Uncertaintybased Information Elements of Generalized Information Theory

Three Music Courses in One: Comprehensive Music Theory and Music Skills Development. Music theory you can use.

It can be seen from the title that we shall be dealing here with a mathemati- cal theory based on precise notions and definitions. The central object of this theory is an invariant toroidal manifold of a dynamical system considered in a Euclidean space En or in its product with an n-dimensional torus, that is, in the space En X T m . Taking into account the fact that a quasi-periodic solution of a dynamical system in En "sweeps out" an invariant torus of this sytem, the relation between the theory of invariant tori and the theory of multi-frequency oscillations becomes clear; the existence of such tori is a necessary condition for the existence of multi-frequency oscillations of quasi-periodic solutions of dynamical systems. By defining multi-frequency oscillations as a motion of a dynamical system, describing a recurrent trajectory on an invariant toroidal manifold of the system, we make the invariant toroidal manifold into the main subject of the mathematical theory of multi-frequency oscillations; the exis- tence of such a manifold is sufficient for multi-frequency oscillations of the system to exist.

This first part of a two-volume set offers a modern account of the representation theory of finite dimensional associative algebras over an algebraically closed field. The authors present this topic from the perspective of linear representations of finite-oriented graphs (quivers) and homological algebra.

This first part of a two-volume set offers a modern account of the representation theory of finite dimensional associative algebras over an algebraically closed field. The authors present this topic from the perspective of linear representations of finite-oriented graphs (quivers) and homological algebra.

This first part of a two-volume set offers a modern account of the representation theory of finite dimensional associative algebras over an algebraically closed field. The authors present this topic from the perspective of linear representations of finite-oriented graphs (quivers) and homological algebra. The self-contained treatment constitutes an elementary, up-to-date introduction to the subject using, on the one hand, quiver-theoretical techniques and, on the other, tilting theory and integral quadratic forms.

Elements of Large Sample Theory provides a unified treatment of first-order large-sample theory. It discusses a broad range of applications including introductions to density estimation, the bootstrap, and the asymptotics of survey methodology written at an elementary level. The book is suitable for students at the Master's level in statistics and in aplied fields who have a background of two years of calculus.