Aklilu Zeleke

Tempered fractional time series model for turbulence in geophysical flows

We propose a new time series model for velocity data in turbulent flows. The new model employs tempered fractional calculus to extend the classical 5/3 spectral model of Kolmogorov. Application to wind speed and water velocity in a large lake are presented, to demonstrate the practical utility of the model.

Summation identities for representation of certain real numbers

We present identities used to represent real numbers of the form xum±yvn for appropriately chosen real numbers x, y, u, v and nonnegative integers m and n. We present the proofs of the identities by applying Zeilbergers algorithm.

Starting and Sustaining an Undergraduate Research Program: The SURIEM Experience at Michigan State University

Abstract Mentoring undergraduate students in research is both rewarding and challenging. In this paper we present how we established a summer Research Experience for Undergraduates (REU) program in the mathematical sciences at Michigan State University. A goal of our REU is to include students who are at an early stage of their study of mathematics. We share our experiences in recruiting students, designing research projects, and mentoring our participants. We discuss the challenges we faced and the solutions we found while working with a diverse group of undergraduate students from across the nation.

Extending the Constant Coefficient Solution Technique to Variable Coefficient Ordinary Differential Equations.

Abstract We introduce a class of second-order ordinary differential equations (ODEs) with variable coefficients whose closed-form solutions can be obtained by the same method used to solve ODEs with constant coefficients. General solutions for the homogeneous case are discussed.

Freshman rules in calculus

In this note we present a class of functions (f, g) that satisfy ‘freshman rules’ in calculus.