A sequential sampling rule for selecting the most probable multinomial event

Summary A sequential sampling rule is given for selecting the most probable event from a multinomial distribution withk cells. A random number of observations is taken from the given multinomial distribution at each stage of sampling, where the number is distributed according to a Poisson distribution with mean λ. The sampling is stopped when the count in any cell is greater than or equal to a given positive integerN. The cell with the highest count is selected for the most probable event. The mathematical analysis of the problem is simplified as a result of the statistical independence of the cell frequencies due to the randomization of the sample number. The expected value of the stage when the sampling terminates is decreasing in λ. The sequential sampling scheme in which one observation is taken at a time until the highest cell count is equal toN, corresponds to λ→0. A table is given showing some properties of the given selection procedure.     

On a packing problem for infinite graphs and independence spaces

In this paper several infinite extensions of the well-known results for packing bases in finite matroids are considered. A counterexample is given to a conjecture of Nash-Williams on edge-disjoint spanning trees of countable graphs, and a sufficient condition is proved for the packing problem in independence spaces over a countably infinite set.     

Tightly controlled linear hashing without separate overflow storage

A hashing method is presented where the amount of storage required for a file can expand and shrink by very large factors. The performance of this method as measured by lookup time, insertion time and deletion time is very good even when the total storage utilization is as high as 90 percent. The user can completely control the storage utilization between two chosen bounds so that the storage requirement varies linearly with the number of records currently in the file.Unlike previous methods, no separate overflow storage pool is involved and one need not be concerned with expected and worst case requirements for overflow space. Indeed, the absence of requirements for such a separate overflow pool could allow the use of this method with primitive microprocessor operating systems.The choice of hashing functions is discussed and simulation results show great danger in blindly using the popular remainder method.Both an elementary analysis and simulation results are given.This research was supported by the National Science and Engineering Research Council of Canada.     

Generalized charge in the eight-component spin-1/2 wave equation

A conserved current is given for the hypermass generalization of the Dirac equation. The generalization of charge to an invariant quaternion is given which provides insight into a new vector space for relativistic quantum theory. This charge generalization also ensures the independence of the eight internal degrees of freedom in the wave equation.     

A Mössbauer measurement of some lattice properties of a smectic H liquid crystal

The angular dependence of the Mössbauer recoil-free fraction of two single line Sn-absorber molecules is used to determine the tilt angle and the lattice contribution to the vibrational anisotropy (at 77°K) in a smectic H liquid crystal.