Explicit inverse of a tridiagonal k−Toeplitz matrix

Summary We obtain explicit formulas for the entries of the inverse of a nonsingular and irreducible tridiagonal k–Toeplitz matrix A. The proof is based on results from the theory of orthogonal polynomials and it is shown that the entries of the inverse of such a matrix are given in terms of Chebyshev polynomials of the second kind. We also compute the characteristic polynomial of A which enables us to state some conditions for the existence of A^–1. Our results also extend known results for the case when the residue mod k of the order of A is equal to 0 or k–1 (Numer. Math., 10 (1967), pp. 153–161.).The work was supported by CMUC (Centro de Matemática da Universidade de Coimbra) and by Acção Integrada Luso-Espanhola E-6/03     

U-Closure Operators and Compactness

A notion of compactness with respect to a previously introduced notion of functor induced closure operator is presented and analyzed. Even though this new notion shows very similar properties to compactness with respect to the classical notion of categorical closure operator, in general the two concepts are different. Examples are provided.     

A quaternion QR algorithm

Summary This paper extends the Francis QR algorithm to quaternion and antiquaternion matrices. It calculates a quaternion version of the Schur decomposition using quaternion unitary similarity transformations. Following a finite step reduction to a Hessenberg-like condensed form, a sequence of implicit QR steps reduces the matrix to triangular form. Eigenvalues may be read off the diagonal. Eigenvectors may be obtained from simple back substitutions. For serial computation, the algorithm uses only half the work and storage of the unstructured Francis QR iteration. By preserving quaternion structure, the algorithm calculates the eigenvalues of a nearby quaternion matrix despite rounding errors.     

On symmetries and conservation laws of the equations of shallow water with an axisymmetric profile of bottom

The local symmetries and conservation laws are calculated for the equations of shallow water with an axisymmetric profile of bottom under the assumption that the corresponding generating functions may depend only on all variables and their derivatives up to the second order. It is shown that if the bottom has the form of a paraboloid of revolution, then there are many symmetries and conservation laws generalizing those for the case of plane bottom.     

Finite L 2-gain with nondifferentiable storage functions

We consider affine control systems with the finite L₂-gain property in the case the storage function is nondifferentiable. We generalize some classical results concerning the connection of the finite L₂-gain property with the stability properties of the unforced system, the characterization of finite L₂-gain by means of partial differential inequalities of the Hamilton-Jacobi type and the problem of giving to a system the finite L₂-gain property by means of a feedback law. Moreover, we introduce and study the apparently new notion of exact storage function.     

Cauchy problem of the generalized double dispersion equation

In this paper, the existence and the uniqueness of the global solution for the Cauchy problem of the generalized double dispersion equation are proved. The blow-up of the solution for the Cauchy problem of the generalized double dispersion equation is discussed by the concavity method under some conditions.     

Interior estimates for solutions of a fourth order nonlinear partial differential equation

Let be a locally strongly convex hypersurface, given by the graph of a convex function xn+1=f(x₁,…,xn) defined in a convex domain Ω⊂Rn. M is called a α-extremal hypersurface, if f is a solution of

     

硫含量对GCr15轴承钢摩擦学性能影响的试验研究

冶炼了3炉不同硫含量的GCr15轴承钢,采用MM-200、MPX-200和Falex摩擦磨损试验机对其进行了不同条件下的摩擦磨损试验,研究了硫含量对GCr15轴承钢摩擦学性能的影响规律。结果表明,随着硫含量的增加,GCr15轴承钢的摩擦系数降低,耐磨性能和抗咬合性能提高。作者根据金相分析、电子探针线扫描和电解分离法的测试结果指出,硫在GCr15轴承钢中主要是以化合态的形式存在,并对其作用机理进行了初步探讨。     

Lipoxygenase inhibitory activity of Cuspidaria pulchra and isolated compounds

This work evaluated the in vitro inhibitory activity of the crude ethanolic extract from the aerial parts of Cuspidaria pulchra (Cham.) L.G. Lohmann against 15-lipoxygenase (15-LOX). The bioassay-guided fractionation of the n-butanol fraction, which displayed the highest activity, led to the isolation of three compounds: caffeoylcalleryanin (1), verbascoside (2) and 6-hydroxyluteolin-7-O-β-glucoside (3). Assessment of the ability of the isolated compounds to inhibit 15-LOX revealed that compounds 1, 2 and 3 exerted strong 15-LOX inhibitory activity; IC₅₀ values were 1.59, 1.76 and 2.35 μM respectively. The XTT assay showed that none of the isolated compounds seemed to be significantly toxic.     

Fast determination of Ziziphora tenuior L. essential oil by inorganic–organic hybrid material based on ZnO nanoparticles anchored to a composite made from polythiophene and hexagonally ordered silica

In this paper, for the first time, an inorganic–organic hybrid material based on ZnO nanoparticles was anchored to a composite made from polythiophene and hexagonally ordered silica (ZnO/PT/SBA-15) for use in solid-phase fibre microextraction (SPME) of medicinal plants. A homemade SPME apparatus was used for the extraction of volatile components of Ziziphora tenuior L. A simplex method was used for optimisation of five different parameters affecting the efficiency of the extraction. The main constituents extracted by ZnO/PT/SBA-15 and PDMS fibres and hydrodistillation (HD) methods, respectively, included pulegone (51.25%, 53.64% and 56.68%), limonene (6.73%, 6.58% and 8.3%), caryophyllene oxide (5.33%, 4.31% and 4.53%) and 1,8-cineole (4.21%, 3.31% and 3.18%). In comparison with the HD method, the proposed technique could equally monitor almost all the components of the sample, in an easier way, in a shorter time and requiring a much lower amount of the sample.