Related papers: Total Representations
This book is mainly an exposition of the author's works and his joint works with his former students on explicit representations of finite-dimensional simple Lie algebras, related partial differential equations, linear orthogonal algebraic…
We investigate the representation and complete representation classes for algebras of partial functions with the signature of relative complement and domain restriction. We provide and prove the correctness of a finite equational…
We change the definition of the vertex representations. As a result the vertex representations has one parameter.
Theory of representations of universal algebra is a natural development of the theory of universal algebra. In the book, I considered representation of universal algebra, diagram of representations and examples of representation. Morphism…
In this short review, we pay attention to some subtleties in the study of projective representations, contrasting local to global properties and their interplay. The analysis is exposed rigorously, showing and demonstrating the main…
We establish a computable version of Gelfand Duality. Under this computable duality, computably compact presentations of metrizable spaces uniformly effectively correspond to computable presentations of unital commutative $C^*$ algebras.
Alternative partial Boolean structures, implicit in the discussion of classical representability of sets of quantum mechanical predictions, are characterized, with definite general conclusions on the equivalence of the approaches going back…
As dynamic and control systems become more complex, relying purely on numerical computations for systems analysis and design might become extremely expensive or totally infeasible. Computer algebra can act as an enabler for analysis and…
We give a survey on the theory of representation-finite and certain minimal representation-infinite algebras.The main goals are the existence of multiplicative bases and of coverings with good properties. Both are attained via…
Computable analysis and effective descriptive set theory are both concerned with complete metric spaces, functions between them and subsets thereof in an effective setting. The precise relationship of the various definitions used in the two…
We define Collatz representations for a subset of rational numbers and prove that each real number \( x \notin (-1,1) \) can be approximated arbitrarily well by rational numbers which have only \( 2 \)'s and \( 1 \)'s in their Collatz…
The study of representations is of fundamental importance to any form of communication, and our ability to exploit them effectively is paramount. This article presents a novel theory -- Representational Systems Theory -- that is designed to…
What is computable with limited resources? How can we verify the correctness of computations? How to measure computational power with precision? Despite the immense scientific and engineering progress in computing, we still have only…
We prove a number of elementary facts about computability in partial combinatory algebras (pca's). We disprove a suggestion made by Kreisel about using Friedberg numberings to construct extensional pca's. We then discuss separability and…
A notable feature of the TTE approach to computability is the representation of the argument values and the corresponding function values by means of infinitistic names. Two ways to eliminate the using of such names in certain cases are…
We show that the theory of the partial order of computably enumerable equivalence relations (ceers) under computable reduction is 1-equivalent to true arithmetic. We show the same result for the structure comprised of the dark ceers and the…
In this chapter we provide an overview of computational modeling for semantic change using large and semi-large textual corpora. We aim to provide a key for the interpretation of relevant methods and evaluation techniques, and also provide…
In the present paper we propose a new approach on `distributed systems': the processes are represented through total orders and the communications are characterized by means of biorders. The resulting distributed systems capture situations…
We prove that many seemingly simple theories have Borel complete reducts. Specifically, if a countable theory has uncountably many complete 1-types, then it has a Borel complete reduct. Similarly, if $Th(M)$ is not small, then $M^{eq}$ has…
The increasing data availability and imported analyzing tools from computer science and physical science have sharply changed traditional methodologies of social sciences, leading to a new branch named computational socioeconomics that…