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Abstract. In this paper, we study unconditionally secure codes that provide authentication without secrecy.

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We study the discrete and discrete fractional representation of a pharmacokinetics - pharmacodynamics (PK-PD) model describing tumor growth and anti-cancer effects in continuous time considering a time scale $h\mathbb{N}_0^h$, where h > 0. Since the measurements of the tumor volume in mice were taken daily, we consider h = 1 and obtain the model in discrete time (i.e. daily). We then continue with fractionalizing the discrete nabla operator to obtain the model as a system of nabla fractional difference equations. The nabla fractional difference operator is considered in the sense of Riemann-Liouville definition of the fractional derivative. In order to solve the fractional discrete system analytically we state and prove some theorems in the theory of discrete fractional calculus. For the data fitting purpose, we use a new developed method which is known as an improved version of the partial sum method to estimate the parameters for discrete and discrete fractional models. Sensitivity analysis is conducted to incorporate uncertainty/noise into the model. We employ both frequentist approach and Bayesian method to construct 90 percent confidence intervals for the parameters. Lastly, for the purpose of practicality, we test the discrete models for their efficiency and illustrate their current limitations for application.

An (n, m, w)-perfect hash family is a set of functions F such thatfor each f E F, and for any X { 1, . . . , n } such that (XI = w, there exists at least one f E F such that flx is one-to-one. Perfect hash families have been extensively studied by computer scientists for over 15 years, mainly due to their applications in database management. In particular, much attention has been given to finding efficient algorithms to construct perfect hash families. In this article, we study perfect hash families from a combinatorial viewpoint, and describe some new recursive constructions for these objects. 0 1996 John Wiley & Sons, Inc.