Approximate recursive equilibrium with minimal state space

This paper shows existence of approximate recursive equilibrium with minimal state space in an environment of incomplete markets. We prove that the approximate recursive equilibrium implements an approximate sequential equilibrium which is always close to a Magill and Quinzii equilibrium without short sales for arbitrarily small errors. This implies that the competitive equilibrium can be implemented by using forecast statistics with minimal state space provided that agents will reduce errors in their estimates in the long run. We have also developed an alternative algorithm to compute the approximate recursive equilibrium with incomplete markets and heterogeneous agents through a procedure of iterating functional equations and without using the rst order conditions of optimality.

Análise não suave e aplicações em otimização

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Uma abordagem para problemas e controle ótimo via métodos de Runge-Kutta e análise de erro

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Numerical methods for strong solutions of stochastic differential equations: an overview

This paper gives a review of recent progress in the design of numerical methods for computing the trajectories (sample paths) of solutions to stochastic differential equations. We give a brief survey of the area focusing on a number of application areas where approximations to strong solutions are important, with a particular focus on computational biology applications, and give the necessary analytical tools for understanding some of the important concepts associated with stochastic processes. We present the stochastic Taylor series expansion as the fundamental mechanism for constructing effective numerical methods, give general results that relate local and global order of convergence and mention the Magnus expansion as a mechanism for designing methods that preserve the underlying structure of the problem. We also present various classes of explicit and implicit methods for strong solutions, based on the underlying structure of the problem. Finally, we discuss implementation issues relating to maintaining the Brownian path, efficient simulation of stochastic integrals and variable-step-size implementations based on various types of control.

Mechanistic studies of organotellurium chemistry

The oxidation of bis(p-ethoxyphenyl) ditelluride by hydrogen peroxide has been studied kinetically. The reaction monitored was an oxidation from tellurium(I) to tellurium(II). The reaction stoichiometry ratio was found to depend upon the initial reagent concentrations. The presence of dioxygen was found to retard the rate and attributed to a dioxygen-ditelluride adduct. The rate varies in the following order of different atmospheres N2> Air> > O2. The final product obtained from the oxidation has been characterised by IR, NMR and ESR spectroscopy. A mechanism for the oxidation has been suggested. The reduction of p-EtOPhTeCl3 by the hydrazinium ion has been studied kinetically. The stoichiometric measurements show that four moles p-EtOPhTeCl3 are equivalent to three moles hydrazinium ion. The kinetics were studied under pseudo first order conditions. No ammonia was detected as a nitrogen containing product. The reduction proceeds via a two-electron process which indicates that it is inner-sphere in nature. A mechanism for the reduction is suggested. The solvolysis of p-EtOPhTeCl3 by methanol in benzene/methanol media has been studied. The study shows that the solvolysis is a reversible, acid catalysed reaction. Replacement of the chlorides on tellurium by methanol is agreed to be associative and replacement of the first chloride is rate determining. The rate of solvolysis varies in the order trichloride > tribromide > triiodide. A mechanism for the solvolysis is suggested. The synthesis of some tellurium heterocyclics is reported. The synthesis and characterisation of telluranthrene is reported. The attempted synthesis of telluraxanthene was unsuccessful.

l-stable Functions and Constrained Optimization

Иван Гинчев - Класът на ℓ-устойчивите в точка функции, дефиниран в [2] и разширяващ класа на C1,1 функциите, се обобщава от скаларни за векторни функции. Доказани са някои свойства на ℓ-устойчивите векторни функции. Показано е, че векторни оптимизационни задачи с ограничения допускат условия от втори ред изразени чрез посочни производни, което обобщава резултати от [2] и [5].

Late Transition Metal-Oxo complexes: Synthesis, and Biorelevant Reactivity

High-valent terminal metal-oxygen adducts are supposed to be potent oxidising intermediates in enzymatic catalyses. In contrast to those from groups 6-8, oxidants that contain late transition metals (Co, Ni, Cu) are poorly understood. Because of their high reactivity, only a few examples of these compounds have been observed. The aim of this project was to investigate the reactivity of high-valent Ni(III) complexes, containing a monodentate oxygen-donor ligands, in hydrogen atom abstraction (HAA) and oxygen atom transfer (OAT) reactions which are typical of biological high-valent metal-oxygen species. Particularly, the Ni(III) complexes were generated in situ, at low temperature, from the oxidation of the Ni(II) species.The nickel complexes studied during this work were supported by tridentate ligands, with a strong σ-donating ability and exceedingly resistant to several common degradation pathways. These complexes vary based on the monodentate group in the fourth coordination position site, which can be neutral or anionic. In particular, we prepared four different Ni(III) complexes [NiIII(pyN2Me2)(OCO2H)] (12), [NiIII(pyN2Me2)(ONO2)] (14), [NiIII(pyN2Me2)(OC(O)CH3)] (18) and [NiIII(pyN2Me2)(OC(O)H)] (25). They feature a bicarbonate (-OCO2H), nitrate (-ONO2), acetate (-OC(O)CH3) and formate (-OC(O)H) group, respectively.HAA and OAT reactions were performed by adding 2,6-di-tert-butylphenol (2,6-DTBP) at -40°C, and triphenylphosphine (PPh3) at -80°C, to the in situ generated Ni(III) complexes, respectively. These reactions were carried out by adding 7 to 500 equivalents of substrate, in order to ensure pseudo-first order conditions. Since, the reactivity of the Ni(III) complex featured by the bicarbonate group has been studied in a previous work, we only investigated that of the species bearing the nitrate, acetate and formate ligand. Finally we compared the value of the reaction rate of all the four species in the HAA and OAT reactions.

Search of symmetric composition methods of symmetric integrators

Composition methods are useful when solving Ordinary Differential Equations (ODEs) as they increase the order of accuracy of a given basic numerical integration scheme. We will focus on sy-mmetric composition methods involving some basic second order symmetric integrator with different step sizes [17]. The introduction of symmetries into these methods simplifies the order conditions and reduces the number of unknowns. Several authors have worked in the search of the coefficients of these type of methods: the best method of order 8 has 17 stages [24], methods of order 8 and 15 stages were given in [29, 39, 40], 10-order methods of 31, 33 and 35 stages have been also found [24, 34]. In this work some techniques that we have built to obtain 10-order symmetric composition methods of symmetric integrators of s = 31 stages (16 order conditions) are explored. Given some starting coefficients that satisfy the simplest five order conditions, the process followed to obtain the coefficients that satisfy the sixteen order conditions is provided.

Existence Results for Second Order Differential Equations with Nonlocal Conditions in Banach Spaces

This work is concerned with implicit second order abstract differential equations with nonlocal conditions. Assuming that the involved operators satisfy sonic compactness properties, we establish the existence of local mild solutions, the existence of global mild solutions and the existence of asymptotically almost periodic solutions.

Positive solutions of fourth order problems with clamped beam boundary conditions

n this paper we make an exhaustive study of the fourth order linear operator u((4)) + M u coupled with the clamped beam conditions u(0) = u(1) = u'(0) = u'(1) = 0. We obtain the exact values on the real parameter M for which this operator satisfies an anti-maximum principle. Such a property is equivalent to the fact that the related Green's function is nonnegative in [0, 1] x [0, 1]. When M < 0 we obtain the best estimate by means of the spectral theory and for M > 0 we attain the optimal value by studying the oscillation properties of the solutions of the homogeneous equation u((4)) + M u = 0. By using the method of lower and upper solutions we deduce the existence of solutions for nonlinear problems coupled with this boundary conditions. (C) 2011 Elsevier Ltd. All rights reserved.

Positive solutions for a fourth order equation with nonlinear boundary conditions

Existence of positive solutions for a fourth order equation with nonlinear boundary conditions, which models deformations of beams on elastic supports, is considered using fixed points theorems in cones of ordered Banach spaces. Iterative and numerical solutions are also considered. (C) 2010 IMACS. Published by Elsevier B.V. All rights reserved.

Monotone positive solutions for a fourth order equation with nonlinear boundary conditions

This work is concerned with the existence of monotone positive solutions for a class of beam equations with nonlinear boundary conditions. The results are obtained by using the monotone iteration method and they extend early works on beams with null boundary conditions. Numerical simulations are also presented. (C) 2009 Elsevier Ltd. All rights reserved.

A Direct Numerov Sixth-order Numerical Scheme to Accurately Solve the Unidimensional Poisson Equation with Dirichlet Boundary Conditions

In this article, we present an analytical direct method, based on a Numerov three-point scheme, which is sixth order accurate and has a linear execution time on the grid dimension, to solve the discrete one-dimensional Poisson equation with Dirichlet boundary conditions. Our results should improve numerical codes used mainly in self-consistent calculations in solid state physics.

Analysis of various conditions in order to measure electromyography of isometric contractions in water and on air

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Experimental dissolution of molybdenum-sulphides at low oxygen concentrations: A first-order approximation of late Archean atmospheric conditions

The abundance of atmospheric oxygen and its evolution through Earth's history is a highly debated topic. The earliest change of the Mo concentration and isotope composition of marine sediments are interpreted to be linked to the onset of the accumulation of free O2 in Earth's atmosphere. The O2 concentration needed to dissolve significant amounts of Mo in water is not yet quantified, however. We present laboratory experiments on pulverized and surface-cleaned molybdenite (MoS2) and a hydrothermal breccia enriched in Mo-bearing sulphides using a glove box setup. Duration of an experiment was 14 days, and first signs of oxidation and subsequent dissolution of Mo compounds start to occur above an atmospheric oxygen concentration of 72 ± 20 ppmv (i.e., 2.6 to 4.6 × 10−4 present atmospheric level (PAL)). This experimentally determined value coincides with published model calculations supporting atmospheric O2 concentrations between 1 × 10−5 to 3 × 10−4 PAL prior to the Great Oxidation Event and sets an upper limit to the molecular oxygen needed to trigger Mo accumulation and Mo isotope variations recorded in sediments. In combination with the published Mo isotope composition of the rock record, this result implies an atmospheric oxygen concentration prior to 2.76 Ga of below 72 ± 20 ppmv.