Related papers: A Class of Recursive Sets
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…
This paper presents a novel approach to constructing finite generating sets for infinitely generated ideals. By integrating algebraic and computational techniques, we provide a method to identify finite generators, demonstrated through…
Collective classification of vertices is a task of assigning categories to each vertex in a graph based on both vertex attributes and link structure. Nevertheless, some existing approaches do not use the features of neighbouring vertices…
In this note we study the convergence of recursively defined infinite series. We explore the role of the derivative of the defining function at the origin (if it exists), and develop a comparison test for such series which can be used even…
We present classes of discrete reversible systems which are at the same time chaotic and solvable.
User defined recursive types are a fundamental feature of modern functional programming languages like Haskell, Clean, and the ML family of languages. Properties of programs defined by recursion on the structure of recursive types are…
We define impulse response sequence in the set of all linear recurring sequences satisfying a linear recurrence relation of order $r$. The generating function and expression of the impulse response sequence are presented. Some identities of…
We develop an axiomatic set theory -- the Theory of Hyperfinite Sets THS, which is based on the idea of existence of proper subclasses of big finite sets. We demonstrate how theorems of classical continuous mathematics can be transfered to…
Simple methods permit to generalize the concepts of iteration and of recursive processes. We shall see briefly on several examples what these methods generate. In additive sequences, we shall encounter not only the golden or the silver…
We introduce a class of stochastic integer sequences. In these sequences, every element is a sum of two previous elements, at least one of which is chosen randomly. The interplay between randomness and memory underlying these sequences…
We consider estimation procedures which are recursive in the sense that each successive estimator is obtained from the previous one by a simple adjustment. We study rate of convergence of recursive estimation procedures for the general…
One possible approach to tackle the class imbalance in classification tasks is to resample a training dataset, i.e., to drop some of its elements or to synthesize new ones. There exist several widely-used resampling methods. Recent research…
Recursive coalgebras provide an elegant categorical tool for modelling recursive algorithms and analysing their termination and correctness. By considering coalgebras over categories of suitably indexed families, the correctness of the…
We consider a stack sorting algorithm where only the appropriate output values are popped from the stack and then any remaining entries in the stack are run through the stack in reverse order. We identify the basis for the $2$-reverse pass…
We define a class of sequences ${a_n}$ by $a_1=a$ and $a_{n+1}=P(a_n)$, where $P(x)$ is a polynomial with real coefficients. We then find out for which values $a$ and for which polynomials $P(x)$ these sequences will be constant after a…
Complete residue systems play an integral role in abstract algebra and number theory, and a description is typically found in any number theory textbook. This note provides a concise overview of complete residue systems, including a robust…
A classical method for partition generating functions is developed into a tool with wide applications. New expansions of well-known theorems are derived, and new results for partitions with n copies of n are presented.
The purpose of this note is twofold. First, we survey results on the construction of large class groups of number fields by specialization of finite covers of curves. Then we give examples of applications of these techniques.
We will use overlays and templates derived from two-dimensional recurrence relations to build the arrays, and we will study the structure of the overlays, including initial conditions and basis arrays.
This work is meant to demonstrate new class of prime numbers -- cyclic prime numbers, that can be derived from any prime number at certain numeric systems. Cyclic prime numbers are also related to the cyclic numbers and full reptend prime…