相关论文: A natural construction for the real numbers
This paper is devoted to a systematic study of a class of binary trees encoding the structure of rational numbers both from arithmetic and dynamical point of view. The paper is divided into two parts. The first one is a critical review of…
We describe a combinatorial approach for investigating properties of rational numbers. The overall approach rests on structural bijections between rational numbers and familiar combinatorial objects, namely rooted trees. We emphasize that…
We introduce several classes of pseudorandom sequences which represent a natural extension of classical methods in random number generation. The sequences are obtained from constructions on labeled binary trees, generalizing the well-known…
If \(A \) is a set of natural numbers containing \(0 \), then there is a unique nonempty "reciprocal" set \(B \) of natural numbers (containing \(0 \)) such that every positive integer can be written in the form \(a + b \), where \(a \in A…
We construct a commutative version of the group ring and show that it allows one to translate questions about the normal generation of groups into questions about the generation of ideals in commutative rings. We demonstrate this with an…
We study a natural extension to complex numbers of the standard continued fractions. The basic algorithm is due to Lagrange and Gauss, though it seems to have gone mostly unnoticed as a way to create continued fractions. The new…
In the course of many mathematical developments involving 'number systems' like $\mathbb{N}, \mathbb{Z}, \mathbb{Q}, \mathbb{R}, \mathbb {C}$ etc., it sometimes becomes necessary to abstract away and study certain properties of the number…
Override and update are natural constructions for combining partial functions, which arise in various program specification contexts. We use an unexpected connection with combinatorial geometry to provide a complete finite system of…
The aim of the work is to construct new polynomial systems, which are solutions to certain functional equations which generalize the second-order differential equations satisfied by the so called classical orthogonal polynomial families of…
We give a new formula for the rotation number (or Whitney index) of a smooth closed plane curve. This formula is obtained from the winding numbers associated with the regions and the crossing points of the curve. One difference with the…
This note presents a procedure of constructing a higher dimensional sphere map from a lower dimensional one and gives an explicit formula for smooth sphere map with a given degree. As an application a new proof of a generalized…
In this paper, we study rotation numbers of random dynamical systems on the circle. We prove the existence of rotation numbers and the continuous dependence of rotation numbers on the systems. As an application, we prove a theorem on…
This paper is concerned with the foundations of the Calculus of Algebraic Constructions (CAC), an extension of the Calculus of Constructions by inductive data types. CAC generalizes inductive types equipped with higher-order primitive…
In this paper we consider particular generalized compositions of a natural number with a given number of parts. Its number is a weighted polynomial coefficient. The number of all generalized compositions of a natural number is a weighted…
A cyclically ordered quiver is a quiver endowed with an additional structure of a cyclic ordering of its vertices. This structure, which naturally arises in many important applications, gives rise to new powerful mutation invariants.
The sets used to construct other mathematical objects are pure sets, which means that all of their elements are sets, which are themselves pure. One set may therefore be within another, not as an element, but as an element of an element, or…
Contracting the $h$-deformation of $\SL(2,\Real)$, we construct a new deformation of two dimensional Poincar\'e algebra, the algebra of functions on its group and its differential structure. It is also shown that the Hopf algebra is…
It is formally constructed a normal form for a class of real-formal surfaces defined near a CR Singularity.
It is a ubiquitous opinion among mathematicians that a real number is just a point in the line. If this rough definition is not enough, then a mathematician may provide a formal definition of the real numbers in the set theoretic and…
This paper presents mathematics as a general science of computation in a way different from the tradition. It is based on the radical philosophical standpoint according to which the content, meaning and justification of experience lies in…