Connected Hopf algebras of finite Gelfand-Kirillov dimension

Following the seminal work of Zhuang, connected Hopf algebras of finite GK-dimension over algebraically closed fields of characteristic zero have been the subject of several recent papers. This thesis is concerned with continuing this line of research and promoting connected Hopf algebras as a natural, intricate and interesting class of algebras. We begin by discussing the theory of connected Hopf algebras which are either commutative or cocommutative, and then proceed to review the modern theory of arbitrary connected Hopf algebras of finite GK-dimension initiated by Zhuang. We next focus on the (left) coideal subalgebras of connected Hopf algebras of finite GK-dimension. They are shown to be deformations of commutative polynomial algebras. A number of homological properties follow immediately from this fact. Further properties are described, examples are considered and invariants are constructed. A connected Hopf algebra is said to be "primitively thick" if the difference between its GK-dimension and the vector-space dimension of its primitive space is precisely one . Building on the results of Wang, Zhang and Zhuang,, we describe a method of constructing such a Hopf algebra, and as a result obtain a host of new examples of such objects. Moreover, we prove that such a Hopf algebra can never be isomorphic to the enveloping algebra of a semisimple Lie algebra, nor can a semisimple Lie algebra appear as its primitive space. It has been asked in the literature whether connected Hopf algebras of finite GK-dimension are always isomorphic as algebras to enveloping algebras of Lie algebras. We provide a negative answer to this question by constructing a counterexample of GK-dimension 5. Substantial progress was made in determining the order of the antipode of a finite dimensional pointed Hopf algebra by Taft and Wilson in the 1970s. Our final main result is to show that the proof of their result can be generalised to give an analogous result for arbitrary pointed Hopf algebras.

Non-ambient solid-state characterization of crystalline molecular organic semiconductors

The research project is focused on the investigation of the polymorphism of crystalline molecular material for organic semiconductor applications under non-ambient conditions, and the solid-state characterization and crystal structure determination of the different polymorphic forms. In particular, this research project has tackled the investigation and characterization of the polymorphism of perylene diimides (PDIs) derivatives at high temperatures and pressures, in particular N,N’-dialkyl-3,4,9,10-perylendiimide (PDI-Cn, with n = 5, 6, 7, 8). These molecules are characterized by excellent chemical, thermal, and photostability, high electron affinity, strong absorption in the visible region, low LUMO energies, good air stability, and good charge transport properties, which can be tuned via functionalization; these features make them promising n-type organic semiconductor materials for several applications such as OFETs, OPV cells, laser dye, sensors, bioimaging, etc. The thermal characterization of PDI-Cn was carried out by a combination of differential scanning calorimetry, variable temperature X-ray diffraction, hot-stage microscopy, and in the case of PDI-C5 also variable temperature Raman spectroscopy. Whereas crystal structure determination was carried out by both Single Crystal and Powder X-ray diffraction. Moreover, high-pressure polymorphism via pressure-dependent UV-Vis absorption spectroscopy and high-pressure Single Crystal X-ray diffraction was carried out in this project. A data-driven approach based on a combination of self-organizing maps (SOM) and principal component analysis (PCA) is also reported was used to classify different π-stacking arrangements of PDI derivatives into families of similar crystal packing. Besides the main project, in the framework of structure-property analysis under non-ambient conditions, the structural investigation of the water loss in Pt- and Pd- based vapochromic potassium/lithium salts upon temperature, and the investigation of structure-mechanical property relationships in polymorphs of a thienopyrrolyldione endcapped oligothiophene (C4-NT3N) are reported.

The combinatorics of Hilbert-Poincaré series of matroids

In this thesis we explore the combinatorial properties of several polynomials arising in matroid theory. Our main motivation comes from the problem of computing them in an efficient way and from a collection of conjectures, mainly the real-rootedness and the monotonicity of their coefficients with respect to weak maps. Most of these polynomials can be interpreted as Hilbert--Poincaré series of graded vector spaces associated to a matroid and thus some combinatorial properties can be inferred via combinatorial algebraic geometry (non-negativity, palindromicity, unimodality); one of our goals is also to provide purely combinatorial interpretations of these properties, for example by redefining these polynomials as poset invariants (via the incidence algebra of the lattice of flats); moreover, by exploiting the bases polytopes and the valuativity of these invariants with respect to matroid decompositions, we are able to produce efficient closed formulas for every paving matroid, a class that is conjectured to be predominant among all matroids. One last goal is to extend part of our results to a higher categorical level, by proving analogous results on the original graded vector spaces via abelian categorification or on equivariant versions of these polynomials.

A mathematical model of the early visual system and border completion via subriemannian Hamiltonian geodesics

In this thesis, we aim to discuss a simple mathematical model for the edge detection mechanism and the boundary completion problem in the human brain in a differential geometry framework. We describe the columnar structure of the primary visual cortex as the fiber bundle R2 × S1, the orientation bundle, and by introducing a first vector field on it, explain the edge detection process. Edges are detected through a lift from the domain in R2 into the manifold R2 × S1 and are horizontal to a completely non-integrable distribution. Therefore, we can construct a subriemannian structure on the manifold R2 × S1, through which we retrieve perceived smooth contours as subriemannian geodesics, solutions to Hamilton’s equations. To do so, in the first chapter, we illustrate the functioning of the most fundamental structures of the early visual system in the brain, from the retina to the primary visual cortex. We proceed with introducing the necessary concepts of differential and subriemannian geometry in chapters two and three. We finally implement our model in chapter four, where we conclude, comparing our results with the experimental findings of Heyes, Fields, and Hess on the existence of an association field.

Rational algorithms for the decomposition of Feynman integrals via intersection theory

The decomposition of Feynman integrals into a basis of independent master integrals is an essential ingredient of high-precision theoretical predictions, that often represents a major bottleneck when processes with a high number of loops and legs are involved. In this thesis we present a new algorithm for the decomposition of Feynman integrals into master integrals with the formalism of intersection theory. Intersection theory is a novel approach that allows to decompose Feynman integrals into master integrals via projections, based on a scalar product between Feynman integrals called intersection number. We propose a new purely rational algorithm for the calculation of intersection numbers of differential $n-$forms that avoids the presence of algebraic extensions. We show how expansions around non-rational poles, which are a bottleneck of existing algorithms for intersection numbers, can be avoided by performing an expansion in series around a rational polynomial irreducible over $\mathbb{Q}$, that we refer to as $p(z)-$adic expansion. The algorithm we developed has been implemented and tested on several diagrams, both at one and two loops.

Design and Characterization of an Active Three-Phase EMI Noise Separator for Three-Phase Power Electronics Systems

One of the major issues for power converters that are connected to the electric grid are the measurement of three phase Conduced Emissions (CE), which are regulated by international and regional standards. CE are composed of two components which are Common Mode (CM) noise and Differential Mode (DM) noise. To achieve compliance with these regulations the Equipment Under Test (EUT) includes filtering and other electromagnetic emission control strategies. The separation of differential mode and common mode noise in Electromagnetic Interference (EMI) analysis is a well-known procedure which is useful especially for the optimization of the EMI filter, to improve the CM or DM attenuation depending on which component of the conducted emissions is predominant, and for the analysis and the understanding of interference phenomena of switched mode power converters. However, separating both components is rarely done during measurements. Therefore, in this thesis an active device for the separation of the CM and DM EMI noise in three phase power electronic systems has been designed and experimentally analysed.

A quantidade de matéria nas ciências clássicas

The chemical amount values vary in a discrete or continuous form, depending on the approach used to describe the system. In classical sciences, the chemical amount is a property of the macroscopic system and, like any other property of the system, it varies continuously. This is neither inconsistent with the concept of indivisible particles forming the system, nor a mere approximation, but it is a sound concept which enables the use of differential calculus, for instance, in chemical thermodynamics. It is shown that the fundamental laws of chemistry are absolutely compatible to the continuous concept of the chemical amount.

Equipamento microprocessado para geração de sinal de correção diferencial, em tempo real, para GPS

This work presents the development of low cost microprocessor-based equipment for generation of differential GPS correction signal, in real time, and configuration and supervision of the GPS base. The developed equipment contains a dedicated microcontroller connected to the GPS receiver, alphanumeric display and multifunction keyboard for configuration and operation of the system and communication interfaces. The electronic circuit has the function of receiving the information from GPS base; interpret them, converting the sentence in the RTCM SC-104 protocol. The microcontroller software makes the conversion of the signal received by the GPS base from the specific format to RTCM SC-104 protocol. The processing main board has two serials RS-232C standard interfaces. One of them is used for configuration and receiving the information generated by the GPS base. The other operates as output, sending the differential correction signal for the transmission system. The development of microprocessor-based equipment showed that it is possible the construction of a low cost private station for real time generation of differential GPS correction signal.

Medida da capacidade antioxidante de fluidos biologicos por voltametria de pulso diferencial associada ao uso de surfactante como resposta as adaptações geradas pelo exercicio

Universidade Estadual de Campinas . Faculdade de Educação Física

Efeitos de diferentes frequencias semanais de treinamento com pesos sobre a composição corporal e capacidades motoras em homens idosos

Universidade Estadual de Campinas . Faculdade de Educação Física

Termo do 1º Consenso em Disfunção Temporomandibular e Dor Orofacial

O Termo do 1º Consenso em Disfunção Temporomandibular e Dor Orofacial* foi criado com o propósito de substituir divergências por evidência científica dentro dessa especialidade da Odontologia. O documento oferece informações claras e fundamentadas para orientar o cirurgião-dentista e demais profissionais de saúde sobre os cuidados demandados pelo paciente, tanto no processo de diagnóstico diferencial quanto na fase de aplicação das terapias de controle da dor e disfunção. O Termo foi aprovado no mês de janeiro de 2010 em reunião realizada durante o Congresso Internacional de Odontologia do Estado de São Paulo e converge o pensamento dos profissionais mais conceituados do Brasil na especialidade Disfunção Temporomandibular e Dor Orofacial.

ProbFAST: Probabilistic Functional Analysis System Tool

Background: The post-genomic era has brought new challenges regarding the understanding of the organization and function of the human genome. Many of these challenges are centered on the meaning of differential gene regulation under distinct biological conditions and can be performed by analyzing the Multiple Differential Expression (MDE) of genes associated with normal and abnormal biological processes. Currently MDE analyses are limited to usual methods of differential expression initially designed for paired analysis. Results: We proposed a web platform named ProbFAST for MDE analysis which uses Bayesian inference to identify key genes that are intuitively prioritized by means of probabilities. A simulated study revealed that our method gives a better performance when compared to other approaches and when applied to public expression data, we demonstrated its flexibility to obtain relevant genes biologically associated with normal and abnormal biological processes. Conclusions: ProbFAST is a free accessible web-based application that enables MDE analysis on a global scale. It offers an efficient methodological approach for MDE analysis of a set of genes that are turned on and off related to functional information during the evolution of a tumor or tissue differentiation. ProbFAST server can be accessed at http://gdm.fmrp.usp.br/probfast.

Multiple classical limits in relativistic and nonrelativistic quantum mechanics

The existence of a classical limit describing the interacting particles in a second-quantized theory of identical particles with bosonic symmetry is proved. This limit exists in addition to the previously established classical limit with a classical field behavior, showing that the limit h -> 0 of the theory is not unique. An analogous result is valid for a free massive scalar field: two distinct classical limits are proved to exist, describing a system of particles or a classical field. The introduction of local operators in order to represent kinematical properties of interest is shown to break the permutation symmetry under some localizability conditions, allowing the study of individual particle properties.

ZETA DETERMINANT AND OPERATOR DETERMINANTS

We apply techniques of zeta functions and regularized products theory to study the zeta determinant of a class of abstract operators with compact resolvent, and in particular the relation with other spectral functions.

Algebraic Bethe ansatz for the anisotropic supersymmetric U model

We present an algebraic Bethe ansatz for the anisotropic supersymmetric U model for correlated electrons on the unrestricted 4(L)-dimensional electronic Hilbert space x(n=l)(L)C(4)(where L is the lattice length). The supersymmetry algebra of the local Hamiltonian is the quantum superalgebra U-q[gl(2\1)] and the model contains two symmetry-preserving free real parameters; the quantization parameter q and the Hubbard interaction parameter U. The parameter U arises from the one-parameter family of inequivalent typical four-dimensional irreps of U-q[gl(2\1)]. Eigenstates of the model are determined by the algebraic Bethe ansatz on a one-dimensional periodic lattice.