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May 09, 2022Open AccessArticle
Because of the growing role of Binomial Theorem in various fields in Mathematics, such as in calculus and number theory, and even in societal advancements, such in technology and business, mathematicians continue to explore new developments in this interesting theorem. In this case, this study explored some of the unveiled concepts of Binomial Theorem for further studies, specifically on observing the relationships of the indices of the binomials to obtaining oddvalued binomial coefficients. Us...
Jun 15, 2020Open AccessArticle
The Stirling numbers of second kind and related problems are widely used in combinatorial mathematics and number theory, and there are a lot of research results. This article discuss the function:
∑A^{C1}_{1} A^{C2}_{2} ···A^{Ck}_{k} (C_{1} C_{2} ·· ...
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 4cycle and 4 cycle complete.
Aug 27, 2019Open AccessArticle
For a connected graph G, the Schultz and modified Schultz polynomials are defined as, respectively, where the summations are taken over all unordered pairs of distinct vertices in V(G), is the degree of vertex u, is the distance between u and v and V(G) is the vertex set of G. In this paper, we find Schultz and modified Schultz polynomials of the Cogspecial graphs such as a complete graph, ...
Dec 20, 2017Open AccessArticle
We introduce a derivative of a relation over the ring of integers modulo an odd number which is based on the very fundamental concepts which helped in the evolution of derivative of a function over the real number field, namely slope. Then, for a prime field GF(p ...
Oct 17, 2016Open AccessArticle
Stock market networks
commonly involve uncertainty, and the theory of soft sets emerges as a powerful
tool to handle it. In this study, we present a soft analogue of the
differential of a vibrational potential function acting on a stock market
network as vibrational force. For this purpose, we first study the vibrational
potential function operating on each vertex by using the Laplacian of the
neighborhood graph, then applied the ...
Jun 27, 2016Open AccessArticle
This paper investigates the logconcavity of the centered mgonal figurate number sequences. The author proves that for m≥3, the sequence {C_{n}(m)} ...
May 19, 2015Open AccessArticle
The paper proposes a logical model of combinatorial problems; it also
gives an example of a problem of the class NP that cannot be solved in
polynomial time on the dimension of the problem.
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