This thesis addresses three different realizations of a truly two-dimensional electron system (2DES), established at the surface of elemental semiconductors, i.e., Pt/Si(111), Au/Ge(111), and Sn/Si(111). Characteristic features of atomic structures at surfaces have been studied using scanning tunneling microscopy and low energy electron diffraction with special emphasis on Pt deposition onto Si(111). Topographic inspection reveals that Pt atoms agglomerate as trimers, which represent the structural building block of phase-slip domains. Surprisingly, each trimer is rotated by 30° with respect to the substrate, which results in an unexpected symmetry breaking. In turn, this represents a unique example of a chiral structure at a semiconductor surface, and marks Pt/Si(111) as a promising candidate for catalytic processes at the atomic scale. Spin-orbit interactions (SOIs) play a significant role at surfaces involving heavy adatoms. As a result, a lift of the spin degeneracy in the electronic states, termed as Rashba effect, may be observed. A candidate system to exhibit such physics is Au/Ge(111). Its large hexagonal Fermi sheet is suggested to be spin-split by calculations within the density functional theory. Experimental clarification is obtained by exploiting the unique capabilities of three-dimensional spin detection in spin- and angle-resolved photoelectron spectroscopy. Besides verification of the spin splitting, the in-plane components of the spin are shown to possess helical character, while also a prominent rotation out of this plane is observed along straight sections of the Fermi surface. Surprisingly and for the first time in a 2DES, additional in-plane rotations of the spin are revealed close to high symmetry directions. This complex spin pattern must originate from crystalline anisotropies, and it is best described by augmenting the original Rashba model with higher order Dresselhaus-like SOI terms. The alternative use of group-IV adatoms at a significantly reduced coverage drastically changes the basic properties of a 2DES. Electron localization is strongly enhanced, and the ground state characteristics will be dominated by correlation effects then. Sn/Si(111) is scrutinized with this regard. It serves as an ideal realization of a triangular lattice, that inherently suffers from spin frustration. Consequently, long-range magnetic order is prohibited, and the ground state is assumed to be either a spiral antiferromagnetic (AFM) insulator or a spin liquid. Here, the single-particle spectral function is utilized as a fundamental quantity to address the complex interplay of geometric frustration and electronic correlations. In particular, this is achieved by combining the complementary strengths of ab initio local density approximation (LDA) calculations, state-of-the-art angle-resolved photoelectron spectroscopy, and the sophisticated many-body LDA+DCA. In this way, the evolution of a shadow band and a band backfolding incompatible with a spiral AFM order are unveiled. Moreover, beyond nearest-neighbor hopping processes are crucial here, and the spectral features must be attributed to a collinear AFM ground state, contrary to common expectation for a frustrated spin lattice. / In der vorliegenden Arbeit werden drei unterschiedliche Beispiele für ein zweidimensionales Elektronensystem (2DES) auf der Oberfläche von Elementhalbleitern behandelt: Pt/Si(111), Au/Ge(111) und Sn/Si(111). Atomare Strukturen und deren spezielle Merkmale wurden mit Rastertunnelmikroskopie (STM) und Elektronenbeugung (LEED) untersucht, wobei ein Schwerpunkt die Abscheidung von Pt auf Si(111) war. Hervorzuheben ist hier die Anordnung von Pt Atomen als Trimere, die das Grundgerüst phasenverschobener Domänen bilden. Interessanterweise sind die Trimere um 30° gegenüber dem Substrat verdreht, was einen unerwarteten Symmetriebruch bedeutet. Daher stellt Pt/Si(111) ein einzigartiges Beispiel einer chiralen Struktur auf Halbleitern dar und könnte außerdem für katalytische Prozesse im atomaren Bereich interessant sein. Die Spin-Bahn Wechselwirkung ist auf Oberflächen, die schwere Elemente enthalten, von großer Bedeutung. Hier kann die Spin-Entartung in den elektronischen Zuständen aufgehoben sein, was als Rashba-Effekt bekannt ist. Rechnungen mittels Dichtefunktionaltheorie (DFT) zeigen, dass eine solche Aufspaltung in der hexagonalen Fermi-Fläche von Au/Ge(111) existiert. Experimentell wurde dies mit dreidimensionaler spin- und winkelaufgelöster Photoelektronenspektroskopie bestätigt. Dabei folgt die planare Spin-Komponente einem kreisförmigen Umlaufsinn, während zudem eine starke Aufrichtung des Spins aus der Ebene hinaus entlang gerader Abschnitte der Fermi-Fläche auftritt. Hierbei wurden zum ersten Mal in einem 2DES zusätzliche Rotationen des planaren Spinanteils in der Oberflächenebene nahe von Hochsymmetrierichtungen nachgewiesen. Dieses komplexe Spin-Muster resultiert aus den kristallinen Anisotropien und kann exzellent modelliert werden, indem das Rashba-Modell um Dresselhaus-artige Spin-Bahn Terme höherer Ordnung erweitert wird. Die alternative Verwendung von Gruppe-IV Adatomen bei einer geringeren Bedeckung ändert die Eigenschaften eines 2DES deutlich. Kennzeichnend sind eine verstärkte Ladungsträger-Lokalisierung und ein von Korrelationen bestimmter Grundzustand. Dabei stellt Sn/Si(111) ein Modell-System dar, das zudem ein spin-frustriertes Dreiecksgitter bildet. In einem solchen fehlt üblicherweise die langreichweitige magnetische Ordnung und der Grundzustand ist entweder ein isolierender spiralförmiger Antiferromagnet (AF) oder eine Spin-Flüssigkeit. Zur Analyse des Wechselspiels von geometrischer Frustration und elektronischen Korrelationen dient die Ein-Teilchen Spektralfunktion als Basisgröße. Dazu wurden die sich ergänzenden Stärken von Bandstruktur-Rechnungen in der lokalen Dichtenäherung (LDA), winkelaufgelöster Photoelektronenspektroskopie und Viel-Teilchen Modellen (hier LDA+DCA) kombiniert. Dabei wurde die Existenz eines Schattenbandes und einer Bandrückfaltung nachgewiesen, wobei letztere einen spiralförmigen AF als Grundzustand ausschließt. Vielmehr sind Hüpfprozesse über den nächsten Nachbarn im Gitter hinaus relevant und die spektralen Merkmale sind, trotz der Spin-Frustration, durch einen langreichweitigen kollinearen AF als Grundzustand erklärbar.

This art project concerns itself with the notion of travelling space as a continuous state of experience perceived by a traveller, in contrast to something that has previously taken place. Travelling space takes into account the physical movement of a traveller and also that of the space travelled by a viewer - it reveals a dichotomy: that of travelling within a certain space; and the space created through the act of travelling.Travelling space is to negotiate thresholds of seeing, experience, imagination and movement. The travel, made evident through video-trace, installed in spatial arrangements within a gallery context project the possibility of a third dimension to travelling space - that of a homeless state where viewers may abandon the space created by video sequences, to travel a virtual space of their own making.

<p>Femte dimension (5D) är ett internationellt nätverk för forskare, lärare, elever och studenter. I den här uppsatsen har jag genom en studie i Femte dimensionens anda utforskat vad ett IKT- inriktat samarbete mellan fältet och högskola innebär för de inblandade och diskuterat frågan om hur samarbetet med hjälp av IKT kan se ut. Studien genomfördes på LHS under våren 2007 tillsammans med lärarstudenter, lärare och elever från en närliggande skola.Jag vill bidra till en ökad förståelse om IKT´s roll i kollaborativt lärande och samtidigt skaffa mig egna erfarenheter av lärmodellen 5D för att se om denna metod kan vara ett bra sätt att integrera IKT i kurserna på lärarutbildningen. Metoden 5D bygger på kollaborativt arbetssätt. Det är en ide och ett modellsystem för lärandemiljöer som kännetecknas av samarbete, rikhet på verktyg, lek samt ett undersökande och kreativt arbetssätt. För att optimera lärandet och utvecklingen i den sociala interaktionen utvecklades metoden med hjälp av bl.a. Vygotsky´s tankar om ”den proximala utvecklingszonen”. Studien är gjord utifrån ett sociokulturellt perspektiv. Genom kvalitativa forskningsstudier kan man gå nära in på lärandesituationer, beskriva dem och analysera vad som faktiskt sker där. Som metod har jag använt deltagande observation samt analys av insamlat material. Jag har samlat in data på många olika sätt; genom intervjuer, utvärderingar, observationer, video- och ljudupptagningar och genom studenternas loggboksanteckningar. I min analys har jag utgått ifrån Pierre Dillenbourgs kriterier av kollaborativt lärande: situationen (symmetri, arbetsfördelning), interaktionen (symmetri, jämkande av åsikter), processen (byggande av gemensam grund, gemensamt kunskapsbygge) och effekterna. Resultatet av studien visar att Dillebourgs kriterier är mycket användbara som verktyg när man vill studera kollaborativt lärande i grupper. Studien visade flera exempel på de tre första kriterierna. Intervjuerna med andra forskare och de gjorda utvärderingarna av sudien visar att modellen 5D är användbar i lärarutbildningen.</p>

Let S and T be numerical semigroups and let k be a positive integer. We say that S is the quotient of T by k if an integer x belongs to S if and only if kx belongs to T. Given any integer k larger than 1 (resp., larger than 2), every numerical semigroup S is the quotient T/k of infinitely many symmetric (resp., pseudo-symmetric) numerical semigroups T by k. Related examples, probabilistic results, and applications to ring theory are shown. Given an arbitrary positive integer k, it is not true in general that every numerical semigroup S is the quotient of infinitely many numerical semigroups of maximal embedding dimension by k. In fact, a numerical semigroup S is the quotient of infinitely many numerical semigroups of maximal embedding dimension by each positive integer k larger than 1 if and only if S is itself of maximal embedding dimension. Nevertheless, for each numerical semigroup S, for all sufficiently large positive integers k, S is the quotient of a numerical semigroup of maximal embedding dimension by k. Related results and examples are also given.

Given a limited number of samples for classification, several issues arise with respect to design, performance and analysis of classifiers. This is especially so in the case of microarray-based classification. In this paper, we use a complexity measure based mixture model to study classifier performance for small sample problems. The motivation behind such a study is to determine the conditions under which a certain class of classifiers is suitable for classification, subject to the constraint of a limited number of samples being available. Classifier study in terms of the VC dimension of a learning machine is also discussed.

Femte dimension (5D) är ett internationellt nätverk för forskare, lärare, elever och studenter. I den här uppsatsen har jag genom en studie i Femte dimensionens anda utforskat vad ett IKT- inriktat samarbete mellan fältet och högskola innebär för de inblandade och diskuterat frågan om hur samarbetet med hjälp av IKT kan se ut. Studien genomfördes på LHS under våren 2007 tillsammans med lärarstudenter, lärare och elever från en närliggande skola.Jag vill bidra till en ökad förståelse om IKT´s roll i kollaborativt lärande och samtidigt skaffa mig egna erfarenheter av lärmodellen 5D för att se om denna metod kan vara ett bra sätt att integrera IKT i kurserna på lärarutbildningen. Metoden 5D bygger på kollaborativt arbetssätt. Det är en ide och ett modellsystem för lärandemiljöer som kännetecknas av samarbete, rikhet på verktyg, lek samt ett undersökande och kreativt arbetssätt. För att optimera lärandet och utvecklingen i den sociala interaktionen utvecklades metoden med hjälp av bl.a. Vygotsky´s tankar om ”den proximala utvecklingszonen”. Studien är gjord utifrån ett sociokulturellt perspektiv. Genom kvalitativa forskningsstudier kan man gå nära in på lärandesituationer, beskriva dem och analysera vad som faktiskt sker där. Som metod har jag använt deltagande observation samt analys av insamlat material. Jag har samlat in data på många olika sätt; genom intervjuer, utvärderingar, observationer, video- och ljudupptagningar och genom studenternas loggboksanteckningar. I min analys har jag utgått ifrån Pierre Dillenbourgs kriterier av kollaborativt lärande: situationen (symmetri, arbetsfördelning), interaktionen (symmetri, jämkande av åsikter), processen (byggande av gemensam grund, gemensamt kunskapsbygge) och effekterna. Resultatet av studien visar att Dillebourgs kriterier är mycket användbara som verktyg när man vill studera kollaborativt lärande i grupper. Studien visade flera exempel på de tre första kriterierna. Intervjuerna med andra forskare och de gjorda utvärderingarna av sudien visar att modellen 5D är användbar i lärarutbildningen.

The purpose of this study is to examine some factors that make a human grouse hunter to prolong and increase its hunting effort. The theory of optimal foraging is used for explaining their behavior. The data of this study is collected from a web-based inquiry from 2007 answered by grouse hunters in Sweden. The method that has been used is mainly bivariate statistics and logistic regression analysis. Key findings shows that an experienced grouse hunter has more than 5 times the chance of prolonging hunting effort when grouse density is high, compared to a beginner grouse hunter. On the same time experienced grouse hunters also stop hunting in advance when grouse density is low to a larger extent than inexperienced hunters. Other factors of importance for prolonging the hunting effort for a day are age and the travel distance to the hunting area. A hunter in the age of 35-60 years has got half the likelihood of prolong a good hunting day, compared to a hunter younger than 35 years old. A hunter that has travelled more than 300 km to the hunting area has got half the likelihood of prolonging, compared to a hunter with less than 300 km from its home adress to the hunting area. Conclusions: The result suggests that the behaviour of an experienced hunter is easier to explain by optimal foraging theory than less experienced hunters.

This thesis presents the theory of affine algebraic sets defined over an arbitrary field K. We define basic concepts such as the Zariski topology, coordinate ring of functions, regular functions, and dimension. We are interested in the relationship between the geometry of an affine algebraic set over a field K and its geometry induced by the algebraic closure of K. Various versions of Hilbert-Nullstellensatz are presented, introducing a new variant over finite fields. Examples are provided throughout the paper and a question on the dimension of irreducible affine algebraic sets is formulated.

Infinite dimensional systems such as flexible airplane wings and Vertical Axis Wind Turbine (VAWT) blades may require control to improve performance. Traditional control techniques use position and velocity information feedback, but velocity information for infinite dimensional systems is not easily attained. This research investigates the use of reduced-sensing control for these applications. Reduced-sensing control uses feedback of position measurements and an associated filter state to stabilize the system dynamics. A filter state is a nonphysical entity that appends an additional ordinary differential equation to the system dynamics. Asymptotic stability of a system using this control approach is confirmed through a sequence of existing mathematical tools. These tools include equilibrium point solutions, Lyapunov functions for stability and control, and Mukherjee and Chen's Asymptotic Stability Theorem. This thesis research investigates the stability of a beam representing an airplane wing or a VAWT blade controlled using feedback of position and filter state terms only. Both of these infinite dimensional systems exhibit asymptotic stability with the proposed reduced-sensing control design. Additionally, the analytical stability response of the VAWT is verified through numerical simulation.

This study developed a conceptual model for exploring the correlation between relational dimension of social capital and relation models in hope to reveal to what extent each elements in relational dimension of social capital influences the combination of relation models of knowledge sharing. Further we investigated the impact of each relation model on the effectiveness of knowledge sharing and attempt to present an efficient mechanism based on the combination of the four relation models. We adopted the survey method and focus on the members in IS project team to collect research data. Canonical correlation analysis was employed to examine the correlation between the two constructs, the relational dimension of social capital and the relation models of knowledge sharing, and two significant canonical functions with powerful explanation were derived. The first canonical function with major explanatory power showed that all the elements in the relational dimension of social capital are highly related with the models, CS, EM and MP, in the construct of relation models. The second canonical function, in which obligation is highly related with MP and AR, was derived with inferior explanatory power to the first one. Stepwise regression analysis was conducted to investigate the relationship between each relation model and the effectiveness of knowledge sharing. CS, among the four relation models, was found to have the highest positive significance with the effectiveness, followed by EM and MP sequentially, while AR was found no significant relation with the effectiveness of knowledge in our observations. With the results of this study, we hope to present an efficient mechanism for practitioners to promote knowledge management by enhancing corresponding social capital in relational dimension and offer comprehensive perspectives for researchers to achieve a better insight of the dynamics of knowledge sharing.