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.

Ecuaciones integrales en el contexto de espacios de Hilbert

Las ideas básicas de la teoría de los espacios de Hilbert tienen como origen diversos problemas del análisis funcional, entre los cuales podemos citar los relativos a ciertas ecuaciones integrales lineales. Concretamente, un precedente de los métodos de la teoría espectral de operadores fue precisamente el enfoque de I. Fredholm de resolución de ciertas ecuaciones integrales mediante la teoría de matrices y determinantes infinitos utilizando el método de coeficientes indeterminados. Imitando la técnica de von Koch para desarrollar determinantes infinitos, Fredholm desarrolló su famoso teorema de alternativa en la resolución de las ecuaciones que llevan su nombre. Algunos tipos de ecuaciones integrales lineales están relacionados con operadores acotados completamente continuos y la teoría espectral para esta clase de operadores se podrá aplicar en la resolución de estas ecuaciones. En esta memoria se estudian distintos aspectos de estas y otras ecuaciones integrales. En el capítulo 1 se definen los conceptos básicos necesarios para el seguimiento de la misma, como es la de operador lineal y sus propiedades. Se distingue una clase importante de operadores, los compactos. Y se demuestra que todo operador integral pertenece a esta clase de operadores. En los capítulos 2 y 3 se introduce el concepto de ecuación integral, diferenciando las de Fredholm de las de Volterra, y se estudian diferentes técnicas de resolución de dichas ecuaciones, como son el teorema de alternativa, el teorema espectral para operadores compactos y autoadjuntos, ecuaciones integrales con núcleos degenerados y resolución por el método de aproximaciones sucesivas. Para finalizar, en el apéndice se resuelven algunos ejercicios utilizando los diferentes métodos estudiados.

Fourteenth Annual Report for the year ended 31st March, 1965

This is the fourteenth Annual report of the Cumberland River Board on information of its activities and responsibilities on river management in its area between the beginning of April 1964, to the end of March 1965. The report contains 5 main sections on water resources, land drainage, fisheries, pollution, and finally the expenditure and income for the 12 month period. The first area that the report deals with is water resources, which includes information on the completion of gauging stations, abstraction of water and rainfall and river flow. The section on land drainage looks at work on improvement schemes, floods and information on maintenance work carried out on rivers including Wampool, Waver, Wiza, Ellen, Cocker, Keekle, Marron, Ehen, Bleng, Esk, Mite, Caldew and Petteril. The fisheries section covers 5 districts of the River Eden, Esk, Derwent, Ellen and South West Cumberland. It includes angling information and a general report for salmon and sea trout, brown trout and freshwater fish. Fish disease and fish hatchery are also covered as well as Byelaws and fisheries protection. The fourth section on pollution deals with water quality and information on sewage and trade effluents. The River Boards preceded the Environment Agency which came into existence in 1996.