The geometry and number of the root invariant regions for linear systems

The stability domain is a feasible set for numerous optimization problems. D-decomposition technique is targeted to describe the stability domain in the parameter space for linear parameter-dependent systems. This technique is very simple and efficient for robust stability analysis and design of low-order controllers. However, the geometry of the arising parameter space decomposition into root invariant regions has not been studied in detail; it is an objective of the present paper. We estimate the number of root invariant regions and provide examples, where this number is attained.     

Inequalities for characteristic functions of multidimensional distributions

We obtain lower and upper bounds for the absolute values of characteristic functions of multivariate distributions F and also derive a lower bound on the norm of the zeroes of a characteristic function in terms of moments of the norm of the random vector with distribution F. Similar results are obtained for characteristic functions of probability measures on a separable Hilbert space.     

On the minimal energy ordering of trees with perfect matchings

The energy of a graph is defined as the sum of the absolute values of all eigenvalues of the adjacency matrix of the graph. Zhang and Li [F. Zhang, H. Li, On acyclic conjugated molecules with minimal energies, Discrete Appl. Math. 92 (1999) 71–84] determined the first two smallest-energy trees of a fixed size with a perfect matching and showed that the third minimal energy is between two trees. This paper characterizes trees of a fixed size with a perfect matching with third minimal, fourth minimal and fifth minimal energies for n≥86 and third minimal, fourth minimal energies for 14≤n≤84.     

On the spectral radii of unicyclic graphs with fixed matching number

In this paper, the first five sharp upper bounds on the spectral radii of unicyclic graphs with fixed matching number are presented. The first ten spectral radii over the class of unicyclic graphs on a given number of vertices and the first four spectral radii of unicyclic graphs with perfect matchings are also given, respectively.     

On the dominance of roots of characteristic equations for neutral functional differential equations

We present a sufficient condition for a zero of a function that arises typically as the characteristic equation of a linear functional differential equations of neutral type, to be simple and dominant. This knowledge is useful in order to derive the asymptotic behaviour of solutions of such equations. A simple characteristic equation, arisen from the study of delay equations with small delay, is analyzed in greater detail.     

On a global upper bound for Jensen's inequality

In this paper we shall give a global upper bound for Jensen's inequality without restrictions on the target convex function f. We also introduce a characteristic c(f) i.e. an absolute constant depending only on f, by which the global bound is improved.     

Some inequalities for characteristic functions

In a recent paper, Matysiak and Szablowski [V. Matysiak, P.J. Szablowski, Theory Probab. Appl. 45 (2001) 711-713] posed an interesting conjecture about a lower bound of real-valued characteristic functions. Under a suitable moment condition on distributions, we prove the conjecture to be true. The unified approach proposed here enables us to obtain new inequalities for characteristic functions. We also show by example that the improvement in the bounds is significant if more information about the distribution is available.     

光声光谱在蜂蜜品质鉴定中的应用

利用单光束光声光谱实验装置,分别测量了葡萄糖溶液、 蔗糖溶液和蜂蜜溶液在可见光波段的光声光谱,并与分光光度法测得的数据进行了比较。上述溶液的光谱特征表明：不同种类的溶液,光谱背景强度和轮廓有明显差异。三种溶液的光谱在485和655 nm处都有较强峰,但二者的强度比在不同溶液中有一定差异。另外,葡萄糖还在475,576和630 nm处有特征峰;蔗糖在632 nm处出现明显特征峰;这些光谱特征为鉴别天然蜂蜜中是否有葡萄糖或蔗糖掺假提供了依据。比较同种溶液的两种光谱发现：光声信号强度随波长的变化更灵敏, 说明在物质成分检测中,光声光谱法具有更高的灵敏度。     

基于溶剂化效应的BDE-15分子振动光谱增强特征振动研究

利用密度泛函与自洽反应场理论在B3LYP/6-31+G(d)水平下分别计算气态及24种不同极性溶剂中4,4’-二溴二苯醚(4,4’-dibrominated diphenyl ethers, BDE-15)的分子振动光谱(红外光谱、拉曼光谱),以气态分子振动光谱为基准,筛选出对溶剂极性敏感的特征振动作为指标构建溶剂对BDE-15振动光谱溶剂化效应指标体系,探究溶剂对BDE-15分子振动频率、红外/拉曼峰强溶剂化效应及综合效应,并寻求显著增强BDE-15分子特征振动频移/强度的溶剂。研究表明：从分子振动频率角度,溶剂极性敏感的(频移>1 cm-1)分子特征振动均为伸缩振和面外弯曲振,但24种溶剂对BDE-15分子振动频率溶剂化效应并不显著;从分子振动峰强角度,24种溶剂对BDE-15分子振动光谱峰强的增强效应主要发生在红外光谱的中低频区及拉曼光谱的高频区,其中起显著增强(红外/拉曼效应指标值分别大于6与5)的溶剂为醇类、乙腈、二甲亚砜、硝基苯;不同极性溶剂对BDE-15拉曼峰强溶剂化效应及综合效应指标值均表现出随溶剂介电常数增长由线性到对数的增长趋势,而红外峰强只保留低介电常数溶剂时的线性关系。利用上述BDE-15分子振动光谱峰强增强方法对BDE-153,BDE-154和BDE-209进行验证,醇类、乙腈、二甲亚砜、硝基苯对三者的振动光谱红外/拉曼峰强的效应指标值分别大于6与5,且最大峰强增倍数皆大于33,说明所建BDE-15分子振动光谱增强特征振动方法有助于进一步开展基于分子振动光谱的PBDEs同系物间辨识研究。     

超导体中的双体间的作用研究

本文根据高温超导体材料的结构特征建立了全元素作用哈密顿函数及量子力学方程,采用具有共识的层状结构为主体,经适当的简化,采用含时微扰法以回避一般的高次微扰项的发散困难,经求解,得出一些有意义的结果.