Ein bedeutender Satz von L. Bungart und H. Grauert besagt, dass, für eine Gruppe G von invertierbaren Elementen einer Banachalgebra, je zwei G-wertige holomorphe Kozyklen über einer beliebigen Steinschen Mannigfaltigkeit holomorph äquivalent sind, wenn sie dort stetig äquivalent sind. Eine einfachere Form dieses Satzes wurde erstmals von K. Oka bewiesen. Aussagen dieser Art werden deshalb auch Okasche Prinzipe oder Oka-Grauert-Prinzipe genannt. Der Bungert-Grauert-Satz ist auch in dem Fall von Bedeutung, in dem die Steinsche Mannigfaltigkeit ein Gebiet in der komplexen Ebene ist. Man kann deshalb in der Literatur auch direkte Beweise für den Spezialfall finden, in dem ein G-wertiger holomorpher, stetig trivialer Kozyklus betrachtet wird. Dieser ist, nach dem oben erwähnten Satz, dann auch holomorph trivial. Ziel dieser Dissertation ist es, den Bungart-Grauert-Satz für Gebiete in der komplexen Ebene auch im allgemeinen Fall direkt zu beweisen. Dieser direkte Beweis ist wesentlich einfacher als der bisherige und muss nicht, wie bei L. Bungart und H. Grauert, auf eine Theorie von mehreren Veränderlichen zurückgreifen. Wie in den Arbeiten von L. Bungart und H. Grauert gezeigt, kann dies durch das sogenannte Verdrillen, einer Methode aus einer allgemeinen Theorie von holomorphen Kozyklen mit Werten in Bündeln von Gruppen, erzielt werden. Der größte Teil der Dissertation besteht deshalb darin, eine solche Theorie im Fall von Gebieten in der komplexen Ebene direkt aufzubauen. / An important theorem of L. Bungart and H. Grauert says that for the group G of invertible elements of a banachalgebra, two holomorphic, G-valued cocycles over a Stein manifold, which are continiously equivalent, are holomorphically equivalent there. A simpler form of that theorem was first proven by K. Oka. That''s why theorems like this are known as Oka-Grauert-priciples as well. The Bungart-Grauert theorem is also significant if the Stein manifold is a domain in the complex plane. That''s why direct proofs of the special case, in which a continiously trivial, holomorphic cocycle is considered, can also be found in literature. Following the Bungart-Grauert theorem mentioned above, such a cocycle is also holomorphically trivial. The goal of this thesis is to prove the general case of the Bungart-Grauert theorem for a domain in the complex plane directly. That direct proof is much more simple than the old one. Furthermore this direct proof doesn''t have to resort to a theory of multiple variables, unlike the proof from L. Bungart and H. Grauert does. As shown in the original works, such a proof can be archieved by using the so called twisting. Twisting is a method from a theory of holomorphic cocycles with values in bundles of groups. In the main part of this thesis such a theory is build directly for domains in the complex plane.

In the review part of the thesis we summarize various modified theories of gravity, especially those that are characterized by additional curvature invariants in the Lagrangian density. Further, we review non-twisting geometries, especially their Kundt subclass. Finally, from the principle of least action we derive field equations for the case with the Lagrangian density corresponding to an arbitrary function of the curvature invariants. In the original part of the thesis we explicitly express particular components of the field equations for non-gyratonic Kundt geometry in generic quadratic gravity in arbitrary dimension. Then we discuss how this, in general fourth order, field equations restrict the Kundt metric in selected geome- trically privileged situations. We also analyse the special case of Gauss-Bonnet theory. 1

Twist plays an important role to impart tensile strength in yarn during the spinning process. In the most widely used ring-spinning machine for short staple yarn production, a combination of ring and traveler is used for inserting twist and winding the yarn on cops. The main limitation of this twisting mechanism is the friction between the ring and traveler, which generates heat at higher speed and limits the productivity. This limitation can be overcome by the implementation of a magnetic bearing system based on superconducting technology, which replaces completely the existing ring/traveler system of the ring-spinning machine. This superconducting magnet bearing consists of a circular superconductor and permanent magnet ring. After cooling the superconductor below its transition temperature, the permanent magnet ring levitates and is free to rotate above the superconductor ring according to the principles of superconducting levitation and pinning. Thus the superconducting magnetic bearing (SMB) ensures a friction-free operation during spinning and allows one to increase spindle speed and productivity drastically. The yarn properties using the SMB system have also been investigated and they remain nearly identical to those of conventional ring yarns.

There is currently a high demand for electric power from renewablesources. One source that remains relatively untapped is the motionof ocean waves. Anders Hagnestål has been developing a uniquelyefficient and simplified design for a point-absorb buoy generator byconverting its linear motion directly into alternating electric power usinga linear PM engine. To test this method, a smaller prototype isbuilt. Its characteristics present some unusual challenges in the designand construction of its winding.Devices of this type typically use relatively low voltage (690V typicallyfor a wind turbine, compared to the 10kV range of traditionalpower plants). To achieve high power, they need high current, whichin turn requires splitting the conductors in the winding into isolatedparallel strands to avoid losses due to eddy currents and current crowding.However, new losses from circulating currents can then arise. Inorder to reduce said losses, the parallel conductors should be transposedin such a way that the aggregate electromotive force the circuitsthat each pair of them forms is minimized.This research and prototyping was performed in absence of advancedindustrial means of construction, with limited space, budget,materials, manpower, know-how, and technology. Manual ingenuityand empirical experimentation were required to find a practical implementationfor: laying the cables, fixing them in place, transferringthem to the machine, stripping their coating at the ends and establishinga reliable connection to the current source.Using theoretical derivations and FEM simulation, a sufficientlygood transposition scheme is proposed for the specific machine thatthe winding is built for. A bobbin replicating the shape of the enginecore is built to lay down the strands.The parallel strands are then organized each into their respectivebobbin, with a bobbin rack and conductor funneling device being designedand constructed to gather them together into a strictly-organizedbundle. An adhesive is found to set the cables in place.Problems with maintaining the orientation and configuration of thecables in the face of repeated torsion are met and solved. A chemicalsolution is used to strip the ends of the conductors, and a reliableconnection is established by crimping the conductors into a bi-metalCu-Al lug.ivIn conclusion, the ideal transposition schemes required to cancelout circulating currents due to magnetic flux leakage are impossibleto put in practice without appropriate technological means. The feasibletransposition scheme turns out to be a simple mirroring of conductors’positions, implemented by building each half of the windingseparately around replicas of the core and then connecting them usingcrimping lugs. / Efterfrågan på el från förnybara källor är hög och inget tyder på att det kommer ändras den närmsta tiden. En källa till förnybar el som än idag står relativt orörd är den där man använder energin från havsvå- gor. Det är denna förnybara källa Anders Hagnestål haft i åtanke när han nu bygger en unikt effektiv generator med syftet att i ett senare skede utvinna el med hjälp av flytande punktabsorberande vågkraft- system. Generatorn är av den linjära typen och omvandlar det punk- tabsorberande systemet rörelse till el. För att testa denna generator- modell så påbörjades bygget av två fullskaliga prototyper 2017. Denna uppsats behandlar specifikt arbetet med generatorlindningen till pro- totyperna och innefattar processen från design till själva byggnatio- nen. Lindingen består av flertalet mindre och isolerade lindningsleda- re med uppgift att bland annat minska skinneffekt och virvelströms- förluster. När man använder denna metod så uppkommer dock ett nytt problem vilket härstammar från att lindningsledarna är samman- kopplade i vardera ända och bildar på så sätt n slutna strömkretsar. Konsekvensen kan vara stora förluster från cirkulerande strömmar på grund av det magnetiska ströflöde som finns runt järnkärnan som lindningen omsluter. Utgångspunkten för att minimera dessa cirkule- rande strömmar är att transponera alla lindningsledare på ett sätt så att den resulterande elektromotoriska spänningen för varje strömkrets blir så liten som möjligt. Med hjälp av förenklade modeller samt FEM simuleringar så bestämdes ett lämpligt sätt att transponera lindningstrådarna utifrån oli- ka kriterier. Lösningen blev att lindningstrådarna endast transponera- des en gång med en så kallad 180 grader transponering. Detta ger en tillräckligt god minimering av de cirkulerande ström- marna, men den stora fördelen med denna lösning är att det är möjligt att linda maskinen med de små resurser projektet hade tillgång till, dock var detta till en stor nackdel då väldigt mycket tid gick till att hitta egna tillvägagångsätt för att utföra byggandet av lindningen på ibland okonventionella sätt.