相关论文: Generalizations of certain representations of real…

The article is devoted to introduce and investigation of new numeral systems. These representations are generalizations of classical representations of real numbers. The main properties of investigating representations are described. The…

In this article, for modelling numeral systems, the operator approach, which is introduced in [25], is generalized for a certain case. An example of such numeral systems is introduced and considered.

Using a genealogically ordered infinite regular language, we know how to represent an interval of R. Numbers having an ultimately periodic representation play a special role in classical numeration systems. The aim of this paper is to…

This note states and proves a representation theorem for regular quantity functions, based on the theory of quantity spaces, thereby giving a new perspective on dimensional analysis and the classical $\pi$ theorem.

In this expository article, the real numbers are defined as infinite decimals. After defining an ordering relation and the arithmetic operations, it is shown that the set of real numbers is a complete ordered field. It is further shown that…

This work presents a formalization of analogy on numbers that relies on generalized means. It is motivated by recent advances in artificial intelligence and applications of machine learning, where the notion of analogy is used to infer…

We develop the theory of Wigner representations for general probabilistic theories (GPTs), a large class of operational theories that include both classical and quantum theory. The Wigner representations that we introduce are a natural way…

We consider the representation of real numbers by alternating Perron series ($P^-$-representation), which is a generalization of representations of real numbers by Ostrogradsky-Sierpi\'nski-Pierce series (Pierce series), alternating…

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

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…

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 article is devoted to the alternating Cantor series. It is proved that any real number belonging to $[a_0-1;a_0]$, where $a_0=\sum^{\infty} _{k=1} {\frac{d_{2k}-1}{d_1d_2...d_{2k}}} $, has no more than two representations by the series…

The aim of the present article is to explore the possibilities of representing positive integers as sums of other positive integers and highlight certain fundamental connections between their multiplicative and additive properties. In…

Lattice polytope representation of natural numbers is introduced based on the fundamental theorem of arithmetic. The combinatorial and geometric properties of the polytopes are studied using Polymake and Qhull software. The volume of the…

A generalization of metric space is presented which is shown to admit a theory strongly related to that of ordinary metric spaces. To avoid the topological effects related to dropping any of the axioms of metric space, first a new, and…

We discuss the notion about physical quantities as having values represented by real numbers, and its limiting to describe nature to be understood in relation to our appreciation that the quantum theory is a better theory of natural…

In this paper, we consider representations of integers as sums of at most four distinct $m$-gonal numbers (allowing a fixed number of repeats of each polygonal number occurring in the sum). We show that the number of such representations…

In this article, we prove a representation theorem that any generic line arrangement in the plane over an ordered field which has global cyclicity can be represented isomorphically by a line arrangement with a given set of distinct slopes…

A new definition of a real number is that it is a rule which says Yes or No based on whether the real number ought to be in a given rational interval. This is a teaser paper for formalizing, exploring, and generalizing this definition. The…

We provide a setting-independent definition of reals by introducing the notion of a streak. We show that various standard constructions of reals satisfy our definition. We study the structure of reals by noting that its pieces correspond to…