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‣ The direct determination of rare earth elements in basaltic and related rocks using ICP-MS: Testing the efficiency of microwave oven sample decomposition procedures

NAVARRO, Margareth S.; Andrade, Sandra; Ulbrich, Horstpeter Herberto Gustavo Jose; Gomes, Celso de Barros; Girardi, Vicente Antonio Vitorio
Fonte: WILEY-BLACKWELL Publicador: WILEY-BLACKWELL
Tipo: Artigo de Revista Científica
Português
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Tests are described showing the results obtained for the determination of REE and the trace elements Rb, Y, Zr, Nb, Cs, Ba, Hf, Ta, Pb, Th and U with ICP-MS methodology for nine basaltic reference materials, and thirteen basalts and amphibolites from the mafic-ultramafic Niquelandia Complex, central Brazil. Sample decomposition for the reference materials was performed by microwave oven digestion (HF and HNO(3), 100 mg of sample), and that for the Niquelandia samples also by Parr bomb treatment (5 days at 200 degrees C, 40 mg of sample). Results for the reference materials were similar to published values, thus showing that the microwave technique can be used with confidence for basaltic rocks. No fluoride precipitates were observed in the microwave-digested solutions. Total recovery of elements, including Zr and Hf, was obtained for the Niquelandia samples, with the exception of an amphibolite. For this latter sample, the Parr method achieved a total digestion, but not so the microwave decomposition; losses, however, were observed only for Zr and Hf, indicating difficulty in dissolving Zr-bearing minerals by microwave acid attack.

‣ Técnicas de decomposição de domínio em computação paralela para simulação de campos eletromagnéticos pelo método dos elementos finitos; Domain decomposition and parallel processing techniques applied to the solution of systems of algebraic equations issued from the finite element analysis of eletromagnetic phenomena.

Palin, Marcelo Facio
Fonte: Biblioteca Digitais de Teses e Dissertações da USP Publicador: Biblioteca Digitais de Teses e Dissertações da USP
Tipo: Tese de Doutorado Formato: application/pdf
Publicado em 18/06/2007 Português
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Este trabalho apresenta a aplicação de técnicas de Decomposição de Domínio e Processamento Paralelo na solução de grandes sistemas de equações algébricas lineares provenientes da modelagem de fenômenos eletromagnéticos pelo Método de Elementos Finitos. Foram implementadas as técnicas dos tipos Complemento de Schur e o Método Aditivo de Schwarz, adaptadas para a resolução desses sistemas em cluster de computadores do tipo Beowulf e com troca de mensagens através da Biblioteca MPI. A divisão e balanceamento de carga entre os processadores são feitos pelo pacote METIS. Essa metodologia foi testada acoplada a métodos, seja iterativo (ICCG), seja direto (LU) na etapa de resolução dos sistemas referentes aos nós internos de cada partição. Para a resolução do sistema envolvendo os nós de fronteira, no caso do Complemento de Schur, utilizou-se uma implementação paralisada do Método de Gradientes Conjugados (PCG). S~ao discutidos aspectos relacionados ao desempenho dessas técnicas quando aplicadas em sistemas de grande porte. As técnicas foram testadas na solução de problemas de aplicação do Método de Elementos Finitos na Engenharia Elétrica (Magnetostática, Eletrocinética e Magnetodinâmica), sejam eles de natureza bidimensional com malhas não estruturadas...

‣ Estudo comparativo de métodos de preparo de amostras de tinta para a determinação de metais e metalóides por técnicas de espectrometria atômica; Paint samples preparation methods for metals and methaloids determination by atomic spectrometry techniques

Bentlin, Fabrina Regia Stumm; Pozebon, Dirce; Depoi, Fernanda dos Santos
Fonte: Universidade Federal do Rio Grande do Sul Publicador: Universidade Federal do Rio Grande do Sul
Tipo: Artigo de Revista Científica Formato: application/pdf
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This work deals with paint decomposition methods for major, minor and trace elements determination. Three methods were investigated: (1) decomposition in closed quartz vessel and heating in microwave oven; (2) decomposition in open vessel using HNO and ashing, following the ASTM D 3335-85a method; and (3) decomposition in open vessel using HNO3 + HF and ashing. Paints of different types and colours were analyzed, in which several elements were determined using inductively coupled plasma mass spectrometry (ICP-MS) and inductively coupled plasma optical emission spectrometry (ICP OES). It was observed that method (1) is appropriate for trace, minor and major elements determination, while method (3) is appropriate for Ti.

‣ Técnicas de geração de colunas e decomposição de Dantzig-Wolfe aplicadas ao problema de planejamento florestal; Column generation and Dantzig-Wolfe decomposition applied to forest planning problem

André Gambaro
Fonte: Biblioteca Digital da Unicamp Publicador: Biblioteca Digital da Unicamp
Tipo: Dissertação de Mestrado Formato: application/pdf
Publicado em 09/01/2015 Português
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A gestão florestal é uma área de significativa importância para a indústria e sociedade e traz consigo desafios consideráveis de planejamento de curto e longo prazo onde modelos matemáticos têm sido propostos para apoio das decisões envolvidas. Neste contexto, o presente trabalho busca revisar a literatura em busca de apresentar os principais modelos e sistemas utilizados, em particular os modelos de simulação e de programação linear de tipo I e II para o problema de planejamento florestal de longo prazo. É proposta também para este problema uma abordagem que utiliza a técnica de decomposição de Dantzig-Wolfe e geração de colunas para integrar os aspectos de sistemas de simulação de intervenções florestais com a programação linear. A abordagem explora de perto as estruturas de rede dos subproblemas que são associados ao problema de caminho mínimo e resolvidos via programação dinâmica e programação linear. Por fim testes são realizados com a implementação da abordagem em instâncias do problema e os resultados apresentados.; The forest management has been of significative importance for industry and society along the years and brings with it considerable long and short term planning challenges where mathematical models have been proposed to support the decisions involved. In this context...

‣ An overview of statistical decomposition techniques applied to complex systems

Tuncer, Yalcin; Tanik, Murat M.; Allison, David B.
Fonte: PubMed Publicador: PubMed
Tipo: Artigo de Revista Científica
Publicado em 20/01/2008 Português
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The current state of the art in applied decomposition techniques is summarized within a comparative uniform framework. These techniques are classified by the parametric or information theoretic approaches they adopt. An underlying structural model common to all parametric approaches is outlined. The nature and premises of a typical information theoretic approach are stressed. Some possible application patterns for an information theoretic approach are illustrated. Composition is distinguished from decomposition by pointing out that the former is not a simple reversal of the latter. From the standpoint of application to complex systems, a general evaluation is provided.

‣ Optimal Generation Expansion Planning for Electric Utilities Using Decomposition and Probabilistic Simulation Techniques

Bloom, Jeremy A.
Fonte: Massachusetts Institute of Technology, Operations Research Center Publicador: Massachusetts Institute of Technology, Operations Research Center
Tipo: Trabalho em Andamento Formato: 1746 bytes; 1643929 bytes; application/pdf
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Three related methods are presented for determining the least-cost generating capacity investments required to meet given future demands for electricity. The models are based on application of large-scale mathematical programming decomposition techniques. In the first method, decomposition techniques are applied to linear programming models such as those presented by Anderson (Bell Journal of Economics, Spring 1972). An important result is that the subproblems, representing optimal operation of a set of plants of given capacity in each year, can be solved essentially by inspection. In the second method, decomposition is applied to an equivalent non-linear programming model, with the same result that the subproblems are very simple to solve. The third method extends the second to include the probabilistic simulation technique of Baleriaux and Booth (IEEE Transactions on Power Apparatus and Systems, Jan.-Feb., 1972), which determines the optimal operating costs when plants can fail randomly. Though the model is non-linear, the subproblems involving the probabilistic simulation can be solved without using non-linear programming.; Research supported by the Energy Research and Development Administration through Contract 421072-S with Brookhaven National Laboratory and by the U.S. Army Research Office (Durham) under Contract DAAG29-76-C-0064.

‣ Accounting for Mexican Income Inequality during the 1990s

De Hoyos, Rafael E.
Fonte: World Bank, Washington, DC Publicador: World Bank, Washington, DC
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The author implements several inequality decomposition methods to measure the extent to which total household income disparities can be attributable to sectoral asymmetries and differences in skill endowments. The results show that at least half of total household inequality in Mexico is attributable to incomes derived from entrepreneurial activities, an income source rarely scrutinized in the inequality literature. He shows that education (skills) endowments are unevenly distributed among the Mexican population, with positive shifts in the market returns to schooling associated with increases in inequality. Asymmetries in the allocation of education explain around 20 percent of overall household income disparities in Mexico during the 1990s. Moreover, the proportion of inequality attributable to education endowments increases during stable periods and reduces during the crisis. This pattern is explained by shifts in returns to schooling rather than changes in the distribution of skills. Applying the same techniques to decompose within-sector income differences...

‣ Advanced hybrid approaches based on graph theory decomposition, modified evolutionary algorithms and deterministic optimisation techniques for the design of water distribution systems.

Zheng, Feifei
Fonte: Universidade de Adelaide Publicador: Universidade de Adelaide
Tipo: Tese de Doutorado
Publicado em //2013 Português
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The cost of water distribution system (WDS) design or rehabilitation is normally expensive. Over the past 40 years, a number of optimization¹ techniques have therefore been developed to find optimal designs for WDSs in order to save costs, while satisfying the specified design criteria. Often there are a large number of decision variables involved. The majority of currently available optimization techniques exhibit limitations when dealing with large WDSs. Two limitations include (i) finding only local optimal solutions and/or (ii) exhibiting computational inefficiency. The research undertaken in this dissertation has focused on developing advanced optimization techniques that are able to find good quality solutions for real-world sized or large WDS design or rehabilitation strategies with great efficiency. There were three objectives for the research: (i) the modification and improvement of currently available optimization techniques; (ii) the development of advanced hybrid optimization techniques (evolutionary algorithms combined with traditional deterministic optimization techniques) and (iii) the proposal of novel optimization methods with the incorporation of graph decomposition techniques. The most novel feature of this research is that graph decomposition techniques have been successfully incorporated to facilitate the optimization for WDS design. A number of decomposition techniques have been developed to decompose WDSs by the use of graph theory in this research. Real-world sized or large WDSs are used to demonstrate the effectiveness of the proposed advanced optimization techniques described in this thesis. Results show that these advanced methods are capable of obtaining sound optimal solutions with significantly improved efficiency compared to currently available optimization techniques. The main contribution of this thesis is the provision of effective and efficient optimization techniques for real-world sized or large WDS designs or rehabilitation problems. ¹American spelling has been used in this thesis as all the publications included in this thesis have been submitted to or published in American journals.; Thesis (Ph.D.) -- University of Adelaide...

‣ A new decomposition method applied to optimization problems arising in power systems: Local and global behavior

Conejo, Antonio J.; Nogales, Francisco J.; Prieto, Francisco J.
Fonte: Universidade Carlos III de Madrid Publicador: Universidade Carlos III de Madrid
Tipo: Trabalho em Andamento Formato: application/pdf
Publicado em /06/1999 Português
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In this report a new decomposition methodology for optimization problems is presented. The proposed procedure is general, simple and efficient. It avoids most disadvantages of other common decomposition techniques, such as Lagrangian Relaxation or Augmented Lagrangian Relaxation. The new methodology is applied to a problem coming from interconnected power systems. The application of the new method to this problem allows the computation of an optimal coordinated but decentralized solution. Local and global convergence properties of the proposed decomposition algorithm are described. Numerical results show that the new decentralized methodology has a lower computational cost than other decomposition techniques, and in large-scale cases even lower than a centralized approach.

‣ Solving dynamic stochastic economic models by mathematical programming decomposition methods

Esteban-Bravo, Mercedes; Nogales, Francisco J.
Fonte: Elsevier Publicador: Elsevier
Tipo: Artigo de Revista Científica Formato: text/plain; application/pdf
Publicado em /01/2008 Português
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Discrete-time optimal control problems arise naturally in many economic problems. Despite the rapid growth in computing power and new developments in the literature, many economic problems are still quite challenging to solve. Economists are aware of the limitations of some of these approaches for solving these problems due to memory and computational requirements. However, many of the economic models present some special structure that can be exploited in an efficient manner. This paper introduces a decomposition methodology, based on a mathematical programming framework, to compute the equilibrium path in dynamic models by breaking the problem into a set of smaller independent subproblems. We study the performance of the method solving a set of dynamic stochastic economic models. The numerical results reveal that the proposed methodology is efficient in terms of computing time and accuracy

‣ A decomposition methodology applied to the multiarea optimal power flow problem

Nogales, Francisco J.; Prieto, Francisco J.; Conejo, Antonio J.
Fonte: Springer Publicador: Springer
Tipo: info:eu-repo/semantics/acceptedVersion; info:eu-repo/semantics/article Formato: application/pdf
Publicado em /04/2003 Português
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This paper describes a decomposition methodology applied to the multi-area optimal power fiow problem in the context of an electric energy system. The proposed procedure is simple and efficient, and presents sorne advantages with respect to other common decomposition techniques such as Lagrangian relaxation and augmented Lagrangian decomposition. The application to the multi-area optimal power fiow problem allows the computation of an optimal coordinated but decentralized solution. The proposed method is appropriate for an Independent System Operator in charge of the electric energy system technical operation. Convergence properties of the proposed decomposition algorithm are described and related to the physical coupling between the areas. Theoretical and numerical results show that the proposed decentralized methodology has a lower computational cost than other decomposition techniques, and in large large-scale cases even lower than a centralized approach.; Research supported by Spanish grants PB98-0728 and BEC 2000-0167. Research partly supported by Ministerio de Ciencia y Tecnología of Spain, project CICYT DPI-2000- 0654.; The original publication is available at www.springerlink.com

‣ Improving the Army's joint platform allocation tool (JPAT)

Harrop, John P.
Fonte: Monterey, California: Naval Postgraduate School Publicador: Monterey, California: Naval Postgraduate School
Tipo: Tese de Doutorado
Português
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Approved for public release; distribution is unlimited; The U.S. Army's joint platform allocation tool (JPAT) is an integer linear program that was developed by the Army's Training and Doctrine Command Analysis Center and the Naval Postgraduate School to help inform acquisition decisions involving aerial reconnaissance and surveillance (R&S) resources. JPAT evaluates inputs such as mission requirements, locations of available equipment, and budgetary constraints to determine an effective assignment of unmanned aerial R&S assets to missions. As of September 2013, JPAT is solved using a rolling horizon approach, which produces a sub-optimal solution, and requires substantial computational resources to solve a problem of realistic size. Because JPAT is an integer linear program, it is a suitable candidate for using decomposition techniques to improve its computational efficiency. This thesis conducts an analysis of multiple approaches for increasing JPAT's computational efficiency. First, we reformulate JPAT using Benders decomposition. Then, we solve both the original and decomposed formulations using the simplex and barrier algorithms with multiple size datasets. In addition, we experiment with an initial heuristic solution and other techniques in our attempts to improve JPAT's runtime. We find that while Benders decomposition does not result in significant improvements in computation time for the instances considered in this thesis...

‣ The Rise and Fall of Brazilian Inequality : 1981-2004

Ferreira, Francisco H.G.; Leite, Phillippe G.; Litchfield, Julie A.
Fonte: World Bank, Washington, DC Publicador: World Bank, Washington, DC
Tipo: Publications & Research :: Policy Research Working Paper; Publications & Research
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Measured by the Gini coefficient, income inequality in Brazil rose from 0.57 in 1981 to 0.63 in 1989, before falling back to 0.56 in 2004. This latest figure would lower Brazil's world inequality rank from 2nd (in 1989) to 10th (in 2004). Poverty incidence also followed an inverted U-curve over the past quarter century, rising from 0.30 in 1981 to 0.33 in 1993, before falling to 0.22 in 2004. Using standard decomposition techniques, this paper presents a preliminary investigation of the determinants of Brazil's distributional reversal over this period. The rise in inequality in the 1980s appears to have been driven by increases in the educational attainment of the population in a context of convex returns, and by high and accelerating inflation. While the secular decline in inequality, which began in 1993, is associated with declining inflation, it also appears to have been driven by four structural and policy changes which have so far not attracted sufficient attention in the literature, namely sharp declines in the returns to education; pronounced rural-urban convergence; increases in social assistance transfers targeted to the poor; and a possible decline in racial inequality. Although poverty dynamics since the Real Plan of 1994 have been driven primarily by economic growth...

‣ Decomposition approach for generation and transmission expansion planning with implicit multipliers evaluation

Thomé,Fernanda S.; Binato,Silvio; Pereira,Mario V.F.; Campodónico,Nora; Fampa,Marcia H.C.; Costa Jr,Luiz Carlos da
Fonte: Sociedade Brasileira de Pesquisa Operacional Publicador: Sociedade Brasileira de Pesquisa Operacional
Tipo: Artigo de Revista Científica Formato: text/html
Publicado em 01/12/2013 Português
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In an electric power systems planning framework, decomposition techniques are usually applied to separate investment and operation subproblems to take benefits from the use of independent solution algorithms. Real power systems planning problems can be rather complex and their detailed representation often leads to greater effort to solve the operation subproblems. Traditionally, the algorithms used in the solution of transmission constrained operation problems take great computational advantage with compact representation of the model, which means the elimination of some variables and constraints that don't affect the problem's optimal solution. This work presents a new methodology for solving generation and transmission expansion planning problems based on Benders decomposition where the incorporation of the traditional operation models require an additional procedure for evaluating the Lagrange's multipliers associated to the constraints which are not explicitly represented yet are used in the construction of the Benders cuts during the iterative process. The objective of this work is to seek for efficiency and consistency in the solution of expansion planning problems by allowing specialized algorithms to be applied in the operation model. It is shown that this methodology is particularly interesting when applied to stochastic hydrothermal problems which usually require a large number of problems to be solved. The results of this methodology are illustrated by a Colombian system case study.

‣ Decomposition Techniques for Bilinear Saddle Point Problems and Variational Inequalities with Affine Monotone Operators on Domains Given by Linear Minimization Oracles

Cox, Bruce; Juditsky, Anatoli; Nemirovski, Arkadi
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Português
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The majority of First Order methods for large-scale convex-concave saddle point problems and variational inequalities with monotone operators are proximal algorithms which at every iteration need to minimize over problem's domain X the sum of a linear form and a strongly convex function. To make such an algorithm practical, X should be proximal-friendly -- admit a strongly convex function with easy to minimize linear perturbations. As a byproduct, X admits a computationally cheap Linear Minimization Oracle (LMO) capable to minimize over X linear forms. There are, however, important situations where a cheap LMO indeed is available, but X is not proximal-friendly, which motivates search for algorithms based solely on LMO's. For smooth convex minimization, there exists a classical LMO-based algorithm -- Conditional Gradient. In contrast, known to us LMO-based techniques for other problems with convex structure (nonsmooth convex minimization, convex-concave saddle point problems, even as simple as bilinear ones, and variational inequalities with monotone operators, even as simple as affine) are quite recent and utilize common approach based on Fenchel-type representations of the associated objectives/vector fields. The goal of this paper is to develop an alternative (and seemingly much simpler) LMO-based decomposition techniques for bilinear saddle point problems and for variational inequalities with affine monotone operators.

‣ Decomposition Techniques for Subgraph Matching

Zampelli, Stephane; Mann, Martin; Deville, Yves; Backofen, Rolf
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 07/05/2008 Português
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In the constraint programming framework, state-of-the-art static and dynamic decomposition techniques are hard to apply to problems with complete initial constraint graphs. For such problems, we propose a hybrid approach of these techniques in the presence of global constraints. In particular, we solve the subgraph isomorphism problem. Further we design specific heuristics for this hard problem, exploiting its special structure to achieve decomposition. The underlying idea is to precompute a static heuristic on a subset of its constraint network, to follow this static ordering until a first problem decomposition is available, and to switch afterwards to a fully propagated, dynamically decomposing search. Experimental results show that, for sparse graphs, our decomposition method solves more instances than dedicated, state-of-the-art matching algorithms or standard constraint programming approaches.; Comment: 15 pages

‣ Adaptive Robust Transmission Network Expansion Planning using Structural Reliability and Decomposition Techniques

Mínguez, Roberto; García-Bertrand, Raquel; Arroyo, José Manuel
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 26/01/2015 Português
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Structural reliability and decomposition techniques have recently proved to be appropriate tools for solving robust uncertain mixed-integer linear programs using ellipsoidal uncertainty sets. In fact, its computational performance makes this type of problem to be an alternative method in terms of tractability with respect to robust problems based on cardinality constrained uncertainty sets. This paper extends the use of these techniques for solving an adaptive robust optimization (ARO) problem, i.e. the adaptive robust solution of the transmission network expansion planning for energy systems. The formulation of this type of problem materializes on a three-level mixed-integer optimization formulation, which based on structural reliability methods, can be solved using an ad-hoc decomposition technique. The method allows the use of the correlation structure of the uncertain variables involved by means of their variance-covariance matrix, and besides, it provides a new interpretation of the robust problem based on quantile optimization. We also compare results with respect to robust optimization methods that consider cardinality constrained uncertainty sets. Numerical results on an illustrative example, the IEEE-24 and IEEE 118-bus test systems demonstrate that the algorithm is comparable in terms of computational performance with respect to existing robust methods with the additional advantage that the correlation structure of the uncertain variables involved can be incorporated straightforwardly.; Comment: 32 pages...

‣ On the use of advanced pattern recognition techniques for the analysis of MRS and MRSI data in neuro-oncology

Ortega-Martorell, Sandra; Borrell, Joan
Fonte: [Barcelona] : Universitat Autònoma de Barcelona, Publicador: [Barcelona] : Universitat Autònoma de Barcelona,
Tipo: Tesis i dissertacions electròniques; info:eu-repo/semantics/doctoralThesis; info:eu-repo/semantics/publishedVersion Formato: application/pdf
Publicado em //2014 Português
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El cáncer es una de las principales causas de muerte en el mundo. Los tumores cerebrales tienen una incidencia relativamente baja en comparación con otras patologías cancerígenas más generalizadas, pero la prognosis de algunos es muy pobre, contribuyendo significativamente a su morbilidad. La gestión clínica de una masa anormal en el cerebro es materia delicada y difícil, por lo que los expertos han de basarse en mediciones indirectas no invasivas de las características del tumor y de su crecimiento. En la práctica radiológica actual, estas mediciones se realizan a menudo mediante técnicas de resonancia magnética (MR), como la imagen (MRI) y la espectroscopia (MRS). La vasta información contenida en las señales de MR les hace ideales para la aplicación de técnicas de reconocimiento de patrones (PR). Durante las dos últimas décadas, estas técnicas se han aplicado con éxito al problema de la extracción de conocimiento a partir de datos de tumores cerebrales humanos, para su diagnóstico y pronóstico. No obstante, la discriminación de algunos tipos y subtipos de tumores, así como la delimitación precisa del área tumoral, continúan siendo un reto para los investigadores. En esta tesis, abordamos tales retos mediante la aplicación de un conjunto de técnicas avanzadas de PR. En primera instancia...

‣ Domain Decomposition Methods via Boundary Integral Equations

Hsiao, George C.; Steinbach, O.; Wendland, W.L.
Fonte: Department of Mathematical Sciences Publicador: Department of Mathematical Sciences
Tipo: Relatório Formato: 230007 bytes; application/pdf
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Domain decomposition methods are designed to deal with coupled or transmission problems for partial differential equations. Since the original boundary value problem is replaced by local problems in substructures, domain decomposition methods are well suited for both parallelization and coupling of different discretization schemes. In general, the coupled problem is reduced to the Schur complement equation on the skeleton of the domain decomposition. Boundary integral equations are used to describe the local Steklov-Poincare operators which are basic for the local Dirichlet-Neumann maps. Using different representations of the Steklov-Poincare operators we formulate and analyze various boundary element methods employed in local discretization schemes. We give sufficient conditions for the global stability and derive corresponding a priori error estimates. For the solution of the resulting linear systems we describe appropriate iterative solution strategies using both local and global preconditioning techniques.

‣ Short-term generation planning by primal and dual decomposition techniques

Marmolejo-Saucedo,José Antonio; Rodríguez-Aguilar,Román
Fonte: DYNA Publicador: DYNA
Tipo: Artigo de Revista Científica Formato: text/html
Publicado em 01/06/2015 Português
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This paper addresses the short-term generation planning (STGP) through thermoelectric units. The mathematical model is presented as a Mixed Integer Non Linear Problem (MINLP). Several works on the state of art of the problem have revealed that the computational effort of this problem grows exponentially with the number of time periods and number of thermoelectric units. Therefore, we present two alternatives to solve a STGP based on Benders' partitioning algorithm and Lagrangian relaxation in order to reduce the computational effort. The proposal is to apply primal and dual decomposition techniques, which exploit the structure of the problem to reduce solution time by decomposing the STGP into a master problem and a subproblem. For Benders' algorithm, the master problem is a Mixed Integer Problem (MIP) and for the subproblem, it is a Non Linear Problem (NLP). For Lagrangian relaxation, the master problem and the subproblem are MINLP. The computational experiments show the performance of both decomposition techniques applied to the STGP. These techniques allow us to save computation time when compared to some high performance commercial solvers.