62 research outputs found
On Some Geometric Properties of Slice Regular Functions of a Quaternion Variable
The goal of this paper is to introduce and study some geometric properties of
slice regular functions of quaternion variable like univalence, subordination,
starlikeness, convexity and spirallikeness in the unit ball. We prove a number
of results, among which an Area-type Theorem, Rogosinski inequality, and a
Bieberbach-de Branges Theorem for a subclass of slice regular functions. We
also discuss some geometric and algebraic interpretations of our results in
terms of maps from to itself. As a tool for subordination we
define a suitable notion of composition of slice regular functions which is of
independent interest
Harmonic analysis and hypercomplex function theory in co-dimension one
Fundamentals of a function theory in co-dimension one for Clifford algebra valued functions over ℝn+1 are considered. Special attention is given to their origins in analytic properties of holomorphic functions of one and, by some duality reasons, also of several complex variables. Due to algebraic peculiarities caused by non-commutativity of the Clifford product, generalized holomorphic functions are characterized by two different but equivalent properties: on one side by local derivability (existence of a well defined derivative related to co-dimension one) and on the other side by differentiability (existence of a local approximation by linear mappings related to dimension one). As important applications, sequences of harmonic Appell polynomials are considered whose definition and explicit analytic representations rely essentially on both dual approaches.The work of the first, second and fourth authors was supported by Portuguese funds through the CIDMA - Center for Research and Development in Mathematics and Applications, and the Portuguese Foundation for
Science and Technology (“FCT-Fundação para a Ciência e Tecnologia”), within project PEst-OE/MAT/UI4106/2013. The work of the second author was supported by Portuguese funds through the CMAT - Centre of Mathematics and FCT within the Project UID/MAT/00013/2013
The algebraic theory of switching circuits
The Algebraic Theory of Switching Circuits covers the application of various algebraic tools to the delineation of the algebraic theory of switching circuits for automation with contacts and relays.This book is organized into five parts encompassing 31 chapters. Part I deals with the principles and application of Boolean algebra and the theory of finite fields (Galois fields). Part II emphasizes the importance of the sequential operation of the automata and the variables associated to the current and to the contacts. This part also tackles the recurrence relations that describe operations of
Theoretical Study of the Real Functioning of Binary Switching Elements-Non-Binary Switching Elements
A Kind of Riemann-Hilbert Problem for Non-Classical Systems of Partial Differential Equations
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