Zero cancellation for general rational matrix functions

The problem of cancelling a specified part of the zeros of a completely general rational matrix function by multiplication with an appropriate invertible rational matrix function is investigated from different standpoints. Firstly, the class of all factors that dislocate the zeros and feature minimal McMillan degree are derived. Further, necessary and sufficient existence conditions together with the construction of solutions are given when the factor fulfills additional assumptions like being J-unitary, or J-inner, either with respect to the imaginary axis or to the unit circle. The main technical tool are centered realizations that deliver a sufficiently general conceptual support to cope with rational matrix functions which may be polynomial, proper or improper, rank deficient, with arbitrary poles and zeros including at infinity. A particular attention is paid to the numerically-sound construction of solutions by employing at each stage unitary transformations, reliable numerical algorithms for eigenvalue assignment and efficient Lyapunov equation solvers.     

大功率微波诱导空气等离子体发射光谱中易电离元素的基体干扰研究

研究了由Okamoto腔产生的大功率微波诱导空气等离子体发射光谱中易电离元素Na和Ca的基体干扰。结果表明,Na和Ca的存在可使电离能较低的元素的原子线的发射强度增强,而使电离能较高的元素的原子线和几乎所有的离子线的发射强度降低。基体干扰随Na和Ca浓度的增大而增强,随等离子体微波功率的增大而减弱。Na和Ca的存在致使等离子体激发温度降低,电子密度增大。基体干扰是由于易电离元素使待测元素在等离子体中的电离平衡移动和激发能力减弱所致。     

MALDI-TOF-MS测定溶菌酶的相对分子质量中在线纯化技术的应用

用基质辅助激光解吸电离飞行时间质谱(MALDI-TOF-MS)测定溶菌酶的相对分子质量,采用硝酸纤维素膜作为溶菌酶的固相载体,在质谱仪上进行在线纯化溶菌酶样品,在测试前尽可能除去样品中的添加剂,以消除一些盐和蛋白质变性剂抑制样品峰的情形;此法简单、快速,并可明显增强离子峰的强度,提高测试的灵敏度。     

线性双折射对光学玻璃电流传感器输出特性影响的理论分析

对线性双折射及入射起偏角对光学玻璃电流传感器输出特性的影响进行了理论推导与分析,给出了光学玻璃电流传感器在非理想状态下线性双折射对输出电压的调制函数的数学表达式,并给出了入射起偏角对系统影响的数学表达式及其对系统有无影响的条件.结果表明,线性双折射会以Sa(δ)函数(抽样函数)的形式调制理想光学玻璃电流传感器输出信号的尺度因子,同时以－sin２(δ／2)为影响因子决定入射起偏角对系统影响的大小;当入射起偏角取某些特殊值时其对系统的影响为零.该工作结果对于光学玻璃电流传感器的研究、设计具有一定的理论参考意义.     

Computing matrix functions solving coupled differential models

In this paper a modification of the method proposed in [E. Defez, L. Jódar, Some applications of Hermite matrix polynomials series expansions, Journal of Computational and Applied Mathematics 99 (1998) 105–117] for computing matrix sine and cosine based on Hermite matrix polynomial expansions is presented. An algorithm and illustrative examples demonstrate the performance of the new proposed method.     

Some variations of the Bohman–Korovkin theorem

In this paper we develop the main aspects of the Bohman–Korovkin theorem on approximation of continuous functions with the use of A-statistical convergence and matrix summability method which includes both convergence and almost convergence. Since statistical convergence and almost convergence methods are incompatible we conclude that these methods can be used alternatively to get some approximation results.     

Skew-symmetric methods for nonsymmetric linear systems with multiple right-hand sides

By transforming nonsymmetric linear systems to the extended skew-symmetric ones, we present the skew-symmetric methods for solving nonsymmetric linear systems with multiple right-hand sides. These methods are based on the block and global Arnoldi algorithm which is formed by implementing orthogonal projections of the initial matrix residual onto a matrix Krylov subspace. The algorithms avoid the tediously long Arnoldi process and highly reduce expensive storage. Numerical experiments show that these algorithms are effective and give better practical performances than global GMRES for solving nonsymmetric linear systems with multiple right-hand sides.     

S~(GS*)类图簇的伴随多项式的因式分解及其色性

通过研究SGS*类图簇的伴随多项式的因式分解,证明了这类图簇的补图的色等价图的结构特征.     

Double piling structure of matrix monotone functions and of matrix convex functions

There are basic equivalent assertions known for operator monotone functions and operator convex functions in two papers by Hansen and Pedersen. In this note we consider their results as correlation problem between two sequences of matrix n-monotone functions and matrix n-convex functions, and we focus the following three assertions at each label n among them:

(i) f(0)0 and f is n-convex in [0,α),

(ii) For each matrix a with its spectrum in [0,α) and a contraction c in the matrix algebra M_n,

f(cac)cf(a)c,