We review our work on the relation between integrability and infinite-dimensional algebras. We first consider the question of what sets of commuting charges can be constructed from the current of a U(1) Kac-Moody algebra. It emerges that there exists a set S n of such charges for each positive integer n > 1; the corresponding value of the central charge in the Feigin-Fuchs realization of the st...

We present a generic method for establishing interpolation properties by ‘borrowing’ across logical systems. The framework used is that of the so-caled ‘institution theory’ which is a categorical abstract model theory providing a formal definition for the informal concept of ‘logical system’ and a mathematical concept of ‘homomorphism’ between logical systems. We develop three different styles ...

We analyze a primal-dual interior-point method for nonlinear programming. We prove the global convergence for a wide class of problems under the standard assumptions on the problem.

We consider primal-dual IP methods where the linear system arising at each iteration is formulated in the reduced (augmented) form and solved approximately. Focusing on the iterates close to a solution, we analyze the accuracy of the so-called inexact step, i.e., the step that solves the unreduced system, when combining the effects of both different levels of accuracy in the inexact computation...

Many recent convergence results obtained for primal-dual interior-point methods for nonlinear programming, use assumptions of the boundedness of generated iterates. In this paper we replace such assumptions by new assumptions on the NLP problem, develop a modification of a primal-dual interior-point method implemented in software package loqo and analyze convergence of the new method from any i...

We obtain a characterization in terms of dynamical systems of those r-discrete groupoids for which the groupoid C∗algebra is approximately finite-dimensional (AF). These ideas are then used to compute the K-theory for AF algebras by utilizing the actions of these partial homeomorphisms, and these K-theoretic calculations are applied to some specific examples of AF algebras. Finally, we show tha...

In this paper we present a complete quantifier-free axiomatization of several logics on region-based theory of space based on contact relation and connectedness predicates. We prove completeness theorems for the logics in question with respect to three different semantics: algebraic – with respect to several important classes of contact algebras, topological – based on the contact algebras over...

This paper gives a comprehensive analysis of algebras of Colombeau-type generalized functions in the range between the diffeomorphism-invariant quotient algebra G = EM/N introduced in part I and Colombeau’s original algebra G . Three main results are established: First, a simple criterion describing membership in N (applicable to all types of Colombeau algebras) is given. Second, two counterexa...

In the early stages of a large-scale housing project, many interior design alternatives remain to be confirmed after a rough review of the costs. The project participants move on to the later stages of budgeting and construction without the exact information on the interior costs, and several occasions may arise when costs increase or time delays occur, driven by interior design specification c...