Petar Kenderov - Academia.edu (original) (raw)

Papers by Petar Kenderov

Research paper thumbnail of Achievements and Problems in the In-service Teacher Education in Inquiry Based Style

Report published in the Proceedings of the National Conference on "Education and Research in... more Report published in the Proceedings of the National Conference on "Education and Research in the Information Society", Plovdiv, May, 2015The paper deals with the experience of the authors in promoting the Inquiry Based Learning (IBL) in mathematics and science education within international and national projects. The emphasis is on in-service teacher education. Various types of activities and resources in support of all levels of IBL are considered, e.g. professional development courses, seminars, workshop, and performances; implementation of resources stimulating students to behave like working mathematicians. The first visible positive effects and potential problems in the implementation of IBL in the Bulgarian schools are discussed.Association for the Development of the Information Society, Institute of Mathematics and Informatics Bulgarian Academy of Sciences, Plovdiv University "Paisii Hilendarski

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Research paper thumbnail of Serdica Journal of Computing EXTENDING THE CLASS OF MATHEMATICAL PROBLEMS SOLVABLE IN SCHOOL

The problems of practical importance which are considered in school today necessarily have to lea... more The problems of practical importance which are considered in school today necessarily have to lead to a mathematical model that can be solved by school mathematics knowledge. This includes systems of equations of at most second degree, some simple trigonometry and/or some basic geometry. This restricts severely the class of such problems and conveys the impression that mathematics is not applicable enough. We provide examples of problems related to practice which are difficult to solve by means of traditional school mathematics but are amenable for solving (at least with a certain precision) with the use of software systems dealing with mathematical problems. We also present the results of an experiment with such problems that were given to school students participating in the second round of the competition "VIVA Mathematics with Computer".

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Research paper thumbnail of Norm attaining functionals on 𝐶(𝑇)

Proceedings of the American Mathematical Society, 1998

It is shown that for any infinite compact Hausdorff space T T , the Bishop-Phelps set in C ( T ) ... more It is shown that for any infinite compact Hausdorff space T T , the Bishop-Phelps set in C ( T ) ∗ C(T)^* is of the first Baire category when C ( T ) C(T) has the supremum norm.

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Research paper thumbnail of Online Competition “VIVA Mathematics with Computer”

Mathematics and Informatics, 2021

The characteristic features of the online competition “VIVA Mathematics with Computer”, organized... more The characteristic features of the online competition “VIVA Mathematics with Computer”, organized by the Institute of Mathematics and Informatics of the Bulgarian Academy of Sciences, the Union of Mathematicians in Bulgaria and the telecommunications company VIVACOM are described. The tasks are classified according to the type of their answers. The GeoGebra help-files accompanying some of the tasks are discussed as tools for simultaneous development of students‘ digital and mathematical competence. An analysis of the results of the competition, held on April 25, 2020, is presented.

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Research paper thumbnail of Generic differentiability of convex functions on the dual of a Banach space

Pacific Journal of Mathematics, 1996

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Research paper thumbnail of When does the metric projection admit a continuous selection?

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Research paper thumbnail of Continuous Selections and Approximate Selection for Set-Valued Mappings and Applications to Metric Projections

SIAM Journal on Mathematical Analysis, 1983

Continuous Selections and Approximate Selection for Set-Valued Mappings and Applications to Metri... more Continuous Selections and Approximate Selection for Set-Valued Mappings and Applications to Metric Projections. [SIAM Journal on Mathematical Analysis 14, 185 (1983)]. Frank Deutsch, Petar Kenderov. Abstract. Two new ...

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Research paper thumbnail of Lower Semicontinuity Concepts, Continuous Selections, and Set Valued Metric Projections

Journal of Approximation Theory, 2002

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Research paper thumbnail of Extending the Class of Mathematical Problems Solvable in School

Serdica Journal of Computing

The problems of practical importance which are considered in school today necessarily have to lea... more The problems of practical importance which are considered in school today necessarily have to lead to a mathematical model that can be solved by school mathematics knowledge. This includes systems of equations of at most second degree, some simple trigonometry and/or some basic geometry.This restricts severely the class of such problems and conveys theimpression that mathematics is not applicable enough. We provide examples ofproblems related to practice which are difficult to solve by means of traditional schoolmathematics but are amenable for solving (at least with a certain precision) with the use of software systems dealing with mathematical problems.We also present the results of an experiment with such problems that were given toschool students participating in the second round of the competition “VIVA Mathematics with Computer”.ACM Computing Classification System (1998): K.3.1.

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Research paper thumbnail of A weak Asplund space whose dual is not weak$^*$ fragmentable

Proceedings of the American Mathematical Society

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Research paper thumbnail of Three Decades of International Informatics Competitions : How did IOI Start

OLYMPIADS IN INFORMATICS

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Research paper thumbnail of Competitions and mathematics education

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Research paper thumbnail of Generic Gâteaux-differentiability of convex functions on small sets

Journal of Mathematical Analysis and Applications, 1990

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Research paper thumbnail of Identification, Motivation and Support of School Students with Higher Mathematical Abilities (The Project “Matheu”)

In many countries the standard education in mathematics is mainly oriented to serve the average a... more In many countries the standard education in mathematics is mainly oriented to serve the average ability students. This is natural because such students form a majority in schools. Special care is usually assigned to lower ability students so that they could cover the educational standards. Less attention is paid however to students with higher than average abilities in mathematics. The standard curriculum and syllabus requirements are no challenge for these students. As a result, a lot of mathematical abilities (and even mathematical talents) remain undiscovered and undeveloped. On the other hand, the higher ability individuals provide a critical resource for the development of the society, if they are properly educated, motivated to work and supported. With this in mind a project named MATHEU was started aimed at developing tools for identification, motivation and support of students with higher ability (and perhaps talent) in mathematics. The project has been carried out with the ...

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Research paper thumbnail of Variational Principles for Maximization Problems with Lower-semicontinuous Goal Functions

Set-Valued and Variational Analysis

Let X be a completely regular topological space and f a real-valued bounded from above lower semi... more Let X be a completely regular topological space and f a real-valued bounded from above lower semicontinuous function in it. Let C(X) be the space of all bounded continuous real-valued functions in X endowed with the usual sup-norm. We show that the following two properties are equivalent: X is ι-favourable (in the sense of the Banach-Mazur game); The set of functions h in C(X) for which f + h attains its supremum in X contains a dense and Gδ-subset of the space C(X). In particular, property (b) has place if X is a compact space or, more generally, if X is homeomorphic to a dense Gδ subset of a compact space.We show also the equivalence of the following stronger properties: X contains some dense completely metrizable subset; the set of functions h in C(X) for which f + h has strong maximum in X contains a dense and Gδ-subset of the space C(X). If X is a complete metric space and f is bounded, then the set of functions h from C(X) for which f + h has both strong maximum and strong min...

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Research paper thumbnail of Semi-continuity of set-valued monotone mappings

Fundamenta Mathematicae

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Research paper thumbnail of Most of the Optimization Problems have Unique Solution

International Series of Numerical Mathematics / Internationale Schriftenreihe zur Numerischen Mathematik / Série internationale d’Analyse numérique, 1984

ABSTRACT

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Research paper thumbnail of Duality theory for topological vector spaces over a discrete field

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Research paper thumbnail of The quasi-differentiable functionals are almost everywhere differentiable

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Research paper thumbnail of Points of single-valuedness of multivalued monotone mappings in finite dimensional spaces

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Research paper thumbnail of Achievements and Problems in the In-service Teacher Education in Inquiry Based Style

Report published in the Proceedings of the National Conference on "Education and Research in... more Report published in the Proceedings of the National Conference on "Education and Research in the Information Society", Plovdiv, May, 2015The paper deals with the experience of the authors in promoting the Inquiry Based Learning (IBL) in mathematics and science education within international and national projects. The emphasis is on in-service teacher education. Various types of activities and resources in support of all levels of IBL are considered, e.g. professional development courses, seminars, workshop, and performances; implementation of resources stimulating students to behave like working mathematicians. The first visible positive effects and potential problems in the implementation of IBL in the Bulgarian schools are discussed.Association for the Development of the Information Society, Institute of Mathematics and Informatics Bulgarian Academy of Sciences, Plovdiv University "Paisii Hilendarski

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Research paper thumbnail of Serdica Journal of Computing EXTENDING THE CLASS OF MATHEMATICAL PROBLEMS SOLVABLE IN SCHOOL

The problems of practical importance which are considered in school today necessarily have to lea... more The problems of practical importance which are considered in school today necessarily have to lead to a mathematical model that can be solved by school mathematics knowledge. This includes systems of equations of at most second degree, some simple trigonometry and/or some basic geometry. This restricts severely the class of such problems and conveys the impression that mathematics is not applicable enough. We provide examples of problems related to practice which are difficult to solve by means of traditional school mathematics but are amenable for solving (at least with a certain precision) with the use of software systems dealing with mathematical problems. We also present the results of an experiment with such problems that were given to school students participating in the second round of the competition "VIVA Mathematics with Computer".

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Research paper thumbnail of Norm attaining functionals on 𝐶(𝑇)

Proceedings of the American Mathematical Society, 1998

It is shown that for any infinite compact Hausdorff space T T , the Bishop-Phelps set in C ( T ) ... more It is shown that for any infinite compact Hausdorff space T T , the Bishop-Phelps set in C ( T ) ∗ C(T)^* is of the first Baire category when C ( T ) C(T) has the supremum norm.

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Research paper thumbnail of Online Competition “VIVA Mathematics with Computer”

Mathematics and Informatics, 2021

The characteristic features of the online competition “VIVA Mathematics with Computer”, organized... more The characteristic features of the online competition “VIVA Mathematics with Computer”, organized by the Institute of Mathematics and Informatics of the Bulgarian Academy of Sciences, the Union of Mathematicians in Bulgaria and the telecommunications company VIVACOM are described. The tasks are classified according to the type of their answers. The GeoGebra help-files accompanying some of the tasks are discussed as tools for simultaneous development of students‘ digital and mathematical competence. An analysis of the results of the competition, held on April 25, 2020, is presented.

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Research paper thumbnail of Generic differentiability of convex functions on the dual of a Banach space

Pacific Journal of Mathematics, 1996

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Research paper thumbnail of When does the metric projection admit a continuous selection?

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Research paper thumbnail of Continuous Selections and Approximate Selection for Set-Valued Mappings and Applications to Metric Projections

SIAM Journal on Mathematical Analysis, 1983

Continuous Selections and Approximate Selection for Set-Valued Mappings and Applications to Metri... more Continuous Selections and Approximate Selection for Set-Valued Mappings and Applications to Metric Projections. [SIAM Journal on Mathematical Analysis 14, 185 (1983)]. Frank Deutsch, Petar Kenderov. Abstract. Two new ...

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Research paper thumbnail of Lower Semicontinuity Concepts, Continuous Selections, and Set Valued Metric Projections

Journal of Approximation Theory, 2002

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Research paper thumbnail of Extending the Class of Mathematical Problems Solvable in School

Serdica Journal of Computing

The problems of practical importance which are considered in school today necessarily have to lea... more The problems of practical importance which are considered in school today necessarily have to lead to a mathematical model that can be solved by school mathematics knowledge. This includes systems of equations of at most second degree, some simple trigonometry and/or some basic geometry.This restricts severely the class of such problems and conveys theimpression that mathematics is not applicable enough. We provide examples ofproblems related to practice which are difficult to solve by means of traditional schoolmathematics but are amenable for solving (at least with a certain precision) with the use of software systems dealing with mathematical problems.We also present the results of an experiment with such problems that were given toschool students participating in the second round of the competition “VIVA Mathematics with Computer”.ACM Computing Classification System (1998): K.3.1.

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Research paper thumbnail of A weak Asplund space whose dual is not weak$^*$ fragmentable

Proceedings of the American Mathematical Society

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Research paper thumbnail of Three Decades of International Informatics Competitions : How did IOI Start

OLYMPIADS IN INFORMATICS

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Research paper thumbnail of Competitions and mathematics education

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Research paper thumbnail of Generic Gâteaux-differentiability of convex functions on small sets

Journal of Mathematical Analysis and Applications, 1990

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Research paper thumbnail of Identification, Motivation and Support of School Students with Higher Mathematical Abilities (The Project “Matheu”)

In many countries the standard education in mathematics is mainly oriented to serve the average a... more In many countries the standard education in mathematics is mainly oriented to serve the average ability students. This is natural because such students form a majority in schools. Special care is usually assigned to lower ability students so that they could cover the educational standards. Less attention is paid however to students with higher than average abilities in mathematics. The standard curriculum and syllabus requirements are no challenge for these students. As a result, a lot of mathematical abilities (and even mathematical talents) remain undiscovered and undeveloped. On the other hand, the higher ability individuals provide a critical resource for the development of the society, if they are properly educated, motivated to work and supported. With this in mind a project named MATHEU was started aimed at developing tools for identification, motivation and support of students with higher ability (and perhaps talent) in mathematics. The project has been carried out with the ...

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Research paper thumbnail of Variational Principles for Maximization Problems with Lower-semicontinuous Goal Functions

Set-Valued and Variational Analysis

Let X be a completely regular topological space and f a real-valued bounded from above lower semi... more Let X be a completely regular topological space and f a real-valued bounded from above lower semicontinuous function in it. Let C(X) be the space of all bounded continuous real-valued functions in X endowed with the usual sup-norm. We show that the following two properties are equivalent: X is ι-favourable (in the sense of the Banach-Mazur game); The set of functions h in C(X) for which f + h attains its supremum in X contains a dense and Gδ-subset of the space C(X). In particular, property (b) has place if X is a compact space or, more generally, if X is homeomorphic to a dense Gδ subset of a compact space.We show also the equivalence of the following stronger properties: X contains some dense completely metrizable subset; the set of functions h in C(X) for which f + h has strong maximum in X contains a dense and Gδ-subset of the space C(X). If X is a complete metric space and f is bounded, then the set of functions h from C(X) for which f + h has both strong maximum and strong min...

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Research paper thumbnail of Semi-continuity of set-valued monotone mappings

Fundamenta Mathematicae

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Research paper thumbnail of Most of the Optimization Problems have Unique Solution

International Series of Numerical Mathematics / Internationale Schriftenreihe zur Numerischen Mathematik / Série internationale d’Analyse numérique, 1984

ABSTRACT

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Research paper thumbnail of Duality theory for topological vector spaces over a discrete field

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Research paper thumbnail of The quasi-differentiable functionals are almost everywhere differentiable

Bookmarks Related papers MentionsView impact

Research paper thumbnail of Points of single-valuedness of multivalued monotone mappings in finite dimensional spaces

Bookmarks Related papers MentionsView impact