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OSCILLATORY BEHAVIOUR OF A CLASS OF NONLINEAR DIFFERENTIAL EQUATIONS OF THIRD ORDER

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Acta Mathematica Scientia 2001年第2期21卷 182-188页

作者： A. Tiryaki department of mathematics, gazi university faculty of arts and sciences Teknik Okullar, 06500 ankara, turkey S. (Yaman) Pasinlio■u department of mathematics, Hacettepe university, 06532 Beytepe, ankara, turkey department of mathematics Gazi University Faculty of Arts and Sciences Teknik Okullar 06500 Ankara Turkey department of mathematics Hacettepe University 06532 Beytepe Ankara Turkey

This paper investigates the oscillatory and nonoscillatory behaviour of solu- tions of a class of third order nonlinear differential equations. Results extend and improve some known results in the literature.

关键词： Oscillatory solution nonoscillatory solution behaviour of solution nonlinear differential equation

Bonnet Ruled Surfaces

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Acta Mathematica Sinica,English Series 2005年第3期21卷 623-630页

作者： Filiz KANBAY department of mathematics faculty of arts and science Yildiz Technical university 34210 Esenler/ turkey department of mathematics Faculty of Arts and Science Yıldız Technical University Esenler/İstanbul Turkey

We consider the Bonnet ruled surfaces which admit only one non-trivial isometry that preserves the principal curvatures. We determine the Bonnet ruled surfaces whose generators and orthogonal trajectories form a speci... 详细信息

关键词： Bonnet surface Associate surface Isometry Ruled surface A-net Principal curvature

ASYMPTOTIC BEHAVIOUR OF EIGENVALUES FOR THE DISCONTINUOUS BOUNDARY-VALUE PROBLEM WITH FUNCTIONAL-TRANSMISSION CONDITIONS

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Acta Mathematica Scientia 2002年第3期22卷 335-345页

作者： O.Sh.Mukhtarov department of mathematics, science and arts faculty, gaziosmanpasa university, Tokat, turkeyMustafa Kandemir department of mathematics, faculty of A mas y a Education, Ondokuz Mayis university, Amasya, turkey department of mathematics Science and Arts Faculty Gaziosmanpasa University Tokat Turkey department of mathematics Faculty of Amasya Education Ondokuz Mayis University Amasya Turkey

In this study, the boundary-value problem with eigenvalue parameter generated by the differential equation with discontinuous coefficients and boundary conditions which contains not only endpoints of the considered interval, but also point of discontinuity and linear functionals is investigated. So, the problem is not pure boundary-value. The authors single out a class of linear functionals and find simple algebraic conditions on coefficients, which garantee the existence of infinit number eigenvalues. Also the asymptotic formulas for eigenvalues are found.

关键词： Asymptotic behaviour of eigenvalues boundary-value problems functional-conditions discontinuous coefficients

ALGORITHMS FOR IMPLEMENTATION OF GENERAL LIMIT REPRESENTATIONS OF GENERALIZED INVERSES

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Journal of Computational mathematics 2001年第6期19卷 561-570页

作者： Predarg S. Stanimirovic (university of Nis, faculty of science, department of mathematics, Cirila i Metodija 2, 18000 Nis, Yugoslavia ) university of Nis 南斯拉夫

Investigates three various algorithms for computation and implementation of general limit representations of generalized inverses. Introduction and preliminaries; Details of the generalized imbedding method; Limit rep... 详细信息

关键词： Generalized inverses Limit representation Finite algorithm Imbedding method.

LOCAL AND GLOBAL EXPOSED POINTS

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Acta Mathematica Scientia 1995年第3期15卷 335-341页

作者： M.Beltagy(mathematics department,faculty of science Tanta university,Egypt.) mathematics department Faculty of Science Tanta University Egypt

In this paper we derive sufficient conditions for strict convexity of subsets in a complete simply connected smooth Riemanian manifold without focal points in terms of local and global exposed points.

关键词： exposed points strict convexity focal points.

On triangular algebras with noncommutative diagonals

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science China mathematics 2008年第10期51卷 1937-1944页

作者： DONG AiJu department of mathematics, Xi’an university of arts and science, Xi’an 710065, China department of mathematics Xi’an University of Arts and Science Xi’an China

We construct a triangular algebra whose diagonals form a noncommutative algebra and its lattice of invariant projections contains only two nontrivial projections. Moreover we prove that our triangular algebra is maximal.

关键词： triangular algebra von Neumann algebra reflexive algebra reflexive lattice 47L75 46L10

Mode-I crack in a two-dimensional fibre-reinforced generalized thermoelastic problem

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Chinese Physics B 2012年第1期21卷 244-253页

作者： Kh.Lotfy department of mathematics Faculty of ScienceZagazig UniversityZagazig P.O.Box 44519Egypt department of mathematics Faculty of Science and ArtsAl-mithnabQassim UniversityP.O.Box 931Buridah 51931Al-mithnabKingdom of Saudi Arabia

A general model of the equations of the Lord-Sulman theory including one relaxation time and the Green-Lindsay theory with two relaxation times, as well as the classical dynamical coupled theory, are applied to the study of the influence of reinforcement on the total deformation for an infinite space weakened by a finite linear opening mode- I crack. We study the influence of reinforcement on the total deformation of rotating thermoelastic half-space and their interaction with each other. The material is homogeneous isotropic elastic half space. The crack is subjected to prescribed temperature and stress distributions. The normal mode analysis is used to obtain the exact expressions for displacement components, force stresses, and temperature. The variations of the considered variables with the horizontal distance are illustrated graphically. Comparisons are made with the results obtained in the three theories with and without rotation. A comparison is also made between the two theories for different depths.

关键词： mode-I crack Lord -Sulman theory thermoelasticity normal mode analysis.

On the generalized Busemann-Petty problem

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science China mathematics 2007年第8期50卷 1103-1116页

作者： Song-jun L~(1,2+) Gang-song LENG~1 1.College of mathematics and Computer science,Chongqing Normal university,Chongqin 400047,China 2.department of mathematics,Shanghai university,Shanghai 200444,China College of mathematics and Computer science Chongqing Normal University Chongqin China department of mathematics Shanghai University Shanghai China

The generalized Busemann-Petty problem asks whether the origin-symmetric convex bodies in ? n with a larger volume of all i-dimensional sections necessarily have a larger volume. As proved by Bourgain and Zhang, the answer to this question is negative if i > 3. The problem is still open for i = 2, 3. In this article we prove two specific affirmative answers to the generalized Busemann-Petty problem if the body with a smaller i-dimensional volume belongs to given classes. Our results generalize Zhang’s specific affirmative answer to the generalized Busemann-Petty problem.

关键词： star body cross i-section dual mixed volume Radon transform 52A30 52A40

EXISTENCE AND NONEXISTENCE OF GLOBAL POSITIVE SOLUTIONS FOR DEGENERATE PARABOLIC EQUATIONS IN EXTERIOR DOMAINS

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Acta Mathematica Scientia 2010年第3期30卷 713-725页

作者：曾宪忠刘振海 department of mathematics and Computational science Hunan University of Science and Technology department of mathematics Central South University

This article deals with the degenerate parabolic equations in exterior domains and with inhomogeneous Dirichlet boundary conditions. We obtain that pc = （σ ＋ m ）n / （ n-σ- 2 ） is its critical exponent provided max{-1, [ （1- m ）n- 2] / （ n ＋ l ） } 〈 σ 〈 n- 2. This critical exponent is not the same as that for the corresponding equations with the boundary value 0, but is more closely tied to the critical exponent of the elliptic type degenerate equations. Futhermore, we demonstrate that if max（1, σ ＋ m）〈 p 〈 pc, then every positive solution of the equations blows up in finite time; whereas for p 〉 pc, the equations admit global positive solutions for some boundary values and initial data. Meantime, we also demonstrate that its positive solutions blow up in finite time provided n〈σ＋2.

关键词： Degenerate parabolic equations exterior domains -inhomogeneous dirichlet boundary conditions critical exponent blow-up global existence