Results on proximal and generalized weak proximal contractions including the case of iteration-dependent range sets

This paper presents some further results on proximal and asymptotic proximal contractions and on a class of generalized weak proximal contractions in metric spaces. The generalizations are stated for non-self-mappings of the forms for and , or , subject to and , such that converges uniformly to T, and the distances are iteration-dependent, where , , and are non-empty subsets of X, for , where is a metric space, provided that the set-theoretic limit of the sequences of closed sets and exist as and that the countable infinite unions of the closed sets are closed. The convergence of the sequences in the domain and the image sets of the non-self-mapping, as well as the existence and uniqueness of the best proximity points, are also investigated if the metric space is complete. Two application examples are also given, being concerned, respectively, with the solutions through pseudo-inverses of both compatible and incompatible linear algebraic systems and with the parametrical

Common Fixed Points of Generalized Rational Type Cocyclic Mappings in Multiplicative Metric Spaces

The aim of this paper is to present fixed point result of mappings satisfying a generalized rational contractive condition in the setup of multiplicative metric spaces. As an application, we obtain a common fixed point of a pair of weakly compatible mappings. Some common fixed point results of pair of rational contractive types mappings involved in cocyclic representation of a nonempty subset of a multiplicative metric space are also obtained. Some examples are presented to support the results proved herein. Our results generalize and extend various results in the existing literature.

Implementação de um algoritmo numérico para solução da equação de Christoffel generalizada em acustoelasticidade.

Extensos estudos realizados nas últimas décadas sobre a propagação de ondas ultrassônicas em sólidos levaram ao desenvolvimento de técnicas não destrutivas para a avaliação da segurança e integridade de estruturas e componentes industriais. O interesse na aplicação de técnicas ultrassônicas para medição de tensões aplicadas e residuais decorre da mudança mensurável da velocidade das ondas ultrassônicas na presença de um campo de tensões, fenômeno conhecido como efeito acustoelástico. Uma teoria de acustoelasticidade fornece um meio atrativo e não destrutivo de medir a tensão média ao longo do caminho percorrido pela onda. O estudo da propagação das ondas ultrassônicas em meios homogêneos anisotrópicos sob tensão conduz a um problema não linear de autovalores dado pela equação de Christoffel generalizada. A característica não linear deste problema decorre da interdependência entre as constantes elásticas efetivas do material e as tensões atuantes. A medição experimental de tensões por técnicas ultrassônicas é um problema inverso da acustoelasticidade. Esta dissertação apresenta a implementação de um algoritmo numérico, baseado no método proposto por Degtyar e Rokhlin, para solução do problema inverso da acustoelasticidade em sólidos ortotrópicos sujeitos a um estado plano de tensões. A solução da equação de Christoffel generalizada apresenta dificuldades de natureza numérica e prática. A estabilidade e a precisão do algoritmo desenvolvido, bem como a influência das incertezas na medição experimental das velocidades das ondas ultrassônicas, foram então investigadas. Dados sintéticos para as velocidades das ondas ultrassônicas de incidência oblíqua em uma placa sujeita a um estado plano de tensões foram gerados pela solução direta da equação de Christoffel generalizada para ilustrar a aplicação do algoritmo desenvolvido. O objetivo maior desta dissertação é a disponibilização de uma nova ferramenta de cálculo para suporte às atividades experimentais de medição de tensões por ultrassom no país.

Addressing students' difficulties with Faraday's law: A guided problem solving approach

In traditional teaching, the fundamental concepts of electromagnetic induction are usually quickly analyzed, spending most of the time solving problems in a more or less rote manner. However, physics education research has shown that the fundamental concepts of the electromagnetic induction theory are barely understood by students. This article proposes an interactive teaching sequence introducing the topic of electromagnetic induction. The sequence has been designed based on contributions from physics education research. Particular attention is paid to the relationship between experimental findings (macroscopic level) and theoretical interpretation (microscopic level). An example of the activities that have been designed will also be presented, describing the implementation context and the corresponding findings. Since implementing the sequence, a considerable number of students have a more satisfactory grasp of the electromagnetic induction explicative model. However, difficulties are manifested in aspects that require a multilevel explanation, referring to deep structures where the system description is better defined.

Distribution of Healthcare resources II.Study and Comparison of a Linear Programming Problem and its Dual. Resolution and Evaluation of a Practical Case and its Programming using Excel and Win QSB.

[EN]This research had as primary objective to model different types of problems using linear programming and apply different methods so as to find an adequate solution to them. To achieve this objective, a linear programming problem and its dual were studied and compared. For that, linear programming techniques were provided and an introduction of the duality theory was given, analyzing the dual problem and the duality theorems. Then, a general economic interpretation was given and different optimal dual variables like shadow prices were studied through the next practical case: An aesthetic surgery hospital wanted to organize its monthly waiting list of four types of surgeries to maximize its daily income. To solve this practical case, we modelled the linear programming problem following the relationships between the primal problem and its dual. Additionally, we solved the dual problem graphically, and then we found the optimal solution of the practical case posed through its dual, following the different theorems of the duality theory. Moreover, how Complementary Slackness can help to solve linear programming problems was studied. To facilitate the solution Solver application of Excel and Win QSB programme were used.

Contributions to time series data mining departing from the problem of road travel time modeling

194 p.