Synthesis of rhodium N-heterocyclic carbene complexes and their catalytic activity in the hydrosilylation of alkenes in ionic liquid medium

Rhodium complexes bearing N-heterocyclic carbene (NHC) ligands were prepared from bis(η⁴-1,5-cyclooctadiene) dichlorodirhodium and 1-alkyl-3-methylimidazolium-2-carboxylate, and the catalytic properties of rhodium complexes prepared in the hydrosilylation of alkenes in ionic liquid media were investigated. It was found that both the catalytic activity and selectivity of the rhodium complexes bearing NHC ligands were influenced by the attached substituents of the imidazolium cation. Additionally, rhodium complexes bearing NHC ligands in ionic liquid BMimPF₆ could be reused without noticeable loss of catalytic activity and selectivity.     

On the research of avalanche photodiodes-based heterodyne in FM/cw laser rangefinder

An avalanche photodiodes (APDs)-based heterodyne technique for FM/cw laser rangefinder (FM/cw LRF) is described. Based on a modified APDs model, the properties of heterodyne are theoretically analyzed and experimentally demonstrated under different illumination intensities and multiplications, both the amplitude and the signal to noise ratio (SNR) of the difference frequency signal are inversely proportional to the unmultiplied current at a high multiplication and are proportional to the square of multiplication at a low multiplication.     

含二茂铁基希夫碱及其配合物的研究

本文报道了含二茂铁基希夫碱-1,2-亚乙基双(二茂铁甲酰基异丙亚胺)及其某些d,f过渡金属配合物的合成,并对其结构进行了表征。     

Grobner-Shirshov Basis for Degenerate Ringel-Hall Algebras of Type F4

In this paper, by using the Frobenius morphism and the multiplication formulas of the generic extension monoid algebra, the authors first give a presentation of the degenerate Ringel-Hall algebra, and then construct the Gr\"{o}bner-Shirshov basis for degenerate Ringel-Hall algebras of type $F_4.$     

Combined complex-source beam and spherical-multipole analysis for the electromagnetic probing of conical structures

The paper addresses the combination of the spherical-multipole analysis in sphero-conal coordinates with a uniform complex-source beam (CSB) in order to analyze the scattering of a localized electromagnetic plane wave by any desired part of a perfectly conducting elliptic cone. The concept of uniform CSB is introduced and rigorously applied to the diffraction by a semi-infinite elliptic cone. The analysis takes into account the fact that the incident CSB does not satisfy the radiation condition. A new modal form of the Green's function for the elliptic cone is derived based on the principle that there is no energy loss to infinity. The numerical evaluation includes the scattered far fields of a CSB incident on the corner of a plane angular sector with different opening angles.     

C60Pd（Ph2POCH2CH2OPPh2）的合成与光电转化性能

C60Pd（Ph2POCH2CH2OPPh2）的合成与光电转化性能;富勒烯;钯配合物;光电性能     

Matrices with convolutions of binomial functions and Krawtchouk matrices

We introduce a class S_N of matrices whose elements are terms of convolutions of binomial functions of complex numbers. A multiplication theorem is proved for elements of S_N. The multiplication theorem establishes a homomorphism of the group of 2 by 2 nonsingular matrices with complex elements into a group G_N contained in S_N. As a direct consequence of representation theory, we also present related spectral representations for special members of G_N. We show that a subset of G_N constitutes the system of Krawtchouk matrices, which extends published results for the symmetric case.     

Multiplication of distributions in any dimension: Applications to δ-function and its derivatives

In two previous papers the author introduced a multiplication of distributions in one dimension and he proved that two one-dimensional Dirac delta functions and their derivatives can be multiplied, at least under certain conditions. Here, mainly motivated by some engineering applications in the analysis of the structures, we propose a different definition of multiplication of distributions which can be easily extended to any spatial dimension. In particular we prove that with this new definition delta functions and their derivatives can still be multiplied.     

Bilinear complexity of algebras and the Chudnovsky–Chudnovsky interpolation method

We give new improvements to the Chudnovsky–Chudnovsky method that provides upper bounds on the bilinear complexity of multiplication in extensions of finite fields through interpolation on algebraic curves. Our approach features three independent key ingredients.

•

We allow asymmetry in the interpolation procedure. This allows to prove, via the usual cardinality argument, the existence of auxiliary divisors needed for the bounds, up to optimal degree.     

从混合模空间到 Bloch -型空间微分算子与乘子的积

设H(D) 表示单位圆盘D上的解析函数空间,u ∈ H(D). 该文研究了从混合模空间到Bloch -型空间微分算子与乘子的积DM_u 的有界性与紧性.