Using the new generalized exp-function method, we were able to derive significant novel closed form solutions nonlinear dispersive modified Benjamin–Bona–Mahony (DMBBM) equation. The general framework of method has been given. Many have obtained in hyperbolic, trigonometric, and rational function solutions. computer application Wolfram Mathematica 10, plotted 2D, 3D, contour surfaces found this...

also known as the diffusion equation, describes in typical applications of the evolution in time of the density u u x, t of some quantities such as heat and chemical concentration 1, page 44 . In this case, the thermal diffusivity and thermal conductivity of the medium are assumed to be constant. However, in some media such as gases, the parameters are proportional to the temperature of the med...

Let m, q > 1 be two integers that are co-prime and A be any subset of Zm. Let P be any multi-variate polynomial of degree d in n variables over Zm. We show that the MODq boolean function on n variables has correlation at most exp(−Ω(n/(m2 ))) with the boolean function f defined by f(x) = 1 iff P (x) ∈ A for all x ∈ {0, 1}. This improves on the bound of exp(−Ω(n/(m2))) obtained in the breakthrou...

Up to now, the known derandomization methods for BPP have been derived assuming the existence of an ExP function that has a "hard" average-case circuit complexity. In this paper we instead present the first construction of a de-randomization method for BOP that relies on the existence of an EXP function that is hard only in the worst-case. The construction is based on a new method that departs ...

Abstract In this work, we investigate the solutions of (2+1)-dimensional Bogoyavlenskii-Kadomtsev-Petviashvili (BKP) equation by three powerful analytical methods: $$\exp _{a}$$ exp a function method, $$(\frac{G'}{G})$$ ( <mml:msu...

Background: Male factors, mainly spermatogenesis disorder, are responsible for 20-30% of infertility occurs in different societies. One of the known causes of spermatogenesis disorder is chemotherapy in patients with cancer. The side effect of chemotherapic agents may last from 10 years up to the end of the life. Since dividing cells are mainly affected by anticancer drugs, the aim of the prese...

For simplicity, we adopt the following convention: a, x denote real numbers, n denotes a natural number, A denotes a closed-interval subset of R, f , f1 denote partial functions from R to R, and Z denotes an open subset of R. One can prove the following propositions: (1) Suppose Z ⊆ dom((the function sec) · 1 idZ ). Then (i) −(the function sec) · 1 idZ is differentiable on Z, and (ii) for every...