Hessel de Vries contributed to radiocarbon (14C) dating for only one short decade. Yet, his development of proportional CO2 counting greatly facilitated 14C measurements, improved their reproducibility, and lowered both the amount of carbon needed for a measurement and the 14C detection limit by at least a factor ten. Validating Libby’s 14C method by checking its basic assumptions with improved sensitivity, de Vries documented relatively minor violations. Natural variations in atmospheric 14C concentrations, found in tree rings, marked the start of 14C tree-ring calibration. Variable differences in 14C concentration between the atmosphere and aquatic reservoirs revealed reservoir ages, leading to further studies. De Vries applied analogue modeling to gain a better understanding of the influence of cosmogenic 14C production and the global carbon cycle, inclusive CO2 exchange across the air-water boundary, on atmospheric 14C concentrations. In close collaboration with colleagues in archaeology and geology, de Vries documented climate fluctuations and archaeological developments over the last 50,000+ years and placed them on a common 14C time scale.

In this paper we use a simple transient Markov process with an absorbing point to investigate the qualitative behavior of a large-scale storage network of nonreliable file servers across which files can be duplicated. When the size of the system goes to ∞, we show that there is a critical value for the maximum number of files per server such that, below this quantity, most files have a maximum number of copies. Above this value, the network loses a significant number of files until some equilibrium is reached. When the network is stable, we show that, with convenient time scales, the evolution of the network towards the absorbing state can be described via a stochastic averaging principle.

In this paper, some criteria for the existence of positive solutions of a class of systems of impulsive dynamic equations on time scales are obtained by using a fixed point theorem in cones.

This paper is mainlyconcerned with a class of optimal control problems of systemsgoverned by the nonlinear dynamic systems on time scales.Introducing the reasonable weak solution of nonlinear dynamicsystems, the existence of the weak solution for the nonlineardynamic systems on time scales and its properties are presented.Discussing L1-strong-weak lower semicontinuity of integralfunctional, we give sufficient conditions for the existence ofoptimal controls. Using integration by parts formula and Hamiltonianfunction on time scales, the necessary conditions of optimality arederived respectively. Some examples on continuous optimal controlproblems, discrete optimal control problems, mathematicalprogramming and variational problems are also presented for demonstration.

In this paper we describe an elementary method for calculating the matrix exponential on an arbitrary time scale. An example is also given to illustrate the result.