Journal of Prime Research in Mathematics

Abstract: Let K = Q(θ), where θ = √6 d, be a pure sextic field with d ̸= 1 a square free integer. In this paper, we characterize completely whether {1, θ, . . . , θ5} is an integral basis of K or do not. When d ̸≡ ±1, ±17, ±10, −15, −11, −7, −3, 5, 13(mod 36) we prove that K has a power integral basis. Furthermore, for the other cases we present an integral basis.

Abstract: Topological indices are extensively used for establishing relationship between the chemical structure and their physico-chemical properties. Motivated by chemical applications of topological indices in the QSPR/QSAR analysis, we introduce a new topological indices that we call, second BM Index and fourth BM Index, is denoted by BM2(G) and BM4(G). Also we introduce second and fourth BM polynomials and is denoted by BM2(G, x) and BM4(G, x). In this paper, BM2(G) and BM4(G) is tested with physico-chemical properties of octane isomers such as entropy, acentric factor, enthalpy of vaporization (HVAP) and standard enthalpy of vaporization (DHVAP) using the linear models. The BM2(G) and BM4(G) shows excellent correlation with these chemical properties. Specially, BM2(G) and BM4(G) highly correlates with acentric factor (coefficient of correlation 0.9906546 and 0.9783643). Furthermore, we obtain BM2(G), BM4(G) indices and BM2(G, x), BM4(G, x) polynomials of dominating oxide network, regular triangulate oxide network, H-Naphtalenic nanotubes and nanocones of molecular graphs

Abstract: The key task of this paper is to investigate a nonlinear fourth-order delay differential equation. By virtue of the fixed point theory and the Green’s functions method, we establish some new results on the existence, uniqueness and continuous dependence on parameters of periodic solutions. In addition, an example is given to corroborate the validity of our main results. Up to now, no work has been carried out on this topic. So, the findings of this paper are new and complement the available works in the literature to some degree.

Abstract: In this paper, authors have established Chen’s inequalities for the submanifolds of quaternionic Kaehler manifolds characterized by Ricci quarter-symmetric metric connection. Other than these inequalities, generalized normalized Casorati curvature inequalities have been derived.

Abstract: One of the fundamental issues in engineering, computer graphics, data visualization, interpolation and many more areas is to create a shape preserving surface from supplied data points. Data can be characterized as convex, monotone and positive. This research focuses on developing new smooth and efficient shape preserving schemes for convex, monotone and positive 3D data set positioned on a rectangular mesh. For this purpose, a GC1 continuous cubic function with two free parameters have been advanced to GC1 bicubic coons surface patches. There are eight free shape parameters in each rectangular patch which are constrained to ascertain these intrinsic data attributes that is convexity, positivity and monotonicity. The proposed interpolant governs the shape of data locally and data dependent constraints on shape parameters manage the shape preservation. Moreover, proposed scheme is verified and demonstrated graphically

Abstract: This paper proposes a new semi-analytical method known as the variational iteration transform method (VITM) to obtain the solutions of the nonlinear Caputo–Fabrizio fractional partial differential equations arising in applied mathematics. For nonlinear equations in general, there is no method that gives an exact solution and, therefore, only approximate analytical solutions can be derived by using procedures such as linearization or perturbation. This method is combined form of the Aboodh transform and the variational iteration method. The advantage of VITM is the simplicity of the computations and the non-requirement of linearization or smallness assumptions. Moreover, this method enables us to overcome the difficulties arising in identifying the general Lagrange multiplier. For further illustrations of the efficiency and reliability of VITM, some numerical applications are pesented. The numerical results showed that the proposed method is efficient and precise to obtain the solutions of nonlinear fractional partial differential equations.