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Contributors History and Feedback Vicky Hall 2 years, 2 months ago
The answer to part a) in the advice is wrong. There's also an issue with the answer to part b). You give all lengths and the angle to the student to two decimal places but then you calculate the answ... |
Browse/search for people Mr Joseph Najnudel
Mr Joseph Najnudel Reader in Mathematics PhD Summary
Random matrix theory: study of random unitary matrices (in particular the Circular Unitary Ensemble), random permutation matrices and related infinite-dimensional limiting objects, link between random matrix theory and numb... |
I cannot claim to be an expert on AQFT, but the parts that I'm familiar with rely on local fields quite a bit.
First, a clarification. In your question, I think you may be conflating two ideas: local fields ($\phi(x)$, $F^{\mu\nu}(x)$, $\bar{\psi}\psi(x)$, etc) and unobservable local fields ($A_\mu(x)$, $g_{\mu\nu}(x)$... |
The equivalence is not correct.
To see this, consider any divergent series of real numbers $\sum a_n$ such that $a_n\to 0$ as $n\to \infty$; for example $a_n=\frac1n$. Then define $x_n=a_1+\dots +a_n$. This is a non-Cauchy sequence (as any non-convergent sequence of real numbers), but $x_{n+k}-x_n=a_{n+1}+\dots +a_{n+k... |
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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 ... |
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Now showing items 1-1 of 1
Anisotropic flow of inclusive and identified particles in Pb–Pb collisions at $\sqrt{{s}_{NN}}=$ 5.02 TeV with ALICE
(Elsevier, 2017-11)
Anisotropic flow measurements constrain the shear $(\eta/s)$ and bulk ($\zeta/s$) viscosity of the quark-gluon plasma created in heavy-ion collisions... |
A brief description of the 18 electron rule
A valence shell of a transition metal contains the following: 1 $s$ orbital, 3 $p$ orbitals and 5 $d$ orbitals; 9 orbitals that can collectively accommodate 18 electrons (as either bonding or nonbonding electron pairs). This means that, the combination of these nine atomic or... |
No, this is very false in general. For example, if $X=Y=S^n$ ($n>0$), the connected components of the space $Y^X$ of continuous maps from $X$ to $Y$ are in bijection with $\mathbb{Z}$ (the integer corresponding to a map $f:X\to Y$ is known as the degree of $f$). For $n>1$, $X$ and $Y$ are simply connected. In general, ... |
I'm asked to prove that the cardinality of the set of all bijections in $\mathbb{N} \to \mathbb{N}$ is $\mathfrak {c}$.
Note: $\mathfrak {c}$ is the cardinality of the real numbers.
I would appreciate some help understanding the following solution:
Let's denote this set as $|A|$. On the one hand, $|A| \subseteq \mathbb... |
Say that the exterior differential system (EDS) corresponding to a PDE system is:
$$df-f_x\,dx-f_y\,dy-f_w\,dw-f_z\,dz=0,\\ a_1\,f_x+a_2\,f_y=0,\tag{sys}$$
Of course we also require the independence condition, $dx\wedge dy\wedge dw\wedge dz\neq 0$.
Instead of (sys) can I simply use the following? $$ df +\dfrac{a_2}{a_1... |
Question: Use the fact that the power series, centered at x = 0, for \(\frac{1}{1-x}\) is \(\sum\limits_{n=0}^{\infty }{{{x}^{n}}}\), find the power series for the following, with center at x = c.
(a) \(\frac{1}{x+3}\),
c = 5
(b) \(\frac{1}{{{\left( 1-x \right)}^{3}}}\),
c = 0 |
ok, suppose we have the set $U_1=[a,\frac{a+b}{2}) \cup (\frac{a+2}{2},b]$ where $a,b$ are rational. It is easy to see that there exists a countable cover which consists of intervals that converges towards, a,b and $\frac{a+b}{2}$. Therefore $U_1$ is not compact. Now we can construct $U_2$ by taking the midpoint of eac... |
Given a topological space $X$ and a presheaf of abelian groups on $X$, $A$, we can construct the set of germs at a point $x\in X$ by taking $\mathscr{A}_x=\lim\limits_{\rightarrow} A(U)$ where $x\in U\subseteq X$ and $U$ is open. In
Sheaf Theory by Bredon, he claims there is a canonical group structure on $\mathscr{A}_... |
Motivation
In the finance literature, authors seem to use returns, : \begin{equation} R_{t+1}=\frac{p_{t+1}}{p_t} \end{equation} and log returns, : \begin{equation} r_{t+1}=log\left( \frac{p_{t+1}}{p_t} \right)=log(R_{t+1}) \end{equation} interchangeably (this notation is standard, following the convention that lower c... |
I am currently working on problem that I think could be expressed as an integer lattice problem.
Given $u \in \mathbb{R}^n$ and a
bounded integer lattice $L = \mathbb{Z}^n \cap [-M,M]^n$ I would like to find an integer vector $v \in L$ that minimizes the angle between $u$ and $v$. That is, I would like $$v \in \text{ar... |
Impulse Response DT Convolution CT Convolution Properties of LTI Systems Deriving the Convolution Integral
Consider an arbitrary input $x(t)$,(1)
Suppose $h_p$ is the response of the system to an input $\frac{1}{T_p}rect\bigg(\frac{t-nT_p}{T_p}\bigg)$.Then $y(t)$ corresponding to $x(t)$ is $y(t)=\sum T_px(nT_p)h_p(t-nT... |
My calculation shows that
$$I(\epsilon)
:= \int_{0}^{\infty} \frac{dx}{\sinh^{2}(\epsilon\sqrt{x^{2}+1})}
= \frac{\pi}{2\epsilon^{2}} - \frac{1}{\epsilon} + \pi \epsilon \sum_{n=1}^{\infty} \frac{1}{(\pi^{2}n^{2} + \epsilon^{2})^{3/2}} \tag{1}. $$
In particular, if we expand the infinite sum on the RHS, we get
$$ I(\ep... |
I need to find $\lim _{x \to 0} \cot(3x)\sin(4x)$. However, I am having trouble finding a way to do that. I am a Calculus 1 student and the only ways I know to handle a problem like this are by multiplying by a conjugate, or L'Hospital's Rule. Neither of which seems to work here.
I think I need to identify the correct ... |
There is a minor ambiguity in the term "Riemann integral": it tends to be used both for Riemann's original formulation -- which involves tagged partitions and requires convergence in a very strong sense: uniformly in the
mesh (or norm) $||\mathcal{P}||$ of the partition $\mathcal{P}$ -- and also G. Darboux's later simp... |
How to compute the following trigonometric question $$\sqrt2\sin10 (\sec5+\frac{2\cos 40}{\sin5}-4\sin35)=...$$ I am having problem to solve this trigonometric question. I tried to use identity $\sin10=2\sin5\cos5,\cos40=\cos(45-5), and \sin35=\sin(30+5)$ but it became complicated and I cannot simplify into a simpler t... |
Group Set
context $G$ definiendum $ \langle G,* \rangle \in \mathrm{it}$ inclusion $\langle G,* \rangle \in \mathrm{monoid}(G)$ let $e$ such that $\forall g.\, e*a=a*e=a$ range $g,g^{-1}\in G$ postulate $\forall g.\,\exists g^{-1}.\;(g*g^{-1}=g^{-1}*g=e)$ Alternative definitions Sharper definitions
We could just define... |
ä is in the extended latin block and n is in the basic latin block so there is a transition there, but you would have hoped \setTransitionsForLatin would have not inserted any code at that point as both those blocks are listed as part of the latin block, but apparently not.... — David Carlisle12 secs ago
@egreg you are... |
First, let me introduce my little story:
I started searching information about the famous Dirichlet Divisor Problem: getting the exact asymptotic behaviour of the sum of the divisor function up to an integer $x$. More specifically, the aim of the problem is to bound $\theta$ in:
$$D(x)=\sum_{n \le x} d(n) = x \log x +x... |
I will illustrate with the example in the question, because a general answer is too complicated to write down.
Let $F$ be the common distribution function. We will need the distributions of the order statistics $x_{[1]} \le x_{[2]} \le \cdots \le x_{[n]}$. Their distribution functions $f_{[k]}$ are easy to express in t... |
In the Kerr metric the ring singularity is located at the coordinate radius $r=0$, which corresponds to a ring with the cartesian radius $R=a$.
So the center of the ring singularity in cartesian coordinates is at $r=-a, \ \theta=\pi/2$.
But the center in cartesian coordinates is also at $r=0, \ \theta=0$ (at $r=0$ all ... |
I am confused. In the static correlation, we use combination of Slater determinants to account for electronic correlation (known as CI or configuration interaction) and the wave function is represented as a sum of various SD where the HF SD is the base function and higher excited SD contributes some parts. Similarly, i... |
The following argument is essentially an application of the path lifting property for covering spaces.
Let's think about $\mathbb{R}P^2$ as being the quotient space you get by identifying antipodal points on the sphere $S^2$. That is, let $x\sim -x$, let $\mathbb{R}P^2=S^2/\sim$ and let $p\colon S^2\rightarrow\mathbb{R... |
Let $\sigma_1,\sigma_2$ be the real and comlex embeddings, and let $f = (\sigma_1,\sigma_2) : K \to \Bbb R \times \Bbb C$.
Then $f$ preserves addition and multiplication, and $N(x) = \sigma_1(x)|\sigma_2(x)|$.
So units are all on the surface $S = \{(y,z) \in \Bbb R \times \Bbb C \mid y|z|=1 \}$.Suppose that you have fo... |
A \(\varGamma \)-magic Rectangle Set and Group Distance Magic Labeling Abstract
A \(\varGamma \)-distance magic labeling of a graph \(G = (V, E)\) with \(|V| = n\) is a bijection \(\ell \) from
V to an Abelian group \(\varGamma \) of order n such that the weight \(w(x) =\sum _{y\in N_G(x)}\ell (y)\) of every vertex \(x... |
In the chapter on Artinian rings in "Introduction to Commutative Algebra" by Atiyah and MacDonald, we have:
Proposition 8.6. Let $(A,\mathfrak{m})$ be a local Noetherian ring. Then exactly one of the following holds:
$\frak{m}^n\neq\frak{m}^{n+1}$ for all $n \in \mathbb{N}$;
$\frak{m}$ is a nilpotent ideal, in which ca... |
In Euclidean domains, such as $\mathbb Z$ and $\rm\:F[x],\:$ the gcd is often defined as a common divisor that is "greatest" as measured by the Euclidean valuation, here $\rm\:|n|\:$ and $\rm\:deg\ f(x)\:$ resp. But general integral domains may not come equipped with such structure, so in this more rarified atmosphere ... |
Let $\{(x_i, y_i), 1\le i\le n\}$ be the pairwise values of the observations and responses respectively. Let us fit the linear regression model: $y_i=b_0+b_1 x_i+\epsilon_i, \epsilon_i\sim\mathcal{N}(0,\sigma^2)$ are iid.
I'd like to find a necessary and sufficient condition for this above model to be identifiable.
Let... |
In his book, Algorithmic Trading: Winning Strategies and Their Rationale, Ernie Chan shows how to use a Kalman filter to improve the returns of a cointegrated portfolio. Recall that the state equation is: $$\beta_t=\alpha\cdot\beta_{t-1}+\omega_{t-1}$$ Here, $\alpha$ is the state transition matrix, $\beta_t$ is the sta... |
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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 ... |
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Now showing items 21-30 of 165
Long-range angular correlations of π, K and p in p–Pb collisions at $\sqrt{s_{NN}}$ = 5.02 TeV
(Elsevier, 2013-10)
Angular correlations between unidentified charged trigger particles and various species of charged associated particles (unidentified particles, pions, kaons, protons ... |
I'm interested because I want to show that $x^2-34y^2\equiv -1\pmod{m}$ has solutions for all integers $m$. I started by using the following reasoning:
If $3\nmid m$, then $gcd(m,3)=1$. Then there exists a multiplicative inverse $\bar{3}$ modulo $m$. I note that $5^2-34=-(3^2)$, and thus $\bar{3}^2(5^2-34)\equiv (\bar{... |
Cardinality of Set Union/2 Sets
Jump to navigation Jump to search
Theorem
Let $S_1$ and $S_2$ be finite sets.
Then:
$\card {S_1 \cup S_2} = \card {S_1} + \card {S_2} - \card {S_1 \cap S_2}$ Proof
We have that Cardinality is Additive Function.
$\card {S_1 \cup S_2} + \card {S_1 \cap S_2} = \card {S_1} + \card {S_2}$
fro... |
Coriolis acceleration
Coriolis acceleration is the acceleration due to the rotation of the earth, experienced by particles (water parcels, for example) moving along the earth's surface. Ocean currents are influenced by Coriolis acceleration.
Coriolis acceleration is generated by the eastward rotation of the earth aroun... |
PDE Geometric Analysis seminar
The seminar will be held in room B115 of Van Vleck Hall on Mondays from 3:30pm - 4:30pm, unless indicated otherwise.
Contents 1 Previous PDE/GA seminars 2 Seminar Schedule Fall 2013 3 Seminar Schedule Spring 2014 4 Seminar Schedule Fall 2014 5 Abstracts Seminar Schedule Fall 2013
date spe... |
These are both wrong, as they don't obey the syntactic rules of first-order logic. The rules are:
if $P$ is an $n$-ary predicate and $x_1, \dots, x_n$ are variables, then $P(x_1, \dots, x_n)$ is a formula; if $\varphi$ and $\psi$ are formulas, then $\neg \varphi$, $\varphi\wedge\psi$ and $\varphi\vee\psi$ are formulas;... |
Can be easily proved that the following series onverges/diverges?
$$\sum_{k=1}^{\infty} \frac{\tan(k)}{k}$$
I'd really appreciate your support on this problem. I'm looking for some easy proof here. Thanks.
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals i... |
Consider the empty set $\emptyset$ as a topological space. Since the power set of it is just $\wp(\emptyset)=\{\emptyset\}$, this means that the only topology on $\emptyset$ is $\tau=\wp(\emptyset)$.
Anyway, we can make $\emptyset$ into a topological space and therefore talk about its homeomorphisms. But here, we seem ... |
The term "imaginary" is somewhat disingenuous. It's a real concept, with real (at least theoretical) application, just like all the "real" numbers.
Think back to that algebra class. You were asked to solve a polynomial equation; that is, find all the values of X for which the entire equation evaluates to zero. You lear... |
Trying to apply Cavalieri's method of indivisibles to calculate the volume of a cylinder with radius $R$ and height $h$, I get the following paradoxical argument.
A cylinder with radius $R$ and height $h$ can be seen as a solid obtained by rotating a rectangle with height $h$ and base $R$ about its height. Therefore, t... |
Oozing honey through pipes
The solution below is for a very viscous fluid which has negligible inertia and large viscosity. It is wrong for water in real pipes, because it neglects the pressure drop which comes with the changing velocity of water. This term is higher order in v, but it is obviously relevant for real wa... |
Suppose a particle with mass $m_1$ and speed $v_{1i}$ undergoes an elastic collision with stationary particle of mass $m_2$. After the collision, particle of mass $m_1$ moves with speed $v_{1f}$ in a direction of angle $\theta$ above the line it was moving previously. Particle with mass $m_2$ moves with speed $v_{2f}$ ... |
A Hilbert space is a kind of linear vector space.
In chemistry which encounter it when quantum mechanics, when we can represent wavefunctions by their contributions from different orthonormal single particle states. It is these single particle states which we build up out our atomic orbitals (AOs).
Example:
Consider a ... |
This blog discusses a problematic situation that can arise when we try to implement certain digital filters. Occasionally in the literature of DSP we encounter impractical digital IIR filter block diagrams, and by impractical I mean block diagrams that cannot be implemented. This blog gives examples of impractical digi... |
A series of the form $a b^k, a b^{k+1}, \ldots, a b^{l}$, where $a$ and $b$ can be any {\em complex} number is called a geometric series with $l-k+1$ terms. For example, $1,\frac{1}{2},\frac{1}{4},\ldots$ is an infinite geometric series with $a=1$, $b=\frac12$. You may have seen these before, but in this class often we... |
Let me just introduce some notation first to make this easier. Let's denote the total number of data points in the full sample as $N$. The variance of the full sample is
$$\sigma_N^2 = \frac{1}{N} \sum_{n=0}^{N} (x_i - \mu_N)^2$$
for the total sample mean $\mu_N$, where you might change the normalisation factor to $N-1... |
Why does it seems like every number $ababab$, where $a$ and $b$ are integers $[0, 9]$ is divisible by $13$?
Ex: $747474$, $101010$, $777777$, $989898$, etc...
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 sig... |
Summary
It turns out that even relatively low-mass ocean planets are capable of forming some of the exotic ices you name in their cores. Ice VII appears to form at the centers of planets of $0.015M_{\oplus}$ (Earth masses), while ice X forms at the centers of planets of $1.256M_{\oplus}$. Interestingly, despite the inc... |
The game is actually an instance of two-persons Pebble game, as @HendrikJan pointed out, and as such is proven to be $EXPTIME-complete$. The following is a summary based on a proof by Kasai, Adachi and Iwata in SICOMP 8 (4).
For starters, it's pretty obvious that the game is in $EXPTIME$ - we can simply check all the p... |
Knowledge of the specific fact that $(\sin x)' = \cos x$ actually predates the general knowledge of calculus and derivatives. It was known in the following form: that for very small $\Delta x$, when you increase $x$ to $x + \Delta x$, the increase in value of the sine, from $\sin x$ to $\sin (x + \Delta x)$, is proport... |
AI News, What is the difference between a Perceptron, Adaline, and neural network model? What is the difference between a Perceptron, Adaline, and neural network model?
learning algorithms can actually be summarized by 4 simple steps – given that we use stochastic gradient descent for Adaline: We write the weight updat... |
It is an interesting news on conduction heat transfer.
The new article reports that
vanadium dioxide conducts electricity much better than it conducts heat at near room temperature:
Abstract
In electrically conductive solids, the Wiedemann-Franz law requires the electronic contribution to thermal conductivity to be pro... |
Equivalence of Definitions of Ordering Contents 1 Theorem 2 Proof 1 3 Proof 2 Theorem
An
ordering on $S$ is a relation $\mathcal R$ on $S$ such that:
\((1)\) $:$ $\mathcal R$ is reflexive \(\displaystyle \forall a \in S:\) \(\displaystyle a \mathop {\mathcal R} a \) \((2)\) $:$ $\mathcal R$ is transitive \(\displaystyl... |
Integral
One of the central notions in mathematical analysis and all of mathematics, which arose in connection with two problems: to recover a function from its derivative (for example, the problem of finding the law of motion of a material object along a straight line when the velocity of this point is known); and to ... |
MCQs with Answers
In this one PDF, MCQs of all chapters of FSc Part1 are given. There are seven chapters. Answers of MCQs is starting from page 71.
SAMPLE MCQs $i^{13}=$…………. (A) $i$ (B) 1 (C) -1 (D) 2 Set of all possible subsets of $S$ is called (A) Equivalent sets (B) Empty set (C) Power set (D) subset Cube root of u... |
Particle number expectation value
Set
context $ w $ … grand canonical weight definiendum $ \langle\hat N\rangle(\beta,\mu) := \sum_{N=0}^\infty w_N(\beta,\mu)\cdot N $ Discussion
The notation “$\langle\hat N\rangle$” is chosen for the function because we can also introduce the sequence of observables $\hat N$ defined t... |
I have to solve a linear system of three equations and 3 unknowns and can't find a way to solve it. Applying Cramer's rule I obtain $\Delta = 0$, $\Delta_x \neq 0$, $\Delta_y \neq 0$, $\Delta_z \neq 0$ so that may exist a solution. How to deal with the system in such a situation?
Just solve it directly by applying Gaus... |
ISSN:
2156-8472
eISSN:
2156-8499 Mathematical Control & Related Fields
March 2012 , Volume 2 , Issue 1
Select all articles
Export/Reference:
Abstract:
We consider a finite planar network of 1-$d$ thermoelastic rods using Fourier's law or Cattaneo's law for heat conduction, we show that the system is exponentially stabl... |
A Markov View of the Phase Vocoder Part 1 Introduction
Hello! This is my first post on dsprelated.com. I have a blog that I run on my website, http://www.christianyostdsp.com. In order to engage with the larger DSP community, I'd like to occasionally post my more engineering heavy writing here and get your thoughts.
To... |
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Now showing items 1-10 of 17
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... |
Its really a great question and let us go by simple definition.
Defination:
As per what wikepedia says:
A yo-yo (also spelled yoyo) is a toy which in its simplest form is an
object consisting of an axle connected to two disks, and a length of
string looped around the axle, similar to a slender spool.
Working:
But what ... |
When finding the maximum margin separator in the primal form we have the quadratic program
$$min\frac{1}{2}||\theta||^2$$ $$\text{ subject to: } y^{(t)}(\theta \cdot x^{(t)} + \theta_0) \geq 1, \ t=1,...,n,$$
saying basically to find the maximum margin separator. The margin size will be:
$$\frac{1}{||\theta||}.$$
Does ... |
I have to build the stability diagram of mercury and I have a problem with this couple:
$\ce{Hg^2+}/\ce{Hg2^2+}$ $E^\circ=0.91\ \mathrm{V}$
The exercise says that a the border the concentration is $C=0.10\ \mathrm{mol \cdot L^{-1}}$ for all ions.
So I have : $\ce{2Hg^2+ +2e^- <=> Hg2^2+}$
Then by Nernst relation I have... |
Difference between revisions of "Linear representation theory of symmetric group:S5"
(→Character table)
(→Family contexts)
(10 intermediate revisions by the same user not shown) Line 8: Line 8:
==Summary==
==Summary==
+
{| class="sortable" border="1"
{| class="sortable" border="1"
! Item !! Value
! Item !! Value
|-
|-
... |
Let $R$ be an order on a class $X$. A subclass $S$ of $X$ is called an $R$-segment if $$(\forall s \in S) (\forall x \in X) ((x,s) \in R \implies x \in S).$$ If $a \in X$, then the set $S_{X,R} (a) = \{x : x \in X ,\, x \lneq a \}$ is an initial $R$-segment determined by $a$.
Let $R$ be a well-ordering on set $X$. Show... |
A duality is a sort-of equivalence between two objects or theories under a certain condition. Very useful in QFT and string theory.
List of some dualities in physics:
Involves the reciprocal of the coupling constant. Theory A is said to be S-dual to Theory B if Theory A with coupling constant $g$ is the equivalent of T... |
Learning Objectives
Relate the work done during a time interval to the power delivered Find the power expended by a force acting on a moving body
The concept of work involves force and displacement; the work-energy theorem relates the net work done on a body to the difference in its kinetic energy, calculated between t... |
I recently began browsing the 5e PHB when I noticed that there was no distance per round when falling under the Falling category. Is there a set fall speed and if so, what is it?
[This answer superseded by the release of Xanathar's Guide to Everything, Nov 2017, as detailed in this answer.] The rules have no explicit g... |
I'm reading the article Robust Uncertainty Principles: Exact Signal Reconstruction from Highly Incomplete Frequency Information (Candes, Romberg and Tao, 2004).
In this article they are talking about recovering the function $f$ whose fourier coefficients are known on some domain $\Omega$, by solving the following optim... |
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... |
Terms sourced from: http://iupac.org/publications/pac/65/4/0819/
"Nomenclature for chromatography (IUPAC Recommendations 1993)", Ettre, L.S.,
Pure and Applied Chemistry 1993, 65(4), 819
adsorption chromatography affinity chromatography anion exchange anion exchanger anticircular elution ascending elution
capillary colu... |
Article Title Keywords
Interval arithmetic, generalized coupled matrix equations, AE-solution set
Abstract
In this work, the interval generalized coupled matrix equations \begin{equation*} \sum_{j=1}^{p}{{\bf{A}}_{ij}X_{j}}+\sum_{k=1}^{q}{Y_{k}{\bf{B}}_{ik}}={\bf{C}}_{i}, \qquad i=1,\ldots,p+q, \end{equation*} are stud... |
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Now showing items 1-2 of 2
Search for new resonances in $W\gamma$ and $Z\gamma$ Final States in $pp$ Collisions at $\sqrt{s}=8\,\mathrm{TeV}$ with the ATLAS Detector
(Elsevier, 2014-11-10)
This letter presents a search for new resonances decaying to final states with a vector boson produced in association with a... |
I have a separable function $f[x,y]$, and I would like to find two functions $g[x]$ and $h[y]$ with
$f[x,y]=g[x] h[y]$
where $g[x]$ doesn't depend on $y$ and $h[y]$ doesn't depend on $x$. Ideally, $g$ and $h$ should have the same magnitude, to prevent overflows/underflows. I have a hackish approach that works, but invo... |
It simply is
probability, you can call it "predicted" as suggested by others.
I see from the discussion that you disagree with such name, so let me proove you that this
is probability.
First, recall that if $X$ is a Bernoulli distributed random variable parametrized by $p$, then $E(X) = p$. Second, take an intercept-on... |
Dataset Open Access
Radice, David; Bernuzzi, Sebastiano; Ott, Christian D.
We distribute complete gravitational-wave signals in the Advanced LIGO band (10 Hz - 8192 Hz) of the inspiral and merger of two neutron stars. These waveforms been constructed by hybridizing numerical-relativity data obtained with the WhiskyTHC ... |
How to represent in first order logic the expression:
"there are infinitely many"
To be honest I'm confused and not even sure whether you can represent them in first order logic.
Computer Science Stack Exchange is a question and answer site for students, researchers and practitioners of computer science. It only takes ... |
This asks whether or not
differentiating both sides of an equation is allowed. Which it isn't, however, can you integrate both sides of an equation?
If we have,
$$x^2=x+1$$
Can we apply the integral operator and get,
$${1 \over 3} \cdot x^3 \ |_a^b={1 \over 2} \cdot x+x \ |_a^b$$
Haha, just kidding. That's too easy, I ... |
I posted a following question in MSE, but I think it should be posted here in MO. Since I don't know how to transfer the post from MSE to MO, I have pasted the question below. Thank you in advance and looking for your comments/suggestions.
My question is two fold:
(1) Is it possible to "solve" (iterative convex/non-con... |
Impulse Response DT Convolution CT Convolution Properties of LTI Systems Procedure
Let $h[n]$ be the impulse response of a linear and time-invariant(LTI) system. If the signal $x[n]$ is input to the system, the output signal from the system is given by:$y[n]=\sum_{k=-\infty}^{\infty}x[k]h[n-k]$
This operation is called... |
I am stuck on a question in Chapter 11 of Advanced Solid State Physics by Philip Phillips, which asks to do the Cooper instability calculation for triplet pairing.
I attempt to solve the Schroedinger equation
$ [-\frac{\hbar^2}{2 m} (\nabla^2_1 + \nabla^2_2)+V(r_1 - r_2)] \psi(r_1,r_2) = E \psi(r_1,r_2)$
with a antisym... |
Interaction of an elastic plate with a linearized inviscid incompressible fluid
1.
Department of Mechanics and Mathematics, Kharkov National University, 4 Svobody sq., 61077, Kharkov, Ukraine
Keywords:nonlinear plate, linearized 3D Euler equations, global attractor., well-posedness, Fluid--structure interaction. Mathem... |
Why Time-Domain Zero Stuffing Produces Multiple Frequency-Domain Spectral Images
This blog explains why, in the process of time-domain interpolation (sample rate increase), zero stuffing a time sequence with zero-valued samples produces an increased-length time sequence whose spectrum contains replications of the origi... |
Working with all sorts of data, it happens sometimes that we want to predict the value of a variable which is not numerical. For those cases, a logistic regression is appropriate. It is similar to a linear regression except that it deals with the fact that the dependent variable is categorical.
Here is the formula for ... |
I'm trying to understand, at least intuitively why the derivative of a function at a point is the tangent vector at this point.
If we see the functions of this form $f:\mathbb R\to \mathbb R$ we see clearly that
$$f'(a)=\lim_{h\to 0}\frac{f(a+h)-f(a)}{h}$$
is the slope of the tangent of $f$ at the point $a\in \mathbb R... |
Version 3 (modified by 4 years ago) (diff), 'perturbative' and 'real' particles; the perturbative weigth 'perturbative' and 'real' particles
(following text is taken - slightly modified - from: O.Buss, PhD thesis, pdf, Appendix B.1)
For some calculations, e.g. low-energetic πA or γA collision, it is a good assumption, ... |
When writing down the the action of the RNS superstring in superspace, all of the sources I have checked (BBS, GSW, Polchinski) seem to just write down the action in conformal gauge, that is$$S_{\text{RNS}}:=\mathrm{i}\, \frac{T}{4}\int _W\mathrm{d}^2\sigma \mathrm{d}^2\theta \, \bar{D}Y\cdot DY,$$where $W$ is the supe... |
This question already has an answer here:
Let $z_1,z_2$ be two complex numbers with $\operatorname{Re}(z_1)\leq0$ and $\operatorname{Re}(z_2)\leq0$. I want to prove: $$\big|e^{z_2}-e^{z_1}\big|\leq\big|z_2-z_1\big|$$
I began by using the reverse triangle inequality: $\big|e^{z_2}-e^{z_1}\big|\geq\bigg|\big|e^{z_2}\big|... |
I am reading the following paper: Takáč, Peter On the Fredholm alternative for the p-Laplacian at the first eigenvalue. Indiana Univ. Math. J. 51 (2002), no. 1, 187–237.
I need help to understand the following argument (page 193 section 2.1):
$\Omega\subset\mathbb{R}^N$ is a bounded regular domain, $p\in (2,\infty)$. L... |
Consider the model
$ \mathbf{y} = f(\mathrm{X}) + \epsilon $.
Here $\mathrm{X}$ is a
fixed $n \times d$ data matrix, and $\epsilon \sim \mathcal{N}(0, \sigma^2 I)$ is iid Gaussian noise. Assume that $\sigma^2$ is known.
First, consider modeling this using a Gaussian process i.e. $f \sim \mathcal{GP}(0, k)$. Then it can... |
Version 5 (modified by 4 years ago) (diff), 'perturbative' and 'real' particles; the perturbative weigth 'perturbative' and 'real' particles
(following text is taken - slightly modified - from: O.Buss, PhD thesis, pdf, Appendix B.1)
Reactions which are so violent that they disassemble the whole target nucleus can be tr... |
Trigonometry Complex Numbers Geometric Series Integrals of Complex Functions and Integration by parts
In this class, we will deal only with integrals of complex functions of a real variable integrated with respected to the real variable. This is identical to integration of real functions of real variables. The $j$ is s... |
Let $G$ be a compact Lie group acting on a manifold $M$. So for each vector $X \in TeG$ we have $X^{\#}$ the vector field on $M$ defined at each point $p \in M$ by the curve $exp(tX) \cdot p$. If the action is free we have that $X^{\#}_p=0 \iff X=0$, I get the instinctive idea but I can not proof it rigorously.
Define ... |
You can see a full exposition of the
Completeness Theorem for propositional logic in every good math log textbook, like :
The
proof system used is Natural Deduction; here is a sketch of the proof.
Lemma 2.5.1 (Soundness) If $Γ \vdash \varphi$, then $Γ \vDash \varphi$.
The proof of it needs the rules of the
proof system... |
I've recently started studying differential geometry and I'm a bit unsure on the notion of a tangent vector on a manifold. Is the point that we can no longer thing of a vector as an arrow (a straight line) extending between two points (in general we cannot compare two points on a manifold), as there is no well-defined ... |
I try to find a good proof for invertibility of strictly diagonally dominant matrices (defined by $|m_{ii}|>\sum_{j\ne i}|m_{ij}|$). There is a proof of this in this paper but I'm wondering whether there are are better proof such as using determinant, etc to show that the matrix is non singular.
The proof in the PDF (T... |
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