News and Events

The purpose of the weekly departmental colloquium is to present research topics and/ or projects in Mathematics, Statistics, Computer Science, Mathematics Education or for sharing new and innovative ideas in teaching Mathematics and Computer Science courses. The colloquium is open for everyone. Please encourage your students to attend and to give presentations.

Finite number of orthonormal basis in a generalized Bergman space to approximate a γ-regular function.

Dejenie Lakew

Department of Mathematics & Computer Science

Virginia State University

Abstract

We will construct a finite number of orthonormal functions in the generalized Bergman space W_Γ^2,k(Ω,Cl_n) ∩ Ker D_γ which are used as basis to approximate a γ-regular function.

Analysis of Time Resolved Fluorescence Using a Laguerre Basis^*

Camisha C. Parker (Graduate student)

Department of Mathematics & Computer Science

Virginia State University

^*This research is supported by the Food and Drug Administration, Center for Devices and Radiological Health in Rockville, MD.

Continuous as well as discrete Laguerre functions form a complete orthogonal basis in a

Hilbert space and therefore have been used ex  tensively in non-parametric modeling of

nonlinear biological systems such as time-resolved fluorescence of cells and tissues. The

approach is based on Volterra-Weiner theory. One of the techniques to investigate the system behavior is to represent it in terms of a Laguerre basis and use nonlinear least squares minimization

obtained by an iterative scheme.  This method is applied to the deconvolution of inherent fluorophore characteristics from nanosecond-scale time-resolved fluorescence decay curves

which contain significant noise levels.  The ability of this approach to resolve small changes in

a noisy system is compared to that of conventional multiexponential method.

A Simple Mathematical Model of the Blood Glucose Regulatory System 

McCarthy Anum-Addo (Undergraduate student)
Department of Mathematics & Computer Science
Virginia State University

Auto-regulation of glucose concentration is explained by a system of first order differential equations using Ackerman et al model which describes the blood regulatory system during a

glucose tolerance test. Synthetic data will be used to distinguish normal individuals from mild diabetics and pre-diabetics. The purpose of this numerical investigation is to understand metabolic/endocrine system and dynamic relationship between glucose and insulin. The theory of mechanical vibrations & non-linear least squares are used as mathematical tools. Numerical computations are done with the help of MATLAP curve fitting toolbox.

A  LaGrange - like Theorem for the Variety of Harmonic Groupoids

Raymond R.  Fletcher III

Department of Mathematics & Computer Science

Virginia State University

Abstract

            A harmonic groupoid is a set H together with a binary operation * defined on H, which  satisfies the axioms:

(1) x * x = x

2) x * y = y * x

(3) (x * y) * (z * w) = (x * z) * ( * w) and

(4) If x * y = x * z then   y = z. 

If we define * on the positive real numbers by x * y = 2xy/(x + y) we obtain a harmonic groupoid. The expression 2xy/(x + y) is the harmonic mean of the real numbers x and y.  If we define * on the set of all real numbers by x * y = (x + y)/2, (the usual mean of x and y), we also obtain a harmonic groupoid. Finite models can also be constructed, and we will show that these must have odd order, and that a finite harmonic groupoid exists of every odd order. If S is a subalgebra of a finite harmonic groupoid H, we shall prove a result analogous to the Theorem of LaGrange for finite groups, namely that |S| must divide |H|.

Additive Preconditioning and Aggregation in Matrix Computations

Mohammad Tabanjeh

Department of Mathematics & Computer Science

Virginia State University

Abstract

Multiplicative preconditioning is a popular tool for handling linear system of equations, but it requires some information about the SVD of the coefficient matrix. We propose additive preconditioners, which are more readily available and better preserve matrix structure. We combine additive preconditioning with aggregation, iterative refinement, and advanced floating-point summation and multiplication to facilitate the solution of linear systems of equations and other fundamental matrix computations. Our extensive analysis and numerical experiments show the power of our algorithm, guide us in selecting most effective policies of preconditioning and aggregation, and provide some new insights into these and related subjects of matrix computations.