偶次中立型泛函微分方程解的振荡性

研究偶次中立型泛函微分方程，给出了该微分方程解的振荡性的充分条件,得到了一些新的结果并给出了一些示例。     

Pseudo almost periodic solutions for the systems of differential equations with piecewise constant argument

In this paper, we investigate the existence and uniqueness of new almost periodic type solutions, so-called pseudo almost periodic solutions for the systems of differential equations with piecewise constant argument by means of introducing the notion of pseudo almost periodic vector sequences.     

Application of the Filter Diagonalization Method to One- and Two-Dimensional NMR Spectra

A new non-Fourier data processing algorithm, the filter diagonalization method (FDM), is presented and applied to phase-sensitive 1D and 2D NMR spectra. FDM extracts parameters (peak positions, linewidths, amplitudes, and phases) directly from the time-domain data by fitting the data to a sum of damped complex sinusoids. Grounded in a quantum-mechanical formalism, FDM shares some of the features of linear prediction and other linear algebraic approaches, but is numerically more efficient, scaling like the fast Fourier transform algorithm with respect to data size, and has the ability to correctly handle spectra with thousands or even millions of lines where the competing methods break down. Results obtained on complex spectra are promising.     

矩阵的广义对角化

定义了矩阵广义对角化的概念 ,并通过引入 s次特征向量组的方法不但给出了矩阵广义对角化的充要条件和判定方法 ,而且还给出矩阵广义对角化的算法     

High dimensional limit theorems and matrix decompositions on the Stiefel manifold

The main purpose of this paper is to investigate high dimensional limiting behaviors, as m becomes infinite (m → ∞), of matrix statistics on the Stiefel manifold V_{k, m}, which consists of m × k (m ≥ k) matrices X such that X′X = I_k. The results extend those of Watson. Let X be a random matrix on V_{k, m}. We present a matrix decomposition of X as the sum of mutually orthogonal singular value decompositions of the projections P X and P X, where and are each a subspace of R^m of dimension p and their orthogonal compliment, respectively (p ≥ k and m ≥ k + p). Based on this decomposition of X, the invariant measure on V_{k, m} is expressed as the product of the measures on the component subspaces. Some distributions related to these decompositions are obtained for some population distributions on V_{k, m}. We show the limiting normalities, as m → ∞, of some matrix statistics derived from the uniform distribution and the distributions having densities of the general forms f(P X) and f(m^1/2P X) on V_{k, m}. Subsequently, applications of these high dimensional limit theorems are considered in some testing problems.     

Normal forms for real quadratic forms

We investigate the non-diagonal normal forms of a quadratic form on , in particular for n = 3. For this case it is shown that the set of normal forms is the closure of a 5-dimensional submanifold in the 6-dimensional Grassmannian of 2-dimensional subspaces of . Received: 27 June 2008     

Optical and piezoelectric anomalies of ordered (Sc,Ga) N and (Sc,In) N ternaries

Theoretical results are presented regarding the incorporation of Scandium into wurtzite GaN and InN binaries. The electric, optical and piezoelectric properties of the resulting ScGaN and ScInN systems are reported by using first-principles Local-density approximation (LDA) within density functional theory (DFT), Berry phase approach within modern theory of polarization and phonon calculations within the density functional perturbation theory. Our results predict the existence of breaking-symmetry structural phase transition in ordered Sc_0.5Ga_0.5N and Sc_0.5In_0.5N alloys when subjected to a compressive or tensile strain. Moreover, our results demonstrate the existence of symmetry preserving pressure-induced isostructural phase transitions in ordered ScGaN and ScInN systems for different Sc concentrations. It has been shown that the existence of isostructural phase transitions leads to dramatic changes in optical, acoustic, and piezoelectric properties of ordered ScGaN and ScInN systems under high pressure. In particular, this study demonstrates that the existence of first-order isostructural phase transitions in Sc₁Ga₁N₂ at a critical hydrostatic pressure of 12.3 GPa leads to a huge enhancement of piezoelectricity (i.e., the e ₃₃ piezoelectric coefficient adopts a huge value as large as 13 C/m²). In addition, It has been shown that ordered Sc_0.5Ga_0.5N and Sc_0.5In_0.5N alloys exhibit tremendous piezoelectric response, associated with a breaking-symmetry phase transition from nonpolar P6₃/mcc(D_6h) space group to a polar P6₃ mc(C_6v) structure, at fixed Ga, In and Sc compositions, as a function of the in-plane compressive and tensile strains. We also reveal the reason behind, and consequences of, these unusual properties associated with the strain-induced and pressure-induced structural phase transitions in the novel ScGaN and ScInN ordered structures.     

Extremal solutions for the first order impulsive functional differential equations with upper and lower solutions in reversed order

This paper studies the existence of solutions of first order impulsive functional differential equations with lower and upper solutions in the reversed order, obtains the sufficient conditions for the existence of solutions by establishing a new comparison principle and using the monotone iterative technique. A concrete example is presented and solved to illustrate the obtained results.