Abstract
Merging NURBS surfaces together and extending existing ones are common problems in CAD
systems. Extending existing surface is usually done by creating a new separate surface and
applying some merging function – result is one continuous surface. In this paper, full description
of a method of direct extending existing surfaces is introduced. The extension of the surface is
recomputed during its construction, and the NURBS surfaces are immediately C1 connected. Full Article



Reducing Bias in Nonparametric Estimation of the Distribution Function of Nonstandard Mixtures E. D. McCune and Sandra L. McCune

Abstract
Nonstandard mixtures occur when a random variable behaves in a continuous manner except at a countable number of discrete mass points. Polansky (2005) introduced a biased kernel estimator of the distribution function of nonstandard mixtures. In this paper, a new estimator of the distribution function of nonstandard mixtures with less bias than Polansky's (2005) estimator is obtained by applying to Polansky's (2005) estimator a nonparametric data transformation bias-reduction technique introduced by Swanepoel and Van Graan (2005). Statistical properties of the new estimator are determined and presented. Full Article



Analyzing Near-Normal Data Using a New Density Function within Azzalini’s Class of Skew Distributions  Hassan Elsalloukh and Jose H. Guardiola

Abstract
A family of distributions, which was first introduced by O’Hagan and Leonard [9] for Bayesian analysis of normal means and was later investigated in detail by Azzalini [3, 4], is modified leading to a new class of asymmetric distributions. A new score test is derived for detecting non-normality within the new class of asymmetric distributions. The maximum likelihood estimates are derived for location, scale, shape, and skewness parameters. Then, the new score test is applied on an example of a real data set within the new class of asymmetric distributions to detect non-normality. Maximum likelihood estimators are used to fit the data with a skew distribution and compared to studies in which researchers used the normal distribution. Full Article



Certain Rings and Semigroups Examining the Regularity Property
M. Azadi, H. Doostie and L. Pourfaraj

Abstract
A number of main properties of the commuting regular rings and commuting regular semigroups have been studied in this paper. Some significant results of which will be used for the commutative rings and a necessary and sufficient condition is given for a semi-group to be commuting regular.  Full Article



The Ricatti Equation in the M I G I ∞ System Busy Cycle Study
Manuel A. M. Ferreira, Marina Andrade, José António Filipe

Abstract
The M I G I ∞ queue system can be applied to model many social problems: sickness,
unemployment, emigration, etc (see, for instance, Ferreira (1995, 1996, 2003a and 2003b)). In
these situations it is very important to study the busy cycle length distribution of that queue
system. It is shown, in this work, that the problem solution may be in the resolution of a Ricatti
equation, following the work of Ferreira (2003). Full Article