OALib Journal
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May 21, 2020Open    AccessArticle

Schultz and Modified Schultz Polynomials of Vertex Identification Chain for Square and Complete Square Graphs

Mahmood M. Abdullah, Ahmed M. Ali
In this paper, we find the polynomials, indices and average distance for Schultz and modified Schultz of vertex identification chain for 4-cycle and 4- cycle complete.


Mar 23, 2020Open    AccessArticle

Shape of Numbers and Calculation Formula of Stirling Numbers

Ji Peng
This article investigated the idea of Shape of numbers and introduced new operators. The idea divides all products of k distinct integers in [1, n ? 1] into 2K?1 catalogs and derives the calculation formula of every catalog. As a simple deduction, a direct formula of the Stirling numbers of the first kind S1(n, n ? k) and a simple recursive formula of Stirling numbers of the second kind S2(n, n ? k) are obtained. By analyzing the Shape of numbers, new congruence formulas are obtained.


Sep 02, 2016Open    AccessArticle

A Power Law Governing Prime Gaps

Raul Matsushita, Sergio Da Silva
A prime gap is the difference between two successive prime numbers. Prime gaps are casually thought to occur randomly. However, the “k-tuple conjecture” suggests that prime gaps are non-random by estimating how often pairs, triples and larger groupings of primes will appear. The k-tuple conjec
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Jun 27, 2016Open    AccessArticle

Log-Concavity of Centered Polygonal Figurate Number Sequences

Fekadu Tolessa Gedefa
This paper investigates the log-concavity of the centered m-gonal figurate number sequences. The author proves that for m≥3, the sequence {Cn(m)}
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Dec 31, 2015Open    AccessArticle

Constructing a Subsequence of (Exp(in))n∈N Converging towards Exp(iα) for a Given α∈R

Vito Lampret
For a given positive irrationaland a real ∈ [0,1), the explicit construction of a sequence of positive integers, such that the sequence of fractional parts of products ...


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