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.     

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.     

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.     

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.     

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.     

Theoretical Study on Non-Linear Optics Properties of Polycyclic Aromatic Hydrocarbons and the Effect of Their Intercalation with Carbon Nanotubes

Results of a theoretical study devoted to comparing NLO (non-linear optics) responses of derivatives of tetracene, isochrysene, and pyrene are reported. The static hyperpolarizability β, the dipole moment μ, the HOMO and LUMO orbitals, and their energy gap were calculated using the CAM-B3LYP density functional combined with the cc-pVDZ basis set. The para-disubstituted NO₂-tetracene-N(CH₃)₂ has the highest NLO response, which is related to a large intramolecular charge transfer. Adding vinyl groups to the para-disubstituted NO₂-tetracene-N(CH₃)₂ results in an increase in the NLO responses. We further investigated the effect of the intercalation of various push–pull molecules inside an armchair single-walled carbon nanotube. The intercalation leads to increased NLO responses, something that depends critically on the position of the guest molecule and/or on functionalization of the nanotube by donor and attractor groups.     

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.     

Computation of the infrared active modes in single-walled boron nitride nanotube bundles

In this work, the infrared active modes are computed for homogeneous bundles of single-walled boron nitride nanotubes (BBNNTs), using the so-called spectral moments method. The dependence of the wavenumber on these modes in terms of diameters, lengths, and numbers of tubes, is investigated. To this end, use is made of a Lennard-Jones potential for describing the van der Waals interactions between tubes in a bundle. We find that, for a finite homogeneous bundle, additional modes appear as a specific signature. Finally, these results are useful for the interpretation of the experimental infrared spectra of BBNNTs.     

Raman spectrum of single-walled boron nitride nanotube

Using the spectral moments method, the calculations of the Raman spectra of single-walled boron nitride nanotubes (SW-BNNTs) were performed in the framework of the force constants model. Spectra were computed for chiral and achiral nanotubes for different diameters and lengths. The Raman scattering intensities were determined using the bond-polarizability model and a good agreement with group theory analysis was found. We show that the modes in the low frequency region are very sensitive to the nanotube diameter variation, whereas the ones associated to the tangential region are chirality dependent. The number of Raman active modes, their frequencies, and intensities depend on the length of the nanotube.