矩阵方程AXAT=C的对称斜反对称解

设A∈Rm×n,C∈Rm×m给定,利用矩阵的广义奇异值分解和对称斜反对称矩阵的性质,得到了矩阵方程(1)AXAT=C存在对称斜反对称解的充要条件和通解表达式;证明了若方程(1)有解,则一定存在唯一极小范数解,并给出了极小范数解的具体表达式和求解步骤.     

On the Duals of Segre Varieties

The reflexivity, the (semi-)ordinariness, the dimension of dual varieties and the structure of Gauss maps are discussed for Segre varieties, where a Segre variety is the image of the product of two or more projective spaces under Segre embedding. A generalization is given to a theorem of A. Hefez and A. Thorup on Segre varieties of two projective spaces. In particular, a new proof is given to a theorem of F. Knop, G. Menzel, I. M. Gelfand, M.M. Kapranov and A. V. Zelevinsky that states a necessary and sufficient condition for Segre varieties to have codimension one duals. On the other hand, a negative answer is given to a problem raised by S. Kleiman and R. Piene as follows: For a projective variety of dimension at least two, do the Gauss map and the natural projection from the conormal variety to the dual variety have the same inseparable degree?     

Effects of several lanthanide trichloride hydrates on the melting behavior and spherulitic superstructure of poly(ethylene oxide)

Binary mixtures of poly(ethylene oxide) (PEO) with the trichloride hydrates of lanthanum, cerium, europium, terbium, and ytterbium have been studied with calorimetry, polarized optical microscopy, and infrared spectroscopy. Melting‐point depression of the PEO‐rich phase occurs in all cases. At sufficiently high concentrations of the low molecular weight lanthanide complex, crystallization of the polymer is absent. The lighter lanthanides with larger ionic radii, such as lanthanum and cerium, are more effective in suppressing PEO crystallization from solution or the molten state because they are more oxophilic. The spherulitic superstructure of PEO disappears at rather low concentrations of the lanthanide salts, between 2 and 8 mol % Ln³⁺. Lanthanum and terbium are most efficient at disrupting the formation of PEO spherulites, and europium is least efficient. Infrared spectroscopy identifies twisting and wagging vibrational absorptions of CH₂ groups in the polymer that are sensitive to the morphologies of these mixtures. Modifications of the PEO infrared absorbances in the presence of these five lanthanide salts correlate more closely with the presence or absence of major PEO melting, not the formation of a spherulitic superstructure. The phase behavior is rather simple, with no evidence of eutectic solidification upon cooling from the molten state. Multiple melting endotherms are observed in the differential scanning calorimetry heating traces of binary mixtures containing 8 mol % Yb³⁺ and between 10 and 20 mol % Eu³⁺, but the concentration dependence of these first‐order endothermic transitions is not characteristic of eutectic phase behavior. The presence of trivalent cations, such as Eu³⁺ or Yb³⁺, in these complexes perturbs the crystallization kinetics of PEO upon cooling from the molten state, as well as the melting behavior upon heating. Ion–dipole or electrostatic interactions between the lanthanide cation and the ether oxygen of PEO might alter the surface free energy at the periphery of the crystalline lamellae and perturb the chain‐folding characteristics of PEO. Consequently, coupling between the amorphous matrix and the PEO crystallites is strengthened, and this provides stability for the existence of multiple‐chain‐folded crystals composed of rather thin lamellae that could be responsible for multiple melting behavior. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 2200–2213, 2003     

Calculation of the Probabilities of Molecular Transitions in Modeling Interisomeric Structural Transformations

The problems of a computational procedure in modeling structural isomer–isomer transitions in multiatomic molecules are considered. A number of approximations that allow one to considerably simplify calculation of the probabilities of these transformations are suggested. In comparison with traditional calculations of potential surfaces and determination of their saddle points, in the proposed approach the relationship between the electronic and vibrational components of a general problem is virtually changed. A particular emphasis is put on the vibrational part, which seems to be more physical. It is shown that the problem of structural isomer–isomer conversions can be solved without resorting at all to explicit calculation of the contribution of an electronic matrix element to the probability of transition. There is no need to study in detail the shapes of potential surfaces; it suffices only to know the positions of their minima. The calculation of multidimensional vibrational integrals is replaced by calculation of one-dimensional integrals. The results obtained form a basis for constructing methods for modeling the dynamic spectra of complex molecules considering their structural transformations.     

Delay-Dependent Criterion for Guaranteed Cost Control of Neutral Delay Systems

In this article, the guaranteed cost control problem for a class of neutral delay systems is investigated. A linear--quadratic cost function is considered as a performance measure for the closed-loop system. Based on the Lyapunov method, delay-dependent criteria, which are expressed in terms of matrix inequalities, are proposed to guarantee the asymptotic stability of the system. The matrix inequalities can be solved easily by various efficient optimization algorithms.     

Decomposable symmetric designs

The first infinite families of symmetric designs were obtained from finite projective geometries, Hadamard matrices, and difference sets. In this paper we describe two general methods of constructing symmetric designs that give rise to the parameters of all other known infinite families of symmetric designs. The method of global decomposition produces an incidence matrix of a symmetric design as a block matrix with each block being a zero matrix or an incidence matrix of a smaller symmetric design. The method of local decomposition represents incidence matrices of a residual and a derived design of a symmetric design as block matrices with each block being a zero matrix or an incidence matrix of a smaller residual or derived design, respectively.     

四元数阵重行列式与复阵行列式的关系

指出四元数阵重行列式可用复阵行列式来表示，于是，复阵的伴随矩阵、求逆阵公式、秩的下界等，都可相应地推广到四元数阵．     

A new formulation of some discrete-time stochastic-parameter state estimation problems

Linear unbiased full-order state estimation problem for discrete-time models with stochastic parameters and additive finite energy type disturbance signals is reformulated in terms of linear matrix inequalities. Two estimation problems that are considered are the design for mean-square bounded estimation error and the design for the mean-square stochastic version of the suboptimal H_∞ estimator. These two designs are shown to apply to both the estimation with random sensor delay and estimation under observation uncertainty.     

金属基陶瓷复合材料的激光热冲击破坏效应

 研究了激光热冲击条件下静态受拉Sic颗粒增强6061铝合金材料的热断裂行为。热冲击用的激光束的脉宽分别为1.0ms和250μs, 激光束辐照在缺口的根部附近。对于热冲击下裂纹的产生及扩展进行细致的宏、微观观察,发现裂纹的产生和扩展的机制是不相同的。     

一阶模糊谓词逻辑公式的解释模型真度理论及其应用

基于一阶模糊谓词逻辑公式的有限和可数解释真度的理论,引入了一阶模糊谓词逻辑公式的解释模型及解释模型真度的概念,并讨论了它们的一系列性质及其在近似推理中的应用.