Asian Research Journal of Mathematics

The analysis of the dynamic buckling of a clamped finite imperfect viscously damped column lying on a quadratic-cubic elastic foundation using the methods of asymptotic and perturbation technique is presented. The proposed governing equation contains two small independent parameters (δ and ϵ) which are used in asymptotic expansions of the relevant variables. The results of the analysis show that the dynamic buckling load of column decreases with its imperfections as well as with the increase in damping. The results obtained are strictly asymptotic and therefore valid as the parameters δ and ϵ become increasingly small relative to unity.

In this paper, some inequalities involving the extension of k-gamma function are presented. Consequently, some previous results are recovered as particular cases of the present results.

In this work we define Magic Polygons P(n, k) and Degenerated Magic Polygons D(n, k) and we obtain their main properties, such as the magic sum and the value corresponding to the root vertex. The existence of magic polygons P(n, k) and degenerated magic polygons D(n, k) are discussed for certain values of n and k.

In this problem, an examination of Casson Nanofluid boundary layer flow over linear slanted extending sheet by fusing the chemical reaction and heat generation impacts are under thought. Nanofluid demonstrate in this examination is developed on Buongiorno model for the thermal efficiencies of the liquid flow in the presence of Brownian movements and thermophoresis impacts. The nonlinear issue for Casson Nanofluid flow over slanted channel is displayed to ponder the heat and mass exchange wonder by considering portant flow parameters to strengthen the boundary layers. The governing nonlinear partial differential equations are decreased to nonlinear normal differential equations and afterward illustrated numerically by methods for the Keller-Box plot. An examination of the set up results in the absence of the joined impacts is performed with the accessible outcomes of Khan and Pop [1] and set up in a decent contract. Numerical and graphical outcomes are additionally exhibited in tables and graphs.

In this paper, we present linear summation formulas for generalized Hexanacci numbers and generalized Gaussian Hexanacci numbers. Also, as special cases, we give linear summation formulas of Hexanacci and Hexanacci-Lucas numbers; Gaussian Hexanacci and Gaussian Hexanacci-Lucas numbers. We present the proofs to indicate how these formulas, in general, were discovered. In fact, all the listed formulas may be proved by induction, but that method of proof gives no clue about their discovery.