Gary R. Waissi

A sigmoid approximation of the standard normal integral

Abstract This paper presents a simple sigmoid function for approximation of cumulative standard normal probabilities. The approximation has an error of ±0.000043 for −8 ≤ Z ≤ 8.

An improved unifying density function

Abstract This paper presents an improved and simplified version of the unifying probability density function of [1]. The improved unifying density function is shown to be the parent of the Rayleigh distribution in addition to the Weibull-, gamma-, Erlang-, χ 2 - and exponential distributions. The means and variances of the relating child distributions can be found easily by substitution using the established relationships.

A unifying probability density function

Abstract This paper presents a new unifying continuous probability density function. It is shown that the continuous distributions Weibull-, gamma-, Erlang-, χ 2 and exponential distributions can be derived from the proposed density function.

Worst case behavior of the Dinic algorithm

Many m-flow phase algorithms use the Dinic algorithm to generate an acyclic network in the iirst phase, and then solve the maximal flow problem in such a network in the second phase. This process is then repeated until the maximum value flow is found in the original network. In this paper a class of networks is presented where the Dinic algorithm always attains its worst ca8e bound. The Dinic algorithm requires (n - 1) network generations, where n is the number of nodes in the original network for finding the maximum value flow in the original network.

A new Karzanov-type O(n3) max-flow algorithm

A new algorithm is presented for finding maximal and maximum value flows in directed single commodity networks. The algorithm gradually converts a combination of blocking preflows and backflows to a maximal flow in the network. Unlike other maximal flow algorithms, the algorithm treats the network more symmetrically by attempting to increase flow on both the ForwardStep and the BackwardStep. The algorithm belongs to the so called phase algorithms, and is applied to Dinic-type layered networks. With an effort of at most O(n^3) for maximum value flow, the algorithm ties with the fastest maximum flow algorithms in dense networks, where m ~ n^2, and can therefore be seen as a significant alternate technique. The algorithm is based on the Karzanov [1] algorithm, and shares features with the algorithm of Tarjan [2]. The first version of this algorithm was presented by the author in [3].

Transformation of the unifying density to the normal distribution

Abstract This paper shows that the improved unifying density function of [1] transforms to the normal and standard normal distributions. The list of the unifying density function child distributions contains then seven continuous distributions: the Weibull-, gamma-, Erlang-, χ 2 -, exponential-, Rayleigh-, as well as the normal distribution.

Assessment of Operational Feasibility Anticipated Quality and Cost Performance of a New Exterior Coating System in Automotive Manufacturing

A new radiation curable exterior coating system for automotive applications, called the UV-system, shows considerable promise in terms of improvement of quality, simplification of assembly process, and cost savings for future exterior coating systems