neutrino and a $\gamma$-ray flare from the blazar TXS 0506+056, we calculate the expected high-energy neutrino signal from past,... |
Search
Now showing items 1-10 of 34
Lifetime of helium metastable spin-states in a helium discharge
(1965)
The lifetime of a helium 23s1 metastable atom electronic spin-state is measured in helium gas using optical pumping techniques. The metastable atoms are created by an RF electrical discharge. The spin-state lifeti... |
Can I be a pedant and say that if the question states that $\langle \alpha \vert A \vert \alpha \rangle = 0$ for every vector $\lvert \alpha \rangle$, that means that $A$ is everywhere defined, so there are no domain issues?
Gravitational optics is very different from quantum optics, if by the latter you mean the quant... |
For a typical hypothesis test with simple null hypothesis $H_0$ and simple alternative hypothesis $H_1$, and a continuous random variable $X$ as the observation, let the pdf of $X$ be denoted by $f_0(x)$ whenever the null hypothesis is true and by $f_1(x)$ whenever the alternative hypothesis is true. If $\Gamma_1$ deno... |
19 0
I am currently studying the Massive Thirring Model (MTM) with the Lagrangian
$$ \mathcal{L} = \imath {\bar{\Psi}} (\gamma^\mu {\partial}_\mu - m_0 )\Psi - \frac{1}{2}g: \left( \bar{\Psi} \gamma_\mu \Psi \right)\left( \bar{\Psi} \gamma^\mu \Psi \right): . $$ and Hamiltonian $$ \int \mathrm{d}x \imath \Psi^\dagger \... |
Often in topos theory, one starts with a geometric morphism $f: \mathcal Y \to \mathcal X$, but quickly passes to the Grothendieck fibration $U_f: \mathcal Y \downarrow f^\ast \to \mathcal X$, which is "$\mathcal Y$ regarded as an $\mathcal X$-topos". This maneuver takes one outside of the category of toposes and geome... |
Some questions on the main site have formulae in titles, and it's difficult to discuss such things in the meta without mutilating the titles. It would be nice to have MathJax enabled on the Meta as well.
Can someone from SE please revisit this request now that we're out of beta. Signal processing is sufficiently math h... |
Here's a geometric argument, but it isn't as slick as some of the Calculus-based ones.
Consider the unit circle about $O$, through $R$ and $S$, with $\theta = \angle ROS$. The perpendicular from $S$ to $\overline{OR}$ has length $\sin\theta$, while the perpendicular from $R$ up to $T$ on the extension of $\overline{OS}... |
For each $n = 1, 2, ....$, suppose that $X_n$ is a continuous random variable with density $$\hspace{10mm}\mathrm{f}(x) = \begin{cases} \frac{1}{2}(1+x)e^{-x}, & \text{if $x \ge 0$ } \\[2ex] 0, & \text{if $x\le 0$} \end{cases}$$ Set $Y_n$=min{$X_1,X_2,....X_n$}. Does n$\cdot$$Y_n$ converges in distribution as n$\to \in... |
Consider the finite sum
rs[x_, n_] := x/n Sum[n^2/(i + (n - i) x)^2, {i, 1, n}]
Is there a way to bring
Mathematica to calculate the limit for
n -> ∞?
I have tried
Limit[] as well as
NLimit[] without success.
Mathematica Stack Exchange is a question and answer site for users of Wolfram Mathematica. It only takes a minu... |
Déposez votre fichier ici pour le déplacer vers cet enregistrement.
Déposez votre fichier ici pour le déplacer vers cet enregistrement.
Research schools
Works by Sarig and Benovadia have built symbolic dynamics for arbitrary diffeomorphisms of compact manifolds. This shows thatthere can be at most countably many ergodi... |
I'm not sure where I could pose a challenge to find best $f(n)$ so people will join in. $n\ge 5$ will never probably be proven optimal, but some lucky computations or out of the box analysis might give nice results.
(Given $n$ fixed digits and operations $(+,-,\times,\div)$, whats the highest $N\in\mathbb N$, such that... |
Wythoff's game is as follows: there are two players $A$ and $B$ ( $A$ being the first player ) and there are $2$ piles of stones. When his turn a player can remove one or more stones from anyone pile or same number of stones from both the piles. A player unable to make a move loses. Also it is assumed that both the pla... |
I want all displayed mathematics in my document to be typeset in the style of inline mathematics. In his answer to this question, Matthew Leingang explains how to do the opposite (typeset all inline mathematics in the style of displayed mathematics) by carefully modifying the
\everymath token list. Reasoning by analogy... |
Let $X_n(\Bbb{Z})$ be the simplicial complex whose vertex set is $\Bbb{Z}$ and such that the vertices $v_0,...,v_k$ span a $k$-simplex if and only if $|v_i-v_j| \le n$ for every $i,j$. Prove that $X_n(\Bbb{Z})$ is $n$-dimensional...
no kidding, my maths is foundations (basic logic but not pedantic), calc 1 which I'm pr... |
Part a) of this is fine, but I'm really stuck on part b) and I have a test on this in an hours time, does anyone have any hints?
closed as off-topic by Toby Mak, Dietrich Burde, Shogun, mrtaurho, Yanior Weg Aug 12 at 19:32
This question appears to be off-topic. The users who voted to close gave this specific reason:
" ... |
As Sasho suggested, I am putting my comment as an answer.
The separations between
monotone versions of $\mathsf{NC}^1/\mathsf{poly}$ and $\mathsf{P/poly}$ versions of complexity are long known (Karchmer-Wigderson, Grigni-Sipser, etc), but in the non-monotone world almost nothing was known. Fortunately, Ben Rossman has ... |
Excitable media
Vladimir S. Zykov (2008), Scholarpedia, 3(5):1834. doi:10.4249/scholarpedia.1834 revision #91246 [link to/cite this article]
Contents Definition
An excitable medium is a dynamical system distributed continuously in space, each elementary segment of which possesses the property of excitability. Neighbori... |
Randomized learning of the second-moment matrix of a smooth function
1.
Institute of Electrical Engineering, École Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland
2.
Department of Electrical Engineering, Colorado School of Mines, Denver, CO 80401, USA
3.
Departments of Statistics and Computer Science, Ru... |
We summarize the discussion of parameters to express numbers suitable to be factored::
$$ N = C_1 r^t + C_2 s^u $$
by the Special Number Field Sieve (SNFS) from the paper "An Implementation of the Number Field Sieve" by Marije Elkenbracht-Huizing (1996).
She describes the Number Field Sieve this way:
Let $n$ be the odd... |
@JosephWright Well, we still need table notes etc. But just being able to selectably switch off parts of the parsing one does not need... For example, if a user specifies format 2.4, does the parser even need to look for e syntax, or ()'s?
@daleif What I am doing to speed things up is to store the data in a dedicated f... |
It is often said that gaussian process regression corresponds (GPR) to bayesian linear regression with a (possibly) infinite amount of basis functions. I am currently trying to understand this in detail to get an intuition for what kind of models I can express using GPR.
Do you think that this is a good approach to try... |
also, if you are in the US, the next time anything important publishing-related comes up, you can let your representatives know that you care about this and that you think the existing situation is appalling
@heather well, there's a spectrum
so, there's things like New Journal of Physics and Physical Review X
which are... |
The halting problem states there is no algorithm that will determine if a given program halts. As a consequence, there should be programs about which we can not tell whether they terminate or not. What are the simplest (smallest) known examples of such programs?
A pretty simple example could be a program testing the Co... |
I have a formula $ \neg((q \implies \neg q) \vee p \vee (\neg q \implies (r \wedge p))) $.
As it contains 3 subformulas between the $\vee$'s, how can i put it into a parse tree, as a parse tree contains 2 branches from each node.
Computer Science Stack Exchange is a question and answer site for students, researchers an... |
I have an encoding of an unambiguous grammar $G$. Can I apply a morphism $σ$ so that the grammar becomes ambiguous?
I have no clear concepts about this, only the idea: "grammar $G$ is ambiguous if there's a string $x \in L(G)$ having two different leftmost derivations in $G$". I would like a good explanation and if it'... |
Error analysis of discontinuous Galerkin method for the time fractional KdV equation with weak singularity solution
1.
School of Mathematics and Statistics, Shandong Normal University, Jinan 250014, China
2.
School of Mathematic and Quantitative Economics, Shandong University of Finance and Economics, Jinan 250014, Chi... |
School, from our house as the crow flies, is 5.73 km. If we neglect air resistance and deal strictly with ballistic flight then we can materialize a wonderful fantasy. Starting in the backyard, extending over the top of the house, is a
launch-o-rocket, a rail-like launcher that accelerates the school-bound student unti... |
The travelling salesman problem (TSP) asks the following question: Given a list of cities and the distances between each pair of cities, what is the shortest possible route that visits each city exactly once and returns to the origin city? It is an NP-hard problem in combinatorial optimization, important in operations ... |
Revisiting constraints on sterile neutrino mixing parameters using IceCube atmospheric neutrino data
Pre-published on: 2019 July 22
Published on: —
Abstract
Sterile neutrinos with $\sim 1$ eV mass scale can resolve anomalies reported in short-baseline neutrino oscillation experiments. The same sterile neutrinos can aff... |
Search
Now showing items 1-10 of 108
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 ... |
I tried evaluating the following limit with WA, but I got a wrong answer. The limit is: $$\lim_{n\to\infty}\left| \frac{n\sin^2(n+1)}{(n+1)\sin^2(n)}\right|$$ The result that I obtained from WA was $0$, however it's wrong. Any thoughts? How do I report this?
You can check this by:
WolframAlpha[ "Limit Abs[n Csc(n)^2 Si... |
Dear Uncle Colin Do you have any tips for sketching three-dimensional vectors? Every time we have an A-level question, my teacher says "draw a diagram!" but I don't know how to draw in 3D. - Got A Useless Sketching Situation Hi, GAUSS, and thank you for your message! Three-dimensional vectorsRead More →
That @solvemyma... |
This question arose while addressing Comments on a previous blog post about exponentially distributed delays. One of my ongoing complaints is that many, if not most, popular load-test generation tools do not provide exponential variates as part of a library of time delays or think-time distributions. Not only is this s... |
I think that the matter of the paradox is that it causes explosion and trivializes the formal system, and if this explosion can be prevented, there is no problem.
I'm an unprofessional person but come up with an idea.
At first,
1.discard the general law of excluded middle and disjunctive syllogism.
Next, there are two ... |
Relating to a question I posted here, I have formulated the following question:
Notation: $\max\{ x_1, \cdots, x_n \}$ denotes the maximal number among $x_1, \cdots, x_n$.
How to check the following system of equations is feasible? Assumption: $x_i, b_k$ are all in $[0,1]$
$\max\{x_i\mid i\in J_k\}=b_k$ where $1\leq k\... |
I'm a grad student in psychology, and as I pursue more and more independent studies in statistics, I am increasingly amazed by the inadequacy of my formal training. Both personal and second hand experience suggests that the paucity of statistical rigor in undergraduate and graduate training is rather ubiquitous within ... |
Let $E\to M$ be a real vector bundle of finite rank over a closed differentiable manifold $M$. Let $C^{\infty}(E)$ denote the space of smooth sections of $E$ and let $e\in C^{\infty}(E)$ be a section. I often see statements of the type:
"The tangent space to $C^{\infty}(E)$ at any given section $e\in C^{\infty}(E)$ is ... |
According to page 53 of Modern Computer Arithmetic (pdf), all of the steps in the Schönhage–Strassen Algorithm cost $O(N \cdot \lg(N))$ except for the recursion step which ends up costing $O(N\cdot \lg(N) \cdot \lg(\lg(N)))$.
I don't understand why the same inductive argument used to show the cost of the recursive step... |
@JosephWright Well, we still need table notes etc. But just being able to selectably switch off parts of the parsing one does not need... For example, if a user specifies format 2.4, does the parser even need to look for e syntax, or ()'s?
@daleif What I am doing to speed things up is to store the data in a dedicated f... |
Hey guys! I built the voltage multiplier with alternating square wave from a 555 timer as a source (which is measured 4.5V by my multimeter) but the voltage multiplier doesn't seem to work. I tried first making a voltage doubler and it showed 9V (which is correct I suppose) but when I try a quadrupler for example and t... |
Does anybody know an efficient mechanism to prove the possession of a digital signature (e.g. RSA) on a certain attribute (message) in zero-knowledge? That is, without revealing the actual signature (against tracking, for privacy) prove that you have one? Thanks a lot in advance!
Guillou and Quisquater (link) present a... |
By "surface bundle over a surface" I mean a compact, oriented 4-manifold $X$ which is the total space of an oriented fiber bundle $X\to B $ over an oriented 2-manifold $B$. Assume that the signature of the 4-manifold $X$ is non-trivial.
Conjecture 1: $X$ and $B$ can be given complex structures such that the map $X \to ... |
Dear Uncle Colin, I have the simultaneous equations $3x^2 - 3y = 0$ and $3y^2 - 3x = 0$. I've worked out that $x^2 = y$ and $y^2 = x$, but then I'm stuck! - My Expertise Relatedto1 Simultaneous Equations? Not Nearly Enough! Hi, MERSENNE, and thanks for your message!Read More →
Because I'm insufferably vain, I have a se... |
I answer the question in two steps: in the first one I prove that the class functions $f$ in question are Riemann integrable even if not bounded. To see this let's recall the following definitions
Definition 1. The measure of an interval $[a,b]$ is its length $\mu ([a,b])=\ell ([a-b])=a-b$.
Definition 2. A set $S\subse... |
Let $ X_n $ be a family of random variables an $X$ a rv with $X_n \overset{D}\rightarrow X$. Let $ a_n$ a sequence of real numbers with $a_n \overset{n \rightarrow \infty} \rightarrow a $. We say that the Distribution function of $X$ is continuous.
a) Proof that for all $x \in \mathbb{R}$ an every $\epsilon >0$ there e... |
First, a quick reminder regarding Fourier series. It's well-known that in the Hilbert space of measurable functions $f:[0,T]\to\mathbb{C}$ such that $\int_0^T|f(t)|^2dt<\infty$ (with inner product $\langle f,g\rangle = \int_0^T\overline{f(t)}g(t)dt$), henceforth denoted $L^2([0,T])$, the trigonometric system forms a cl... |
An In-Depth Look at Spherical Aberration Compensation Plates
Optical aberrations are deviations from a perfect, mathematical model. It is important to note that they are not caused by any physical, optical, or mechanical flaws. Rather, they can be caused by the lens shape itself, or placement of optical elements within... |
Update:Since, it seems there is no progress regarding this question, any idea, conjecture, hunch, or advice is welcome. For example, are there any partial or incomplete results? What are the main challenges? Which techniques may be amenable to make any progress?Any observation (irrespective of whether it is insightful ... |
Thank you to Lazarus from Colyton Grammar School and Andrei fromTudor Vianu National College, Bucharest for your solutions to thisproblem. We see that in all three cases the ratio $XZ$ to $XY$ isthe Golden Ratio.
In the first diagram, taking the circle to have unit radius, $AO =BO = CO = ZO$.
Triangle $BXO$ is similar ... |
Resonance Contents Classical Derivations Series Resonance
The classical circuit to demonstrate series resonance is the RLC circuit shown in the figure right, which shows a voltage source connected to R, L and C impedances in series. Given a fixed ac voltage source U operating at angular frequency [math] \omega [/math],... |
We let $\mathcal{F}_\infty=\bigvee_n\mathcal{F}_n$. (What does $\bigvee$ usually denote? Is $\bigvee$ different from $\cup$? Can't find it in the text.)
The theorem tells us when we have $\lim_n E(Y|\mathcal{F}_n)=E(Y|\mathcal{F}_\infty)$.
I'd like to know:
Is $\mathcal{F}_\infty$ a $\sigma$-algebra? Is it true that $A... |
The problem is:
Define a sequence by $a_{1} = 1, a_{2} = 1, a_{n+2} = \sqrt{a_{n+1} + a_{n}}, \forall n \geq 1.$
(a) Prove that $a_{n} < 2$, for all positive integer $n$.
(b) Prove that for all positive integer $n$ such that $n \geq 2$, we have $a_{n+1} > a_{n}$.
I have trouble with part (b). What I did is as follows:
... |
There are reasons that any modern example is likely to resemble the status of Legendre's constant. Most (but not all) interesting numbers admit a polynomial-time algorithm to compute their digits. In fact, there is an interesting semi-review by Borwein and Borwein that shows that most of the usual numbers in calculus (... |
But if you don't want to have a Google account: Chrome is really good. Much faster than FF (I can't run FF on either of the laptops here) and more reliable (it restores your previous session if it crashes with 100% certainty).
And Chrome has a Personal Blocklist extension which does what you want.
: )
Of course you alr... |
Real-time computation (or estimation) of the “probability to win” is difficult. We’ve seem that in soccer games, in elections… but actually, as a professor, I see that frequently when I grade my students.
Consider a classical multiple choice exam. After each question, imagine that you try to compute the probability tha... |
School, from our house as the crow flies, is 5.73 km. If we neglect air resistance and deal strictly with ballistic flight then we can materialize a wonderful fantasy. Starting in the backyard, extending over the top of the house, is a
launch-o-rocket, a rail-like launcher that accelerates the school-bound student unti... |
I am to calculate the rate of collision of gas molecules with the
walls of a container with dimensions $3m\times4m\times2m$ at room temperature ( 20°C) and pressure 1atm.For reasons of simplicity I may assume the air in the container to be an ideal gas with an atomic mass of 29.
There are a couple of intuitions on my m... |
It is not possible at an information-theoretic level to do what you want to do.
Let us suppose we have two pure states: $|\phi\rangle$ and $|\psi\rangle$, where$$|\phi\rangle = \frac{1}{\sqrt{N}}\sum_{i=1}^N |x_i\rangle$$and $|\psi\rangle$ is similar to $|\phi\rangle$ but with a few of the coefficients tweaked in some ... |
Search
Now showing items 1-1 of 1
Production of charged pions, kaons and protons at large transverse momenta in pp and Pb-Pb collisions at $\sqrt{s_{NN}}$ = 2.76 TeV
(Elsevier, 2014-09)
Transverse momentum spectra of $\pi^{\pm}, K^{\pm}$ and $p(\bar{p})$ up to $p_T$ = 20 GeV/c at mid-rapidity, |y| $\le$ 0.8, in pp and ... |
The first result is an immediate consequence of the fact that if $p$ is an odd prime, it has exactly as many QR as NR in the interval $[1,p-1]$.
For the second, I take it we want to find $\sum_1^{p-2}\left(\frac{k(k+1)}{p}\right)$.
Let $k^\ast$ be (the least positive residue of) the inverse of $k$ modulo $p$. Then$$\le... |
I'm attempting to prepare data in the same manner as section 2 of this paper.
I'm finding it a bit of a struggle. Could someone check (/improve upon) my interpretation regarding the 2 sections I have highlighted (below)?
In the first section (highlighted in yellow):
We note that price momentum is a cross-sectional phen... |
Understanding Spatial Filters
Spatial Filters are designed to be used with lasers to "clean up" the beam. Often times a laser system does not produce a beam with a smooth intensity profile. In order to produce a clean Gaussian beam, a spatial filter is used to remove the unwanted multiple-order energy peaks and pass on... |
EDIT: I moved my original question down to the bottom. The question here at the top is related, at least I suppose that the same phenomenon is behind both of them.
In the article "Valeurs de fonctions L et périods d'intégrales" (p. 333/334), Deligne sketches how to define the motive $M(f)$ attached to a newform $f=\sum... |
We consider perturbations to the rest state of heat conductive compressible fluid in a three-dimensional exterior domain. In the regularity class $ {\cal V}_s $ , we show stability of L 2 -norms of these perturbations, while in the more restrictive class $ {\cal V}_d $ we show convergence to zero of these perturbations... |
Answer
The work done by the weightlifter is zero.
Work Step by Step
By definition, the work is only done when an object changes its position after a force acts on it. The weightlifter is just holding a barbell above his head. Due to this, the weightlifter’s body is just shaking but not moving from his position. So, the... |
I'm trying to design a data structure that supports the following operations in $O(1)$ time:
$\operatorname{query}(\ell)$: Yield some auxiliary datum associated with list $\ell$ (just a single integer for my use case). $\operatorname{update}(\ell,v)$: Set the auxiliary datum of list $\ell$ to $v$. $\operatorname{list}(... |
I have a problem with what seems a very simple functional maximization. Let's define:
$$ J[z]=\int \left( u(z)-\frac{\dot z^2}{2} \right) dt $$
Where $u(z)=-z^2+5$. The problem is to find
$$ \arg\max_z J[z]$$
Said in a colloquial way, to maximize the function $u(z)$ without varying too much $z$ with time. The second va... |
X
Search Filters
Format
Subjects
Library Location
Language
Publication Date
Click on a bar to filter by decade
Slide to change publication date range
1. Measurement with the ATLAS detector of multi-particle azimuthal correlations in p+Pb collisions at sNN=5.02 TeV
Physics Letters B, ISSN 0370-2693, 08/2013, Volume 725,... |
The very first thing one usually does in a logic course is to defines a formal language for the propositional logic.
I don't want to bother what a "logic" is and why we need a "language" which we define know for a "logic".
A language consists of an ALPHABET and a GRAMMAR.
An alphabet $\mathcal{A}$ is a union of three d... |
Why Mathematica 11.1.1 seems to hang on
DSolve[y'[x] == Log[1 + y[x]^2], y[x], x]
Since this ODE is separable, it becomes just an integration problem.
Mathematica knows that
Integrate[1/Log[y^2 + 1], y] have no closed form solution as it returns
instantly unevaluated the integration of the left side
The question is: Wh... |
I'm a Calculus 2 Student. But don't worry, this isn't a "do my HW" problem. I have a question about improper integrals.
I just realized something that's got me quite curious about the behaviors of infinite limits and I was hoping someone could explain what I'm observing.
If we're given the integral:
$$ \int_a^\infty [f... |
Suppose we color the edges $\{1,\ldots, {n \choose 2}\}$ of the complete graph on $n$ vertices with $m$ colors each edge being assigned a color picked uniformly at random from $\{1,\ldots, m\}.$
I would like to estimate the probability that the obtained random coloring is proper, that is all edges incident with a verte... |
My reference is "A Course on Mathematical Logic" by S.M. Srivastava. I have trouble understanding some points in this remarkable book.
Substituting a term in place of a variable in a formula. Why is substitution defined as it is?
This is in the context of first order logic. Take a language $L$ (variables, constant symb... |
What you want to keep in mind is that when we say a quantum state is represented by a state $\mid \psi \rangle$ in a Hilbert space we haven't yet committed ourselves to a particular Hilbert space.
When a system has a classical analogue we introduce hermitian operators $X$ and $P$ which obey a canonical commutation rela... |
I don't really understand the difference. Shouldn't roll down and pull to par be the same technically? If a bond is trading as a discount it "increases" in value because everyday gets closer to par, and it rolls into another issue which has gotten closer? I feel that pull to par is incorporated within roll down because... |
253 23 Homework Statement Two identical uniform triangular metal played held together by light rods. Caluclate the x coordinate of centre of mass of the two mass object. Give that mass per unit area of plate is 1.4g/cm square and total mass = 25.2g Homework Equations -
Not sure what I went wrong here, anyone can help m... |
How to create a sharp mesh from a function without even trying
In part 1 and part 2 of the series, we looked at the Marching Cubes algorithm, and how it can turn any function into a grid based mesh. In this article we’ll look at some of the shortcomings and how we can do better.
Marching Cubes is easy to implement, and... |
Preprints (rote Reihe) des Fachbereich Mathematik Refine Year of publication 1996 (22) (remove)
284
A polynomial function \(f : L \to L\) of a lattice \(\mathcal{L}\) = \((L; \land, \lor)\) is generated by the identity function id \(id(x)=x\) and the constant functions \(c_a (x) = a\) (for every \(x \in L\)), \(a \in L... |
Functiones et Approximatio Commentarii Mathematici Funct. Approx. Comment. Math. Volume 60, Number 1 (2019), 87-96. A note on the Diophantine equation $2^{n-1}(2^{n}-1)=x^3+y^3+z^3$ Abstract
Motivated by a recent result of Farhi we show that for each $n\equiv \pm 1\pmod{6}$ the title Diophantine equation has at least t... |
This article provides answers to the following questions, among others:
How does a siphon work? What is the maximum height to the apex of the flexible tube that can be covered? Why does a siphon not contradict the law of conservation of energy? Introduction
If, for example, you want to empty a pool by a garden hose, yo... |
Consider a $C^k$, $k\ge 2$, Lorentzian manifold $(M,g)$ and let $\Box$ be the usual wave operator $\nabla^a\nabla_a$. Given $p\in M$, $s\in\Bbb R,$ and $v\in T_pM$, can we find a neighborhood $U$ of $p$ and $u\in C^k(U)$ such that $\Box u=0$, $u(p)=s$ and $\mathrm{grad}\, u(p)=v$?
The tog is a measure of thermal resist... |
For a pair of positive integers $m$ and $n$, put
$$\displaystyle \Psi(m,n) = 2^{-\omega(m)} \sum_{a | m} \left(\frac{n}{a}\right),$$ where $\left(\frac{\cdot}{\cdot}\right)$ is the Jacobi symbol. Let $\sum^\ast$ denote a sum over square-free numbers. Let $X$ be a positive number. Can one evalute the sum
(1)
$$\displays... |
The authors set to study the “averaging” properties of dropout in a quantitative manner in the context of fully connected, feed forward networks understood as DAGs. In particular, architectures other than sequential are included, cf. Figure 1. In the linear case with no activations, the output of some layer $h$ (no dro... |
In this great question by Nathaniel Johnston, and in its answers, we can learn the following remarkable inequality: For all $v,w \in \mathbb{R}^n$ we have \begin{align*} \|v^2\| \, \|w^2\| - \langle v^2, w^2 \rangle \le \|v\|^2 \|w\|^2 - \langle v,w \rangle^2; \quad (*) \end{align*} here, $\langle\cdot,\cdot\rangle$ de... |
Let $K$ compact in a metric space $M$, $N$ is a metric space, $\mathcal{C}(K,N)$ the space of continuous functions $f: K \longrightarrow N$ and $E \subset \mathcal{C}(K,N)$ a family of functions such that $\overline{E}$ is compact in $\mathcal{C}(K,N)$ with respect to the topology generated by the metric of uniform con... |
Help:Editing
The MediaWiki software is extremely easy to use. Viewing pages is self-explanatory, but adding new pages and making edits to existing content is extremely easy and intuitive as well. No damage can be done that can't be easily fixed. Although there are some differences, editing SDIY wiki is much the same as... |
The Annals of Statistics Ann. Statist. Volume 17, Number 1 (1989), 107-124. Uniformly Powerful Goodness of Fit Tests Abstract
The simple hypothesis is tested that the distribution of independent random variables $X_1, X_2, \cdots, X_n$ is a given probability measure $P_0$. Let $\pi_n$ be any sequence of partitions. The... |
This is an elementary question, but a little subtle so I hope it is suitable for MO.
Let $T$ be an $n \times n$ square matrix over $\mathbb{C}$.
The characteristic polynomial $T - \lambda I$ splits into linear factors like $T - \lambda_iI$, and we have the Jordan canonical form:
$$ J = \begin{bmatrix} J_1 \\\ & J_2 \\\... |
Let consider a steady state CSTR in which occurs the following reaction:
$$\ce{aA + bB \leftrightarrow cC}$$
Notations:
$F_i$ is the molar flow of $i$, $r$ is the rate of reaction, $V$ is the volume, $X$ is the conversion at the end of the reactor, $\nu_i$ is the stoichiometric coefficient of $i$ and $\xi$ is the exten... |
This question is motivated by this one.
Suppose $l$ is the minimum measurable unit of length. What is entropy of a spinless particle contained in this interval?
We know that entropy of a two-level system depends on the probabilities of the respective levels, if the probability of the state 0 is $p_0$, then the entropy ... |
Today, we will discuss about the Daily Magic Spell problem given on January 2, 2017:
Problem: Find the value of $\displaystyle \frac{20!-19!}{18!}$. Solution: Note that
$\displaystyle \frac{20!-19!}{18!} = \frac{20(19!) - 19!}{18!} = \frac{19(19!)}{18!} = 19\times 19 = 361$.
Some students may attempt to evaluate $20!$,... |
Search
Now showing items 1-9 of 9
Measurement of $J/\psi$ production as a function of event multiplicity in pp collisions at $\sqrt{s} = 13\,\mathrm{TeV}$ with ALICE
(Elsevier, 2017-11)
The availability at the LHC of the largest collision energy in pp collisions allows a significant advance in the measurement of $J/\ps... |
Search
Now showing items 1-10 of 26
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 ... |
I will like to animate a list of parametric spirals over a list of packed spheres. The effect I am after is illustrated in this gif by Étienne Jacob :
By looking at the gif above, we will divide our implementation into two parts:
Sphere Packing, where we try to find a list of locations and radii for the sphere such tha... |
The Leibniz rule is as follows:
$$\frac{d}{d\alpha} \int_{a(\alpha)}^{b(\alpha)} f(x, \alpha) dx = \frac{db(\alpha)}{d\alpha} f(b(\alpha), \alpha) - \frac{da(\alpha)}{d\alpha} f(a(\alpha), \alpha) + \int^{b(\alpha)}_{a(\alpha)} \frac{\partial}{\partial\alpha} f(x, \alpha) dx$$
What I would like to know is how to apply ... |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.