Submitted by Johnny Rodrigues (johnnyrodrigues@ufcg.edu.br) on 2018-07-22T13:41:27Z No. of bitstreams: 1 SUENE FERREIRA CAMPOS - DISSERTAÇÃO PPGMAT 2008..pdf: 741113 bytes, checksum: 7fc13ffd22412553f540977137401f24 (MD5) / Made available in DSpace on 2018-07-22T13:41:27Z (GMT). No. of bitstreams: 1 SUENE FERREIRA CAMPOS - DISSERTAÇÃO PPGMAT 2008..pdf: 741113 bytes, checksum: 7fc13ffd22412553f540977137401f24 (MD5) Previous issue date: 2008-12 / Neste trabalho apresentamos um estudo sobre o comportamento das identidades polinomiais dos produtos tensoriais de álgebras T-primas sobre corpos infinitos com diferentes características. Mais precisamente, apresentamos o Teorema sobre Produto Tensorial (TPT), descrito por Kemer para corpos de característica zero, e verificamos a sua validade sobre corpos infinitos com característica positiva. Incialmente, a partir de resultados apresentados por Azevedo e Koshlukov, estudamos os T-ideais das álgebras M1,1(G) eG⊗G, para corpos infinitos com característica zero e característicap > 2. Aqui, G = G0⊕G1 é a álgebra de Grassmann de dimensão infinita eM1,1(G) é a subálgebra de M2(G) que consiste das matrizes de ordem 2 que têm na diagonal principal entradas emG0 e na diagonal secundária entradas emG1. Em seguida, utilizando métodos introduzidos por Regev e desenvolvidos por Azevedo, Fidélis e Koshlukov, verificamos a validade do TPT para corpos de característica positiva, quando o mesmo é restrito a polinômios multilineares. Finalmente, apresentamos alguns resultados obtidos por Alves, Azevedo, Fidélis e Koshlukov, que comprovam que o TPT é falso quando o corpo base é infinito e tem característicap>2. / In this work we present a study about the behavior of polynomial identities of tensor products of T-prime T-ideals over infinite fields of different characteristics. More precisely, we present the Tensor Product Theorem (TPT), described by Kemer for fields of characteristic zero, and verify its validity over infinite fields with positive characteristic. First, based on results of Azevedo and Koshlukov, we study the Tideals of the algebrasM1,1(G) eG⊗G, for infinite fields of characteristic zero and characteristicp>2. Here,G=G0 ⊕G1 is the Grassmann algebra of infinite dimension andM1,1(G) is the subalgebras ofM2(G) consisting of matrices of order2 which main diagonal entries are inG0 and the secondary diagonal entries are inG1. Second, using methods introduced by Regev and developed by Azevedo, Fidélis and Koshlukov, we verify the validity of the TPT for fields of positive characteristic, when it is restricted to multilinear polynomials. Finally, we present some results of Alves, Azevedo, Fidelis and Koshlukov, which show that the TPT is false when the basis field is infinite and has characteristicp>2.

Submitted by Izabel Franco (izabel-franco@ufscar.br) on 2016-09-23T19:38:10Z No. of bitstreams: 1 DissGCIF.pdf: 1709329 bytes, checksum: 237db6a30fde160e22a9171ebb48cdb8 (MD5) / Approved for entry into archive by Marina Freitas (marinapf@ufscar.br) on 2016-09-26T20:45:16Z (GMT) No. of bitstreams: 1 DissGCIF.pdf: 1709329 bytes, checksum: 237db6a30fde160e22a9171ebb48cdb8 (MD5) / Approved for entry into archive by Marina Freitas (marinapf@ufscar.br) on 2016-09-26T20:45:22Z (GMT) No. of bitstreams: 1 DissGCIF.pdf: 1709329 bytes, checksum: 237db6a30fde160e22a9171ebb48cdb8 (MD5) / Made available in DSpace on 2016-09-26T20:45:29Z (GMT). No. of bitstreams: 1 DissGCIF.pdf: 1709329 bytes, checksum: 237db6a30fde160e22a9171ebb48cdb8 (MD5) Previous issue date: 2015-04-22 / Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) / The nonabelian tensor square GG of a group G was introduced by R. K. Dennis [8] in a search for new homology functors having a close relationship to K-theory and it is based on the work of C. Miller [14]. Subsequently R. Brown and J.-L. Loday [6] discovered a topological significance for the tensor square, namely, that the third homotopy group of the suspension of an Eilenberg MacLane space K(G; 1) satisfies _3 �����SK(G; 1) _ _= ker(_1), where _1 : GG ! G is the “comutator homomorphism”: _1(gh) = [g; h] = ghg�����1h�����1, 8g; h 2 G. They also defined the tensor product GH of two distinct groups acting “compatibly” on each other and showed that it arose in a certain “universal crossed square”. The main purpose of this work is to present the first properties of the nonabelian tensor product of groups and its applications in homotopy theory. / O quadrado tensorial não-abeliano GG de um grupo G foi introduzido por R. K. Dennis [8] em uma busca por novos funtores de homologia tendo uma íntima relação com a K-teoria e é baseado no trabalho de C. Miller [14]. Após isso, R. Brown e J.-L. Loday [6] descobriram uma importância topológica para o quadrado tensorial, a saber, que o terceiro grupo de homotopia da suspensão de um espaço de Eilenberg MacLane K(G; 1) satisfaz _3 SK(G; 1) __= ker(_1), em que _1 : G G ! G é o “homomorfismo comutador”: _1(gh) = [g; h] = ghg1h1, 8g; h 2 G. Os autores também definiram o produto tensorial GH de dois grupos quaisquer agindo “compativelmente” um no outro e mostraram que este aparece em um certo “quadrado cruzado universal”. O objetivo desse trabalho é apresentar o produto tensorial de grupos não-abelianos, suas primeiras propriedades e a aplicação dele na teoria de homotopia. / Processo 2013/01245-7

No description available.

Strongly correlated systems have been a major challenge for a long time in the field of theoretical chemistry. For such systems, the relevant portion of the Hilbert space scales exponentially, preventing efficient simulation on large systems. However, in many cases, the Hilbert space can be partitioned into clusters on the basis of strong and weak interactions. In this work, we mainly focus on an approach where we partition the system into smaller orbital clusters in which we can define many-particle cluster states and use traditional many-body methods to capture the rest of the inter-cluster correlations. This dissertation can be mainly divided into two parts. In the first part of this dissertation, the clustered ansatz, termed as tensor product states (TPS), is used to study large strongly correlated systems. In the second part, we study a particular type of strongly correlated system, correlated triplet pair states that arise in singlet fission. The many-body expansion (MBE) is an efficient tool that has a long history of use for calculating interaction energies, binding energies, lattice energies, and so on. We extend the incremental full configuration interaction originally proposed for a Slater determinant to a tensor product state (TPS) based wavefunction. By partitioning the active space into smaller orbital clusters, our approach starts from a cluster mean-field reference TPS configuration and includes the correlation contribution of the excited TPSs using a many-body expansion. This method, named cluster many-body expansion (cMBE), improves the convergence of MBE at lower orders compared to directly doing a block-based MBE from an RHF reference. The performance of the cMBE method is also tested on a graphene nano-sheet with a very large active space of 114 electrons in 114 orbitals, which would require 1066 determinants for the exact FCI solution. Selected CI (SCI) using determinants becomes intractable for large systems with strong correlation. We introduce a method for SCI algorithms using tensor product states which exploits local molecular structure to significantly reduce the number of SCI variables. We demonstrate the potential of this method, called tensor product selected configuration interaction (TPSCI), using a few model Hamiltonians and molecular examples. These numerical results show that TPSCI can be used to significantly reduce the number of SCI variables in the variational space, and thus paving a path for extending these deterministic and variational SCI approaches to a wider range of physical systems. The extension of the TPSCI algorithm for excited states is also investigated. TPSCI with perturbative corrections provides accurate excitation energies for low-lying triplet states with respect to extrapolated results. In the case of traditional SCI methods, accurate excitation energies are obtained only after extrapolating calculations with large variational dimensions compared to TPSCI. We provide an intuitive connection between lower triplet energy mani- folds with Hückel molecular orbital theory, providing a many-body version of Hückel theory for excited triplet states. The n-body Tucker ansatz (which is a truncated TPS wavefunction) developed in our group provides a good approximation to the low-lying states of a clusterable spin system. In this approach, a Tucker decomposition is used to obtain local cluster states which can be truncated to prune the full Hilbert space of the system. As a truncated variational approach, it has been observed that the self-consistently optimized n-body Tucker method is not size- extensive, a property important for many-body methods. We explore the use of perturbation theory and linearized coupled-cluster methods to obtain a robust yet efficient approximation. Perturbative corrections to the n-body Tucker method have been implemented for the Heisenberg Hamiltonian and numerical data for various lattices and molecular systems has been presented to show the applicability of the method. In the second part of this dissertation, we focus on studying a particular type of strongly correlated states that occurs in singlet fission material. The correlated triplet pair state 1(TT) is a key intermediate in the singlet fission process, and understanding the mechanism by which it separates into two independent triplet states is critical for leveraging singlet fission for improving solar cell efficiency. This separation mechanism is dominated by two key interactions: (i) the exchange interaction (K) between the triplets which leads to the spin splitting of the biexciton state into 1(TT),3(TT) and 5(TT) states, and (ii) the triplet-triplet energy transfer integral (t) which enables the formation of the spatially separated (but still spin entangled) state 1(T...T). We develop a simple ab initio technique to compute both the triplet-triplet exchange (K) and triplet-triplet energy transfer coupling (t). Our key findings reveal new conditions for successful correlated triplet pair state dissociation. The biexciton exchange interaction needs to be ferromagnetic or negligible compared to the triplet energy transfer for favorable dissociation. We also explore the effect of chromophore packing to reveal geometries where these conditions are achieved for tetracene. We also provide a simple connectivity rule to predict whether the through-bond coupling will be stabilizing or destabilizing for the (TT) state in covalently linked singlet fission chromophores. By drawing an analogy between the chemical system and a simple spin-lattice, one is able to determine the ordering of the multi-exciton spin state via a generalized usage of Ovchinnikov's rule. In the case of meta connectivity, we predict 5(TT) to be formed and this is later confirmed by experimental techniques like time-resolved electron spin resonance (TR-ESR). / Doctor of Philosophy / The study of the correlated motion of electrons in molecules and materials allows scientists to gain useful insights into many physical processes like photosynthesis, enzyme catalysis, superconductivity, chemical reactions and so on. Theoretical quantum chemistry tries to study the electronic properties of chemical species. The exact solution of the electron correlation problem is exponentially complex and can only be computed for small systems. Therefore, approximations are introduced for practical calculations that provide good results for ground state properties like energy, dipole moment, etc. Sometimes, more accurate calculations are required to study the properties of a system, because the system may not adhere to the as- sumptions that are made in the methods used. One such case arises in the study of strongly correlated molecules. In this dissertation, we present methods which can handle strongly correlated cases. We partition the system into smaller parts, then solve the problem in the basis of these smaller parts. We refer to this block-based wavefunction as tensor product states and they provide accurate results while avoiding the exponential scaling of the full solution. We present accurate energies for a wide variety of challenging cases, including bond breaking, excited states and π conjugated molecules. Additionally, we also investigate molecular systems that can be used to increase the efficiency of solar cells. We predict improved solar efficiency for a chromophore dimer, a result which is later experimentally verified.

Made available in DSpace on 2014-12-17T14:08:44Z (GMT). No. of bitstreams: 1 DanielE_DISSERT.pdf: 1217613 bytes, checksum: edb565b9e30a0c09780fcf4efd4a52dc (MD5) Previous issue date: 2011-04-05 / Coordena??o de Aperfei?oamento de Pessoal de N?vel Superior / In the Hydrocarbon exploration activities, the great enigma is the location of the deposits. Great efforts are undertaken in an attempt to better identify them, locate them and at the same time, enhance cost-effectiveness relationship of extraction of oil. Seismic methods are the most widely used because they are indirect, i.e., probing the subsurface layers without invading them. Seismogram is the representation of the Earth s interior and its structures through a conveniently disposed arrangement of the data obtained by seismic reflection. A major problem in this representation is the intensity and variety of present noise in the seismogram, as the surface bearing noise that contaminates the relevant signals, and may mask the desired information, brought by waves scattered in deeper regions of the geological layers. It was developed a tool to suppress these noises based on wavelet transform 1D and 2D. The Java language program makes the separation of seismic images considering the directions (horizontal, vertical, mixed or local) and bands of wavelengths that form these images, using the Daubechies Wavelets, Auto-resolution and Tensor Product of wavelet bases. Besides, it was developed the option in a single image, using the tensor product of two-dimensional wavelets or one-wavelet tensor product by identities. In the latter case, we have the wavelet decomposition in a two dimensional signal in a single direction. This decomposition has allowed to lengthen a certain direction the two-dimensional Wavelets, correcting the effects of scales by applying Auto-resolutions. In other words, it has been improved the treatment of a seismic image using 1D wavelet and 2D wavelet at different stages of Auto-resolution. It was also implemented improvements in the display of images associated with breakdowns in each Auto-resolution, facilitating the choices of images with the signals of interest for image reconstruction without noise. The program was tested with real data and the results were good / Na atividade explorat?ria de hidrocarbonetos a grande inc?gnita ? a localiza??o das jazidas. Grandes esfor?os s?o empreendidos na tentativa de melhor identific?-las, localiz?-las e, ao mesmo tempo, otimizar a rela??o custo-benef?cio da extra??o de Petr?leo. Os m?todos s?smicos s?o os mais utilizados pelo fato de serem indiretos, isto ?, sondam as camadas de subsuperf?cie sem invadi-las. O sismograma ? a representa??o do interior da Terra e de suas estruturas atrav?s de um arranjo convenientemente disposto dos dados obtidos por meio da s?smica de reflex?o. Um grande problema nessa representa??o ? a intensidade e variedade de ru?dos presentes no sismograma, como o ru?do de rolamento superficial que contamina os sinais relevantes e pode mascarar as informa??es desejadas, trazidas por ondas espalhadas em regi?es mais profundas das camadas geol?gicas. Desenvolvemos uma ferramenta para suprimir estes ru?dos que usa transformadas Wavelets 1D e 2D. O programa, em linguagem Java, faz a separa??o das imagens S?smicas considerando as dire??es (horizontal, vertical e mistas ou locais) e faixas de comprimentos de ondas que formam essas imagens, usando Wavelets de Daubechies, Autoresolu??o que duplica o comprimento das ondas e Produto Tensorial das bases de Wavelets. Desenvolvemos a op??o, em uma mesma imagem, de usar o produto tensorial de Wavelets de dimens?o 2 ou produto tensorial de Wavelets de dimens?o 1 pelas identidades. Neste ?ltimo caso, temos a Decomposi??o em Wavelets de um sinal bidimensional em uma ?nica dire??o. Esta decomposi??o permite alongar numa determinada dire??o as Wavelets bidimensionais, corrigindo efeitos de escalas ao aplicarmos Autoresolu??es. Em outras palavras, aperfei?oamos o tratamento de uma imagem s?smica, usandoWavelet 1D eWavelet 2D em etapas diferentes de Autoresolu??es. Tamb?m implementamos melhorias na visualiza??o das imagens associadas ?s decomposi??es em cada Autoresolu??o, facilitando as escolhas das imagens com os sinais de interesse para reconstru??o da imagem sem os ru?dos. O programa foi testado com dados reais e os resultados obtidos foram de boa qualidade

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / The rst aim of this dissertation is to construct the tensor product of nitely many linear spaces from elementary tensors and to show that this is the space through which multilinear mappings can be linearized. Next continuous multilinear mappings between Banach spaces are studied. The projective norm is introduced in the tensor product in order to perform the linearization of continuous multilinear mappings. The last chapter is devoted to the study of operator ideals and their generalization to the multilinear setting. The interplay between the theory of multi-ideals and the projective tensor product is established by the theory of composition multi-ideals. / O primeiro objetivo desta dissertação é construir o produto tensorial de um número finito de espaços vetoriais a partir dos tensores elementares e mostrar que e atraves desse espaco que aplicações multilineares podem ser linearizadas. Em seguida são estudadas as aplicações multilineares contnuas entre espacos de Banach. A norma projetiva e introduzida no produto tensorial para realizar a linearização das aplicações multilineares contnuas. No ultimo captulo os ideais de operadores lineares são estudados e generalizados para o contexto de ideais de aplicações multilineares. A conexão da teoria de multi-ideais com o produto tensorial projetivo e feita atraves dos multi-ideais de composição. / Mestre em Matemática

Made available in DSpace on 2014-07-29T16:02:18Z (GMT). No. of bitstreams: 1 Dissertacao Agenor Freitas de Andrade.pdf: 1042479 bytes, checksum: 049cc003452cdaee484bef8ab2c371b3 (MD5) Previous issue date: 2011-07-01 / Let G and Gj be isomorphic groups. We study the group V (G) which is an extension of the non-abelian tensor square of a group G, G G. Looking for V (G) as an operator in the class of groups, we observe that this operator preserves some properties of the group G such as finiteness, nilpotency and solubility. For a p-group finite G we find an upper bound for the order of G G. Finally, we verified computationally, for some groups, and that the results and also the bounds for the orders of the groups shown here are actually respected. / Sejam G e Gj grupos isomorfos. Estudaremos o grupo V (G) que é uma extensão de grupo do quadrado tensorial não-abeliano de um grupo G, G G. Olhando para V (G) como um operador na classe de grupos, observamos que este operador preserva algumas propriedades do grupo G, tais como finitude, solubilidade e nilpotência. Ainda para um p-grupo finito G encontramos um limitante para ordem de G G: Por fim, verificamos computacionalmente, para alguns grupos, que os resultados e também os limitantes para as ordens dos grupos aqui apresentados são de fato respeitados.

No description available.

In the first part I discuss ancestors of NURBS curves and surfaces, rather Ferguson, Beziere, Coons and B-spline curves and surfaces and furthermore B-spline functions. In the second part I devote to NURBS curves and surfaces, their description as a linear combination of B-spline functions in the projective space. I specify conical arcs more detailed, their submit in the projective space and NURBS surfasec given as tensor product of NURBS curves. Last part is devote to describtion programs for modeling conicals and NURBS surface.

MSc (Statistics) / Department of Statistics / Forecasting of electricity peak demand levels is important for decision makers in Eskom. The overall objective of this study was to develop medium term load forecasting models which will help decision makers in Eskom for planning of the operations of the utility company. The frequency table of hourly daily demands was carried out and the results show that most peak loads occur at hours 19:00 and 20:00, over the period 2009 to 2013. The study used generalised additive models with and without tensor product interactions to forecast electricity demand at 19:00 and 20:00 including daily peak electricity demand. Least absolute shrinkage and selection operator (Lasso) and Lasso via hierarchical interactions were used for variable selection to increase the model interpretability by eliminating irrelevant variables that are not associated with the response variable, this way also over tting is reduced. The parameters of the developed models were estimated using restricted maximum likelihood and penalized regression. The best models were selected based on smallest values of the Akaike information criterion (AIC), Bayesian information criterion (BIC) and Generalized cross validation (GCV) along with the highest Adjusted R2. Forecasts from best models with and without tensor product interactions were evaluated using mean absolute percentage error (MAPE), mean absolute error (MAE) and root mean square error (RMSE). Operational forecasting was proposed to forecast the demand at hour 19:00 with unknown predictor variables. Empirical results from this study show that modelling hours individually during the peak period results in more accurate peak forecasts compared to forecasting daily peak electricity demand. The performance of the proposed models for hour 19:00 were compared and the generalized additive model with tensor product interactions was found to be the best tting model. / NRF