O Problema da Mochila Compartimentada é uma extensão do Problema da Mochila, em que os itens solicitados são divididos em classes, de modo que a mochila deve ser subdividida em compartimentos, os quais têm capacidades limitadas e são carregados com itens da mesma classe. Além disso, a construção de um compartimento tem um custo fixo e ocasiona uma perda no espaço da mochila. O objetivo consiste em maximizar a soma dos valores dos itens, descontado o custo fixo de inclusão de compartimentos. Neste trabalho, são abordados dois métodos de solução. A primeira abordagem é uma heurística, que consiste na combinação de duas heurísticas da literatura. A segunda abordagem é o método Geração de Colunas, que além de fornecer um novo limitante superior para o Problema da Mochila Compartimentada, ao final do método o problema mestre foi resolvido com as variáveis definidas como inteiras, obtendo uma solução factível. Em ambos os métodos, o modelo não-linear é decomposto em dois modelos lineares, no qual, um gera compartimentos e o outro os seleciona. Os resultados obtidos com as duas abordagens foram comparados com um limitante superior e se mostraram bastante satisfatórios / The Compartmentalized Knapsack Problem is an extension of the classical Knapsack Problem, where the ordered items are partitioned into classes, in such way that the knapsack must be divided into compartments, each one having limited capacity. In addition, the building of a compartment has a fixed cost and involves a loss of the overall capacity. The objective is to maximize the sum of the items utility value, minus the fixed costs of the compartments. This dissertation presents two solving methods. The first approach is a heuristic method, which is a combination of two heuristics from the literature. The second approach is a Column Generation method, that apart from it gives a new upper bound to the Compartmentalized Knapsack Problem, in the end of the method the master problem was solved with the variables defined as integer, that supplies a feasible solution. In both methods, the mathematical non linear model is decomposed into two linear models, one generates the compartments, and the other selects them to compose the knapsack. The results obtained with these two approaches were compared with an upper bound and they showed very efficient

Dentro da classe de problemas de corte e empacotamento, existem os problemas de corte de itens irregulares (não-circulares e não-retangulares), os quais visam determinar um arranjo ótimo de objetos irregulares menores (itens), sem sobreposição, dentro de objetos maiores (recipientes) a fim de atender a uma demanda. Possuem grande importância prática, uma vez que surgem em vários tipos de indústrias, como a têxtil, a de móveis e a de calçados, por exemplo. Entre estes problemas, ainda temos o chamado problema de corte de itens irregulares em recipientes, no qual estes últimos são fechados, isto é, possuem dimensões fixas, podendo ser retangulares ou irregulares. Neste caso, o objetivo é arranjar todos os itens de modo a utilizar o menor número possível de recipientes. A estes problemas, uma outra restrição ainda pode ser adicionada: os recipientes podem ter defeitos, isto é, áreas onde não pode ser posicionado qualquer item, e regiões com diferentes níveis de qualidade, chamadas de zonas de qualidades, em que apenas determinados itens podem ser alocados. Neste trabalho, portanto, introduzimos um conjunto de heurísticas construtivas para a resolução do problema de corte de itens irregulares em recipientes irregulares com defeitos e zonas de qualidades. Os experimentos computacionais foram realizados utilizando um conjunto com 15 instâncias adaptadas de outro problema de corte de itens irregulares, uma vez que não encontramos instâncias disponíveis na literatura para o problema abordado neste trabalho. Os resultados mostraram que todos os métodos são capazes de resolver o problema em um tempo computacional considerado baixo, sendo que alguns deles apresentam melhor desempenho que outros. / Within the class of cutting and packing problems, there are some problems known as nesting problems, which aim to determine an optimal arrangement of smaller irregular objects (items), without overlap, inside larger objects (bins) in order to attend a demand. They have practical importance, since they arise in many types of industries, such as textiles, furniture and footwear, for example. Among these problems, we still have the so-called irregular bin packing problem in which the bins are closed, that is, they have fixed dimensions, and may be rectangular or irregular. In this case, the goal is to arrange all items in order to use the least amount of bins. To these problems, another constraint can still be added: the bins may have defects, that is, areas where no item can be placed, and different levels of quality, called quality zones, where only specific items can be allocated. In this work, therefore, we introduce a set of constructive heuristics to solve the irregular bin packing problem in which the bins have defects and quality zones. The computational experiments were carried out using a set of 15 instances adapted from another nesting problem, since we did not find instances available in the literature for the problem addressed in this work. The results showed that all methods can solve the problem in a low computational time, and also that some of them perform better than others.

Wang Jing. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2005. / Includes bibliographical references (leaves 55-59). / Abstracts in English and Chinese. / Acknowledgments --- p.i / Abstract --- p.ii / Introduction --- p.3 / Chapter 1 --- Formulation of the Problem --- p.10 / Chapter 1.1 --- Reformulated Navier-Stokes Equations --- p.10 / Chapter 1.2 --- Linearized Problems --- p.15 / Chapter 2 --- Construction of the Approximate Solution --- p.19 / Chapter 2.1 --- Two-scale Asymptotic Expansions --- p.19 / Chapter 2.2 --- Determination of Each Inner and Boundary Terms --- p.22 / Chapter 2.3 --- Truncation Terms --- p.31 / Chapter 3 --- Estimates of the Error Term of the Approximate Solution and Main Results --- p.33 / Chapter 3.1 --- Error Equations --- p.33 / Chapter 3.2 --- Energy Estimates --- p.36 / Chapter 3.2.1 --- BasicL2 Estimates --- p.36 / Chapter 3.2.2 --- Tangential Derivatives Estimates --- p.38 / Chapter 3.2.3 --- Normal Derivatives Estimates --- p.49 / Chapter 3.3 --- Pointwise Estimates --- p.52 / Bibliography --- p.55

This thesis is motivated by some of the recent results of the solvability of elliptic PDE in Lipschitz domains and the relationships between the solvability of different boundary value problems. The parabolic setting has received less attention, in part due to the time irreversibility of the equation and difficulties in defining the appropriate analogous time-varying domain. Here we study the solvability of boundary value problems for second order linear parabolic PDE in time-varying domains, prove two main results and clarify the literature on time-varying domains. The first result shows a relationship between the regularity and Dirichlet boundary value problems for parabolic equations of the form Lu = div(A∇u)−ut = 0 in Lip(1, 1/2) time-varying cylinders, where the coefficient matrix A = [aij(X, t)] is uniformly elliptic and bounded. We show that if the Regularity problem (R)p for the equation Lu = 0 is solvable for some 1 < p < then the Dirichlet problem (D*) 1 p, for the adjoint equation L*v = 0 is also solvable, where p' = p/(p − 1). This result is analogous to the one established in the elliptic case. In the second result we prove the solvability of the parabolic Lp Dirichlet boundary value problem for 1 < p ≤ ∞ for a PDE of the form ut = div(A∇u)+B ·∇u on time-varying domains where the coefficients A = [aij(X, t)] and B = [bi(X, t)] satisfy a small Carleson condition. This result brings the state of affairs in the parabolic setting up to the current elliptic standard. Furthermore, we establish that if the coefficients of the operator A and B satisfy a vanishing Carleson condition, and the time-varying domain is of VMO-type then the parabolic Lp Dirichlet boundary value problem is solvable for all 1 < p ≤ ∞. This is related to elliptic results where the normal of the boundary of the domain is in VMO or near VMO implies the invertibility of certain boundary operators in Lp for all 1 < p < ∞. This then (using the method of layer potentials) implies solvability of the Lp boundary value problem in the same range for certain elliptic PDE. We do not use the method of layer potentials, since the coefficients we consider are too rough to use this technique but remarkably we recover Lp solvability in the full range of p's as the elliptic case. Moreover, to achieve this result we give new equivalent and localisable definitions of the appropriate time-varying domains.

Dentro da classe de problemas de corte e empacotamento, existem os problemas de corte de itens irregulares (não-circulares e não-retangulares), os quais visam determinar um arranjo ótimo de objetos irregulares menores (itens), sem sobreposição, dentro de objetos maiores (recipientes) a fim de atender a uma demanda. Possuem grande importância prática, uma vez que surgem em vários tipos de indústrias, como a têxtil, a de móveis e a de calçados, por exemplo. Entre estes problemas, ainda temos o chamado problema de corte de itens irregulares em recipientes, no qual estes últimos são fechados, isto é, possuem dimensões fixas, podendo ser retangulares ou irregulares. Neste caso, o objetivo é arranjar todos os itens de modo a utilizar o menor número possível de recipientes. A estes problemas, uma outra restrição ainda pode ser adicionada: os recipientes podem ter defeitos, isto é, áreas onde não pode ser posicionado qualquer item, e regiões com diferentes níveis de qualidade, chamadas de zonas de qualidades, em que apenas determinados itens podem ser alocados. Neste trabalho, portanto, introduzimos um conjunto de heurísticas construtivas para a resolução do problema de corte de itens irregulares em recipientes irregulares com defeitos e zonas de qualidades. Os experimentos computacionais foram realizados utilizando um conjunto com 15 instâncias adaptadas de outro problema de corte de itens irregulares, uma vez que não encontramos instâncias disponíveis na literatura para o problema abordado neste trabalho. Os resultados mostraram que todos os métodos são capazes de resolver o problema em um tempo computacional considerado baixo, sendo que alguns deles apresentam melhor desempenho que outros. / Within the class of cutting and packing problems, there are some problems known as nesting problems, which aim to determine an optimal arrangement of smaller irregular objects (items), without overlap, inside larger objects (bins) in order to attend a demand. They have practical importance, since they arise in many types of industries, such as textiles, furniture and footwear, for example. Among these problems, we still have the so-called irregular bin packing problem in which the bins are closed, that is, they have fixed dimensions, and may be rectangular or irregular. In this case, the goal is to arrange all items in order to use the least amount of bins. To these problems, another constraint can still be added: the bins may have defects, that is, areas where no item can be placed, and different levels of quality, called quality zones, where only specific items can be allocated. In this work, therefore, we introduce a set of constructive heuristics to solve the irregular bin packing problem in which the bins have defects and quality zones. The computational experiments were carried out using a set of 15 instances adapted from another nesting problem, since we did not find instances available in the literature for the problem addressed in this work. The results showed that all methods can solve the problem in a low computational time, and also that some of them perform better than others.

An isohedral tiling is a tiling of congruent polygons that are also transitive, which is to say the configuration of degrees of vertices around each face is identical. Regular tessellations, or tilings of congruent regular polygons, are a special case of isohedral tilings. Viewing these tilings as graphs in planes, both Euclidean and non-Euclidean, it is possible to pose various problems of enumeration on the respective graphs. In this paper, we investigate some near-regular isohedral tilings of triangles and quadrilaterals in the hyperbolic plane. For these tilings we enumerate vertices as classified by number of edges in the shortest path to a given origin, by combinatorially deriving their respective generating functions.

We solve initial boundary value problems with information unavailable at random time-steps. The randomly unavailable information represents asynchrony between processing elements. To approximate the initial boundary value problem, finite difference operators with summation-by-parts proper-ties and weak boundary procedures are used. Utilizing the energy method, we derive energy estimates for synchronous and asynchronous problems. The simulations show that the solutions may remain accurate and stable, even in the asynchronous case.

Mixed elliptic problems are characterised by conditions that have a discontinuity on an interface of the boundary of codimension 1. The case of a smooth interface is treated in [3]; the investigation there refers to additional interface conditions and parametrices in standard Sobolev spaces. The present paper studies a necessary structure for the case of interfaces with conical singularities, namely, corner conormal symbols of such operators. These may be interpreted as families of mixed elliptic problems on a manifold with smooth interface. We mainly focus on second order operators and additional interface conditions that are holomorphic in an extra parameter. In particular, for the case of the Zaremba problem we explicitly obtain the number of potential conditions in this context. The inverses of conormal symbols are meromorphic families of pseudo-differential mixed problems referring to a smooth interface. Pointwise they can be computed along the lines [3].

This study aims to find out the relationship among marital communication patterns, parental attitudes, internalizing and externalizing behavior problems of children. To elaborate, it is aimed to figure out whether marital communication patterns predict parental attitudes, and children internalizing and externalizing behavior problems. Furthermore, it is purposed to investigate the relationship between parental attitudes and children adjustment. Finally, mediator role of parental attitudes between marital communication patterns and children adjustment was investigated. The participants of this study consist of 189 parents of preschool children. In order to measure the variables and characteristics of participants, Demographic Information Form, Communication Patterns Questionnaire (CPQ), Parenting Styles and Dimensions Questionnaire (PSDQ), and Strengths and Difficulties Questionnaire (SDQ) are used. The results of the study revealed that higher levels of destructive communication pattern is significantly associated with higher levels of authoritarian parenting attitudes whereas higher levels of constructive communication pattern is related to lower levels of permissive parenting style. Moreover, there is positive significant relationship was found between mother reported constructive communication pattern and authoritative style. Furthermore, it was shown that mother reported authoritarian and authoritative parenting attitudes are linked to emotional problems of children. Another finding of the current study revealed that constructive communication pattern is related to prosocial behavior of children. Besides inattention problems of children was found to be associated with aggressive communication pattern and mother reported permissive parenting style. However, no significant mediation effect was found. The significance, limitations, and clinical implications were discussed in the light of related literature.

This paper presents the results of a study of dyscalculia. It is a retrospective archival study implemented with a deductive approach. On the basis of established research and theory 18 analytical categories were formulated, before a deductive thematic analysis of empirical material, consisting of journal data of 17 students investigated for dyscalculia, 14 girls (82.4%) and 3 boys (17.6%). The purpose of this study was to investigate the relationship between the concepts formulated in research on dyscalculia and actual mathematical difficulties as those found in practice of students at school. All pupils had early and long-term difficulties with mathematics, while not showing any difficulties in other subjects. Most have had an unsatisfactory learning environment. All had normal intelligence but difficulty with certain cognitive, self-regulatory and linguistic features. Difficulties persisted despite numerous and protracted relief efforts at school. The study highlights that some difficulties are more prominent than others in connection with dyscalculia. This applies particularly to working memory, automation, activity control, spatial functions, certain linguistic abilities, concentration, and executive functions. Pedagogical action adaptation had been completed for most of the students but did not show to have any noticible effect. One question that requires further research would be “ why adaptation does not give the desired effect.” / I denna uppsats redovisas resultatet av en studie av dyskalkyli. Det är en retrospektiv arkivstudie med en deduktiv ansats som genomförts. Med utgångspunkt i etablerad forskning och teoribildning formulerades 18 analytiska kategorier, före en deduktiv tematisk analys, på ett empiriskt material bestående av journaldata för 17 elever utredda med avseende på dyskalkylidiagnos, 14 flickor (82,4 %) och 3 pojkar (17,6 %). Syftet med studien var att undersöka förhållandet mellan de begrepp forskningen formulerat om dyskalkyli och faktiska matematiksvårigheter så som sådana visar sig i praktiken hos elever i skolan. Samtliga elever hade tidiga och långvariga svårigheter i matematik, men vanligen inte i andra ämnen. De flesta hade haft en otillfredsställande inlärningsmiljö. Alla hade normal intelligens men svårigheter med vissa kognitiva, självreglerande och språkliga funktioner. Svårigheterna kvarstod trots många och långvariga hjälpinsatser i skolan. Studien lyfter fram att vissa svårigheter är mer framträdande än andra i samband med dyskalkyli. Det gäller framförallt arbetsminne, automatisering, aktivitetsreglering, spatiala funktioner, vissa språkliga förmågor, koncentration och exekutiva funktioner. Pedagogisk åtgärdsanpassning hade genomförts för de flesta av eleverna men verkade inte ha haft någon större effekt. Varför åtgärdsanpassning inte ger avsedd effekt är ett problem som behöver undersökas vidare.