Revised proof of a theorem concerning an involution with local Engel or power commuting condition

This paper is a correction paper concerned with an important theorem about an involution with Engel condition.     

Binary Lie algebras satisfying the third Engel condition

Let Φ be a unital associative commutative ring with 1/2. The local nilpotency is proved of binary Lie Φ-algebras satisfying the third Engel condition. Moreover, it is proved that this class of algebras does not contain semiprime algebras.     

How to generate local refinements of unstructured tetrahedral meshes satisfying a regularity ball condition

A simple algorithm that generates local refinements of tetrahedral meshes is proposed. Refinements are made by tetrahedra, which are subdivided into eight, four, three, or two smaller tetrahedra. We prove that a regularity ball condition is satisfied for the refined mesh. This guarantees that tetrahedra do not become flat when the mesh size tends to zero. © 1997 John Wiley & Sons, Inc.     

Note on a sufficient condition for a local minimum of a class of nonconvex quadratic programs

A counterexample is given to show that a previously proposed sufficient condition for a local minimum of a class of nonconvex quadratic programs is not correct. This class of problems arises in combinatorial optimization. The problem with the original proof is pointed out. © 1998 The Mathematical Programming Society, Inc. Published by Elsevier Science B.V.     

On the local convergence of a deformed Newton's method under Argyros-type condition

For the iteration which was independently proposed by King [R.F. King, Tangent method for nonlinear equations, Numer. Math. 18 (1972) 298-304] and Werner [W. Werner, Über ein Verfarhren der Ordnung zur Nullstellenbestimmung, Numer. Math. 32 (1979) 333-342] for solving a nonlinear operator equation in Banach space, we established a local convergence theorem under the condition which was introduced recently by Argyros [I.K. Argyros, A unifying local-semilocal convergence analysis and application for two-point Newton-like methods in Banach space, J. Math. Anal. Appl. 298 (2004) 374-397].     

Necessary and sufficient condition for local minima of a class of nonconvex quadratic programs

The author (1992, 1993) earlier studied the equivalence of a class of 0–1 quadratic programs and their relaxed problems. Thus, a class of combinatorial optimization problems can be solved by solving a class of nonconvex quadratic programs. In this paper, a necessary and sufficient condition for local minima of this class of nonconvex quadratic programs is given; this will be the foundation for study of algorithms.Research supported by Huo Yingdong Educational Foundation '93.     

The Nevai condition and a local law of large numbers for orthogonal polynomial ensembles

We consider asymptotics of orthogonal polynomial ensembles, in the macroscopic and mesoscopic scales. We prove both global and local laws of large numbers under fairly weak conditions on the underlying measure μ. Our main tools are a general concentration inequality for determinantal point processes with a kernel that is a self-adjoint projection, and a strengthening of the Nevai condition from the theory of orthogonal polynomials.     

Notes on a new chain condition for prime ideals

A chain condition intermediate to the catenary property and the chain condition for prime ideals (c.c.) is studied. Like the c.c., the condition is inherited from a semi-local domain R by integral extension domains, by local quotient domains, and by factor domains, and a semi-local ring that satisfies the condition is catenary. (Unlike the c.c., none of these statements is true when R is not semi-local.) A number of characterizations of a semi-local domain that satisfies the condition are given in terms of: integral (respectively, algebraic, transcendental) extension domains, Henselizations, completions, Rees rings, associated graded rings and certain discrete valuation over-rings. Then four of the catenary chain conjectures are characterized in terms of this condition.