Most quantum algorithms that are efficient as opposed to their equivalent classical algorithms are solving variants of the Hidden Subgroup Problem (HSP), therefore HSP is a central problem in the field of quantum computing. In this thesis, we offer some interesting results about the subgroup and coset structure of certain groups, including the dihedral group. We describe classical algorithms to solve the HSP over various abelian groups and the dihedral group. We also discuss some existing quantum algorithms to solve the HSP and give our own novel algorithms and ideas to approach the HSP for the dihedral groups.

Die heutige und zukünftige Entwicklung beim Entwurf von Axialverdichtern für die Anwendung in Flugzeugtriebwerken ist immer stärker davon geprägt, ein möglichst großes Druckverhältnis mit möglichst wenigen Stufen zu erzeugen. Ziel ist es, möglichst viel Leistung mit möglichst geringem Gewicht umzusetzen, um die Effizienz der Maschine weiter zu verbessern. Um dies zu erreichen, muss eine Erhöhung der Stufendruckverhältnisse und damit eine Erhöhung der Stufenbelastung in Kauf genommen werden. Die höhere Belastung hat jedoch einen Anstieg der Verluste aufgrund der stärker werdenden Sekundärströmungen zur Folge, und wirkt sich zunächst negativ auf die Stabilität und den Wirkungsgrad der Maschine aus. Diese negativen Effekte können nur durch eine Weiterentwicklung der Schaufelgeometrie kompensiert werden. Hierbei stoßen die derzeit benutzten Entwurfsmethoden jedoch an ihre Grenzen. Aus diesem Grund wurde ein neues Verfahren für den dreidimensionalen Entwurf von Rotoren in Axialverdichtern entwickelt. In dieser Arbeit wird dessen Entwicklung präsentiert. Das Verfahren umfasst die systematische Anwendung von Pfeilung und V-Stellung, sowie die dreidimensionale inverse Berechnung der radialen Skelettlinienverteilung. Um damit eine Verbesserung des Rotorwirkungsgrades zu erreichen, müssen vor allem die kritischen wand- bzw. spaltnahen Bereiche optimal an die Strömungsumgebung angepasst werden. Die vorliegende Arbeit beschreibt ausführlich die theoretischen Grundlagen der Rotorströmung und des Rotorentwurfs. Basierend darauf werden für die Umsetzung eines vollständigen dreidimensionalen Schaufelentwurfs zwei Panelverfahren zur Berechnung der dreidimensionalen jedoch reibungslosen Strömung, zur Lösung der Nachrechen- bzw. der Entwurfsaufgabe, entwickelt. Die Panelverfahren werden angewandt, um eine Methodik für den effektiven Einsatz von Pfeilung, V-Stellung und inverser Skelettlinienberechnung für den dreidimensionalen Rotorentwurf festzulegen. Die gewonnenen Erkenntnisse werden anschließend für den Entwurf eines hochbelasteten Rotors in einem einstufigen Niedergeschwindigkeitsverdichter nach dieser neuen Entwurfsmethodik genutzt. Anhand von Ergebnissen aus Rechnungen und Messungen für diesen Rotor wird die Wirksamkeit des Verfahrens demonstriert. / The recent and future design of axial compressors for aero engines is strongly affected by the aim to generate a high pressure ratio with less stages to increase power and reduce weight to achieve an improved efficiency. This can only be achieved when the stage pressure ratio is raised which leads to increased stage loading. But the higher stage loading results in higher losses caused by stronger secondary flows. This has a negative effect on compressor stability and efficiency. To counteract the negative effects enhanced blade geometries are necessary. With the recently used design methods this is hardly to achieve. For that reason a new method for the three-dimensional design of rotors and stators in axial compressors has been developed. This report summarizes that work. The method accounts for the systematic application of sweep and dihedral as well as the three-dimensional inverse calculation of the camber-line distributions along blade height. To achieve improved efficiency the regions close to the end-walls and the tip and hub gap have to be adapted to the flow environment. The recent report described in detail the theoretical background of the compressor blade flow and compressor blade design. Based on that, two inviscid panel methods for the fully three-dimensional design of compressor blades are described. The panel methods are applied to define a methodology for the effective application of sweep, dihedral and inverse camber-line calculation in a three-dimensional blade design process. Afterwards the findings are used to design a highly-loaded single-stage low-speed research compressor rotor. The validity of the presented design method is proven with CFD and test results.

Based on the success of diacyl-tert-butylhydrazines RH-5849 and RH-1266 in controlling agricultural crop pests, we endeavored to synthesize our own diacylbenzyl- and arylhydrazine derivatives for use against the malaria vector Anopheles gambiae. In the process of producing a library of compounds for assay against An. gambiae, it became clear that employing regioselective acylation techniques (in molecules that feature two nucleophilic, acyclic nitrogen atoms α to one another) would be imperative. Synthesis of the library derivatives proceeded rapidly and after topical assay, we found three compounds that were more toxic than the RH-series leads. One of the three displayed an LD50 value of half that of RH-1266, though patch clamp assay concluded that toxicity was not necessarily linked to inhibition of mosquito K+ channel Kv2.1. The acylation of monoarylhydrazines appears simple, but its regioselectivity is poorly understood when assumed as a function of basicity correlating to nucleophilic strength. We determined the ratio of the rate constants for distal to proximal N-acylation using 19F NMR spectroscopic analysis of reactions of 4-fluorophenylhydrazine with limiting (0.2 equiv) acylating agent in the presence of various bases. Acid anhydrides gave consistent preference for distal acylation. The selectivity of acylation by acyl chlorides when using pyridine gives strong distal preference, whereas use of triethylamine or aqueous base in conjunction with aroyl chlorides showed a moderate preference for proximal acylation. This observation yielded a convenient one-step method to synthesize proximal aroylarylhydrazines in yields comparable or superior to that provided by the standard three-step literature approach. Combined with NMR evidence of the distal nitrogen as the unambigiously stronger base of the two nitrogens, we propose a single electron transfer mechanism that predicts the regiochemistry of arylhydrazines toward acylating agents better than the nucleophilicity model based on pKa values. While synthesizing the acylhydrazine library for assay against An. gambiae, NMR spectroscopy revealed rotational isomerisms of two types: chiral helicity (M)/(P) and acyl (E)/(Z)-isomerism due to hindered rotation. Variable temperature NMR allowed the measurement of N-N bond rotational barriers, as well as estimate the barrier of (E)/(Z) interconversion. We obtained the X-ray crystal structures of four diacylhydrazines to test this hypothesis and revealed both the twist conformation around the N-N bond axis and (E)/(Z)-isomerism around the proximal acyl group. Computation (which agreed with the crystal structures) allowed us to estimate which (E)/(Z)-isomers were most likely being observed in solution at room temperature by NMR spectroscopy. In addition, we were able to calculate transition structures corresponding to N-N bond rotational barriers of (E,Z)- and (Z,Z)-isomers of model molecules and rationalize the difference in coalescence temperatures between (E,Z)- and (Z,Z)-isomers. / Ph. D.

Les résistances aux traitements actuels contre le cancer imposent de trouver de nouvelles cibles thérapeutiques. Une de ces cibles est le réseau vasculaire assurant un apport suffisant en nutriments et en oxygène à la tumeur, et permettant l’apparition de métastases. Détruire la vascularisation de la tumeur par l’utilisation d’agents antivasculaires (VDA)revient à l’asphyxier et à l’affamer, inhibant ainsi la prolifération des cellules tumorales et empêchant le processus métastatique. L’objectif de ce travail de thèse a été d’étudier des analogues contraints de l’isocombrétastatine A-4 (isoCA-4), une molécule phare du laboratoire, ayant un excellent pouvoir d’inhibition de la polymérisation de la tubuline et présentant une activité antivasculaire. Ces structures dont la double liaison est incluse dans différents types de cycles C,ont été étudiées également afin d’évaluer l’influence de l’angle dièdre formé par les noyaux A et B sur les activités biologiques des divers types de structures. Préalablement sélectionnés par modélisation moléculaire, ces analogues contraints sont de type 1-arylnaphtalène, 5-arylbenzoxépine ou 4-arylchromène et ont été préparés par des voies d’ accès originales développées dans le cadre de cette thèse. Parmi les composés synthétisés, l’analogue de type benzoxépine 3-53est aussi cytotoxique que l’isoCA-4 et possède un pouvoir d’inhibition de la polymérisation de la tubuline équivalent. Une évaluation plus poussée de son profil biologique, ainsi que celle des meilleurs représentants de chaque série chimique est actuellement en cours. / Most tumor cells rely on an efficient vascular supply for their survival, making the tumor vasculature an attractive target for anti-cancer therapy. This thesis aimed at the design and synthesis of constrained analogues of isocombretastatin A-4(isoCA-4), an antivascular agent developed in the laboratory, which exerts excellent cytotoxicities against a large panel ofcancer cell lines, and strongly inhibits tubulin polymerization. Conformationally restricted analogues of isoCA-4,featuring 1-arylnaphthalene, 5-arylbenzoxepine or 4-arylchromene skeletons were designed by computational studies andprepared by novel synthetic strategies. Of all synthesized compounds, benzoxepine analogue 3-53 strongly inhibits tubulinpolymerization and shows excellent cytotoxicities against several human cancer cell lines.

Loops automórficos, ou A-loops, são loops nos quais todas as aplicações internas são automorfismos. Esta variedade de loops inclui grupos e loops de Moufang comutativos. Loops automórficos diedrais formam uma classe de A-loops construda a partir da duplicação de grupos abelianos finitos, generalizando a construção do grupo diedral. Outra classe de A-loops é a dos loops automórficos de Lie, construda a partir de anéis de Lie, definindo-se uma nova operação entre seus elementos. Um half-isomorfismo é uma bijeção f entre loops L e L\' onde, para quaisquer x e y pertencentes a L, temos que f(xy) pertence ao conjunto . Dizemos que o half-isomorfismo f é não trivial quando f não é um isomorfismo e nem um anti-isomorfismo. Nesta tese descrevemos propriedades de half-isomorfismos de loops, classificamos os half-isomorfismos entre loops automórficos diedrais e obtivemos o grupo de half-automorfismos nesta classe. Para os loops automórficos de Lie de ordem mpar, mostramos que todo half-automorfismo é trivial. / Automorphic loops, or A-loops, are loops in which every inner mapping is an automorphism. This variety of loops includes groups and commutative Moufang loops. Dihedral automorphic loops form a class of A-loops, constructed from the duplication of finite abelian groups, that generalizes the construction of the dihedral group. Another class of A-loops is the Lie automorphic loops, constructed from Lie rings, where a new operation between its elements is defined. A half-isomorphism is a bijection f between loops L and L\' where, for any x and y belong to L, we have that f(xy) belongs to the set {f(x)f(y),f(y)f(x)}. We say that half-isomorphism f is non trivial when f is neither an isomorphism nor an anti-isomorphism. In this thesis, we describe properties of half-isomorphisms of loops, we classify the half-isomorphisms between dihedral automorphic loops and we obtain the group of half-automorphisms in this class. For the Lie automorphic loops of odd order, we show that every half-automorphism is trivial.

Loops automórficos, ou A-loops, são loops nos quais todas as aplicações internas são automorfismos. Esta variedade de loops inclui grupos e loops de Moufang comutativos. Loops automórficos diedrais formam uma classe de A-loops construda a partir da duplicação de grupos abelianos finitos, generalizando a construção do grupo diedral. Outra classe de A-loops é a dos loops automórficos de Lie, construda a partir de anéis de Lie, definindo-se uma nova operação entre seus elementos. Um half-isomorfismo é uma bijeção f entre loops L e L\' onde, para quaisquer x e y pertencentes a L, temos que f(xy) pertence ao conjunto . Dizemos que o half-isomorfismo f é não trivial quando f não é um isomorfismo e nem um anti-isomorfismo. Nesta tese descrevemos propriedades de half-isomorfismos de loops, classificamos os half-isomorfismos entre loops automórficos diedrais e obtivemos o grupo de half-automorfismos nesta classe. Para os loops automórficos de Lie de ordem mpar, mostramos que todo half-automorfismo é trivial. / Automorphic loops, or A-loops, are loops in which every inner mapping is an automorphism. This variety of loops includes groups and commutative Moufang loops. Dihedral automorphic loops form a class of A-loops, constructed from the duplication of finite abelian groups, that generalizes the construction of the dihedral group. Another class of A-loops is the Lie automorphic loops, constructed from Lie rings, where a new operation between its elements is defined. A half-isomorphism is a bijection f between loops L and L\' where, for any x and y belong to L, we have that f(xy) belongs to the set {f(x)f(y),f(y)f(x)}. We say that half-isomorphism f is non trivial when f is neither an isomorphism nor an anti-isomorphism. In this thesis, we describe properties of half-isomorphisms of loops, we classify the half-isomorphisms between dihedral automorphic loops and we obtain the group of half-automorphisms in this class. For the Lie automorphic loops of odd order, we show that every half-automorphism is trivial.

Abstract Image acquisition devices are always subject to physical limitations that often manifest as distortions in the appearance of the captured image. The most common types of distortions can be divided into two categories: geometric and radiometric distortions. Examples of the latter ones are: changes in brightness, contrast, or illumination, sensor noise and blur. Since image blur can have many different causes, it is usually not convenient and also computationally expensive to develop ad hoc algorithms to correct each specific type of blur. Instead, it is often possible to extract a blur-invariant representation of the image, and utilize such information to make algorithms that are insensitive to blur. The work presented here mainly focuses on developing techniques for the extraction and the application of blur-invariant operators. This thesis contains several contributions. First, we propose a generalized framework based on group theory to constructively generate complete blur-invariants. We construct novel operators that are invariant to a large family of blurs occurring in real scenarios: namely, those blurs that can be modeled by a convolution with a point-spread function having rotational symmetry, or combined rotational and axial symmetry. A second important contribution is represented by the utilization of such operators to develop an algorithm for blur-invariant translational image registration. This algorithm is experimentally demonstrated to be more robust than other state-of-the-art registration techniques. The blur-invariant registration algorithm is then used as pre-processing steps to several restoration methods based on image fusion, like depth-of-field extension, and multi-channel blind deconvolution. All the described techniques are then re-interpreted as a particular instance of Wiener deconvolution filtering. Thus, the third main contribution is the generalization of the blur-invariants and the registration techniques to color images, by using respectively a representation of color images based on quaternions, and the quaternion Wiener filter. This leads to the development of a blur-and-noise-robust registration algorithm for color images. We observe experimentally a significant increase in performance in both color texture recognition, and in blurred color image registration. / Tiivistelmä Kuvauslaitteet ovat aina fyysisten olosuhteiden rajoittamia, mikä usein ilmenee tallennetun kuvan ilmiasun vääristyminä. Yleisimmät vääristymätyypit voidaan jakaa kahteen kategoriaan: geometrisiin ja radiometrisiin distortioihin. Jälkimmäisestä esimerkkejä ovat kirkkauden, kontrastin ja valon laadun muutokset sekä sensorin kohina ja kuvan sumeus. Koska kuvan sumeus voi johtua monista tekijöistä, yleensä ei ole tarkoitukseen sopivaa eikä laskennallisesti kannattavaa kehittää ad hoc algoritmeja erityyppisten sumeuksien korjaamiseen. Sitä vastoin on mahdollista erottaa kuvasta sumeuden invariantin edustuma ja käyttää tätä tietoa sumeudelle epäherkkien algoritmien tuottamiseen. Tässä väitöskirjassa keskitytään esittämään, millaisia eri tekniikoita voidaan käyttää sumeuden invarianttien operaattoreiden muodostamiseen ja sovellusten kehittämiseen. Tämä opinnäyte sisältää useammanlaista tieteellistä vaikuttavuutta. Ensiksi, väitöskirjassa esitellään ryhmäteoriaan perustuva yleinen viitekehys, jolla voidaan generoida sumeuden invariantteja. Konstruoimme uudentyyppisiä operaattoreita, jotka ovat monenlaiselle kuvaustilanteessa ilmenevälle sumeudelle invariantteja. Kyseessä ovat ne rotationaalisesti (ja/tai aksiaalisesti) symmetrisen sumeuden lajit, jotka voidaan mallintaa pistelähteen hajaantumisen funktion (PSF) konvoluutiolla. Toinen tämän väitöskirjan tärkeä tutkimuksellinen anti on esitettyjen sumeuden invarianttien operaattoreiden hyödyntäminen algoritmin kehittelyssä, joka on käytössä translatorisen kuvan rekisteröinnissä. Tällainen algoritmi on tässä tutkimuksessa osoitettu kokeellisesti johtavia kuvien rekisteröintitekniikoita robustimmaksi. Sumeuden invariantin rekisteröinnin algoritmia on käytetty esiprosessointina tässä tutkimuksessa useissa kuvien restaurointimenetelmissä, jotka perustuvat kuvan fuusioon, kuten syväterävyysaluelaajennus ja monikanavainen dekonvoluutio. Kaikki kuvatut tekniikat ovat lopulta uudelleen tulkittu erityistapauksena Wienerin dekonvoluution suodattimesta. Näin ollen tutkimuksen kolmas saavutus on sumeuden invarianttien ja rekisteröintiteknikoiden yleistäminen värikuviin käyttämällä värikuvien kvaternion edustumaa sekä Wienerin kvaternion suodatinta. Havaitsemme kokeellisesti merkittävän parannuksen sekä väritekstuurin tunnistuksessa että sumean kuvan rekisteröinnissä.