故ω 为closed 1-form 但注意到对于单位圆周 γ, ∫γω=2π≠0 ,故它不是exact form 也就是说, R2∖{0} 上不存在一个良定的函数 θ ,使得 dθ=−ydx+xdyx2+y2 Definition 3 pullback of differential forms:设 U1∈Rn,U2∈Rm 和它们之间的光滑映射 ϕ:U1→U2 ,诱导出的映射 Ωp(ϕ)...
We study the dynamics of the Dicke maser model in the limit as the number of atoms becomes infinite and the coupling constant between the atoms and the radiation field goes to zero. We find that the limiting Hamiltonian is integrable and obtain an explicit closed form for the unitary time ev...
Thus, we generated eight compressed versions of each subset D in run-length encoded form (see Fig. 3 for examples of compressed time series). For every compressed dataset, we computed all pairwise DTW distances using the five different algorithms. Fig. 3 Examples of compressed time series ...
Java-Dokumentation fürjava.math.BigInteger.shortValueExact(). Teile dieser Seite sind Änderungen auf der Grundlage von Arbeiten, dievom Android Open Source-Projekterstellt und freigegeben werden und gemäß den in derCreative Commons 2.5 Attribution License beschriebenen Begriffen verwendet werden...
The second is the Petkovšek–Wilf–Zeilberger theory [3], which simplifies a given hypergeometric indefinite or definite sum to a closed form in a completely algorithmic way. Many important sums in physics belong to this class of sums. To our knowledge, these theories have not yet been ...
Any knot in a solid torus, called a pattern or satellite operator, acts on knots in the 3-sphere via the satellite construction. We introduce a generalization of satellite operators which form a group (unlike traditional satellite operat... CW Davis,A Ray - 《Mathematics》 被引量: 17发表:...
We consider the first class of nonlinear second-order partial differential equations compilable in the following general form: utt+a(x,t)uxt+b(t)ut=α(x,t)+G(u)(ut+a(x,t)ux)e−∫b(t)dt, (1) whereudenotes a function of(x,t)∈R2. ...
Preprint arXiv: 0904.4171 (hep- th).Goncalves, B., de Berredo-Peixoto, G., Shapiro, I.L.: Exact formfactors in the one-loop curved-space QED and the nonlocal multiplicative anomaly. Int. J. Mod. Phys. A 25 , 2382–2390 (2010). 0904.4171 ADS MATH View Article...
【题目】二、完形填空Mr.Smith is a teacher.He _1_mathin a school.He likes everything to be exact(精确的).Every_2_, hegoesfor a run along the street.Itis 3_today.Onthe street , Mr.Smith is_4_inthewarm morning sunshine again.A popular song is coming _5_fromhis mouth._6_, ayoun...
In this section, we summarize the current research of the FRMT and unify the results with the proposed coefficient matrices (vectors). Based on the coefficient mechanism, the closed-form distributions of the FRMT are derived in exact and compact expressions. 4.1. Eigenvalue Distributions in the...