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.

Second order gauge theory

A gauge theory of second order in the derivatives of the auxiliary field is constructed following Utiyama's program. A novel field strength G = partial derivative F + fAF arises besides the one of the first order treatment, F = partial derivative A - partial derivative A + fAA. The associated conserved current is obtained. It has a new feature: topological terms are determined from local invariance requirements. Podolsky Generalized Eletrodynamics is derived as a particular case in which the Lagrangian of the gauge field is L-P alpha G(2). In this application the photon mass is estimated. The SU(N) infrared regime is analysed by means of Alekseev-Arbuzov-Baikov's Lagrangian. (c) 2006 Elsevier B.V. All rights reserved.

On the relationship between a 2 x 2 matrix and second-order scalar spectral problems for integrable equations

A simple proof is given that a 2 x 2 matrix scheme for an inverse scattering transform method for integrable equations can be converted into the standard form of the second-order scalar spectral problem associated with the same equations. Simple formulae relating these two kinds of representation of integrable equations are established.

New thought experiment to test the generalized second law of thermodynamics

We propose an extension of the original thought experiment proposed by Geroch, which sparked much of the actual debate and interest on black hole thermodynamics, and show that the generalized second law of thermodynamics is in compliance with it.

Cosmic acceleration from second order gauge gravity

We construct a phenomenological theory of gravitation based on a second order gauge formulation for the Lorentz group. The model presents a long-range modification for the gravitational field leading to a cosmological model provided with an accelerated expansion at recent times. We estimate the model parameters using observational data and verify that our estimative for the age of the Universe is of the same magnitude than the one predicted by the standard model. The transition from the decelerated expansion regime to the accelerated one occurs recently (at similar to 9.3 Gyr).

Superspace approach to the renormalization of the O'Raifeartaigh model up to the second order in the linear delta expansion parameter

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Second-order statistics for equal gain and maximal ratio diversity-combining reception

Exact and closed-form expressions for the level crossing rate and average fade duration are presented for equal gain combining and maximal ratio combining schemes, assuming an arbitrary number of independent branches in a Rayleigh environment. The analytical results are thoroughly validated by simulation.

Second-order statistics for diversity-combining, techniques in Nakagami-fading channels

Exact and closed-form expressions for the level crossing rate and average fade duration are presented for the M branch pure selection combining (PSC), equal gain combining (EGC), and maximal ratio combining (MRC) techniques, assuming independent branches in a Nakagami environment. The analytical results are thoroughly validated by reducing the general case to some special cases, for which the solutions are known, and by means of simulation for the more general case. The model developed here is general and can be easily applied to other fading statistics (e.g., Rice).

Hamilton-Jacobi formulation for singular systems with second-order Lagrangians

Recently, the Hamilton-Jacobi formulation for first-order constrained systems has been developed. In such formalism the equations of motion are written as total differential equations in many variables. We generalize the Hamilton-Jacobi formulation for singular systems with second-order Lagrangians and apply this new formulation to Podolsky electrodynamics, comparing with the results obtained through Dirac's method.

Análise não suave e aplicações em otimização

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Nonsmooth continuous-time optimization problems: Sufficient conditions

We discuss sufficient conditions of optimality for nonsmooth continuous-time nonlinear optimization problems under generalized convexity assumptions. These include both first-order and second-order criteria. (C) 1998 Academic Press.

Optimal Conditions for Biomass and Recombinant Glycerol Kinase Production Using the Yeast Pichia pastoris

The extracellular glycerol kinase gene from Saccharomyces cerevisiae (GUT]) was cloned into the expression vector pPICZ alpha. A and integrated into the genome of the methylotrophic yeast Pichia pastoris X-33. The presence of the GUT1 insert was confirmed by PCR analysis. Four clones were selected and the functionality of the recombinant enzyme was assayed. Among the tested clones, one exhibited glycerol kinase activity of 0.32 U/mL, with specific activity of 0.025 U/mg of protein. A medium optimized for maximum biomass production by recombinant Pichia pastoris in shaker cultures was initially explored, using 2.31 % (by volume) glycerol as the carbon source. Optimization was carried out by response surface methodology (RSM). In preliminary experiments, following a Plackett-Burman design, glycerol volume fraction (phi(Gly)) and growth time (t) were selected as the most important factors in biomass production. Therefore, subsequent experiments, carried out to optimize biomass production, followed a central composite rotatable design as a function of phi(Gly) and time. Glycerol volume fraction proved to have a significant positive linear effect on biomass production. Also, time was a significant factor (at linear positive and quadratic levels) in biomass production. Experimental data were well fitted by a convex surface representing a second order polynomial model, in which biomass is a function of both factors (R(2)=0.946). Yield and specific activity of glycerol kinase were mainly affected by the additions of glycerol and methanol to the medium. The optimized medium composition for enzyme production was: 1 % yeast extract, 1 % peptone, 100 mM potassium phosphate buffer, pH=6.0, 1.34 % yeast nitrogen base (YNB), 4.10(-5) % biotin, 1 %, methanol and 1 %, glycerol, reaching 0.89 U/mL of glycerol kinase activity and 14.55 g/L of total protein in the medium after 48 h of growth.

Gauge formulation for higher order gravity

This work is an application of the second order gauge theory for the Lorentz group, where a description of the gravitational interaction is obtained that includes derivatives of the curvature. We analyze the form of the second field strength, G=partial derivative F+fAF, in terms of geometrical variables. All possible independent Lagrangians constructed with quadratic contractions of F and quadratic contractions of G are analyzed. The equations of motion for a particular Lagrangian, which is analogous to Podolsky's term of his generalized electrodynamics, are calculated. The static isotropic solution in the linear approximation was found, exhibiting the regular Newtonian behavior at short distances as well as a meso-large distance modification.

Influence of drying conditions on ascorbic acid during convective drying of whole persimmons

Degradation kinetics of food constituents may be related to the matrix molecular mobility by glass transition temperature. Our objective was to test this approach to describe ascorbic acid degradation during drying of persimmons in an automatically controlled tray dryer with temperatures (40 to 70 degrees C) and air velocities (0.8 to 2.0 m/s) varying according a second order central composite design. The Williams-Landel-Ferry model was satisfactorily adjusted to degradation curves for both control strategies adopted-constant air temperature and temperature fixed inside the fruit. Degradation rates were higher at higher drying temperatures, independent of the necessary time to attain the desired moisture content.

Viscoelastic behavior of persimmons dried at constant air temperature

The viscoelastic behavior of dried persimmons at different air-drying temperatures and velocities was evaluated. Air temperatures and velocities were varied according to a second-order central composite design, with temperature ranging from 40degreesC to 70degreesC and air velocity from 0.8 to 2.0 m/s. After drying, persimmons were equilibrated at four different water activities: 0.432, 0.576, 0.625 and 0.751. The rheological behavior of dried and conditioned persimmons was studied under uniaxial compression-relaxation tests. Three different rheological models were fitted to the experimental relaxation curves: Maxwell, Generalized Maxwell and Peleg and Normand. Based on the root mean square of residuals, the Generalized Maxwell model showed the best fit and a regression analysis was applied to obtain response surfaces for the model parameters. The dependence of the rheological properties on water activity was also analysed. Results showed that only the linear effect of air temperature was significant at a 5% level on the equilibrium stress and relaxation times. In a general way, these parameters increased with increasing air temperature and decreasing water activity. (C) 2004 Swiss Society of Food Science and Technology. Published by Elsevier Ltd. All rights reserved.