The center conjecture for non-exceptional buildings

We prove the center conjecture for spherical buildings of non-exceptional type. Our proof uses the point-line spaces associated with these buildings.     

Potential theory of infinite dimensional Lévy processes

We study the potential theory of a large class of infinite dimensional Lévy processes, including Brownian motion on abstract Wiener spaces. The key result is the construction of compact Lyapunov functions, i.e., excessive functions with compact level sets. Then many techniques from classical potential theory carry over to this infinite dimensional setting. Thus a number of potential theoretic properties and principles can be proved, answering long standing open problems even for the Brownian motion on abstract Wiener space, as, e.g., formulated by R. Carmona in 1980. In particular, we prove the analog of the known result, that the Cameron-Martin space is polar, in the Lévy case and apply the technique of controlled convergence to solve the Dirichlet problem with general (not necessarily continuous) boundary data.     

Universality properties of Taylor series inside the domain of holomorphy

It is proven that the Taylor series of functions holomorphic in C_∞?{1} generically have certain universality properties on small sets outside the unit disk. Moreover, it is shown that such sets necessarily are polar sets.     

Generating Birth and Death Processes

Associated with an ordered sequence of an even number 2N of positive real numbers is a birth and death process (BDP) on {0, 1, 2,…, N} having these real numbers as its birth and death rates. We generate another birth and death process from this BDP on {0, 1, 2,…, 2N}. This can be further iterated. We illustrate with an example from tan(kz). In BDP, the decay parameter, viz., the largest non-zero eigenvalue is important in the study of convergence to stationarity. In this article, the smallest eigenvalue is found to be useful.     

Flat Power Series over a Finite Field

We define and describe a class of algebraic continued fractions for power series over a finite field. These continued fraction expansions, for which all the partial quotients are polynomials of degree one, have a regular pattern induced by the Frobenius homomorphism.This is an extension, in the case of positive characteristic, of purely periodic expansions corresponding to quadratic power series.     

On the convergence of continued fractions at Runckel’s points

We consider the limit periodic continued fractions of Stieltjes type

An M/M/1 Driven Fluid Queue – Continued Fraction Approach

This paper presents complete solutions of the stationary distributions of buffer occupancy and buffer content of a fluid queue driven by an M/M/1 queue. We assume a general boundary condition when compared to the model discussed in Virtamo and Norros [Queueing Systems 16 (1994) 373–386] and Adan and Resing [Queueing Systems 22 (1996) 171–174]. We achieve the required solutions by transforming the underlying system of differential equations using Laplace transforms to a system of difference equations leading to a continued fraction. This continued fraction helps us to find complete solutions. We also obtain the buffer content distribution for this fluid model using the method of Sericola and Tuffin [Queueing Systems 31 (1999) 253–264].     

On an Inequality of Pual Turan Concerning Polynomials-Ⅱ

Let P(z) be a polynomial of degree n and for any complex number α, let D_αP(z) = nP(z)+(α- z) P′(z) denote the polar derivative of the polynomial P(z) with respect to α. In this paper, we obtain inequalities for the polar derivative of a polynomial having all zeros inside a circle. Our results shall generalize and sharpen some well-known results of Turan, Govil, Dewan et al. and others.