Thèses sur le sujet « Soluble and nilpotent group »
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1
Wharton, Elizabeth. « The model theory of certain infinite soluble groups ». Thesis, University of Oxford, 2006. http://ora.ox.ac.uk/objects/uuid:7bd8d05b-4ff6-4326-8463-f896e2862e25.
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This thesis is concerned with aspects of the model theory of infinite soluble groups. The results proved lie on the border between group theory and model theory: the questions asked are of a model-theoretic nature but the techniques used are mainly group-theoretic in character. We present a characterization of those groups contained in the universal closure of a restricted wreath product U wr G, where U is an abelian group of zero or finite square-free exponent and G is a torsion-free soluble group with a bound on the class of its nilpotent subgroups. For certain choices of G we are able to use this characterization to prove further results about these groups; in particular, results related to the decidability of their universal theories. The latter part of this work consists of a number of independent but related topics. We show that if G is a finitely generated abelian-by-metanilpotent group and H is elementarily equivalent to G then the subgroups gamma_n(G) and gamma_n(H) are elementarily equivalent, as are the quotient groups G/gamma_n(G) and G/gamma_n(H). We go on to consider those groups universally equivalent to F_2(VN_c), where the free groups of the variety V are residually finite p-groups for infinitely many primes p, distinguishing between the cases when c = 1 and when c > 2. Finally, we address some important questions concerning the theories of free groups in product varieties V_k · · ·V_1, where V_i is a nilpotent variety whose free groups are torsion-free; in particular we address questions about the decidability of the elementary and universal theories of such groups. Results mentioned in both of the previous two paragraphs have applications here.
2
Grenham, Dermot. « Some topics in nilpotent group theory ». Thesis, University of Oxford, 1988. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.329954.
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Smith, Jeremy Francis. « Topics in products of nilpotent groups ». Thesis, University of Warwick, 1998. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.340502.
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4
Popov, Vladimir L., et popov@ppc msk ru. « Self-Dual Algebraic Varieties and Nilpotent Orbits ». ESI preprints, 2001. ftp://ftp.esi.ac.at/pub/Preprints/esi978.ps.
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Budde, Julia [Verfasser]. « Wave front sets of nilpotent lie group representations / Julia Budde ». Paderborn : Universitätsbibliothek, 2021. http://d-nb.info/122950415X/34.
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Sohrabi, Mahmood. « Groups elementary equivalent to a free 2-nilpotent group of arbitrary finite rank ». Thesis, McGill University, 2005. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=98801.
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In this thesis we discuss the characterization of groups elementary equivalent to a free 2-nilpotent group G of arbitrary finite rank. We find a characterization and verify it using two different lines of argument. The first one goes through using a construction very similar to the famous Mal'cev correspondence. This strategy is very much in the same spirit as the work of O. V. Belegradek on unitriangular groups. The second method, we call the method of bilinear mappings, is due to Alexei Miasnikov. A bilinear map fG is associated to the nilpotent group G. Then a commutative associative ring P(fG) is recovered via the bilinear mapping fG. This ring is the maximal ring relative to which fG remains bilinear. Under some reasonable conditions the ring P( fG) is absolutely interpretable in G. Then we use this construction to give a second proof for the characterization.
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Gjerling, Andreas. « On rings of quotients of soluble group algebras ». Thesis, Queen Mary, University of London, 1998. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.286813.
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Harkins, Andrew. « Combining lattices of soluble lie groups ». Thesis, University of Newcastle Upon Tyne, 2000. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.341777.
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Uemura, Hideaki. « Off-Diagonal Short Time Expansion of the Heat Kernel on a Certain Nilpotent Lie Group ». 京都大学 (Kyoto University), 1989. http://hdl.handle.net/2433/86399.
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Salminen, Adam D. « On the sources of simple modules in nilpotent blocks ». Connect to resource, 2005. http://rave.ohiolink.edu/etdc/view?acc%5Fnum=osu1124221435.
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Thesis (Ph. D.)--Ohio State University, 2005.Title from first page of PDF file. Document formatted into pages; contains viii, 87 p. Includes bibliographical references (p. 85-87). Available online via OhioLINK's ETD Center
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Wilde, Thomas Stephen. « Cohomology and the subgroup structure of a finite soluble group ». Thesis, University of Warwick, 1992. http://wrap.warwick.ac.uk/35510/.
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The main topic of this thesis is the discovery and study of a cohomological property of the subgroups called F-normalizers in finite soluble groups; namely, the property that with certain coefficient modules the restriction map in cohomology from a soluble group to its F-normalizers vanishes in non-zero degrees. Chapter 3 is devoted to a proof of this fact It turns out that in some classes of soluble groups the F-normalizers are characterized by this property, and the study of these classes occupies Chapters 4 and 5. Various connections with cohomology and group theory are found; the approach seems to offer some unification of disparate results from the theory of soluble groups. The relation between F-normalizers and cohomology was discovered through study of the work of Jacques Thevenaz on the action of a soluble group on its lattice of subgroups. Chapter 1 is a summary of this work and its background, and is included to provide motivation. A link with the rest of the thesis arises through a new result, in which certain subgroups crucial to Thevenaz's analysis of soluble groups are shown to coincide with their system normalizers. A proof of this is given in Chapter 2, which also contains some miscellaneous results on soluble groups from the class considered by Thevenaz, comprising those groups whose lattices of subgroups are complemented. The problem of characterizing F-normalizers in soluble groups by the results of Chapter 3 is proposed in Chapter 4, and in Chapters 4 and 5 two essentially different approaches to this problem are taken, which lead to partial solutions in different sets of circumstances. In Chapter 4, the first cohomology groups of soluble groups are considered, and an application is given to a proof of a recent theorem of Volkmar Welker described in Chapter 1 on the homotopy type of the partially ordered set of conjugacy classes of subgroups of a soluble group. Another application is to the study of local conjugacy of subgroups of soluble groups, and these are combined in a result which shows that the set of conjugacy classes considered by Welker is homotopy equivalent to an analogous set obtained from local conjugacy classes. In Chapter 5 some known results on the local conjugacy of F-normalizers are exhibited, as evidence for a cohomological characterization of these subgroups. The results are used to study groups of p-length one by a 'local' analysis, whereby the problem of characterizing F-normalizers is translated into a question concerning the action of automorphisms on the cohomology rings of p-groups. In the study of this question a natural place to start is the case of abelian groups, whose cohomology rings are known; calculations in this case lead to results on the F-normalizers of A-groups. The question is then considered for other p-groups, revealing an elegant relationship between the cohomology of p-groups, the theory of varieties, and some well-known results on automorphisms of p-groups.
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Crawley-Boevey, W. W. « Polycyclic-by-finite affine group schemes and infinite soluble groups ». Thesis, University of Cambridge, 1985. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.372868.
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Cazzola, Marina. « Local character degrees and the derived length of a finite soluble group ». Thesis, University of Warwick, 1995. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.308581.
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Berning, Douglas E. « New developments in main group and transition metal chemistry of water-soluble phospines / ». free to MU campus, to others for purchase, 1997. http://wwwlib.umi.com/cr/mo/fullcit?p9841266.
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Long, Robert Llewellyn, et bizarrealong@hotmail com. « Improving fruit soluble solids content in melon (Cucumis melo L.) (reticulatus group) in the Australian production system ». Central Queensland University. Biological and Environmental Science, 2005. http://library-resources.cqu.edu.au./thesis/adt-QCQU/public/adt-QCQU20051019.144749.
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Total soluble solids (TSS) is a reliable indicator of melon eating quality, with a minimum standard of 10% recommended. The state of Australian melon production with respect to this quality criterion was considered within seasons, between growing districts and over seasons. It was concluded that improvement in agronomic practice and varietal selection is required to produce sweeter melons. The scientific literature addressing melon physiology and agronomy was summarised, as a background to the work that is required to improve melon production practices in Australia.
The effect of source sink manipulation was assessed for commercially grown and glasshouse grown melon plants. The timing of fruit thinning, pollination scheduling, the application of a growth inhibitor and source biomass removal were assessed in relation to fruit growth and sugar accumulation. Results are interpreted against a model in which fruit rapidly increase in weight until about two weeks before harvest, with sugar accumulation continuing as fruit growth ceases. Thus treatment response is very dependant on timing of application. For example, fruit thinning at 25 days before harvest resulted in further fruit set and increased fruit weight but did not impact on fruit TSS (at 9.8%, control 9.3%), while thinning at 5 days before harvest resulted in a significant (Pless than 0.05) increase in fruit TSS (to 10.8%, control 9.3%) and no increase in fruit weight or number. A cost/ benefit analysis is presented, allowing an estimation of the increase in sale price required to sustain the implementation of fruit thinning.
The effect of irrigation scheduling was also considered with respect to increasing melon yield and quality. To date, recommended practice has been to cause an irrigation deficit close to fruit harvest, with the intent of 'drying out' or 'stressing' the plant, to 'bring on' maturity and increase sugar accumulation. Irrigation trials showed that keeping plants stress-free close to harvest and during harvest, facilitated the production of sweeter fruit.
The maintenance of a TSS grade standard using either batch based (destructive) sampling or (non-invasive) grading of individual fruit is discussed. On-line grading of individual fruit is possible using near infrared spectroscopy (NIR), but the applicability of the technique to melons has received little published attention. Tissue sampling strategy was optimised, in relation to the optical geometry used (in commercial operation in Australia), both in terms of the diameter and depth of sampled tissue. NIR calibration model performance was superior when based on the TSS of outer, rather than inner mesocarp tissue. However the linear relationship between outer and middle tissue TSS was strong (r2 = 0.8) in immature fruit, though less related in maturing fruit (r2 = 0.5). The effect of fruit storage (maturation/senescence) on calibration model performance was assessed. There was a negligible effect of fruit cold storage on calibration performance.
Currently, the agronomist lacks a cost-effective tool to rapidly assess fruit TSS in the field. Design parameters for such a tool were established, and several optical front ends compared for rapid, though invasive, analysis. Further, for visualisation of the spatial distribution of tissue TSS within a melon fruit, a two-dimensional, or hyper-spectral NIR imaging system based on a low cost 8-bit charge coupled device (CCD) camera and filter arrangement, was designed and characterised.
16
Wegner, Alexander. « The construction of finite soluble factor groups of finitely presented groups and its application ». Thesis, University of St Andrews, 1992. http://hdl.handle.net/10023/12600.
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Computational group theory deals with the design, analysis and computer implementation of algorithms for solving computational problems involving groups, and with the applications of the programs produced to interesting questions in group theory, in other branches of mathematics, and in other areas of science. This thesis describes an implementation of a proposal for a Soluble Quotient Algorithm, i.e. a description of the algorithms used and a report on the findings of an empirical study of the behaviour of the programs, and gives an account of an application of the programs. The programs were used for the construction of soluble groups with interesting properties, e.g. for the construction of soluble groups of large derived length which seem to be candidates for groups having efficient presentations. New finite soluble groups of derived length six with trivial Schur multiplier and efficient presentations are described. The methods for finding efficient presentations proved to be only practicable for groups of moderate order. Therefore, for a given derived length soluble groups of small order are of interest. The minimal soluble groups of derived length less than or equal to six are classified.
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Distler, Andreas. « Classification and enumeration of finite semigroups ». Thesis, St Andrews, 2010. http://hdl.handle.net/10023/945.
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Poole, Geoffrey D. « The production of soluble proteins having blood group activity, and their use in quantifying red cell antibodies in pregnant women ». Thesis, University of Portsmouth, 2008. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.500335.
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Haemolytic disease of the fetus and newborn is caused by the placental transfer of maternal IgG antibodies that are directed against fetal red (blood) cell antigens. Fetal spleen mononuclear cells phagocytose IgG coated red cells, removing them from the fetal circulation and causing anaemia and, if untreated, hydrops fetalis and kernicterus, both of which may be severe and occasionally fatal. It has been suggested that some antibodies, anti-K in particular, cause fetal anaemia predominantly through suppression of erythropoiesis rather than through red cell destruction. Antenatal screening for haemolytic disease is regularly undertaken by clinical laboratories. Maternal red cell antibodies are identified and their potential for causing disease may be determined by antibody quantification.
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Etheridge, W. « Production of soluble recombinant complement receptor (CR1) antigens to detect or inhibit antibodies to Knops (KN) blood group system antigens ». Thesis, University of the West of England, Bristol, 2015. http://eprints.uwe.ac.uk/26375/.
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The purpose of this study was to produce a reagent to use in investigation of antibodies directed against the Knops blood group system antigens. A novel reagent based on sr-proteins was produced and used in a new test to inhibit these antibodies. Current investigation of patients with alloantibodies directed against Knops blood group system antigens can be a difficult, time-consuming process and the provision of blood for transfusion of these patients can often be delayed. This is because these antibodies are hard to identify and the most commonly found anti-Knops antibodies react with most reagent or donor cells that they are tested with because the corresponding Knops antigens are found at high frequency in most populations. The presence of Knops related antibodies can mask underlying antibodies that are clinically significant. The Knops antigens are carried on Complement Receptor 1 (CR1) located on the red blood cell membrane. Two DNA constructs encoding different parts of CR1 termed long homologous repeat (LHR) C and D were used to transfect human embryonic kidney (HEK293) cells. The cells were grown in different culture systems. Cell culture supernatant containing soluble recombinant (sr)-LHRC or sr-LHR-D was harvested and purified by affinity gel chromatography. The production and purification processes were optimised in terms of protein yield and cost. The resulting purified sr-LHR-C and sr-LHR-D proteins were used to create a novel reagent containing both proteins. This reagent was used in a new inhibition test based on an indirect antiglobulin technique using commercial gel cards. Using the reagent all examples of previously identified Knops antibodies were inhibited. In addition once these antibodies had been inhibited, underlying antibodies were then detected and identified in some samples. For the first time Knops specific antibodies can be detected and identified using one unique test. Any underlying clinically significant antibodies will be rapidly identified if present due to inhibition of the KN antibodies. Introduction of the inhibition test into nine NHSBT patient testing laboratories will reduce the time taken for investigation of these patients and make provision of blood for patients a safer, faster process.
20
丸橋, 広和. « 単連結べき零Lie群のパラメータ剛性をもつ作用 ». 京都大学 (Kyoto University), 2014. http://hdl.handle.net/2433/188455.
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Milliet, Cédric. « Propriétés algébriques des structures menues ou minces, rang de Cantor Bendixson, espaces topologiques généralisés ». Phd thesis, Université Claude Bernard - Lyon I, 2009. http://tel.archives-ouvertes.fr/tel-00442772.
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Les structures menues apparaissent dans les années 1960 de paire avec la conjecture de Vaught, dont elles sont les seuls contre-exemples possibles. Les structures minces sont introduites par Belegradek, et englobent à la fois les structures minimales et menues. Il est bien connu que les ensembles définissables d'une structure mince sont rangés par le rang de Cantor-Bendixson, lorsque l'on fixe un ensemble fini de paramètres. L'étude de ces structures est rendue difficile par le fait que si l'on augmente cet ensemble de paramètres, le rang croît, et on ne sait maîtriser sa croissance. Nous présentons des propriétés de calcul de ce rang, une condition de chaîne descendante locale sur les groupes définissables (par des formules faisant intervenir des paramètres de la clôture algébrique d'un ensemble fini), ainsi qu'une notion de presque stabilisateur local. Nous en déduisons des propriétés algébriques des structures minces : un corps mince de caractéristique positive est localement de dimension finie sur son centre (une réponse au problème 6.1.5 de Wagner, Simple Theories), et un groupe mince infini a un sous groupe abélien infini (cela répond en particulier à la question 2.8 de Wagner, "Groups in simple theories"). Nous nous intéressons ensuite aux structures menues infiniment définissables, et montrons que les groupes d'arité finie infiniment définissables (par des formules n'utilisant que les paramètres d'un ensemble fini) sont l'intersection de groupes définissables (réponse au problème 6.1.14 du livre de Wagner). Nous étendons le résultat aux demi-groupes, anneaux, corps, catégories et groupoïdes infiniment définissables (toujours avec un nombre fini de paramètres), et donnons des résultats de définissabilité locale pour les groupes et corps simples et menus, infiniment définissables sur un ensemble quelconque de paramètres. Enfin, nous réintroduisons le rang de Cantor dans son contexte topologique et montrons que la dérivée de Cantor peut être vue comme un opérateur de dérivation dans un semi-anneau d'espaces topologiques. Dans l'idée de trouver un rang de Cantor global pour les théories stables, nous essayons de nous débarrasser du mot dénombrable omniprésent lorsque l'on fait de la topologie, en le remplaçant par un cardinal régulier k. Nous développons une notion d'espace k-métrique, de k-topologie, de k-compacité etc. et montrons un k-analogue du lemme de métrisabilité d'Urysohn, et du théorème de Cantor-Bendixson.
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Hedén, Isac. « Ga-actions on Complex Affine Threefolds ». Doctoral thesis, Uppsala universitet, Matematiska institutionen, 2013. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-203708.
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This thesis consists of two papers and a summary. The papers both deal with affine algebraic complex varieties, and in particular such varieties in dimension three that have a non-trivial action of one of the one-dimensional algebraic groups Ga := (C, +) and Gm := (C*, ·). The methods used involve blowing up of subvarieties, the correspondances between Ga - and Gm - actions on an affine variety X with locally nilpotent derivations and Z-gradings respectively on O(X) and passing from a filtered algebra A to its associated graded algebra gr(A). In Paper I, we study Russell’s hypersurface X , i.e. the affine variety in the affine space A4 given by the equation x + x2y + z3 + t2 = 0. We reprove by geometric means Makar-Limanov’s result which states that X is not isomorphic to A3 – a result which was crucial to Koras-Russell’s proof of the linearization conjecture for Gm -actions on A3. Our method consist in realizing X as an open part of a blowup M −→ A3 and to show that each Ga -action on X descends to A3 . This follows from considerations of the graded algebra associated to O(X ) with respect to a certain filtration. In Paper II, we study Ga-threefolds X which have as their algebraic quotient the affine plane A2 = Sp(C[x, y]) and are a principal bundle above the punctured plane A2 := A2 \ {0}. Equivalently, we study affine Ga -varieties Pˆ that extend a principal bundle P over A2, being P together with an extra fiber over the origin in A2. First the trivial bundle is studied, and some examples of extensions are given (including smooth ones which are not isomorphic to A2 × A). The most basic among the non-trivial principal bundles over A2 is SL2 (C) −→ A2, A 1→ Ae1 where e1 denotes the first unit vector, and we show that any non-trivial bundle can be realized as a pullback of this bundle with respect to a morphism A2 −→ A2. Therefore the attention is then restricted to extensions of SL2(C) and find two families of such extensions via a study of the graded algebras associated with the coordinate rings O(Pˆ) '→ O(P ) with respect to a filtration which is defined in terms of the Ga -actions on P and Pˆ respectively.
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Lima, Francismar Ferreira 1985. « Pontos fixos por grupos finitos agindo sobre grupos solúveis de tipo FP infinito ». [s.n.], 2013. http://repositorio.unicamp.br/jspui/handle/REPOSIP/306924.
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Orientador: Dessislava Hristova KochloukovaDissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matemática Estatística e Computação Científica
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Mestre em Matemática
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Gomez, John Hermes Castillo. « Propriedades de Lie de elementos simétricos sob involuções orientadas em álgebras de grupo ». Universidade de São Paulo, 2012. http://www.teses.usp.br/teses/disponiveis/45/45131/tde-04012013-170011/.
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Sejam $F$ um corpo de característica diferente de $2$ e $G$ um grupo. A partir da involução clássica, que envia cada elemento em seu inverso, e uma orientação do grupo $G$ é possível definir uma involução clássica orientada na álgebra de grupo $FG$. O objetivo desta tese é estudar propriedades de Lie do conjunto dos elementos simétricos $(FG)^+$ e, em alguns casos, do conjunto dos elementos anti-simétricos $(FG)^-$. Primeiro, abordamos o caso quando $G$ não tem elementos de ordem $2$. Aqui, mostramos que se $(FG)^+$ (ou $(FG)^-$) é Lie nilpotente ou Lie $n$-Engel, então $FG$ também é Lie nilpotente ou Lie $m$-Engel, respectivamente. Depois, consideramos o caso quando $G$ contém uma cópia do grupo quatérnio de ordem $8$. Neste caso, caracterizamos completamente as álgebras de grupo tais que $(FG)^+$ é fortemente Lie nilpotente, Lie nilpotente e Lie $n$-Engel. Como consequência, provamos que o conjunto das unidades simétricas deste tipo de grupos é nilpotente. Estudamos também o caso em que quando $G$ não contém uma cópia do grupo quatérnio de ordem $8$. Em particular, apresentamos um exemplo que mostra que os resultados obtidos em pesquisas anteriores, com a involução clássica, não devem ser esperados ao trabalhar com involuções clássicas orientadas. Não entanto, damos alguns casos especiais de grupos nos quais esses resultados são obtidos. Finalmente, estudamos o índice de Lie nilpotência de $(FG)^+$. Estabelecemos uma condição necessária e suficiente, para que o índice de Lie nilpotência de $(FG)^+$ e a classe de nilpotência das unidades simétricas de uma álgebra de grupo Lie nilpotente sejam o maior possível. Além disso, consideramos a situação em que o grupo $G$ contém uma cópia de $Q_8$.Let $F$ be a field of characteristic different from $2$ and $G$ a group. From the classical involution, which sends each element in its inverse and an orientation of $G$, it is possible to define an oriented classical involution on the group algebra $FG$. The goal of this thesis is to study Lie properties of the set of symmetric elements $(FG)^+$ and, in some cases, of the set of skew-symmetric elements $(FG)^-$. We first deal with the case when $G$ does not have elements of order $2$. In this situation, we show that if $(FG)^+$ (or $(FG)^-$) is Lie nilpotent or Lie $n$-Engel, then the whole group algebra $FG$ satisfies the same property. Later we consider the case when $G$ contains a copy of the quaternion group of order $8$. In this instance, we give a complete description of the group algebras such that $(FG)^+$ is strongly Lie nilpotent, Lie nilpotent and Lie $n$-Engel. As a consequence, we get that the set of symmetric units of this kind of groups is nilpotent. Furthermore, we study the case when $G$ does not contain a copy of the quaternion group of order $8$. Here, we present an example that shows that the previews results obtained in former works, with the classical involution, may not hold with an oriented classical involution. However, we give some kinds of groups for which those results are achieved. Finally, we study the Lie nilpotency index of $(FG)^+$. It is given a necessary and sufficient condition to the Lie nilpotency index of $(FG)^+$ and the nilpotency class of the symmetric units to be maximal, in a Lie nilpotent group algebra. In addition, we consider the situation when $G$ contains a copy of the quaternion group of order $8$.
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Haubold, Niko. « Compressed Decision Problems in Groups ». Doctoral thesis, Universitätsbibliothek Leipzig, 2012. http://nbn-resolving.de/urn:nbn:de:bsz:15-qucosa-85413.
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Wir beschäftigen uns mit Problemen der algorithmischen Gruppentheorie und untersuchen dabei die Komplexität von komprimierten Versionen des Wortproblems und des Konjugationsproblems für endlich erzeugte Gruppen.
Das Wortproblem fragt für eine feste, endlich erzeugte Gruppe ob ein gegebenes Wort über der Erzeugermenge das neutrale Element der Gruppe repräsentiert. Wir betrachten das gegebene Wort jedoch in einer komprimierten Form, als Straight-line Program (SLP) und untersuchen die Komplexität dieses Problems, das wir \'komprimiertes Wortproblem\' nennen. SLPs sind kontextfreie Grammatiken, die genau einen String erzeugen. Die Eingabegröße ist dabei stets die Größe des gegebenen SLPs. Eine Hauptmotivation ist dabei, dass für eine feste endlich erzeugte Gruppe das Wortproblem ihrer Automorphismengruppe durch eine Turingmaschine in Polynomialzeit auf das komprimierte Wortproblem der Gruppe selbst reduzierbar ist.
Wir untersuchen das komprimierte Wortproblem für die verbreiteten Gruppenerweiterungen HNN-Erweiterungen (amalgamierte Produkte und Graphprodukte) und können zeigen, dass sich Instanzen des komprimierten Wortproblems von einer Turingmaschine in Polynomialzeit auf Instanzen des komprimierten Wortproblems der Basisgruppe (respektive Basisgruppen und Knotengruppen) reduzieren lassen. Weiterhin zeigen wir, dass das komprimierte Wortproblem für endlich erzeugte nilpotente Gruppen von einer Turingmaschine in Polynomialzeit entscheidbar ist.
Wir betrachten außerdem eine komprimierte Variante des Konjugationsproblems. Das unkomprimierte Konjugationsproblem fragt für zwei gegebene Wörter über den Erzeugern einer festen endlich erzeugten Gruppe, ob sie in dieser Gruppe konjugiert sind. Beim komprimierten Konjugationsproblem besteht die Eingabe aus zwei SLPs und es wird gefragt, ob die beiden Wörter die von den SLPs erzeugt werden in der Gruppe konjugierte Elemente präsentieren. Wir konnten zeigen, dass sich das komprimierte Konjugationsproblem für Graphgruppen in Polynomialzeit entscheiden lässt.
Weiterhin haben wir das Wortproblem der äußeren Automorphismengruppen von Graphprodukten endlich erzeugter Gruppen untersucht. Durch den engen Zusammenhang des komprimierten Konjugationsproblems einer Gruppe mit dem Wortproblem der äußeren Automorphismengruppe konnten wir zeigen, dass sich das Wortproblem der äußeren Automorphismengruppe eines Graphprodukts von endlich erzeugten Gruppen durch eine Turingmaschine in Polynomialzeit auf Instanzen von simultanen komprimierten Konjugationsproblemen der Knotengruppen und Instanzen von komprimierten Wortproblemen der Knotengruppen reduzieren lässt.
Als Anwendung gelten obige Resultate auch für right-angled Coxetergruppen und Graphgruppen, da beide spezielle Graphprodukte sind. So folgt beispielsweise, dass das komprimierte Wortproblem einer right-angled Coxetergruppe in Polynomialzeit entscheidbar ist.
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Amirou, Yanis. « Les bornes uniformes pour la longueur des mots et groupe des éléments bornés ». Thesis, Université Paris sciences et lettres, 2020. http://www.theses.fr/2020UPSLE004.
Texte intégralRésumé :
Cette thèse étudie la question suivante : étant donné un groupe de type fini G quels sont les éléments dont la longueur est uniformément borné pour toute longueur des mots sur G? Ce travail introduit et étudie le sous-groupe Gbound formé par les éléments dont la longueur des mots est uniformément bornées par rapport au changement de parties génératrices de G. Nous montrons que ce sous-groupe est caractéristique, qu’il est fini quand le groupe G est virtuellement abélien, qu’il est trivial quand le groupe est hyperbolique non-élémentaire. Nous montrons que pour tout groupe fini A, il existe un groupe infini G tel que Gbound = A. Nous montrons que pour les groupes nilpotents de classe 2, Gbound est le plus grand sous-groupe fini de la suite centrale descendante. Nous étudions également une généralisation de Gbound dépendre des cardinaux des parties génératrices considéréesThis thesis studies the following question: given a finitely generated group G which are the elements whose length is uniformly bounded for any word-length in G ?. This work introduces and studies the subgroup Gbound consisting of elements of uniformly bounded word-length with respect to any generating set of G. We show that this subgroup is characteristic, that it is finite when the group G is virtually abelian, that it is trivial when the group is non-elementary hyperbolic. We show that for every finite group A, there exists an infinite group G such that Gbound = A. It is shown that for nilpotent groups of class 2, Gbound is the largest finite subgroup of the lower central series. We also study a generalization of Gbound by making it depend on the cardinals of the generating sets considered
27
Richtár, Jan. « Syntéza a charakterizace nových organických materiálů pro organickou elektroniku ». Doctoral thesis, Vysoké učení technické v Brně. Fakulta chemická, 2020. http://www.nusl.cz/ntk/nusl-433253.
Texte intégralRésumé :
Organická elektronika a bioelektronika zažívá v moderním věku obrovskou snahu o vývoj nových organických materiálů s vlastnostmi, které běžná elektronika na bázi křemíku obvykle nedosahuje. Tato práce se zabývá syntézou a charakterizací nových organických materiálů pro organickou elektroniku. Zaobírá se přípravou nových pentafluorsulfanylových heterocyklických stavebních bloků, alkylovaných vysokoúčinných organických pigmentů a bioinspirovaných organických -konjugovaných materiálů s modifikovatelnými fyzikálně-chemickými vlastnostmi a racionálními syntetickými přístupy k jejich přípravě. Pentafluorsulfanylová skupina (SF5) je ceněna pro svou vysokou elektronegativitu, lipofilitu, tepelnou a chemickou stabilitu. Pozitivně ovlivňuje optické a elektronické vlastnosti, rozpustnost a stabilitu v často lepší míře než u zavedených CF3-analogů. Šesti a čtyřkrokovou syntézou byly připraveny dva typy derivátů 3-SF5-substituovaných pyrrolidinů, které mohou sloužit jako všestranné stavební jednotky pro začlenění do pokročilých aromatických a heteroaromatických -konjugovaných systémů prostřednictvím atomů dusíku jako fluorované terminální skupiny. Modelový derivát byl zaveden jako terminální skupina do elektronově chudého heteroaromatického systému nukleofilní substitucí. Vodíkovými můstky vázané vysokovýkonné organické pigmenty přitahují velkou pozornost díky svým působivým polovodivým vlastnostem, silné 2D molekulární asociaci, vysoké tepelné, chemické a fotochemické stabilitě a nízké toxicitě. Přesto jsou pouze omezeně rozpustné a zpracovatelné, což lze vyřešit zavedením solubilizačních skupin. Je známo, že obzvláště objemné rigidní skupiny nesoucí adamantyl zlepšují uspořádání molekulární struktury, tepelnou stabilitu a výsledné vlastnosti díky samoorganizační schopnosti adamantanu. Adamantylmethylová a adamantylethylová skupina byla zavedena do vybraných barviv a pigmentů ze skupiny karbonylových azaacenů, rylen-diimidů a indigoidů pomocí nukleofilní substituce se zaměřením na zvýšení rozpustnosti a zpracovatelnosti při zachování tepelné stability a efektivní molekulární organizaci v pevné fázi. Fyzikálně-chemické studie série derivátů quinacridonu a epindolidionu ukázaly srovnatelnou, nebo vyšší tepelnou stabilitu než u nesubstituovaných derivátů, dobrou rozpustnost v organických rozpouštědlech, silnou fluorescenci v pevné fázi a roztoku v oblasti VIS a unikátní krystalovou strukturu pozorovanou z RTG analýzy. Flaviny jsou všudypřítomné bioinspirované organické materiály s nepostradatelnými biologickými funkcemi, výhodnými fyzikálně-chemickými vlastnostmi, chemickou a aplikační všestranností. Cílem práce byla modifikace optických, elektronických, elektrochemických, tepelných a dalších vlastností rozšířením -konjugovaného systému syntetizovaných materiálů. V první fázi byly navrženy dva syntetické přístupy pro přípravu série NH-nesubstituovaných flavinů, u kterých byly provedeny komplexní fyzikálně-chemické studie. Poté byly navrženy dva přístupy k syntéze N,N'-dialkylovaných flavinů s inkorporovaným butylovým, adamantylethylovým a triethylenglykolovým substituentem. Alkylací byla zvýšena rozpustnost v organických rozpouštědlech a vodném prostředí, zesílena fluorescence v pevné fázi a v roztocích a modifikovány tepelné vlastnosti v závislosti na zavedeném alkylovém substituentu.
28
FRATI, MARCO. « Unipotent Automorphisms of Soluble Groups ». Doctoral thesis, 2013. http://hdl.handle.net/2158/806278.
Texte intégral
29
Tolcachier, Alejandro. « Grupos de Bieberbach y holonomía de solvariedades planas ». Bachelor's thesis, 2018. http://hdl.handle.net/11086/11323.
Texte intégralRésumé :
Tesis (Lic. en Matemática)--Universidad Nacional de Córdoba, Facultad de Matemática, Astronomía, Física y Computación, 2018.Una solvariedad es una variedad compacta de la forma L/G donde G es un grupo de Lie soluble simplemente conexo y L es un retículo de G. En este trabajo estudiamos solvariedades equipadas con una métrica riemanniana plana, a partir de la caracterización dada por Milnor de los grupos de Lie que admiten una métrica riemanniana invariante a izquierda plana. Las solvariedades planas son ejemplos de variedades compactas planas, por lo cual podemos aplicar los teoremas clásicos de Bieberbach para describir el grupo fundamental L de la variedad L/G. En particular, todo grupo de Bieberbach posee un subgrupo abeliano maximal de índice finito. Más aún, el cociente del grupo L por este subgrupo es finito y se identifica con la holonomía riemanniana de la variedad compacta plana. Probamos primero que el grupo de holonomía riemanniana de cualquier solvariedad plana es abeliano y que todo grupo abeliano finito se puede obtener así. Luego, nos restringimos al caso de grupos de Lie casi abelianos, para los cuales hay un criterio para determinar la existencia de retículos, el cual utilizamos para clasificar las solvariedades planas en dimensión 3, 4 y 5. Para dimensiones mayores, probamos que para todo n>2 la dimensión mínima de una variedad compacta plana con grupo de holonomía Z_n coincide con la dimensión mínima de una solvariedad plana con grupo de holonomía Z_n.
A solvmanifold is a compact manifold L/G where G is a simply connected solvable Lie group and L is a lattice of G. In this article we study solvmanifolds equipped with a flat Riemannian metric, according to Milnor's characterization of Lie groups that admit a flat left invariant metric. Flat solvmanifolds are examples of compact flat manifolds, so we can apply the classic theory of Bieberbach groups to describe the fundamental group L of the manifold L/G. In particular, every Bieberbach group has a maximal normal abelian subgroup which has finite index. Fruthermore, the quotient of the group L by this subgroup is finite and can be with the riemannian holonomy group of the compact flat manifold. First, we prove that the holonomy group of every flat solvmanifold is abelian and, conversely, that every finite abelian group can be obtained as a holonomy group of a flat solvmanifold. Then, we focus on almost abelian Lie groups, for which there is a well known criterion to determine the existence of lattices that we use to classify flat solvmanifolds of dimension 3, 4 and 5. Concerning arbitrary dimensions, we prove that for every n>2 the minimum dimension of a compact flat manifold with holonomy group Z_n is equal to the minimum dimension of a flat solvmanifold with holonomy group Z_n.
30
Higginbottom, Ryan Sterling. « The Nilpotent filtration in group cohomology / ». 2005. http://wwwlib.umi.com/dissertations/fullcit/3189320.
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31
Wakefield, Max. « Group Representations, Nilpotent Algebras and Finite Algebra Groups ». Master's thesis, 2018. http://hdl.handle.net/1885/173612.
Texte intégralRésumé :
The purpose of this thesis is introduce the reader to representations of finite algebra groups and summarise some key results concerning such representations. The work that follows begins by reviewing key properties of finite group representations and nilpotent algebras. The representations studied are for the most part complex representations, however much of the theory applies equally to many other Fields. We follow this discussion with an introduction to finite algebra groups by exploring the relationship that exists between these groups and the Jacobson Radical of algebras over finite fields. Then we consider the work of Zoltan Halasi in significant detail and attempt to clarify some of the ambiguites a reader may face in reading his paper. In addition, we prove and state many of the excluded facts and results on which his arguments rely. Finally, we conclude by analysing the irreducible representations of a specific class of finite algebra groups. This is our working example. In doing so, we highlight how the work of Halasi simplifies the search for irreducible representations. We end the final section by introducing a non-finite algebra group that shares many similarities to the class of groups considered in our working example. Determining whether or not an analagous theorem to the one proved by Halasi holds for these groups is an open problem. It is the belief of the author that a person who is interested in exploring the irreducible representations of such groups may find this thesis a solid introduction.
32
Lubisi, Elliot. « The effect of the group structure of a group Q on its non-cancellation set ». Thesis, 2018. https://hdl.handle.net/10539/26176.
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33
Ahlin, Ashley Reiter. « The large scale geometry of nilpotent-by-cycle groups / ». 2002. http://wwwlib.umi.com/dissertations/dlnow/3048360.
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34
Su, Meng-Hsiung, et 蘇盟雄. « Synthesis and Characterization of Soluble Polyamide-imides with tert-butyl group ». Thesis, 2002. http://ndltd.ncl.edu.tw/handle/dug5ne.
Texte intégralRésumé :
碩士國立成功大學
化學工程學系碩博士班
90
Abstract An imide ring-containing dicarboxylic acid was prepared by the condensation of 1,4-Bis(4-aminophenoxy)-2-tert-butyl benzene (BATB) and trimellitic anhydride(TMA) .A series of soluble poly(amide-imide)s containing tert-butyl units were synthesized via the triphenyl phosphite-activated direct polycondensation of this diimide-diacid with various aromatic diamines.Four of the obtained polymer had inherent viscosities of 0.53(dl/g)∼0.86(dl/g) and afforded flexible films. These compounds are discussed and compared with those of polyimides which do not contain amide units and also with the poly(amide-imide) which do not contain tert-butyl units .All the polymers were then characterized by FTIR、H1-NMR、Instron、DSC、DMA and XRD .Most of resulting poly(amide-imide)s containing tert-butyl units showed an amorphous nature and were readily soluble in polar solvents such as NMP、DMF and DMAc .The glass transition temperature could be determined with the help of DMA clearly,which were recorded in the range 243∼266℃.Their 5﹪weight loss temperature were recorded in the range 473∼480℃ in nitrogen. These polymer exhibited a desired combination of propertiesrequiring high-performance materials that include excellent thermal stability and excellent solubility in organic solvents.
35
Niemeyer, Alice C. « Computing presentations for finite soluble groups ». Phd thesis, 1993. http://hdl.handle.net/1885/133191.
Texte intégralRésumé :
The work in this thesis was carried out in the area of computational group
theory. The latter is concerned with designing algorithm s and developing their
practical implementations for investigating problem s regarding groups. An important class of groups are finite soluble groups. These can be described in a
computationally convenient way by power conjugate presentations. In practice,
however, they are usually supplied differently. The aim of this thesis is to propose
algorithm s for computing power conjugate presentations for finite soluble groups.
This is achieved in two different ways.
One of the ways in which a finite soluble group is often supplied is as a quotient
of a finitely presented group. T he first p art of the thesis is concerned with designing
an algorithm to compute a power conjugate presentation for a finite soluble group
given in this way. T he theoretical background for the algorithm is provided and
its practicality is investigated on an implementation.
T he second p a rt of the thesis describes the theoretical aspects of an algorithm
to compute all pow er conjugate presentations for a certain class of finite soluble
groups of a given order.
36
Lu, Hsin-Yi, et 呂信誼. « Synthesis and Characterization of New Organic Soluble Polyamides and Polyimides With Trifluoromethyl Group ». Thesis, 2003. http://ndltd.ncl.edu.tw/handle/37292365341592942055.
Texte intégralRésumé :
碩士國立臺灣科技大學
化學工程系
91
A new cardo diamine monomer, 1,1-bis[4-(3-trifluoromethyl-4-amino phenoxy)phenyl]-4-tert-butylcyclohexane containing tert-butylcyclohexylidene unit was prepared in three steps from 4-tert-butylcyclohexanone. The monomer was reacted with various aromatic tetracarboxylic dianhydrides and dicarboxylic acids to produce polyimides and polyamides, respectively. These cardo polymers exhibited good solubility in a variety of solvents. Almost all the polymers dissolved in N-methyl-2-pyrrolidinone (NMP), N,N-dimethylacetamide (DMAc), N,N-dimethylformamide (DMF), pyridine, and even in cyclohexanone. These polyimides and polyamides showed glass transition temperatures between 231－262℃and 243－266 ℃, decomposition temperature at 10 % mass loss temperatures ranging from 437－543 and 413－502℃ in nitrogen and air, respectively. The transparency of these polymer films (in the range of 80% to 90%) at 500nm solar wavelength. A new noncoplanar diamine monomer containing trifluoromethyl group on either side, 2,2'-dimethyl-4,4'-bis(2-trifluoromethyl-4- aminophenoxy)biphenyl (DBTFAPB) was synthesized and its structure was indentified by 1H-NMR, 13C-NMR, FTIR spectroscopy, X-ray crystallographic and elemental analyses. Polyamides were synthesized from the diamines with various aromatic dicarboxylic acids. The polymers with trifluoromethyl substituents exhibited low dielectric constants ranging from 3.07 to 3.75. These polymers showed glass transition temperatures between 230－255 ℃. The polymers possessed a coefficient of thermal expension (CTE) of 52－94 ppm/℃. All the polymers showed excellent solubility in the organic solvents: N-methyl-2-pyrrolidinone (NMP), N,N- dimethylacetamide (DMAc), N,N-dimethylformamide (DMF), dimethyl sulfoxide (DMSO), pyridine, tetrahydrofuran (THF), cyclohexanone and γ-butyrolactone. Inherent viscosities of the polymers were found to range between 0.93 and 1.34 dL‧g-1. Thermogravimetric analysis of the polymers revealed a high thermal stability; decomposition temperature in excess of 440 ℃ in nitrogen. The 10 % weight loss temperature was found to be in the range 465－487℃ and 442－463℃ in nitrogen and air, respectively. The polymer films had a tensile strength range of 92－124 MPa; an elongation at break range of 9－15 %; and a tensile modulus range of 1.9－2.6 GPa. Transparency of the films ( in the range of 82 % to 85 % ) were high at 400－780 nm in the visible regions and were entirely colorless. The UV-vis absorption spectra revealed that most of the polymers had absorption maxima around 258－308 nm. The average refractive index varied from 1.5793－1.6121, and birefringence varied in the range of 0.0093－0.0413.
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CHIU, PEI-FANG, et 邱沛芳. « Design and Synthesis a Water-soluble Group for Ether-linkage of 10-Hydroxycamptothecin Prodrug ». Thesis, 2017. http://ndltd.ncl.edu.tw/handle/686w4t.
Texte intégralRésumé :
碩士嘉南藥理大學
藥學系
105
Camptothecin has good anti-cancer activity, and current clinical use of two derivatives are Topotecan and Irinotecan which improve poor water solubility of Camptothecin by chemical modification. However, the lack of drugs specificity of tumor will cause severe side effects. Therefore, our laboratory designed and synthesized two glucuronide prodrugs of Camptothecin (9-ACG and 10-HCG) which will mainly be activated at tumor site expressing large number of β-glucuronidase. According to previous studies, 9-ACG and 10-HCG was 1800 and 20 times soluble than 10-HCG, respectively; 9-ACG and 10-HCG was 30-fold and 10-fold less toxic than the parent drug to cells, respectively; Enzyme kinetic studies showed that β-glucuronidase exhibited 520 times higher catalytic efficiency for 10-HCG than for 9-ACG, and molecular modeling studies predicted that 10-HCG would have a higher binding affinity to enzyme than 9-ACG. In this study, we design and synthesize the target compound 10-HCPG by creating N-methyl piperazine on the benzyl group of 10-HCG, expect for good water solubility, stable in blood, low cytotoxicity, good affinity with β-glucuronidase and specific to tumor cells.
38
« The Investigation and Characterization of the Group 3 [NiFe]-Hydrogenases Using Protein Film Electrochemistry ». Doctoral diss., 2012. http://hdl.handle.net/2286/R.I.15001.
Texte intégralRésumé :
abstract: Hydrogenases, the enzymes that reversibly convert protons and electrons to hydrogen, are used in all three domains of life. [NiFe]-hydrogenases are considered best suited for biotechnological applications because of their reversible inactivation with oxygen. Phylogenetically, there are four groups of [NiFe]-hydrogenases. The best characterized group, "uptake" hydrogenases, are membrane-bound and catalyze hydrogen oxidation in vivo. In contrast, the group 3 [NiFe]-hydrogenases are heteromultimeric, bifunctional enzymes that fulfill various cellular roles. In this dissertation, protein film electrochemistry (PFE) is used to characterize the catalytic properties of two group 3 [NiFe]-hydrogenases: HoxEFUYH from Synechocystsis sp. PCC 6803 and SHI from Pyrococcus furiosus. First, HoxEFUYH is shown to be biased towards hydrogen production. Upon exposure to oxygen, HoxEFUYH inactivates to two states, both of which can be reactivated on the timescale of seconds. Second, we show that PfSHI is the first example of an oxygen tolerant [NiFe]-hydrogenase that produces two inactive states upon exposure to oxygen. Both inactive states are analogous to those characterized for HoxEFUYH, but oxygen exposed PfSHI produces a greater fraction that reactivates at high potentials, enabling hydrogen oxidation in the presence of oxygen. Third, it is shown that removing the NAD(P)-reducing subunits from PfSHI leads to a decrease in bias towards hydrogen oxidation and renders the enzyme oxygen sensitive. Both traits are likely due to impaired intramolecular electron transfer. Mechanistic hypotheseses for these functional differences are considered.Dissertation/Thesis
Ph.D. Biochemistry 2012
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(10942799), Robert Llewellyn Long. « Improving fruit soluble solids content in melon (Cucumis melo L.) (reticulatus group) in the Australian production system ». Thesis, 2005. https://figshare.com/articles/thesis/Improving_fruit_soluble_solids_content_in_melon_Cucumis_melo_L_reticulatus_group_in_the_Australian_production_system/13421951.
Texte intégralRésumé :
"Total soluble solids (TSS) is a reliable indicator of melon eating quality, with a minimum standard of 10% recommended. The state of Australian melon production with respect to this quality criterion was considered within seasons, between growing districts and over seasons. It was concluded that improvement in agronomic practice and varietal selection is required to produce sweeter melons. The scientific literature addressing melon physiology and agronomy was summarised, as a background to the work that is required to improve melon production practices in Australia. The effect of source sink manipulation was assessed for commercially grown and glasshouse grown melon plants. The timing of fruit thinning, pollination scheduling, the application of a growth inhibitor and source biomass removal were assessed in relation to fruit growth and sugar accumulation. Results are interpreted against a model in which fruit rapidly increase in weight until about two weeks before harvest, with sugar accumulation continuing as fruit growth ceases. Thus treatment response is very dependant on timing of application. For example, fruit thinning at 25 days before harvest resulted in further fruit set and increased fruit weight but did not impact on fruit TSS (at 9.8%, control 9.3%), while thinning at 5 days before harvest resulted in a significant (Pless than 0.05) increase in fruit TSS (to 10.8%, control 9.3%) and no increase in fruit weight or number. A cost/ benefit analysis is presented, allowing an estimation of the increase in sale price required to sustain the implementation of fruit thinning. The effect of irrigation scheduling was also considered with respect to increasing melon yield and quality. To date, recommended practice has been to cause an irrigation deficit close to fruit harvest, with the intent of 'drying out' or 'stressing' the plant, to 'bring on' maturity and increase sugar accumulation. Irrigation trials showed that keeping plants stress-free close to harvest and during harvest, facilitated the production of sweeter fruit. The maintenance of a TSS grade standard using either batch based (destructive) sampling or (non-invasive) grading of individual fruit is discussed. On-line grading of individual fruit is possible using near infrared spectroscopy (NIR), but the applicability of the technique to melons has received little published attention. Tissue sampling strategy was optimised, in relation to the optical geometry used (in commercial operation in Australia), both in terms of the diameter and depth of sampled tissue. NIR calibration model performance was superior when based on the TSS of outer, rather than inner mesocarp tissue. However the linear relationship between outer and middle tissue TSS was strong (r2 = 0.8) in immature fruit, though less related in maturing fruit (r2 = 0.5). The effect of fruit storage (maturation/senescence) on calibration model performance was assessed. There was a negligible effect of fruit cold storage on calibration performance. Currently, the agronomist lacks a cost-effective tool to rapidly assess fruit TSS in the field. Design parameters for such a tool were established, and several optical front ends compared for rapid, though invasive, analysis. Further, for visualisation of the spatial distribution of tissue TSS within a melon fruit, a two-dimensional, or hyper-spectral NIR imaging system based on a low cost 8-bit charge coupled device (CCD) camera and filter arrangement, was designed and characterised." -- abstract
40
Schneider, Jakob. « On the length of group laws ». 2016. https://tud.qucosa.de/id/qucosa%3A36487.
Texte intégralRésumé :
Let C be the class of finite nilpotent, solvable, symmetric, simple or semi-simple groups and n be a positive integer. We discuss the following question on group laws: What is the length of the shortest non-trivial law holding for all finite groups from the class C of order less than or equal to n?:Introduction
0 Essentials from group theory
1 The two main tools
1.1 The commutator lemma
1.2 The extension lemma
2 Nilpotent and solvable groups
2.1 Definitions and basic properties
2.2 Short non-trivial words in the derived series of F_2
2.3 Short non-trivial words in the lower central series of F_2
2.4 Laws for finite nilpotent groups
2.5 Laws for finite solvable groups
3 Semi-simple groups
3.1 Definitions and basic facts
3.2 Laws for the symmetric group S_n
3.3 Laws for simple groups
3.4 Laws for finite linear groups
3.5 Returning to semi-simple groups
4 The final conclusion
Index
BibliographySei C die Klasse der endlichen nilpotenten, auflösbaren, symmetrischen oder halbeinfachen Gruppen und n eine positive ganze Zahl. We diskutieren die folgende Frage über Gruppengesetze: Was ist die Länge des kürzesten nicht-trivialen Gesetzes, das für alle endlichen Gruppen der Klasse C gilt, welche die Ordnung höchstens n haben?:Introduction 0 Essentials from group theory 1 The two main tools 1.1 The commutator lemma 1.2 The extension lemma 2 Nilpotent and solvable groups 2.1 Definitions and basic properties 2.2 Short non-trivial words in the derived series of F_2 2.3 Short non-trivial words in the lower central series of F_2 2.4 Laws for finite nilpotent groups 2.5 Laws for finite solvable groups 3 Semi-simple groups 3.1 Definitions and basic facts 3.2 Laws for the symmetric group S_n 3.3 Laws for simple groups 3.4 Laws for finite linear groups 3.5 Returning to semi-simple groups 4 The final conclusion Index Bibliography
41
Küchenmeister, Frank. « Sustainable grassland herbage production under drought stress - the role of plant species number and functional group composition ». Doctoral thesis, 2013. http://hdl.handle.net/11858/00-1735-0000-001D-C0F8-D.
Texte intégralRésumé :
Grünlandfutter mit einem hohen Ertrag und gutem Futterwert ist eine Grundvoraussetzung für die effiziente Produktion von wiederkäuenden Nutztieren. Im Zuge des prognostizierten Klimawandels werden sich die Niederschlagsmuster ändern und das Auftreten von Extremwetterereignissen, wie temporärer Trockenheit, wird sich erhöhen. Besonders produktives Grünland benötigt aber eine ausreichende und regelmäßige Wasserversorgung während der Wachstumsperiode. Deshalb werden die Futterproduktion von Grünland, die Ertragsstabilität und der Futterwert von temporärer Trockenheit beeinflusst werden. Aus diesem Grund sind Anpassungsstrategien nötig, um eine zukünftige und nachhaltige Grünlandfuttererzeugung zu sichern.
Erhöhte pflanzliche Biodiversität wird oft als Möglichkeit angesehen, Funktionen von Ökosystemen, wie Produktivität und Futterwert, im Grünland zu verbessern. Es gibt eine fortlaufende Diskussion wie eine erhöhte Artenzahl auf Stress, besonders Trockenstress, reagiert und wie dabei Produktivität, Futterwert und Wassernutzung beeinflusst werden. Andere Untersuchungen zeigten, dass Artidentität und die Zusammensetzung der funktionellen Gruppen wichtige Faktoren für Produktivität und Futterwert sind.
Auf Grund dessen haben wir von Juli 2009 bis Juni 2011 ein Trockenstressexperiment in einer Vegetationshalle durchgeführt. Verschiedene temporäre Trockenstressereignisse wurden in drei Aufwüchsen in zwei Vegetationsperioden durchgeführt. Die klimatischen Verhältnisse in der Vegetationshalle folgten normalen saisonalen Verläufen mit Frost im Winter und höheren Temperaturen im Sommer. Trockenstress wurde induziert, indem, nach einer anfänglichen Bewässerung, die Wasserversorgung für einen bestimmten Zeitraum eingestellt wurde. Die Wasserverfügbarkeit des Bodens konnte dabei immer kontrolliert werden. Für das Experiment wählten wir ertragsstarke und landwirtschaftlich nutzbare Arten des Grünlands der gemäßigten Zonen aus. Die Arten wurden in Monokultur und Drei- sowie Fünfartenmischungen gesät und enthielten die funktionellen Gruppen Leguminose (Trifolium repens L.), Gras (Lolium perenne L., Dactylis glomerata L.) und Kraut (Plantago lanceolata L., Taraxacum officinale F.H. Wigg. agg.). Der von uns gewählt Umfang der Artenzahl zeigte schon in anderen Biodiversitätsexperimenten einen Einfluss auf die Produktion. Untersucht wurden die Effekte von Artenzahl und funktionellen Gruppen auf Ertrag, Ertragsstabilität, Wassernutzung und Futterwert (Rohprotein, wasserlösliche Kohlenhydrate, neutrale und saure Detergenzienfasern). Als Indikatoren für die Ertragsentwicklung und die agronomische Wassernutzungseffizienz (Verhältnis von Ertrag zu Wasserverbrauch) dienten der Stickstoffertrag und die Stickstoffkonzentration der Bestände sowie δ13C Signaturen, sowohl mit unlimitierter Wasserversorgung als auch mit Trockenstress. Überdies führten wir 2009 ein Kurzzeitfeldexperiment auf einem alten Grünlandbestand auf dem Versuchsgut der Universität Göttingen in Reliehausen durch. In diesem Versuch wurde ebenso der Einfluss von Trockenstress und Artenzahl auf den Ertrag und die Wassernutzung untersucht.
Unsere Daten zeigten, dass Trockenstress die Produktivität verringert und die Wassernutzung beeinflusst, beides abhängig von der Stärke des Stresses. Bei moderatem Stress war die agronomische Wassernutzungseffizienz unverändert oder stieg leicht an, bei starkem Stress verringerte sie sich jedoch. Der Stickstoffertrag und die Stickstoffkonzentration waren brauchbare Indikatoren für die agronomische Wassernutzungseffizienz, wohingegen δ13C weniger geeignet war. Die agronomische Wassernutzungseffizienz wurde von Stickstoff erhöht. Es gab keinen oder nur einen sehr geringen Einfluss von Trockenstress auf den Futterwert. Saisonale Effekte hatten mehr Einfluss auf den Futterwert. Allgemein scheint der Ertragsrückgang wichtiger als die Veränderungen des Futterwerts zu sein.
Die Artenzahl beeinflusste den Futterwert und die Ertragsstabilität über die Vegetationsperiode nicht. Mit Hilfe des “sampling effect“ (Probennahmeeffekt) können der manchmal positive Einfluss der Artenzahl auf den Ertrag und die agronomische Wassernutzungseffizienz und der Rückgang dieses Einflusses unter Trockenheit erklärt werden. Mit erhöhter Artenzahl stieg der Anteil der leistungsfähigen, aber trockenheitssensitiven Leguminose. Weiterhin gab es einen Hinweis, dass die Artenzahl die Geschwindigkeit des Wasserverbrauchs erhöht. Die Ergebnisse des Feldexperiments bekräftigten die Befunde bezüglich der Effekte des Trockenstresses, des Ertrages und der Wassernutzung. Aus diesen Gründen kann die „insurance hypothesis“ (Versicherungshypothese), die besagt, dass eine erhöhte Artenzahl Ökosystemfunktionen gegenüber Umweltveränderungen stabilisieren kann, nicht bestätigt werden.
Jedoch waren die funktionellen Gruppen wichtige und bestimmende Faktoren der Leistung unter nicht Wasser limitierten Bedingungen und Trockenstress. Die Leguminose hatte besonders auf Ertrag, agronomische Wassernutzungseffizienz und Rohprotein einen positiven Einfluss, jedoch erhöhte sie auch den Wasserverbrauch und die saisonale Variabilität. Gräser stabilisierten den Ertrag und den Wasserverbrauch und erhöhten die wasserlöslichen Kohlenhydrate sowie die Faserfraktionen, während sie den Ertrag und die agronomische Wassernutzungseffizienz unter den stickstofflimitierten Bedingungen unseres Experiments verringerten. Die funktionelle Gruppe Kräuter zeigte ähnliche Ergebnisse bezüglich Ertrag und Wassernutzung, aber sie erhöhte das Rohprotein.
Unsere Ergebnisse demonstrieren, dass die vorhergesagte Zunahme von Trockenstressereignissen die Produktion reduzieren und die Wassernutzung ändern wird. Änderungen im Futterwert werden dabei weniger wichtig als der Ertragsrückgang sein. Für die Produktion, die Wassernutzung und den Futterwert wird die Artenanzahl weniger relevant sein als die funktionelle Zusammensetzung von Grünland. Deshalb wird eine angepasste Grasnarbenzusammensetzung für die Sicherung der Produktion von wiederkäuenden Nutztieren unter den Bedingungen des erwarteten Klimawandels Bedeutung erlangen.
42
Francalanci, Giulio. « Nilpotence relations in products of groups ». Doctoral thesis, 2020. http://hdl.handle.net/2158/1197496.
Texte intégralRésumé :
Let C be a class of groups, let G be a group and A, B two subgroups of G. We will say that A and B are C-connected if for all element a and b belonging respectively to A and B, the group < a, b > is in the class C. In particular we will focus on N-connection, where N is the class of nilpotent groups. Moreover, G is said to be the product of A and B, i.e. G=AB, if and only if for all element g in G, there exists a in A and b in B such that g=ab.
In this thesis, given G=AB where A and B are N-connected subgroups, we discuss how some properties of the subgroups A and B can influence the structure of the whole group G.
43
Procházková, Zuzana. « Význačné prvky grupových okruhů ». Master's thesis, 2021. http://www.nusl.cz/ntk/nusl-448402.
Texte intégralRésumé :
Title: Distinguished elements of group rings Author: Bc. Zuzana Procházková Department: Department of Algebra Supervisor: doc. Mgr. et Mgr. Jan Žemlička, Ph.D., Department of Algebra Abstract: This thesis is about finding idempotents in a group ring. We describe three techniques of finding idempotents in a semisimple group ring and in the last chapter there is an attempt to find idempotents in a group ring that does not have to be semisimple. The first technique uses representations and characters of a group. The second technique finds idempotents through the use of Shoda pairs. The third technique lifts idempotent from the factor ring with the help of CNC system of ideals, which is a generalization of a well-known technique with nilpotent ideals, and it is here extended to group rings formed by non-abelian group and noncommutative ring. iii
44
Γκοτζαμάνης, Γεώργιος. « Ανάπτυξη νέων "ευφυών" κατά συστάδες συμπολυμερών τύπου ομοπολυμερές-στατιστικό συμπολυμερές ». Thesis, 2007. http://nemertes.lis.upatras.gr/jspui/handle/10889/613.
Texte intégralRésumé :
Στην παρούσα Διδακτορική Διατριβή σχεδιάστηκαν και συντέθηκαν με πολυμερισμό μέσω μεταφοράς ομάδας (group transfer polymerization, GTP) τέσσερα νέα πρότυπα “ευφυή” υδατοδιαλυτά συμπολυμερή, τα οποία αυτοοργανώνονται σε υδατικά διαλύματα σε δομές μικκυλίων ή ελαστικού φυσικού δικτύου, αποκρινόμενα άμεσα σε μεταβολές του pH, της θερμοκρασίας και της ιοντικής ισχύος του διαλύματος. Η καινοτομία των πολυμερών που συντέθηκαν οφείλεται στο γεγονός ότι σε ένα συσταδικό συμπολυμερές ενσωματώθηκε μία στατιστική συστάδα, η οποία παρουσιάζει ιδιότητες που είναι συνδυασμός των ιδιοτήτων των μονομερών που την αποτελούν. Ο γενικός τύπος των πολυμερών που μελετήθηκαν είναι A-b-(B-co-C) και A-b-(B-co-C)-b-A. Η συστάδα Α μπορούσε να είναι υδρόφιλη ή υδρόφοβη ενώ η στατιστική συστάδα ήταν είτε ένας πολυαμφολύτης με ρυθμιζόμενο ισοηλεκτρικό σημείο (ΙΗΣ), είτε μια υδρόφιλη συστάδα με ρυθμιζόμενη κατώτερη κρίσιμη θερμοκρασία διάλυσης (LCST). Ο πολυαμφολύτης φορτίζεται θετικά σε όξινα διαλύματα, καθίσταται ουδέτερος στο ισοηλεκτρικό του σημείο και τέλος φορτίζεται αρνητικά σε διαλύματα με υψηλό pH.
Συμπολυμερή του τύπου A-b-(B-co-C)
Συντέθηκαν τρία διαφορετικά συμπολυμερή αυτού του τύπου: Στην πρώτη περίπτωση η συστάδα Α είναι το υδρόφοβο PMMA και η στατιστική συστάδα είναι ο πολυαμφολύτης P(DEA-co-MAA). Το πολυμερές PMMA-b-P(DEA-co-MAA) σχηματίζει μικκύλια σε υδατικά διαλύματα με τη συστάδα PMMA στον πυρήνα και τη στατιστική συστάδα στην κορώνα να είναι είτε θετικά φορτισμένη σε χαμηλό pH είτε αρνητικά φορτισμένη σε υψηλό pH. Στο ΙΗΣ του πολυαμφολύτη το πολυμερές συσσωματώνεται και καθιζάνει. Εμπνεόμενοι από τη δομή των μικκυλιακών συσσωματωμάτων συντέθηκε το επαμφοτερίζον αστεροειδές πολυμερές [PMMA-b-P(DEA-co-MAA)]n, το οποίο δημιουργεί μονομοριακά μικκύλια με πυρήνα PMMA και κορόνα που αλλάζει φορτίο ανάλογα με το pH του διαλύματος.
Στη δεύτερη περίπτωση η στατιστική συστάδα παραμένει o πολυαμφολύτης P(DEA-co-MAA) και η συστάδα Α είναι το υδρόφιλο PEGMA, το οποίο παρουσιάζει LCST και σε υδατικά διαλύματα του πολυμερούς σχηματίζονται τρία είδη μικκυλίων. Στο ΙΗΣ και σε θερμοκρασία δωματίου σχηματίζονται μικκύλια με τη συστάδα P(DEA-co-MAA) στον πυρήνα και την υδρόφιλη συστάδα PEGMA στην κορώνα. Ωστόσο σε θεμρμοκρασία μεγαλύτερη από την LCST και σε pH εκτός της περιοχής του ΙΗΣ του πολυαμφολύτη, η συστάδα PEGMA συρρικνώνεται, οπότε δημιουργούνται μυκκίλια με πυρήνα τη συστάδα PEGMA και κορώνα τη συστάδα P(DEA-co-MAA). Σε χαμηλό pH η κορώνα είναι θετικά φορτισμένη, ενώ σε υψηλό είναι αρνητικά φορτισμένη.
Τέλος στο τρίτο πολυμερές η στατιστική συστάδα αποτελείται από ένα υδρόφιλο και ένα υδρόφοβο μονομερές P(EGMA-co-MMA) και η LCST της συστάδας αυτής μειώνεται με αύξηση του ποσοστού του υδρόφοβου μονομερούς. Ο συνδιασμός μιας τέτοιας συστάδας και μιας συστάδας κατιονικού πολυηλεκτρολύτη (PDEA) σε ένα δισυσταδικό συμπολυμερές οδηγει σε ένα υλικό με πλούσιες ιδιότητες επηρεαζόμενες από τη θερμοκρασία και το pH. Σε χαμηλές θερμοκρασίες και όξινο περιβάλλον είναι μοριακά διαλυτό, αφού και οι δύο συστάδες είναι υδρόφιλες. Με αύξηση του pH ή της θερμοκρασίας συμπολυμερές αυτο-οργανώνεται αυτόματα σε δύο διαφορετικά μικκυλιακά συσσωματώματα με τον πυρήνα και την κορώνα να εναλλάσσονται μεταξύ τους (“σχιζοφρενική” συμπεριφορά). Τέλος με ταυτόχρονη αύξηση του pH και της θερμοκρασίας το συμπολυμερές καταβυθίζεται.
Συμπολυμερή του τύπου A-b-(B-co-C)-b-A
Με βάση το πολυμερές PMMA-b-P(DEA-co-MAA) συντέθηκε ο τηλεχηλικός πολυαμφολύτης PMMA-b-P(DEA-co-MAA)-b-PMMA. Σε διαλύματα του πολυμερούς και σε pΗ έξω από την περιοχή του ΙΗΣ του πολυαμφολύτη, δημιουργούνται συσσωματώματα πεπερασμένου μεγέθους (στην ημιαραιή περιοχή συγκεντρώσεων), ενώ σε πυκνά διαλύματα σχηματίζεται άπειρο φυσικό δίκτυο. Υδατοπηκτώματα του πολυμερούς είναι δυνατό να δημιουργηθούν και από διόγκωση πολυμερικών φιλμ με απορρόφηση ύδατος. Το δίκτυο που σχηματίζεται έχει ελαστική συμπεριφορά τόσο σε χαμηλό όσο και σε υψηλό pH.In the present thesis four new model and “smart” water-soluble copolymers were designed and synthesized via the group transfer polymerization method. These copolymers self-assemble in aqueous solutions into micelles or elastically physical network (depending on the copolymer architecture), responding readily to changes of the external stimuli such as pH, temperature and ionic strength. The innovation of these polymers is due to the fact that a block copolymer incorporates a statistical block, the physicochemical properties of which, result from combination of the properties of the structural monomers. These copolymers had general type A-b-(B-co-C) or A-b-(B-co-C)-b-A. The homopolymer block A could be either hydrophilic (neutral or cationic) or hydrophobic, while the statistical block (B-co-C) was either a polyampholyte with tunable isoelectric point (IEP), or a hydrophilic block with tunable lower critical solution temperature (LCST). The polyampholyte block could be positively charged in acidic conditions and negatively charged in basic conditions, while at the IEP became neutral. Copolymers of the type A-b-(B-co-C) Three different copolymers of the type A-b-(B-co-C) were synthesized. In the first case block A was the hydrophobic PMMA and the statistical block was the polyampholyte P(DEA-co-MAA). When the copolymer PMMA-b-P(DEA-co-MAA) was dissolved in aqueous media, spherical micelles with PMMA core and P(DEA-co-MAA) corona were formed at room temperature and at pH out of the IEP region. At the IEP the copolymer precipitated from the solution due to the neutralization of the statistical polyampholyte block. Inspired by the morphology of the micelles formed by the linear copolymer PMMA-b-P(DEA-co-MAA), the star amphoteric copolymer was synthesized [PMMA-b-P(DEA-co-MAA)]n, which forms unimolecular PMMA-core micelles and corona that changes the charge sign upon changing the solution pH. In the second case the statistical block was the same as above, while the homopolymer block consisted of the hydrophilic PEGMA, which exhibits LCST and becomes hydrophobic above it. Due to the double sensitivity of this copolymer to pH and temperature, three types of micelles were formed in aqueous solutions. At the IEP and room temperature neutral-corona micelles were formed, at which the core consisted of the statistical P(DEA-co-MAA) block. Multimolecular association took place also at temperatures above LCST of the PEGMA block and at pH below and above the IEP of the polyampholyte Block. In the latter cases PEGMA block formed the core of the micelles. Finally, in the third copolymer the statistical block P(EGMA-co-MMA) consisted of one hydrophilic and one hydrophobic monomer and its LCST was reduced by increasing the MMA content. The combination of this block with the weak cationic polyelectrolyte PDEA block resulted in a double hydrophilic, double-responsive polymeric system. At ambient temperature and acidic environment the P(EGMA-co-MMA)-b-PDEA copolymer was molecularly dissolved. By increasing either the pH or the temperature of the solution, “schizophrenic” PDEA-core or P(EGMA-co-MMA)-core micelles were formed, respectively. With simultaneous increment oh pH and temperature the copolymer precipitated. Copolymers of the type A-b-(B-co-C)-b-A Inspired by the copolymer PMMA-b-P(DEA-co-MAA), the triblock telechelic polyampholyte PMMA-b-P(DEA-co-MAA)-b-A was prepared. Physical networks of this copolymer were formed at pH values out of the isoelectric point (IEP) region of the polyampholyte block. The hydrogel was formed by water absorbion of a dry polymer film and exhibited elastic behavior at acidic as well as at basic conditions. Finally in the semi-dilute regime a large number of polymer chains incorporated to form finite size clusters. These aggregates increased their size by increasing the ionization degree of the polymer chain, as a result of the electrostatic repulsive forces between the charged monomer units.
45
Haubold, Niko. « Compressed Decision Problems in Groups ». Doctoral thesis, 2011. https://ul.qucosa.de/id/qucosa%3A11370.
Texte intégralRésumé :
Wir beschäftigen uns mit Problemen der algorithmischen Gruppentheorie und untersuchen dabei die Komplexität von komprimierten Versionen des Wortproblems und des Konjugationsproblems für endlich erzeugte Gruppen.
Das Wortproblem fragt für eine feste, endlich erzeugte Gruppe ob ein gegebenes Wort über der Erzeugermenge das neutrale Element der Gruppe repräsentiert. Wir betrachten das gegebene Wort jedoch in einer komprimierten Form, als Straight-line Program (SLP) und untersuchen die Komplexität dieses Problems, das wir \''komprimiertes Wortproblem\'' nennen. SLPs sind kontextfreie Grammatiken, die genau einen String erzeugen. Die Eingabegröße ist dabei stets die Größe des gegebenen SLPs. Eine Hauptmotivation ist dabei, dass für eine feste endlich erzeugte Gruppe das Wortproblem ihrer Automorphismengruppe durch eine Turingmaschine in Polynomialzeit auf das komprimierte Wortproblem der Gruppe selbst reduzierbar ist.
Wir untersuchen das komprimierte Wortproblem für die verbreiteten Gruppenerweiterungen HNN-Erweiterungen (amalgamierte Produkte und Graphprodukte) und können zeigen, dass sich Instanzen des komprimierten Wortproblems von einer Turingmaschine in Polynomialzeit auf Instanzen des komprimierten Wortproblems der Basisgruppe (respektive Basisgruppen und Knotengruppen) reduzieren lassen. Weiterhin zeigen wir, dass das komprimierte Wortproblem für endlich erzeugte nilpotente Gruppen von einer Turingmaschine in Polynomialzeit entscheidbar ist.
Wir betrachten außerdem eine komprimierte Variante des Konjugationsproblems. Das unkomprimierte Konjugationsproblem fragt für zwei gegebene Wörter über den Erzeugern einer festen endlich erzeugten Gruppe, ob sie in dieser Gruppe konjugiert sind. Beim komprimierten Konjugationsproblem besteht die Eingabe aus zwei SLPs und es wird gefragt, ob die beiden Wörter die von den SLPs erzeugt werden in der Gruppe konjugierte Elemente präsentieren. Wir konnten zeigen, dass sich das komprimierte Konjugationsproblem für Graphgruppen in Polynomialzeit entscheiden lässt.
Weiterhin haben wir das Wortproblem der äußeren Automorphismengruppen von Graphprodukten endlich erzeugter Gruppen untersucht. Durch den engen Zusammenhang des komprimierten Konjugationsproblems einer Gruppe mit dem Wortproblem der äußeren Automorphismengruppe konnten wir zeigen, dass sich das Wortproblem der äußeren Automorphismengruppe eines Graphprodukts von endlich erzeugten Gruppen durch eine Turingmaschine in Polynomialzeit auf Instanzen von simultanen komprimierten Konjugationsproblemen der Knotengruppen und Instanzen von komprimierten Wortproblemen der Knotengruppen reduzieren lässt.
Als Anwendung gelten obige Resultate auch für right-angled Coxetergruppen und Graphgruppen, da beide spezielle Graphprodukte sind. So folgt beispielsweise, dass das komprimierte Wortproblem einer right-angled Coxetergruppe in Polynomialzeit entscheidbar ist.
46
Czenky, Agustina Mercedes. « Sobre las categorías modulares de dimensión impar ». Bachelor's thesis, 2019. http://hdl.handle.net/11086/11747.
Texte intégralRésumé :
Tesis (Lic. en Matemática)--Universidad Nacional de Córdoba, Facultad de Matemática, Astronomía, Física y Computación, 2019.El objetivo de este trabajo es presentar de la manera más autocontenida posible a las categorías modulares de dimensión impar, sus propiedades e invariantes. En la primera parte se exponen las nociones de categorías tensoriales y categorías de fusión. Se presentan construcciones útiles, como la graduación y la equivariantización por grupos finitos, y clases distinguidas de categorías: punteadas, de tipo grupo, nilpotentes, solubles, entre otras. En una segunda parte se aborda el estudio de las categorías modulares y se tratan algunos de sus invariantes: S-matriz, T -matriz, Sumas de Gauss e Indicadores de Frobenius-Schur. Finalmente se discuten algunos problemas actuales y nuevas herramientas, como el Teorema de Cauchy para categorías de fusión esféricas, la clasificación de categorías modulares de dimensión impar de rango pequeño y la clasificación de categorías modulares casi libres de cuadrados de dimensión impar. Se presentan además algunos resultados propios vinculados a dichos problemas y técnicas.
The main goal of this work is to present, in the most comprehensive way we can achieve, odd dimensional modular categories, their properties and invariants. The first part sets out the notions of tensor and fusion categories. Useful constructions are included, such as grading and equivariantization by finite groups, and distinguished classes of categories are introduced: pointed, group-theoretical, nilpotent and solvable, among others. A second part approaches the study of modular categories and some of their invariants: S-matrix, T -matrix, Gauss Sums and Frobenius-Schur Indicators. Finally, some current problems and new techniques are discussed, such as the Cauchy Theorem for spherical fusion categories, the classification of odd dimensional modular categories of small rank and the classification of odd dimensional almost square-free modular categories. Some original results related to the mentioned problems and techniques are exhibited.
47
Origlia, Marcos Miguel. « Estructuras localmente conformes Kähler y localmente conformes simplécticas en solvariedades compacta ». Doctoral thesis, 2017. http://hdl.handle.net/11086/5837.
Texte intégralRésumé :
Tesis (Doctor en Matemática)--Universidad Nacional de Córdoba, Facultad de Matemática, Astronomía, Física y Computación, 2017.En esta tesis estudiamos las estructuras localmente conformes Kähler (LCK) y localmente conformes simplécticas (LCS) invariantes a izquierda en grupos de Lie, o equivalentemente tales estructuras en álgebras de Lie. Luego se buscan retículos (subgrupos discretos co-compactos) en dichos grupos. De esta manera obtenemos estructuras LCK o LCS en las solvariedades compactas (cociente de un grupo de Lie por un retículo). Específicamente estudiamos las estructuras LCK en solvariedades con estructuras complejas abelianas. Luego describimos explícitamente la estructura de las álgebras de Lie que admiten estructuras de Vaisman. También determinamos los grupos de Lie casi abelianos que admiten estructuras LCK o LCS y además analizamos la existencia de retículos en ellos. Finalmente desarrollamos un método para construir de manera sistemática ejemplos de álgebras de Lie equipadas con estructuras LCK o LCS a partir de un álgebra de Lie que ya admite tales estructuras y una representación compatible.
In this thesis we study left invariant locally conformal Kähler (LCK) structures and locally conformal symplectic structures (LCS) on Lie groups, or equivalently such structures on Lie algebras. Then we analize the existence of lattices (co-compact discrete subgroups) on these Lie groups. Therefore, we obtain LCK or LCS structures on compact solvmanifolds (quotients of a Lie group by a lattice). Specifically we study LCK structures on solvmanifold where the complex structure is abelian. Then we describe the structure of a Lie algebra admitting a Vaisman structure. On the other hand we determine the almost abelian Lie groups equipped with a LCK or LCS structures, and we also analize the existence of lattices on these groups. Finally we construct a method to produce examples of Lie algebras admitting LCK or LCS structures beginning with a Lie algebra with these structures and a compatible representation.
48
Jauffret, Colin. « Modules réflexifs de rang 1 sur les variétés nilpotentes ». Thèse, 2016. http://hdl.handle.net/1866/19543.
Texte intégralRésumé :
Soit G un groupe algébrique linéaire complexe, simple, connexe et simplement connexe.
Étant donné un sous-groupe parabolique P G et un idéal nilpotent n p, il existe un
morphisme propre d’effondrement G x P n = Gn. Il se factorise en une variété affine et
normale N := SpecC [G P n] que nous appelons variété nilpotente.
Sous l’hypothèse que l’effondrement soit génériquement fini, nous décrivons le groupe
des classes de diviseurs équivariants de N à l’aide de C[N]-modules réflexifs équivariants
de rang 1. Un représentant de chaque classe peut être choisi comme les sections globales
d’un fibré en droite sur G x P' n' où G x P' n' = Gn' est un effondrement possiblement
distinct qui se factorise à travers la même variété nilpotente.
Dans le cas où le groupe G est de type A ou dans le cas d’un effondrement provenant de
certains diagrammes de Dynkin pondérés spécifiques, nous démontrons que les représentants
proviennent de poids qui peuvent être choisis comme dominants. Dans ce cas, nous
démontrons que si le module représente un élément torsion du groupe des classes, alors il
est Cohen–Macaulay. Nous en déduisons un théorème d’annulation en cohomologie.Let G be a simple, connected, simply connected complex linear algebraic group with parabolic subgroup P G and nilpotent ideal n p. The proper collapsing map G x P n = Gn factors through the normal affine variety N := SpecC [G x P n] which is called a nilpotent variety. Assuming the collapsing is generically finite, we describe the equivariant divisor class group of N using rank 1 reflexive equivariant C[N]-modules. A representative of each class may be chosen as global sections of a line bundle over G x P' n' where G x P' n' = Gn' is a possibly distinct collapsing that factors through the same nilpotent variety. Assuming either G is of type A or the collapsing comes from specific weighted Dynkin diagrams,we showthat each representative arise from a weight that may be chosen dominant. Moreover, if the module represents a torsion element within the class group, then it is Cohen– Macaulay and we deduce a cohomological vanishing theorem.
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Zakiyanov, Oskar. « Nové biomarkery u pacientů s onemocněním ledvin ». Doctoral thesis, 2014. http://www.nusl.cz/ntk/nusl-338466.
Texte intégralRésumé :
Chronic kidney disease (CKD) and acute kidney injury (AKI) are major public health problems. It is important to be able to identify those at high risk of adverse outcome, CKD progression and associated cardiovascular disease. The aim of the thesis was to study novel promising biomarkers, their relationship to kidney function, chronic inflammation and/or cardiovascular risk - placental growth factor (PlGF), pregnancy associated plasma protein A (PAPP-A), matrix metalloproteinase 2 (MMP-2), matrix metalloproteinase 9 (MMP-9), soluble receptor for advanced glycation end products (sRAGE), calcium binding protein S100A12 or extracellular newly identified RAGE binding protein (EN-RAGE), and high mobility group box protein-1 (HMGB-1) in patients with renal diseases including CKD, haemodialysis (HD), AKI patients, and healthy controls for comparison. First study revealed that PlGF is elevated in patients with decreased renal function. Second study demonstrated the association of MMP-2 and PAPP-A with proteinuria in patients with CKD. Moreover, serum MMP-2, MMP-9 and PAPP-A levels significantly differed in patients with various nephropathies. EN-RAGE levels are not elevated in patients with CKD, but are related to inflammatory status. PAPP-A, EN-RAGE and HMGB-1 levels are significantly elevated, but sRAGE and PlGF...