A mathematical model for weighing investments

This model assumes three separate investors each with a set amount of money. The full amount is to be invested in six investments, namely: long‐term bonds, short‐term bonds, treasury bonds, common stock, treasury bills, and commercial paper. The investment is made according to weights assigned to safety of principal, growth, current income, taxable income and volatility. The weights are derived by obtaining pairwise comparison matrices and then using an averaging process.     

Uniqueness for Boundary Value Problems for Second Order Finite Difference Equations

We establish maximum principles for second order difference equations and apply them to obtain uniqueness for solutions of some boundary value problems.     

Microsolvation of a partially bonded complex by non-polar and weakly polar microsolvents: a microwave and ab initio study of HCN–SO3–Ar and HCN–SO3–CO – ARTICLE WITHDRAWN

WITHDRAWN TO APPEAR IN SPECIAL ISSUE IN 2007     

A computer‐supplemented revision course

The authors have developed a computer‐supplemented course suitable for use as a revision aid in obstetrics and gynaecology. It can be used on an interactive basis using time‐sharing facilities. Additional notes are printed out for each question. It provides individualized instruction but is also suitable for small group discussion.     

Transitivity and Dense Periodicity for Graph Maps

In 1984, Blokh proved [A. M. Blockh, On transitive mappings of one-dimensional branched manifolds, Differential-Difference Equations and Problems of Mathematical physics (Russian), Akad. Nauk Ukrain. SSR Inst. Mat., Kiev, 131, pp. 3–9, 1984] that any topologically transitive continuous map from a graph into itself which has periodic points has a dense set of periodic points and has positive topological entropy (in this proof a crucial role is played by the specification property, which implies these two statements). Also, he characterized the topologically transitive continuous graph maps without periodic points. Unfortunately, this clever paper is only available in Russian (except for a translation to English of the statements of the theorems without proofs—see [A. M. Blockh, The connection between entropy and transitivity for one-dimensional mappings, Uspekhi Mat. Nauk, 42(5(257)) (1987), pp. 209–210]).     

Discrete Dichotomies and Asymptotic Behavior for Abstract Retarded Functional Difference Equations in Phase Space

We study the problem of asymptotic behavior between weighted bounded solutions of a system of homogeneous linear functional difference equations and its perturbation under non-classical dichotomic properties and also we obtain some results about approximation. We apply our results to Volterra difference systems with infinite delay.     

Modelling of a sugarcane sett cutting operation by Monte Carlo technique

This paper describes a mathematical model capable of analysing a sugarcane sett cutting operation. Monte Carlo technique is applied for generating the hypothetical sugarcanes to be cut into setts of uniform length. The probability density functions of the variables such as the sugarcane lengths, nodal spacings and the end piece lengths for a given sugarcane variety constitute the inputs to the model. The experimental and model predicted proportions of the multibudded setts for a few arbitrarily selected cut lengths are compared and further improvements in the model are discussed. It is shown that the developed model can be effectively used to analyse the sugar cane sett cutting operation to meet the selection criteria for the multibudded setts.