Existence of Solution for a Class of Quasilinear Systems

This paper proves the existence of nontrivial solution for a class of quasilinear systems oil bounded domains in R(N), N >= 2, whose nonlinearity has a double criticality. The proof is based oil a linking theorem without the Palais-Smale condition.

A linear optimization approach to the combined production planning model

Two fundamental processes usually arise in the production planning of many industries. The first one consists of deciding how many final products of each type have to be produced in each period of a planning horizon, the well-known lot sizing problem. The other process consists of cutting raw materials in stock in order to produce smaller parts used in the assembly of final products, the well-studied cutting stock problem. In this paper the decision variables of these two problems are dependent of each other in order to obtain a global optimum solution. Setups that are typically present in lot sizing problems are relaxed together with integer frequencies of cutting patterns in the cutting problem. Therefore, a large scale linear optimizations problem arises, which is exactly solved by a column generated technique. It is worth noting that this new combined problem still takes the trade-off between storage costs (for final products and the parts) and trim losses (in the cutting process). We present some sets of computational tests, analyzed over three different scenarios. These results show that, by combining the problems and using an exact method, it is possible to obtain significant gains when compared to the usual industrial practice, which solve them in sequence. (C) 2010 The Franklin Institute. Published by Elsevier Ltd. All rights reserved.

Structural modeling of high-affinity thyroid receptor-ligand complexes

Understanding the molecular basis of the binding modes of natural and synthetic ligands to nuclear receptors is fundamental to our comprehension of the activation mechanism of this important class of hormone regulated transcription factors and to the development of new ligands. Thyroid hormone receptors (TR) are particularly important targets for pharmaceuticals development because TRs are associated with the regulation of metabolic rates, body weight, and circulating levels of cholesterol and triglycerides in humans. While several high-affinity ligands are known, structural information is only partially available. In this work we obtain structural models of several TR-ligand complexes with unknown structure by docking high affinity ligands to the receptors` ligand binding domain with subsequent relaxation by molecular dynamics simulations. The binding modes of these ligands are discussed providing novel insights into the development of TR ligands. The experimental binding free energies are reasonably well-reproduced from the proposed models using a simple linear interaction energy free-energy calculation scheme.

Erbium and Ytterbium Codoped Titanoniobophosphate Glasses for Ion-Exchange-Based Planar Waveguides

This work presents the optical properties of erbium-doped and erbium/ytterbium codoped Na(2)O-Al(2)O(3)-TiO(2)-Nb(2)O(5)-P(2)O(5) glass systems and also the characterization of planar waveguides obtained by typical thermally assisted Ag+<-> Na+ ion-exchange process. The glass systems allow the preparation of single mode and multimode planar waveguides presenting a strong and relatively broad emission at 1536 nm. The emission signal in the infrared region is intensified for silver-containing samples when compared with free-silver samples. The emission signal intensification may be attributed to a nonplasmonic energy transfer from silver species to Er3+ ions as no bands related to surface plasmon resonance (SPR) of silver nanoparticles were observed.

Equivalent Circuits and Nanoplasmonics

We show how a circuit analysis, used widely in electrical engineering, finds application to problems of light wave injection and transport in subwavelength structures in the optical frequency range. Lumped circuit and transmission-line analysis may prove helpful in the design of plasmonic devices with standard, functional properties.

Pseudo Focal Points Along Lorentzian Geodesics and Morse Index

Given a Lorentzian manifold (M,g), a geodesic gamma in M and a timelike Jacobi field Y along gamma, we introduce a special class of instants along gamma that we call Y-pseudo conjugate (or focal relatively to some initial orthogonal submanifold). We prove that the Y-pseudo conjugate instants form a finite set, and their number equals the Morse index of (a suitable restriction of) the index form. This gives a Riemannian-like Morse index theorem. As special cases of the theory, we will consider geodesics in stationary and static Lorentzian manifolds, where the Jacobi field Y is obtained as the restriction of a globally defined timelike Killing vector field.

On the Multiplicity of Orthogonal Geodesics in Riemannian Manifold With Concave Boundary. Applications to Brake Orbits and Homoclinics

Let (M, g) be a complete Riemannian Manifold, Omega subset of M an open subset whose closure is diffeomorphic to an annulus. If partial derivative Omega is smooth and it satisfies a strong concavity assumption, then it is possible to prove that there are at least two geometrically distinct geodesics in (Omega) over bar = Omega boolean OR partial derivative Omega starting orthogonally to one connected component of partial derivative Omega and arriving orthogonally onto the other one. The results given in [6] allow to obtain a proof of the existence of two distinct homoclinic orbits for an autonomous Lagrangian system emanating from a nondegenerate maximum point of the potential energy, and a proof of the existence of two distinct brake orbits for a. class of Hamiltonian systems. Under a further symmetry assumption, it is possible to show the existence of at least dim(M) pairs of geometrically distinct geodesics as above, brake orbits and homoclinics.