Dynamical interaction between input data and simple insertion sort algorithm

The main aim is to show that the actual approach for algorithms complexity analysis based on Turing machine and its properties can be extended trough the systems approach. It means that the actual existing paradigm, which assumes that the analysis of algorithm behavior is done when the independence

between input set and algorithm is assumed can be expanded by the approach that allows a new view on possible phenomena that can occur during algorithmic processing. Presented considerations allow to establish a connection between Turing machines and physics of processing as a part of paradigm that considers computer systems as the complex ones.

Website: http://www.arjonline.org/mathematics/american-research-journal-of-mathematics/

On the Homotopy Perturbation Method for the Exact Solution of Fitzhugh–Nagumo Equation

the Homotopy Perturbation Method (HPM) is used to solve the Fitzhugh–Nagumo non-linear differential equations. In order to obtain the exact solution of Fitzhugh–Nagumo equation, two case study problems of the equation are solved by using the HPM. The trend of the rapid convergence of the sequences constructed by the method towards the exact solution is also numerically shown. As a result, the rapid convergence towards the exact solutions of HPM indicates that the method is powerful and efficient technique to solve the Fitzhugh–Nagumo non-linear differential equations. Also, the results present validity and great potential of the method as a powerful algorithm in order to obtain the exact solution of nonlinear differential equations.

Website: http://www.arjonline.org/mathematics/american-research-journal-of-mathematics/

Some new estimations of diagonally dominant degree and eigenvalue inclusion sets for the Schur complement of block diagonally dominant matrices

Some new estimations of diagonally dominant degree and eigenvalue inclusion sets for the Schur complement of I(II)-block diagonally dominant matrices are given and it is proved that the new estimations on diagonally dominant degree are more accurate than those in [Liu et al., Theorems on Schur complement of block diagonally dominant matrices and their application in reducing the order for the solution of large scale linear systems, Linear Algebra Appl. 435 (2011), 3085–3100], and the new eigenvalue inclusion sets are contained in the sets given by liu et al.. Finally, a numerical example is given to illustrate the advantages of our results.

Website: http://www.arjonline.org/mathematics/american-research-journal-of-mathematics/

Aggregation Method for Gene Mining Based on Mutual Information Network

Increasing number of methodologies are developed to understand functional genomic correlations from mRNA express data. In this work, we propose a method that combines rank aggregation with mutual information relevance network to identify differentially coexpressed key genes. For two expression data profiles from experimental and control sample groups, we construct mutual information networks G1 and G2, respectively, and define

several structural parameter of the network. All the parameters are heterogeneous and yield to different ranks of genes, in which top-ranked genes are more important w.r.t. the corresponding parameter. In order to select the functional key genes with overall significance, rank aggregation technique are employed to integrate the different ranks to a final “super-list”. Finally the expression profiles of yeast Saccharomyces cerevisiae.

Website: http://www.arjonline.org/mathematics/american-research-journal-of-mathematics/

M[x]/G/1 Retrial Queue with Two Phases of Service, Bernoulli Vacation and Server Break Down

A repairable batch arrival retrial queuing system with two phases of service, Bernoulli vacation and random server breakdown is considered. At the arrival epoch, if the server is busy the whole batch joins the orbit, whereas if the server is free, then one of the arriving customers starts its service immediately and the rest joins the orbit. For each customer the server provides two phases of service. After completion of each service, the server may take a vacation with probability θ or may continue in the system with complimentary probability. The steady state distribution of the server state and the number of customer in the orbit/system are obtained. While the server working with any phase of service, it may break down at any instant and the service channel will fail for a short interval of time and it is repaired immediately. Numerical example is presented to illustrate the influence of the parameters on several performance characteristics.

Website: http://www.arjonline.org/mathematics/american-research-journal-of-mathematics/

Annals of Fuzzy Mathematics and Informatics

Annals of Fuzzy Mathematics and Informatics (AFMI) is an international journal published by Kyung Moon Sa Co, since 2011. The journal is to provide rapid publication of high quality, refereed articles in the theory and applications of Fuzzy Sciences based on Mathematics and Information Sciences. There are no page charges to individuals or institutions, and the journal offers free access to anyone. The authors have to use the LaTeX Style Files for the final preparation of the accepted manuscript. The language of publication is English only.

Website: http://www.arjonline.org/mathematics/american-research-journal-of-mathematics/

Bulletin of the International Mathematical Virtual Institute

Bulletin of the International Mathematical Virtual Institute is edited and published by International Mathematical Virtual Institute (www.imvibl.org). Bulletin of the International Mathematical Virtual Institute is a continuation of the earlier publication Bulletin of the Society of Mathematicians Banja Luka, whish was founded in 1994 and whose last issue Vol. 17(2010). Bulletin of the International Mathematical Virtual Institute publishes original shorter papers (less than 15 pages) in all fields of mathematics that contained new, substantial and significant results, whith complete proofs and of interest for a large number of mathematicians. Papers are published in English.

Website: http://www.arjonline.org/mathematics/american-research-journal-of-mathematics/