Vector Course

Mathematics Course 111: Algebra I Part IV: Vector Spaces

A vector space over some field K is an algebraic structure consisting of a set V on which are defined two algebraic operations: a binary operation referred to as addition, and an operation of multiplication by scalars in which elements of the vector space are multiplied by elements of the given field K. These two operations are required to satisfy certain axioms that correspond to many of the p...

Control for Ship Course-Keeping Using Optimized Support Vector Machines

Abstract: Support vector machines (SVM) are proposed in order to obtain a robust controller for ship course-keeping. A cascaded system is constructed by combining the dynamics of the rudder actuator with the dynamics of ship motion. Modeling errors and disturbances are taken into account in the plant. A controller with a simple structure is produced by applying an SVM and L2-gain design. The SV...

Vector Optimization Problems and Generalized Vector Variational-Like Inequalities

In this paper, some properties of  pseudoinvex functions, defined by means of  limiting subdifferential, are discussed. Furthermore, the Minty vector variational-like inequality,  the Stampacchia vector variational-like inequality, and the  weak formulations of these two inequalities  defined by means of limiting subdifferential are studied. Moreover, some relationships  between the vector vari...

An equivalence functor between local vector lattices and vector lattices

We call a local vector lattice any vector lattice with a distinguished positive strong unit and having exactly one maximal ideal (its radical). We provide a short study of local vector lattices. In this regards, some characterizations of local vector lattices are given. For instance, we prove that a vector lattice with a distinguished strong unit is local if and only if it is clean with non no-...

Course 212: Hilary Term 2001 Part III: Normed Vector Spaces and Functional Analysis