Abstract: A matrix is called a ray pattern matrix if its entries are either 0 or a ray in complex plane which originates from 0. A ray pattern A of order n is called spectrally arbitrary if the complex matrices in the ray pattern class of A give rise to all possible nth degree complex polynomial. Otherwise, it is said to be spectrally non-arbitrary ray pattern. We call that a spectrally arbitrary ray pattern A of order n is minimally spectrally arbitrary if any nonzero entry of A is replaced, then A is not spectrally arbitrary. In this paper, we find that is not spectrally arbitrary when n equals to 4 for any θ which is greater than or equal to 0 and less than or equal to n. In this article, we give several ray patterns A(θ) of order n that are not spectrally arbitrary for some θ which is greater than or equal to 0 and less than or equal to n. by using the nilpotent-Jacobi method. One example is given in our paper.
Abstract: Design patterns describe good solutions to common
and reoccurring problems in program design. Applying design
patterns in software design and implementation have significant
effects on software quality metrics such as flexibility, usability,
reusability, scalability and robustness. There is no standard rule for
using design patterns. There are some situations that a pattern is
applied for a specific problem and this pattern uses another pattern.
In this paper, we study the effect of using chain of patterns on
software quality metrics.
Abstract: This paper looks into areas not covered by prominent
Agent-Oriented Software Engineering (AOSE) methodologies.
Extensive paper review led to the identification of two issues, first
most of these methodologies almost neglect semantic web and
ontology. Second, as expected, each one has its strength and
weakness and may focus on some phases of the development
lifecycle but not all of the phases. The work presented here builds
extensions to a highly regarded AOSE methodology (MaSE) in order
to cover the areas that this methodology does not concentrate on. The
extensions include introducing an ontology stage for semantic
representation and integrating early requirement specification from a
methodology which mainly focuses on that. The integration involved
developing transformation rules (with the necessary handling of nonmatching
notions) between the two sets of representations and
building the software which automates the transformation. The
application of this integration on a case study is also presented in the
paper. The main flow of MaSE stages was changed to smoothly
accommodate the new additions.
Abstract: Motivated by Berman et al. [Sign patterns that allow eventual positivity, ELA, 19(2010): 108-120], we concentrate on the potential eventual positivity of irreducible tridiagonal sign patterns. The minimal potential eventual positivity of irreducible tridiagonal sign patterns of order less than six is established, and all the minimal potentially eventually positive tridiagonal sign patterns of order · 5 are identified. Our results indicate that if an irreducible tridiagonal sign pattern of order less than six A is minimal potentially eventually positive, then A requires the eventual positivity.