A potential approach to claims problems

Hart and Mas Colell (1989) introduce the potential function for cooperative TU games. In this paper, we extend this approach to claims problems, also known as bankruptcy or rationing problems. We show that for appropriate subproblems, the random arrival rule, the rules in the TAL-family (which include the uniform gains rule, the uniform losses rule and the Talmud rule), the minimal overlap rule, and the proportional rule admit a potential. We also study the balanced contributions property for these rules. By means of a potential, we introduce a generalization of the random arrival rule and mixtures of the minimal overlap rule and the uniform losses rule.

On the uniqueness of singular solutions to boundary-initial value problems in linear elastodynamics

This investigation deals with certain generalizations of the classical uniqueness theorem for the second boundary-initial value problem in the linearized dynamical theory of not necessarily homogeneous nor isotropic elastic solids. First, the regularity assumptions underlying the foregoing theorem are relaxed by admitting stress fields with suitably restricted finite jump discontinuities. Such singularities are familiar from known solutions to dynamical elasticity problems involving discontinuous surface tractions or non-matching boundary and initial conditions. The proof of the appropriate uniqueness theorem given here rests on a generalization of the usual energy identity to the class of singular elastodynamic fields under consideration.

Following this extension of the conventional uniqueness theorem, we turn to a further relaxation of the customary smoothness hypotheses and allow the displacement field to be differentiable merely in a generalized sense, thereby admitting stress fields with square-integrable unbounded local singularities, such as those encountered in the presence of focusing of elastic waves. A statement of the traction problem applicable in these pathological circumstances necessitates the introduction of "weak solutions'' to the field equations that are accompanied by correspondingly weakened boundary and initial conditions. A uniqueness theorem pertaining to this weak formulation is then proved through an adaptation of an argument used by O. Ladyzhenskaya in connection with the first boundary-initial value problem for a second-order hyperbolic equation in a single dependent variable. Moreover, the second uniqueness theorem thus obtained contains, as a special case, a slight modification of the previously established uniqueness theorem covering solutions that exhibit only finite stress-discontinuities.

Applications of plasticity theory to selected problems in soil mechanics

Two topics in plane strain perfect plasticity are studied using the method of characteristics. The first is the steady-state indentation of an infinite medium by either a rigid wedge having a triangular cross section or a smooth plate inclined to the direction of motion. Solutions are exact and results include deformation patterns and forces of resistance; the latter are also applicable for the case of incipient failure. Experiments on sharp wedges in clay, where forces and deformations are recorded, showed a good agreement with the mechanism of cutting assumed by the theory; on the other hand the indentation process for blunt wedges transforms into that of compression with a rigid part of clay moving with the wedge. Finite element solutions, for a bilinear material model, were obtained to establish a correspondence between the response of the plane strain wedge and its axi-symmetric counterpart, the cone. Results of the study afford a better understanding of the process of indentation of soils by penetrometers and piles as well as the mechanism of failure of deep foundations (piles and anchor plates).

The second topic concerns the plane strain steady-state free rolling of a rigid roller on clays. The problem is solved approximately for small loads by getting the exact solution of two problems that encompass the one of interest; the first is a steady-state with a geometry that approximates the one of the roller and the second is an instantaneous solution of the rolling process but is not a steady-state. Deformations and rolling resistance are derived. When compared with existing empirical formulae the latter was found to agree closely.

The microbiological quality of water: the nature of the problem

Improvements in methods for the detection and enumeration of microbes in water, particularly the application of techniques of molecular biology, have highlighted shortcomings in the ”standard methods” for assessing water quality. Higher expectations from the consumer and increased publicity associated with pollution incidents can lead to an uncoupling of the cycle which links methodological development with standard-setting and legislation. The new methodology has also highlighted problems within the water cycle, related to the introduction, growth and metabolism of microbes. A greater understanding of the true diversity of the microbial community and the ability to transmit genetic information within aquatic systems ensures that the subject of this symposium and volume provides an ideal forum to discuss the problems encountered by both researcher and practitioner.

Coleta Seletiva Solidária de resíduos recicláveis dirigida à rede estadual de ensino do Rio de Janeiro - estudo de caso.

O aumento da demanda de água, energia, bem como a mudança na composição e na quantidade dos resíduos, associados aos impactos socioambientais que eles provocam, tornaram-se um dos grandes desafios atuais para a sociedade e, em particular, para as escolas públicas. Nesse contexto, o governo do estado do Rio de Janeiro, dentro de seu Plano Estadual de Gerenciamento Integrado de Resíduos Sólidos, criou o Programa Coleta Seletiva Solidária (PCSS), em outubro de 2009, realizado em parceria entre o Instituto Estadual do Ambiente (INEA), a Universidade do Estado do Rio de Janeiro (UERJ) e a Secretaria de Estado de Educação (SEEDUC). Este Programa assessora a implantação da Coleta Seletiva Solidária (CSS) de materiais recicláveis nos municípios do estado. O eixo-escolas, uma das suas linhas de ações, assessora a implantação da CSS na rede estadual, conforme determina o Decreto Estadual 40.645/07. Considerando os problemas relacionados aos resíduos e a exigência legal, boa parte das escolas estaduais não implantaram ainda a Coleta Seletiva Solidária, por diversos fatores. O objetivo da pesquisa é estudar o modelo de Coleta Seletiva proposto pelo PCSS nas escolas da rede estadual de ensino do Rio de Janeiro. Como estudo de caso, esse modelo foi aplicado no Colégio Estadual Souza Aguiar (CESA). Utilizou-se da pesquisa-ação como abordagem metodológica e o instrumento de coleta de dados foi o questionário dirigido aos participantes das oficinas de capacitação na UERJ. No CESA foram aplicados questionários aos alunos e acompanhado o processo de implantação da CSS através da observação participante. Conclui-se que os resultados da pesquisa não podem ser generalizados para toda a rede estadual de ensino do Rio de Janeiro. Contudo, ele possibilitou identificar questões importantes e sugerir recomendações para o aperfeiçoamento do modelo estudado. Destaca-se a importância de formalizar o compromisso institucional dos dirigentes das escolas com a implantação da CSS, contribuindo com a formação de cidadãos comprometidos com a sustentabilidade socioambiental do estado do Rio de Janeiro.

Instances of combinatorial optimization problems: complexity and generation

138 p.