Non-compact generalized variational inequalities for quasi-monotone and hemi-continuous operators with applications

Some results are obtained for non-compact cases in topological vector spaces for the existence problem of solutions for some set-valued variational inequalities with quasi-monotone and lower hemi-continuous operators, and with quasi-semi-monotone and upper hemi-continuous operators. Some applications are given in non-reflexive Banach spaces for these existence problems of solutions and for perturbation problems for these set-valued variational inequalities with quasi-monotone and quasi-semi-monotone operators.

Eigenvalue computations in the context of data-sparse approximations of integral operators

In this work, we consider the numerical solution of a large eigenvalue problem resulting from a finite rank discretization of an integral operator. We are interested in computing a few eigenpairs, with an iterative method, so a matrix representation that allows for fast matrix-vector products is required. Hierarchical matrices are appropriate for this setting, and also provide cheap LU decompositions required in the spectral transformation technique. We illustrate the use of freely available software tools to address the problem, in particular SLEPc for the eigensolvers and HLib for the construction of H-matrices. The numerical tests are performed using an astrophysics application. Results show the benefits of the data-sparse representation compared to standard storage schemes, in terms of computational cost as well as memory requirements.

Local fractional variational iteration and decomposition methods for wave equation on cantor sets within local fractional operators

We perform a comparison between the fractional iteration and decomposition methods applied to the wave equation on Cantor set. The operators are taken in the local sense. The results illustrate the significant features of the two methods which are both very effective and straightforward for solving the differential equations with local fractional derivative.

Semigroup operators and applications

Dissertação de mestrado em Matemática

On spectral approximation, Folner sequences and crossed products

In this article we review first some of the possibilities in which the notions of Fo lner sequences and quasidiagonality have been applied to spectral approximation problems. We construct then a canonical Fo lner sequence for the crossed product of a concrete C* -algebra and a discrete amenable group. We apply our results to the rotation algebra (which contains interesting operators like almost Mathieu operators or periodic magnetic Schrödinger operators on graphs) and the C* -algebra generated by bounded Jacobi operators.

Induced aggregation operators in decision making with the Dempster-Shafer belief structure

We study the induced aggregation operators. The analysis begins with a revision of some basic concepts such as the induced ordered weighted averaging (IOWA) operator and the induced ordered weighted geometric (IOWG) operator. We then analyze the problem of decision making with Dempster-Shafer theory of evidence. We suggest the use of induced aggregation operators in decision making with Dempster-Shafer theory. We focus on the aggregation step and examine some of its main properties, including the distinction between descending and ascending orders and different families of induced operators. Finally, we present an illustrative example in which the results obtained using different types of aggregation operators can be seen.

Induced aggregation operators in decision making with the Dempster-Shafer belief structure

We study the induced aggregation operators. The analysis begins with a revision of some basic concepts such as the induced ordered weighted averaging (IOWA) operator and the induced ordered weighted geometric (IOWG) operator. We then analyze the problem of decision making with Dempster-Shafer theory of evidence. We suggest the use of induced aggregation operators in decision making with Dempster-Shafer theory. We focus on the aggregation step and examine some of its main properties, including the distinction between descending and ascending orders and different families of induced operators. Finally, we present an illustrative example in which the results obtained using different types of aggregation operators can be seen.

Renormalization of gauge-invariant operators and the axial anomaly

The renormalization properties of gauge-invariant composite operators that vanish when the classical equations of motion are used (class II^a operators) and which lead to diagrams where the Adler-Bell-Jackiw anomaly occurs are discussed. It is shown that gauge-invariant operators of this kind do need, in general, nonvanishing gauge-invariant (class I) counterterms.

Some spectral properties of the canonical solution operator to $\bar\partial$ on weighted Fock spaces

We characterize the Schatten class membership of the canonical solution operator to $\overline{\partial}$ acting on $L^2(e^{-2\phi})$, where $\phi$ is a subharmonic function with $\Delta\phi$ a doubling measure. The obtained characterization is in terms of $\Delta\phi$. As part of our approach, we study Hankel operators with anti-analytic symbols acting on the corresponding Fock space of entire functions in $L^2(e^{-2\phi})$

Lagrangian-Hamiltonian unified formalism for field theory

The RuskSkinner formalism was developed in order to give a geometrical unified formalism for describing mechanical systems. It incorporates all the characteristics of Lagrangian and Hamiltonian descriptions of these systems (including dynamical equations and solutions, constraints, Legendre map, evolution operators, equivalence, etc.). In this work we extend this unified framework to first-order classical field theories, and show how this description comprises the main features of the Lagrangian and Hamiltonian formalisms, both for the regular and singular cases. This formulation is a first step toward further applications in optimal control theory for partial differential equations. 2004 American Institute of Physics.

Decision-making with distance measures and inducedaggregation operators

[spa] Se presenta un nuevo modelo para la toma de decisiones basado en el uso de medidas de distancia y de operadores de agregación inducidos. Se introduce la distancia media ponderada ordenada inducida (IOWAD). Es un nuevo operador de agregación que extiende el operador OWA a través del uso de distancias y un proceso de reordenación de los argumentos basado en variables de ordenación inducidas. La principal ventaja el operador IOWAD es la posibilidad de utilizar una familia parametrizada de operadores de agregación entre la distancia individual máxima y la mínima. Se estudian algunas de sus principales propiedades y algunos casos particulares. Se desarrolla un ejemplo numérico en un problema de toma de decisiones sobre selección de inversiones. Se observa que la principal ventaja de este modelo en la toma de decisiones es la posibilidad de mostrar una visión más completa del proceso, de forma que el decisor está capacitado para seleccionar la alternativa que está más cerca de sus intereses.

Decision-making with distance measures and inducedaggregation operators

[spa] Se presenta un nuevo modelo para la toma de decisiones basado en el uso de medidas de distancia y de operadores de agregación inducidos. Se introduce la distancia media ponderada ordenada inducida (IOWAD). Es un nuevo operador de agregación que extiende el operador OWA a través del uso de distancias y un proceso de reordenación de los argumentos basado en variables de ordenación inducidas. La principal ventaja el operador IOWAD es la posibilidad de utilizar una familia parametrizada de operadores de agregación entre la distancia individual máxima y la mínima. Se estudian algunas de sus principales propiedades y algunos casos particulares. Se desarrolla un ejemplo numérico en un problema de toma de decisiones sobre selección de inversiones. Se observa que la principal ventaja de este modelo en la toma de decisiones es la posibilidad de mostrar una visión más completa del proceso, de forma que el decisor está capacitado para seleccionar la alternativa que está más cerca de sus intereses.

Decision making techniques with similarity measures and OWA operators

We analyse the use of the ordered weighted average (OWA) in decision-making giving special attention to business and economic decision-making problems. We present several aggregation techniques that are very useful for decision-making such as the Hamming distance, the adequacy coefficient and the index of maximum and minimum level. We suggest a new approach by using immediate weights, that is, by using the weighted average and the OWA operator in the same formulation. We further generalize them by using generalized and quasi-arithmetic means. We also analyse the applicability of the OWA operator in business and economics and we see that we can use it instead of the weighted average. We end the paper with an application in a business multi-person decision-making problem regarding production management

Decision making techniques with similarity measures and OWA operators

We analyse the use of the ordered weighted average (OWA) in decision-making giving special attention to business and economic decision-making problems. We present several aggregation techniques that are very useful for decision-making such as the Hamming distance, the adequacy coefficient and the index of maximum and minimum level. We suggest a new approach by using immediate weights, that is, by using the weighted average and the OWA operator in the same formulation. We further generalize them by using generalized and quasi-arithmetic means. We also analyse the applicability of the OWA operator in business and economics and we see that we can use it instead of the weighted average. We end the paper with an application in a business multi-person decision-making problem regarding production management