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Full-Text Articles in Education
On The Simplification Of Certain Q-Multisums, Andrew Sills
On The Simplification Of Certain Q-Multisums, Andrew Sills
Department of Mathematical Sciences Faculty Publications
Some examples of naturally arising multisum q-series which turn out to have representations as fermionic single sums are presented. The resulting identities are proved using transformation formulas from the theory of basic hypergeometric series.
Bounds And Comparisons For Weighted Renewal-Type Integral Equations, Broderick O. Oluyede
Bounds And Comparisons For Weighted Renewal-Type Integral Equations, Broderick O. Oluyede
Department of Mathematical Sciences Faculty Publications
In this note, inequalities and bounds for weighted renewal-type integral equations are presented. Some upper and lower bounds for the weighted renewal-type integral equations with monotone weight functions are derived. Some upper and lower bounds for the weighted renewal-type equations with monotone weight functions are derived. Bounds for the difference between two weighted renewal functions as well between the parent and weighted renewal functions are obtained in terms of the parent renewal reliability functions and their first and second moments. Relations for renewal-type integrals of the ruin probability are presented. Some inequalities, bounds and convergence results are also established.
On Energy And Expected Uncertainty Measures In Weighted Distributions, Broderick O. Oluyede, Mekki Terbeche
On Energy And Expected Uncertainty Measures In Weighted Distributions, Broderick O. Oluyede, Mekki Terbeche
Department of Mathematical Sciences Faculty Publications
In this note, bounds and inequalities for the comparisons of weighted energy functions, entropy, and discrimination information measures and their unweighted counterparts are presented. Inequalities for weighted expected uncertainty, cross-entropy or discrimination information measures are also presented. A useful result on the convergence of the weighted kernel density informational energy estimates is given and some informational energy applications presented.
Closure Under Transfinite Extensions, Edgar Enochs, Alina Iacob, Overtoun Jenda
Closure Under Transfinite Extensions, Edgar Enochs, Alina Iacob, Overtoun Jenda
Department of Mathematical Sciences Faculty Publications
The closure under extensions of a class of objects in an abelian category is often an important property of that class. Recently the closure of such classes under transfinite extensions (both direct and inverse) has begun to play an important role in several areas of mathematics, for example, in Quillen's theory of model categories and in the theory of cotorsion pairs. In this paper we prove that several important classes are closed under transfinite extensions.
A Note On Relations For Reliability Measures In Zero-Adjusted Models, Broderick O. Oluyede, Mavis Pararai
A Note On Relations For Reliability Measures In Zero-Adjusted Models, Broderick O. Oluyede, Mavis Pararai
Department of Mathematical Sciences Faculty Publications
In this note we examine and study relations in zero-adjusted models. Relations for reliability measures in the adjusted and unadjusted models are established and appropriate comparisons including the relative error are presented. The relative error is shown to be a decreasing function of the counts. Some inequalities and comparisons for weighted zero-adjusted models are established.