Related papers: On some generalizations of real numbers representa…

In the present article, real number representations, that are generalizations of classical positive and alternating representations of numbers, are introduced and investigated. The main metric relation, properties of cylinder sets are…

Primarily this paper presents an expository report on alternatives to the traditional methods of classifying representations of finite dimensional algebras. Some new results illustrating such alternatives for algebras with only finitely…

The article is devoted to modeling of the nega-$\tilde Q$-representation of real numbers. The representation is a generalization of representation by alternating Cantor series and positive $\tilde Q$-representation is a generalization of…

We show how to represent an interval of real numbers in an abstract numeration system built on a language that is not necessarily regular. As an application, we consider representations of real numbers using the Dyck language. We also show…

The present article is devoted to the description of further investigations of the author of this article. These investigations (in terms of various representations of real numbers) include the generalized Salem functions and…

This book is an introduction to a fast developing branch of mathematics - the theory of representations of groups. It presents classical results of this theory concerning finite groups.

In this paper some new ways of generalizing perfect numbers are investigated, numerical results are presented and some conjectures are established.

This paper is a survey on invariants of representations of quivers and their generalizations. We present the description of generating systems for invariants and relations between generators.

This lecture addresses some general ideas behind numerical computations ranging from representation of numbers in computers to stability and accuracy of standard algorithms for some simple mathematical problems.

We present a comprehensive survey of constructions of the real numbers (from either the rationals or the integers) in a unified fashion, thus providing an overview of most (if not all) known constructions ranging from the earliest attempts…

In this paper, we propose new generalizations of amicable numbers. We also give examples and prove properties of these new concepts.

In this paper some generalizations of the sum of powers of natural numbers is considered. In particular, the class of sums whose generating function is the power of the generating function for the classical sums of powers is studying. The…

Some class of sums which naturally include the sums of powers of integers is considered. A number of conjectures concerning a representation of these sums is made.

We study the computational complexity of converting one representation of real numbers into another representation. Typical examples of representations are Cauchy sequences, base-10 expansions, Dedekind cuts and continued fractions.

We introduce a uniform representation of general objects that captures the regularities with respect to their structure. It allows a representation of a general class of objects including geometric patterns and images in a sparse, modular,…

This is an introduction to: (1) the enumerative geometry of rational curves in equivariant symplectic resolutions, and (2) its relation to the structures of geometric representation theory. Written for the 2015 Algebraic Geometry Summer…

We introduce the continued logarithm representation of real numbers and prove results on the occurrence and frequency of digits with respect to this representation

In this paper we introduce generalised Markov numbers and extend the classical Markov theory for the discrete Markov spectrum to the case of generalised Markov numbers. In particular we show recursive properties for these numbers and find…

We define natural classes of rational and polynomial representations of the Yangian of the general linear Lie algebra. We also present the classification and explicit realizations of all irreducible rational representations of the Yangian.

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…