Journal of Prime Research in Mathematics

Abstract: We study the composition of F. R. Cohen’s map B_n → B_nk with the standard representation of B_nk, where B_n is the braid group on n strings. We prove that the obtained representation of B_n is isomorphic to the direct sum of k copies of the standard representation of B_n. A similar work is done for the welded braid group 𝓌B_n.

Abstract: Consider the Diophantine equation 2^x + 2^y = z², where x, y and z are nonnegative integers. As thisequation has infinitely many solutions, in this paper we study its solutions in case where the unknowns represent Fibonacci and/or Lucas numbers. In other words, we completely resolve the equation in case of (x, y, z) ∈ {(F_i, F_j , F_k),(F_i, F_j ,L_k),(L_i,L_j ,L_k),(L_i,L_j , F_k),(F_i,L_j ,L_k),(F_i,L_j , F_k)} with i, j, k ≥ 1 and F_n and L_n denote the general terms of Fibonacci and Lucas numbers, respectively.

Abstract: Carbon nanotubes are widely used in various fields such as composites, energy devices, electronic applications, and medical applications. The most commonly used nanotubes and nanotubes are V -phenylenic nanotubes and nanotori. Topological analysis of a molecule involves translating its molecular structure into a unique number. In this article, Sombor indices for molecular graph, line graph, and subdivision graph of the V -phenylenic nanotubes and nanotori are calculated.

Abstract: In this article, we study the split equality problem involving nonexpansive semigroup and convex minimization problem. Using a Halpern iterative algorithm, we establish a strong convergence result for approximating a common solution of the aforementioned problems. The iterative algorithm introduced in this paper is designed in such a way that it does not require the knowledge of the operator norm. We display a numerical example to show the relevance of our result. Our result complements and extends some related results in literature.

Abstract: Epidemics was always great problems in the human history and mathematicians have been challenged to bring their contribution to the management of epidemics, by using their abstract concepts in studying and forecasting their evolution. Compartmental models, have been remarkable for analysis the spread of epidemics. This paper has three objectives: to purpose a multi-group SEIRV epidemic model for studying the spread of an epidemics, to present conditions of existence for a solution to the purposed generalized SEIRV model and an example of simulations. The principal conclusion is that, the theory of fixed points can be used for the analysis of epidemics. The results of this paper adapt the results obtained in (Bucur, 2022, in International Journal of Advance Study and Research Work (IJASRW) 5(11)) and in (Guran, Bota and Naseem, 2020, in Symmetry 12, 856) to a generalization of the SEIR model.

Abstract: An inner dual graph of a planar rigid benzenoid (hexagonal) system is a subgraph of the triangular lattice with the constraint that any two adjacent faces in the corresponding hexagonal system must be connected via an edge in the inner dual. The maximum degree of any vertex in an inner dual graph of a hexagonal system is 6. In contrast with the already existing algorithms in the literature that are used to check a given degree sequence to be graphically realizable, in this paper, we use a a simple technique to check the realizable degree sequences of inner dual graphs of benzenoid systems that form a rich class of molecular graphs in theoretical chemistry. We restrict the maximum degree to 3 and identify, by providing necessary and sufficient conditions on the values of α, β and γ, all the degree sequences of the form d = (3α, 2β, 1γ) that are graphically (inner dual of planar rigid hexagonal system) realizable. That is, we provide general constructions of the graphs (inner dual of planar rigid hexagonal system) realizing the degree sequences of the form d = (3α, 2β, 1γ).