An e-pseudovariety is a class of finite regular semigroups closed under the taking of homomorphic images, regular subsemigroups and finite direct products. Chapter One consists of a survey of those results from algebraic semigroup theory, universal algebra and lattice theory which are used in the following two chapters. In Chapter Two, a theory of generalised existence varieties is developed. A generalised existence variety is a class of regular semigroups closed under the taking of homomorphic images, regular subsemigroups, finite direct products and arbitrary powers. Equivalently, a generalised e-variety is the union of a directed family of existence varieties. It is demonstrated that a class of finite regular semigroups is an e-pseudovariety if and only if the class consists only of the finite members of some generalised existence variety. The relationship between certain lattices of e-pseudovarieties and generalised existence varieties is explored and a usefu l complete surjective lattice homomorphism is found. A study of complete congruences on lattices of existence varieties and e-pseudovarieties forms Chapter Three. In particular it is shown that a certain meet congruence, whose description is relatively simple, can be extended to yield a complete congruence on a lattice of e-pseudovarieties of finite regular semigroups. Ultimately, theorems describing the method of construction of all complete congruences of lattices of e-pseudovarieties whose members are finite E-solid or locally inverse regular semigroups are proved.

<p>This thesis is a survey of the field of languages over infinite sequences. There is active research going on in this field, during the last year several new results where published. </p><p>We investigate the language containment problem for infinite sequences, with focus on complementation of Büchi automata. Our main focus is on the approach with alternating automata by Kupferman&Vardi. The language containment problem has been proved to be in EXPSPACE. We identify some cases when we can avoid the exponential blow-up by taking advantage of properties of the input automaton. </p><p>Some of the algorithms we explain are also implemented in a Sicstus Prolog library.</p>

Constructive methods for obtaining the regular grammar counterparts for some sub-classes of the context free grammars (cfg) have been investigated by many researchers. An important class of grammars for which this is always possible is the one-letter cfg. We show in this paper a new constructive method for transforming arbitrary one-letter cfg to an equivalent regular expression of star-height 0 or 1. Our new result is considerably simpler than a previous construction by Leiss, and we also propose a new normal form for a regular expression with single-star occurrence. Through an alphabet factorization theorem, we show how to go beyond the one-letter cfg in a straight-forward way. / Singapore-MIT Alliance (SMA)

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The first part of this thesis studies tail probabilities forelliptical distributions and probabilities of extreme eventsfor multivariate stochastic processes. It is assumed that thetails of the probability distributions satisfy a regularvariation condition. This means, roughly speaking, that thereis a non-negligible probability for very large or extremeoutcomes to occur. Such models are useful in applicationsincluding insurance, finance and telecommunications networks.It is shown how regular variation of the marginals, or theincrements, of a stochastic process implies regular variationof functionals of the process. Moreover, the associated tailbehavior in terms of a limit measure is derived. The second part of the thesis studies problems related toparameter estimation in stochastic models with long memory.Emphasis is on the estimation of the drift parameter in somestochastic differential equations driven by the fractionalBrownian motion or more generally Volterra-type processes.Observing the process continuously, the maximum likelihoodestimator is derived using a Girsanov transformation. In thecase of discrete observations the study is carried out for theparticular case of the fractional Ornstein-Uhlenbeck process.For this model Whittle’s approach is applied to derive anestimator for all unknown parameters.

This thesis focuses on stochastic processes and some of their properties are investigated which are necessary to determine the tools, the extremal index and the extremogram. Both mathematical tools measure extremal dependency within random time series. Two different models are introduced and related properties are discussed. The probability function of the Agent based model is surveyed explicitly and strong stationarity is proven. Data sets for both processes are simulated and clustering of the data is investigated with two different methods. Finally an estimation of the extremogram is used to interpret dependency of extremes within the data.

Abstract   The purpose of this study was to examine how teachers in regular classrooms include pupils with special educational needs. I also wanted to find out what support teachers get of special education teachers, and the teaching perspective the teachers have when they work whit pupils. The teachers that have been interviewed and observed in this study work in regular classes.   This report is a qualitative study based on interviews and observations whit four teachers. The results indicate that the teachers are conscious of how they teach and their teaching strategies. The teachers agree that all students should be included in regular education, because learning occurs in the interaction between individuals. No one should be excluded from their regular classroom. But for students with special needs to receive an equal education, there should be more resources in the classroom. Special educators should be more involved in the regular teaching, to create conditions to a school for all pupils.     Keywords: Inclusion, pupils whit special educational needs, regular classroom teaching, special education, teaching strategies, a school for all.

Finite difference and finite element methods exhibit first order convergence when applied to static interface problems where the grid and interface are not aligned. Although modified and unstructured grid methods would address the issue of misalignment for finite elements, application to large models of stratified media, such as those encountered in exploration geophysics, may require not only manual mesh manipulation but also more degrees of freedom than are ultimately necessary to resolve the solution. Instead using fitted or otherwise modified grids, this thesis details an improvement to an existing upscaling method that incorporates fine-scale variations of material properties by composing standard piecewise linear basis functions with a specific type of harmonic map. This technique requires that the problem domain be discretized using two meshes: one fine mesh where the harmonic map is computed to resolve fine-scale structures, and a coarse mesh where the solution to the problem is approximated. The implementation of this method in the literature restricts these composite basis functions to triangular elements in 2D leading to a non-conforming finite element method and suboptimal convergence. However, the support of these basis functions in harmonic coordinates is triangular. I present a mesh-mesh intersection algorithm that exploits this alternative representation to determine the true support of the composite basis functions in terms of the fine mesh. The result is a conforming, high-resolution finite element basis that is associated with the original coarse mesh nodes. Leveraging this fine scale information, I develop a new finite element matrix assembly algorithm. Knowing the shape of the basis support leads naturally to an integration method for computing the finite element matrix entries that is exact up to the accuracy of the harmonic map approximation. This new conforming method is shown to improve the accuracy of solutions to elliptic PDE with discontinuous coefficients on coarse, regular grids.

The purpose of this study is to do a comparison between luxurious fashion stores and normal/regular ones, describe the differences in terms of the store design and discuss the influences and their impact on the customer experience. The second purpose is to give suggestions to normal/regular fashion stores from Sweden regarding improvements that they might need to enhance the customer’s shopping experience. In order to complete this study, both primary and secondary data were collected. Primary data was collected by performing three different methods. First was an observation, which was done in both luxurious and normal/regular fashion stores. An interview was performed with the manager of H&amp;M Västerås. Last but not least method was to apply a questionnaire in order to find out the customer’s opinion concerning their shopping experience. The secondary data was gathered from Mälardalen’s University data bases and library and also from online resources. Conclusion:               The luxurious fashion stores have a unique way of displaying their garments, which gives an idea of neatness, comfort and order. They also have special services that add to the customer’s shopping experience, enhancing it. Even thought normal/regular fashion stores are different from luxurious, they give a big importance to the quality, the price and displaying their garments in a specific order. When it comes to the shopping experience customers’ encounter, most of them considered that it is important to have helpful staff, right temperature, appropriate music and light and clean environment. Overall it can be seen, that even thought they are completely different, the normal/regular fashion stores still try to offer the best experience to their customers.

The syntactic complexity of a regular language is the cardinality of its syntactic semigroup. The syntactic complexity of a subclass of the class of regular languages is the maximal syntactic complexity of languages in that class, taken as a function of the state complexity n of these languages. We study the syntactic complexity of suffix-, bifix-, and factor-free regular languages, star-free languages including three subclasses, and R- and J-trivial regular languages. We found upper bounds on the syntactic complexities of these classes of languages. For R- and J-trivial regular languages, the upper bounds are n! and ⌊e(n-1)!⌋, respectively, and they are tight for n >= 1. Let C^n_k be the binomial coefficient ``n choose k''. For monotonic languages, the tight upper bound is C^{2n-1}_n. We also found tight upper bounds for partially monotonic and nearly monotonic languages. For the other classes of languages, we found tight upper bounds for languages with small state complexities, and we exhibited languages with maximal known syntactic complexities. We conjecture these lower bounds to be tight upper bounds for these languages. We also observed that, for some subclasses C of regular languages, the upper bound on state complexity of the reversal operation on languages in C can be met by languages in C with maximal syntactic complexity. For R- and J-trivial regular languages, we also determined tight upper bounds on the state complexity of the reversal operation.