AN ALGORITHM FOR JORDAN CANONICAL FORM OF A QUATERNION MATRIX

In this paper, we first introduce a concept of companion vector, and study the Jordan canonical forms of quaternion matrices by using the methods of complex rep resentation and companion vector, not only give out a practical algorithm for Jordan canonical form J of a quaternion matrix A, but also provide a practical algorithm for corresponding nonsingular matrix P with P-1AP = J.     

复调和函数及其在无穷远点的性质

本文讨论了复调和函数在无穷远点的性质,揭示出有界区域上复调和函数的两类表示式之间的关系.     

均布荷载作用下压电材料简支梁的解析解

采用逆解法求解了均布荷载作用下压电材料简支梁的解析解。首先给出应力函数和电位移函数的多项式表达式,进而根据相容方程以及应力和电位移、位移和电势的边界条件,求得了同时考虑材料弹性参数、密度参数和压电参数呈梯度变化时,简支梁在均布荷载作用下的解析解。作为特例还得到了常体力以及材料参数为常数时的解答。并对结果进行了讨论。     

On vector-valued random Fourier series

Consider a (complex) Banach spaceX, such thatX C_O, and vectors(X _i ) _i ofX. Consider an independent standard normal sequence(g _i ) _i . Then if anX-valued random Fourier series _{|k| n} e ^ikt g _k x _k satisfies

Matroid Shellability, β-Systems,and Affine Hyperplane Arrangements

The broken-circuit complex is fundamental to the shellability and homology of matroids, geometric lattices, and linear hyperplane arrangements. This paper introduces and studies the -system of a matroid, nbc(M), whose cardinality is Crapo's -invariant. In studying the shellability and homology of base-pointed matroids, geometric semilattices, and afflne hyperplane arrangements, it is found that the -system acts as the afflne counterpart to the broken-circuit complex. In particular, it is shown that the -system indexes the homology facets for the lexicographic shelling of the reduced broken-circuit complex , and the basic cycles are explicitly constructed. Similarly, an EL-shelling for the geometric semilattice associated with M is produced,_and it is shown that the -system labels its decreasing chains.Basic cycles can be carried over from The intersection poset of any (real or complex) afflnehyperplane arrangement is a geometric semilattice. Thus the construction yields a set of basic cycles, indexed by nbc(M), for the union of such an arrangement.     

Perfectly normal non-metrizable non-Archimedean spaces are generalized Souslin lines

In this paper we prove the equivalence between the existence of perfectly normal, non-metrizable, non-archimedean spaces and the existence of ``generalized Souslin lines", i.e., linearly ordered spaces in which every collection of disjoint open intervals is -discrete, but which do not have a -discrete dense set. The key ingredient is the observation that every first countable linearly ordered space has a dense non-archimedean subspace.

     

Controlling Surface Interactions with Grafted Polymers

The interactions between surfaces modified with grafted polymers is studied theoretically. The aim of this work is to find polymer surface modifications that will result in localized attractive interactions between the surfaces. The practical motivation of the work is to find means to control the distance between bilayers and solid supports in supported membranes. Two theoretical approaches are used, the analytical treatment of Alexander and a molecular theory. It is found that grafting each end of the polymer to each surface results in an interaction with a well defined minimum. The location of the minima is found to be very close to the thickness of the polymer layer when the chains are grafted to only one of the surfaces. The predictions of the analytical theory are in excellent agreement with the molecular approach in this case. It is found that increasing the surface coverage increases the strength of the interaction. However, increasing the polymer chain length at fixed surface coverage results in a decrease of the free energy cost associated with separating the surfaces from their optimal distance. For the cases in which grafting to both surfaces is not possible, the molecular theory is used to study the effect of functionalizing segments of the chain to achieve an attractive well. It is found that by functionalizing the free end-groups of the polymers with segments attracted to the membrane, the range of the attractive interaction is significantly larger than the thickness of the unperturbed layer. Functionlizing the middle segments of the chains results in a shorter range attraction but of the same strength as in the end-functionalized layers. The optimal polymer modification is found to be such that the functionlized groups are attracted to the bare surface but are not attracted to the grafting surface. The relevance of the results to the design of experimental surface modifiers is discussed.     

Infrared spectra of carbon monoxide-hydrogen sulfide van der Waals complexes in the C-O stretching region

The CO-stretching vibration-rotation spectra of CO-H₂S, CO-D₂S, and CO-HDS complexes have been studied in the 2150 cm⁻¹ region using a supersonic slit-jet expansion and a tunable diode laser spectrometer. The spectra were analyzed with the help of very recent microwave pure rotational studies of the same complexes. Two bands were assigned for each of the symmetric hydrogen sulfide isotopes, corresponding to the two nuclear spin modifications, para and ortho. The band origins were blue shifted, relative to the free CO molecule, by about 3.8 cm⁻¹ for CO-H₂S and 4.3 cm⁻¹ for CO-D₂S. These are considerably smaller shifts than exhibited by the related CO-water complexes, indicating that the intermolecular forces in CO-H₂S are weaker and more isotropic.     

复杂网络时空混沌同步的Backstepping设计

利用Backstepping设计进行了复杂网络时空混沌的同步研究.首先将实现两个混沌系统同步的Backstepping设计推广到由m个时空混沌系统构成任意结构的复杂网络的同步研究中.进一步依据稳定性理论确定了网络同步时配置系数和控制增益满足的关系.整个网络实现同步仅需要在网络中的一个节点施加控制输入即可.进一步通过仿真实验验证了同步机理的有效性.     

Ge组分分布对基区杂质非均匀分布的SiGe HBT温度特性的影响

众所周知, 双极型晶体管的设计主要是基区的设计. 一般而言, 基区的杂质分布是非均匀的. 本文首先研究了非均匀的杂质高斯分布对器件温度分布、增益和截止频率的温度特性的影响, 发现增益和截止频率具有正温度系数, 体内温度较高. 随后研究了基区Ge组分分布对这些器件参数的影响. 均匀Ge组分分布和梯形Ge组分分布的SiGe 异质结双极型晶体管增益和截止频率具有负温度系数, 具有较好的体内温度分布. 进一步的研究表明, 具有梯形Ge组分分布的SiGe 异质结双极型晶体管, 由于Ge组分缓变引入了少子加速电场, 不但使它的增益和截止频率具有较高的值, 而且保持了较弱的温度敏感性, 在增益、特征频率大小及其温度敏感性、体内温度分布达到了很好的折中.