The speech of a person speaking in a noisy environment can be enhanced through electronic beamforming using spatially distributed microphones. As this approach demands precise information about the microphone locations, its application is limited in places where microphones must be placed quickly or changed on a regular basis. Highly precise calibration or measurement process can be tedious and time consuming. In order to understand tolerable limits on the calibration process, the impact of microphone position error on the intelligibility is examined. Analytical expressions are derived by modeling the microphone position errors as a zero mean uniform distribution. Experiments and simulations were performed to show relationships between precision of the microphone location measurement and loss in intelligibility. A variety of microphone array configurations and distracting sources (other interfering speech and white noise) are considered. For speech near the threshold of intelligibility, the results show that microphone position errors with standard deviations less than 1.5cm can limit losses in intelligibility to within 10% of the maximum (perfect microphone placement) for all the microphone distributions examined. Of different array distributions experimented, the linear array tends to be more vulnerable whereas the non-uniform 3D array showed a robust performance to positional errors.

The ranking method used for testing the equivalence of two distributions has been studied for decades and is widely adopted for its simplicity. However, due to the complexity of calculations, the power of the test is either estimated by normal approximation or found when an appropriate alternative is given. Here, via a Finite Markov chain imbedding (FMCI) technique, we are able to establish the marginal and joint distributions of the rank statistics considering the shift and scale parameters, respectively and simultaneously, under two continuous distribution functions. Furthermore, the procedures of distribution equivalence tests and their power functions are discussed. Numerical results of a joint distribution of two rank statistics under the standard normal distribution and the powers for a sequence of alternative normal distributions with mean from -20 to 20 and standard deviation from 1 to 9 and their reciprocals are presented. In addition, we discuss the powers of the rank statistics under the Lehmann alternatives. Wallenstein et. al. (1993, 1994) discussed power via combinatorial calculations for the scan statistic against a pulse alternative; however, unless certain proper conditions are given, computational difficulties exist. Our work extends their results and provides an alternative way to obtain the distribution of a scan statistic under various alternative conditions. An efficient and intuitive expression for the distribution as well as the power of the scan statistic are introduced via the FMCI. The numerical results of the exact power for a discrete scan statistic against various conditions are presented. Powers through the finite Markov chain imbedding method and a combinatorial algorithm for a continuous scan statistic against a pulse alternative of a higher risk for a disease on a specified subinterval time are also discussed and compared.

Svenska elevers låga matematikresultat i internationella jämförelser vittnar om att det krävs förändring i skolans matematikundervisning. Vissa skolor/kommuner har utvecklat matematikplaner i syfte att höja måluppfyllelsen. Syftet med studien är att få insikt i två av dessa matematikplaner och pedagogers tankar om hur de används och gynnar SUM-elever.   I den teoretiska bakgrunden belyses Bedömning, God undervisning och Samverkan kopplat till Systematiskt kvalitetsarbete, och i relation till SUM-elever, vilka är i fokus. Studien har en kvalitativ ansats och är en fallstudie av två matematikplaner och hur de används. Gruppintervjuer valdes som datainsamlingsmetod.   Resultatet visar att användandet av matematikplanerna och konsekvenserna av dem är relativt lika trots olikheterna i deras innehåll. Pedagogernas uppfattning är att planerna är ett stöd för att höja måluppfyllelsen för alla elever, inklusive SUM-elever, vilket också är syftet med ett Systematiskt kvalitetsarbete. / Swedish students' low mathematics result, in comparisons to international results, shows that it requires change in school mathematics teaching. Some schools/municipalities have developed mathematic plans in order to raise achievement. The purpose of the study is to gain insight into two of these mathematic plans and pedagogues’ thoughts about their use and benefits for SEM-students.   Theoretical backgrounds highlight Assessment, Good Teaching and Collaboration, related to Systematic Quality Work and SEM-students, whom are in focus. The study has a qualitative approach and is a case study of two mathematic plans and how they are used. Group interviews are chosen as the data collection method.   The result shows that the use of mathematic plans and the consequences of them are relatively similar despite the differences in structure and content. The pedagogues’ perception is that the plans are a support to raise the level of achievements for all students, including SEM-students, which is also the purpose of Systematic Quality Work.

In many applications that deal with high dimensional data, it is important to not store the high dimensional object itself, but its representation in a data sparse way. This aims to reduce the storage and computational complexity. There is a general scheme for representing tensors with the help of sums of elementary tensors, where the summation structure is defined by a graph/network. This scheme allows to generalize commonly used approaches in representing a large amount of numerical data (that can be interpreted as a high dimensional object) using sums of elementary tensors. The classification does not only distinguish between elementary tensors and non-elementary tensors, but also describes the number of terms that is needed to represent an object of the tensor space. This classification is referred to as tensor network (format). This work uses the tensor network based approach and describes non-linear block Gauss-Seidel methods (ALS and DMRG) in the context of the general tensor network framework. Another contribution of the thesis is the general conversion of different tensor formats. We are able to efficiently change the underlying graph topology of a given tensor representation while using the similarities (if present) of both the original and the desired structure. This is an important feature in case only minor structural changes are required. In all approximation cases involving iterative methods, it is crucial to find and use a proper initial guess. For linear iteration schemes, a good initial guess helps to decrease the number of iteration steps that are needed to reach a certain accuracy, but it does not change the approximation result. For non-linear iteration schemes, the approximation result may depend on the initial guess. This work introduces a method to successively create an initial guess that improves some approximation results. This algorithm is based on successive rank 1 increments for the r-term format. There are still open questions about how to find the optimal tensor format for a given general problem (e.g. storage, operations, etc.). For instance in the case where a physical background is given, it might be efficient to use this knowledge to create a good network structure. There is however, no guarantee that a better (with respect to the problem) representation structure does not exist.

The scalar mesons have caused much debate amongst hadronic physicists for many years. Even today the number of scalars is hotly contested, and there is almost no agreement on the composition of any of the experimentally observed states, except perhaps for the K*(_0) (1430). This thesis attempts to shed light on both of these problems via the application of analyticity to two different quantities. Recently a number of authors have proposed the existence of a light, strange, scalar meson known as the k. We perform a direct search of the best available πK scattering data to determine whether or not this resonance exists. This is done by constructing contour integrals from these data and determining the number of poles present inside the contour. We do not need to model either the internal dynamics of the state nor the form of the background scattering. The number of poles found tells us the number of resonances present and their positions allow us to estimate the resonance parameters. We find that there is only one resonance in scalar πK scattering below 1800 MeV and this is identified with the established K*(_0)(1430). We find no evidence for the k. Secondly, applying Cauchy's Theorem to the vacuum polarisation function leads to a relation between experimental and theoretical integrals known as a Finite Energy Sum Rule (FESR). FESRs are used to explore the scalar, isoscalar non-strange current and allow us to determine which of the experimentally observed scalar, isoscalar mesons is most likely to be the uũ + dd state. We find that the lightest scalar, isoscalar uũ dd state is not the fo(980) as suggested by some authors, but is rather the light, broad object known as the fo(400 - 1200). We are also able to estimate the average light quark mass and find m(_q)(l GeV(^2)) = 4.7 ± 0.9 MeV which is consistent with the recent estimates of this quantity from unquenched lattice QCD.

We will survey some of the major directions of research in arithmetic combinatorics and their connections to other fields. We will then discuss three new results. The first result will generalize a structural theorem from Balog and Szemerédi. The second result will establish a new tool in incidence geometry, which should prove useful in attacking combinatorial estimates. The third result evolved from the famous sum-product problem, by providing a partial categorization of bivariate polynomial set functions which induce exponential expansion on all finite sets of real numbers.

The author's Habilitationsschrift--Universität Düsseldorf. / Some text in French. Includes bibliographical references and indexes.

Στην παρούσα εργασία σχεδιάστηκε και εφαρμόστηκε ένας νέος αλγόριθμος χειρισμού των ηλεκτροστατικών αλληλεπιδράσεων. Οι αλληλεπιδράσεις ηλεκτροστατικής φύσεως αποτελούν αντικείμενο εκτενούς μελέτης στον ερευνητικό κλάδο των μοριακών προσομοιώσεων. Ιδιαίτερα σε βιολογικά μοριακά συστήματα, τα οποία αποτελούνται από υδατικά διαλύματα πολυηλεκτρολυτών, οι ηλεκτροστατικές αλληλεπιδράσεις κυριαρχούν. Η ευρέως διαδεδομένη μέθοδος άθροισης κατά Ewald η οποία χαρακτηρίζεται για την ακρίβεια της, είναι ιδιαίτερα απαιτητική σε υπολογιστικό χρόνο δεδομένου ότι κλιμακώνεται ως Ν2, όπου Ν ο συνολικός αριθμός φορτίων του συστήματος. Στην παρούσα εργασία περιγράφεται η προσεγγιστική μέθοδος σφαιρικής αποκοπής για την περίπτωση πολυηλεκτρολυτών. Έως σήμερα, η μέθοδος της σφαιρικής αποκοπής έχει εφαρμοστεί σε μοριακά συστήματα ιοντικών κρυστάλλων. Σύμφωνα με τη μέθοδο αυτή, εισάγοντας μια σφαιρική αποκοπή στον υπολογισμό του ηλεκτροστατικού δυναμικού και παράλληλα επιτυγχάνοντας ηλεκτροουδετερότητα του υπό εξέταση σφαιρικού συστήματος, πραγματοποιείται μείωση του υπολογιστικού χρόνου σε δίχως σημαντικές απώλειες σε ακρίβεια. Στην παρούσα εργασία σχεδιάστηκε ο αλγόριθμος της σφαιρικής αποκοπής για δύο κατηγορίες μορίων: τους πολυηλεκτρολύτες χωρίς ενδομοριακές αλληλεπιδράσεις όπως είναι το μόριο του νερού και τους πολυηλεκτρολύτες με ενδομοριακές αλληλεπιδράσεις όπως είναι τα μόρια CiEj των αλκυλικών αιθέρων πολυ-(οξυ-αιθυλενίου). Επιπρόσθετα, επεκτείναμε τη μέθοδο άθροισης κατά Ewald για την εφαρμογή της σε πολυηλεκτρολύτες, χωρίς και με ενδομοριακές αλληλεπιδράσεις προκειμένου να προχωρήσουμε σε σύγκριση της ακριβής μεθόδου Ewald με τα αποτελέσματα του νέου αλγορίθμου της σφαιρικής αποκοπής. Συγκρίνοντας τα αριθμητικά αποτελέσματα των δύο μεθόδων για τα δύο διαφορετικά είδη πολυηλεκτρολυτών ( H2Ο και CiEj ) από ατομιστικές προσομοιώσεις μοριακής δυναμικής οδηγηθήκαμε σε πλήρη συμφωνία των δύο μεθόδων γεγονός που επιβεβαιώνει την εγκυρότητας της νέας μεθόδου. Επίσης, μέσω των αποτελεσμάτων των προσομοιώσεων μοριακής δυναμικής μελετήθηκαν οι θερμοδυναμικές, δομικές και δυναμικές ιδιότητες των δύο συστημάτων. Η παρούσα εργασία είναι δομημένη ως εξής: Στο πρώτο κεφάλαιο γίνεται μια εισαγωγή στο θεωρητικό υπόβαθρο προσομοιώσεων μοριακής δυναμικής. Στο δεύτερο κεφάλαιο περιγράφονται οι μέθοδοι χειρισμού των ηλεκτροστατικών αλληλεπιδράσεων που συναντούμε έως σήμερα στη βιβλιογραφία. Στη συνέχεια, στο κεφάλαιο 3 περιγράφεται ο αλγόριθμος της σφαιρικής αποκοπής. Στο τέταρτο κεφάλαιο παρουσιάζονται τα αποτελέσματα από τις προσομοιώσεις μοριακής δυναμικής με τις μεθόδους σφαιρικής αποκοπής και άθροισης κατά Ewald. / -

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / Neste trabalho calculamos os fatores de forma e constantes de acoplamento para os vértices B*sBK, B*BsK e BsBK* usando as Regras de Soma da Cromodinâmica Quântica (QCD). Ainda estão incluídos os diagramas não perturbativos. Nós usamos a técnica de considerar dois mésons fora da camada de massa para obter dois fatores de forma diferentes a fim de diminuir as incertezas. Os cálculos das incertezas foram incluídos neste trabalho. / In this work, we calculate the Form Factors and the Coupling Constants for the vertices B*sBK, BsB*K and BsBK* using the QCD Sum Rules. We use the technique of considering two mesons of shell to obtaining two differents form factors in order to give less uncertainty to the obtaining of the coupling constant. The evaluation of the uncertaints were included in this work.

Neste trabalho são obtidos os coeficientes do modelo da Soma-Ponderada-dos-gases-cinza (WSGG) a partir do banco de dados HITEMP 2010, permitindo o uso do modelo com os dados mais precisos disponíveis atualmente. Neste trabalho também se faz uma comparação dos valores de emitância total obtidos a partir do modelo WSGG com valores benchmark, obtidos nesse trabalho, mostrando uma excelente concordância. Com os coeficientes obtidos, problemas unidimensionais de transferência de calor radiante são resolvidos de modo a comparar a solução obtida pelo modelo WSGG com a solução obtida pela integração LBL (solução benchmark). Nas comparações, diferentes perfis de temperatura, comprimentos de trajeto, gradientes de temperatura e concentrações de espécies são utilizadas. Em todos os casos é possível verificar uma boa concordância entre os resultados WSGG e LBL. Para comparações com perfil de temperatura parabólico, verifica-se erros locais abaixo de 8%. Para perfis de temperatura cossenoidais, é possível observar erros de até 18% para alguns casos, porém com erros médios menores que 1,6%. / In this work the coefficients for the Weighted Sum-of-Gray-Gases model (WSGG) are determined from HITEMP 2010 database, allowing the use of the model with the most accurate data available nowadays. This study also makes a comparison of the total emittance values obtained from the model with benchmark values, obtained in this work, showing an excellent agreement. With the obtained coefficients, one-dimensional radiant heat transfer problems are solved in order to compare the solution obtained by the WSGG model with the solution obtained by the LBL integration (benchmark solution). In the comparisons, different temperature profiles, path lengths, temperature gradients and species concentrations are used. In all cases it is possible to verify the good agreement of the WSGG and LBL results. For comparisons with parabolic temperature profile, the local error is below 8%. For cosine temperature profile, the local error is about 18% for some cases, but with average errors less than 1,6%.