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May 30, 2022Open Access
This work presents a scalar self-consistent quantum model for molecular simulation. This model employs Bäcklund transformations to eliminate the wave function from Klein-Gordon and Schrödinger-type equations. The nonlinear PDE obtained after coupling the quantum model with the Gauss law of electromagnetism contains only the interaction potential. The analytical solutions obtained reproduce some relevant effects related to the evolution of the electronic clouds induced by nonlinear scat...
May 09, 2022Open Access
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 odd-valued binomial coefficients. Us...
Jun 15, 2020Open Access
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:
∑AC11 AC22 ···ACkk (C1 C2 ·· ...
May 21, 2020Open Access
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.
Aug 27, 2019Open Access
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 Cog-special graphs such as a complete graph, ...
Dec 20, 2017Open Access
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 Access
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 Access
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)} ...
May 19, 2015Open Access
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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