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Inertia
In power systems engineering, "inertia" is a concept that typically refers to rotational inertia or rotational kinetic energy. For synchronous systems that run at some nominal frequency (i.e. 50Hz or 60Hz), inertia is the energy that is stored in the rotating masses of equipment electro-mechanically coupled to ... |
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Now showing items 1-9 of 9
Measurement of $J/\psi$ production as a function of event multiplicity in pp collisions at $\sqrt{s} = 13\,\mathrm{TeV}$ with ALICE
(Elsevier, 2017-11)
The availability at the LHC of the largest collision energy in pp collisions allows a significant advance in the measurement of $J/\ps... |
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Now showing items 1-10 of 33
The ALICE Transition Radiation Detector: Construction, operation, and performance
(Elsevier, 2018-02)
The Transition Radiation Detector (TRD) was designed and built to enhance the capabilities of the ALICE detector at the Large Hadron Collider (LHC). While aimed at providing electron... |
I have a symmetric positive-definite matrix $A\in R_{n\times n}$.
Its eigenvectors $e_i$ are an orthonormal basis of $R_n$.
Are the $n^2$ matrices $[e_i\,e_j^T]$ a basis of $R_{n\times n}$?
I have noticed an interesting property: $[e_i\,e_j^T]$ commute with $A$ iff $\lambda_i=\lambda_j$
If $A$ does not commute with $[e... |
Series of Power over Factorial Converges Theorem Proof
If $x = 0$ the result is trivially true as:
$\forall n \ge 1: \dfrac {0^n} {n!} = 0$
If $x \ne 0$ we have:
$\left|{\dfrac{\left({\dfrac {x^{n+1}} {(n+1)!}}\right)}{\left({\dfrac {x^n}{n!}}\right)}}\right| = \dfrac {\left|{x}\right|} {n+1} \to 0$
as $n \to \infty$.
... |
Cameron Murray has a great post about the challenge of reforming economics in which he points out two challenges: social and technical. The social challenge is that different "schools" are tribal, and reconciliation isn't rewarded. Just read Murray on this.
The second challenge is something that I have tried to work to... |
These notes contain a proof. The digraph used in this proof is a little more complicated than the one that you have in mind: each point of the partial order corresponds to
two vertices of the digraph.
Let $\langle P,\preceq\rangle$ be the partially ordered set; I’ll write $p\prec q$ to indicate that $p\preceq q$ and $p... |
(Sorry was asleep at that time but forgot to log out, hence the apparent lack of response)
Yes you can (since $k=\frac{2\pi}{\lambda}$). To convert from path difference to phase difference, divide by k, see this PSE for details http://physics.stackexchange.com/questions/75882/what-is-the-difference-between-phase-differ... |
Experimental implementation of a quantum computing algorithm strongly relieson the ability to construct required unitary transformations applied to theinput quantum states. In particular, near-term linear optical computingrequires universal programmable interferometers, capable of implementing anarbitrary transformatio... |
(Sorry was asleep at that time but forgot to log out, hence the apparent lack of response)
Yes you can (since $k=\frac{2\pi}{\lambda}$). To convert from path difference to phase difference, divide by k, see this PSE for details http://physics.stackexchange.com/questions/75882/what-is-the-difference-between-phase-differ... |
The bounty period lasts 7 days. Bounties must have a minimum duration of at least 1 day. After the bounty ends, there is a grace period of 24 hours to manually award the bounty. Simply click the bounty award icon next to each answer to permanently award your bounty to the answerer. (You cannot award a bounty to your ow... |
The tale that hash tables are amortized $\Theta(1)$ is
a lie an oversimplification.
This is only true if:
- The amount of data to hash per item is trivial compared to the number of Keys and the speed of hashing a Key is fast - $k$. - The number of Collisions is small - $c$. - We do not take into account time needed to ... |
Fundamental principle I: stars are self-gravitating bodies in dynamical equilibrium due to a balance of gravity and internal pressure forces. Equation of hydrostatic equilibrium: consider a small volume element at a distance r from the centre- cross section δS, length δr,
Equation of distribution of mass
Dimensional an... |
Suppose $A\in\mathbb{R}^{n\times n}$ is symmetric and positive definite and that we have several symmetric matrices $B_i\in\mathbb{R}^{n\times n}$ that are low-rank and indefinite.
I need an algorithm for solving the following optimization problem:$$\begin{align*}\min_{x\in\mathbb{R}^n}\ & x^\top Ax\\\textrm{s.t.}\ & \... |
The magnetic field due to a magnetic dipole moment, $\boldsymbol{m}$ at a point $\boldsymbol{r}$ relative to it may be written $$ \boldsymbol{B}(\boldsymbol{r}) = \frac{\mu_0}{4\pi r^3}[3\boldsymbol{\hat{r}(\boldsymbol{\hat{r}} \cdot \boldsymbol{m}) - \boldsymbol{m}}], $$ where $\mu_0$ is the vacuum permeability. In ge... |
I have never encountered this before (encountered it now in Sean Carroll's GR text when discussing the benefit of solving problems in locally inertial references frame).
Let $\gamma$ be the Lorentz factor, $g_{\mu\nu}$ be the metric tensor, and let $U^\mu$ and $V^\mu$ be 2 four-velocities.
Can anyone explain the follow... |
Bull. Korean Math. Soc. Published online August 6, 2019
Saadoun Mahmoudi and Karim SameiBu Ali Sina
Abstract : In this paper, we introduce $SR$-additive codes as a generalization of the classes of $\mathbb{Z}_{p^r}\mathbb{Z}_{p^s}$ and $\mathbb{Z}_{2}\mathbb{Z}_{2}[u]$-additive codes, where $S$ is an $R$-algebra and an... |
Basically, you do not compute these lengths $2^n$ or $n^2$, but only the from-to computations that the automaton would be able to make on input with this particular lengths.
For the first two problems the automaton computes (in its internal states) the relation $E_\ell = \{ (p,q)\in Q\times Q \mid q\in\delta^*(p,y) \te... |
The Schwinger effect can be calculated in the world-line formalism by coupling the particle to the target space potential $A$.
My question relates to how this calculation might extend to computing particle creation in an accelerating frame of reference, i.e. the Unruh effect. Consider the one-loop world-line path integ... |
Show that if $0\leq x < n, n \geq 1$, and $n\in\mathbb{N}$ then
$$ 0 \leq e^{-x} - \left( 1 - \frac{x}{n} \right)^n \leq \frac{x^2e^{-x}}{n}. $$
By using
induction.
Progress: Decided to split the problem up into two parts, (i) and (ii).
(i) $ 0 \leq e^{-x} - \left ( 1- \frac{x}{n} \right ) ^ n $.
(i) $e^{-x} - \left ( ... |
In studying some physical propagator, I came across the following sum$$\sum_{n = -\infty}^{+\infty} \frac{ a^n }{ \sin^2(z + n \pi \tau) }\ . $$Obviously, my question is
how to evaluate this sum.
To some extent, I understand the result when $a = 1$. Loosely speaking, without properly regularizing, we have $$ \sum_{n \i... |
I was presented with the following problem;
Show that if $\sum b_n$ is a rearrangement of a series $\sum a_n$ , and $a_n$ diverges to $\infty$, then $\sum b_n = \infty$.
How would one solve this? It seems intuitively true, but how could I show it?
Mathematics Stack Exchange is a question and answer site for people stud... |
Let $A$ be the free associative algebra over a field $k$ generated by countably many indeterminates $x_1, x_2, \ldots$.
I want to show that for any $n$, $x_1 \ldots x_n$ is not in the ideal $I$ generated by $S=\{x_i^2, x_ix_j+x_jx_i : i,j \geq 0\}$.
My attempt:Suppose for a contradiction that it is. Then it would be a ... |
I have a matrix of $n \times n$ dimension: $$ K - \omega^2 M = \begin{pmatrix} 2\omega_0^2 - \omega^2 & - \omega_0^2 & 0 & \cdots & 0 \\ - \omega_0^2 & 2\omega_0^2 - \omega^2 & -\omega_0^2 & \cdots & 0 \\ 0 & -\omega_0^2 & 2\omega_0^2-\omega^2 & \cdots & 0 \\ \vdots & \vdots & \vdots & \ddots & \vdots \\ 0 & 0 & 0 & \c... |
On $C$-Bochner curvature tensor of a contact metric manifold
Bull. Korean Math. Soc. 2005 Vol. 42, No. 4, 713-724 Published online December 1, 2005
Jeong-Sik Kim, Mukut Mani Tripathi, and Jaedong Choi Mathematical Information Yosu National University, Lucknow University, Korea Air Force Academy
Abstract : We prove that... |
Let's try an example. Let's say you're trying to prove the following:
Simple Theorem over the natural numbers: If $n$ is even, then $n+1$ is odd.
What he's trying to say is that you don't need an independent proof that $n$ is even. In the natural numbers, this isn't even true, since not all numbers are even. What he's ... |
On $(\alpha, \beta)$-fuzzy subalgebras of $BCK/BCI$-algebras
Bull. Korean Math. Soc. 2005 Vol. 42, No. 4, 703-711 Published online December 1, 2005
Young Bae Jun Gyeongsang National University
Abstract : Using the \emph{belongs to} relation ($\in$) and \emph{quasi-coincidence with} relation (q) between fuzzy points and... |
For example, consider the electromagnetic theory given by\begin{align}I=-\frac{1}{4}\int d^4x\, F_{\mu\nu}F^{\mu\nu},\end{align}where $F_{\mu\nu}=\partial_\mu A_\nu-\partial_\nu A_\mu$. The action has a symmetry given by the space-time translations\begin{align}\delta A_\mu=-\epsilon^\alpha\partial_\alpha A_\mu,\end{ali... |
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... |
(Sorry was asleep at that time but forgot to log out, hence the apparent lack of response)
Yes you can (since $k=\frac{2\pi}{\lambda}$). To convert from path difference to phase difference, divide by k, see this PSE for details http://physics.stackexchange.com/questions/75882/what-is-the-difference-between-phase-differ... |
(Sorry was asleep at that time but forgot to log out, hence the apparent lack of response)
Yes you can (since $k=\frac{2\pi}{\lambda}$). To convert from path difference to phase difference, divide by k, see this PSE for details http://physics.stackexchange.com/questions/75882/what-is-the-difference-between-phase-differ... |
I just wanted to clarify the difference between the Algebra and $\sigma$-algebra:
Algebra: If $A_1, A_2 \ldots $ are in $\mathscr A$, then $\bigcup_{i = 1}^{n} A_i \in \mathscr A$ $\sigma$- Algebra: $A_1, A_2 \ldots $ are in $\mathscr A$, then $\bigcup_{i = 1}^{\infty} A_i \in \mathscr A$
Notice the difference is just ... |
Let us take the $\mathcal{F}$ presheaf of bounded real functions on the real line $\mathbb{R}$. Then for each $U\subset \mathbb{R}$ open we have $$U \mapsto \mathcal{F}(U) = \{ f\colon U \longrightarrow \mathbb{R} \mid \sup_U |f| < \infty \}$$It is clearly a presheaf. Now let's see the sheaf requirements.
Fix $U\subset... |
Bolzano-Weierstrass Theorem/General Form Theorem Proof
The proof of this theorem will be given as a series of lemmas that culminate in the actual theorem in the end.
Unless otherwise stated, all real spaces occurring in the proofs are equipped with the euclidean metric/topology.
Lemma 0: Suppose $S' \subseteq S \subset... |
Note
The constant acceleration equations apply from the first instant in time after the projectile leaves the launcher to the last instant in time before the projectile hits something, such as the ground. Once the projectile makes contact with the ground, the ground exerts a huge force on the projectile causing a drast... |
Consider the 1D Poisson equation $$\nabla^2 u = f.$$ Using finite difference method on cell corner data and a uniform grid with ghost points, I think we can write the system of equations with Neumann BCs as: $$Au = f-Au_{BC},$$ where $$ \begin{aligned} A &= \frac{1}{\Delta x^2} \left[\begin{array}{ccccccccc} -2 & 2 & &... |
An important concept in plasma physics is the Debye length, which describes the screening of a charge's electrostatic potential due to the net effect of the interactions it undergoes with the other mobile charges (electrons and ions) in the system. It can be shown that, given a set of reasonable assumptions about the b... |
Inertia
In power systems engineering, "inertia" is a concept that typically refers to rotational inertia or rotational kinetic energy. For synchronous systems that run at some nominal frequency (i.e. 50Hz or 60Hz), inertia is the energy that is stored in the rotating masses of equipment electro-mechanically coupled to ... |
Definition:Free Group on Set
Jump to navigation Jump to search
The
Contents Definition
Let $X$ be a set.
that can be defined as follows:
Definition 1: by universal property For every $X$-pointed group $(G, \kappa)$ there exists a unique group homomorphism $\phi : F \to G$ such that $\phi \circ \iota = \kappa$, that is,... |
Recently, I asked a question on Math SE. No response yet. This question is related to that question, but more technical details toward computer science.
Given two DFAs $A = (Q, \Sigma, \delta, q_1, F_1)$ and $B = (Q, \Sigma, \delta, q_2, F_2)$ where the set of states, the input alphabet and the transition function of $... |
Conditions for C^1 Smooth Solution of Euler's Equation to have Second Derivative Theorem
Let $y$ be a real function.
Let $y$ have a continuous first derivative and satisfy Euler's equation:
$F_y - \dfrac \d {\d x} F_{y'} = 0$ Then $\map y x$ has continuous second derivatives wherever: $F_{y' y'} \sqbrk{x, \map y x, \ma... |
Zeta-function method for regularization zeta-function regularization
Regularization and renormalization procedures are essential issues in contemporary physics — without which it would simply not exist, at least in the form known today (2000). They are also essential in supersymmetry calculations. Among the different m... |
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... |
Assume a random sample X1, ..., Xn with a normal distribution with mean μ and variance σ2. How do we know the following estimator is unbiased, but inconsistent?
closed as off-topic by Giskard, Kenny LJ, Adam Bailey, Maarten Punt, Dan Feb 1 at 23:26
This question appears to be off-topic. The users who voted to close gav... |
My question is as follows. Suppose we have a function $f(r)$ and we want to study its asymptotic behavior at infinity ($r\rightarrow \infty$). For example, the function may reduce to $-\frac{a}{r}$ or $b e^{-cr}$ at infinity. How do I identify the constants $a,b$ and $c$ using
Mathematica? Or, more generally, how do I ... |
I want to have common subexpression elimination of comlicated functions where the elimination is done by factoring out the expressions. The result is not to be digested by a compiler, it should remain symbolic. I want this to work in general, without choosing things by hand.
As an example of what I want to do, take to ... |
I am a beginner at mathematica, so I have made huge blunders in my code which gave too many errors so I did not think it would be relevant to post it. I will try and explain my target as well as possible.
I am trying to trace the motion of a particle in a varying electric field. I have the initial position and initial ... |
2018-09-11 04:29
Proprieties of FBK UFSDs after neutron and proton irradiation up to $6*10^{15}$ neq/cm$^2$ / Mazza, S.M. (UC, Santa Cruz, Inst. Part. Phys.) ; Estrada, E. (UC, Santa Cruz, Inst. Part. Phys.) ; Galloway, Z. (UC, Santa Cruz, Inst. Part. Phys.) ; Gee, C. (UC, Santa Cruz, Inst. Part. Phys.) ; Goto, A. (UC,... |
Nested Collection Policies in Off-Policy Evaluation
Off-policy evaluation allows you to estimate the reward of a policy using feedback data collected from a different policy. The standard method is to use inverse propensity scores (IPS) based on importance sample reweighting, i.e., reweighting with respect to the ratio... |
The transcendental numbers form a field, or so I thought. I'm familiar with the fact that the algebraic numbers form a field which implies that reciprocals of transcendental numbers must be again transcendental (if reciprocal is not transcendental, then the reciprocal of the reciprocal, the transcendental element itsel... |
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The New England Journal of Medicine, ISSN 0028-4793, 11/2017, Volume 377, Issue 18, pp. 1713 - 1722
Fifteen children with spinal muscular atrophy type 1 received gene-rep... |
Seminars 2014:
December 4, 2014, 10:00
Gerard Freixas (Jussieu, Paris) : Reciprocity laws on Riemann surfaces, connections on Deligne pairings and holomorphic torsio.
Abstract:
In this talk I will recall classical reciprocity laws on Riemann surfaces and explain how they translate into the language of connections on De... |
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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 ... |
We conisder structure: $X=\langle A,\le\rangle$. Thinnish linear order is such order that for each $x,y$ that $x<y$ there exists only finitely many $z\in A$ such that $x<z<y$. Prove that there is no such set $\Delta$ of first order formulas that $\Delta\models X$ $\leftrightarrow X$ is thinnish linear order.
I should u... |
Shear modulus also known as
Modulus of rigidity is the measure of the rigidity of the body, given by the ratio of shear stress to shear strain. Often denoted by G sometimes by S or μ. What is Shear Modulus?
Shear Modulus of elasticity is one of the measures of mechanical properties of solids. Other elastic moduli are Y... |
The Laplacian operator is called an operator because it does something to the function that follows: namely, it produces or generates the sum of the three second-derivatives of the function. Of course, this is not done automatically; you must do the work, or remember to use this operator properly in algebraic manipulat... |
Sum of k Choose m up to n Contents Theorem
Let $m, n \in \Z: m \ge 0, n \ge 0$.
Then: $\displaystyle \sum_{k \mathop = 1}^n \binom k m = \binom {n + 1} {m + 1}$
where $\displaystyle \binom k m$ is a binomial coefficient.
Proof
Proof by induction:
For all $n \in \N$, let $\map P n$ be the proposition:
$\displaystyle \su... |
I'm attempting to construct the thermodynamic potential for an economy by elaborate analogy -- demand/output is analogous to energy, price to pressure and supply to volume. What does this help with? For one thing, it leads toward a way to introduce a chemical potential (which after writing this post, I realize might no... |
Definition:Class/Zermelo-Fraenkel Definition
In $\textrm{ZF}$,
classes are written using class builder notation: $\left\{{x : P \left({x}\right)}\right\}$
\(\displaystyle y \in \left\{ {x: P \left({x}\right)}\right\}\) \(\quad \text{for} \quad\) \(\displaystyle P \left({y}\right)\) \(\displaystyle \left\{ {x: P \left({... |
I am having problems minimizing a potential:
$\text{V}(h,\eta)=\gamma \left(-h^2\right) \left(\eta ^2 \cos ^2(\theta )+\eta \cos (\delta ) \sqrt{-\eta ^2-h^2+1} \sin (2 \theta )+\left(-\eta ^2-h^2+1\right) \sin ^2(\theta )\right)$ (Input code below)
V = -h^2 γ (η^2 Cos[θ]^2 + (1 - h^2 - η^2) Sin[θ]^2 + η Sqrt[1 - h^2 -... |
I've been reading up on the construction of derived categories. I understand why we prefer localizing with respect to a localizing class of morphisms (to get a nice representation of morphisms as simple roofs thanks to the Ore conditions). Also, it's clear to me where the proof that quasi-isomorphisms form a localizing... |
Suppose the Fresnel equations give us complex reflexion co-effcients $R_p$ and $R_s$ for $p$- and $s$-polarized light, respectively. Then the intensity reflexion co-efficient (power reflexion coefficient) for depolarized light is (in most cases):
$\frac{1}{2} (|R_s|^2 + |R_p|^2)$
You do likewise for the transmission co... |
I am having a bit of difficulty in trying to understand a paper. The paper uses spectral method to solve for an eigenvalue that comes from a system of coupled ODEs. I will write out only one equation now, because it is enough to get to the crux of my question(s).
The equation is
$V[r] = \frac{e^{-(\nu[r] +\lambda[r])}}... |
How can I generate the higher $n$ quantum harmonic oscillator wavefunction (in position space) numerically? Here, higher means around $n=500$, or say $n=2000$, where $n$ is the $n$th oscillator wavefunction.
The position-space wavefunction of the $n$th state involves Hermite polynomials of order n (see Griffith's book ... |
We will describe the economic laws of supply and demand as the result of an information transfer model. Much of the description of the information transfer model follows [1].
Following Shannon [3] we have a system that transfers information $I_q$ from a source $q$ to a destination $u$ (see figure above). Any process ca... |
Logblog: Richard Zach's Logic Blog
You are looking at an archived page. The website has moved to richardzach.org.
Last week I gave my decision problem talk at Berkeley. I briefly mentioned the 1917/18 Hilbert/Bernays completeness proof for propositional logic. It (as well as Post's 1921 completeness proof) made essenti... |
Subgroup Action is Group Action Theorem
Let $\struct {G, \circ}$ be a group.
Let $\struct {H, \circ}$ be a subgroup of $G$.
Let $*: H \times G \to G$ be the subgroup action defined for all $h \in H, g \in G$ as:
$\forall h \in H, g \in G: h * g := h \circ g$ Then $*$ is a group action. Proof
Let $g \in G$.
First we not... |
Droop Control
Droop control is a control strategy commonly applied to generators for primary frequency control (and occasionally voltaqe control) to allow parallel generator operation (e.g. load sharing).
Contents Background
Recall that the active and reactive power transmitted across a lossless line are:
[math]P = \fr... |
I am trying to understand this paper: http://link.aps.org/doi/10.1103/PhysRevLett.99.236809
(Here is an arXiv version: http://arxiv.org/abs/0709.1274)
In the introduction, they mention certain symmetry arguments (the two paragraphs in the second column of the first page). Unfortunately, I am ill-equipped to understand ... |
I defined such a model for stock price
(1).... $$dS = \mu\ S\ dt + \sigma\ S\ dW + \rho\ S(dH - \mu) $$
, where $H$ is a so-called "resettable poisson process" defined as
(2).... $$dH(t) = dN_{\lambda}(t) - H(t-)dN_{\eta}(t) $$
, and $\mu := \frac{\lambda}{\eta}$.
Is it possible to derive some analytic results similar ... |
The bounty period lasts 7 days. Bounties must have a minimum duration of at least 1 day. After the bounty ends, there is a grace period of 24 hours to manually award the bounty. Simply click the bounty award icon next to each answer to permanently award your bounty to the answerer. (You cannot award a bounty to your ow... |
Hi, Can someone provide me some self reading material for Condensed matter theory? I've done QFT previously for which I could happily read Peskin supplemented with David Tong. Can you please suggest some references along those lines? Thanks
@skullpatrol The second one was in my MSc and covered considerably less than my... |
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... |
May be it helps you to see more easily the way to attack the problem.The first that you could try it's find or understand the recursive relation behind
Floyd-Warshall Algorithm. As the next function $f$.
$$f(u,v,k) = \begin{cases}w_{u,v} & k = 0\\\min\, (\ f(u,v, k-1),\ f(u,k,k-1) + f(k,v,k-1)) & \text{otherwise}\end{c... |
I'm looking for a hint for solving the following problem :
Given an array $A[1, \dots, k]$ of integers where $A[1] < A[2] < \dots < A[k]$ write pseudocode for an algorithm that determines whether $A[j]=j$ for some $j\in \{1,\dots,k\}$. Worst-case running time should be $\Theta(\log k)$.
I shall find an easy to calculat... |
Consider the tunneling Hamiltonian in the Hubbard model for a 1D lattice of quantum dots.
$$\begin{align}\hat{H}_t=t\displaystyle\sum_{i,j,\sigma}c_{i,\sigma}^{\dagger}c_{j\sigma}+c^{\dagger}_{j,\sigma}c_{i,\sigma}\hspace{5mm}\text{where } i\neq j\label{one} \tag{1}\end{align} $$
where $i,j\in {1,2}$ (we will only be l... |
In physics, the line integrals are used, in particular, for computations of
mass of a wire; center of mass and moments of inertia of a wire; work done by a force on an object moving in a vector field; magnetic field around a conductor (Ampere’s Law); voltage generated in a loop (Faraday’s Law of magnetic induction).
Co... |
Two events are independent if whatever happesn does not affect the other one at all.
The probability of happening of two independent events is the product of the probability of both happenings. $$$p(X=x \& Y=y)=p(X=x) \cdot p(Y=y)$$$
The probability to get a $$6$$ in each of two independent dices $$A$$ and $$B$$ is: $$... |
Sorry to bring up an old thread. But here's something that might be relevant.
Let
pCFL be the class of permutation-closed CFLs. The equality problem for pCFL is decidable.
Given $L$ in $\Sigma = \{ \sigma_1 , \dots , \sigma_n \}$, let $W_L = \{ \langle \#_{a_1}(w) , \dots , \#_{a_n}(w) \rangle \mid w \in L\}$. By Parik... |
It is well known that:
$\displaystyle \mathcal{H}_n = \log{n} + \gamma - \sum_{k=1}^\infty \frac{B_{k}}{k \, n^{k}}$
Where $\displaystyle B_k$ are the Bernoulli Numbers
A similar asymptotic expansion for the Harmonic Numbers begins with the logarithm shifted slightly:
$\displaystyle \mathcal{H}_n = \log{\left(n+\frac{1... |
First note that enumerable usually means can be
effectively enumerated, where as you seem to ask if it is countable (or denumerable).
The conclusion is wrong, so the approach cannot be right. The set
is countable. As for the approach, note that you are defining a polynomial with infinitely many non-zero coefficients, w... |
I am trying to verify the following formula involving Bessel functions of the first kind and am having no luck. The formula is
$$ \int{\omega} J_n(\rho \omega)\mathrm d\omega = \frac {1} {\rho} \left\{ -\omega J_{n-1} (\rho \omega) + n \int{J_{n-1}(\rho \omega)\mathrm d\omega } \right\} $$
I apologize if this is painfu... |
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Now showing items 1-10 of 20
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... |
Direction Cosines
When a directed line
passing through the origin makes \(\alpha \), \(\beta\) and \( \gamma\) angles with the \(x\), \(y \) and \(z \) axis respectively with OP Oas the reference, these angles are referred as the direction angles of the line and the cosine of these angles give us the direction cosines.... |
Qualitative properties of positive solutions for mixed integro-differential equations
1.
Departamento de Ingeniería Matemática and Centro de Modelamiento, Matemático, Universidad de Chile, Santiago, Chile
2.
Department of Mathematics, Jiangxi Normal University, Nanchang, Jiangxi 330022, China
$\begin{equation}\left\{ \... |
I have to diagonalize, within a Fortran-written code, a block tridiagonal Toeplitz Hermitian matrix, e.g.
$$ \left[ \begin{array}{ccccc} \ddots & \hat{A} & & & \\ \hat{A}^\dagger & \hat{B} & \hat{A} & & \\ & \hat{A}^\dagger & \hat{B} & \hat{A} & \\ & & \hat{A}^\dagger & \hat{B} & \hat{A} \\ & & & \hat{A}^\dagger & \ddo... |
Classification of Compact One-Manifolds Contents Theorem Corollary
Any compact one-manifold has an even number of points in its boundary.
Proof Lemma 1
Let $f$ be a function on $[a,b]$ that is smooth and has a positive derivative everywhere except one interior point, $c$. Then there exists a globally smooth function $g... |
$\Gamma(\Upsilon(1S) \to \ell^+\ell^-)$ to NNNLO (in session "Standard Model")
ALICE: bottomonium results in p-Pb and Pb-Pb (in session "Quarkonium In Media")
ATLAS measurements of associated vector boson plus quarkonium production at the LHC (in session "Production")
Bc Physics at LHCb (in session "Spectroscopy")
Bott... |
Nick Rowe has a new post up and it inspired me to take up his challenge (entering as a non-economist). Rowe is probably one of the best economist bloggers out there if you want to get more technical than the typical post from Scott Sumner or Paul Krugman. His question is this:
Q. Assume an economy where there are (say)... |
I've come across this problem while trying to work out a table-formatting algorithm.
It's very similar to standard linear programming (though it uses $>$ instead of $<$; I'm not extremely familiar with linear programming, but I believe this doesn't matter much).
Let $\vec v = (v_1, \dots, v_n)$ be a vector of positive-... |
I'm currently studying for my qualifying exam in algebraic topology, and I'm looking over old exam questions. The first part of the question was to show that $\mathbb{R} P^3$ is not homotopy equivalent to $\mathbb{R} P^2 \vee S^3$, which is fairly straightforward to do using either covering spaces or the cohomology rin... |
Hello! I'm back from a short vacation and slowly getting to the comments.
As I mentioned here, there might be a bit more to the information equilibrium picture of the Solow model than just the basic mechanics -- in particular I pointed out we might be able to figure out some dynamics of the savings rate relative to dem... |
Exercises Exercise \(\PageIndex{1}\)
Find the general solution.
(a) \(y'+ay=0\) (\(a\)=constant)
(b) \(y'+3x^2y=0\)
(c) \(xy'+(\ln x)y=0\)
(d) \(xy'+3y=0\)
(e) \(x^2y'+y=0\)
Answer
Add texts here. Do not delete this text first.
Exercise \(\PageIndex{2}\)
Solve the initial value problem.
(a) \({y'+\left({1+x\over x}\rig... |
In Exercises \((3.5E.1)\) to \((3.5E.6)\), find all solutions.
Exercise \(\PageIndex{1}\)
\(\displaystyle{y'={3x^2+2x+1\over y-2}}\)
Answer
Add texts here. Do not delete this text first.
Exercise \(\PageIndex{2}\)
\((\sin x)(\sin y)+(\cos y)y'=0\)
Answer
Add texts here. Do not delete this text first.
Exercise \(\PageIn... |
Simon Wren-Lewis sends us via Twitter to Medium for an exquisite example of my personal definition of mathiness: using math to obscure rather than enlighten.
Here's the article in a nutshell:
Any proposed government policy is challenged with the same question: “how are you going to pay for it”. The answer is: “by spend... |
Assume the Earth to be a uniform sphere of mass M and radius R. Also let the Earth be stationary initially. Assume further that there is all other stellar bodies are very far away so as to have no influence in this problem.
A ball of mass $m$ is to be thrown from the surface of the Earth so that it ultimately ends up m... |
Vitali variation
A generalization to functions of several variables of the Variation of a function of one variable, proposed by Vitali in [Vi] (see also [Ha]). The same definition of variation was subsequently proposed by H. Lebesgue [Le] and M. Fréchet [Fr] and it is sometimes called Fréchet variation. However the mod... |
This might be a slightly daft question as I'm a physicist rather than a chemist, but I have a slight problem in using Henry's law which I think I can circumvent using the ideal gas law – I'd be grateful if anyone can confirm or deny my logic!
I have an equation that yields the volume of oxygen gas per unit mass of tiss... |
Let $f(x)$ be a one-one, polynomial function such that $f(x)f(y)+2=f(x)+f(y)+f(xy) \ \forall \ x,y \in \mathbb R - \{0\}$, $f(1) \neq 1$, $f'(1)=3$. Find $f(x)$.
I tried to find the degree of the polynomial from the equation by using suitable substitution, but it didn't work. Also, I found that $f(1)=2$ and then I subs... |
Specific Heats, Isotherms, Adiabatics Introduction: the Ideal Gas Model, Heat, Work and Thermodynamics
The Kinetic Theory picture of a gas (outlined in the previous lecture) is often called the
Ideal Gas Model. It ignores interactions between molecules, and the finite size of molecules. In fact, though, these only beco... |
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