Иновации в математическото образование: европейските проекти InnoMathEd и Fibonacci

Petar Kenderov The paper considers the participation of the Institute of Mathematics and Informatics at the Bulgarian Academy of Sciences, into two European projects, InnoMathEd and Fibonacci. Both projects address substantial innovations in mathematics education and their dissemination on European level. Inquiry based learning is the central focus of the two projects. A special emphasis is paid on the outcomes of the projects in terms of didactic concepts, pedagogical methodologies and innovative learning environments aimed at pupils’ active, self-responsible and exploratory learning.

Description Reduction for Restricted Sets of (0,1) Matrices

* The research is supported partly by INTAS: 04-77-7173 project, http://www.intas.be

Experimental Support of Argument-based Syntactic Computation

Linguistic theory, cognitive, information, and mathematical modeling are all useful while we attempt to achieve a better understanding of the Language Faculty (LF). This cross-disciplinary approach will eventually lead to the identification of the key principles applicable in the systems of Natural Language Processing. The present work concentrates on the syntax-semantics interface. We start from recursive definitions and application of optimization principles, and gradually develop a formal model of syntactic operations. The result – a Fibonacci- like syntactic tree – is in fact an argument-based variant of the natural language syntax. This representation (argument-centered model, ACM) is derived by a recursive calculus that generates a mode which connects arguments and expresses relations between them. The reiterative operation assigns primary role to entities as the key components of syntactic structure. We provide experimental evidence in support of the argument-based model. We also show that mental computation of syntax is influenced by the inter-conceptual relations between the images of entities in a semantic space.

Алгоритмы Решения Систем Линейных Диофантовых Уравнений в Дискретных Областях

Abstract.The algorithms for computation of minimal supported set of solutions for systems of linear Diophantine homogeneous equations over set of natural numbers and basis of systems of linear Diophantine homogeneous and inhomogeneous equations in ring and field of remainders on modulo of a number.

Многокритериальные Задачи на Комбинаторном Множестве Полиразмещений: Структурные Свойства Решений

Рассматривается многокритериальная задача дискретной оптимизации на допустимом комбинаторном множестве полиразмещений. Исследуются структурные свойства допустимой области и различных видов эффективных решений. На основе развития идей евклидовой комбинаторной оптимизации и метода главного критерия предложены и обоснованы возможные подходы для решения многокритериальной комбинаторной задачи на множестве полиразмещений.

Векторные Задачи на Комбинаторном Множестве Полиразмещений: Условия Оптимальности и Подход к Решению

Рассматривается многокритериальная задача дискретной оптимизации на комбинаторном множестве полиразмещений. Исследуются структурные свойства множеств эффективных решений. Получены необходимые и достаточные условия различных видов оптимальности решений. На основе развития идей евклидовой комбинаторной оптимизации, методов главного критерия, декомпозиции, отсекающих плоскостей Келли, релаксации разработаны и обоснованы возможные подходы для решения многокритериальной комбинаторной задачи на множестве полиразмещений.

Generating More Boundary Elements of Subset Projections

Composition problem is considered for partition constrained vertex subsets of n dimensional unit cube E^n . Generating numerical characteristics of E^n subsets partitions is considered by means of the same characteristics in 1 − n dimensional unit cube, and construction of corresponding subsets is given for a special particular case. Using pairs of lower layer characteristic vectors for E^(1-n) more characteristic vectors for E^n are composed which are boundary from one side, and which take part in practical recognition of validness of a given candidate vector of partitions.

Number Sequences in an Integral Form with a Generalized Convolution Property and Somos-4 Hankel Determinants

MSC 2010: 11B83, 05A19, 33C45