Equilibrium Problems with Applications to Eigenvalue Problems

In this paper, we consider equilibrium problems and introduce the concept of (S)₊ condition for bifunctions. Existence results for equilibrium problems with the (S)₊ condition are derived. As special cases, we obtain several existence results for the generalized nonlinear variational inequality studied by Ding and Tarafdar (Ref. 1) and the generalized variational inequality studied by Cubiotti and Yao (Ref. 2). Finally, applications to a class of eigenvalue problems are given.     

Existence of Solutions and Algorithms for Bilevel Vector Equilibrium Problems: An Auxiliary Principle Technique

The main goal of this paper is to introduce and study bilevel vector equilibrium problems. We first establish some existence results for solutions of vector equilibrium problems and mixed vector equilibrium problems. We study the existence of solutions of bilevel vector equilibrium problems by considering a vector Thikhonov-type regularization procedure. By using this regularization procedure and existence results for mixed vector equilibrium problems, we establish some existence results for solutions of bilevel vector equilibrium problems. By using the auxiliary principle, we propose an algorithm for finding the approximate solutions of bilevel vector equilibrium problems. The strong convergence of the proposed algorithm is also studied.     

Existence results for equilibrium problems with applications to evolution equations

In this paper, we consider evolution equations with time-dependent pseudomonotone and quasimonotone operators by a new approach based on equilibrium problems theory. We establish new existence results for equilibrium problems associated to pseudomonotone and quasimonotone bifunctions in the topological sense. The results obtained are then applied to derive existence of solutions for evolution equations. The approach is new and leads to improve and unify most of the results obtained in this direction.     

On Generalized Vector Equilibrium Problems

In this paper we prove the existence of solutions of the generalized vector equilibrium problem in the setting of Hausdorff topological vector spaces. As applications, we present some relevant particular cases: a generalized vector variational-like inequality in Hausdorff topological vector spaces, and equilibrium problem in the case of pseudomonotone real functions, and a generalized weak Pareto optima problem.     

Generalized Vector Equilibrium Problems with Trifunctions

In this paper, we study the existence of strong and weak solutions of the generalized vector equilibrium problems for trifunctions. Two special classes of vector-valued trifunctions are introdcued, called the classes of (SPM) and (GPM), respectively. Some existence results for strong solutions associated to functions of these classes are given.     

Regularized Equilibrium Problems with Application to Noncoercive Hemivariational Inequalities

In this paper, we are concerned with noncoercive equilibrium problems associated with a bifunction which does not satisfy necessarily an algebraic monotonicity assumption. Our tool is a regularization procedure which we develop for equilibrium problems. The abstract existence result established is then applied to the solution of noncoercive hemivariational inequalities.     

Synthesis of the seco-Limonoid BCD Ring System Identifies a Hsp90 Chaperon Machinery (p23) Inhibitor

D-Ring-seco-limonoids (tetranortriterpenoids), such as gedunin and xylogranin B display anti-cancer activity, acting via inhibition of Hsp90 and/or associated chaperon machinery (e.g., p23). Despite this, these natural products have received relatively little attention, both in terms of an enabling synthetic approach (which would allow access to derivatives), and as a consequence their structure–activity relationship (SAR). Disclosed herein is a generally applicable synthetic route to the BCD ring system of the seco-D-ring double bond containing limonoids. Furthermore, cell based assays revealed the first skeletal fragment that exhibited inhibition of the p23 enzyme at a level which was equipotent to that of gedunin, despite being much less structurally complex.     

Magnons coherent transmission and heat transport at ultrathin insulating ferromagnetic nanojunctions

A model calculation is presented for the magnons coherent transmission and corresponding heat transport at insulating magnetic nanojunctions. The system consists of a ferromagnetically ordered ultrathin insulating junction between two semi-infinite ferromagnetically ordered leads with ideally flat crystal interfaces. The ground state of the system is depicted by an exchange Hamiltonian neglecting smaller dipolar and anisotropy terms. The spin dynamics are analyzed using the equations of motion for the spin precession displacements, valid in the limit of low temperatures compared to an order-disorder transition temperature characteristic of the system. The coherent transmission and reflection spectra at the nanojunction boundary are calculated in the Landauer-Buttiker formalism using the matching theory, for all the magnons in the lead bulk, at arbitrary angles of incidence on the boundary, and for variable temperatures. The model calculations yield the thermal conductivity κ _m due to the magnons coherent transmission between the two leads maintained at slightly different temperatures. The model is general, and is applied in particular to the Fe/Gd/Fe system to calculate the coherent transmission of magnons and their thermal conductivity at the junction boundary, for different thicknesses of the Gd junction and its corresponding magnetic order. The calculated results elucidate the comparison between the heat transport from magnons with that in parallel channels from electrons and phonons, at the nanojunction boundary.     

Topological pseudomonotonicity and vector equilibrium problems

In this paper, we introduce the topological pseudomonotonicity to vector valued bifunctions, and derive some existence results for vector equilibrium problems with the corresponding bifunctions topologically pseudomonotone. Some applications to vector variational inequalities and existence of Pareto optima are given.