A general lagrangian approach for non-concave moral hazard problems

We establish a general Lagrangian for the moral hazard problem which generalizes the well known first order approach (FOA). It requires that besides the multiplier of the first order condition, there exist multipliers for the second order condition and for the binding actions of the incentive compatibility constraint. Some examples show that our approach can be useful to treat the finite and infinite state space cases. One of the examples is solved by the second order approach. We also compare our Lagrangian with 1\1irrlees'.

A general lagrangian approach for non-concave moral hazard problems

We establish a general Lagrangian for the moral hazard problem which generalizes the well known first order approach (FOA). It requires that besides the multiplier of the first order condition, there exist multipliers for the second order condition and for the binding actions of the incentive compatibility constraint. Some examples show that our approach can be useful to treat the finite and infinite state space cases. One of the examples is solved by the second order approach. We also compare our Lagrangian with 1\1irrlees'.

Preparação e caracterização de um material híbrido, à base de vermiculita modificada com quitosana, para a remoção de íons de chumbo presentes em efluentes sintéticos

Actually, surveys have been developed for obtaining new materials and methodologies that aim to minimize environmental problems due to discharges of industrial effluents contaminated with heavy metals. The adsorption has been used as an alternative technology effectively, economically viable and potentially important for the reduction of metals, especially when using natural adsorbents such as certain types of clay. Chitosan, a polymer of natural origin, present in the shells of crustaceans and insects, has also been used for this purpose. Among the clays, vermiculite is distinguished by its good ion exchange capacity and in its expanded form enhances its properties by greatly increasing its specific surface. This study aimed to evaluate the functionality of the hybrid material obtained through the modification of expanded vermiculite with chitosan in the removal of lead ions (II) in aqueous solution. The material was characterized by infrared spectroscopy (IR) in order to evaluate the efficiency of modification of matrix, the vermiculite, the organic material, chitosan. The thermal stability of the material and the ratio clay / polymer was evaluated by thermogravimetry. To evaluate the surface of the material was used in scanning electron microscopy (SEM) and (BET). The BET analysis revealed a significant increase in surface area of vermiculite that after interaction with chitosan, was obtained a value of 21, 6156 m2 / g. Adsorption tests were performed according to the particle size, concentration and time. The results show that the capacity of removal of ions through the vermiculite was on average 88.4% for lead in concentrations ranging from 20-200 mg / L and 64.2% in the concentration range of 1000 mg / L. Regarding the particle size, there was an increase in adsorption with decreasing particle size. In fuction to the time of contact, was observed adsorption equilibrium in 60 minutes with adsorption capacity. The data of the isotherms were fitted to equation Freundlich. The kinetic study of adsorption showed that the pseudo second- order model best describes the adsorption adsorption, having been found following values K2=0,024 g. mg-1 min-1and Qmax=25,75 mg/g, value very close to the calculated Qe = 26.31 mg / g. From the results we can conclude that the material can be used in wastewater treatment systems as a source of metal ions adsorbent due to its high adsorption capacity

Third-body perturbation in the case of elliptic orbits for the disturbing body

This work presents a semi-analytical and numerical study of the perturbation caused in a spacecraft by a third-body using a double averaged analytical model with the disturbing function expanded in Legendre polynomials up to the second order. The important reason for this procedure is to eliminate terms due to the short periodic motion of the spacecraft and to show smooth curves for the evolution of the mean orbital elements for a long-time period. The aim of this study is to calculate the effect of lunar perturbations on the orbits of spacecrafts that are traveling around the Earth. An analysis of the stability of near-circular orbits is made, and a study to know under which conditions this orbit remains near circular completes this analysis. A study of the equatorial orbits is also performed. Copyright (C) 2008 R. C. Domingos et al.

Some experiments with high order compact methods using a computer algebra software - Part I

We consider a procedure for obtaining a compact fourth order method to the steady 2D Navier-Stokes equations in the streamfunction formulation using the computer algebra system Maple. The resulting code is short and from it we obtain the Fortran program for the method. To test the procedure we have solved many cavity-type problems which include one with an analytical solution and the results are compared with results obtained by second order central differences to moderate Reynolds numbers. (c) 2005 Elsevier B.V. All rights reserved.

A kinetic model for the ultrasound catalyzed hydrolysis of solventless TEOS-water mixtures and the role of the initial additions of ethanol

The acid and ultrasound catalyzed hydrolysis of solventless TEOS-water mixtures are studied, as a function of the initial additions of ethanol to the mixtures, by means of flux calorimetry measurements. A device was specially designed for this purpose. Under acid conditions, our proposed method has been able to resolve hydrolysis from other condensation reactions, by detecting the exothermal hydrolysis reaction heat. The process has been explained by a dissolution and reaction mechanism. Ultrasound forces the dissolution process to start the reaction. The alcohol produced in the reaction helps the dissolution process to further enhance the hydrolysis. Initial amounts of pure ethanol added to the mixtures shorten the start time of the reaction, due to an additional effect of dissolution, and diminish the reaction rate, as a result of the solvent dilution effect. Our dissolution and reaction mechanism modeling describes the main points arising from the experimental data and yields k(H) = 0.24 M(-1) min(-1) for the second-order hydrolysis rate constant at 39 degrees C.

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.

Initial-condition problem for a chiral Gross-Neveu system

A time-dependent projection technique is used to treat the initial-value problem for self-interacting fermionic fields. On the basis of the general dynamics of the fields, we derive formal equations of kinetic-type for the set of one-body dynamical variables. A nonperturbative mean-field expansion can be written for these equations. We treat this expansion in lowest order, which corresponds to the Gaussian mean-field approximation, for a uniform system described by the chiral Gross-Neveu Hamiltonian. Standard stationary features of the model, such as dynamical mass generation due to chiral symmetry breaking and a phenomenon analogous to dimensional transmutation, are reobtained in this context. The mean-field time evolution of nonequilibrium initial states is discussed.

Braneworlds scenarios in a gravity model with higher order spatial three-curvature terms

In this work we study a Hořava-like 5-dimensional model in the context of braneworld theory. The equations of motion of such model are obtained and, within the realm of warped geometry, we show that the model is consistent if and only if λ takes its relativistic value 1. Furthermore, we show that the elimination of problematic terms involving the warp factor second order derivatives are eliminated by imposing detailed balance condition in the bulk. Afterwards, Israel's junction conditions are computed, allowing the attainment of an effective Lagrangian in the visible brane. In particular, we show that the resultant effective Lagrangian in the brane corresponds to a (3 + 1)-dimensional Hořava-like model with an emergent positive cosmological constant but without detailed balance condition. Now, restoration of detailed balance condition, at this time imposed over the brane, plays an interesting role by fitting accordingly the sign of the arbitrary constant β, insuring a positive brane tension and a real energy for the graviton within its dispersion relation. Also, the brane consistency equations are obtained and, as a result, the model admits positive brane tensions in the compactification scheme if, and only if, β is negative and the detailed balance condition is imposed. © 2013 Springer-Verlag Berlin Heidelberg and Società Italiana di Fisica.

Semigrupos de operadores lineares limitados: soluções Mild e Weak

Pós-graduação em Matemática - IBILCE

On Global Attractors for a Class of Parabolic Problems

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

Problemas de máximos e mínimos no Ensino Médio

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Radial sign-changing solutions to biharmonic nonlinear Schrodinger equations

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

Maximum principle, mean value operators and quasi boundedness in non-euclidean settings

This work deals with some classes of linear second order partial differential operators with non-negative characteristic form and underlying non- Euclidean structures. These structures are determined by families of locally Lipschitz-continuous vector fields in RN, generating metric spaces of Carnot- Carath´eodory type. The Carnot-Carath´eodory metric related to a family {Xj}j=1,...,m is the control distance obtained by minimizing the time needed to go from two points along piecewise trajectories of vector fields. We are mainly interested in the causes in which a Sobolev-type inequality holds with respect to the X-gradient, and/or the X-control distance is Doubling with respect to the Lebesgue measure in RN. This study is divided into three parts (each corresponding to a chapter), and the subject of each one is a class of operators that includes the class of the subsequent one. In the first chapter, after recalling “X-ellipticity” and related concepts introduced by Kogoj and Lanconelli in [KL00], we show a Maximum Principle for linear second order differential operators for which we only assume a Sobolev-type inequality together with a lower terms summability. Adding some crucial hypotheses on measure and on vector fields (Doubling property and Poincar´e inequality), we will be able to obtain some Liouville-type results. This chapter is based on the paper [GL03] by Guti´errez and Lanconelli. In the second chapter we treat some ultraparabolic equations on Lie groups. In this case RN is the support of a Lie group, and moreover we require that vector fields satisfy left invariance. After recalling some results of Cinti [Cin07] about this class of operators and associated potential theory, we prove a scalar convexity for mean-value operators of L-subharmonic functions, where L is our differential operator. In the third chapter we prove a necessary and sufficient condition of regularity, for boundary points, for Dirichlet problem on an open subset of RN related to sub-Laplacian. On a Carnot group we give the essential background for this type of operator, and introduce the notion of “quasi-boundedness”. Then we show the strict relationship between this notion, the fundamental solution of the given operator, and the regularity of the boundary points.

Spectral and variational characterizations of solutions to semilinear eigenvalue problems

Die vorliegende Arbeit befaßt sich mit einer Klasse von nichtlinearen Eigenwertproblemen mit Variationsstrukturin einem reellen Hilbertraum. Die betrachteteEigenwertgleichung ergibt sich demnach als Euler-Lagrange-Gleichung eines stetig differenzierbarenFunktionals, zusätzlich sei der nichtlineare Anteil desProblems als ungerade und definit vorausgesetzt.Die wichtigsten Ergebnisse in diesem abstrakten Rahmen sindKriterien für die Existenz spektral charakterisierterLösungen, d.h. von Lösungen, deren Eigenwert gerade miteinem vorgegeben variationellen Eigenwert eines zugehörigen linearen Problems übereinstimmt. Die Herleitung dieserKriterien basiert auf einer Untersuchung kontinuierlicher Familien selbstadjungierterEigenwertprobleme und erfordert Verallgemeinerungenspektraltheoretischer Konzepte.Neben reinen Existenzsätzen werden auch Beziehungen zwischenspektralen Charakterisierungen und denLjusternik-Schnirelman-Niveaus des Funktionals erörtert.Wir betrachten Anwendungen auf semilineareDifferentialgleichungen (sowieIntegro-Differentialgleichungen) zweiter Ordnung. Diesliefert neue Informationen über die zugehörigenLösungsmengen im Hinblick auf Knoteneigenschaften. Diehergeleiteten Methoden eignen sich besonders für eindimensionale und radialsymmetrische Probleme, während einTeil der Resultate auch ohne Symmetrieforderungen gültigist.