Solid-Phase Organic Synthesis of Methyl Isoxazole-5-carboxylates Based on Wang Resin–Bound 1-Phenylselenoacrylate

A novel Wang resin–bound 1-phenylselenoacrylate reagent has been developed and used as dipolarophile for the 1,3-dipolar cycloaddition with nitrile oxides to the regioselective synthesis of methyl 3-substituted isoxazole-5-carboxylates in good yields and purities.     

Classes of general H-matrices

Let M(A) denote the comparison matrix of a square H-matrix A, that is, M(A) is an M-matrix. H-matrices such that their comparison matrices are nonsingular are well studied in the literature. In this paper, we study characterizations of H-matrices with either singular or nonsingular comparison matrices. The spectral radius of the Jacobi matrix of M(A) and the generalized diagonal dominance property are used in the characterizations. Finally, a classification of the set of general H-matrices is obtained.     

An intrinsic approach to Lichnerowicz conjecture

In this paper we give a proof of Lichnerowicz conjecture for compact simply connected manifolds which is intrinsic in the sense that it avoids thenice embeddings into eigenspaces of the Laplacian. Even if one wants to use these embeddings, this paper gives a more streamlined proof. As a byproduct, we get a simple criterion for a polynomial to be a Jacobi polynomial.     

New Exact Solutions of the N-Coupled Nonlinear Schroedinger System

In this letter, abundant families of Jacobi elliptic function envelope solutions of the N-coupled nonlinear Schroedinger （NLS） system are obtained directly. When the modulus m → 1, those periodic solutions degenerate as the corresponding envelope soliton solutions, envelope shock wave solutions. Especially, for the 3-coupled NLS system, five types of Jacobi elliptic function envelope solutions are illustrated both analytically and graphically. Two types of those degenerate as envelope soliton solutions.     

A new class of three-variable orthogonal polynomials and their recurrences relations

A new class of three-variable orthogonai polynomials,defined as eigenfunctions of a second order PDE operator,is studied.These polynomials are orthogonal over a curved tetrahedron region, which can be seen as a mapping from a traditional tetrahedron,and can be taken as an extension of the 2-D Steiner domain.The polynomials can be viewed as Jacobi polynomials on such a domain.Three- term relations are derived explicitly.The number of the individual terms,involved in the recurrences relations,are shown to be independent on the total degree of the polynomials.The numbers now are determined to be five and seven,with respect to two conjugate variables z,(?) and a real variable r, respectively.Three examples are discussed in details,which can be regarded as the analogues of the Chebyshev polynomials of the first and the second kinds,and Legendre polynomials.     

A certain Dirichlet series of Rankin-Selberg type associated with the Ikeda lifting

We consider a certain Dirichlet series of Rankin-Selberg type associated with two Siegel cusp forms of the same integral weight with respect to Spn(Z). In particular, we give an explicit formula for the Dirichlet series associated with the Ikeda lifting of cuspidal Hecke eigenforms with respect to SL₂(Z). We also comment on a contribution to the Ikeda's conjecture on the period of the lifting.     

Two novel methods for vibration diagnosis to characterize non-linear response

Poincaré maps have been proved to be a valuable tool in the analysis of non-linear dynamical systems, which usually reduce a continuous phase flow into a two-dimensional discrete map. However, they may be inconvenient for reflecting some characteristics of the system response. In this paper, two novel methods, using the period sampling peak-to-peak value (PSP) diagram and the modified Poincaré map, are presented for characterizing different types of non-linear response. These two methods take advantage of some parameters of the response, such as the peak-to-peak value within an exterior excitation period and the mean value of the displacement. In the PSP diagram method, a two-dimensional graph is plotted by taking the peak-to-peak value as ordinate and the sequential periodically sampling number as abscissa. On the other hand, the modified Poincaré map takes the mean value of the velocity within an exterior excitation period as ordinate and the relevant mean value of the displacement as abscissa. The non-linear responses of a Duffing system, a pendulum with circular motion support and an oscillating circuit are studied by these methods. We also studied the intermittent chaos of the Lorenz system by the PSP diagram method. The PSP diagram is a set of mapping points, which form: a straight line for a one-period response; multi-straight lines for a multi-period response; orderly periodic curves for a quasi-period response; long lines interrupted by transitoriness confusion points for intermittent chaos; and totally out-of-order points for chaos. The figures for the modified Poincaré maps for the period, multi-period, quasi-period responses and chaos are almost identical to those for the Poincaré maps, but the modified maps take more sampling points and can reflect the mean values of the responses. Some numerical results are given based on these methods to show their efficiency in distinguishing different non-linear responses.     

Eigenvalue bounds in the gaps of Schrödinger operators and Jacobi matrices

We consider C=A+B where A is selfadjoint with a gap (a,b) in its spectrum and B is (relatively) compact. We prove a general result allowing B of indefinite sign and apply it to obtain a (δV)^d/2 bound for perturbations of suitable periodic Schrödinger operators and a (not quite) Lieb–Thirring bound for perturbations of algebro-geometric almost periodic Jacobi matrices.     

求条件极值的一种新方法

利用线性代数的理论方法，对多元函数求条件极值的拉格朗日乘数法加以改进，建立了求条件极值的一种新方法     

广义Jacobi矩阵的逆特征问题

本文主要讨论广义Jacobi阵及多个特征对的广义Jacobi阵逆特征问题.通过相似变换将广义Jacobi阵变换为三对角对称矩阵,其特征不变、特征向量只作线性变换,再应用前人理论求得广义Jacobi阵元素ai,|bi|,|ci|有唯一解的充要条件及其具体表达式.