Synthesis of constrained tricyclic nucleosides and the core of nagilactone B

Cette thèse décrit deux thèmes principaux: 1) la conception, la synthèse, et l'évaluation biophysique des nucléosides tricycliques, et 2) la synthèse de nagilactone B, un produit naturel norditerpenoïde dilactone de la famille de produits naturels “podolactone”. Le premier chapitre décrit la stratégie de design rationnel des nucléosides nommé “restriction conformationnelle double” basée sur les études de modélisation structurales des duplex ADN–ARN modifiés. Cette stratégie implique un blocage du cycle furanose dans une configuration de type N- ou S, et une restriction de la rotation torsionelle autour de l’angle γ. La première contrainte a été incorporée avec un pont méthylène entre l’oxygène en position 2′ et le carbone 4′ du nucléoside. Cette stratégie a été inspirée par les acides nucléiques bloqués (ou “locked nucleic acid”, LNA). La deuxième contrainte a été réalisée en ajoutant un carbocycle supplémentaire dans l'échafaud de l’acide nucléique bloqué. Les défis synthétiques de la formation des nucléotides modifiés à partir des carbohydrates sont décrits ainsi que les améliorations aux stabilités thermiques qu’ils apportent aux duplex oligonucléïques dont ils font partie. Chapitres deux et trois décrivent le développement de deux voies synthétiques complémentaires pour la formation du noyau de nagilactone B. Ce produit naturel a des implications pour le syndrome de Hutchinson–Gilford, à cause de son habilité de jouer le rôle de modulateur de l’épissage d’ARN pré-messager de lamine A. Ce produit naturel contient sept stereocentres différents, dont deux quaternaires et deux comprenant un syn-1,2-diol, ainsi que des lactones à cinq ou six membres, où le cycle à six ressemble à un groupement α-pyrone. La synthèse a débuté avec la cétone de Wieland-Miescher qui a permis d’adresser les défis structurels ainsi qu’explorer les fonctionnalisations des cycles A, B et D du noyau de nagilactone B.

L'implication de la Cycline B dans le processus de cytocinèse

Un dérèglement du cycle cellulaire peut causer le cancer. Lors de la cytocinèse un anneau contractile d’actine et de myosine se forme, se contracte, et donne un anneau du midbody qui mène à l’abscision. Le processus de cytocinèse est sous le contrôle de protéines telles que la GTPase Rho qui active la cytocinèse et les cyclines-Cdks qui l'inhibent. La Drosophile possède 3 cyclines mitotiques CycA/ CycB/ CycB3 qui sont successivement dégradées en fin de mitose et permettent l'initiation de la cytocinèse. La dernière étape d’abscission est un phénomène qui reste encore peu connu. Les protéines Vps4 et CHMP4C liées à ANCHR vont, sous la dépendance de la kinase Aurora B, promouvoir l’abscision mais, suite à quelques études récentes, il semble y avoir une implication de la cycline B. Ici, le but était de tester l’implication de cette cycline dans les processus de cytocinèse et d’abscision, elle a été menée par microscopie à haute résolution en temps réel avec des cellules S2 de l’organisme Drosophila melanogaster par le suivi de protéines recombinantes fluorescentes. L’étude a été divisée en deux axes : gain et perte de fonction par l’intermédiaire respectivement de la protéine Cycline B recombinante stable, non dégradable (CycBstable-GFP) et l’inhibition par l’utilisation d’ARN double brin (ARNdb) sur l’endogène. La CycBstable-GFP a perturbé la cytocinèse en induisant plusieurs anneaux contractiles et midbodies. En revanche la réduction de l’expression de CycB n'a pas eu d’effet observable, et elle ne semble pas avoir d’action sur l’abscission malgré le recrutement de CycB-GFP au midbody tardif. En revanche la protéine Cdk1 semble avoir un rôle dans l'abscision puisque sa réduction d’expression a induit un délai. Elle a donc une implication potentielle sur la cytocinèse.

Studies on the Synthesis and Transformations of a Few 2(3H)- and 3(2H)-Furanones

The thesis entitled studies on the synthesis and transformations of a few 2(3H)- and 3(2H)- furanones. Furanones represent an interesting class of heterocyclic compounds, which constitute the central ring system of many natural products. The derivatives of furan is divided, depending on their structure 2(3H)-furanones(I), 2(5H)-furanones(II), and 3(2H)-furanones(III). Systems I&II are unsatured gama lactones known as ‘butenolides’. Compounds of this type also known as ‘crotonolactones’ based on the parent crotonic acid. In conclusion a number of 2(3H)-and 3(2H)- furanones were synthesized from dibenzoylalkene precursors and were characterized on the basis of spectral analytical and X-ray data. On direct irradiation 3,3-bis(4-chloropheneyl)-5-aryl-3H-furan -2-ones underwent decarbonylation to yield the corresponding alpha, beta- unsaturated carbonyl compounds and upon sensitized irradiation they underwent dimersation arising through a 2+2 cycloaddition reaction. Our studies on 3(2H)-furanones revealed that these compounds are thermally stable, while they undergo extensive decomposition to intractable mixtures under the influence of light. Similarly, the novel dibenzoylalkenes- type systems containing hetroatomatic rings synthesized by us also underwent extensive decomposition under the influence of heat. Some of the 3(2H)-furanones synthesized by us exhibit remarkable anti-proliferative activity.

Comparison of Electromagnetic Band Gap and Split-Ring Resonator Microstrip Lines as Stop Band Structures

In this paper, microstrip lines magnetically coupled to splitring resonators (SRRs) are conquved to electromagnetic bundgup (EBG) nr,rrostrip lines in terns q/ their stop-heard penjbrnmrnce and dimensions. In bath types o/ trunsmis•siou lines, signal propagation is inhibited in it certain jequency bwuL For EBG microstrip lines, the central frequency of such a forbidden band is determined by the period of the structure, whereas in SRR-hased microstrip lines the position of the frequency gap depends on the quasi-static resonant frequency of the rings. The main relevant conrributiun of this paper is to provide a tuning procedure to control the gap width in SRR microstrip lines, and to show that by using SRRs, device dimensions ale much smaller than those required by EBGs in order to obtain similar stop-banal performance. This has been demonstrated by fill-wave electromagnetic simulations and experimentally verified from the characterization ql two fabricated microstrip lines: one with rectangular SRRs etched on the upper substrate side, and the other with a periodic perturbation cf'strip width. For similar rejection and 1-(;H,. gap width centered at 4.5 Gllz, it has been found that the SRR microstrip line is•,fve times shorter. In addition, no ripple is appreciable in the allowed band for the .SRR-hared structure, whereas due to dispersion, certain mismatch is expected in the EBG prototype. Due to the high-frequency selectivity, controllable gap width, and small dimensions, it is believed that SRR coupled to planar transmission lines can have an actual impact on the design of stop-band filters compatible with planar technology, and can be an alternative to present solutions based on distributed approaches or EBG

Influence of Processing Variables on Protein Quality and Frozen Storage Stability of Two Commercially Important Species of Squid (Loligo duvaucelii and Doryteuthis sibogae )

Cephalopods are utilized as an important food item in various countries because of its delicacy as raw consumed food. Mainly sepia and loligo are consumed raw by Japanese and Russians. The freshness of the products is very important when the product is consumed raw. The major species that dominate our squid catch are Loligo duvaucelii and Doryteuthis sibogae. There is a noticeable difference in the quality of both the species. The needle squid (Doryteuthis sibogae ) contributes about 35% of the total squid landing. Due to the fast deterioration , a major portion of the needle squid, which is caught during the first few hauls, is thrown back to sea. The catch in the last hauls only are taken to the landing centers. At present the needle squid is processed as blanched rings and the desired quality is not obtained if it is processed as whole, whole cleaned or as tubes. In this study an attempt is made to investigate the biochemical characteristics in both the species of squid in relation to their quality and, the process control measures to be adopted. The effect of various treatments on their quality and the changes in proteolytic and lysosomal enzymes under various processing conditions are also studied in detail.Thus this study can provide the seafood industry with relevant suggestions and solutions for effective utilization of both the species of squid with emphasis on needle squid.

Strange attractors in the Saturn ring system

The theory of deterministic chaos is used to study the three rings A, B, and C of Saturn and the French and Cassini divisions in between them. The data set comprises Voyager photopolarimeter measurements. The existence of spatially distributed strange attractors is shown, implying that the system is open, dissipative, nonequilibrium, and non-Markovian in character.

On infinite graphs and related matrices

This thesis Entitled On Infinite graphs and related matrices.ln the last two decades (iraph theory has captured wide attraction as a Mathematical model for any system involving a binary relation. The theory is intimately related to many other branches of Mathematics including Matrix Theory Group theory. Probability. Topology and Combinatorics . and has applications in many other disciplines..Any sort of study on infinite graphs naturally involves an attempt to extend the well known results on the much familiar finite graphs. A graph is completely determined by either its adjacencies or its incidences. A matrix can convey this information completely. This makes a proper labelling of the vertices. edges and any other elements considered, an inevitable process. Many types of labelling of finite graphs as Cordial labelling, Egyptian labelling, Arithmetic labeling and Magical labelling are available in the literature. The number of matrices associated with a finite graph are too many For a study ofthis type to be exhaustive. A large number of theorems have been established by various authors for finite matrices. The extension of these results to infinite matrices associated with infinite graphs is neither obvious nor always possible due to convergence problems. In this thesis our attempt is to obtain theorems of a similar nature on infinite graphs and infinite matrices. We consider the three most commonly used matrices or operators, namely, the adjacency matrix

Investigations on the electrical and structural properties of polyaniline doped with camphor sulphonic acid

Polyaniline is chemically synthesised and doped with camphor sulphonic acid. FTIR studies carried out on these samples indicate that the aromatic rings are retained after polymerisation. The percentage of crystallinity for polyaniline doped with camphor sulphonic acid has been estimated from the X-ray diffraction studies and is around 56% with respect to polyaniline emeraldine base. The change in dielectric permittivity with respect to temperature and frequency is explained on the basis of interfacial polarisation. AC conductivity is evaluated from the observed dielectric permittivity. The values of AC and DC conductivity and activation energy are calculated. The activation energy values suggested that the hopping conduction is the prominent conduction mechanism in this system.

N0-[(E)-Furan-2-ylmethylidene]pyridine- 3-carbohydrazide

The title compound, C11H9N3O2, exists in the E conformation with respect to the azomethane C N bond, and has the keto form. There are two independent molecules in the asymmetric unit and each of these features a slight slanting of the pyridine and furan rings, which form a dihedral angle of 14.96 (10) in one of the molecules and 5.53 (10) in the other. The crystal structure is stabilized by N—H O and N—H N hydrogen bonds, weak C—H O and C—H N hydrogen bonds and C—H interactions and – interactions [shortest centroid–centroid distance = 3.7864 (15) A ° ].

Synthesis, Characterization and Applications of Modified TiO2 Systems

This thesis is divided in to 9 chapters and deals with the modification of TiO2 for various applications include photocatalysis, thermal reaction, photovoltaics and non-linear optics. Chapter 1 involves a brief introduction of the topic of study. An introduction to the applications of modified titania systems in various fields are discussed concisely. Scope and objectives of the present work are also discussed in this chapter. Chapter 2 explains the strategy adopted for the synthesis of metal, nonmetal co-doped TiO2 systems. Hydrothermal technique was employed for the preparation of the co-doped TiO2 system, where Ti[OCH(CH3)2]4, urea and metal nitrates were used as the sources for TiO2, N and metals respectively. In all the co-doped systems, urea to Ti[OCH(CH3)2]4 was taken in a 1:1 molar ratio and varied the concentration of metals. Five different co-doped catalytic systems and for each catalysts, three versions were prepared by varying the concentration of metals. A brief explanation of physico-chemical techniques used for the characterization of the material was also presented in this chapter. This includes X-ray Diffraction (XRD), Raman Spectroscopy, FTIR analysis, Thermo Gravimetric Analysis, Energy Dispersive X-ray Analysis (EDX), Scanning Electron Microscopy(SEM), UV-Visible Diffuse Reflectance Spectroscopy (UV-Vis DRS), Transmission Electron Microscopy (TEM), BET Surface Area Measurements and X-ray Photoelectron Spectroscopy (XPS). Chapter 3 contains the results and discussion of characterization techniques used for analyzing the prepared systems. Characterization is an inevitable part of materials research. Determination of physico-chemical properties of the prepared materials using suitable characterization techniques is very crucial to find its exact field of application. It is clear from the XRD pattern that photocatalytically active anatase phase dominates in the calcined samples with peaks at 2θ values around 25.4°, 38°, 48.1°, 55.2° and 62.7° corresponding to (101), (004), (200), (211) and (204) crystal planes (JCPDS 21-1272) respectively. But in the case of Pr-N-Ti sample, a new peak was observed at 2θ = 30.8° corresponding to the (121) plane of the polymorph brookite. There are no visible peaks corresponding to dopants, which may be due to their low concentration or it is an indication of the better dispersion of impurities in the TiO2. Crystallite size of the sample was calculated from Scherrer equation byusing full width at half maximum (FWHM) of the (101) peak of the anatase phase. Crystallite size of all the co-doped TiO2 was found to be lower than that of bare TiO2 which indicates that the doping of metal ions having higher ionic radius into the lattice of TiO2 causes some lattice distortion which suppress the growth of TiO2 nanoparticles. The structural identity of the prepared system obtained from XRD pattern is further confirmed by Raman spectra measurements. Anatase has six Raman active modes. Band gap of the co-doped system was calculated using Kubelka-Munk equation and that was found to be lower than pure TiO2. Stability of the prepared systems was understood from thermo gravimetric analysis. FT-IR was performed to understand the functional groups as well as to study the surface changes occurred during modification. EDX was used to determine the impurities present in the system. The EDX spectra of all the co-doped samples show signals directly related to the dopants. Spectra of all the co-doped systems contain O and Ti as the main components with low concentrations of doped elements. Morphologies of the prepared systems were obtained from SEM and TEM analysis. Average particle size of the systems was drawn from histogram data. Electronic structures of the samples were identified perfectly from XPS measurements. Chapter 4 describes the photocatalytic degradation of herbicides Atrazine and Metolachlor using metal, non-metal co-doped titania systems. The percentage of degradation was analyzed by HPLC technique. Parameters such as effect of different catalysts, effect of time, effect of catalysts amount and reusability studies were discussed. Chapter 5 deals with the photo-oxidation of some anthracene derivatives by co-doped catalytic systems. These anthracene derivatives come underthe category of polycyclic aromatic hydrocarbons (PAH). Due to the presence of stable benzene rings, most of the PAH show strong inhibition towards biological degradation and the common methods employed for their removal. According to environmental protection agency, most of the PAH are highly toxic in nature. TiO2 photochemistry has been extensively investigated as a method for the catalytic conversion of such organic compounds, highlighting the potential of thereof in the green chemistry. There are actually two methods for the removal of pollutants from the ecosystem. Complete mineralization is the one way to remove pollutants. Conversion of toxic compounds to another compound having toxicity less than the initial starting compound is the second way. Here in this chapter, we are concentrating on the second aspect. The catalysts used were Gd(1wt%)-N-Ti, Pd(1wt%)-N-Ti and Ag(1wt%)-N-Ti. Here we were very successfully converted all the PAH to anthraquinone, a compound having diverse applications in industrial as well as medical fields. Substitution of 10th position of desired PAH by phenyl ring reduces the feasibility of photo reaction and produced 9-hydroxy 9-phenyl anthrone (9H9PA) as an intermediate species. The products were separated and purified by column chromatography using 70:30 hexane/DCM mixtures as the mobile phase and the resultant products were characterized thoroughly by 1H NMR, IR spectroscopy and GCMS analysis. Chapter 6 elucidates the heterogeneous Suzuki coupling reaction by Cu/Pd bimetallic supported on TiO2. Sol-Gel followed by impregnation method was adopted for the synthesis of Cu/Pd-TiO2. The prepared system was characterized by XRD, TG-DTG, SEM, EDX, BET Surface area and XPS. The product was separated and purified by column chromatography using hexane as the mobile phase. Maximum isolated yield of biphenyl of around72% was obtained in DMF using Cu(2wt%)-Pd(4wt%)-Ti as the catalyst. In this reaction, effective solvent, base and catalyst were found to be DMF, K2CO3 and Cu(2wt%)-Pd(4wt%)-Ti respectively. Chapter 7 gives an idea about the photovoltaic (PV) applications of TiO2 based thin films. Due to energy crisis, the whole world is looking for a new sustainable energy source. Harnessing solar energy is one of the most promising ways to tackle this issue. The present dominant photovoltaic (PV) technologies are based on inorganic materials. But the high material, low power conversion efficiency and manufacturing cost limits its popularization. A lot of research has been conducted towards the development of low-cost PV technologies, of which organic photovoltaic (OPV) devices are one of the promising. Here two TiO2 thin films having different thickness were prepared by spin coating technique. The prepared films were characterized by XRD, AFM and conductivity measurements. The thickness of the films was measured by Stylus Profiler. This chapter mainly concentrated on the fabrication of an inverted hetero junction solar cell using conducting polymer MEH-PPV as photo active layer. Here TiO2 was used as the electron transport layer. Thin films of MEH-PPV were also prepared using spin coating technique. Two fullerene derivatives such as PCBM and ICBA were introduced into the device in order to improve the power conversion efficiency. Effective charge transfer between the conducting polymer and ICBA were understood from fluorescence quenching studies. The fabricated Inverted hetero junction exhibited maximum power conversion efficiency of 0.22% with ICBA as the acceptor molecule. Chapter 8 narrates the third order order nonlinear optical properties of bare and noble metal modified TiO2 thin films. Thin films were fabricatedby spray pyrolysis technique. Sol-Gel derived Ti[OCH(CH3)2]4 in CH3CH2OH/CH3COOH was used as the precursor for TiO2. The precursors used for Au, Ag and Pd were the aqueous solutions of HAuCl4, AgNO3 and Pd(NO3)2 respectively. The prepared films were characterized by XRD, SEM and EDX. The nonlinear optical properties of the prepared materials were investigated by Z-Scan technique comprising of Nd-YAG laser (532 nm,7 ns and10 Hz). The non-linear coefficients were obtained by fitting the experimental Z-Scan plot with the theoretical plots. Nonlinear absorption is a phenomenon defined as a nonlinear change (increase or decrease) in absorption with increasing of intensity. This can be mainly divided into two types: saturable absorption (SA) and reverse saturable absorption (RSA). Depending on the pump intensity and on the absorption cross- section at the excitation wavelength, most molecules show non- linear absorption. With increasing intensity, if the excited states show saturation owing to their long lifetimes, the transmission will show SA characteristics. Here absorption decreases with increase of intensity. If, however, the excited state has strong absorption compared with that of the ground state, the transmission will show RSA characteristics. Here in our work most of the materials show SA behavior and some materials exhibited RSA behavior. Both these properties purely depend on the nature of the materials and alignment of energy states within them. Both these SA and RSA have got immense applications in electronic devices. The important results obtained from various studies are presented in chapter 9.

Zur Synthese von alpha-Aminoaldehyden und Aminosäuren mit alpha-quartären Zentren durch Aziridinierung funktionalisierter Olefine

Ziel dieser Arbeit war, durch Aziridinierung homochiraler 5-Methyl-4H-1,3-dioxinen eine neue Methode zur Synthese von alpha-Aminoaldehyden und den ableitbaren Aminosäuren mit alpha-quartären Zentren zu entwickeln. Die chiralen 5-Methyl-4H-1,3-dioxine sind mit hohen Enantiomerenüberschüssen durch asymmetrische Doppelbindungsisomerisierung von 5-Methylen-1,3-dioxanen zugänglich. Die Metall-katalysierte Aziridinierung der 5-Methyl-4H-1,3-dioxine mit der Nitrenquelle (N-Tosylimino)phenyliodinan führte direkt zu N-Tosyl-geschützen 4-Methyl-1,3-oxazolidin-4-carbaldehyden. Vermutlich über ein Aziridin als nicht isolierbare Zwischenstufe werden über eine Ringöffnungs-/Ringverengungsreaktion die Oxazolidinderivate gebildet, vorzugsweise in Gegenwart von Cu(I)-Katalysatoren, während die Rhodium-katalysierte Reaktion ausschließlich zu Insertionsprodukten führt. In der Cu-katalysierten Aziridinierung ist das Verhältnis von Aziridinierung/Insertion abhängig von der Katalysatorkonzentration. Die Aziridinierung mit N-(p-Nitrobenzolsulfonyl)- und N-(Trimethylsilylethylsulfonyl)- substituierten Nitrenquellen führt zu Oxazolidinderivaten mit leichter abspaltbaren Schutzgruppen. Diese Nitrenquellen können in situ aus den korrespondierenden Sulfonamiden mit Iodosobenzol dargestellt werden. Bei dem Einsatz homochiraler 4H-1,3-Dioxine ist Erhalt der Stereoinformation abhängig vom Substituenten in 2-Position der Dioxine sowie von der Polarität des Lösungsmittels. Die höchsten Selektivitäten wurden in tert-Butylmethylether erzielt. In Falle des 2-tert-Butyl-4-methyl-3-(toluol-4-sulfonyl)-1,3-oxazolidin-4-carbaldehyds kristallisiert das Hauptdiastereomer in enantiomerenreiner Form. Die Absolutkonfiguration wurde durch Röntgenkristallstrukturanalyse ermittelt. Das Anwendungspotential dieser neuen Methode konnte durch Überführen der Serinale in Aminoalkohole und alpha-Methylserin-Derivate sowie in der Synthese der unnatürlichen Aminosäure alpha-Vinylalanin gezeigt werden.

Entwicklung eines Bewertungssystems für die Aschuaiat-Gebiete mit Hilfe des Geographischen Informationssystems (GIS) am Beispiel des Stadtteils Manshiet Nasser in Kairo

Der Schwerpunkt dieser Arbeit handelt sich um die informelle Siedlungen in Kairo (die wir Asch- Gebiete nennen). Der Begriff "Aschuaiat" bezeichnet ganz speziell und treffend dieses Phänomen. Die Probleme der Aschuaiat haben seit den 70er Jahren auf ganz Ägypten und die Stadt Kairo sehr negative Auswirkungen, die im Laufe der Zeit zu massiven Problemen geworden sind. Die Entscheidungsträger versuchten für diese Schwierigkeiten Lösungen zu finden, aber die Ergebnisse waren nicht befriedigend. Dieses Phänomen sieht wie ein städtebauliches Problem aus, kann aber in Wirklichkeit nicht von den ökologischen und sozialen Verhältnisse einer Region getrennt werden. Die Aschuaiat entstehen normalerweise in städtebaulichen Zentren und in größeren Städten als Ergebnisse ihrer Anziehungskraft, da solche Städte ein gutes Angebot an Arbeitsplätzen, insbesondere im Bereich der Dienstleistungen, haben. Im Gegensatz dazu stehen die landwirtschaftlichen Gebiete: sie zeichnen sich insbesondere durch steigende Arbeitslosigkeit und Mangel an Dienstleistungen aus. Deshalb wandert ein Großteil der Bevölkerung vom Land in die Stadt ab, um hier auf die Suche nach einem Arbeitsplatz zu gehen und insgesamt bessere Lebensbedingungen vorzufinden. Die Zahl der Zuwanderer steigt stetig; die Städte können die Bedürfnisse der Bevölkerung an Angeboten für Wohnungen, Arbeitsplätzen und Dienstleistungen nicht erfüllen. Deswegen nimmt die Bevölkerung, ihre Probleme selbst in die Hand. Dies führt in den meisten Fällen zu einer klaren Form von Aschuaiat innerhalb und um die städtebaulichen Zentren herum. Die Anzahl der Aschuaiat, die sich rings um Kairo befinden, beträgt 76 Zonen mit einer Gesamtfläche von 23,10 km² und einer Einwohnerzahl von 2.098.469. Die Anzahl der illegalen Wohnungseinheiten beträgt 70 Prozent des Gesamtwertes legaler, staatlicher oder privater Wohneinheiten. Diese wurden im Zeitraum zwischen 1980 und 2000 erbaut. Jede Provinz in Ägypten hat Asch-Gebiete - mit Ausnahme der Provinzen Süd Sina und Neues Tal. Die meisten konzentrieren sich in den Provinzen El Dakahlia (121) und Dumiat (88). Die wenigsten Asch-Gebiete (jeweils nur eine Zone) gibt es in den Provinzen Rotes Meer und Nord Sina. In Ägypten wird die Einwohnerzahl der Aschuaiat auf 37 Prozent der Gesamtbevölkerung der städtebaulichen Gebiete geschätzt. Über die genaue Anzahl der Aschuaiat liegen jedoch keine zuverlässigen Informationen vor, die statistischen Daten der staatlichen Organisationen weisen unterschiedliche Resultate auf. Das Ministerium für lokale Entwicklung verkündete, dass die Zahl der Aschuaiat im Jahr 2000 ca. 916 und im Jahr 2003 ca. 1.228 Zonen betragen hat; das Informationszentrum zur Unterstützung von Sachentscheidungen registrierte jedoch für das Jahr 2000 eine Zahl von 1.034 Zonen; demgegenüber liegt die von CAPMAS registrierte Anzahl für 2000 bei 909 Zonen. Diese Unterschiede in der Erfassung der statistischen Daten kann darauf zurückgeführt werden, dass es in Ägypten keine einheitliche Definition für Aschuaiat gibt. Dieses Problem verstärkt den Bedarf an geeignetem Bewertungssystem für die Bewertung der Qualität solcher Gebiete in ganz Ägypten. Das vorgeschlagene Bewertungssystem basiert auf der Analyse und Bewertung der Hauptstrukturen, die die eigentliche Zusammensetzung einer Siedlung repräsentieren. Diese Strukturen spiegeln in der Regel die sozialen, städtebaulichen und infrastrukturellen Eigenschaften eines Gebietes wider. Konkret befasst sich diese Untersuchung mit den verschiedenen Strukturen, die die Lebens- und Siedlungsqualität in den Aschuaiat beeinflussen.

Fourier-Matrizen und Ringe mit Basis

Bei der Bestimmung der irreduziblen Charaktere einer Gruppe vom Lie-Typ entwickelte Lusztig eine Theorie, in der eine sogenannte Fourier-Transformation auftaucht. Dies ist eine Matrix, die nur von der Weylgruppe der Gruppe vom Lie-Typ abhängt. Anhand der Eigenschaften, die eine solche Fourier- Matrix erfüllen muß, haben Geck und Malle ein Axiomensystem aufgestellt. Dieses ermöglichte es Broue, Malle und Michel füur die Spetses, über die noch vieles unbekannt ist, Fourier-Matrizen zu bestimmen. Das Ziel dieser Arbeit ist eine Untersuchung und neue Interpretation dieser Fourier-Matrizen, die hoffentlich weitere Informationen zu den Spetses liefert. Die Werkzeuge, die dabei entstehen, sind sehr vielseitig verwendbar, denn diese Matrizen entsprechen gewissen Z-Algebren, die im Wesentlichen die Eigenschaften von Tafelalgebren besitzen. Diese spielen in der Darstellungstheorie eine wichtige Rolle, weil z.B. Darstellungsringe Tafelalgebren sind. In der Theorie der Kac-Moody-Algebren gibt es die sogenannte Kac-Peterson-Matrix, die auch die Eigenschaften unserer Fourier-Matrizen besitzt. Ein wichtiges Resultat dieser Arbeit ist, daß die Fourier-Matrizen, die G. Malle zu den imprimitiven komplexen Spiegelungsgruppen definiert, die Eigenschaft besitzen, daß die Strukturkonstanten der zugehörigen Algebren ganze Zahlen sind. Dazu müssen äußere Produkte von Gruppenringen von zyklischen Gruppen untersucht werden. Außerdem gibt es einen Zusammenhang zu den Kac-Peterson-Matrizen: Wir beweisen, daß wir durch Bildung äußerer Produkte von den Matrizen vom Typ A(1)1 zu denen vom Typ C(1) l gelangen. Lusztig erkannte, daß manche seiner Fourier-Matrizen zum Darstellungsring des Quantendoppels einer endlichen Gruppe gehören. Deswegen ist es naheliegend zu versuchen, die noch ungeklärten Matrizen als solche zu identifizieren. Coste, Gannon und Ruelle untersuchen diesen Darstellungsring. Sie stellen eine Reihe von wichtigen Fragen. Eine dieser Fragen beantworten wir, nämlich inwieweit rekonstruiert werden kann, zu welcher endlichen Gruppe gegebene Matrizen gehören. Den Darstellungsring des getwisteten Quantendoppels berechnen wir für viele Beispiele am Computer. Dazu müssen unter anderem Elemente aus der dritten Kohomologie-Gruppe H3(G,C×) explizit berechnet werden, was bisher anscheinend in noch keinem Computeralgebra-System implementiert wurde. Leider ergibt sich hierbei kein Zusammenhang zu den von Spetses herrührenden Matrizen. Die Werkzeuge, die in der Arbeit entwickelt werden, ermöglichen eine strukturelle Zerlegung der Z-Ringe mit Basis in bekannte Anteile. So können wir für die meisten Matrizen der Spetses Konstruktionen angeben: Die zugehörigen Z-Algebren sind Faktorringe von Tensorprodukten von affinen Ringe Charakterringen und von Darstellungsringen von Quantendoppeln.

Computing Generators of Free Modules over Orders in Group Algebras

Let E be a number field and G be a finite group. Let A be any O_E-order of full rank in the group algebra E[G] and X be a (left) A-lattice. We give a necessary and sufficient condition for X to be free of given rank d over A. In the case that the Wedderburn decomposition E[G] \cong \oplus_xM_x is explicitly computable and each M_x is in fact a matrix ring over a field, this leads to an algorithm that either gives elements \alpha_1,...,\alpha_d \in X such that X = A\alpha_1 \oplus ... \oplusA\alpha_d or determines that no such elements exist. Let L/K be a finite Galois extension of number fields with Galois group G such that E is a subfield of K and put d = [K : E]. The algorithm can be applied to certain Galois modules that arise naturally in this situation. For example, one can take X to be O_L, the ring of algebraic integers of L, and A to be the associated order A(E[G];O_L) \subseteq E[G]. The application of the algorithm to this special situation is implemented in Magma under certain extra hypotheses when K = E = \IQ.

Computations in Relative Algebraic K-Groups

Let G be finite group and K a number field or a p-adic field with ring of integers O_K. In the first part of the manuscript we present an algorithm that computes the relative algebraic K-group K_0(O_K[G],K) as an abstract abelian group. We solve the discrete logarithm problem, both in K_0(O_K[G],K) and the locally free class group cl(O_K[G]). All algorithms have been implemented in MAGMA for the case K = \IQ. In the second part of the manuscript we prove formulae for the torsion subgroup of K_0(\IZ[G],\IQ) for large classes of dihedral and quaternion groups.