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May 21, 2020Open AccessArticle
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
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 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 ...
Jun 27, 2016Open AccessArticle
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)} ...
Dec 31, 2015Open AccessArticle
For a given positive irrational  and a real t ∈ [ 0, 1), the explicit
construction of a sequence  of positive
integers, such that the sequence of fractional parts of products ...
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