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I'm wondering how a set of keys could be assigned to nodes in a 2-3-4 tree in order to minimize the height of the tree?
Does the sequence of insertion matter with 2-3-4 trees?
Computer Science Stack Exchange is a question and answer site for students, researchers and practitioners of computer science. It only takes a m... |
There are thousands of NP-complete problems in the literature, and most pairs do not have explicit reductions. Since polynomial-time many-one reductions compose, it suffices for researchers to stop when the graph of published reductions is strongly connected, making research into NP-completeness a much more scalable ac... |
I've been try to either prove or find a counter-example to the idea of jointly-wss being transitive.
In other words: does ($x$ and $y$ are jointly wss) $\wedge$ ($y$ and $z$ are jointly wss) imply that $x$ and $z$ are jointly wss? Obviously it boils down to only asking about the cross-correlation condition, so one can ... |
Suppose $f:\mathbb{R_+} \to \mathbb{R}$ is a continuous and strictly increasing function. Define $g(x) = \frac{f(x+1)-f(1)}{f(x)-f(0)}$. For which $f$ the function $g$ satisfies $g(x) \geq g(1)$ for all $x \geq 0$?
Comment: this is part of a larger project where the existence of a solution boils down to the condition $... |
Let $a\mathop{.}b \stackrel{\text{def}}{=} aba^{-1} $ denote conjugation by $a$
Suppose we define a matrix $M$, the "conjugation table", associated with our finite group $G = (X,*_{\small{G}})$ as follows. (I'm considering the cells of $M$ to be formal sums of group elements (with the product of monomials defined in te... |
In this worked example we use source transformation to simplify a circuit.
Source transformation is introduced here.
Written by Willy McAllister.
Contents Review
Source transformation between Thévenin and Norton forms,
The resistor value is the same for the Thévenin and Norton forms, $\text R_\text T = \text R_\text N$... |
Three Important Riemann Surfaces
It occurred to me recently that my little blog is woefully short of posts about complex analysis. To remedy this situation, I've decided to use the next few posts to prove the following four facts:
But before I do, let's have
A Little Motivation
Perhaps you're wondering,
Why should I ca... |
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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... |
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 ... |
Let $L$ be the language $L=\{<,=,+,-,\cdot, 0,1\}$, with standard interpretations, and let $\mathcal{A}=\langle\mathbb{R}, <,=,+,-,\cdot,0,1\rangle$. Let $S\subseteq\mathbb{R}^n$. Show that if $S$ is definable, then the topological closure of $S$, given as $$\bar{S}:=\{a\in\mathbb{R}^n:\text{every open ball centered at... |
This question already has an answer here:
I am looking for a proof that the derivative is the best linear approximation that makes this property "feel" fundamental. I have a proof below that somewhat gets close to what I am going for. But, first, I will explain my problems with it.
Ideally, the
best linear approximatio... |
The papers you should read for this question are Vaidman, Lev. "Torque and force on a magnetic dipole." Am. J. Phys
58.10 (1990): 978-983 (Paywall-free version) and Haus, H. A., and P. Penfield. "Force on a current loop." Physics Letters A 26.9 (1968): 412-413. (References 8 and 9 in Vaidman's paper are also worth read... |
Let's begin with the following experiment: we throw a dice of six faces and see what the result is. Let's consider the following events $$A = \{ 2, 3 \}$$, $$B = \{ 1 , 2 \}$$, $$C = \{ 5 \}$$.
We observe that if we extract $$2$$, then $$A$$ is satisfied as well as $$B$$. We say that the events are compatible, this mea... |
Difference between revisions of "Extendible"
(→Virtually extendible cardinals: unless...)
(→Virtually extendible cardinals: +1)
Line 140: Line 140:
* If there is a proper class of $n$-remarkable cardinals, then $gVP(Σ_{n+1})$ holds.<cite>GitmanHamkins2018:GenericVopenkaPrincipleNotMahlo</cite>
* If there is a proper cl... |
Every where and book I search I get that the definition of linear momentum is the amount of speed (quantity of motion) contained in it or simply it is mass $\times$velocity? So, what is an appropriate definition of linear momentum? What did Newton think when he discovered it? He certainly did not think it as the amount... |
Also known as "Nate slowly deciphers ESL to conceptual understanding/plainer language", part two (see part one) Help me understand this (bullets added)
The term $\hat{β}_0$ is the intercept, also known as the
biasin machine learning. Often it is convenient to include the constant variable 1 in $X$, include $\hat{β}_0$ ... |
Here's my take on it, those conditions are wrong when it comes to defining if the feedback is positive/negative, so
1-) β being negative causes 180 degree phase shift so there is positive feedback
For this block diagram, if \$A\$ is considered the plant, the feedback is negative if \$\beta>0\$ (doesn't mean it will sta... |
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1. Measurements of the branching fractions for D + →K S 0 K S 0 K + ,K S 0 K S 0 π + and D 0 →K S 0 K S 0 ,K S 0 K S 0 K S 0
Physics Letters, Section B: Nuclear, Elementa... |
What's a Quotient Group, Really? Part 1
I realize that most of my posts for the past, er,
few months have been about some pretty hefty duty topics. Today, I'd like to dial it back a bit and chat about some basic group theory! So let me ask you a question: When you hear the words "quotient group," what do you think of? ... |
Learning Outcomes Create and interpret a line of best fit
Data rarely fit a straight line exactly. Usually, you must be satisfied with rough predictions. Typically, you have a set of data whose scatter plot appears to “fit” a straight line. This is called a
Line of Best Fit or Least-Squares Line. Example
A random sampl... |
How can i evaluate this indefinite integral.
$$ \int { \frac { 1 }{ \sqrt { 8-{ x }^{ 2 }-2x } } } \,dx$$
I know it involves completing square but i don't know how to do it.
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It only takes ... |
What's a Quotient Group, Really? Part 2
Today we're resuming our informal chat on quotient groups. Previously we said that belonging to a (normal, say) subgroup $N$ of a group $G$ just means you satisfy some property. For example, $5\mathbb{Z}\subset\mathbb{Z}$ means "You belong to $5\mathbb{Z}$ if and only if you're d... |
This is the problem:
We can determine the solubility equilibrium for silver bromide using cell:
Ag (s) | AgNO3 (aq) || KBr (aq) | AgBr (s) | Ag (s)
We know that:
$\text{AgBr} + \text{e}^- \rightarrow \text{Ag} + \text{Br}^- \ \ \ \text{E}^0=0.095 \text{V}$
$\text{Ag}^+ + \text{e}^- \rightarrow \text{Ag}\ \ \ \text{E}^0... |
Limited regularity of solutions to fractional heat and Schrödinger equations
Department of Mathematical Sciences, Copenhagen University, Universitetsparken 5, DK-2100 Copenhagen, Denmark
When $ P$ is the fractional Laplacian $ (-\Delta )^a$, $ 0<a<1$, or a pseudodifferential generalization thereof, the Dirichlet proble... |
Let $f$ be a meromorphic function in a domain $D$. The set of zeros $Z_f$ and the set of poles $P_f$ are both discrete in $D$; it means that doesn't exist a sequence of zeros (risp. sequence of poles) that converges to a zero of $f$ (risp. to a pole of $f$). My question is the following:
Let $a\in D$ such that $a\not\i... |
Main Page Contents The Problem
Let [math][3]^n[/math] be the set of all length [math]n[/math] strings over the alphabet [math]1, 2, 3[/math]. A
combinatorial line is a set of three points in [math][3]^n[/math], formed by taking a string with one or more wildcards [math]x[/math] in it, e.g., [math]112x1xx3\ldots[/math],... |
I understand that in CLT, we have
$\sqrt{N} \left( \frac{\bar{X}_N - \mu}{\sigma} \right) \overset{d}\to N\left(0,1\right) \qquad (*)$
where $\bar{X}_N := \frac{1}{N} \sum_{i=1}^N X_i$ is the sample mean, and $\sqrt{N}$ inflates the $\frac{\bar{X}_N - \mu}{\sigma}$ to a $\mathcal{O}_p(1)$, while without the $\sqrt{N}$,... |
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Now showing items 1-5 of 5
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... |
Consider the balanced chemical equation (i.e., catalytic oxidation of ammonia) such as
\[ 4 \text{ N} \text{H}_{3} (g) + 5 \text{O}_{2} (g) \rightarrow 4 \text{ N} \text{O} (g) + 6 \text{ H}_{2} \text{O} (g) \label{1}\]
not only tells how many molecules of each kind are involved in a reaction, it also indicates the
amo... |
When proving functional equation for Riemann zeta function one starts at the definition of gamma function $$\Gamma(s) = \int_0^{\infty} x^{s-1} e^x\mathrm dx\tag1$$ After a few steps we arrive at $$ \pi^{-\frac{s}{2}} \Gamma \left(\frac{s}{2} \right) \zeta(s) = \frac{1}{s(1-s)} - \int_1^{\infty} \left( x^{\frac{s}{2}} ... |
Rigorous Theory for Accurate Multi-scale Analysis with Non Well-seperated Length Scales
The Generalized Finite Element Method (GFEM) is a domain decomposition method based upon a partition of unity of a computational domain. This method is initiated and developed in (Babuska, Caloz, and Osborne, 1994), (Babuska and Mel... |
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−
In the case of M8-M20 sequence, we
+
In the case of M8-M20 sequence, we used "Winsorized Sigma Clipping" in "Average stacking with rejection" to remove satellite tracks (<math>\sigma_{low}=4</math> and <math>\sigma_{high}=2</math>).
<!--T:8-->
<!--T:8-->
[[File:Siril stacking s... |
I am going to consider Freivald's algorithm in the field mod 2. So in this algorithm we want to check wether $$AB = C$$ and be correct with high probability.
The algorithm choose a random $r$ n-bit vector and if $$A(Br) = Cr$$ then outputs YES, otherwise outputs no.
I want to show that it has has one-sided success prob... |
I am seeing how the Berry connection $\mathcal{A}(k)$ transforms under time reversal symmetry. I seem to have a hiccup over something simple. I may have overcomplicated things but I think it points to some misconceptions I may have.
From the definition of the Berry curvature as per usual: \begin{align} \mathcal{A}(k) &... |
The distribution or table of frequencies is a table of the statistical data with its corresponding frequencies.
Absolute frequency: number of times that a value appears. It is represented as $$f_i$$ where the subscript represents each of the values. The sum of the absolute frequencies is equal to the total number of da... |
Answer
$$\cos\frac{\theta}{2}=\frac{R-b}{R}$$
Work Step by Step
(The image is shown below) We see in the image that $BC$ is a circular curve where $OB=OC=R$. That means $OA=R$ as $A$ is a point in the circular curve. Thus, $OH=OA-AH=R-b$ As triangle $OHC$ is a right triangle, we can calculate $\cos\frac{\theta}{2}$ usi... |
I'm stuck on one really simple example, I can't figure out what's happening to energy here...
(This is
not homework)
Let's consider an uncharged electric cable, we'll model it by an infinite cylinder on the axis $(Oz)$ with radius $a$ and conductivity $\gamma$ with uniform, constant current $I$, and we'll obviously use... |
Symmetry of singular solutions for a weighted Choquard equation involving the fractional $ p $-Laplacian
Division of Computational Mathematics and Engineering, Institute for Computational Science, Ton Duc Thang University, Ho Chi Minh City, Vietnam
Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi... |
You are right.
A way to confirm your intuition is that the step response exhibits a single time constant (i.e., one pole) \$\tau=-4\$ and a steady state of \$y(\infty)=1\$. Even without going through calculations, you can then argue
$$ T(s)=\frac{4}{s+4}. $$
Anyway your friend's answer is wrong not only because of the ... |
The Pseudo-Hyperbolic Metric and Lindelöf's Inequality
Let $\Delta$ denote the unit disc in the complex plane $\mathbb{C}$. For any two points $z,a\in \Delta$, we define the
pseudo-hyperbolic metric on $\Delta$ by $$d(z,a)=|\varphi_a(z)|=\bigg|\frac{z-a}{1-\bar a z}\bigg|.$$Observe that if $f:\Delta\to\Delta$ is holomo... |
Difference between revisions of "ORD is Mahlo"
m (link)
(+1)
Line 13: Line 13:
Relation to the [[Vopenka|Vopěnka principle]]:<cite>GitmanHamkins2018:GenericVopenkaPrincipleNotMahlo</cite>
Relation to the [[Vopenka|Vopěnka principle]]:<cite>GitmanHamkins2018:GenericVopenkaPrincipleNotMahlo</cite>
* The [[Vopenka|Vopěnka... |
Gabriel Romon
Student at ENSAE Paristech and ENS Paris-Saclay (MVA Master's degree). Interested in statistics and machine learning.
A few recent good answers of mine:
DCT for convergence in probability
$\frac{S_n}{\sqrt n}$ is dense in $\mathbb R$ almost surely $\cos(2^n)$ is dense in $[-1,1]$ Showing $(X_n >c_n \text{... |
I was watching Geoff Hinton's lecture from May 2013 about the history of deep learning and his comments on the rectified linear units (ReLU's) made more sense that my previous reading on them had. Essentially he noted that these units were just a way of approximating the activity of a large number of sigmoid units with... |
Suppose $f:\mathbb R\to\mathbb R^n$ satisfies $$ f'(t) = A(t)f(t), $$ where $A$ is a smooth matrix-valued function. If I know that the matrix $A(t)$ is asymptotically nilpotent, how could I prove a sub-exponential estimate for the solution $f$?
To be more explicit, suppose $A(t)^2\to0$ but $A(t)\not\to0$ as $t\to\infty... |
Why are metals opaque? Is it due to the free electrons in a metal or a material's intrinsic properties?
closed as unclear what you're asking by Kyle Kanos, Jon Custer, stafusa, Qmechanic♦ Jan 4 '18 at 22:28
Please clarify your specific problem or add additional details to highlight exactly what you need. As it's curren... |
In general, you won't be able to replicate the option by a portfolio of the form $\Delta_t S_t + B_t$, though it is possible to do so with a portfolio of the form $\Delta_t^1 S_t + \Delta_t^2B_t$; see Chapter 3 of this book. Here, $B_t=e^{rt}$ is the value of the money-market account, and $r$ is the risk-free interest ... |
By definition, a renormalizable quantum field theory (RQFT) has the following two properties (only the first one matters in regard to this question):
i) Existence of a
formal continuum limit: The ultraviolet cut-off may be taken to infinite, the physical quantities are independent of the regularization procedure (and o... |
I got Aircraft Design: A conceptual approach for Christmas, and I'm having a hard time with lift coefficients because I honestly have no idea what "lift force per unit span" means, so can someone please explain this to me?
The concept of lift force per unit span comes from potential flow theory. It will need some backg... |
The average number of positions addressed is $$ \frac{1}{2} \left(1 + \frac{1}{1-\alpha}\right) $$for linear probing and $1 + \alpha/2$ for chained hashing. Here $\alpha$ is the load factor. For each constant $\alpha$, this average is constant, but it depends on $\alpha$. The expression $1/(1-\alpha)$ blows up as the t... |
Preprints (rote Reihe) des Fachbereich Mathematik Refine Keywords average density (3) (remove)
303
We show that the intersection local times \(\mu_p\) on the intersection of \(p\) independent planar Brownian paths have an average density of order three with respect to the gauge function \(r^2\pi\cdot (log(1/r)/\pi)^p\)... |
We derive the $\Delta \leftrightarrow \text Y$ transformation equations.
The first derivation is from $\Delta$ to $\text Y$.
The second derivation goes the opposite direction, from $\text Y$ to $\Delta$. The algebra for this one is harder and there are two versions presented. The first version does it strictly by algeb... |
Electronic Communications in Probability Electron. Commun. Probab. Volume 24 (2019), paper no. 57, 12 pp. On the eigenvalues of truncations of random unitary matrices Abstract
We consider the empirical eigenvalue distribution of an $m\times m$ principle submatrix of an $n\times n$ random unitary matrix distributed acco... |
In this article, I want to discuss how the intersection area of two circles can be calculated. Given are only the two circles with their corresponding centre point together with the radius and the result is the area which both circles share in common. First, I want to take a look at how the intersection area can be cal... |
Ex.5.4 Q5 Arithmetic progressions Solutions - NCERT Maths Class 10 Question
A small terrace at a football ground comprises of \(15\) steps each of which is \(50\, \rm{m}\) long and built of solid concrete. Each step has a rise of \(\begin{align}\frac{1}{4}\,\rm{m} \end{align}\) and a tread of \(\begin{align}\frac{1}{2}... |
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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 ... |
Essay and Opinion A new graph density
Version 1Released on 08 April 2015 under Creative Commons Attribution 4.0 International License Authors' affiliations Laboratoire Electronique, Informatique et Image (Le2i). CNRS : UMR6306 - Université de Bourgogne - Arts et Métiers ParisTech Keywords Community discovery Density @G... |
The time series is governed by the equation $S(T)=S(0)e^{(\mu-\frac{\delta^2}{2})T+\delta(w(T)-w(0))}$, in which $w(t)$ is a standard Brownian motion. Now given the data $\{S(t)\}_{t=0}^{t=T}$， how to estimate $\delta$ and $\mu$?
By considering the log of the time series, i.e.
$$ \{\log{S(t)}\}_{t=0}^{t=T}$$
we have
$$... |
Why do we use the term "asymptotic" in complexity. Although I know what an asymptote is, but what is an asymptote doing here?
There are several answers to this.
"Asymptotic" here means "as something tends to infinity". It has indeed nothing to do with curves.
There is no such thing as "complexity notation". We denote "... |
If $\sqrt{64}$ is equal to $\pm{}8$, is $-64$ equal to $\pm{}8i$, or just $8i$?
$\sqrt{a}$, for real $a$, is almost always defined to be the positive solution of the equation $x^2 - a = 0$, so $\sqrt{64}$ is $8$ and
not $\pm 8$. The reason the square root only takes on one value is because it is a function and so each ... |
In signal processing, cross-correlation is a measure of similarity of two waveforms as a function of a time-lag applied to one of them. This is also known as a sliding dot product or sliding inner-product. It is commonly used for searching a long signal for a shorter, known feature. It has applications in pattern recog... |
The answer is yes for continuous functions $f$ on continuous curves $C$. The reason for this is that the line integral (with respect to arc length) satisfies the inequality
$$ \min(f) \cdot L_C \leq \int_C f(x_1, \ldots x_n) \,ds \leq \max(f) \cdot L_C $$
which can be rearranged as
$$ \min(f) \leq \cfrac{1}{L_C} \int_C... |
Since moving to a Mac a bit over a year ago, I've had only a few reasons to look back (the business with the HP LJ1022 printer being one of them). I'm now rather close to the end of my tether, and the reason is fonts.
As an academic and a computer scientist, I end up writing quite a lot of papers and presentations with... |
I came to a conclusion here by applying the Euler-Lagrange operator to the given Lagrangian:
$L^{2}=g_{ij}(x)\dot{x}^{i}\dot{x}^{j}$
Doing the algebra I find that:
$\ddot{x}^{i}+\Gamma^{i}_{jk}\dot{x}^{j}\dot{x}^{k}=\frac{dL}{ds}\dot{x}^{i} \qquad(1)$
Now, according to this webpage the condition for a vector to be tran... |
$\alpha$ need not be a random variable.
The most natural choice for $(\Omega, \mathcal{F}, P)$ is product space: let $\Omega = [0,1]^{[0,1] \cup \{2\}}$ and for $A \subset [0,1] \cup 2$, let $\pi_A : \Omega \to [0,1]^A$ be the projection map. (For $a \in [0,1] \cup 2$, we let $\pi_a$ denote $\pi_{\{a\}} : \Omega \to [0... |
The Law of Large Numbers does not say as much as you seem to think it says. There is a great deal of misunderstanding about this. Suppose that the probability of a coin's toss being heads is one half. The Law of Large Numbers says nothing at all about what the asymptotic results
will be. It only says what the probabili... |
Research Open Access Published: ( t,n) multi-secret sharing scheme extended from Harn-Hsu’s scheme EURASIP Journal on Wireless Communications and Networking volume 2018, Article number: 71 (2018) Article metrics
558 Accesses
2 Citations
Abstract
Multi-secret sharing scheme has been well studied in recent years. In most... |
When performing orbital calculations, under what circumstances should I assume:
Since this answer is a bit longish, a TL;DR is in order. Depending on the application, one should use
A point mass / spherical mass distribution model. A model that incorporates the effects of the Earth's oblateness. This is subtly differen... |
Ex.4.4 Q2 Quadratic Equations Solutions - NCERT Maths Class 10 Question
Find the value of \(k\) for each of the following quadratic equation , so that they have two equal roots.
(i) \(2x^\text{2}+kx+3=0\)
(ii) \(kx \left(x-2\right)+6=0\)
Text Solution What is known?
value of \(k.\)
What is Known?
Quadratic equation has... |
Geometry and Topology Seminar Contents Fall 2016 Spring 2017
date speaker title host(s) Jan 20 Carmen Rovi (University of Indiana Bloomington) "The mod 8 signature of a fiber bundle" Maxim Jan 27 Feb 3 Feb 10 Feb 17 Yair Hartman (Northwestern University) "TBA" Dymarz Feb 24 March 3 Mark Powell (Université du Québec à M... |
The 2n law of thermodynamics can be stated in terms of entropy as follows
$dS \geq \frac{dQ}{T},$
which holds for all quasistatic processes (reversible and irreversible ones).
Is there a generalization of this statement to a general process between two equilibrium states $e_1$ and $e_2$ (a non-quasistatic process)? I.e... |
I'll write down the idea of "method of Lagrange multiplier" here for my note. For simplicity, the number of variables would be 3.
Supposedly, a function $\psi: \Omega \to \mathbb{R}$ differential for each variable, and satisfies a restriction $\psi(x,y,z)=0$.
If a function $f : \mathbb{R}^3 \to \mathbb{R}$ realizes ext... |
Is the triplet representation of $SU(2)$ the same as its adjoint representation? Where the convention for the adjoint representation used is the one used in particle physics, where the structure constants are real and antisymmetric:
$$ \mathrm{ad}(t^b_G)_{ac} = i f^{abc} $$
I was under the impression that is was, but I... |
There are already several good answers. However, the off-shell aspect related to Noether Theorem has not been addressed so far. (The words
on-shell and off-shell refer to whether the equations of motion (e.o.m.) are satisfied or not.) Let me rephrase the problem as follows.
Consider a (not necessarily isolated) Hamilto... |
I recently came across this in a textbook (NCERT class 12 , chapter: wave optics , pg:367 , example 10.4(d)) of mine while studying the Young's double slit experiment. It says a condition for the formation of interference pattern is$$\frac{s}{S} < \frac{\lambda}{d}$$Where $s$ is the size of ...
The accepted answer is c... |
Two principles here:
When dealing with a differential equation, you define intermediate state variables so everything is in terms of first derivatives. This system is nonlinear, so the state-space equations won't be in terms of matrices.
Applying these principles, we define a state vector:$$\mathbf x = [x_1, x_2]^T,$$w... |
Here is a shot in the dark (Disclosure: I really know nothing about this problem).
Let $G:=\mathsf{SU}(2)$ act on $G^3$ by simultaneous conjugation; namely, $$g\cdot(a,b,c)=(gag^{-1},gbg^{-1},gcg^{-1}).$$ Then the quotient space is homeomorphic to $S^6$ (see Bratholdt-Cooper).
The evaluation map shows that the characte... |
On small oscillations of mechanical systems with time-dependent kinetic and potential energy
1.
Dipartimento di Matematica Pura e Applicata, Università de L'Aquila, I-67100 L'Aquila
2.
Bolyai Institute, University of Szeged, Aradi vértanúk tere 1, H-6720 Szeged, Hungary
$\sum$
n k=1$(a_{ik}(t)\ddot q_k+c_{ik}(t)q_k)=0,... |
De Bruijn-Newman constant
For each real number [math]t[/math], define the entire function [math]H_t: {\mathbf C} \to {\mathbf C}[/math] by the formula
[math]\displaystyle H_t(z) := \int_0^\infty e^{tu^2} \Phi(u) \cos(zu)\ du[/math]
where [math]\Phi[/math] is the super-exponentially decaying function
[math]\displaystyle... |
For example, rationalizing expressions like $$\frac{1}{\pm \sqrt{a} \pm \sqrt{b}}$$ Is straightforward. Moreover cases like $$\frac{1}{\pm \sqrt{a} \pm \sqrt{b} \pm \sqrt{c}}$$ and $$\frac{1}{\pm \sqrt{a} \pm \sqrt{b} \pm \sqrt{c} \pm \sqrt{d}}$$
Are still easy to rationalize. But my question is in the more general cas... |
Black holes are states at thermal equilibrium, at a positive temperature inversely proportional to the mass, and they therefore emit black body radiation at that temperature. Everybody knows that. But why? By far the most common explanation in divulgation is in terms of pair production of particles at the horizon, whic... |
Colloquia/Fall18 Contents 1 Mathematics Colloquium 1.1 Spring 2018 1.2 Spring Abstracts 1.2.1 January 29 Li Chao (Columbia) 1.2.2 February 2 Thomas Fai (Harvard) 1.2.3 February 5 Alex Lubotzky (Hebrew University) 1.2.4 February 6 Alex Lubotzky (Hebrew University) 1.2.5 February 9 Wes Pegden (CMU) 1.2.6 March 2 Aaron Be... |
$\DeclareMathOperator{\erfc}{erfc} \DeclareMathOperator{\Ei}{Ei} $ What is the series expansion of $f$ for small $q$? \begin{align} U(q) &= q e^{q^2}\erfc q\\ I(q,q') &= \int_0^{2\pi} \frac{d\phi}{2\pi} U(\sqrt{q^2 + q'^2 -2qq'\cos\phi})-U(q')\\ f(q) &= \int_{0}^{\infty} dq'\,I(q,q') \end{align} Even better, perhaps yo... |
Let $S_n$ be the symmetric group on $n$ elements. The Robinson-Schensted-Knuth (RSK) correspondence sends a permutation $\pi\in S_n$ to a pair of Standard Young Tableaux $(P,Q)$ with equal shapes $\mbox{sh}(P)=\mbox{sh}(Q)=\lambda$, where $\lambda=(\lambda_1,\lambda_2,\ldots,\lambda_r)$ and $\lambda_1\geq\lambda_2\geq\... |
Homology, Homotopy and Applications Homology Homotopy Appl. Volume 12, Number 1 (2010), 1-10. The gluing problem does not follow from homological properties of $\Delta_p(G)$ Abstract
Given a block $b$ in $kG$ where $k$ is an algebraically closed field of characteristic $p$, there are classes $\alpha_Q \in H^2 (Aut_\mat... |
Practical and theoretical implementation discussion.
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I've had a question that I couldn't answer myself and haven't found any formal derivation on the topic. If one has a point light with position \(\vec{c}\) and intensity \(I\), then the irradiance at point \(\vec{p}\) at some surface c... |
Let $T = {\mathbb R}/{\mathbb Z}$ be the $1$-torus. Let $a_{ij}$ be integer numbers, $1 \leq i \leq m$, $1 \leq j \leq n$ and $A$ the $m \times n$ matrix whose $(i,j)$ entry is $a_{ij}$. Consider the following system of $m$ linear equations:
$$\left\{\begin{array}{rl} a_{11}x_1 + a_{12}x_2 + \cdots + a_{1n}x_n & = \ove... |
Practical and theoretical implementation discussion.
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1of 1
I've had a question that I couldn't answer myself and haven't found any formal derivation on the topic. If one has a point light with position \(\vec{c}\) and intensity \(I\), then the irradiance at point \(\vec{p}\) at some surface c... |
Practical and theoretical implementation discussion.
Post Reply
10 posts • Page
1of 1
I've had a question that I couldn't answer myself and haven't found any formal derivation on the topic. If one has a point light with position \(\vec{c}\) and intensity \(I\), then the irradiance at point \(\vec{p}\) at some surface c... |
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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 ... |
Machine learning algorithms are designed to generalize from past observations across different problem settings. The goal of learning theory is to analyze statistical and computational properties of learning algorithms and to provide guarantees on their performance. To do so, it poses these tasks in a rigorous mathemat... |
Practical and theoretical implementation discussion.
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10 posts • Page
1of 1
I've had a question that I couldn't answer myself and haven't found any formal derivation on the topic. If one has a point light with position \(\vec{c}\) and intensity \(I\), then the irradiance at point \(\vec{p}\) at some surface c... |
Arithmetic
Category : 5th Class
Arithmetic
'Percent' means 'for every hundred'.
Symbol for percentage is %.
To convert a percentage to a decimal, divide the number by 100.
e.g., 68% = \[\frac{68}{100}\] = 0.68
To convert a decimal to a percentage, multiply the number by 100%.
e.g., \[0.59 = 0.59\times 100% = 59%\]
To c... |
Answer
The reduction formula is $$\sin\theta$$
Work Step by Step
*Summary of the method: For a formula $f(Q\pm\theta)$ 1) See that $Q$ terminates on the $x$ or $y$ axis. If it terminates on the $x$ axis, go for Case 1. If it terminates on the $y$ axis, go for Case 2. 2) Case 1: - For a small positive value of $\theta$,... |
Cross-posted from MSE, where this question was asked over a year ago with no answers.
Suppose I have a large system of polynomial equations in a large number of real-valued variables. \begin{align} f_1(x_1, x_2, &\dots, x_m) = 0 \\ f_2(x_1, x_2, &\dots, x_m) = 0 \\ &\vdots \\ f_n(x_1, x_2, &\dots, x_m) = 0 \\ \end{alig... |
I was doing my homework when I came across this question:
Three equal point charges, each with charge $1.40 \, \rm\mu C$ , are placed at the vertices of an equilateral triangle whose sides are of length $0.250 \,\rm m$. What is the electric potential energy $U$ of the system? (Take the potential energy of the three cha... |
Difference between revisions of "Main Page"
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Kalai.29: A sort of generic attack one can try with Sperner is to look at f=1_A and express using the Fourier expansion of f the expression \int f(x)f(y)1_{x<y} where x<y is the partial order (=containment) for 0-1 vect... |
Creating Symbolic Links
The function
CreateSymbolicLink allows you to create symbolic links using either an absolute or relative path.
Symbolic links can either be absolute or relative links. Absolute links are links that specify each portion of the path name; relative links are determined relative to where relative–li... |
The aim of this example is to determine the "shape of highest probability" for the hydrogen molecule ion. For a given volume, the task is to use Monte Carlo integration to find the ratio between the semi-principal axes of an ellipsoid, such that the probability of finding the electron inside the ellipsoid is maximised.... |
A square is a topological manifold with boundary but not a smooth manifold with boundary because of its corners. But I am confused about it. I think since for a specific corner $p$, there is only one chart to cover $P$ (in order to be compatible), say $(U,f)$ , thus in the NBHD of $P$ the transition maps can only be $f... |
Let $\{A_\alpha:\alpha \in \Lambda\}$ be an indexed collection of sets. If $\bigcap \{A_\alpha:\alpha \in \Lambda\} \neq \emptyset$, then for each $\beta \in \Lambda$, $A_\beta \neq \emptyset$.
My thought was a proof through contraposition:
Assume $A_\beta = \emptyset$ for some $\beta \in \Lambda.$ It would follow that... |
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