On the Entangled Fractional Fourier Transform in Tripartite Entangled State Representation

Based on the newly constructed two mutually conjugate 3-mode entangled states of continuum variablesin three-mode Fock space we introduce entangled fractional Fourier transform (EFFT) for the tripartite entangled staterepresentations, which are not a direct product of three 1-dimensional FFTs. The eigenmodes of EFFT are obtained,which is different from the usual Hermite polynomials. The EFFT of the three-mode squeezed state is derived.     

Comparison of higher-order accurate schemes for solving the two-dimensional unsteady Burgers' equation

This paper is devoted to the testing and comparison of numerical solutions obtained from higher-order accurate finite difference schemes for the two-dimensional Burgers' equation having moderate to severe internal gradients. The fourth-order accurate two-point compact scheme, and the fourth-order accurate Du Fort Frankel scheme are derived. The numerical stability and convergence are presented. The cases of shock waves of severe gradient are solved and checked with the fourth-order accurate Du Fort Frankel scheme solutions. The present study shows that the fourth-order two-point compact scheme is highly stable and efficient in comparison with the fourth-order accurate Du Fort Frankel scheme.     

高阶Bernoulli多项式和高阶Euler多项式的关系

利用发生函数的方法，讨论了高阶Bernoulli数和高阶Euler数，高阶Bernoulli多项式和高阶Euler多项式之间的关系，得到了经典Bernoulli数和Euler数，经典Bernoulli多项式和Euler多项式之间的新型关系。     

沉积铁钝化膜的傅立叶变换表面增强拉曼光谱

利用恒电流沉积技术、傅立叶变换表面增强拉曼散射技术现场研究了0 1mol/LNaOH溶液中铁金属电极在不同电位下的表面氧化物的组成。结果表明,在电极预钝化区,表面首先生成的Fe(OH)2可由拉曼谱图中出现的550cm-1表征,证实了以往的研究结果。进入钝化区,表面二价氧化物逐步转化为高价氧化物Fe3O4及α 、δ 和γ FeOOH。在电位回扫的过程中,各氧化产物的还原以及铁表面SERS活性的逐渐消失导致谱峰强度降低。     

Evaluation formulas for Tornheim's type of alternating double series

In this paper, we give some evaluation formulas for Tornheim's type of alternating series by an elementary and combinatorial calculation of the uniformly convergent series. Indeed, we list several formulas for them by means of Riemann's zeta values at positive integers.

     

Determining radii of meromorphy via orthogonal polynomials on the unit circle

Using a convergence theorem for Fourier–Padé approximants constructed from orthogonal polynomials on the unit circle, we prove an analogue of Hadamard's theorem for determining the radius of m-meromorphy of a function analytic on the unit disk and apply this to the location of poles of the reciprocal of Szeg functions.     

Romanovski polynomials in selected physics problems

We briefly review the five possible real polynomial solutions of hypergeometric differential equations. Three of them are the well known classical orthogonal polynomials, but the other two are different with respect to their orthogonality properties. We then focus on the family of polynomials which exhibits a finite orthogonality. This family, to be referred to as the Romanovski polynomials, is required in exact solutions of several physics problems ranging from quantum mechanics and quark physics to random matrix theory. It appears timely to draw attention to it by the present study. Our survey also includes several new observations on the orthogonality properties of the Romanovski polynomials and new developments from their Rodrigues formula.     

氟化类金刚石薄膜的拉曼和红外光谱结构研究

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Fourier regularization for a backward heat equation

In this paper a simple and convenient new regularization method for solving backward heat equation—Fourier regularization method is given. Meanwhile, some quite sharp error estimates between the approximate solution and exact solution are provided. A numerical example also shows that the method works effectively.     

INJECTIVE PRECOVERS AND MODULES OF GENERALIZED INVERSE POLYNOMIALS

Let (S,≤) be an ordered set. Recall that (S,≤) is artinian if every strictly decreasingsequence of elements of S is ?nite, and that (S,≤) is narrow if every subset of pairwiseorder-incomparable elements of S is ?nite. Let S be a commutative monoid. Unl…