The new integrable systems associated to the space of elliptic branched coverings are constructed. The relationship of these systems with elliptic Schlesinger's system Takasaki [1] is described. For the standard twofold elliptic coverings the integrable system is written explicitly. The trigonometric degeneration of our construction is presented.

A number of families of elliptic-type integrals have been studied recently due to their importance and potential for applications in some problems of radiation physics. The object of this work is to present a unified and generalized form of such elliptic-type integrals and to study its properties, including recurrence formulas and asymptotic expansion.

Elliptic curves play a natural and important role in elliptic cohomology. In earlier work with I. Kriz, these elliptic curves were interpreted physically in two ways: as corresponding to the intersection of M2 and M5 in the context of (the reduction of M-theory to) type IIA and as the elliptic fiber leading to F-theory for type IIB. In this paper we elaborate on the physical setting for various...

This study in centered on models accounting for stochastic deformations of sample paths of random walks, embedded either in Z or in Z. These models are immersed in multi-type particle systems with exclusion. Starting from examples, we give necessary and sufficient conditions for the underlying Markov processes to be reversible, in which case their invariant measure has a Gibbs form. Letting the...

In this article, we study the existence of positive solutions for the quasilinear elliptic system −∆pu = f(x, u, v) x ∈ Ω, −∆pv = g(x, u, v) x ∈ Ω, u = v = 0 x ∈ ∂Ω. Using degree theoretic arguments based on the degree map for operators of type (S)+, under suitable assumptions on the nonlinearities, we prove the existence of positive weak solutions.

and Applied Analysis 3 where F x, t ∫ t 0 f x, s ds; one positive solutions for 1.7 was obtained. It is well known that condition AR plays an important role for showing the boundedness of Palais-Smale sequences. More recently, Corrêa and Nascimento in 13 studied a nonlocal elliptic system of p-Kirchhoff type

In this paper we find explicit lower bounds for Dirichlet eigenvalues of a weighted quasilinear elliptic system of resonant type in terms of the eigenvalues of a single p-Laplace equation. Also we obtain asymptotic bounds by studying the spectral counting function which is defined as the number of eigenvalues smaller than a given value.

Chosen-message attack on RSA is usually considered as an inherent property of its homomorphic structure. In this paper, we show that nonhomomorphic RSA-type cryptosystems are also susceptible to a chosen-message attack. In particular, we prove that only one message is needed to mount a successful chosen-message attack against the Lucas-based systems and Demytko’s elliptic curve system.

We consider a multigrid method for solving the discretized optimality system of a PDE-constrained optimization problem. In particular, we discuss the construction of an additive Schwarz-type smoother for a class of elliptic optimal control problems. A rigorous multigrid convergence analysis yields level-independent convergence rates. Numerical experiments indicate that the convergence rates are...

Since A. Ambrosetti and P.H. Rabinowitz proposed the mountain pass theorem in 1973 (see [1]), critical point theory has become one of the main tools for finding solutions to elliptic problems of variational type. Especially, elliptic problem (1.2) has been intensively studied for many years. One of the very important hypotheses usually imposed on the nonlinearities is the following Ambrosetti-R...