In this paper, we develop two new theorems relating to the series of floor and ceiling functions. We then use these more than forty distinct novel results. Furthermore, provide specific cases for corollaries which show that our results constitute a generalisation currently available such as summation first n Fibonacci numbers Pascal’s identity. Finally, three miscellaneous examples showcase vas...

In this paper, non-polynomial spline method for solving Coupled Burgers Equations are presented. We take a new spline function. The stability analysis using Von-Neumann technique shows the scheme is unconditionally stable. To test accuracy the error norms 2L, L are computed and give two examples to illustrate the sufficiency of the method for solving such nonlinear partial differential equation...

This paper is a survey of recent contributions to and developments in the relationship between efficiency and productivity via the production function. The objective is to provide a brief discussion on data and on the methods of measuring efficiency and productivity. First, we introduce the reader to the measurement of partial and total factor productivity in the context of static and firm - sp...

This paper proposes a novel exponential rational function method, modification of the well-known exp-function to find exact solutions time fractional Cahn-Allen equation and Phi-4 equation. The solution procedure is reduced solve system algebraic equations, which then solved by Wu?s method. results show that present method effective, can be applied other differential equations.