Costas Drossos | University of Patras (original) (raw)
Papers by Costas Drossos
De Gruyter eBooks, Dec 31, 2000
In this paper the minimurn. distance esti m~ tor is proved that it possesses both invariant and e... more In this paper the minimurn. distance esti m~ tor is proved that it possesses both invariant and equi-varL1nt· ·proper\: ies • . l:l. plausibility confidence interval based on n inimum distance estimator is introduced using relational orde r systems. Th e properties which are used to characterize distances in metric spaces are main ly dictated from convergence purposes. For example, uniqueness 6f limits are very important in analy-sis .IIm· mver r in Statistics and in the case v;here no asym.rtot:!-c meth~ds are used and thus no limits are involved, the tern udis-tance" is used in a broader sense. What is essential is the non-negativerwss of the distance function and its being zero v:hen and only when the arguments are indentical. It is known, also , (see p.32 in (14)) that in passing frorn metric spaces to gene-ral topoloqical spaces · we lose ·the syrmnetry property of ou1:· no-tion of closeness in addition to other properties. If y is close to x in a ~etric space, then x is c...
Soft Computing - A Fusion of Foundations, Methodologies and Applications, 1998
Working in the framework of the infinite-valued propositional calculus of |ukasiewicz we develop ... more Working in the framework of the infinite-valued propositional calculus of |ukasiewicz we develop a generalization of the notion of boolean partition. Applications are given to handle the dependent and the independent variable in approximate definitions by cases-as softly, tractably and robustly as possible.
This is an introduction to Random Vectors: A Coordinate Free Approach
This a talk (In Greek) given in the General Seminar of Mathematics, Department of Math, Univ. of ... more This a talk (In Greek) given in the General Seminar of Mathematics, Department of Math, Univ. of Patras. The main objective is to review the connections of probability and mathematics. In particular deals with probabilistic Metric Spaces.
In this talk we intent to discuss the following topics: (i) The relevance of the basic concepts o... more In this talk we intent to discuss the following topics: (i) The relevance of the basic concepts of Husserl's Phenomenology to the Intentional Nonstandard Analysis (NSA). The main aspect here is the dialectics of the following du-ality: (1) The penetration of the "observer" by the facts and phenomena of the exten-sively objective real world, which on the basis of the "eidetic reduction", are reduced to essences, like the ones in ZFC. (2) The intentional character of the mentality involves on the part of the "ob-server", some perceptional limitations, which are expressed by the introduction of a local horizon with vague boundaries, and shows an attitude directed towards something, which is not necessarily real. Vague or external predicates and quantifiers, are referring to this horizon. (ii) The non-Cantorian interpretation (vague predicates, horizon of observation, con-tinuous prolongation, e.t.c.) of Internal Set Theory. This interpretation may supp...
There were three important decisions: .The presentation of NFU set theory, which is consistent. .... more There were three important decisions: .The presentation of NFU set theory, which is consistent. .The transitive class as a model of set theory. .The relativisation of second incompleteness Godel theorem, which has impplication in this type of proofs. The consistency of set theory means the consistency of mathematics, as set theory is a foundation for mathematics.
In this talk, it is exposed the view that mathematics can be considered as a kind of "scienc... more In this talk, it is exposed the view that mathematics can be considered as a kind of "science" and exprerianve can change the nature of mathematics and the logic and rules with which we are referring to mathematical objects.
First a survey of some basic ingredients, like cognition and intelligence and split brain researc... more First a survey of some basic ingredients, like cognition and intelligence and split brain research is presented. Then, some proposals on which this paper is based are exposed. We proceed with an exposition of the main points in the development of the concepts of 'structure' and 'points', while efforts shall be made to delineate the concept of 'structure' and the Protean nature and the dialectics of the concept of 'point' in various characteristic cases. On the basis of the above the concept of 'level of reality' is examined in connection with the concept of 'completeness' and its importance in mathematics in general. Finally some conclusions for mathematics are drawn and a survey of the present state of the philosophy of mathematics is presented, pointing out also some omissions, that we usually find in the current literature. G. Sica (ed.
De Gruyter eBooks, Dec 31, 2000
In this paper the minimurn. distance esti m~ tor is proved that it possesses both invariant and e... more In this paper the minimurn. distance esti m~ tor is proved that it possesses both invariant and equi-varL1nt· ·proper\: ies • . l:l. plausibility confidence interval based on n inimum distance estimator is introduced using relational orde r systems. Th e properties which are used to characterize distances in metric spaces are main ly dictated from convergence purposes. For example, uniqueness 6f limits are very important in analy-sis .IIm· mver r in Statistics and in the case v;here no asym.rtot:!-c meth~ds are used and thus no limits are involved, the tern udis-tance" is used in a broader sense. What is essential is the non-negativerwss of the distance function and its being zero v:hen and only when the arguments are indentical. It is known, also , (see p.32 in (14)) that in passing frorn metric spaces to gene-ral topoloqical spaces · we lose ·the syrmnetry property of ou1:· no-tion of closeness in addition to other properties. If y is close to x in a ~etric space, then x is c...
Soft Computing - A Fusion of Foundations, Methodologies and Applications, 1998
Working in the framework of the infinite-valued propositional calculus of |ukasiewicz we develop ... more Working in the framework of the infinite-valued propositional calculus of |ukasiewicz we develop a generalization of the notion of boolean partition. Applications are given to handle the dependent and the independent variable in approximate definitions by cases-as softly, tractably and robustly as possible.
This is an introduction to Random Vectors: A Coordinate Free Approach
This a talk (In Greek) given in the General Seminar of Mathematics, Department of Math, Univ. of ... more This a talk (In Greek) given in the General Seminar of Mathematics, Department of Math, Univ. of Patras. The main objective is to review the connections of probability and mathematics. In particular deals with probabilistic Metric Spaces.
In this talk we intent to discuss the following topics: (i) The relevance of the basic concepts o... more In this talk we intent to discuss the following topics: (i) The relevance of the basic concepts of Husserl's Phenomenology to the Intentional Nonstandard Analysis (NSA). The main aspect here is the dialectics of the following du-ality: (1) The penetration of the "observer" by the facts and phenomena of the exten-sively objective real world, which on the basis of the "eidetic reduction", are reduced to essences, like the ones in ZFC. (2) The intentional character of the mentality involves on the part of the "ob-server", some perceptional limitations, which are expressed by the introduction of a local horizon with vague boundaries, and shows an attitude directed towards something, which is not necessarily real. Vague or external predicates and quantifiers, are referring to this horizon. (ii) The non-Cantorian interpretation (vague predicates, horizon of observation, con-tinuous prolongation, e.t.c.) of Internal Set Theory. This interpretation may supp...
There were three important decisions: .The presentation of NFU set theory, which is consistent. .... more There were three important decisions: .The presentation of NFU set theory, which is consistent. .The transitive class as a model of set theory. .The relativisation of second incompleteness Godel theorem, which has impplication in this type of proofs. The consistency of set theory means the consistency of mathematics, as set theory is a foundation for mathematics.
In this talk, it is exposed the view that mathematics can be considered as a kind of "scienc... more In this talk, it is exposed the view that mathematics can be considered as a kind of "science" and exprerianve can change the nature of mathematics and the logic and rules with which we are referring to mathematical objects.
First a survey of some basic ingredients, like cognition and intelligence and split brain researc... more First a survey of some basic ingredients, like cognition and intelligence and split brain research is presented. Then, some proposals on which this paper is based are exposed. We proceed with an exposition of the main points in the development of the concepts of 'structure' and 'points', while efforts shall be made to delineate the concept of 'structure' and the Protean nature and the dialectics of the concept of 'point' in various characteristic cases. On the basis of the above the concept of 'level of reality' is examined in connection with the concept of 'completeness' and its importance in mathematics in general. Finally some conclusions for mathematics are drawn and a survey of the present state of the philosophy of mathematics is presented, pointing out also some omissions, that we usually find in the current literature. G. Sica (ed.