Locally nilpotent groups of units in tiled rings

We consider locally nilpotent subgroups of units in basic tiled rings A, over local rings O which satisfy a weak commutativity condition. Tiled rings are generalizations of both tiled orders and incidence rings. If, in addition, O is Artinian then we give a complete description of the maximal locally nilpotent subgroups of the unit group of A up to conjugacy. All of them are both nilpotent and maximal Engel. This generalizes our description of such subgroups of upper-triangular matrices over O given in M. Dokuchaev, V. Kirichenko, and C. Polcino Milies (2005) [3]. (C) 2010 Elsevier Inc. All rights reserved.

Encoding through generalized polynomial codes

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

A formalized optimum code search for q-ary trellis codes

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Toeplitz operators on finite and infinite dimensional spaces with associated psi *-Fréchet algebras

The present thesis is a contribution to the multi-variable theory of Bergman and Hardy Toeplitz operators on spaces of holomorphic functions over finite and infinite dimensional domains. In particular, we focus on certain spectral invariant Frechet operator algebras F closely related to the local symbol behavior of Toeplitz operators in F. We summarize results due to B. Gramsch et.al. on the construction of Psi_0- and Psi^*-algebras in operator algebras and corresponding scales of generalized Sobolev spaces using commutator methods, generalized Laplacians and strongly continuous group actions. In the case of the Segal-Bargmann space H^2(C^n,m) of Gaussian square integrable entire functions on C^n we determine a class of vector-fields Y(C^n) supported in complex cones K. Further, we require that for any finite subset V of Y(C^n) the Toeplitz projection P is a smooth element in the Psi_0-algebra constructed by commutator methods with respect to V. As a result we obtain Psi_0- and Psi^*-operator algebras F localized in cones K. It is an immediate consequence that F contains all Toeplitz operators T_f with a symbol f of certain regularity in an open neighborhood of K. There is a natural unitary group action on H^2(C^n,m) which is induced by weighted shifts and unitary groups on C^n. We examine the corresponding Psi^*-algebra A of smooth elements in Toeplitz-C^*-algebras. Among other results sufficient conditions on the symbol f for T_f to belong to A are given in terms of estimates on its Berezin-transform. Local aspects of the Szegö projection P_s on the Heisenbeg group and the corresponding Toeplitz operators T_f with symbol f are studied. In this connection we apply a result due to Nagel and Stein which states that for any strictly pseudo-convex domain U the projection P_s is a pseudodifferential operator of exotic type (1/2, 1/2). The second part of this thesis is devoted to the infinite dimensional theory of Bergman and Hardy spaces and the corresponding Toeplitz operators. We give a new proof of a result observed by Boland and Waelbroeck. Namely, that the space of all holomorphic functions H(U) on an open subset U of a DFN-space (dual Frechet nuclear space) is a FN-space (Frechet nuclear space) equipped with the compact open topology. Using the nuclearity of H(U) we obtain Cauchy-Weil-type integral formulas for closed subalgebras A in H_b(U), the space of all bounded holomorphic functions on U, where A separates points. Further, we prove the existence of Hardy spaces of holomorphic functions on U corresponding to the abstract Shilov boundary S_A of A and with respect to a suitable boundary measure on S_A. Finally, for a domain U in a DFN-space or a polish spaces we consider the symmetrizations m_s of measures m on U by suitable representations of a group G in the group of homeomorphisms on U. In particular,in the case where m leads to Bergman spaces of holomorphic functions on U, the group G is compact and the representation is continuous we show that m_s defines a Bergman space of holomorphic functions on U as well. This leads to unitary group representations of G on L^p- and Bergman spaces inducing operator algebras of smooth elements related to the symmetries of U.

Concording EU trade and production data over time. National Bank of Belgium Working Paper No. 239, December 2012

This paper provides concordance procedures for product-level trade and production data in the EU and examines the implications of changing product classifications on measured product adding and dropping at Belgian firms. Using the algorithms developed by Pierce and Schott (2012a, 2012b), the paper develops concordance procedures that allow researchers to trace changes in coding systems over time and to translate product-level production and trade data into a common classification that is consistent both within a single year and over time. Separate procedures are created for the eightdigit Combined Nomenclature system used to classify international trade activities at the product level within the European Union as well as for the eight-digit Prodcom categories used to classify products in European domestic production data. The paper further highlights important differences in coverage between the Prodcom and Combined Nomenclature classifications which need to be taken into account when generating combined domestic production and international trade data at the product level. The use of consistent product codes over time results in less product adding and dropping at continuing firms in the Belgian export and production data.

DRAMA: Dynamic re-allocation of meshes for parallel finite element applications

In many areas of simulation, a crucial component for efficient numerical computations is the use of solution-driven adaptive features: locally adapted meshing or re-meshing; dynamically changing computational tasks. The full advantages of high performance computing (HPC) technology will thus only be able to be exploited when efficient parallel adaptive solvers can be realised. The resulting requirement for HPC software is for dynamic load balancing, which for many mesh-based applications means dynamic mesh re-partitioning. The DRAMA project has been initiated to address this issue, with a particular focus being the requirements of industrial Finite Element codes, but codes using Finite Volume formulations will also be able to make use of the project results.

INTEGRABLE MODULES FOR AFFINE LIE SUPERALGEBRAS

Irreducible nonzero level modules with finite-dimensional weight spaces are discussed for nontwisted affine Lie superalgebras. A complete classification of such modules is obtained for superalgebras of type A(m, n)(boolean AND) and C(n)(boolean AND) using Mathieu's classification of cuspidal modules over simple Lie algebras. In other cases the classification problem is reduced to the classification of cuspidal modules over finite-dimensional cuspidal Lie superalgebras described by Dimitrov, Mathieu and Penkov. Based on these results a. complete classification of irreducible integrable (in the sense of Kac and Wakimoto) modules is obtained by showing that any such module is of highest weight, in which case the problem was solved by Kac and Wakimoto.

Factoriality and the pin-reutenauer procedure

We consider implicit signatures over finite semigroups determined by sets of pseudonatural numbers. We prove that, under relatively simple hypotheses on a pseudovariety V of semigroups, the finitely generated free algebra for the largest such signature is closed under taking factors within the free pro-V semigroup on the same set of generators. Furthermore, we show that the natural analogue of the Pin-Reutenauer descriptive procedure for the closure of a rational language in the free group with respect to the profinite topology holds for the pseudovariety of all finite semigroups. As an application, we establish that a pseudovariety enjoys this property if and only if it is full.

Equations of hyperelliptic Shimura curves

We describe an algorithm that computes explicit models of hyperelliptic Shimura curves attached to an indefinite quaternion algebra over Q and Atkin-Lehner quotients of them. It exploits Cerednik-Drinfeld’s nonarchimedean uniformisation of Shimura curves, a formula of Gross and Zagier for the endomorphism ring of Heegner points over Artinian rings and the connection between Ribet’s bimodules and the specialization of Heegner points, as introduced in [21]. As an application, we provide a list of equations of Shimura curves and quotients of them obtained by our algorithm that had been conjectured by Kurihara.

Dénombrement des polynômes irréductibles unitaires dans les corps finis avec différentes contraintes sur les coefficients.

Le but de ce mémoire est de dénombrer les polynômes irréductibles unitaires dans les corps finis avec certaines conditions sur les coefficients. Notre première condition sera de fixer la trace du polynôme. Par la suite, nous choisirons la cotrace lorsque la trace sera déjà fixée à zéro. Finalement, nous discuterons du cas où la trace et le terme constant sont fixés en même temps.

Parity of the Number of Irreducible Factors for Composite Polynomials

Various results on parity of the number of irreducible factors of given polynomials over finite fields have been obtained in the recent literature. Those are mainly based on Swan’s theorem in which discriminants of polynomials over a finite field or the integral ring Z play an important role. In this paper we consider discriminants of the composition of some polynomials over finite fields. The relation between the discriminants of composed polynomial and the original ones will be established. We apply this to obtain some results concerning the parity of the number of irreducible factors for several special polynomials over finite fields.

Is a Genome a Codeword of an Error-Correcting Code?

Since a genome is a discrete sequence, the elements of which belong to a set of four letters, the question as to whether or not there is an error-correcting code underlying DNA sequences is unavoidable. The most common approach to answering this question is to propose a methodology to verify the existence of such a code. However, none of the methodologies proposed so far, although quite clever, has achieved that goal. In a recent work, we showed that DNA sequences can be identified as codewords in a class of cyclic error-correcting codes known as Hamming codes. In this paper, we show that a complete intron-exon gene, and even a plasmid genome, can be identified as a Hamming code codeword as well. Although this does not constitute a definitive proof that there is an error-correcting code underlying DNA sequences, it is the first evidence in this direction.

Packet Level Coding for Mobile Broadcasting

The thesis deals with channel coding theory applied to upper layers in the protocol stack of a communication link and it is the outcome of four year research activity. A specific aspect of this activity has been the continuous interaction between the natural curiosity related to the academic blue-sky research and the system oriented design deriving from the collaboration with European industry in the framework of European funded research projects. In this dissertation, the classical channel coding techniques, that are traditionally applied at physical layer, find their application at upper layers where the encoding units (symbols) are packets of bits and not just single bits, thus explaining why such upper layer coding techniques are usually referred to as packet layer coding. The rationale behind the adoption of packet layer techniques is in that physical layer channel coding is a suitable countermeasure to cope with small-scale fading, while it is less efficient against large-scale fading. This is mainly due to the limitation of the time diversity inherent in the necessity of adopting a physical layer interleaver of a reasonable size so as to avoid increasing the modem complexity and the latency of all services. Packet layer techniques, thanks to the longer codeword duration (each codeword is composed of several packets of bits), have an intrinsic longer protection against long fading events. Furthermore, being they are implemented at upper layer, Packet layer techniques have the indisputable advantages of simpler implementations (very close to software implementation) and of a selective applicability to different services, thus enabling a better matching with the service requirements (e.g. latency constraints). Packet coding technique improvement has been largely recognized in the recent communication standards as a viable and efficient coding solution: Digital Video Broadcasting standards, like DVB-H, DVB-SH, and DVB-RCS mobile, and 3GPP standards (MBMS) employ packet coding techniques working at layers higher than the physical one. In this framework, the aim of the research work has been the study of the state-of-the-art coding techniques working at upper layer, the performance evaluation of these techniques in realistic propagation scenario, and the design of new coding schemes for upper layer applications. After a review of the most important packet layer codes, i.e. Reed Solomon, LDPC and Fountain codes, in the thesis focus our attention on the performance evaluation of ideal codes (i.e. Maximum Distance Separable codes) working at UL. In particular, we analyze the performance of UL-FEC techniques in Land Mobile Satellite channels. We derive an analytical framework which is a useful tool for system design allowing to foresee the performance of the upper layer decoder. We also analyze a system in which upper layer and physical layer codes work together, and we derive the optimal splitting of redundancy when a frequency non-selective slowly varying fading channel is taken into account. The whole analysis is supported and validated through computer simulation. In the last part of the dissertation, we propose LDPC Convolutional Codes (LDPCCC) as possible coding scheme for future UL-FEC application. Since one of the main drawbacks related to the adoption of packet layer codes is the large decoding latency, we introduce a latency-constrained decoder for LDPCCC (called windowed erasure decoder). We analyze the performance of the state-of-the-art LDPCCC when our decoder is adopted. Finally, we propose a design rule which allows to trade-off performance and latency.

Hypersurfaces with many singularities

1. Teil: Bekannte Konstruktionen. Die vorliegende Arbeit gibt zunächst einen ausführlichen Überblick über die bisherigen Entwicklungen auf dem klassischen Gebiet der Hyperflächen mit vielen Singularitäten. Die maximale Anzahl mu^n(d) von Singularitäten auf einer Hyperfläche vom Grad d im P^n(C) ist nur in sehr wenigen Fällen bekannt, im P^3(C) beispielsweise nur für d<=6. Abgesehen von solchen Ausnahmen existieren nur obere und untere Schranken. 2. Teil: Neue Konstruktionen. Für kleine Grade d ist es oft möglich, bessere Resultate zu erhalten als jene, die durch allgemeine Schranken gegeben sind. In dieser Arbeit beschreiben wir einige algorithmische Ansätze hierfür, von denen einer Computer Algebra in Charakteristik 0 benutzt. Unsere anderen algorithmischen Methoden basieren auf einer Suche über endlichen Körpern. Das Liften der so experimentell gefundenen Hyperflächen durch Ausnutzung ihrer Geometrie oder Arithmetik liefert beispielsweise eine Fläche vom Grad 7 mit $99$ reellen gewöhnlichen Doppelpunkten und eine Fläche vom Grad 9 mit 226 gewöhnlichen Doppelpunkten. Diese Konstruktionen liefern die ersten unteren Schranken für mu^3(d) für ungeraden Grad d>5, die die allgemeine Schranke übertreffen. Unser Algorithmus hat außerdem das Potential, auf viele weitere Probleme der algebraischen Geometrie angewendet zu werden. Neben diesen algorithmischen Methoden beschreiben wir eine Konstruktion von Hyperflächen vom Grad d im P^n mit vielen A_j-Singularitäten, j>=2. Diese Beispiele, deren Existenz wir mit Hilfe der Theorie der Dessins d'Enfants beweisen, übertreffen die bekannten unteren Schranken in den meisten Fällen und ergeben insbesondere neue asymptotische untere Schranken für j>=2, n>=3. 3. Teil: Visualisierung. Wir beschließen unsere Arbeit mit einer Anwendung unserer neuen Visualisierungs-Software surfex, die die Stärken mehrerer existierender Programme bündelt, auf die Konstruktion affiner Gleichungen aller 45 topologischen Typen reeller kubischer Flächen.

Direction finding in the presence of a more realistic environment model

Direction-of-arrival (DOA) estimation is susceptible to errors introduced by the presence of real-ground and resonant size scatterers in the vicinity of the antenna array. To compensate for these errors pre-calibration and auto-calibration techniques are presented. The effects of real-ground constituent parameters on the mutual coupling (MC) of wire type antenna arrays for DOA estimation are investigated. This is accomplished by pre-calibration of the antenna array over the real-ground using the finite element method (FEM). The mutual impedance matrix is pre-estimated and used to remove the perturbations in the received terminal voltage. The unperturbed terminal voltage is incorporated in MUSIC algorithm to estimate DOAs. First, MC of quarter wave monopole antenna arrays is investigated. This work augments an existing MC compensation technique for ground-based antennas and proposes reduction in MC for antennas over finite ground as compared to the perfect ground. A factor of 4 decrease in both the real and imaginary parts of the MC is observed when considering a poor ground versus a perfectly conducting one for quarter wave monopoles in the receiving mode. A simulated result to show the compensation of errors direction of arrival (DOA) estimation with actual realization of the environment is also presented. Secondly, investigations for the effects on received MC of λ/2 dipole arrays placed near real-earth are carried out. As a rule of thumb, estimation of mutual coupling can be divided in two regions of antenna height that is very near ground 0