In this paper, we first show that the exponential Diophantine equation 2x + 1 = z2has unique solution (x, z) (3, 3). We then for n > 1, exponential. M 2y z2 where Mn := 2n − is nth Mersenne number, has exactly two solutions in non-negative integers viz., 0, 3) and (n 2, 1). Also, prove w4 y, w, n) (5, 3, . Finally, w2m, m 2 no integral solutions. conclude with some examples to illustrate our...

hf level of ab initio calculations with basis-set 6-31g including full counterpoise correction hasbeen applied to compute the asphis potential with the ser and hisser potential with the asp inasphisser trimer. the potential energy surface has a minimum of -16.765 kcal/mol in r1=1.912nm and r2=2.719 nm. the optimum computed curves for two interactions were fitted withintermolecular pair potentia...

  Spreading and coating of nano and micro droplets on solid surfaces is important in a wide variety of applications including plasma spray coating, ink jet printing, DNA synthesis and etc. In spraying processes, most of droplets collide obliquely to the surface. The purpose of this article is to study the distribution of nano and micro droplets spreading when droplets impact at an oblique a...

This paper deals with the initial boundary value problem of Petrovsky type equation degenerate damping. Under some appropriate conditions, we study finite time blow up and exponential growth solutions negative energy.