Finite Doubly Transitive Affine Planes

AbstractIn this article, we classify the finite affine planes admitting doubly transitive collineation groups

Goal Programming Approach for Selection of COTS Components in Designing a Fault Tolerant Modular Software System under Consensus Recovery Block Scheme

The application of computer systems has now crossed many different fields. Systems are becoming more software intensive. The requirements of the customer for a more reliable software led to the fact that software reliability is now an important research area. One method to improve software reliability is by the application of redundancy. A careful use of redundancy may allow the system to tolerate faults generated during software design and coding thus improving software reliability. The fault tolerant software systems are usually developed by integrating COTS (commercial off-the-shelf) software components. This paper is designed to select optimal components for a fault tolerant modular software system so as to maximize the overall reliability of the system with simultaneously minimizing the overall cost. A chance constrained goal programming model has been designed after considering the parameters corresponding to reliability and cost of the components as random variable. The random variable in this case has been considered as value which has known mean and standard deviation. A chance constraint goal programming technique is used to solve the model. The issue of compatibility among different commercial off-the shelf alternatives is also considered in the paper. Numerical illustrations are provided to demonstrate the model

Translation planes of order q2q2 admitting collineation groups of order q3uq3u preserving a parabolic unital

The set of translation planes of order $q2$ that admit collineation groups of order $q3u$, where u is a prime p-primitive divisor of $q2-1$, consists of exactly the Desarguesian plane, assuming that the group does not contain a translation subgroup of order a multiple of $q2$. This applies to show that if the group preserves a parabolic unital then the plane is forced to be Desarguesian

Infinite hyper-regulus Sperner spaces

New constructions of infinite hyper-reguli are given, which produce a variety of new translation planes and Sperner spaces