Open Access Original Research Article

Dynamic Buckling of a Clamped Finite Column Resting on a Non – linear Elastic Foundation

E. Julius, Bassey, M. Anthony, Ette, U. Joy, Chukwuchekwa, C. Atulegwu, Osuji

Asian Research Journal of Mathematics, Page 1-47
DOI: 10.9734/arjom/2019/v14i430132

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.

Open Access Original Research Article

Open Access Original Research Article

Magic Polygons and Degenerated Magic Polygons: Characterization and Properties

Danniel Dias Augusto, Josimar da Silva Rocha

Asian Research Journal of Mathematics, Page 1-18
DOI: 10.9734/arjom/2019/v14i430134

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.

Open Access Original Research Article

Keller-box Study on Casson Nano Fluid Flow over a Slanted Permeable Surface with Chemical Reaction

Khuram Rafique, Muhammad Imran Anwar, Masnita Misiran

Asian Research Journal of Mathematics, Page 1-17
DOI: 10.9734/arjom/2019/v14i430135

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.

Open Access Original Research Article

On Summing Formulas of Generalized Hexanacci and Gaussian Generalized Hexanacci Numbers

Yüksel Soykan

Asian Research Journal of Mathematics, Page 1-14
DOI: 10.9734/arjom/2019/v14i430136

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.