ISSN 1556-6757











Volume 2, Issue 1, 2009

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

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

Direct extending of NURBS surfaces
David Prochazka and Jana Prochazkova

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

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

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

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

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

The Relationships among Number Theoretic Functions
Mohammed R. Karim


There are several number theoretic functions which play important roles in multiplicative and additive number theory. Earlier authors have established relationships among some of these functions, but not all of them. In this paper, the author presents relationships between some of the remaining functions. The paper shows relationships among most of the number theoretic functions, making it possible to find the relationship between any two number theoretic functions. Full Article

Evidence evaluation in DNA mixture traces
Marina Andrade, Manuel A. M. Ferreira, José António Filipe

Nowadays the use of DNA profiles in forensic identification problems is a very common
procedure. The observance of a mixture trace resulting of a crime that has been committed
is a very interesting and challenging phenomenon for the laboratories and for the judicial
systems. The hypotheses that can be considered and compared in cases of mixture traces
are discussed in this work. In court two hypotheses, the prosecution hypothesis and the
defence hypothesis, lead the dispute in the case presented. The use of Bayesian networks
in the analysis of DNA mixture traces is a powerful tool in complex cases. That allows an
easy evaluation of the likelihoods for the whole hypotheses suggested by each case.
Full Article

E–convex programming
J.Sheiba Grace and P.Thangavelu


Youness introduced the concepts of E–convex sets and E–convex functions and studied their
properties. In this paper it is shown that Theorem 3.1 of Youness is incorrect by giving some
counter examples. Theorem 3.1 of Youness is modified and the modified theorem is applied to
solve an E–convex programming problem.
  Full Article