Darbe apžvelgiama trimačio pakavimo problemos tipologija. Nagrinėjama trimečio konteinerių pakavimo problema ir jos sprendimo būdai. Pateikiama šakos ir ribos, bei tabu paieškos algoritmų formulavimas ir jų rezultatų analizė. / The paper gives an overview of three-dimensional packing problem typology. There are investigating issue of container packing problem and its solutions. Branch and bound, TSpack algorithms formulation and analysis of their results.

The problems we study in this thesis arise in computer science, extremal set theory and quantum computing. The first common feature of these problems is that each can be reduced to characterizing the independent sets of maximum size in a suitable graph. A second common feature is that the size of these independent sets meets an eigenvalue bound due to Delsarte and Hoffman. Thirdly, the graphs that arise belong to association schemes that have already been studied in other contexts. Our first problem involves covering arrays on graphs, which arises in computer science. The goal is to find a smallest covering array on a given graph <i>G</i>. It is known that this is equivalent to determining whether <i>G</i> has a homomorphism into a <i>covering array graph</i>, <i>CAG(n,g)</i>. Thus our question: Are covering array graphs cores? A covering array graph has as vertex set the partitions of <i>{1,. . . ,n}</i> into <i>g</i> cells each of size at least <i>g</i>, with two vertices being adjacent if their meet has size <i>g²</i>. We determine that <i>CAG(9,3)</i> is a core. We also determine some partial results on the family of graphs <i>CAG(g²,g)</i>. The key to our method is characterizing the independent sets that meet the Delsarte-Hoffman bound---we call these sets <i>ratio-tight</i>. It turns out that <i>CAG(9,3)</i> sits inside an association scheme, which will be useful but apparently not essential. We then turn our attention to our next problem: the Erdos-Ko-Rado theorem and its <i>q</i>-analogue. We are motivated by a desire to find a unifying proof that will cover both versions. The EKR theorem gives the maximum number of pairwise disjoint <i>k</i>-sets of a fixed <i>v</i>-set, and characterizes the extremal cases. Its <i>q</i>-analogue does the same for <i>k</i>-dimensional subspaces of a fixed <i>v</i>-dimensional space over <i>GF(q)</i>. We find that the methods we developed for covering array graphs apply to the EKR theorem. Moreover, unlike most other proofs of EKR, our argument applies equally well to the <i>q</i>-analogue. We provide a proof of the characterization of the extremal cases for the <i>q</i>-analogue when <i>v=2k</i>; no such proof has appeared before. Again, the graphs we consider sit inside of well-known association schemes; this time the schemes play a more central role. Finally, we deal with the problem in quantum computing. There are tasks that can be performed using quantum entanglement yet apparently are beyond the reach of methods using classical physics only. One particular task can be solved classically if and only if the graph &Omega;(<i>n</i>) has chromatic number <i>n</i>. The graph &Omega;(<i>n</i>) has as vertex set the set of all <i>?? 1</i> vectors of length <i>n</i>, with two vertices adjacent if they are orthogonal. We find that <i>n</i> is a trivial upper bound on the chromatic number, and that this bound holds with equality if and only if the Delsarte-Hoffman bound on independent sets does too. We are thus led to characterize the ratio-tight independent sets. We are then able to leverage our result using a recursive argument to show that <i>&chi;</i>(&Omega;(<i>n</i>)) > <i>n</i> for all <i>n</i> > 8. It is notable that the reduction to independent sets, the characterization of ratio-tight sets, and the recursive argument all follow from different proofs of the Delsarte-Hoffman bound. Furthermore, &Omega;(<i>n</i>) also sits inside a well-known association scheme, which again plays a central role in our approach.

The present study provides a description of the standardization process of Persian orthography since the introduction of the Arabic alphabet, with a focus on this process in modern times (1850-2000). Using theories related to orthography standardization as its background, this work seeks an explanation for the prolonged standardization process of Persian orthography, and presents the frameworks within which this standardization has been carried out. The most recent state of Persian orthography is presented through an investigation of the current attitudes towards the problems of Persian orthography and possible frameworks for a potential reform, as well as through an investigation of the current tendencies in the manner of presenting different orthographic parameters within Persian contemporary texts. How and by whom the orthography of today’s Persian texts is governed is another aspect to be examined here. The most important conclusion to be drawn from the present study is that there is a strong tendency towards approving reform proposals that can be integrated with the present orthography, and maintain the present appearance of Persian orthography as much as possible. One of the main reasons behind this tendency is the concern of an interruption in cultural continuity in the event of an alphabet reform or any other drastic change in the present appearance of the orthography. This concern takes into account the political, social, cultural, structural, and economic conditions in Iran, as well as the complexity of language planning projects.

The problem of this study was to determine if study habits can be used to predict academic achievement. The purpose of this study was to determine the relationships between selected study skill habits and attitudes and achievement of secondary students in English, mathematics, and spelling. The sample for this study consisted of 82 secondary school students participating in Upward Bound programs at two universities in the north Texas area in a six week period during the summer of 1988. Eighteen different high schools were represented in the study. The sizes of the schools ranged from small to very large. Instruments used were the Survey of Study Habits and Attitudes, (SSHA) the Stanford Test of Academic Skills, (TASK), and the Otis-Lennon Mental Abilities Test (OLMAT). The statistical analysis indicated that the four subscores of the SSHA are not accurate predictors of academic achievement. However, some of the correlations among the subscores for the SSHA and the TASK were significant. Most noteable of these were work methods and mathematics, teacher acceptance and mathematics, and work methods and spelling. The recommendation is made that the SSHA should not be used to predict academic achievement in Upward Bound programs. Improving study habits and attitudes should be addressed as a method of refining academic programs, not of predicting academic achievement.

The development of an analytical method for the determination of total organic-bound chlorine (TOCl) produced during the chlorination of municipal wastewater effluents is presented. Sewage effluent from the Denton, Texas municipal treatment plant was chlorinated at high chlorine doses (1000 - 4000 ppm), as well as typical treatment levels. Chlororganics present in the wastewater, before and after chlorination, were concentrated by adsorption on Amberlite XAD-2 macroreticular resin, followed by elution with diethyl ether. After concentration, the extracts were analyzed for TOC1 by microcoulometry. Analysis of wastewater extracts revealed the production of substantial amounts of new chlorinated organics when effluents were treated with chlorine. The method shows good precision and estimated accuracy is favorable.

L’objet du travail est d’étudier les prolongements de sous-copules. Un cas important de l’utilisation de tels prolongements est l’estimation non paramétrique d’une copule par le lissage d’une sous-copule (la copule empirique). Lorsque l’estimateur obtenu est une copule, cet estimateur est un prolongement de la souscopule. La thèse présente au chapitre 2 la construction et la convergence uniforme d’un estimateur bona fide d’une copule ou d’une densité de copule. Cet estimateur est un prolongement de type copule empirique basé sur le lissage par le produit tensoriel de fonctions de répartition splines. Le chapitre 3 donne la caractérisation de l’ensemble des prolongements possibles d’une sous-copule. Ce sujet a été traité par le passé; mais les constructions proposées ne s’appliquent pas à la dépendance dans des espaces très généraux. Le chapitre 4 s’attèle à résoudre le problème suivant posé par [Carley, 2002]. Il s’agit de trouver la borne supérieure des prolongements en dimension 3 d’une sous-copule de domaine fini. / The extension of subcopulas is an important domain. One of possible applications is the nonparametric estimation of a copula: it consists of the smoothing of a subcopula (the empirical copula) while preserving the copulas properties. In Chapter 2, we present an extension of the empirical copula based on the tensor product of splines functions. Our estimators are bona fide estimators of the copula. Chapter 3 tackles the problem of finding all possible extensions of a given subcopula. This subject has been treated in the literature but these characterizations do not apply on very general spaces. Chapter 4 deals with the following problem: finding the expression of the upper bound of the extensions of a finite subcopula in dimension 3.

Durant cette thèse, nous avons principalement travaillé sur deux sujets liés à l'analyse de la performance GPU (Graphics Processing Unit - Processeur graphique). Dans un premier temps, nous avons développé une méthode analytique et un outil d'estimation temporel (TEG) pour prédire les performances d'applications CUDA s’exécutant sur des GPUs de la famille GT200. Cet outil peut prédire les performances avec une précision approchant celle des outils précis au cycle près. Dans un second temps, nous avons développé une approche pour estimer la borne supérieure des performances d'une application GPU, en se basant sur l'analyse de l'application et de son code assembleur. Avec cette borne, nous connaissons la marge d'optimisation restante, et nous pouvons décider des efforts d'optimisation à fournir. Grâce à cette analyse, nous pouvons aussi comprendre quels paramètres sont critiques à la performance. / In this thesis work, we have mainly worked on two topics of GPU performance analysis. First, we have developed an analytical method and a timing estimation tool (TEG) to predict CUDA application's performance for GT200 generation GPUs. TEG can predict GPU applications' performance in cycle-approximate level. Second, we have developed an approach to estimate GPU applications' performance upper bound based on application analysis and assembly code level benchmarking. With the performance upper bound of an application, we know how much optimization space is left and can decide the optimization effort. Also with the analysis we can understand which parameters are critical to the performance.

L’optimisation sans dérivées (OSD) a connu un regain d’intérêt ces dernières années, principalement motivée par le besoin croissant de résoudre les problèmes d’optimisation définis par des fonctions dont les valeurs sont calculées par simulation (par exemple, la conception technique, la restauration d’images médicales ou de nappes phréatiques).Ces dernières années, un certain nombre de méthodes d’optimisation sans dérivée ont été développées et en particulier des méthodes fondées sur un modèle de région de confiance se sont avérées obtenir de bons résultats.Dans cette thèse, nous présentons un nouvel algorithme de région de confiance, basé sur l’interpolation, qui se montre efficace et globalement convergent (en ce sens que sa convergence vers un point stationnaire est garantie depuis tout point de départ arbitraire). Le nouvel algorithme repose sur la technique d’auto-correction de la géométrie proposé par Scheinberg and Toint (2010). Dans leur théorie, ils ont fait avancer la compréhension du rôle de la géométrie dans les méthodes d’OSD à base de modèles. Dans notre travail, nous avons pu améliorer considérablement l’efficacité de leur méthode, tout en maintenant ses bonnes propriétés de convergence. De plus, nous examinons l’influence de différents types de modèles d’interpolation sur les performances du nouvel algorithme.Nous avons en outre étendu cette méthode pour prendre en compte les contraintes de borne par l’application d’une stratégie d’activation. Considérer une méthode avec ensemble actif pour l’optimisation basée sur des modèles d’interpolation donne la possibilité d’économiser une quantité importante d’évaluations de fonctions. Il permet de maintenir les ensembles d’interpolation plus petits tout en poursuivant l’optimisation dans des sous-espaces de dimension inférieure. L’algorithme résultant montre un comportement numérique très compétitif. Nous présentons des résultats sur un ensemble de problèmes-tests issu de la collection CUTEr et comparons notre méthode à des algorithmes de référence appartenant à différentes classes de méthodes d’OSD.Pour réaliser des expériences numériques qui intègrent le bruit, nous créons un ensemble de cas-tests bruités en ajoutant des perturbations à l’ensemble des problèmes sans bruit. Le choix des problèmes bruités a été guidé par le désir d’imiter les problèmes d’optimisation basés sur la simulation. Enfin, nous présentons des résultats sur une application réelle d’un problème de conception de forme d’une aile fourni par Airbus. / Derivative-free optimization (DFO) has enjoyed renewed interest over the past years, mostly motivated by the ever growing need to solve optimization problems defined by functions whose values are computed by simulation (e.g. engineering design, medical image restoration or groundwater supply).In the last few years, a number of derivative-free optimization methods have been developed and especially model-based trust-region methods have been shown to perform well.In this thesis, we present a new interpolation-based trust-region algorithm which shows to be efficient and globally convergent (in the sense that its convergence is guaranteed to a stationary point from arbitrary starting points). The new algorithm relies on the technique of self-correcting geometry proposed by Scheinberg and Toint [128] in 2009. In their theory, they advanced the understanding of the role of geometry in model-based DFO methods, in our work, we improve the efficiency of their method while maintaining its good theoretical convergence properties. We further examine the influence of different types of interpolation models on the performance of the new algorithm.Furthermore, we extended this method to handle bound constraints by applying an active-set strategy. Considering an active-set method in bound-constrained model-based optimization creates the opportunity of saving a substantial amount of function evaluations. It allows to maintain smaller interpolation sets while proceeding optimization in lower dimensional subspaces. The resulting algorithm is shown to be numerically highly competitive. We present results on a test set of smooth problems from the CUTEr collection and compare to well-known state-of-the-art packages from different classes of DFO methods.To report numerical experiments incorporating noise, we create a test set of noisy problems by adding perturbations to the set of smooth problems. The choice of noisy problems was guided by a desire to mimic simulation-based optimization problems. Finally, we will present results on a real-life application of a wing-shape design problem provided by Airbus.

The subject of the present thesis are some aspects of impurities affecting mesoscopic systems with regard to their topological properties and related effects like Majorana fermions and quantized conductance. A focus is on two-dimensional systems including both topological insulators and superconductors. First, the question of whether individual nonmagnetic impurities can induce zero-energy states in time-reversal invariant superconductors from Altland-Zirnbauer (AZ) symmetry class DIII is addressed, and a class of symmetries which guarantee the existence of such states for a specific value of the impurity strength is defined. These general results are applied to the time-reversal invariant p-wave phase of the doped Kitaev-Heisenberg model, where it is also demonstrated how a lattice of impurities can drive a topologically trivial system into the nontrivial phase. Second, the result about the existence of zero-energy impurity states is generalized to all AZ symmetry classes. This is achieved by considering, for general Hamiltonians H from the respective symmetry classes, the “generalized roots of det H”, which subsequently are used to further explore the opportunities that lattices of nonmagnetic impurities provide for the realization of topologically nontrivial phases. The 1d Kitaev chain model, the 2d px + ipy superconductor, and the 2d Chern insulator are considered to show that impurity lattices generically enable topological phase transitions and, in the case of the 2d models, even provide access to a number of phases with large Chern numbers. Third, elastic backscattering in helical edge modes caused by a magnetic impurity with spin S and random Rashba spin-orbit coupling is investigated. In a finite bias steady state, the impurity induced resistance is found to slightly increase with decreasing temperature for S > 1/2. Since the underlying backscattering mechanism is elastic, interference between different scatterers can explain reproducible conductance fluctuations. Thus, the model is in agreement with central experimental results on edge transport in 2d topological insulators.

The South African government spends huge sums of funds on schools with an aim to redress past inequalities. Schools receive resource budget allocations to exclusively procure learning materials to ensure that the government’s aim is realised. This study examines availability and enactment of learning materials to enhance effective curriculum delivery. Four township public ordinary primary schools participated in this study. Focus was mainly on Grade 3 home language lessons. I used the case study methods to interview one teacher from each school and scrutinized their documents to establish what learning materials they have in their possession. Additionally I observed and analysed three lessons per educator. Analysis across the cases reveals different collections and variations in usage of learning materials. The former covers the standard, mix and match, and limited collections. Whereas the latter refers to the textbook bound, productive blend and the haphazard approaches. Significantly, the study also explored principles in line with the “ideal teacher”- under which desired results can be achieved.