Manuel Ordóñez | Universidad de Sevilla (original) (raw)

Papers by Manuel Ordóñez

Analele Universității București: Istorie. Universitatea din București

Revista Internacional de Métodos Numéricos para Cálculo y Diseño en Ingeniería

Revista Internacional de Métodos Numéricos para Cálculo y Diseño en Ingeniería, 2014

ABSTRACT The objective of this paper is exploring implementation of a realistic images reconstruc... more ABSTRACT The objective of this paper is exploring implementation of a realistic images reconstruction 3D using geometric algebra (GA). We illustrate the suitability of GA for representing structures and developing algorithms in computer graphics, especially for engineering applications as 3D images modeling. A first consequence is to propose an efficient framework model to be implemented in hardware programmable. The obtained results showed that using GA, the computations are less complex and shows as simple computations geometrical operations. The obtained model to hardware can be implemented as a next step in 3D image reconstruction. We also include the potential of GA for optimizations and highly efficient implementations.

IET Circuits, Devices & Systems, 2008

A generalised and multivectorial proof of Tellegen's theorem in multiterminal systems is presente... more A generalised and multivectorial proof of Tellegen's theorem in multiterminal systems is presented using a new power multivector concept defined in the frequency domain. This approach permits in nonsinusoidal/linear and nonlinear situations formulating Tellegen's theorem in a novel complex-multivector representation, similar to Steinmetz's phasor model, based on complex numbers and limited to the purely sinusoidal case. In this sense, a suitable notation of voltage and current complex-vectors, associated to the elements and nodes of the network, is defined for easy development to Kirchhoff's laws in this environment. A numerical example illustrates the clear advantages of the suggested proof. Ã conjugated operation

Geometric Algebra (GA) is a suitable framework to understand the power flow in multi-sinusoidal s... more Geometric Algebra (GA) is a suitable framework to understand the power flow in multi-sinusoidal systems linear/non-linear operation. GA it is based on the concepts of geometrical objects with different dimension: vector, bivector, trivector… Some of these entities can be used to represent any electromagnetic quantity as an " electromagnetic geometrical object " . In this paper, these objects are correlated with the energy flow components of an arbitrary " electrical object " in order to explain the role of Poynting Multivector. Moreover, our work deals with a innovative theory that applying the Poynting Vector philosophy provides a physical foundation to the power theory.

Applied Mathematics

The intention of this article is to introduce a new structure, that we will call de-creasing syst... more The intention of this article is to introduce a new structure, that we will call de-creasing system , which generalize the well-known convex geometries introduced by (PH Edelman, RE Jamison (1985)). We will introduce these structures through the dualization another known structure, augmenting system (Bilbao, 2003). In this article we axiomatize the Shapley and Banzhaf values on this new structure.

Discrete Applied Mathematics, 2015

... presented. It is based on a frequency-domain Clifford vector space approach. ... 978-1-4244-2... more ... presented. It is based on a frequency-domain Clifford vector space approach. ... 978-1-4244-2130-5/08/$25.00 ©2008 IEEE II. CLIFFORD SPACE-VECTOR THEORY: GENERALIZED COMPLEX GEOMETRIC ALGEBRA ( CCI" ) B ...

ABSTRACT Several approaches have been developed to define the non-active power concept under nons... more ABSTRACT Several approaches have been developed to define the non-active power concept under nonsinusoidal situations in electrical systems. Nevertheless, these contributions do not provide a complete and satisfactory solution to the non-active power reversibility between frequency domain and time domain. This paper presents a non-active power multivector concept, based on an original vector space frequency-domain approach that bridges the gap between both domains. The suggested correspondence can provide a convenient descriptive language to reconcile Fryze's instantaneous non-active power with Budeanu's deactive-power. To clarify this correspondence, a basis example is considered.

Melecon 2010 - 2010 15th IEEE Mediterranean Electrotechnical Conference, 2010

This paper is a new contribution to the clarification of the non-active power concept. It is base... more This paper is a new contribution to the clarification of the non-active power concept. It is based on a Generalized Complex Geometric Algebra (CGn) spanned by a frequency-domain vector space.The classic definition of this quantity is usually associated to the use of the scalar product of voltages and currents rms values. We show that the non-active power can be deduced

Progress In Electromagnetics Research B, 2009

The purpose of this paper is to explain an exact derivation of apparent power in n-sinusoidal ope... more The purpose of this paper is to explain an exact derivation of apparent power in n-sinusoidal operation founded on electromagnetic theory, until now unexplained by simple mathematical models. The aim is to explore a new tool for a rigorous mathematical and physical analysis of the power equation from the Poynting Vector (PV) concept. A powerful mathematical structure is necessary and Geometric Algebra offers such a characteristic. In this sense, PV has been reformulated from a new Multivectorial Euclidean Vector Space structure (CG n -R 3 ) to obtain a Generalized Poynting Multivector (S). Consequently, fromS, a suitable multivectorial form (P andD) of the Poynting Vector corresponds to each component of apparent power. In particular, this framework is essential for the clarification of the connection between a Complementary Poynting Multivector (D) and the power contribution due to cross-frequency products. A simple application example is presented as an illustration of the proposed power multivector analysis.

Fuzzy Sets and Systems, 2013

Cite this article as: A. Jiménez-Losada, J.R. Fernández and M. Ordóñez, Myerson values for games ... more Cite this article as: A. Jiménez-Losada, J.R. Fernández and M. Ordóñez, Myerson values for games with fuzzy communication structure, Fuzzy Sets and Systems, http://dx.

Fuzzy Sets and Systems, 2013

In 2012, Jiménez-Losada et al introduced several extensions of the Myerson value for games with f... more In 2012, Jiménez-Losada et al introduced several extensions of the Myerson value for games with fuzzy communication structure. In a fuzzy communication structure the membership of the players and the relations among them are leveled. Now we study a Banzhaf value for these situations. The Myerson model is followed to define the fuzzy graph Banzhaf value under the point of view Choquet by graphs. We propose an axiomatization for this value introducing leveled amalgam of players. An algorithm to calculate this value is provided and its complexity is studied. Finally we show an applied example computing by this fuzzy value the power of the groups in the European Parliament.

European Journal of Operational Research, 2009

This paper deals with cooperative games in which only certain coalitions are allowed to form. The... more This paper deals with cooperative games in which only certain coalitions are allowed to form. There have been previous models developed to confront the problem of unallowable coalitions. Games restricted by a communication graph were introduced by Myerson and Owen. In their model, the feasible coalitions are those that induce connected subgraphs. Another type of model is introduced in Gilles, Owen and van den Brink. In their model, the possibilities of coalition formation are determined by the positions of the players in a so-called permission structure. Faigle proposed another model for cooperative games defined on lattice structures. We introduce a combinatorial structure called augmenting system which is a generalization of the antimatroid structure and the system of connected subgraphs of a graph. In this framework, the Shapley value of games on augmenting systems is introduced and two axiomatizations of this value are showed. j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / e j o r dummy and efficiency axioms, and the hierarchical strength axiom instead the chain axiom.

European Journal of Operational Research, 2010

a b s t r a c t used graph-theoretic ideas to analyze cooperation structures in games. In his mod... more a b s t r a c t used graph-theoretic ideas to analyze cooperation structures in games. In his model, he considered the players in a cooperative game as vertices of a graph, which undirected edges defined their communication possibilities. He modified the initial games taking into account the graph and he established a fair allocation rule based on applying the Shapley value to the modified game. Now, we consider a fuzzy graph to introduce leveled communications. In this paper players play in a particular cooperative way: they are always interested first in the biggest feasible coalition and second in the greatest level (Choquet players). We propose a modified game for this situation and a rule of the Myerson kind.

In this paper, a generalization of the concept of electrical power for periodic current and volta... more In this paper, a generalization of the concept of electrical power for periodic current and voltage waveforms based on a new generalized complex geometric algebra (GCGA) is proposed. This powerful tool permits, in -sinusoidal/nonlinear situations, representing and calculating the voltage, current, and apparent power in a single-port electrical network in terms of multivectors. The new expressions result in a novel representation of the apparent power, similar to the Steinmetz's phasor model, based on complex numbers, but limited to the purely sinusoidal case. The multivectorial approach presented is based on the frequency-domain decomposition of the apparent power into three components: the real part and the imaginary part of the complex-scalar associated to active and reactive power respectively, and distortion power, associated to the complex-bivector. A geometrical interpretation of the multivectorial components of apparent power is discussed. Numerical examples illustrate the clear advantages of the suggested approach.

Nonlinear Analysis: Real World Applications, 2013

Some techniques to show the existence and uniqueness of limit cycles, typically stated for smooth... more Some techniques to show the existence and uniqueness of limit cycles, typically stated for smooth vector fields, are extended to continuous piecewiselinear differential systems.

Analele Universității București: Istorie. Universitatea din București

Revista Internacional de Métodos Numéricos para Cálculo y Diseño en Ingeniería

Revista Internacional de Métodos Numéricos para Cálculo y Diseño en Ingeniería, 2014

ABSTRACT The objective of this paper is exploring implementation of a realistic images reconstruc... more ABSTRACT The objective of this paper is exploring implementation of a realistic images reconstruction 3D using geometric algebra (GA). We illustrate the suitability of GA for representing structures and developing algorithms in computer graphics, especially for engineering applications as 3D images modeling. A first consequence is to propose an efficient framework model to be implemented in hardware programmable. The obtained results showed that using GA, the computations are less complex and shows as simple computations geometrical operations. The obtained model to hardware can be implemented as a next step in 3D image reconstruction. We also include the potential of GA for optimizations and highly efficient implementations.

IET Circuits, Devices & Systems, 2008

A generalised and multivectorial proof of Tellegen's theorem in multiterminal systems is presente... more A generalised and multivectorial proof of Tellegen's theorem in multiterminal systems is presented using a new power multivector concept defined in the frequency domain. This approach permits in nonsinusoidal/linear and nonlinear situations formulating Tellegen's theorem in a novel complex-multivector representation, similar to Steinmetz's phasor model, based on complex numbers and limited to the purely sinusoidal case. In this sense, a suitable notation of voltage and current complex-vectors, associated to the elements and nodes of the network, is defined for easy development to Kirchhoff's laws in this environment. A numerical example illustrates the clear advantages of the suggested proof. Ã conjugated operation

Geometric Algebra (GA) is a suitable framework to understand the power flow in multi-sinusoidal s... more Geometric Algebra (GA) is a suitable framework to understand the power flow in multi-sinusoidal systems linear/non-linear operation. GA it is based on the concepts of geometrical objects with different dimension: vector, bivector, trivector… Some of these entities can be used to represent any electromagnetic quantity as an " electromagnetic geometrical object " . In this paper, these objects are correlated with the energy flow components of an arbitrary " electrical object " in order to explain the role of Poynting Multivector. Moreover, our work deals with a innovative theory that applying the Poynting Vector philosophy provides a physical foundation to the power theory.

Applied Mathematics

The intention of this article is to introduce a new structure, that we will call de-creasing syst... more The intention of this article is to introduce a new structure, that we will call de-creasing system , which generalize the well-known convex geometries introduced by (PH Edelman, RE Jamison (1985)). We will introduce these structures through the dualization another known structure, augmenting system (Bilbao, 2003). In this article we axiomatize the Shapley and Banzhaf values on this new structure.

Discrete Applied Mathematics, 2015

... presented. It is based on a frequency-domain Clifford vector space approach. ... 978-1-4244-2... more ... presented. It is based on a frequency-domain Clifford vector space approach. ... 978-1-4244-2130-5/08/$25.00 ©2008 IEEE II. CLIFFORD SPACE-VECTOR THEORY: GENERALIZED COMPLEX GEOMETRIC ALGEBRA ( CCI" ) B ...

ABSTRACT Several approaches have been developed to define the non-active power concept under nons... more ABSTRACT Several approaches have been developed to define the non-active power concept under nonsinusoidal situations in electrical systems. Nevertheless, these contributions do not provide a complete and satisfactory solution to the non-active power reversibility between frequency domain and time domain. This paper presents a non-active power multivector concept, based on an original vector space frequency-domain approach that bridges the gap between both domains. The suggested correspondence can provide a convenient descriptive language to reconcile Fryze's instantaneous non-active power with Budeanu's deactive-power. To clarify this correspondence, a basis example is considered.

Melecon 2010 - 2010 15th IEEE Mediterranean Electrotechnical Conference, 2010

This paper is a new contribution to the clarification of the non-active power concept. It is base... more This paper is a new contribution to the clarification of the non-active power concept. It is based on a Generalized Complex Geometric Algebra (CGn) spanned by a frequency-domain vector space.The classic definition of this quantity is usually associated to the use of the scalar product of voltages and currents rms values. We show that the non-active power can be deduced

Progress In Electromagnetics Research B, 2009

The purpose of this paper is to explain an exact derivation of apparent power in n-sinusoidal ope... more The purpose of this paper is to explain an exact derivation of apparent power in n-sinusoidal operation founded on electromagnetic theory, until now unexplained by simple mathematical models. The aim is to explore a new tool for a rigorous mathematical and physical analysis of the power equation from the Poynting Vector (PV) concept. A powerful mathematical structure is necessary and Geometric Algebra offers such a characteristic. In this sense, PV has been reformulated from a new Multivectorial Euclidean Vector Space structure (CG n -R 3 ) to obtain a Generalized Poynting Multivector (S). Consequently, fromS, a suitable multivectorial form (P andD) of the Poynting Vector corresponds to each component of apparent power. In particular, this framework is essential for the clarification of the connection between a Complementary Poynting Multivector (D) and the power contribution due to cross-frequency products. A simple application example is presented as an illustration of the proposed power multivector analysis.

Fuzzy Sets and Systems, 2013

Cite this article as: A. Jiménez-Losada, J.R. Fernández and M. Ordóñez, Myerson values for games ... more Cite this article as: A. Jiménez-Losada, J.R. Fernández and M. Ordóñez, Myerson values for games with fuzzy communication structure, Fuzzy Sets and Systems, http://dx.

Fuzzy Sets and Systems, 2013

In 2012, Jiménez-Losada et al introduced several extensions of the Myerson value for games with f... more In 2012, Jiménez-Losada et al introduced several extensions of the Myerson value for games with fuzzy communication structure. In a fuzzy communication structure the membership of the players and the relations among them are leveled. Now we study a Banzhaf value for these situations. The Myerson model is followed to define the fuzzy graph Banzhaf value under the point of view Choquet by graphs. We propose an axiomatization for this value introducing leveled amalgam of players. An algorithm to calculate this value is provided and its complexity is studied. Finally we show an applied example computing by this fuzzy value the power of the groups in the European Parliament.

European Journal of Operational Research, 2009

This paper deals with cooperative games in which only certain coalitions are allowed to form. The... more This paper deals with cooperative games in which only certain coalitions are allowed to form. There have been previous models developed to confront the problem of unallowable coalitions. Games restricted by a communication graph were introduced by Myerson and Owen. In their model, the feasible coalitions are those that induce connected subgraphs. Another type of model is introduced in Gilles, Owen and van den Brink. In their model, the possibilities of coalition formation are determined by the positions of the players in a so-called permission structure. Faigle proposed another model for cooperative games defined on lattice structures. We introduce a combinatorial structure called augmenting system which is a generalization of the antimatroid structure and the system of connected subgraphs of a graph. In this framework, the Shapley value of games on augmenting systems is introduced and two axiomatizations of this value are showed. j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / e j o r dummy and efficiency axioms, and the hierarchical strength axiom instead the chain axiom.

European Journal of Operational Research, 2010

a b s t r a c t used graph-theoretic ideas to analyze cooperation structures in games. In his mod... more a b s t r a c t used graph-theoretic ideas to analyze cooperation structures in games. In his model, he considered the players in a cooperative game as vertices of a graph, which undirected edges defined their communication possibilities. He modified the initial games taking into account the graph and he established a fair allocation rule based on applying the Shapley value to the modified game. Now, we consider a fuzzy graph to introduce leveled communications. In this paper players play in a particular cooperative way: they are always interested first in the biggest feasible coalition and second in the greatest level (Choquet players). We propose a modified game for this situation and a rule of the Myerson kind.

In this paper, a generalization of the concept of electrical power for periodic current and volta... more In this paper, a generalization of the concept of electrical power for periodic current and voltage waveforms based on a new generalized complex geometric algebra (GCGA) is proposed. This powerful tool permits, in -sinusoidal/nonlinear situations, representing and calculating the voltage, current, and apparent power in a single-port electrical network in terms of multivectors. The new expressions result in a novel representation of the apparent power, similar to the Steinmetz's phasor model, based on complex numbers, but limited to the purely sinusoidal case. The multivectorial approach presented is based on the frequency-domain decomposition of the apparent power into three components: the real part and the imaginary part of the complex-scalar associated to active and reactive power respectively, and distortion power, associated to the complex-bivector. A geometrical interpretation of the multivectorial components of apparent power is discussed. Numerical examples illustrate the clear advantages of the suggested approach.

Nonlinear Analysis: Real World Applications, 2013

Some techniques to show the existence and uniqueness of limit cycles, typically stated for smooth... more Some techniques to show the existence and uniqueness of limit cycles, typically stated for smooth vector fields, are extended to continuous piecewiselinear differential systems.