In this thesis, we will present examples of Voronoi diagrams that are not tessellations. Moreover, we will find sufficient conditions on subspaces of E2, S2 and the Poincaré disk and the sets of sites that guarantee that the Voronoi diagrams are pre-triangulations. We will also study g-spaces, which are metric spaces with ‘extendable’ geodesics joining any 2 points and give properties for a set of sites in a g-space that again guarantees that the Voronoi diagram is a pre-triangulation.

The goal of this thesis is to first give an overview of the modern approach, using the paper of A. Vershik and A. Okounkov, to inductively parametrizing all irreducible representations of the symmetric groups. This theory is then used to answer questions concerning to central projections in the group algebra. We index units first by partitions, and then by so called standard tableaux. We also present a new result and discuss future research exploring the connections between this theory and Quantum Information.

In this thesis, we will present examples of Voronoi diagrams that are not tessellations. Moreover, we will find sufficient conditions on subspaces of E2, S2 and the Poincaré disk and the sets of sites that guarantee that the Voronoi diagrams are pre-triangulations. We will also study g-spaces, which are metric spaces with ‘extendable’ geodesics joining any 2 points and give properties for a set of sites in a g-space that again guarantees that the Voronoi diagram is a pre-triangulation.

En ökad efterfrågan på biogas har lett till att matavfallsinsamlingen i Sverige ökar, då detta är en god råvara för produktion av biogas. Det finns flera olika insamlingssystem att välja bland, alla med sina för- respektive nackdelar. Beroende på vilket insamlingssystem som implementeras, får detta konsekvenser för hur renhållningsarbetarnas arbetsmiljö blir. Vad renhållningsarbetarna själva anser vara viktiga aspekter för en god arbetsmiljö samt hur dessa aspekter påverkas av de olika insamlingssystemen har hittills varit okänt. Genom systemanalys innehållandes fallstudier, Corporate Social Responsibility-analys (CSR) och skapandet av Casual Loop Diagrams (CLD) har problematiken undersökts i detta arbete. Fallstudierna är genomförda hos olika matavfallsinsamlande entreprenörer i städerna Solna, Västerås och Borås och som sköter insamlingen enligt de två vanligaste insamlingssystemen i Sverige idag. CSR-analysen visar hur respektive entreprenör kommunicerar sina visioner och mål samt hur detta påverkar de anställda. CLDer skapades med samtliga entreprenörer, där arbetsmiljöaspekter för en god arbetsmiljö och dess relationer beskrevs. Detta arbete visar att maskinella insamlingssystem generellt skapar en bättre fysisk arbetsmiljö, men att manuella insamlingssystem är bättre sett till psykosociala aspekter. Renhållningsarbetarna själva efterfrågar förbättringar inom båda dessa områden, men de psykosociala aspekterna är mest avgörande för en god arbetsmiljö. Resultaten visar att även i fysiskt krävande arbeten spelar de psykosociala aspekterna en avgörande roll för hur god arbetsmiljön blir för de anställda. Renhållningsarbetarna väljer själva en potentiellt sämre fysisk arbetsmiljö för att istället säkerställa goda psykosociala förhållanden på arbetet. Arbetet med att förbättra den fysiska arbetsmiljön för denna arbetsgrupp måste fortsätta, samtidigt som de psykosociala aspekterna måste ges prioritet för att skapa en långsiktig, god arbetsmiljö. / An increased demand for biogas has led to increased food waste collection in Sweden, as it is a suitable raw material for biogas production. There are several different collection systems to choose from, each with its advantages and disadvantages. Depending on which collection system is implemented, this may affect the waste collectors' work environment. What waste collectors themselves consider important aspects of a healthy work environment and how these aspects are affected by the different collection systems have so far been unknown. Through systems analysis that includes case studies, Corporate Social Responsibility analysis (CSR) and the creation of Casual Loop Diagrams (CLD) the problem has been investigated in this study. The case studies are conducted with different food waste collector entrepreneurs in the cities of Solna, Västerås and Borås and manage food waste collection through the two most common collection systems in Sweden today. CSR analysis shows how each entrepreneur communicates their visions and goals and how this affects the employees. CLD’s were created with all the entrepreneurs, where the social aspects of a healthy work environment and their relationships were described. This study shows that mechanical collection systems generally create a better physical working environment, but manual collection systems are better in terms of psychosocial aspects. Waste collectors themselves ask for improvement in both areas, but the psychosocial aspects are most critical to a healthy work environment. The results show that even in physically demanding jobs, the psychosocial aspects play a crucial role in how good the work environment is for the employees. Waste collectors themselves choose a potentially worse physical work environment to instead ensure good psychosocial conditions at work. Efforts to improve the physical work of this work force should continue, while the psychosocial aspects must be given priority in order to create a long-term, healthy work environment.

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Making electronic business systems, products of information technologies or solving real time tasks more and more IT specialists their designing work connect to UML language. The usage of this language provides opportunities to arrange documentation more simply, allows to communicate different position employees more easily, guarantee IT systems compatibility with business needs and requirements. One of the diagrams types used is activity diagram, which could be used to describe business processes, firms or its unit, compose official, activity or users instructions, show systems behaviour. Any investigative, designed or management activity at some cases is connected to modelling. Commonly designing systems, where parallel events could take place or, if necessary, to give an opportunity gradually, taking in account the reality, show events or state proceeding with the help of Petri nets. It is both graphical and mathematical design method. Designing activity diagrams of IT systems UML editors are used. To research and show events proceeding Petri nets are used. So the problem area is to compose a design system, which could transfer the elements of activity diagrams into Petri nets and model the functionality of the project. The major purpose of this study paper is to compose UML language activity diagrams modelling system, examine the functionality and design opportunities of system’s activity diagrams into Petri nets.

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In the present study, dilute alloys in the Mg-rich corner of the Mg-Ce-In ternary system in the composition range 0 to 3% In and 0 to 1.5% Ce were synthesized. Cooling curve analysis was used to determine the liquidus points in order to construct the liquidus surface of the ternary phase diagram in the Mg corner. Energy dispersive spectroscopy (EDS), wavelength dispersive spectroscopy (WDS), and x-ray diffraction (XRD) techniques were used to examine phases present at the compositions studied. A thermal arrest presumed to represent a eutectic transformation was discovered at 580°C. Two new intermetallic compounds, designated tau and theta, were found. Trace silicon present in the alloys was found to concentrate in one of the intermetallic compounds. / To further investigate these compounds, an induction furnace was used to synthesize alloys containing the concentrations of Ce and In seen in electron probe micro-analysis (EPMA) examinations of these compounds. The alloys were examined using the cooling curve technique and XRD, and proved to contain the compounds already observed with some variation in dissolved indium content. In addition, differential scanning calorimetry (DSC) was used to confirm the liquidus and solidus values determined using cooling curve analysis. / A diffusion couple with terminal compositions of pure Ce and a Mg-In alloy was prepared in order to determine the equilibrium phases present in the system between these two compositions at 390°C. EPMA was used to identify the zones obtained, and confirmed the presence of several Mg-Ce compounds with 1 at% dissolved indium, as well as a ternary compound corresponding to the theta compound found in the dilute alloys. / Finally, literature values and experimental data were used to calculate a preliminary ternary phase diagram using FACTSage, in collaboration with the CTRC at Ecole Polytechnique, in order to affirm the validity of the experimentally determined values as well as to project the diagram beyond the studied composition range.

By extending the diagrams of materials science, the field is broadened in a natural way. For example, binary phase diagrams are like black boxes, used in the design and simulation of microstructures. They explore a balance of two chemical species, but real alloys have several chemical species, and merit a higher dimensional space. The n-dimensional extension is simplified by dividing the problem into discrete and continuous components. / "Discrete" is the identification of behavioural regimes, and their interactions, in a network graph. "Continuous" includes the curvature of boundaries, and the motion through the space. In thermochemical phase spaces, a homogenous alloy is mapped to a particle, whose motion represents the evolution of the alloy. Likewise, non-homogeneous alloys evolve as multidimensional continua. / The classical diagrams may also be hybridized. For example, TTT-curves may be treated as extra dimensions of a thermochemical phase space; the resulting hybrid synthesizes microstructural thermodynamics and kinetics.