Vector-valued discrete Fourier transforms (DFTs) and ambiguity functions are defined. The motivation for the definitions is to provide realistic modeling of multi-sensor environments in which a useful time-frequency analysis is essential. The definition of the DFT requires associated uncertainty principle inequalities. The definition of the ambiguity function requires a component that leads to ...

abstract. We consider frames that can be deened by polynomials over states and transitions. States are elements from the natural numbers with pairing, and (state-)transitions are labeled with actions from some nite set. We study a connection with process algebra: pointing a frame by distinguishing either two states that function as a root and a tail, respectively, implements a terminating proce...

Recent results from real algebraic geometry and the theory of polynomial optimization are related in a new framework to the existence question of multivariate tight wavelet frames whose generators have at least one vanishing moment. Namely, several equivalent formulations of the so-called Unitary Extension Principle (UEP) from [33] are interpreted in terms of hermitian sums of squares of certai...

In previous work it was shown that there is an epireflection ψ of the category of all compact normal, joinfit frames, with skeletal maps, in the full subcategory of frames which are also strongly projectable, and that ψ restricts to the epicompletion ε, which is the absolute reflection on compact regular frames. In the first part of this paper it is shown that ψ is a monoreflection and that the...

This paper introduces an algebraic framework for a topological analysis of time-varying 2D digital binary{valued images, each of them de ned as 2D arrays of pixels. Our answer is based on an algebraictopological coding, called AT{model, for a nD (n = 2; 3) digital binaryvalued image I consisting simply in taking I together with an algebraic object depending on it. Considering AT{models for all ...

Operator overloading is a powerful feature of modern object-oriented programming languages; it can be used to customize the default algebraic operators to a point where the programming syntax can accommodate new algebras acting on complex objects. The present work introduces a custom T (T, ) algebra which can be used to express kinematic transformations in chains of frames that move in threedim...

$%675$&7 In this paper we discuss an extension of the Algebra of Expressions, an algebraic structure introduced in an earlier paper, consisting of a set of operators and related properties defined over a set that is a generalization of the MPEG-4’s Facial Animation Parameters. In particular, we extend the definition of the operators acting on whole animations, i.e. sequences of frames represent...

Ġ = {G,H}. In particular, the DV F is called an integral if it has zero PB with the Hamiltonian {F,H} = 0. In this case F does not depend on t. In many problems of the classical mechanics DV form elegant algebraic structures which are closed with respect to PB. The Poisson structures with non-linear PB were discussed in [9] and [6]. Sklyanin introduced [9] the so-called quadratic Poisson algebr...

Partial frames provide a rich context in which to do pointfree structured and unstructured topology. A small collection of axioms of an elementary nature allows one to do much traditional pointfree topology, both on the level of frames or locales, and that of uniform or metric frames. These axioms are sufficiently general to include as examples bounded distributive...