On some Density Theorems in Number Theory and Group Theory

Gowers, dans son article sur les matrices quasi-aléatoires, étudie la question, posée par Babai et Sos, de l'existence d'une constante $c>0$ telle que tout groupe fini possède un sous-ensemble sans produit de taille supérieure ou égale a $c|G|$. En prouvant que, pour tout nombre premier $p$ assez grand, le groupe $PSL_2(\mathbb{F}_p)$ (d'ordre noté $n$) ne posséde aucun sous-ensemble sans produit de taille $c n^{8/9}$, il y répond par la négative. Nous allons considérer le probléme dans le cas des groupes compacts finis, et plus particuliérement des groupes profinis $SL_k(\mathbb{Z}_p)$ et $Sp_{2k}(\mathbb{Z}_p)$. La premiére partie de cette thése est dédiée à l'obtention de bornes inférieures et supérieures exponentielles pour la mesure suprémale des ensembles sans produit. La preuve nécessite d'établir préalablement une borne inférieure sur la dimension des représentations non-triviales des groupes finis $SL_k(\mathbb{Z}/(p^n\mathbb{Z}))$ et $Sp_{2k}(\mathbb{Z}/(p^n\mathbb{Z}))$. Notre théoréme prolonge le travail de Landazuri et Seitz, qui considérent le degré minimal des représentations pour les groupes de Chevalley sur les corps finis, tout en offrant une preuve plus simple que la leur. La seconde partie de la thése à trait à la théorie algébrique des nombres. Un polynome monogéne $f$ est un polynome unitaire irréductible à coefficients entiers qui endengre un corps de nombres monogéne. Pour un nombre premier $q$ donné, nous allons montrer, en utilisant le théoréme de densité de Tchebotariov, que la densité des nombres premiers $p$ tels que $t^q -p$ soit monogéne est supérieure ou égale à $(q-1)/q$. Nous allons également démontrer que, quand $q=3$, la densité des nombres premiers $p$ tels que $\mathbb{Q}(\sqrt[3]{p})$ soit non monogéne est supérieure ou égale à $1/9$.

Building Beyond Limits : Fantastic Collisions Between Bodies and Machines in French and English Fin-de-Siècle Literature

«Construire hors limite: collisions fantastiques entre corps et machines dans la littérature fin-de-siècle française et anglaise» explore un ensemble de textes qui ont surgi à la fin du dix-neuvième siècle en réponse et en réaction à la fulgurante évolution de l’environnement scientifique et technologique, et qui considèrent la relation entre l’homme et la machine en fantasmant sur la zone grise où ils s’intersectent. Les principaux textes étudiés comprennent L’Ève future de Villiers de l’Isle-Adam, Le Surmâle d’Alfred Jarry, Trilby de George Du Maurier, Le Château des Carpathes de Jules Verne, ainsi qu’une sélection de contes dont nous pouvons qualifier de «contes à appareils», notamment «La Machine à parler» de Marcel Schwob. Utilisant la théorie des systèmes comme base méthodologique, cette dissertation cherche à réinterpréter les textes de la fin du dix-neuvième siècle qui naviguent les limites de l’humain et du mécanique et les surfaces sensibles où ils se touchent et interagissent en les réinscrivant dans un projet plus vaste de construction d’identité qui défie le temps chronologique et les échelles mathématiques. Le lien entre la théorie des systèmes et l’architecture – comme méthode d’organisation d’espace blanc en espace habitable – est exploré dans le but de comprendre la manière dont nous façonnons et interprétons le néant à l’origine de l’identité individuelle, et par association collective, en pratiquant littéralement la schématisation et la construction du corps. Des auteurs tels Villiers et Jarry imaginent la construction du corps comme une entreprise scientifique nécessairement fondée et réalisée avec les matériaux et les technologies disponibles, pour ensuite démanteler cette proposition en condamnant le corps technologique à la destruction. La construction d’une identité amplifiée par la technologie prend donc des proportions prométhéennes perpétuellement redessinées dans des actes cycliques de rasage (destruction) et d’érection (édification), et reflétées dans l’écriture palimpsestique du texte. L’intégrité du corps organique étant mis en question, le noyau même de ce que signifie l’être (dans son sens de verbe infinitif) humain pourrait bien s’avérer, si l’on considère la correspondance entre perte de voix et état pathologique dans les textes de Du Maurier, Verne et Schwob, être une structure des plus précaires, distinctement hors sens (unsound).

Theory and numerical integration of subsurface light transport

En synthèse d’images, reproduire les effets complexes de la lumière sur des matériaux transluminescents, tels que la cire, le marbre ou la peau, contribue grandement au réalisme d’une image. Malheureusement, ce réalisme supplémentaire est couteux en temps de calcul. Les modèles basés sur la théorie de la diffusion visent à réduire ce coût en simulant le comportement physique du transport de la lumière sous surfacique tout en imposant des contraintes de variation sur la lumière incidente et sortante. Une composante importante de ces modèles est leur application à évaluer hiérarchiquement l’intégrale numérique de l’illumination sur la surface d’un objet. Cette thèse révise en premier lieu la littérature actuelle sur la simulation réaliste de la transluminescence, avant d’investiguer plus en profondeur leur application et les extensions des modèles de diffusion en synthèse d’images. Ainsi, nous proposons et évaluons une nouvelle technique d’intégration numérique hiérarchique utilisant une nouvelle analyse fréquentielle de la lumière sortante et incidente pour adapter efficacement le taux d’échantillonnage pendant l’intégration. Nous appliquons cette théorie à plusieurs modèles qui correspondent à l’état de l’art en diffusion, octroyant une amélioration possible à leur efficacité et précision.

Population Ethics, Social Choice Theory, and Two problems in the Measurement of Economic Poverty

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STUDIES ON THE STRESS FLUCTUATIONS IN SHEARED STOKESIAN SUSPENSIONS USING CHAOS THEORY AND NONLINEAR DYNAMICS

The thesis report results obtained from a detailed analysis of the fluctuations of the rheological parameters viz. shear and normal stresses, simulated by means of the Stokesian Dynamics method, of a macroscopically homogeneous sheared suspension of neutrally buoyant non-Brownian suspension of identical spheres in the Couette gap between two parallel walls in the limit of vanishingly small Reynolds numbers using the tools of non-linear dynamics and chaos theory for a range of particle concentration and Couette gaps. The thesis used the tools of nonlinear dynamics and chaos theory viz. average mutual information, space-time separation plots, visual recurrence analysis, principal component analysis, false nearest-neighbor technique, correlation integrals, computation of Lyapunov exponents for a range of area fraction of particles and for different Couette gaps. The thesis observed that one stress component can be predicted using another stress component at the same area fraction. This implies a type of synchronization of one stress component with another stress component. This finding suggests us to further analysis of the synchronization of stress components with another stress component at the same or different area fraction of particles. The different model equations of stress components for different area fraction of particles hints at the possible existence a general formula for stress fluctuations with area fraction of particle as a parameter

Studies on the Development and Control of Desiccation cracks in compacted clay liner soils

The present study aimed at critically looking at the current practice of the installation of compacted clay liner using bentonite enhanced sand (BES). The application of bentonite is currently the most accepted practice for lining purposes. The ideal bentonite sand combination, which satisfies the liner requirements is 20% bentonite and 80% sand, was selected as one of the liner materials for the investigation of development of desiccation cracks. Locally available sundried marine clay and its combination with bentonite were also included in the study. The desiccation tests on liner materials were conducted for wet/dry cycles to simulate the seasonal variations. Digital image processing techniques were used to measure the crack intensity factor (CIF), a useful and effective parameter for quantification of desiccation cracking. The repeatability of the tests could be well established, as the variation in CIF values of identical samples had a very narrow range of 0 to 2%. The studies on the development of desiccation cracks showed that the CIF of bentonite enhanced sand mixture (BES) was 18.09%, 39.75% and 21.22% for the first, second and third cycles respectively, while it was only 9.83%, 7.52% and 4.58% respectively for sun dried marine clay (SMC). Thus the locally available, alternate liner material suggested, viz SMC, is far superior to BES, when subjected to alternate wet/dry cycles. Further, the improvement of these liner materials when amended with randomly distributed fibre reinforcements was also investigated. Three types of fibres ,namely nylon fibre, polypropylene monofilament and polypropylene fibre mesh were used for the study of fibre amended BES and SMC.The influence of these amendments on the properties of the above liner materials is also studied. The results showed that there is definite improvement in the properties of the liner materials when it is reinforced with discrete random fibres. The study also proved that the desiccation cracks could be controlled with the help of fibre reinforcement.

Financial crisis: theory and practice

In the last 50 years, we have had approximately 40 events with characteristics related to financial crisis. The most severe crisis was in 1929, when the financial markets plummet and the US gross domestic product decline in more than 30 percent. Recently some years ago, a new crisis developed in the United States, but instantly caused consequences and effects in the rest of the world. This new economic and financial crisis has increased the interest and motivation for the academic community, professors and researchers, to understand the causes and effects of the crisis, to learn from it. This is the one of the main reasons for the compilation of this book, which begins with a meeting of a group of IAFI researchers from the University of Barcelona, where researchers form Mexico and Spain, explain causes and consequences of the crisis of 2007. For that reason, we believed this set of chapters related to methodologies, applications and theories, would conveniently explained the characteristics and events of the past and future financial crisis This book consists in 3 main sections, the first one called "State of the Art and current situation", the second named "Econometric applications to estimate crisis time periods" , and the third one "Solutions to diminish the effects of the crisis". The first section explains the current point of view of many research papers related to financial crisis, it has 2 chapters. In the first one, it describe and analyzes the models that historically have been used to explain financial crisis, furthermore, it proposes to used alternative methodologies such as Fuzzy Cognitive Maps. On the other hand , Chapter 2 , explains the characteristics and details of the 2007 crisis from the US perspective and its comparison to 1929 crisis, presenting some effects in Mexico and Latin America. The second section presents two econometric applications to estimate possible crisis periods. For this matter, Chapter 3, studies 3 Latin-American countries: Argentina, Brazil and Peru in the 1994 crisis and estimates the multifractal characteristics to identify financial and economic distress. Chapter 4 explains the crisis situations in Argentina (2001), Mexico (1994) and the recent one in the United States (2007) and its effects in other countries through a financial series methodology related to the stock market. The last section shows an alternative to prevent the effects of the crisis. The first chapter explains the financial stability effects through the financial system regulation and some globalization standards. Chapter 6, study the benefits of the Investor activism and a way to protect personal and national wealth to face the financial crisis risks.

Financial planning and Control in public sector undertakings in kerala

Today India is seeking a speedy transformation of her semi-stagnant economy to a dynamic one by means of economic planning in a democratic set up. In the context of this growth oriented endeavour public sector has a vital role to play. After three decades of planned development, it has become important that India must make fresh appraisals on the role of public sector in the economic renaissance of the country. Almost no comprehensive study has been made on this vital segment of the economy vis-a-vis the growth economics. This study is an attempt to fill this need in a very modest way. It presents the subject in a new perspective. An earnest attempt is made to reveal the critical problems inhibiting the growth of the public sector from a new angle which focusses the spot-light on the economics of development.

Socio economic factors influencing the persistence and control of filariasis in Kerala-A case study of malayan filariasis in Cherthala

In general the behavioural sciences have contributed very little to filariasis research.Man's actions in creating vector breeding sites have been noted and discussed frequently inthe frlariasis literature. but virtually no systematic studies of these fonns of behavior have been undertaken (Dunn. 1979). Human behavioural observations and inquires into values and attitudes atfecting behavior that inhibits or promotes vector breeding are essential if any progress is to be made in developing self help programmes of vector control. Therefore, a systematic study on the socio-economic aspect of the community is warranted before undertaking any control programme against filariasis. In view of this the present study has been carried out which reveals the knowledge, attitude and practice concerning the causation, transmission, treatment and control of the disease. Socio economic factors that influence the creation and maintenance of vector breeding habitats were identified. characterization and ranking of these sociological factors will be helpful in identifying the determinants of human behavioural changes towards the containment of the disease- Information on the existing indigenous perception of the disease and the factors that hinder the control will be useful in developing a sound strategy from the human angle, which can be put to practical use.

Some Lattice Problems In Fuzzy Set Theory And Fuzzy Topology

It is believed that every fuzzy generalization should be formulated in such a way that it contain the ordinary set theoretic notion as a special case. Therefore the definition of fuzzy topology in the line of C.L.CHANG E9] with an arbitrary complete and distributive lattice as the membership set is taken. Almost all the results proved and presented in this thesis can, in a sense, be called generalizations of corresponding results in ordinary set theory and set topology. However the tools and the methods have to be in many of the cases, new. Here an attempt is made to solve the problem of complementation in the lattice of fuzzy topologies on a set. It is proved that in general, the lattice of fuzzy topologies is not complemented. Complements of some fuzzy topologies are found out. It is observed that (L,X) is not uniquely complemented. However, a complete analysis of the problem of complementation in the lattice of fuzzy topologies is yet to be found out

Quasilocal density functional theory and its application within the extended Thomas-Fermi approximation

In this paper we propose a generalization of the density functional theory. The theory leads to single-particle equations of motion with a quasilocal mean-field operator, which contains a quasiparticle position-dependent effective mass and a spin-orbit potential. The energy density functional is constructed using the extended Thomas-Fermi approximation and the ground-state properties of doubly magic nuclei are considered within the framework of this approach. Calculations were performed using the finite-range Gogny D1S forces and the results are compared with the exact Hartree-Fock calculations

Arbitrage Pricing Theory and Return Generating Process: A Macroeconomic Approach to Indian Stock Market

A study focusing on the identification of return generating factors and to the extent of their influence on share prices the outcome will be a tool for investment analysis in the hands of investors portfolio managers and mutual funds who are mostly concerned with changing share prices. Since the study takes into account the influence of macroeconomic variables on variations in share returns by using the outcome the government can frame out suitable policies on long term basis and that will help in nurturing a healthy economy and resultant stock market. As every company management tries to maximize the wealth of the share holders a clear idea about the return generating variables and their influence will help the management to frame various policies to maximize the wealth of the shareholders.

Finite size effects on the electrical properties of sol–gel synthesized CoFe2O4 powders: deviation from Maxwell–Wagner theory and evidence of surface polarization effects

Fine particles of cobalt ferrite were synthesized by the sol–gel method. Subsequent heat treatment at different temperatures yielded cobalt ferrites having different grain sizes. X-ray diffraction studies were carried out to elucidate the structure of all the samples. Dielectric permittivity and ac conductivity of all the samples were evaluated as a function of frequency, temperature and grain size. The variation of permittivity and ac conductivity with frequency reveals that the dispersion is due to Maxwell–Wagner type interfacial polarization in general, with a noted variation from the expected behaviour for the cold synthesized samples. High permittivity and conductivity for small grains were explained on the basis of the correlated barrier-hopping model

Studies on scattering and thermodynamics of black holes in f(R) theory and Einstein's theory

One of the interesting consequences of Einstein's General Theory of Relativity is the black hole solutions. Until the observation made by Hawking in 1970s, it was believed that black holes are perfectly black. The General Theory of Relativity says that black holes are objects which absorb both matter and radiation crossing the event horizon. The event horizon is a surface through which even light is not able to escape. It acts as a one sided membrane that allows the passage of particles only in one direction i.e. towards the center of black holes. All the particles that are absorbed by black hole increases the mass of the black hole and thus the size of event horizon also increases. Hawking showed in 1970s that when applying quantum mechanical laws to black holes they are not perfectly black but they can emit radiation. Thus the black hole can have temperature known as Hawking temperature. In the thesis we have studied some aspects of black holes in f(R) theory of gravity and Einstein's General Theory of Relativity. The scattering of scalar field in this background space time studied in the first chapter shows that the extended black hole will scatter scalar waves and have a scattering cross section and applying tunneling mechanism we have obtained the Hawking temperature of this black hole. In the following chapter we have investigated the quasinormal properties of the extended black hole. We have studied the electromagnetic and scalar perturbations in this space-time and find that the black hole frequencies are complex and show exponential damping indicating the black hole is stable against the perturbations. In the present study we show that not only the black holes exist in modified gravities but also they have similar properties of black hole space times in General Theory of Relativity. 2 + 1 black holes or three dimensional black holes are simplified examples of more complicated four dimensional black holes. Thus these models of black holes are known as toy models of black holes in four dimensional black holes in General theory of Relativity. We have studied some properties of these types of black holes in Einstein model (General Theory of Relativity). A three dimensional black hole known as MSW is taken for our study. The thermodynamics and spectroscopy of MSW black hole are studied and obtained the area spectrum which is equispaced and different thermo dynamical properties are studied. The Dirac perturbation of this three dimensional black hole is studied and the resulting quasinormal spectrum of this three dimensional black hole is obtained. The different quasinormal frequencies are tabulated in tables and these values show an exponential damping of oscillations indicating the black hole is stable against the mass less Dirac perturbation. In General Theory of Relativity almost all solutions contain singularities. The cosmological solution and different black hole solutions of Einstein's field equation contain singularities. The regular black hole solutions are those which are solutions of Einstein's equation and have no singularity at the origin. These solutions possess event horizon but have no central singularity. Such a solution was first put forward by Bardeen. Hayward proposed a similar regular black hole solution. We have studied the thermodynamics and spectroscopy of Hay-ward regular black holes. We have also obtained the different thermodynamic properties and the area spectrum. The area spectrum is a function of the horizon radius. The entropy-heat capacity curve has a discontinuity at some value of entropy showing a phase transition.