Àlgebra vectorial: aplicacions lineals

Oferim als estudiants universitaris i als lectors interessats aquesta guia didàctica de la matemàtica universitària com a fruit dels nostres anys de docència de les matemàtiques a la Universitat. El resultat final ha esdevingut una col·lecció de setze petits volums agrupats en els dos mòduls d'Àlgebra Lineal i de Càlcul Infinitesimal. En aquest volum es generalitza en primer lloc el concepte d'aplicació entre dos espais vectorials i s'introdueix la important definició d'aplicació lineal. Pel seu estudi s'utilitza l'àlgebra matricial. A continuació es desenvolupen els temes de valors i vectors propis, la diagonalització d'endomorfismes i l'estudi de les formes quadràtiques

Àlgebra vectorial: vectors

Oferim als estudiants universitaris i als lectors interessats aquesta guia didàctica de la matemàtica universitària com a fruit dels nostres anys de docència de les matemàtiques a la Universitat. El resultat final ha esdevingut una col·lecció de setze petits volums agrupats en els dos mòduls d'Àlgebra Lineal i de Càlcul Infinitesimal. Amb aquest sisè volum de la col•lecció iniciem l’estudi de l’Àlgebra vectorial a partir de conceptes propers a la intuïció com són els vectors del pla i de l’espai per, a continuació, fer una generalització del concepte de vector a altres ens matemàtics com polinomis, successions, magnituds econòmiques, etc. En aquest volum utilitzarem sovint la notació matricial, ja coneguda i emprada en volums anteriors, i que esdevé una eina idònia per facilitar la notació dels conceptes i del càlcul entre vectors. Seguim amb l’estudi axiomàtic de l’estructura d’espai vectorial i les seves propietats, que com veurem en el proper volum ens permetrà, entre altres aplicacions a l’economia, deduir els valors i vectors propis d’un endomorfisme i diagonalitzar formes quadràtiques

Implicit vector equilibrium problems with applications

Let X and Y be Hausdorff topological vector spaces, K a nonempty, closed, and convex subset of X, C: K--> 2(Y) a point-to-set mapping such that for any x is an element of K, C(x) is a pointed, closed, and convex cone in Y and int C(x) not equal 0. Given a mapping g : K --> K and a vector valued bifunction f : K x K - Y, we consider the implicit vector equilibrium problem (IVEP) of finding x* is an element of K such that f (g(x*), y) is not an element of - int C(x) for all y is an element of K. This problem generalizes the (scalar) implicit equilibrium problem and implicit variational inequality problem. We propose the dual of the implicit vector equilibrium problem (DIVEP) and establish the equivalence between (IVEP) and (DIVEP) under certain assumptions. Also, we give characterizations of the set of solutions for (IVP) in case of nonmonotonicity, weak C-pseudomonotonicity, C-pseudomonotonicity, and strict C-pseudomonotonicity, respectively. Under these assumptions, we conclude that the sets of solutions are nonempty, closed, and convex. Finally, we give some applications of (IVEP) to vector variational inequality problems and vector optimization problems. (C) 2003 Elsevier Science Ltd. All rights reserved.

Generalized interval vector spaces and interval optimization

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Stability for parametric implicit vector equilibrium problems

In this paper, we consider a class of parametric implicit vector equilibrium problems in Hausdorff topological vector spaces where a mapping f and a set K are perturbed by parameters is an element of and lambda respectively. We establish sufficient conditions for the upper semicontinuity and lower semicontinuity of the solution set mapping S : Lambda(1) x A(2) -> 2(X) for such parametric implicit vector equilibrium problems. (c) 2005 Elsevier Ltd. All rights reserved.

Vector spaces of entire functions of unbounded type

Let E be an infinite dimensional complex Banach space. We prove the existence of an infinitely generated algebra, an infinite dimensional closed subspace and a dense subspace of entire functions on E whose non-zero elements are functions of unbounded type. We also show that the τδ topology on the space of all holomorphic functions cannot be obtained as a countable inductive limit of Fr´echet spaces. RESUMEN. Sea E un espacio de Banach complejo de dimensión infinita y sea H(E) el espacio de funciones holomorfas definidas en E. En el artículo se demuestra la existencia de un álgebra infinitamente generada en H(E), un subespacio vectorial en H(E) cerrado de dimensión infinita y un subespacio denso en H(E) cuyos elementos no nulos son funciones de tipo no acotado. También se demuestra que el espacio de funciones holomorfas con la topología ? no es un límite inductivo numberable de espacios de Fréchet.

The year's entertainments ... a collection of recitations, dialogues, songs, exercises, etc., arranged as programs for special days and occasions, providing for each month of the school year,

Mode of access: Internet.

Problems in the calculus, with formulas and suggestions,

Mode of access: Internet.

Vector Combinatorial Problems in a Space of Combinations with Linear Fractional Functions of Criteria

The paper considers vector discrete optimization problem with linear fractional functions of criteria on a feasible set that has combinatorial properties of combinations. Structural properties of a feasible solution domain and of Pareto–optimal (efficient), weakly efficient, strictly efficient solution sets are examined. A relation between vector optimization problems on a combinatorial set of combinations and on a continuous feasible set is determined. One possible approach is proposed in order to solve a multicriteria combinatorial problem with linear- fractional functions of criteria on a set of combinations.

Optimality Conditions for D.C. Vector Optimization Problems under D.C. Constraints

2000 Mathematics Subject Classification: Primary 90C29; Secondary 49K30.

Finite dimensional ordered vector spaces with Riesz interpolation and Effros-Shen's unimodularity conjecture

Peer reviewed

The effects of teaching a mathematics problem solving strategy on the problem solving ability of grade nine students

Forty grade 9 students were selected from a small rural board in southern Ontario. The students were in two classes and were treated as two groups. The treatment group received instruction in the Logical Numerical Problem Solving Strategy every day for 37 minutes over a 6 week period. The control group received instruction in problem solving without this strategy over the same time period. Then the control group received the treat~ent and the treatment group received the instruction without the strategy. Quite a large variance was found in the problem solving ability of students in grade 9. It was also found that the growth of the problem solving ability achievement of students could be measured using growth strands based upon the results of the pilot study. The analysis of the results of the study using t-tests and a MANOVA demonstrated that the teaching of the strategy did not significaritly (at p s 0.05) increase the problem solving achievement of the students. However, there was an encouraging trend seen in the data.