Open Access Method Article

Branching Pattern Modeling for Psychotoria species and Their Deterministic Algorithm

Masahiro Watari

Journal of Advances in Mathematics and Computer Science, Page 1-17
DOI: 10.9734/BJMCS/2016/21972

Back Ground: The branching patterns and the subsequent elongations of two shrub Psychotria species, Pyschotoria rubra and Psychotoria manillensis, in Okinawa Island, the Ryukyu Islands, Japan, were examined by Watanabe. His results showed that Hamilton's classi cation for Psychotria species in the South American continent is also applicable to the same species in Okinawa Island. AfterWatanabe's research, the author of the present paper introduced branching pattern models for same species to simulate their branching patterns theoretically. He also determined the branching pattern models in earlier growth stages and calculated their occurrence probabilities. To proceed with the analyses, a systematic construction of the branching pattern models has been required.

Aims: To re ne our earlier branching pattern models of P. rubra and P. manillensis in view of vector representation and to introduce a deterministic algorithm which produces the branching pattern models systematically.

Methodology: Introducing vector representations, we re ne previous branching pattern models for Psychotria species in Okinawa Island. We also study the properties of branching pattern models in view of computational methods. Finally, we describe a deterministic algorithm for branching pattern models of P. rubra and P. manillensis by a pseudo-code.
Results: By studying properties of branching patterns of Psychotria species in mathematical way, we systematize the construction of our branching pattern models as a deterministic algorithm. Running this algorithm, we also succeed in the determination of the third branching pattern models.
Conclusion: A systematic determination algorithm which produces the branching pattern models inductively has been successfully established.

Open Access Short Research Article

Open Access Original Research Article

Open Access Original Research Article

Some Applications of Bipolar Soft Set: Characterizations of Two Isomorphic Hemi-Rings via BSI-h-Ideals

Khizar Hayat, Tahir Mahmood

Journal of Advances in Mathematics and Computer Science, Page 1-21
DOI: 10.9734/BJMCS/2016/22028

In this study, we intended to present insights into bipolar soft set in the union of two isomorphic hemi-rings. This concept provides a new soft algebraic tool in many uncertainties problems. We introduced BS-h-sum and BS-h-product of BS-sets. In particular, we discussed bipolar soft intersectional h-ideals in the union of two isomorphic hemi-rings. In addition, we characterized isomorphic h-hemi-regular hemi-rings using bipolar soft intersectional h-ideals.

Open Access Original Research Article

Optimum Step-Stress Accelerated Life Test Plan for Lomax Distribution with an Adaptive Type-II Progressive Hybrid Censoring

Amal S. Hassan, Salwa M. Assar, A. Shelbaia

Journal of Advances in Mathematics and Computer Science, Page 1-19
DOI: 10.9734/10.9734/BJMCS/2016/21964

The adaptive type-II progressive hybrid censoring has the advantage of saving both the total test time and the cost of the experiment; also it increases the efficiency of the statistical analysis. This article discusses k-level step stress accelerated life tests based on an adaptive type-II progressive hybrid censoring with product's life time following Lomax distribution. The scale parameter of the Lomax failure time distribution at constant levels is assumed to be a log linear function of the stress level. Maximum likelihood estimators of the model parameters are derived. Based on normal approximation to the asymptotic distribution of maximum likelihood estimators, the approximate confidence intervals for model parameters are obtained. The optimal times of changing stress levels are discussed under D-optimality and A-optimality criteria. Such methods maximize the determinant and the trace of Fisher's information matrix for the model parameters. Analysis of the numerical data has been presented for illustrative proposes.

Open Access Original Research Article

A Model of a Pragmatic Secure Intrusion Detection System for Local Area Networks

B. I. Ele, U. R. Alo, B. C. E. Mbam, A. O. Ofem

Journal of Advances in Mathematics and Computer Science, Page 1-15
DOI: 10.9734/BJMCS/2016/22190

Intrusion detection is very imperative in network systems due to outstanding vulnerabilities left unaddressed by current preventive network security measures such as firewalls and encryption software. The inefficiency, inaccuracy, high false alarm rates and lack of self-defensive mechanism of existing network security systems has continued to pose serious concern to network users, administrators and security professionals and thus needs urgent redress. Therefore, the target of this paper is to develop a model of a pragmatic secure intrusion detection system for local area networks using layered framework with conditional random fields that is capable of overcoming the apparent shortcomings of present intrusion detection systems. A critical analysis of existing IDSs was done using the structured system analysis and design methodology (SSADM) due to the sequential configuration of the proposed security system. Furthermore, a real-time response mechanism and a self-defensive mechanism for a network intrusion detection system (NIDS) was developed and implemented. The outcome of this study was a secured IDS that would proactively address potential security vulnerabilities by resisting and detecting attacks and security policy violations reliably and efficiently in local area networks, thus making it inevitable for use in our security conscious environment of the 21st century.

Open Access Original Research Article

The Complementary Exponentiated Inverted Weibull Power Series Family of Distributions and its Applications

Amal S. Hassan, A. M. Abd-Elfattah, Asmaa H. Mokhtar

Journal of Advances in Mathematics and Computer Science, Page 1-20
DOI: 10.9734/BJMCS/2016/21903

In statistical literature, several distributions are used to model lifetime data. But many –if not most– of these distributions lack of certain lifetime context motivation. Recently, attempts have been made to define new families of probability distributions that extended well known families of distributions and at the same time offer great flexibility in a real data modeling. In this paper, a new family of distributions is introduced by compounding exponentiated inverted Weibull and power series distributions. The properties of the new family are discussed, including quantiles, moments and moment generating function. The estimation of the model parameters is performed by the maximum likelihood method. The new family generalizes some new lifetime distributions. In particular, two special models belonging to this family are studied in some details. Applications to real data sets are given to show the flexibility and potentiality of the proposed family of distributions.