This dissertation is concerned with invertibility and one-sided invertibility of Toeplitz operators over the half plane whose generating functions admit homogenous discontinuities, and with stability of their pseudo finite sections. The invertibility criterium is given in terms of invertibility of a family of one dimensional Toeplitz operators with piecewise continuous generating functions. The one-sided invertibility criterium is given it terms of constraints on the partial indices of certain Toeplitz operator valued function.

Pendant de nombreuses années, les liaisons C-H aliphatiques ont été considérées comme dormantes, difficilement exploitables dans le contexte de la chimie organique. Le défi le plus important est de sélectionner une liaison C-H parmi toutes celles que contient une molécule. L’approche la plus utilisée à ce jour est l’utilisation d’un groupement directeur qui permet, en se liant à un métal, de diriger l’activation d’une liaison C-H en particulier. Suite au développement des groupements bicoordinants, nous avons développé notre propre groupement bicoordinant chiral. Cet auxiliaire nous a permis de réaliser de nombreuses transformations diastéréosélectives sur des carbones aliphatiques telles que l'arylation et l'oléfination. Nous l’avons également utilisé pour développer une méthodologie innovante pour la synthèse de produits naturels. Suite à ces travaux, nous avons développé un nouveau ligand chiral qui a été utilisé dans l’arylation et l’alkynylation énantiosélectives de cycloalcanes. / Over the decades, non-activated C-H bonds have been considered as dormant functionalities, hardly exploitable in the context of multistep synthesis of complex scaffolds. The main challenge is to select one C-H bond among all contained in one molecule. To answer to this problem bicoordinating directing groups allowing directed C(sp3)-H activation have been developed. Following the work of Daugulis and Babu, we developed our own chiral bicoordinating directing group, (S)-2-(p-tolylsulfinyl)aniline. This chiral auxiliary allowed us to realise various diastereoselective transformations on aliphatic chains such as arylation, olefination oracetoxylation. We also used it to develop a brand-new methodology for the total synthesis ofcyclopropane-bearing natural products. Moreover we developed a new chiral sulfinyl ligand, N-((S)-1-(4-(tert-butyl)phenyl)-2-((R)-p-tolylsulfinyl)ethyl)acetamide, that has been used for the enantioselective arylation and alkynylation of cycloalkanes.

Fundamental understanding of high strain rate deformation behavior of materials is critical in designing new alloys for wide-ranging applications including military, automobile, spacecraft, and industrial applications. High entropy alloys, consisting of multiple elements in (near) equimolar proportions, represent a new paradigm in structural alloy design providing ample opportunity for achieving excellent performance in high strain rate applications by proper selection of constituent elements and/or thermomechanical processing. This dissertation is focused on fundamental understanding of high strain-rate deformation behavior of several high entropy alloy systems with widely varying microstructures. Ballistic impact testing of face centered cubic Al0.1CoCrFeNi high entropy alloy showed failure by ductile hole growth. The deformed microstructure showed extensive micro-banding and micro-twinning at low velocities while adiabatic shear bands and dynamic recrystallization were seen at higher velocities. The Al0.7CoCrFeNi and AlCoCrFeNi2.1 eutectic high entropy alloys, with BCC and FCC phases in lamellar morphology, showed failure by discing. A network of cracks coupled with small and inhomogeneous plastic deformation led to the brittle mode of failure in these eutectic alloys. Phase-specific mechanical behavior using small-scale techniques revealed higher strength and strain rate sensitivity for the B2 phase compared to the L12 phase. The interphase boundary demonstrated good stability without any cracks at high compressive strain rates. The Al0.3CoCrFeNi high entropy alloy with bimodal microstructure demonstrated an excellent combination of strength and ductility. Ballistic impact testing of Al0.3CoCrFeNi alloy showed failure by ductile hole growth and demonstrated superior performance compared to all the other high entropy alloy systems studied. The failure mechanism was dominated by micro-banding, micro-twining, and adiabatic shear localization. Comparison of all the high entropy alloy systems with currently used state-of-the-art rolled homogenous armor (RHA) steel showed a strong dependence of failure modes on microstructural features.

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Från slutet på 1800-talet till runt 1970-talet gjordes tennisracket i trä och då tekniken inte var så avancerad var de tunga och böjliga. På 1970-talet började dock andra material som exempelvis kolfiber användas som var styvare och gav ett lättare racket. Över tid har metoderna för tillverkningen i trä fallit i glömska vilket gör att undersökningar som denna är intressanta att utföra. Då kolfiber framställs av råolja kan materialet bli mindre attraktivt både ur ett miljö- och ekonomiskt perspektiv då oljepriserna stiger. På grund av detta har företaget Epok Tennis, som arbetet har utförts ihop med, valt att experimentera och prova sig fram i tillverkningen av racket i trä i jakt efter den mest optimala uppsättningen och konstruktionen. Kunskapsläget är dåligt inom området då studie av denna typen generellt görs på större element för användning i exempelvis bostäder och dessa består då framför allt av gran och furu. Därför är det intressant för Epok Tennis att se inverkan av olika träslag som inte vanligtvis används i balkar av i små dimensioner som är jämförbara med tennisracket.Epok Tennis har undersökt hur träracketen byggdes förr och försökt implementera tekniken moderna racket byggs, detta för att skapa en träprodukt som kan fungera lika bra som en modern racket. De viktigaste parametrarna att ta hänsyn till i arbetet var produkternas vikt, styvhet och hållfasthet. I arbetet undersöktes 21 kors- och parallellimmade balkar bestående av totalt sex nordiska träslag. Träslagen i fråga var ask, björk, bok, ek, lönn och valnöt. Sju av balkarna var korslimmade och 14 parallellimade. De korslimmade elementen varierade mellan ett och två tvärgående skikt. Två av balkarna innehöll även produkter som kolfiberduk och linnetyg vilka inte beaktades i beräkningarna men vars resultat var av intresse att analysera. Syftet med arbetet var att undersöka hur olika kombinationer av olika träfanérskivor påverkarböjstyvheten och hållfastheten för en tennisrackets konstruktion. Målet var sedermera att fastställa vilken av balkarna som har högst böjstyvhetoch hållfasthet samt ge förslag om optimal komposituppsättning. Teoretiska beräkningar samt experiment av fyrpunktsböjning utfördes på balkarna där resultaten jämfördes och analyserades. Experimenten utfördes både i balkarnas flat- och kantvisa riktning. Även densiteterna noterades för elementen då konstruktionens totala vikt i slutändan är av stor betydelse.Resultaten av studien visade att de homogena parallellimmade balkarna av björk, lönn och valnöt hade högst böjstyvhet. Vid analys av resultaten noterades att korslimning av elementen generellt försvagade dem i både flat- och kantvis riktning. Till detta ändamål kan det därför vara klokt att endast använda parallellimmade element. I resultatet redovisas även balkarnas knäcklast i kantvisa riktningen.Förekomsten av kvistar i lamellerna ansågs ha en stor inverkan på balkarnas hållfasthet. Därför bör lameller med kvistar försöka undvikas vid framställningen av ramarna till tennisracketen. I förslaget om optimal komposituppsättning har en kombination av lönn och valnöt angetts då dessa visade högst böjstyvhet med avsevärt lägre densitet än björk som dock liknande värde på böjstyvheten.Enligt resultaten av studien är slutsatserna som dragits kortfattat att korslimning generellt försvagar elementen gentemot parallellimning och att bästa komposituppsättning består av lönn och valnöt, i kombination med varandra eller var för sig. / The knowledge of creating wooden tennis rackets has been lost since the emergence of materials like carbon fibre. In this study 21 cross- and parallel laminated beams have been examined, seven of which are cross laminated and 14 parallel laminated. The wood species used were ash, beech, birch, maple, oak and walnut.The purpose of the study was to determine how different combinations of wood lamellas affect strength and stiffness of the beams in terms of bending.The goal was to determine which of the 21 beams had the highest bending stiffness and to give a recommendation of what would be the optimal composite set.Calculations and experiments of four point bending were done in the flat- and edgewise directions, the results of which were compared and analyzed.The results of the study showed that the homogenous parallel laminated beams consisting of birch, maple and walnut had the highest bending stiffness. When analyzing the results, it was found that the parallel laminated beams were generally stronger and stiffer than the cross laminated specimens, for both flat- and edgewise bending.In the recommendation of optimal construction, a combination of maple and walnut has been suggested due to them having similar bending stiffness to birch but significantly lower density.

Da Boryl-Komplexe als Schlüsselintermediate in Borylierungsreaktionen betrachtet werden, gilt Ihnen ein großes experimentelles und theoretisches Interesse. Das Ziel der vorliegenden Dissertation ist daher die Darstellung hoch reaktiver 16 VE-Rhodium(I)-Boryl-Komplexe. Der Fokus der Arbeit liegt auf der Untersuchung ihres Reaktionsverhaltens sowie ihrer katalytischen Aktivität in Reaktionen, die die Bildung neuer Bor-Element-Bindungen zur Folge haben und somit z. B. die Darstellung von Boronsäureestern als wertvolle Synthesebausteine ermöglichen. In dieser Arbeit wird neben der erfolgreichen Darstellung mehrerer Rhodium(I)-Boryl-Komplexe exemplarisch das Reaktionsverhalten des Pinacolatoboryl-Komplexes gegenüber substituierten (Hetero-)Aromaten, Aminen sowie ungesättigten Verbindungen beschrieben. Die Untersuchungen zeigen, dass der Boryl-Komplex mit Aromaten wie Phenyltrifluormethylsulfid oder fluorierten Benzolderivaten chemo- und regioselektiv unter Aktivierung von C-H-Bindungen reagiert und dass mit Aminen wie Anilin hingegen gezielt die N-H-Bindung aktiviert wird. Darüber hinaus erwies sich der Boryl-Komplex als effizienter Katalysator für C-H- und N-H-Borylierungsreaktionen und ist somit zur katalytischen Darstellung borylierter Verbindungen geeignet. Weitere Studien mit Verbindungen, die eine C=X-Bindung (X = O, N, C, S) besitzen, wie Ketone und Imine sowie Stilben und Thioharnstoff zeigen die ausgeprägte Neigung des Rhodium(I)-Boryl-Komplexes, initial unter Insertion der ungesättigten Verbindung in die Rhodium-Bor-Bindung zu reagieren. Diese Beobachtungen können wichtige Informationen über die Teilschritte eines Katalyseprozesses geben. Besonders bemerkenswert ist die Reaktivität des Boryl-Komplexes gegenüber Kohlenstoffdioxid und Schwefelkohlenstoff, die in der Spaltung der stabilen C=X-Bindung (X = O, S) resultiert. Insgesamt verdeutlicht das hier beschriebene breite Reaktivitätsspektrum der Rhodium(I)-Boryl-Komplexe die Relevanz dieses Forschungsgebiets. / Since boryl complexes are regarded as key intermediates in borylation reactions, there is a high experimental and theoretical interest. Therefore, the aim of this dissertation is the synthesis of highly reactive 16 VE rhodium(I) boryl complexes. Moreover, the thesis focuses on their reactivity as well as their catalytic activity in reactions, which afford new boron-element bonds and, thus, enable for example the synthesis of boronic esters as useful building blocks. Herein, in addition to the successful synthesis and characterization of several rhodium(I) boryl complexes, the reactivity of the pinacolato boryl complex towards substituted (hetero)arenes, amines and unsaturated substrates is described. The studies reveal that the treatment of the boryl complex with aromatics like phenyltrifluoromethyl sulfid or fluorinated benzene derivatives leads chemo- and regioselectively to C-H bond activation reactions and that in contrast, with amines like aniline the N-H bond is exclusively activated. Furthermore, the boryl complex turned out to be an efficient catalyst for C-H and N-H borylation reactions and yields borylated compounds in a catalytic way. Further investigations with reagents containing a C=X bond (X = O, N, C, S) like ketones and imines as well as stilbene and thiourea show the pronounced tendency of the rhodium(I) boryl complex to react initially via insertion of the unsaturated unit into the rhodium-boron bond. These results might give a deeper insight into the mechanism of catalytic processes. The remarkable reactivity of the boryl complex towards carbon dioxide and carbon disulfide is reported, too, which result in the cleavage of the thermodynamic stable C=X double bonds (X = O, S). Overall, the here shown wide range of reactivity of rhodium(I) boryl complexes demonstrates the relevance of this research topic.

The thesis deals with the mathematical modelling of economic processes, particulary production. Basic approach, models and methods of modelling concerning the mentioned area are described. Further, specific characterizations are investigated. Application of selected methods to typical examples is presented. In the final part models on concrete data are constructed.

This diploma project works out and is focused on the continual mixing process of the particular matters. The project is divided into following chapters. Chapter 1 includes mixing theory and information of the experimental work of the particular matters for blade using. In chapter 2 there is Evaluation and calculation of the technical parameters for the mixer. Chapter 3 deals with the engine proposal and chapter 4 includes calculation and design work of the gear transmission. Chapter 5 includes the stress analysis of the shaft and blade with the I-deas software. In attachment there are also the mixer arrangement drawing and detailed drawings of the key parts and groups for the mixer.

This thesis is focused on application samples with the inner insert used for Charpy impact test. This insert is welded to additional material by electron beam with pre-selected welded parameters. These parameters were chosen from data of performed experiments on homogenous welds. Resulting heterogenous weld was performed of evaluation of the microstructure, chemical composition and microhardness. Experimental materials were used austenitic steel 17 240 and ferritic steel 17 153 used on high-temperature applications.

Master's thesis aims to design a small water reservoir. It is the dry water reservoir which is situated above a built-up area. The main function of this reservoir is a flood protection. Digital terrain model is created in a program BENTLEY MicroStation V8i – Power Civil. Focusing points in a data file are used in a process of creating of the DTM. Adjustments are done in AutoCAD. Particular hydro-technical calculations are calculated in a program Microsoft Excel. A program HEC-HMS is used for an assessment of a flood wave transformation and a program HEC-RAS is used for a water runoff simulation via emergency spillway.