Manuel Ordoñez - Academia.edu (original) (raw)
Papers by Manuel Ordoñez
OCEANS Conference, 2007
This paper presents the development of an advanced measurement system for real-time characterizat... more This paper presents the development of an advanced measurement system for real-time characterization of Vortex Induced Vibrations (VIV) in large-scale marine risers. Marine risers play a critical role in offshore oil and gas operations by transporting mud, debris, and hydrocarbons from the reservoir to the surface platform. The mechanical structure of the riser is constantly subject to the effect of vortex shedding produced by seawater flow, which may result in severe oscillations known as VIV. At present, the prediction of this potentially destructive phenomenon is a challenging area of research that has gained special attention. While there have been significant research contributions on vortex induced vibrations on small riser models (8-10 m in length), the number of experiments on large-scale risers is limited, mainly due to technical complexity, logistics, and cost involved in large scale testing. Furthermore, the experiments that have been carried out are often proprietary and their publication in scientific literature has been limited. High mode results have been a challenge since it is generally accepted that at least five accelerometers are required to accurately map a cycle, and most of the riser models have been instrumented with no more than ten or twenty accelerometers due to the associated technical challenges. The advanced system described herein is modular and has been tested with sixty-four accelerometers, theoretically capable of mapping 25 modes of vibration. This is, therefore, a significant development towards understanding the vortex shedding phenomenon at high modes. A complete description and design considerations for this advanced measurement system is presented in this paper. This includes aspects such as system architecture, hardware and software design, mounting procedure, and communication protocol for an actual application.
OCEANS Conference, 2007
The focus of this research is on the development and testing of a large-scale model riser (130 m ... more The focus of this research is on the development and testing of a large-scale model riser (130 m in length) undergoing high mode vortex induced vibrations (VIV) in the ocean environment. This large scale model will provide an intermediate step between the common riser models (8-10 m in length) that have mainly been used to research VIV to date and the actual 3,000+ m deepwater risers being used in industry today. During offshore drilling operations, marine risers carry mud and debris from below the sea floor, and during production operations they are responsible for transporting oil or gas from the hydrocarbon reservoir to the surface platform. The integrity of a marine riser is therefore critical to the success of offshore drilling and production. The flow of seawater around marine risers is subject to vortex shedding which excites oscillations known as Vortex Induced Vibrations (VIV). When the VIV frequency approaches one of the natural frequencies of the structure, resonance, or lock-in occurs. This results in enhancement of the vibration amplitude of the structure and may have potentially destructive consequences due to high bending stresses and fatigue damage of the riser. At present, the prediction of this phenomenon is one of the most challenging areas in the offshore industry. In experimental investigations of VIV, large aspect ratio risers, namely long cylinders with relatively small diameters, pose a modeling challenge. This paper focuses on the development of a large-scale model riser capable of transmitting data in real-time under realistic operating conditions.
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.
Discrete Applied Mathematics, 2010
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 a general model for cooperative games defined on lattice structures. In this paper, the restrictions to the cooperation are given by a combinatorial structure called augmenting system which generalizes antimatroid structure and the system of connected subgraphs of a graph. In this framework, the core and the Weber set of games on augmenting systems are introduced and it is proved that monotone convex games have a non-empty core. Moreover, we obtain a characterization of the convexity of these games in terms of the core of the game and the Weber set of the extended game.
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.
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.
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.
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
IEEE Transactions on Circuits and Systems I-regular Papers, 2008
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.
The appearance of orphan sources in steelmaking facilities has become a fact nowadays. Radiation ... more The appearance of orphan sources in steelmaking facilities has become a fact nowadays. Radiation sources, hidden within the scrap, may come into the scrapyard and become part of the melting. As a result, dispersion of the radioactive material that makes up the source takes place throughout the facility. The University of the Basque Country (UPV-EHU), in collaboration with the Empresa
MRS Proceedings, 2014
ABSTRACT Modern concrete has a record of good performance of around 120 years although there are ... more ABSTRACT Modern concrete has a record of good performance of around 120 years although there are structures in perfect conservation made with roman concrete (mixture of lime and natural pozzolans). El Cabril repository has a design life of 300-500 years and therefore, it should keep its integrity much longer than the back experience we have on reinforced concrete structures, which makes necessary a closer monitoring with time on the aging of concrete in real conditions. With this purpose, Enresa has designed in collaboration with IETcc and Geocisa the installation of permanent sensors in a pilot nuclear waste container in buried conditions. The sensors were installed in 1995 for monitoring corrosion parameters and have been working until present. The non-destructive tests (NDT) applied are based in electrochemical measurements (corrosion rate, corrosion potential, electrical resistivity, concrete strains, oxygen availability). Relations between the climatic influence, the buried depth and the corrosion parameters are also presented. The results indicate that temperature is a very relevant variable influencing the measurements. All the other parameters evolve according to seasonal changes. Values of activation energies of the resistivity changes are given although it seems more adequate to model the evolution with time by simply plotting the values registered at 20 ± 2 °C.
Environmental Science & Technology, 2004
Electric arc furnace dust (EAFD), generated by the steelmaking industry, is in itself an intrinsi... more Electric arc furnace dust (EAFD), generated by the steelmaking industry, is in itself an intrinsic hazardous waste; however, the case may also be that scrap used in the process is accidentally contaminated by radioactive elements such as cesium. In this case the resulting EAFD is to be handled as radioactive waste, being duly confined in lowand medium-activity repositories (LMAR). What this paper studies is the reliability of using this radioactive EAFD as an addition in the immobilization mortar of the containers of the LMAR, that is, from the point of view of the durability. Different mixes of mortar containing different percentages of EAFD have been subjected to flexural and compressive strength, initial and final setting time, XRD study, total porosity and pore size distribution, determination of the chloride diffusion coefficient, dimensional stability tests, hydration heat, workability of the fresh mix, and leaching behavior. What is deduced from the results is that for the conditions used in this research, (cement + sand) can be replaced by EAFD up to a ratio [EAFD/ (cement + EAFD)] of 46% in the immobilization mortar of LMAR, apparently without any loss in the long-term durability properties of the mortar.
Environmental Science & Technology, 2004
Electric arc furnace dust (EAFD), generated by the steelmaking industry, is in itself an intrinsi... more Electric arc furnace dust (EAFD), generated by the steelmaking industry, is in itself an intrinsic hazardous waste; however, the case may also be that scrap used in the process is accidentally contaminated by radioactive elements such as cesium. In this case the resulting EAFD is to be handled as radioactive waste, being duly confined in lowand medium-activity repositories (LMAR). What this paper studies is the reliability of using this radioactive EAFD as an addition in the immobilization mortar of the containers of the LMAR, that is, from the point of view of the durability. Different mixes of mortar containing different percentages of EAFD have been subjected to flexural and compressive strength, initial and final setting time, XRD study, total porosity and pore size distribution, determination of the chloride diffusion coefficient, dimensional stability tests, hydration heat, workability of the fresh mix, and leaching behavior. What is deduced from the results is that for the conditions used in this research, (cement + sand) can be replaced by EAFD up to a ratio [EAFD/ (cement + EAFD)] of 46% in the immobilization mortar of LMAR, apparently without any loss in the long-term durability properties of the mortar.
P Po o o r r r u u u n n n a a a V V V e e en n n e e ez z z u u u e e el l la a a M M Me e e j j... more P Po o o r r r u u u n n n a a a V V V e e en n n e e ez z z u u u e e el l la a a M M Me e e j j jo o o r r r
OCEANS Conference, 2007
This paper presents the development of an advanced measurement system for real-time characterizat... more This paper presents the development of an advanced measurement system for real-time characterization of Vortex Induced Vibrations (VIV) in large-scale marine risers. Marine risers play a critical role in offshore oil and gas operations by transporting mud, debris, and hydrocarbons from the reservoir to the surface platform. The mechanical structure of the riser is constantly subject to the effect of vortex shedding produced by seawater flow, which may result in severe oscillations known as VIV. At present, the prediction of this potentially destructive phenomenon is a challenging area of research that has gained special attention. While there have been significant research contributions on vortex induced vibrations on small riser models (8-10 m in length), the number of experiments on large-scale risers is limited, mainly due to technical complexity, logistics, and cost involved in large scale testing. Furthermore, the experiments that have been carried out are often proprietary and their publication in scientific literature has been limited. High mode results have been a challenge since it is generally accepted that at least five accelerometers are required to accurately map a cycle, and most of the riser models have been instrumented with no more than ten or twenty accelerometers due to the associated technical challenges. The advanced system described herein is modular and has been tested with sixty-four accelerometers, theoretically capable of mapping 25 modes of vibration. This is, therefore, a significant development towards understanding the vortex shedding phenomenon at high modes. A complete description and design considerations for this advanced measurement system is presented in this paper. This includes aspects such as system architecture, hardware and software design, mounting procedure, and communication protocol for an actual application.
OCEANS Conference, 2007
The focus of this research is on the development and testing of a large-scale model riser (130 m ... more The focus of this research is on the development and testing of a large-scale model riser (130 m in length) undergoing high mode vortex induced vibrations (VIV) in the ocean environment. This large scale model will provide an intermediate step between the common riser models (8-10 m in length) that have mainly been used to research VIV to date and the actual 3,000+ m deepwater risers being used in industry today. During offshore drilling operations, marine risers carry mud and debris from below the sea floor, and during production operations they are responsible for transporting oil or gas from the hydrocarbon reservoir to the surface platform. The integrity of a marine riser is therefore critical to the success of offshore drilling and production. The flow of seawater around marine risers is subject to vortex shedding which excites oscillations known as Vortex Induced Vibrations (VIV). When the VIV frequency approaches one of the natural frequencies of the structure, resonance, or lock-in occurs. This results in enhancement of the vibration amplitude of the structure and may have potentially destructive consequences due to high bending stresses and fatigue damage of the riser. At present, the prediction of this phenomenon is one of the most challenging areas in the offshore industry. In experimental investigations of VIV, large aspect ratio risers, namely long cylinders with relatively small diameters, pose a modeling challenge. This paper focuses on the development of a large-scale model riser capable of transmitting data in real-time under realistic operating conditions.
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.
Discrete Applied Mathematics, 2010
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 a general model for cooperative games defined on lattice structures. In this paper, the restrictions to the cooperation are given by a combinatorial structure called augmenting system which generalizes antimatroid structure and the system of connected subgraphs of a graph. In this framework, the core and the Weber set of games on augmenting systems are introduced and it is proved that monotone convex games have a non-empty core. Moreover, we obtain a characterization of the convexity of these games in terms of the core of the game and the Weber set of the extended game.
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.
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.
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.
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
IEEE Transactions on Circuits and Systems I-regular Papers, 2008
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.
The appearance of orphan sources in steelmaking facilities has become a fact nowadays. Radiation ... more The appearance of orphan sources in steelmaking facilities has become a fact nowadays. Radiation sources, hidden within the scrap, may come into the scrapyard and become part of the melting. As a result, dispersion of the radioactive material that makes up the source takes place throughout the facility. The University of the Basque Country (UPV-EHU), in collaboration with the Empresa
MRS Proceedings, 2014
ABSTRACT Modern concrete has a record of good performance of around 120 years although there are ... more ABSTRACT Modern concrete has a record of good performance of around 120 years although there are structures in perfect conservation made with roman concrete (mixture of lime and natural pozzolans). El Cabril repository has a design life of 300-500 years and therefore, it should keep its integrity much longer than the back experience we have on reinforced concrete structures, which makes necessary a closer monitoring with time on the aging of concrete in real conditions. With this purpose, Enresa has designed in collaboration with IETcc and Geocisa the installation of permanent sensors in a pilot nuclear waste container in buried conditions. The sensors were installed in 1995 for monitoring corrosion parameters and have been working until present. The non-destructive tests (NDT) applied are based in electrochemical measurements (corrosion rate, corrosion potential, electrical resistivity, concrete strains, oxygen availability). Relations between the climatic influence, the buried depth and the corrosion parameters are also presented. The results indicate that temperature is a very relevant variable influencing the measurements. All the other parameters evolve according to seasonal changes. Values of activation energies of the resistivity changes are given although it seems more adequate to model the evolution with time by simply plotting the values registered at 20 ± 2 °C.
Environmental Science & Technology, 2004
Electric arc furnace dust (EAFD), generated by the steelmaking industry, is in itself an intrinsi... more Electric arc furnace dust (EAFD), generated by the steelmaking industry, is in itself an intrinsic hazardous waste; however, the case may also be that scrap used in the process is accidentally contaminated by radioactive elements such as cesium. In this case the resulting EAFD is to be handled as radioactive waste, being duly confined in lowand medium-activity repositories (LMAR). What this paper studies is the reliability of using this radioactive EAFD as an addition in the immobilization mortar of the containers of the LMAR, that is, from the point of view of the durability. Different mixes of mortar containing different percentages of EAFD have been subjected to flexural and compressive strength, initial and final setting time, XRD study, total porosity and pore size distribution, determination of the chloride diffusion coefficient, dimensional stability tests, hydration heat, workability of the fresh mix, and leaching behavior. What is deduced from the results is that for the conditions used in this research, (cement + sand) can be replaced by EAFD up to a ratio [EAFD/ (cement + EAFD)] of 46% in the immobilization mortar of LMAR, apparently without any loss in the long-term durability properties of the mortar.
Environmental Science & Technology, 2004
Electric arc furnace dust (EAFD), generated by the steelmaking industry, is in itself an intrinsi... more Electric arc furnace dust (EAFD), generated by the steelmaking industry, is in itself an intrinsic hazardous waste; however, the case may also be that scrap used in the process is accidentally contaminated by radioactive elements such as cesium. In this case the resulting EAFD is to be handled as radioactive waste, being duly confined in lowand medium-activity repositories (LMAR). What this paper studies is the reliability of using this radioactive EAFD as an addition in the immobilization mortar of the containers of the LMAR, that is, from the point of view of the durability. Different mixes of mortar containing different percentages of EAFD have been subjected to flexural and compressive strength, initial and final setting time, XRD study, total porosity and pore size distribution, determination of the chloride diffusion coefficient, dimensional stability tests, hydration heat, workability of the fresh mix, and leaching behavior. What is deduced from the results is that for the conditions used in this research, (cement + sand) can be replaced by EAFD up to a ratio [EAFD/ (cement + EAFD)] of 46% in the immobilization mortar of LMAR, apparently without any loss in the long-term durability properties of the mortar.
P Po o o r r r u u u n n n a a a V V V e e en n n e e ez z z u u u e e el l la a a M M Me e e j j... more P Po o o r r r u u u n n n a a a V V V e e en n n e e ez z z u u u e e el l la a a M M Me e e j j jo o o r r r