The notion of central path plays a fundamental role in the development of interior point methods which, in turn, have become important tools for solving various optimization problems. The central path equation is algebraic in nature and is derived from the KKT optimality conditions of a certain logarithmic barrier problem; meanwhile, the primal variable portion of the very same central path can...

Suppose that K is a closed, total cone in a real Banach space X, that A :X!X is a bounded linear operator which maps K into itself, and that A« denotes the Banach space adjoint of A. Assume that r, the spectral radius of A, is positive, and that there exist x ! 1 0 and m& 1 with Am(x ! ) ̄ rmx ! (or, more generally, that there exist x ! a (®K ) and m& 1 with Am(x ! )& rmx ! ). If, in addition, A...

In this paper we present a new algorithm for solving linear programs that requires only Õ( √ rank(A)L) iterations where A is the constraint matrix of a linear program with m constraints and n variables and L is the bit complexity of a linear program. Each iteration of our method consists of solving Õ(1) linear systems and additional nearly linear time computation. Our method improves upon the p...

We show the existence of a unital subalgebra Pn of the symmetric group algebra linearly spanned by sums of permutations with a common peak set, which we call the peak algebra. We show that Pn is the image of the descent algebra of type B under the map to the descent algebra of type A which forgets the signs, and also the image of the descent algebra of type D. The algebra Pn contains a two-side...

We compute the essential norm of a composition operator relatively to the class of Dunford-Pettis opertors or weakly compact operators, on some uniform algebras of analytic functions. Even in the frame of H∞ (resp. the disk algebra), this is new, as well for the polydisk algebras and the polyball algebras. This is a consequence of a general study of weighted composition operators.

In this paper the idea of -locally closed sets in generalized topological space is introduced and study some of their properties. We introduce the notion of (,’)locally closed continuous functions on generalized topological space and investigate some of their characterizations.

The paper considers the role of quantale algebra nuclei in representation of quotients of quantale algebras, and in factorization of quantale algebra homomorphisms. The set of all nuclei on a given quantale algebra is endowed with the structure of quantale semi-algebra.

In this paper, we first discuss the structure of the Ramond N = 2 superconformal algebras. Then we classify the modules of the intermediate series over Ramond N = 2 superconformal algebra.

We investigate the lattice Λ(Df2) of all subvarieties of the variety Df2 of two-dimensional diagonal-free cylindric algebras. We prove that a Df2algebra is finitely representable iff it is finitely approximable, characterize finite projective Df2-algebras, and show that there are no non-trivial injectives and absolute retracts in Df2. We prove that every proper subvariety of Df2 is locally fini...

We describe the role of algebraic extensions in the theory of commutative, unital normed algebras, with special attention to uniform algebras. We shall also compare these constructions and show how they are related to each other. [MSC: 46J05, 46J10]