Maximizing antichains in the cube with fixed size of a shadow

In the n-dimensional cube, we determine the maximum size of antichains having a lower shadow of exactly m elements in the k-th level.     

A chemically sterilizable barrier for the protection of fermentors during automatic sampling into a low-injection system

Two three-way valves are connected by a short stainless steel tube and attached to a model fermentor. A sample can be drawn straight through the valves and into an analyzer for monitoring of oxygen or glucose. The valves are switched to an external solution after the sample has been taken. Solutions of 5% formaldehyde provide a barrier to the intrusion of micro-organisms into the fermentor, whereas water solutions are ineffective. With water in the barrier, infections occur after a few days when the system is provoked by a growing culture ofE.coli at the outlet. The concept of a chemically sterilizable barrier is particularly well suited for the intermittent needs of flow-injection systems used for process monitoring.     

Three Cases of Light-Traffic Insensitivity of the Loss Probability in a GI/G/m/0 Loss System to the Shape of the Service Time Distribution

A GI/G/m/0 loss system is considered. Three cases of light-traffic insensitivity of the loss probability to the shape of the service time distribution, given its first moment, are investigated in a triangle array setting.     

The p-Modular Descent Algebra of the Symmetric Group

The descent algebra of the symmetric group, over a field ofnon-zero characteristic p, is studied. A homomorphism into thealgebra of generalised p-modular characters of the symmetricgroup is defined. This is then used to determine the radical,and its nilpotency index. It also allows the irreducible representationsof the descent algebra to be described. 1991 Mathematics SubjectClassification 20F32.     

Estimating mean time to absorption for a markov chain with limited information

In many applications of absorbing Markov chains, solution of the problem at hand involves finding the mean time to absorption. Moreover, in almost all real world applications of Markov chains, accurate estimation of the elements of the probability matrix is a major concern. This paper develops a technique that provides close estimates of the mean number of stages before absorption with only the row sums of the transition matrix of transient states.