As an extension of the Leray-Schauder degree, we introduce a topological degree theory for a class of demicontinuous operators of generalized (S+) type in real reflexive Banach spaces, based on the recent Berkovits degree. Using the degree theory, we show that the Borsuk theorem holds true for this class. Moreover, we study the Dirichlet boundary value problem involving the p-Laplacian by way o...

Storage operators have been introduced by J. L. Krivine in [5] they are closed x-terms which, for a data type, allow one to simulate a "call by value" while using the "call by name" strategy. In this paper, we introduce the directed ;,-calculus and show that it has the usual properties of the ordinary ;,-calculus. With this calculus we get an equivalent-and simple-definition of the storage oper...

We study the center of two-parameter quantum supergroup $U_{r,s}(osp(1,2))$ using Dickson polynomial. show that Scasimir operator is completely determined by $q$-deformed Chebychev polynomial, generalizing an earlier work Arnaudon and Bauer.

The method of Λ-operators developed by S. Derkachov, G. Korchemsky, A. Ma-nashov is applied to a derivation of eigenfunctions for the open Toda chain. The Sklyanin measure is reproduced using diagram technique developed for these Λ-operators. The properties of the Λ-operators are studied. This approach to the open Toda chain eigenfunctions reproduces Gauss-Givental representation for these eige...

A semiclassical string description is given for correlators of Wilson loops with local operators in N = 4 SYM theory in the regime when operators carry parametrically large R-charge. The OPE coefficients of the circular Wilson loop in chiral primary operators are computed to all orders in the α ′ expansion in AdS 5 × S 5 string theory. The results agree with field-theory predictions.