Open Access Others

Addendum: A Short Elementary Proof of the Unprovability of the Collatz Conjecture

Robin Nag

Journal of Advances in Mathematics and Computer Science, Page 300-301
DOI: 10.9734/BJMCS/2015/12538

Addendum for British Journal of Mathematics & Computer Science, 4(21), 3023-3027, 2014

 

It has been drawn to the journal's attention that there is an addendum for following section of the published paper.:

(1) Formulation of Hasses Algorithm 

Therefore, following the 'SDI Correction and retraction policy' this Addendum was processed and approved. Link of the 'Previously Published Paper'  is available here here.

Open Access Original Research Article

Simulation of Suspensions of Helical Rigid Fibers

Yazid Al-Hassan

Journal of Advances in Mathematics and Computer Science, Page 133-158
DOI: 10.9734/BJMCS/2015/12581

The study at hand presents a numerical method for simulations of the dynamics of slender rigid fibers immersed in an incompressible fluid. The underlying mathematical formulation is based on a slender body approximation as applied to a boundary integral equation for Stokes flow. The curvature and torsion of the fibers can be arbitrarily specified, and we consider fiber shapes ranging from moderately bent to high curvature helical shapes. Two different settings are considered; naturally buoyant fibers in shear flow and heavier fibers sedimenting due to gravity. The dynamics show a very rich behavior, with fiber trajectories that display a very different degree of regularity depending on the initial conditions and fiber shape.

Open Access Original Research Article

Mathematical Modeling of Water Flow for Irrigation in a Permeable Pipe of Elliptical Cross-section

A. W. Ndegwa, M. M. Kimathi, M. N. Kinyanjui, I. Chepkwony

Journal of Advances in Mathematics and Computer Science, Page 159-178
DOI: 10.9734/BJMCS/2015/13157

An unsteady incompressible fully developed flow in a horizontal flexible and permeable annular pipe of elliptic cross-section under the action of gravity is studied. The solution is obtained through a homogenization method by employing a small scale separation parameter that approximates the pipe in the form of a series. The results in terms of velocity and pressure distributions and mass
flow rate inside the pipe and through the pipe wall are presented and discussed. It is shown that the pipe thickness has no influence on the water flow through the pores. We also propose that for the efficient use of water for irrigation, the elliptical pipe should be laid in a vertical position.

Open Access Original Research Article

Three Dimensional Trans-Sasakian Manifold Admitting Quarter Symmetric Metric Connection

B. Sumangala, Venkatesha .

Journal of Advances in Mathematics and Computer Science, Page 179-189
DOI: 10.9734/BJMCS/2015/12737

The object of this paper is to study quarter-symmetric metric connection on a trans-Sasakian manifold. Here we study locally ∅-symmetric,∅-symmetric and concircular ∅-symmetric trans- Sasakian manifold with respect to quarter symmetric metric connection and obtained some interesting results.

Open Access Original Research Article

A Real Time Secured Voice Framework Using the Totally Reconstructed Discrete Wavelet Transformation

Ahmad Azzazi

Journal of Advances in Mathematics and Computer Science, Page 190-203
DOI: 10.9734/BJMCS/2015/11626

In our life today and with the upraise of the mobile computation and mobile phones we are using more voice applications. The voice application could then send voice information with different information over different communication channels, with an increasing need to protect this information without any delay when applying any modification on it. To protect this voice information, we encrypt it. In this paper, we are proposing a Framework using the totally reconstructed Discrete Wavelet Transformation (DWT) to encrypt the voice information in real time, where the sample rate of the encrypted voice signal is equal to the original voice signal sample rate. The framework is designed and tested with sample tests to measure the performance of this Framework, showing the speed and complexity of this Framework.

Open Access Original Research Article

Preliminary Test Stochastic Restricted r-k Class Estimator and Preliminary Test Stochastic Restricted r-d Class Estimator in Linear Regression Model

Sivarajah Arumairajan, Pushpakanthie Wijekoon

Journal of Advances in Mathematics and Computer Science, Page 204-227
DOI: 10.9734/BJMCS/2015/13781

In this study two new preliminary test stochastic restricted estimators, a Preliminary Test stochastic restricted r-k class estimator and a Preliminary Test stochastic restricted r-d class estimator, are proposed. The comparison of one estimator over the other is done in the mean square error matrix sense. Further preliminary test stochastic restricted r-k class estimator is compared with r-k class estimator [1] and stochastic restricted r-k class estimator [2]. Similarly preliminary test stochastic restricted r-d class estimator is compared with r-d class estimator [3] and stochastic restricted r-d class estimator [2]. Finally a numerical example and a Monte Carlo simulation study are done to illustrate the theoretical findings of the proposed estimators.

Open Access Original Research Article

Numeric-analytic Solution to the Second Order Impulsive Differential Equations with Smooth Coefficients

Benjamin Oyediran Oyelami

Journal of Advances in Mathematics and Computer Science, Page 228-246
DOI: 10.9734/BJMCS/2015/13314

In this paper a new method is proposed for finding series solution to the second orders impulsive differential equations with smooth coefficients. The method is applied to two examples using Maple 18 symbolic programming. A criterion for convergence of the series solution is obtained too.

Open Access Original Research Article

Towards a Taxonomy of MANETs Attacks: Attack Attributes-based Taxonomy (AABT)

Noureldien A. Noureldien

Journal of Advances in Mathematics and Computer Science, Page 247-261
DOI: 10.9734/BJMCS/2015/13529

Mobile Ad hoc Networks (MANETs) find a rapid increase of applications and interest. The vulnerabilities of MANETs make the security issue a major concern for researcher and practitioners. MANETs attacks are often described and classified differently, resulting in confusion in what a particular attack actually is and how attacks can be categorized.
Generally, the purpose of attack taxonomy is to provide a useful and consistent means of classifying attacks. A well defined taxonomy will allow previous knowledge to be applied to new attacks as well as providing a structured way to view such attacks.
This paper proposes a new taxonomy to MANETs attacks. The taxonomy is aimed to provide means to create attack categories, to enable highlighting similarities between attacks and to be useful in identifying attack-related detection and prevention countermeasures.
The taxonomy is based on attack attributes. Every attack is characterized by a unique vector of attributes values, where each attribute define a specific attack property which may have different values. The taxonomy uses six attributes; the legitimacy of attacking node/s, the number of nodes participating in the attack, MANETs vulnerabilities utilized by the attack, the network resources exploited by the attacking node/s, the targeted victim and finally, the network security service compromised by the attack.
The analysis of some well known attacks shows the capability of the proposed taxonomy in describing and categorizing these attacks as taxonomy vectors.

Open Access Original Research Article

Generalized Theoretical Criteria for Annihilation of HIV-1 Virions during HAART

Frank Nani, Mingxian Jin

Journal of Advances in Mathematics and Computer Science, Page 262-299
DOI: 10.9734/BJMCS/2015/11394

Aims: This paper is an elaborate and quantitative attempt to construct medically applicable mathematical models and derive criteria for efficacious Highly Active Anti-Retroviral Therapy (HAART) protocol for an AIDS patient. The patho-physiological dynamics of Human Immuno-deficiency Virus type 1 (HIV-1) induced AIDS during HAART is modeled by a system of non-linear deterministic differential equations. The physiologically relevant and clinically plausible equations depict the dynamics of uninfected CD4+ T cells (x1), HIV-1 infected CD4+ T cells (x2), HIV-1 virions in the blood plasma (x3), HIV-1 specific CD8+ T cells (x4), and the concentration of HAART drug molecules (x5). The major objective of this research is to construct an elaborate mathematical model that depicts patho-physiodynamics of HIV-1 virions during HAART. The derived therapeutic criteria are expressed in terms of clinically measurable physiological parameters. Investigative computer simulations which describe certain aspects of HIV-1 dynamics during HAART are also presented in the paper.
Study Design: The mathematical model is constructed based on contemporary research data condensed from the clinical literature on HAART of AIDS. A system of coupled non-linear deterministic differential equations are used to characterize the patho-physiodynamics of HAART during the post chronic phase. The mathematical analysis of the model equations and the computer simulations are performed with regard to HAART protocols with constant continuous intravenous and transdermal drug infusions. A syncytium term with stoichiometric coefficient is introduced into the model to account for the formation of large multinucleated gp120 bearing CD4+ T cells that are observed in some AIDS patients. By assigning a zero value to the stoichiometric coefficient, the role of syncytium is abrogated.
Place and Duration of Study: This research was done at Fayetteville State University, North Carolina USA, and is sponsored by the FSU Mini-Grant Award and the HBCU Graduate STEM Grant. The research was conducted during the Spring of 2012.
Methodology: The deterministic nonlinear dynamics of HIV-1 AIDS equations are analyzed using the techniques of dynamical system theory, principles of linearized stability, non-linear system theory, and other relevant mathematical techniques. The clinically desirable equilibrium states, their local existence, and global stability are analyzed. Investigative computer simulations are performed illustrating some physiological outcomes.
Results: The therapeutic outcomes are presented in the form of theoretical criteria which are obtained from mathematical analysis of the model equations. In particular, the critical parameters which govern the dynamics of HIV-1 virions during HAART are clearly identified. Some clinical implications of HAART are elucidated in the computer simulations using hypothetical physiological parametric configurations.
Conclusion: This research has demonstrated the existence of plausible criteria under which HIV-1 virions can be annihilated using HAART. The latent HIV-1 virion reservoirs are implicated in unsuccessful scenarios of HAART. It has also been demonstrated that the rate constants associated with activation of lymphocytes by cytokine interleukin-2 (IL-2) play a significant role in determining the efficacious outcomes of HAART.