Structures and stability of Al<Subscript><Emphasis Type="Bold">7</Emphasis></Subscript>C and Al<Subscript><Emphasis Type="Bold">7</Emphasis></Subscript>N clusters

We report results of the atomic and electronic structures of Al₇C cluster using ab initio molecular dynamics with ultrasoft pseudopotentials and generalized gradient approximation. The lowest energy structure is found to be the one in which carbon atom occupies an interstitial position in Al₇ cluster. The electronic structure shows that the recent observation [Chem. Phys. Lett. 316, 31 (2000)] of magic behavior of Al₇C^- cluster is due to a large highest occupied and lowest unoccupied molecular orbital (HOMO-LUMO) gap which makes Al₇C^- chemically inert. These results have further led us to the finding of a new neutral magic cluster Al₇N which has the same number of valence electrons as in Al₇C^- and a large HOMO-LUMO gap of 1.99 eV. Further, calculations have been carried out on (Al₇N)₂ to study interaction between magic clusters. Received 28 July 2001     

The instability degree in the diemnsion of spaces of bivariate spline

In this paper, the dimension of the spaces of bivariate spline with degree less that 2r and smoothness order r on the Morgan-Scott triangulation is considered. The concept of the instability degree in the dimension of spaces of bivariate spline is presented. The results in the paper make us conjecture the instability degree in the dimension of spaces of bivariate spline is infinity.     

Solitary waves and their bifurcations of KdV like equation with higher order nonlinearity

We investigate the KdV like equation with higher order nonlinearity ut + a(1 +bun)unux + uxxx = 0with n ≥ 1, a, b ∈ R and α≠ 0. The bifurcations and explicit expressions of solitary wave solutions for theequation are discussed by using the bifurcation method and qualitative theory of dynamical systems. Thebifurcation diagrams, existence and number of the solitary waves are given.     

Can Millimeter Waves Generate Electroporation?

Analysis of the field distributions in a single biological cell under electromagnetic wave is given. With Debye approximation, the dielectric relaxation of each part of the cell, including the extracellular and cellular media, the cell membrane and the nuclear membrane, was taken into account. Making use of some typical parameters for a cell, the voltage across nuclear and cytoplasma membranes under electromagnetic waves are calculated up to millimeter wave frequency range. The calculated result indicates that it is unlikely to generate electroporation by present available millimeter wave sources.     

Note on Bernstein polynomials and Kantorovich polynomials

We obtain two asymptotic representations of remainder of approximation of derivable functions by Bernstein polynomials and Kantorovich polynomials separately.     

The existence of Chern-Simons vortices

A new type of vortices called Chern-Simons vortices is considered and the existence is established.     

火焰原子吸收光谱法测定生物样品中锌、铜和锰

生物样品经消化处理后,用火焰原子吸收光谱法测定样品中锌、铜和锰的含量,平均加标回收率为97.3%-102.4%,相对标准偏差(RSD)为0.65 %-1.40%.锌、铜和锰在给定范围内呈现良好的线性关系,相关系数分别为0.9994、0.9994和0.9983,方法简便,快速,结果可靠.     

Laser induced copper electroless plating on polyimide with Q-switch Nd:YAG laser

The results of laser induced deposition of copper on polyimide substrate from copper electrolyte solution are reported. Unlike most work reported in the literatures where CW Ar⁺ lasers were used, a second harmonic (532 nm wavelength) Q-switch Nd:YAG laser was used for our experiments. The deposition process was conducted by laser-catalyzing of the polyimide surface and subsequent photothermal-accelerated reduction of copper-complex ions in an alkaline reducing environment. The characteristics of the deposited copper line were investigated in terms of laser beam scanning speed, and the number of scans. The surface morphology and chemical composition of the deposited copper were analyzed using field emission scanning electron microscope (FESEM) and energy dispersive spectrometer (EDX). The optimum processing conditions have been identified. The copper deposit was found to adhere well to the substrate.     

Singularity conjecture and constructions of Jacobi forms

This paper verifies the singularity conjecture for Jacobi forms with higher degree in some typical cases, and gives constructions for the Jacobi cusp forms whose Fourier coefficients can be expressed by some kind of Rankin-typeL-series.     

Some degenerate and quasilinear parabolic systems not in divergence form

This paper deals with positive solutions of degenerate and quasilinear parabolic systems not in divergence form: u_t=u^p(Δu+av), v_t=v^q(Δv+bu), with null Dirichlet boundary conditions and positive initial conditions, where p, q, a and b are all positive constants. The local existence and uniqueness of classical solution are proved. Moreover, it will be proved that all solutions exist globally if and only if ab?λ₁², where λ₁ is the first eigenvalue of −Δ in Ω with homogeneous Dirichlet boundary condition.