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- WILEY-BLACKWELL
- Biblioteca Digitais de Teses e Dissertações da USP
- Universidade Federal do Rio Grande do Sul
- Biblioteca Digital da Unicamp
- Massachusetts Institute of Technology, Operations Research Center
- World Bank, Washington, DC
- Universidade de Adelaide
- Universidade Carlos III de Madrid
- Elsevier
- Springer
- Monterey, California: Naval Postgraduate School
- Sociedade Brasileira de Pesquisa Operacional
- Universidade Cornell
- [Barcelona] : Universitat Autònoma de Barcelona,
- Department of Mathematical Sciences
- Mais Publicadores...

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

Fonte: WILEY-BLACKWELL
Publicador: WILEY-BLACKWELL

Tipo: Artigo de Revista Científica

Português

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#rare earth elements#microwave oven acid attack#Parr bombs#ICP-MS#decomposition techniques#PLASMA-MASS SPECTROMETRY#GEOLOGICAL SAMPLES#TRACE-ELEMENTS#PRECISE DETERMINATION#ID-TIMS#SUPPRESSION

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.

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## ‣ 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.

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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#Beowulf cluster#Campo eletromagnético (simulação)#Domain decomposition#Finite elements method#Linear systems#Método dos elementos finitos (aplicações)#Parallel computation#Schur complement#Schwarz additive#Sistemas lineares

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...

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## ‣ 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

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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#Tintas#Paints#Elementos-traço : Determinação#Elements determination#Espectrometria de massa com fonte de plasma indutivamente acoplado#Plasma techniques

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.

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## ‣ 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

Fonte: Biblioteca Digital da Unicamp
Publicador: Biblioteca Digital da Unicamp

Tipo: Dissertação de Mestrado
Formato: application/pdf

Publicado em 09/01/2015
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#Otimização matemática#Manejo florestal - Modelos matemáticos#Método de decomposição#Programação linear#Mathematical optimization#Forest management#Decomposition method#Linear programming

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...

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## ‣ An overview of statistical decomposition techniques applied to complex systems

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.

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

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

Português

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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.

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## ‣ Accounting for Mexican Income Inequality during the 1990s

Fonte: World Bank, Washington, DC
Publicador: World Bank, Washington, DC

Português

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#ADVERSE EFFECT#AGRICULTURAL INCOMES#AVERAGE ANNUAL#AVERAGE INCOME#COUNTERFACTUAL#DEBT#DECOMPOSITION ANALYSIS#DECOMPOSITION RESULTS#DECOMPOSITION TECHNIQUES#DEPENDENT VARIABLE#DESCRIPTIVE STATISTICS

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...

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

Fonte: Universidade de Adelaide
Publicador: Universidade de Adelaide

Tipo: Tese de Doutorado

Publicado em //2013
Português

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#hybrid approaches#graph theory decomposition#evolutionary algorithms#deterministic optimisation techniques#water distribution system design

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...

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

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.

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## ‣ Solving dynamic stochastic economic models by mathematical programming decomposition methods

Fonte: Elsevier
Publicador: Elsevier

Tipo: Artigo de Revista Científica
Formato: text/plain; application/pdf

Publicado em /01/2008
Português

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#Dynamic stochastic economic model#Computation of equilibrium#Mathematical programming#Decomposition techniques#Empresa

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

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

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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#Electric energy systems#Multi-area optimal power fiow#Nonlinear prograrnming#Decomposition methods#Decentralized coordination#Estadística

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

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

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...

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

Fonte: World Bank, Washington, DC
Publicador: World Bank, Washington, DC

Tipo: Publications & Research :: Policy Research Working Paper; Publications & Research

Português

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#ALLOCATION EFFECT#BETWEEN-GROUP COMPONENTS#CALORIC REQUIREMENTS#CASH TRANSFERS#CHANGES IN POVERTY#COLLEGE EDUCATION#CONSUMER PRICE INDEX#CONSUMPTION EXPENDITURES#COST OF FOOD#DATA SET#DATA SETS

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...

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

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
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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.

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

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.

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## ‣ Decomposition Techniques for Subgraph Matching

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

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

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 26/01/2015
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#Computer Science - Computational Engineering, Finance, and Science#Mathematics - Optimization and Control

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...

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

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...

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## ‣ Domain Decomposition Methods via Boundary Integral Equations

Fonte: Department of Mathematical Sciences
Publicador: Department of Mathematical Sciences

Tipo: Relatório
Formato: 230007 bytes; application/pdf

Português

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#domain decomposition#boundary integral equations#boundary element methods#preconditioning techniques

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.

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

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.

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