Fractional Weyl-Riesz Integrodifferentiation of Periodic Functions of Two Variables via the Periodization of the Riesz Kernel

We consider the periodization of the Riesz fractional integrals (Riesz potentials) of two variables and show that already in this case we come across different effects, depending on whether we use the repeated periodization, first in one variable, and afterwards in another one, or the so called double periodization. We show that the naturally introduced doubly-periodic Weyl-Riesz kernel of order 0< f <2 in general coincides with the periodization of the Riesz kernel, the repeated periodization being possible for all 0< f <2 , while the double one is applicable only for 0< f <1 . This is obtained as a realization of a certain general scheme of periodization, both repeated and double versions. We prove statements on coincidence of the corresponding periodic and nonperiodic convolutions and give an application to the case of the Riesz kernel.     

Similarity of $$sgn x( - \tfrac{{d^2 }}{{dx^2 }} + c\delta )$$ Type Operators to Normal and Self-adjoint Operators

Mathematical Notes -     

The evaluation of matrix elements for non-canonical Weyl tableau basis states adapted toU(n 1+n 2)⊃U(n 1)×U(n 2)

Summary This is the first paper of a series of two, which enables the evaluation ofU(n) generator matrix elements in the non-canonical Weyl tableau basis adapted to subgroupU(n ₁)×U(n ₂). In this paper the explicit closed formulae for subduction coefficients are presented. These formulae will become useful through an inductive method to be presented in the second paper.     

飞秒啁啾脉冲放大系统中折叠反射式望远镜对脉冲波前的影响

推导出飞秒激光啁啾脉冲放大系统中使用的折叠反射式望远镜对脉冲波前的影响. 分析和计 算了波前倾斜与反射式望远镜参数之间的关系.结果发现：当脉冲宽度小于100 fs时，波前 倾斜对光束质量的影响不可忽略，并提出了抑制这种脉冲波前倾斜的有效方法. 关键词： 飞秒激光啁啾脉冲放大 波前倾斜 反射式望远镜     

Quadrature formulas for the generalized Riemann-Stieltjes integral

In this paper we propose a technique of approximation for the generalized Riemann-Stieltjes integral and we found an analogue for Newton-Cotes formulas in the case n = 2 and n = 3. *Beneficiary of a Socrates fellowship at the Department of Mathematics, University of Study of Cagliari, Via Ospedale, n. 72, Cagliari, 09124, Italy, in the period February – July 2002.     

Bruhat intervals as rooks on skew Ferrers boards

We characterise the permutations π such that the elements in the closed lower Bruhat interval [id,π] of the symmetric group correspond to non-taking rook configurations on a skew Ferrers board. It turns out that these are exactly the permutations π such that [id,π] corresponds to a flag manifold defined by inclusions, studied by Gasharov and Reiner.Our characterisation connects the Poincaré polynomials (rank-generating function) of Bruhat intervals with q-rook polynomials, and we are able to compute the Poincaré polynomial of some particularly interesting intervals in the finite Weyl groups An and Bn. The expressions involve q-Stirling numbers of the second kind, and for the group An putting q=1 yields the poly-Bernoulli numbers defined by Kaneko.     

Conformally flat tilted Bianchi Type-V cosmological models in general relativity

We have investigated two conformally flat tilted Bianchi Type-V cosmological models in general relativity. To get a determinate solution, we have assumed a supplementary conditionA =B ⁿ between metric potentials wheren is a constant. The behaviour of the model forn = 2 is discussed in detail. Various physical and geometrical aspects of the models are also discussed.     

Crystallized structure for level 0 part of modified quantum affine algebra Uq (sl2)

Crystal base of the level 0 part of the modified quantum affine algebra Uq(sl2)_0 is given by path. Weyl group actions, extremal vectors and crystal structure of all irreducible components are described explicitly.     

氨对硅基铁纳米薄膜高温重凝核的影响

采用弧过滤离子沉积系统（arc filtered deposition，AFD）在纯硅表面制备铁纳米薄膜。研究了750℃下铁纳米薄膜在氢气氛围以及氨气氛围中重凝核的规律。研究表明，在氢气氛围中，铁纳米薄膜重凝核以后形成的铁纳米颗粒随薄膜的厚度增加以及保温时间的延长而增大；但在氨气氛围中，铁纳米薄膜重凝核后形成的纳米颗粒的尺寸随保温时间的变化更为复杂：在氨气作用的初始阶段，铁颗粒的尺寸随氨气作用时间的延长而逐渐变大，但一段时间以后，铁颗粒的尺寸又随氨气作用时间的延长而变小，直到铁颗粒平均直径达到一个最小值（大约在氨气介入后的12min），随后铁颗粒的尺寸又逐渐变大，并最终达到一稳定值。