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Observable Set
context $V$…Hilbert space definiendum $\mathrm{Observable}(V)\equiv\mathrm{SelfAdjoint}(V)\cap\mathrm{End}(V)$ Discussion
Observables are the linear self-adjoint operators.
$\langle\psi|A\ \phi\rangle\in \mathbb C$ is called transition amplitude. $\frac{|\langle\psi|A\ \phi\rangle|^2}{\Vert\psi\Vert^2\Ve... |
Hello, I've never ventured into char before but cfr suggested that I ask in here about a better name for the quiz package that I am getting ready to submit to ctan (tex.stackexchange.com/questions/393309/…). Is something like latex2quiz too audacious?
Also, is anyone able to answer my questions about submitting to ctan... |
Suppose we have $M$ a monoid.
Define $E(M) = \{\alpha : M\rightarrow M : \alpha(xy)=\alpha(x) \cdot y \}$
If $a \in M$, define $\alpha_{a}: M \rightarrow M$ by \begin{align*} \alpha_{a}(x)=ax \quad \forall x \in M \end{align*}
Question is to prove that the function $\theta: M \rightarrow E(M)$ defined by $$\theta(a)=\a... |
Introduction Energy and Power Basic Operations Practice Problems Transformation of signals defined piecewise Even and Odd Signals Commonly encountered signals 1. Real Exponential Signals
These signals are given by:(1)
When $a<0$: Decaying ExponentialWhen $a>0$: Growing Exponential
2. Real Discrete-time Exponential Sign... |
This question already has an answer here:
Is there an exact form of $$f(s)=\sum_{n=0}^\infty {\frac{(-1)^n}{(2n+1)^s}}=1-\frac{1}{3^s}+\frac{1}{5^s}-\frac{1}{7^s}+\dots$$ when $s$ is odd?
Discussion
I have been exploring infinite series and will be spending my evening looking for patterns in this particular class. I in... |
It looks you need to use other
NDSolve options to control the spatial grid size to help
NDSolve a little.
Trying things, found that by increasing the grid size, now this effect you showed goes away.
Grid size needs to be much smaller when the diffusion coefficient is very small since you are effectively in $\lim{k \to ... |
Question: Show that the collection of measurable rectangles form an algebra.
Denote $\Sigma$ by $\sigma$-algebra.
I found the following set operations. Let $A_1, A_2 \in \Sigma_A$, and $B_1, B_2 \in \Sigma_B$. Then, $(A_1 \times B_1) \setminus(A_2 \times B_2) = [(A_1 \cap A_2) \times (B_1 \setminus B_2)] \cup [(A_1 \se... |
Following the idea that
a group is its structure, and reminding of Cayley theorem, I'm wondering whether we can build up virtually any finite group $G=\lbrace a_0,\dots,a_{n-1} \rbrace$ by searching pairs of subgroups of $\operatorname{Sym}(G)$ (the symmetric group over the set $G$), say $\Theta=\lbrace\theta_i,i=0,\do... |
I am asked to evaluate the following integral:
$\int_0^{2\pi} \cos^{10}\theta \mathrm{d}\theta$.
I am using complex analysis. Setting $z = e^{i\theta}$, I get from Eulers formula:
$\cos \theta = \frac{1}{2}\left(e^{i\theta} + e^{-i\theta}\right) = \frac{1}{2}\left(z + z^{-1}\right)$.
Now as $\theta$ goes from $0$ to $2... |
This question already has an answer here:
Some background.
I was asked to find an arithmetic function $f$ such that $f*f=\mathbf 1$ where $\mathbf 1$ is the constant function 1 and $*$ denotes Dirichlet convolution. I was able to prove that there are two solutions $\pm f$ and that $f$ is multiplicative. Next, I would h... |
Optimization
Optimization refers to the maximums or minimums of a function in calculus.
Common types of optimization problems include:
Optimization Area & Perimeter
Optimization Volume & Surface Area
Optimization of the Distance Between a Point on a Curve
First step is to create two or more equations to solve the probl... |
I am working on one of How To Prove It by Velleman's exercise:
"Is the following proof of the theorem correct? Suppose A, B, and C are sets and $A\subseteq B \cup C $. Then either $A\subseteq B$ or $A\subseteq C $.
Proof: Let $x$ be an arbitrary element of $A$. Since $A\subseteq B \cup C$, it follows that either $x \in... |
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Azimuthally differential pion femtoscopy relative to the second and thrid harmonic in Pb-Pb 2.76 TeV collisions from ALICE
(Elsevier, 2017-11)
Azimuthally differential femtoscopic measurements, being sensitive to spatio-temporal characteristics of the source as well as to the collectiv... |
What are the initial and boundary conditions for a Butterfly Option? I want to write up a PDE program for it and I have a rough idea of what the payoff should be (is it just a call and a put at the strike price?) but if anyone can provide me with definitive answers then I'd greatly appreciate it. In particular, I'm aft... |
Returns on an asset are negatively correlated with own variance, and I would like to set up a hedge with a variance swap (no options are traded). I need to decide on the notional of the swap: any ideas how I could calculate it?
EDIT I do not want to trade variance, I want to (imperfectly) hedge the part of the return t... |
Multiple solutions for a class of quasilinear problems
1.
Departamento de Matemática, IMECC - UNICAMP , Caixa Postal 6065, 13081-970 Campinas-SP, Brazil
$-\Delta_p u = g(x,u)$ in $\Omega$
$u = 0 $ on $\partial \Omega$,
where $\Omega \subset \mathbb{R}^N$ is an open bounded domain with smooth boundary $\partial \Omega$,... |
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... |
Skewness Formula
Skewness formula is called so because the graph plotted is displayed in skewed manner. Skewness is a measure used in statistics that helps reveal the asymmetry of a probability distribution. It can either be positive or negative, irrespective of signs. To calculate the skewness, we have to first find t... |
There are several solvers for solving the heat transfer problems in OpenFOAM. In this post, I will try to give a description of how to derive the governing equations of the following two solvers: buoyantBoussinesqSimpleFoam buoyantBoussinesqPimpleFoam
In the presence of gravity body force, the mass and momentum conserv... |
Asymptotic completeness is a strong constraint on quantum field theories that rules out generalized free fields, which otherwise satisfy the Wightman axioms. If we were to take a limit of a list of continuous mass distributions $\rho_n(k^2)$ that approaches a distribution in some topological sense, however, is there an... |
Go to the first, previous, next, last section, table of contents.
The functions described in this chapter accelerate the convergence of a series using the Levin u-transform. This method takes a small number of terms from the start of a series and uses a systematic approximation to compute an extrapolated value and an e... |
A
Partial Differential Equation commonly denoted as PDE is a differential equation containing partial derivatives of the dependent variable (one or more) with more than one independent variable. A PDE for a function u(x 1,……x n) is an equation of the form
The PDE is said to be linear if f is a linear function of u and ... |
ISSN:
1531-3492
eISSN:
1553-524X
All Issues
Discrete & Continuous Dynamical Systems - B
March 2009 , Volume 11 , Issue 2
Select all articles
Export/Reference:
Abstract:
In this paper we prove the existence of a global attractor with respect to the weak topology of a suitable Banach space for a parabolic scalar differen... |
L # 1
Show that
It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi.
Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.
Offline
Last edited by krassi_holmz (2006-03-09 02:44:53)
IPBLE: Increasing Performance By Low... |
This question already has an answer here:
I'm trying to take the limit of a series involving $\sum_{j=1}^\infty\frac{1}{3^j}$ and thinking that this might have a partial sum representation.
Here it says that $\sum_{i=1}^n \frac{1}{3^{i-1}} = \frac{3}{2}(1-\frac{1}{3^n})$ is the partial sum representation for $\sum_{i=1... |
As
background, I don't know if this kind of calculations were in the literature and/or are interestings. I can to prove that being $\lambda\geq 1$ a fixed integer, $n$ is perfect if and only if $$2n=\left(\prod_{p\mid n}\frac{p^{e_p+1}-1}{p^{\lambda e_p+1}-1}\right)\sigma\left(n^\lambda\right),$$ where we suppose that ... |
How do I show that:
$$\frac{1}{\sin^{2}\frac{\pi}{14}} + \frac{1}{\sin^{2}\frac{3\pi}{14}} + \frac{1}{\sin^{2}\frac{5\pi}{14}} = 24$$
This is actually problem
B $4371$ given at this link. Looks like a very interesting problem.
My attempts: Well, I have been thinking about this for the whole day, and I have got some ins... |
The prime number theorem says that the $n$th prime number is $p_n = \Theta(n \log n)$, so the series $\sum_n 1/(p_n \log p_n)$ should converge by comparison to $\sum_n 1/n (\log n)^2$. However this seems like overkill using deep mathematics. Is there a more elementary proof that $\sum_n 1/(p_n \log p_n)$ converges?
A c... |
Found the solution in a 1972's book (George R. Price, Ann. Hum. Genet., Lond, pp485-490, Extension of covariance selection mathematics, 1972).
Biased weighted sample covariance:
$\Sigma=\frac{1}{\sum_{i=1}^{N}w_i}\sum_{i=1}^N w_i \left(x_i - \mu^*\right)^T\left(x_i - \mu^*\right)$
And the unbiased weighted sample covar... |
\red\large e^x=\sum_{n=0}^\infty\frac{x^n}{n!}
\blue\normal\left {\begin{x+\frac{3x-y}{x^2+y^2}=3}\\{y-\frac{x+3y}{x^2+y^2}=0}
\normal f^\prime(x)\ = \lim_{\Delta x\to0}\frac{f(x+\Delta x)-f(x)}{\Delta x}
R=\normal \frac{\displaystyle{\sum_{i=1}^n (x_i-\bar{x})(y_i- \bar{y})}}{\displaystyle{\left[ \sum_{i=1}^n(x_i-\bar... |
Introduction Energy and Power Basic Operations Practice Problems Transformation of signals defined piecewise Even and Odd Signals Commonly Encountered Signals What is a signal?
The word 'signal' has been used in different contexts in the English language and it has several different meanings . In this class, we will us... |
Studying formulas about velocity and acceleration I came up with a question:
if I throw an object in the air with a velocity $v_0$ (suppose i throw it vertically) in how much time its final velocity $v_f$ will reduce to $0$ due to the force go gravity? Here is how I tried to solve the problem: Calculation of the time
I... |
A Markov View of the Phase Vocoder Part 2 Introduction
Last post we motivated the idea of viewing the classic phase vocoder as a Markov process. This was due to the fact that the input signal’s features are unknown to the computer, and the phase advancement for the next synthesis frame is entirely dependent on the phas... |
Given the below coefficients, if the Diophantine equation $Axy + Bx + Cy + D = \lfloor\frac{n}{3}\rfloor$ has exactly one solution, then $n$ is prime, otherwise $n$ is composite. In a sense, this equation models primes by formalizing the factorization of $n$. The nonnegative solutions for $y$ uniquely encode the exhaus... |
This question by caveman is popular, but there were no attempted answers for months until my
controversial one. It may be that the actual answer below is not, in itself, controversial, merely that the questions are "loaded" questions, because the field seems (to me, at least) to be populated by acolytes of AIC and BIC ... |
Based on the previous question and the comment in it, imagine two different mean-field Hamiltonians $H=\sum(\psi_i^\dagger\chi_{ij}\psi_j+H.c.)$ and $H'=\sum(\psi_i^\dagger\chi_{ij}'\psi_j+H.c.)$, we say that
$H$ and $H'$ are gauge equivalent if they have the same eigenvalues and the same projected eigenspaces. And the... |
How is the current related to nF? current and nF have different dimensions?
$nF$ is the charge $C$ transferred during the reaction, while current $i$ is the rate of charge transfer ($dC/dt$).
The following is a derivation, now edited to be more rigorous. The equation you provide is an expression for electrical Joule he... |
Real numbers Framework
$\dots,\,-\frac{\pi}{2},\,0,\,1,\dots$
${\mathbb R}$
Discussion axiomatics and cardinality Specker sequence
Choose a programming language and index all Turing machines (or executable program) by $i$.
Let $h(i,s)$ be $0$ or $1$, depending on whether the machine with index $i$ halts before $s$ step... |
Can I mix formation enthalpies and bond enthalpies in the same calculation?
I
think the answer is no, since they are relative measurements, and possibly relative to different things, but I haven't seen it stated explicitly anywhere.
Chemistry Stack Exchange is a question and answer site for scientists, academics, teach... |
I have $B_s = $ brownian motion at time $s$.
$$ \int_0 ^t B_s \, dB_s$$ $$0 \leq t \leq T$$
And want to check if it is a martingale, first from its closed form expression, and then via conditions on the Ito integral.
From exercises immediately before this one, it is known to me that the closed form expression is $$ \in... |
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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 ... |
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Now showing items 1-10 of 18
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... |
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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 ... |
Does anyone here understand why he set the Velocity of Center Mass = 0 here? He keeps setting the Velocity of center mass , and acceleration of center mass(on other questions) to zero which i dont comprehend why?
@amanuel2 Yes, this is a conservation of momentum question. The initial momentum is zero, and since there a... |
Any integer greater than 1 is called a prime number if and only if its positive factors are 1 and the number p itself. The basic ideology involved in this post is flawed and the post has now been moved to Archives. – The Editor Prime Generating Formulas We all know how hard it is to predict a formula for prime numbers!... |
All about the Light Absorption’s theory on the basis of Jablonski diagram.
According to the
Grotthus – Draper Law of photo-chemical activation:
Only that light which is absorbed by a system,
canbring a photo-chemical change.
However it is not true that all the kind of light(s) that are
absorbed could bring a photo-chem... |
Good evening all, I am determined to determine this determinant:
$$D = \det{\left[x_j^{n-i} - x_j^{2n-i}\right]_{i,j=1}^{n}}$$
Looking at the smaller cases, leads me to believe that
$$D = \prod_{1 \leq i < j \leq n}\left(x_i-x_j\right)\prod_{i=1}^n \left(1-{x_i}^n\right)$$
although I am having trouble showing this. I k... |
#
1
Problem with understanding the proof of Sauer Lemma
I will replicate the proof here which is from the book "Learning from Data"
Sauer Lemma:
$B(N,K) \leq \sum_{i=0}^{k-1}{n\choose i}$
Proof:
The statement is true whenever k = 1 or N = 1 by inspection. The proof is by induction on N. Assume the statement is true for... |
I have a perhaps stupid question about Noether's theorem.
In Abelian gauge theory, say
$$\mathcal{L}=-\frac{1}{4}F_{\mu\nu}F^{\mu\nu}+\bar{\Psi}(iD\!\!\!\!/-m)\Psi, \tag{1.0} $$
where $D_{\mu}=\partial_{\mu}+iA_{\mu}$ is the covariant derivative, the equations of motion are
$$\partial_{\mu}F^{\mu\nu}=J^{\nu} \tag{1.1}$... |
Suppose we know, that the dynamics of theory with chiral fermions (say, left) and gauge field (for simplicity, abelian) leads us to presence of anomalous commutator of canonical momentum $\mathbf E(\mathbf x)$:
$$ [E_{i}(\mathbf x), E_{j}(\mathbf y)] \sim \Delta (A_{i}(\mathbf x), A_{j}(\mathbf y)), \qquad (1) $$ where... |
Using a modified foam evaluation, we give a categorification of the Alexander polynomial of a knot. We also give a purely algebraic version of this knot homology which makes it appear as the...
Pages
We provide a finite dimensional categorification of the symmetric evaluation of \mathfrak{sl}_N-webs using foam technolo... |
Sims and Uhlig argue: although classical (frequentist) -values are asymptotically equivalent to Bayesian posteriors, they should not be interpreted as probabilities. This is because the equivalence breaks down in non-stationary models.
The paper uses small sample sizes, with - This post examines how the results change ... |
1. Introduction
MathJax is an open source JavaScript display engine for mathematics that works in all modern browsers. It allows the author of a web page to use familiar \(\LaTeX\) notations to descibe their maths. Here's a few famous equations to give you a taste:
\[ E = mc^2 \]
Probably the most famous of them all. E... |
Even before quantization, charged bosonic fields exhibit a certain "self-interaction". The body of this post demonstrates this fact, and the last paragraph asks the question.
Notation/ Lagrangians
Let me first provide the respective Lagrangians and elucidate the notation.
I am talking about complex scalar QED with the ... |
Since TMs are equivalent to algorithms, they must be able to perform algoriths like, say, mergesort. But the formal definition allows only for decision problems, i.e, acceptance of languages. So how can we cast the performance of mergesort as a decision problem?
Usually, Turing machines are explained to calculate funct... |
Machine $1$ is currently working. Machine $2$ will be put in use at time $t$ from now. If the lifetime of machine $i$ is exponential with rate $\lambda_i=1,2$, what is the probability that machine $1$ is the first machine to fail?
I tried a few things but I can not get the answer
Let $X_1\sim exp(\lambda_1)$ and $X_2\s... |
AFM has three differing modes of operation. These are contact mode, tapping mode and non-contact mode.
Contact mode
In contact mode the tip contacts the surface through the adsorbed fluid layer on the sample surface. The detector monitors the changing cantilever deflection and the force is calculated using Hooke’s law:... |
(I apologize if this question is too theoretical for this site.)
This is related to the answer here, although I came up with it independently of that. $\:$ Suppose we
have a unit mass planet at each integer point in 1-d space. $\:$ As described in that answer, the sum of the forces acting on any particular planet is ab... |
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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 ... |
Increase in Water Pressure As a Result of a Boat Entering a Lock
According to Archimedes principle 1000kg of water is displaced. Water has a density of 1000kg per cubic metre, so 1 cubic metre of water is displaced. The increse in the water level is
\[\Delta h= \frac{\Delta V}{A}=\frac{1}{10 \times 5}=0.02 m\]or 2 cm.
... |
Let $$a_n = \frac{(-1)^n}{\sin n + \ln n }$$
We wish to show that $\sum a_n$ converges.
In order to do this, first note that $a_n$ is negative when $n$ is odd, and positive when $n$ is even.
We will write $\sum a_n < \sum b_i + \sum c_j$, where $b_i$ are negative terms (with only odd indices $i$) that are smaller in ab... |
Evolution, a change in the trait distribution of a population, occurs by four mechanisms; drift, mutation, migration, and selection. E.g. These mechanisms cause a change in the mean of trait, or variance in a trait etc.. Just to summarise the conditions you gave:
a) Trait $i$ has variation
b) Trait $i$ covaries with fi... |
Urban traffic flow in one area or between any pair of locations can be approximated by a linear combination of three steady basis flows corresponding to commuting, business, and other purposes, with random perturbations.
Motivation
Knowledge of the urban human mobility is essential in traffic modeling for simulation, f... |
I have many a times encountered (and used myself) the following technique:
$$\int \sin x \mathrm{d}x = \int \operatorname{Im}(e^{ix}) \mathrm{d}x = \operatorname{Im} \left( \int e^{ix} \mathrm{d}x \right) = \operatorname{Im}( -ie^{ix}) + C = -\cos x + C$$
Not only in this case, but I've used this kind of transform many... |
My question is somewhat similar to Dimension of a Finite Field Extension is a Power of 2 but there's a small complication.
Claim 1: Let $K$ be a field of characteristic $\neq 2$, and suppose that every polynomial of odd degree in $K[x]$ has a root in $K$. Let $L/K$ be a finite extension. Then $[L:K] = 2^n$ for some $n$... |
This is going to be very long question.
A 1 kg block situated on a rough incline is connected to a spring constant 100Nm as shown in fig. The block is released from rest with the spring in the unstretched position. The block moves 10cm down the incline before coming to rest. Find the coefficient of friction between the... |
GR stands alone in its ability to pass both weak and strong field tests of gravity fields.
From 1905 to 1915, there was renewed interest in a somehow modified scalar field theory. Here is the action of a scalar gravity model, with $z^{\mu}$ a worldline parameterized by $\lambda$:$$\begin{align*}I_{sg} =& - m\int d \lam... |
Classical grand canonical ensemble Set
range $ N\in\mathbb N $ definiendum $ (\ \langle \mathcal M_N, H_N,\pi_N,\pi_{N,0},{\hat\rho}_N,{\hat\rho}_{N,0} \rangle\ )_N \in \mathrm{it} $ postulate $\forall N.\ \langle \mathcal M_N, H_N,\pi_N,\pi_{N,0},{\hat\rho}_N,{\hat\rho}_{N,0} \rangle$ … classical canonical ensemble
A ... |
There are $4!$ ways to place the men in such a way that men and women will sit alternatively.
Place them and label the spots where the men have taken their seats clockwise with $a,b,c,d,e$.
Now we will take a look at the possible configurations for women.
Without further conditions there are $5!$ configurations for wom... |
Definition:Bounded Metric Space Contents Definition
Let $M = \left({A, d}\right)$ be a metric space.
Let $M' = \left({B, d_B}\right)$ be a subspace of $M$.
$M'$ is bounded (in $M$) if and only if: $\exists a \in A, K \in \R: \forall x \in B: d \left({x, a}\right) \le K$
$M'$ is
bounded if and only if: $\exists K \in \R... |
№ 9
All Issues Volume 59, № 12, 2007
Ukr. Mat. Zh. - 2007. - 59, № 12. - pp. 1587–1593
The behavior of closed polynomials, i.e., polynomials $f ∈ k[x_1,…,x_n]∖k$ such that the subalgebra $k[f]$ is integrally closed in $k[x_1,…,x_n]$, is studied under extensions of the ground field. Using some properties of closed polyn... |
Suppose $X(t)$ is a Levy process with almost surely positive increments (for all $t_1 < t_2$ $P(X(t_1) < X(t_2)) = 1$)
Define
$$\nu X(t) := \sup \{\tau \in \mathbb{R_+}| X(\tau) < t\}$$
It is not hard to see, that $\nu X$ is also a stochastic process with almost surely positive increments.
My question is:
Is it a Levy ... |
I know Fermi's Golden Rule in the form
$$\Gamma_{fi} ~=~ \sum_{f}\frac{2\pi}{\hbar}\delta (E_f - E_i)|M_{fi}|^2$$
where $\Gamma_{fi}$ is the probability transition rate, $M_{fi}$ are the transition matrix elements.
I'm struggling to do a derivation based on the density of states. I know that under certain circumstances... |
As @coffeemath noted, your answer is actually the complement of the original expression. So this method is not correct.
I think the easiest way is to use the identities $(x + y)' = x'y'$ and $(xy)' = x' + y'$ (known as De Morgan's laws) and $x'' = x$. We have $$AB' + A'B = ((AB')'(A'B)')' = ((A'+B)(A+B'))'=$$$$=(A'A + ... |
The truth is you've been lied to, or at least that the usual notation makes the innate connection way more difficult to see than necessary.
To see how the two are the same, let me tell you about the wedge product. The wedge product of vectors is like the cross product, in that it is anticommutative--$a \wedge b = -b \w... |
I am trying to implement a numerical scheme for a PDE, and it takes as input dirichlet boundary conditions, i.e. $u=0$ on $\partial\Omega$, as well as the hessian of $u$ on the boundary also.
I am handling a non standard boundary condition, called the second boundary condition, where we prescribe $\Omega,\Omega^*\subse... |
View Answer
question_answer1) From an external point P, tangents PA and PB are drawn to a circle with centre O. If \[\angle PAB=50{}^\circ \], then find \[\angle AOB.\] question_answer2)
In Fig. 1, AB is a 6 m high pole and CD is a ladder inclined at an angle of \[60{}^\circ \] to the horizontal and reaches up to a poi... |
In the theory of relativistic wave equations, we derive the Dirac equation and Klein-Gordon equation by using representation theory of Poincare algebra.
For example, in this paper
the Dirac equation in momentum space (equation [52], [57] and [58]) can be derived from the 1-particle state of irreducible unitary represen... |
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Measurement of electrons from beauty hadron decays in pp collisions at root √s=7 TeV
(Elsevier, 2013-04-10)
The production cross section of electrons from semileptonic decays of beauty hadrons was measured at mid-rapidity (|y| < 0.8) in the transverse momentum range 1 < pT <8 GeV/c w... |
When you write "I do not see how it could be a function
WITHIN first-order arithmetic," it is certainly surprising, but this is in fact the case: figuring out how to internally express the provability predicate is the bulk of Godel's argument. If you actually read the proof, you will see how it is done.
Briefly, the po... |
I've discussed a procedure for divergent summation using the matrix of Eulerian numbers occasionally in the last years (initially here, and here in MSE and MO but not in that generality and thus(?) without conclusive answers)); now I would like to formalize/make waterproof one heuristic.
Consider some (divergent) serie... |
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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 1-2 of 2
D-meson nuclear modification factor and elliptic flow measurements in Pb–Pb collisions at $\sqrt {s_{NN}}$ = 5.02TeV with ALICE at the LHC
(Elsevier, 2017-11)
ALICE measured the nuclear modification factor ($R_{AA}$) and elliptic flow ($\nu_{2}$) of D mesons ($D^{0}$, $D^{+}$, $D^{⁎+}$... |
Note that the equation you give can be trivially restated as$$\left[-\frac{\hbar^2}{2m}\frac{\mathrm{d^2}}{\mathrm{d}x^2}\right]\psi(x) = \left[E-U(x)\right]\psi(x)\text{,}$$where $\hbar = h/2\pi$. So if in this situation we interpret kinetic energy as the difference between total and potential energy, this tells us th... |
I want to compare two Feynman diagrams and be able to say which one describes a process that is more likely to happen.
As far as I understand, this is done by considering the
order of the diagram.
In the case of, for example, $e^+ e^- \rightarrow \mu^+ \mu^-$ (tree level) I have the two electrons coupling to the photon... |
an object must have infinite mass if it is to be traveling at the speed of light
No, that's not true at all. An object's mass is a fixed property that doesn't change, regardless of what speed it travels at. But its
energy does change. The energy increases with increasing speed, according to the formula
$$E = \frac{mc^2... |
In the context of a paper dealing with Statistical Quality Control, I am defining and using the concept of the mean shift divided by the standard deviation of a (normally distributed one-dimensional) random variable, which is
$\delta\; =\; \frac{\left|\;\mu_0-\mu\;\right|}{\sigma_0} \text{,}$
where $\mu_0$ and $\sigma_... |
I'm wondering how would one go on about to calculate the static structure function with the ground state being $|\phi_0\rangle$:
$S_\vec{q}=\frac{1}{N}\langle \phi_0|\hat{n}_{\vec{q}}\hat{n}_{-\vec{q}} | \phi_0\rangle$
for the case $\vec{q}\neq 0$, knowing the operator $\hat{n}_\vec{q}$ is defined as follows:
$\hat{n}_... |
The likelihood of an observation $x$ under a gamma distribution is
$$L(x | \alpha, \beta) \propto \beta^\alpha x^{\alpha-1} \frac {\exp(-x\beta)} {\Gamma(\alpha)}$$
Suppose I have some observations
d from a gamma distribution with unknown shape and reciprocal scale parameters $\alpha$ and $\beta$
I wish to evaluate $ \... |
In a previous post, I presented a case for choosing a non-central version of Fisher’s exact test for most of bioinformatics’ uses of this test. I will now present an implementation of this test in javascript that could easily be embedded in web interfaces.
Although javascript is probably the least likely language to im... |
A general model (with continuous paths) can be written $$ \frac{dS_t}{S_t} = r_t dt + \sigma_t dW_t^S$$where the short rate $r_t$ and spot volatility $\sigma_t$ are stochastic processes.
In the Black-Scholes model both $r$ and $\sigma$ are deterministic functions of time (even constant in the original model). This prod... |
The story is about a compact oriented $4$-manifold $X$. In such case, the degree two cohomology $H^2(X,\mathbb{R})$ has a natural non-degenerate symmetric bilinear pairing, given by Poincaré duality. In terms of differential forms, it is simply
$\alpha.\beta= \int_X \alpha \wedge \beta$
and in terms of homology, it is ... |
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Session 61 - New Views of the Magellanic Clouds.
Display session, Wednesday, June 12
Great Hall,
Three hydrogen recombination lines, H90\alpha, H92\alpha, and H109\alpha have been observed with the Australia Telescope Compact Array toward the 30 Doradus Nebula, the giant HII region in th... |
I've been coming across the condition "IMFCC: having infinitely many finite conjugacy classes" often in recent times and I was wondering if there is any serious difference between having "IMFCC" and having an infinite centre. More precisely:
$\mathbf{Question:}$ Is there a finitely generated group $\Gamma$ which has IM... |
Entry structure Meta Order of keywords
'Entry type' 'Formal definition' 'Comment on formalities' Elaboration Alternative definitions Universal property Discussion Theorems Examples Reference Context Requirements Subset of
The 'Comment on formalities' is a plain text that adds everything that keeps the definition above ... |
In an earlier post, I discussed the basic and most important aspects of Set theory, Functions and Real Number System. In the same, there was a significant discussion about the union and intersection of sets. Restating the facts again, given a collection $ \mathcal{A}$ of sets, the union of the elements of $ \mathcal{A}... |
I don't really follow major breakthroughs, but my favorite paper this year was Raphael Zentner's Integer homology 3-spheres admit irreducible representations in $SL_2(\Bbb C)$.
It has been known for quite some time, and is a corollary of the geometrization theorem, that much of the geometry and topology of 3-manifolds ... |
The issue here is precisely what you mean when you say "regular path $J_t$ of almost complex structures".
I am not particularly expert in the theory of holomorphic curves, so I won't comment on that; I expect the situation is precisely analagous to the finite-dimensional setting I will describe below (I'm sure there ar... |
Here is a variation of a job-scheduling Problem. Let $J = \{j_1,...j_n\}$ be a set of Jobs for $1 \leq i \leq n$. Given Job length $|j_i|\in \mathbb{N}$, deadline $f_i \in \mathbb{N}$, profit $p_i \ge 0$ and starting-time $s_i \in \mathbb{N}$. I am looking for a greedy approximation factor given that the Job length may... |
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Measurement of electrons from beauty hadron decays in pp collisions at root √s=7 TeV
(Elsevier, 2013-04-10)
The production cross section of electrons from semileptonic decays of beauty hadrons was measured at mid-rapidity (|y| < 0.8) in the transverse momentum range 1 < pT <8 GeV/c wit... |
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