Related papers: Does the Zeraoulia Sequences Converges?
We extend previous work on anti-recurrence sequences of Kimberling and Moses, Zaslavsky, and Bosma et al. Kimberling and Moses have formulated several questions on these sequences, which can be combined into the meta-conjecture that…
In this paper we formally define the family of sequences know as "Pea Pattern". We then analyse its behaviour and conditions for fixed and periodic points. The paper ends with a list of fixed points and cycles.
We establish supercongruences for two kinds of Ap\'ery-like numbers, which involve Bernoulli numbers and Bernoulli polynomials. Conjectural supercongruences of the same type for another four kinds of Ap\'ery-like numbers are also proposed.
In this paper, a theory of quandle rings is proposed for quandles analogous to the classical theory of group rings for groups, and interconnections between quandles and associated quandle rings are explored.
The Stirling numbers of the first kind can be represented in terms of a new class of polynomials that are closely related to the Bernoulli polynomials. Recursion relations for these polynomials are given.
We give a survey on the concept of Poissonian pair correlation (PPC) of sequences in the unit interval, on existing and recent results and we state a list of open problems. Moreover, we present and discuss a quite recent multi-dimensional…
Convergent sequences of real numbers play a fundamental role in many different problems in system theory, e.g., in Lyapunov stability analysis, as well as in optimization theory and computational game theory. In this survey, we provide an…
Most of the assertions in the theory of well ordered sets are quite simple. However, one of its central statements, Zermelo's theorem, stands out of this rule, for its well-known proofs are rather complicated. The aim of the current paper…
The present status of Unified Theories is summarized with special emphasis on their possible experimental tests. Outline: i) Unification of couplings; ii) Where can a positive signal come from? iii) HERA anomaly and Unification; iv) Recent…
In this paper, we focus on the topic Synchronization and consensus of Complex Networks and their relationships. It is revealed that two topics are closely relating to each other and all results given in \cite{Li} can be obtained by the…
We generalize the tree-confluent graphs to a broader class of graphs called Delta-confluent graphs. This class of graphs and distance-hereditary graphs, a well-known class of graphs, coincide. Some results about the visualization of…
We briefly review superstring theories, highlighting the important concepts, developments, and open problems of the subject.
In a recent proof of the log-concavity of genus polynomials of some families of graphs, Gross et al. defined the weakly synchronicity relation between log-concave sequences, and conjectured that the convolution operation by any log-concave…
While Liouvillian sequences are closed under many operations, simple examples show that they are not closed under convolution, and the same goes for d'Alembertian sequences. Nevertheless, we show that d'Alembertian sequences are closed…
We investigate exactness of long sequences of homology semimodules associated to Schreier short exact sequences of chain complexes of semimodules.
Here we have introduced the idea of rough convergence of sequences in a cone metric space. Also it has been investigated how far several basic properties of rough convergence as valid in a normed linear space are affected in a cone metric…
We survey the state of the union-closed sets conjecture.
The following general idea looks crazy. What if another integer sequence follows each integer sequence like a shadow? I will demonstrate that this is indeed the case, perhaps not for every integer sequence, but for many of them.
Collatz Conjecture sequences increase and decrease in seemingly random fashion. By identifying and analyzing the forms of numbers, we discover that Collatz sequences are governed by very specific, well-defined rules, which we call cascades.
This is a short review article in which we discuss and summarize the works of various researchers over past four decades on Zeeman topology and Zeeman-like topologies, which occur in special and general theory of relativity. We also discuss…