Thin basement membrane nephropathy (TBMN) or benign familial hematuria, is one of the commonest kidney disorders, characterized by recurrent benign hematuria, which is often associated with a family history (Gregory, 2005). It is generally considered to be a nonprogressive, life long disorder with a rather benign course (Tryggvason & Patrakka, 2006), although data from some studies show that a ...

We present an operator approach to Rogers-type formulas and Mehler’s formulas for the Al-Salam-Carlitz polynomials Un(x, y, a; q). By using the q-exponential operator, we obtain a Rogers-type formula which leads to a linearization formula. With the aid of a bivariate augmentation operator, we get a simple derivation of Mehler’s formula due to AlSalam and Carlitz. By means of the Cauchy companio...

This paper considers a variety of parity questions connected with classical partition identities of Euler, Rogers, Ramanujan and Gordon. We begin by restricting the partitions in the Rogers-Ramanujan-Gordon identities to those wherein even parts appear an even number of times. We then take up questions involving sequences of alternating parity in the parts of partitions. This latter study leads...

We reexamine Alan R. Rogers’ (1994) analysis of the biological basis of the rate of time preference. Although his basic insight concerning the derivation of the utility function holds up, the functional form he uses does not generate equilibrium evolutionary behavior. Moreover, Rogers relies upon an interior solution for a particular kind of intergenerational transfer. We show such interior sol...

On page 26 in his lost notebook, Ramanujan states an asymptotic formula for the generalized Rogers–Ramanujan continued fraction. This formula is proved and made slightly more precise. A second primary goal is to prove another continued fraction representation for the Rogers–Ramanujan continued fraction conjectured by R. Blecksmith and J. Brillhart. Two further entries in the lost notebook are e...