Saddle Point and Second Order Optimality in Nondifferentiable Nonlinear Abstract Multiobjective Optimization

This article deals with a vector optimization problem with cone constraints in a Banach space setting. By making use of a real-valued Lagrangian and the concept of generalized subconvex-like functions, weakly efficient solutions are characterized through saddle point type conditions. The results, jointly with the notion of generalized Hessian (introduced in [Cominetti, R., Correa, R.: A generalized second-order derivative in nonsmooth optimization. SIAM J. Control Optim. 28, 789–809 (1990)]), are applied to achieve second order necessary and sufficient optimality conditions (without requiring twice differentiability for the objective and constraining functions) for the particular case when the functionals involved are defined on a general Banach space into finite dimensional ones.

A relationship between structural and electronic order-disorder effects and optical properties in crystalline TiO2 nanomaterials

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Mathematical models of generalized diffusion

We discuss in this paper equations describing processes involving non-linear and higher-order diffusion. We focus on a particular case (u(t) = 2 lambda (2)(uu(x))(x) + lambda (2)u(xxxx)), which is put into analogy with the KdV equation. A balance of nonlinearity and higher-order diffusion enables the existence of self-similar solutions, describing diffusive shocks. These shocks are continuous solutions with a discontinuous higher-order derivative at the shock front. We argue that they play a role analogous to the soliton solutions in the dispersive case. We also discuss several physical instances where such equations are relevant.

New class of spin projection operators for 3D models

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

DN interaction from meson exchange

A model of the DN interaction is presented which is developed in close analogy to the meson-exchange KN potential of the Jülich group utilizing SU(4) symmetry constraints. The main ingredients of the interaction are provided by vector meson (ρ, ω) exchange and higher-order box diagrams involving D *N, DΔ, and D *Δ intermediate states. The coupling of DN to the π Λ c and π Σ c channels is taken into account. The interaction model generates the Λ c(2595)-resonance dynamically as a DN quasi-bound state. Results for DN total and differential cross sections are presented and compared with predictions of two interaction models that are based on the leading-order Weinberg-Tomozawa term. Some features of the Λ c(2595)-resonance are discussed and the role of the near-by π Σ c threshold is emphasized. Selected predictions of the orginal KN model are reported too. Specifically, it is pointed out that the model generates two poles in the partial wave corresponding to the Λ(1405)-resonance. © 2011 SIF, Springer-Verlag Berlin Heidelberg.

Sistemas dinâmicos discretos: análise de estabilidade

Pós-graduação em Matemática Universitária - IGCE

Formalismo de Hamilton-Jacobi generalizado: teorias de campos com derivadas de ordem superior

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Determination of the pole and (MS)over-bar masses of the top quark from the t(t)over-bar cross section

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Hamilton-Jacobi approach for first order actions and theories with higher derivatives

In this work, we analyze systems described by Lagrangians with higher order derivatives in the context of the Hamilton-Jacobi formalism for first order actions. Two different approaches are studied here: the first one is analogous to the description of theories with higher derivatives in the hamiltonian formalism according to [D.M. Gitman, S.L. Lyakhovich, I.V. Tyutin, Soviet Phys. J. 26 (1983) 730; D.M. Gitman, I.V. Tyutin, Quantization of Fields with Constraints, Springer-Verlag, New York, Berlin, 1990] the second treats the case where degenerate coordinate are present, in an analogy to reference [D.M. Gitman, I.V. Tyutin, Nucl. Phys. B 630 (2002) 509]. Several examples are analyzed where a comparison between both approaches is made. (C) 2007 Elsevier B.V. All rights reserved.

Higher derivative Chern-Simons extension in the noncommutative QED(3)

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Charges and fluxes in Maxwell theory on compact manifolds with boundary

We investigate the charges and fluxes that can occur in higher-order Abelian gauge theories defined on compact space-time manifolds with boundary. The boundary is necessary to supply a destination to the electric lines of force emanating from brane sources, thus allowing non-zero net electric charges, but it also introduces new types of electric and magnetic flux. The resulting structure of currents, charges, and fluxes is studied and expressed in the language of relative homology and de Rham cohomology and the corresponding abelian groups. These can be organised in terms of a pair of exact sequences related by the Poincare-Lefschetz isomorphism and by a weaker flip symmetry exchanging the ends of the sequences. It is shown how all this structure is brought into play by the imposition of the appropriately generalised Maxwell's equations. The requirement that these equations be integrable restricts the world-volume of a permitted brane (assumed closed) to be homologous to a cycle on the boundary of space-time. All electric charges and magnetic fluxes are quantised and satisfy the Dirac quantisation condition. But through some boundary cycles there may be unquantised electric fluxes associated with quantised magnetic fluxes and so dyonic in nature.