##### Decay of a Saw Tooth–profile in Two-phase-flows of Gas-particle Mixture

Kanti Pandey

Journal of Advances in Mathematics and Computer Science, Page 1-11
DOI: 10.9734/BJMCS/2016/24006

Aim: To study the length and decay behavior of a saw tooth-profile in Two-Phase-Flows of gas-particle mixture and compare the analytical solution with numerical solution.

Study Design: Progressive-wave approach is used to obtain asymptotic solution of the non linear system of partial differential equations governing two-phase flows of gas-particle-mixture in reacting gases, which governs the growth and decay of acceleration front. In preparation of graphs origin 7.5 is applied.

Place of Study: Department of Mathematics & Astronomy, Lucknow University, Lucknow-226007, India.

Methodology: Analytical and numerical method (Runge-Kutta method of fourth order) is used.

Results: The evolution equation governs the growth and decay of acceleration front and its analytical solution is obtained. With help of this evolution equation length and decay behavior of saw –tooth profile is investigated. These results are compared numerically with help of Runge-Kutta method of fourth order. Numerical results shows that the applied numerical method is in good agreement for length of Saw-Tooth profile for cylindrical case. In case of decay behavior it is in good agreement with analytical one for plane and cylindrical case.

Conclusion: We conclude that the applied method is in good agreement for length of Saw-Tooth profile of cylindrical case and for decay behavior of Saw-Tooth profile for plane and cylindrical case.

##### Solitary Wave Solutions to the Sharma-Tasso-Olver Equation and the Similar Hirota-Satsuma KdV System through the Modified Simple Equation Method

Huiju Dai, Lianzhong Li

Journal of Advances in Mathematics and Computer Science, Page 1-10
DOI: 10.9734/BJMCS/2016/26702

In this paper, the modified simple equation (MSE) method is applied to find the exact solutions for the Sharma-Tasso-Olver (STO) equation and the similar Hirota-Satsuma KdV system. The MSE method is an effective method in investigating exact solitary wave solutions to nonlinear evolution equations (NLEEs) in the field of applied mathematics, mathematical physics and engineering. And it is very direct and effective.

##### Ubiquitous Computing: An Assistive Surveillance on In and Out Patients with Mental Illness via RFID

Edje E. Abel

Journal of Advances in Mathematics and Computer Science, Page 1-15
DOI: 10.9734/BJMCS/2016/26778

Ubiquitous Computing enable users to utilise computer software and hardware to perform tasks anytime anywhere without visualising them. In other words, software and hardware are embedded in the environment making them invisible while they are effectively in use. Over the last decayed, the use of ubiquitous computing has been exploited in the healthcare sector via Radio Frequency Identification for security purposes. However, it has not been gainfully applied in mental Healthcare wards or homes for observation of patients with mental illness as one of their routine treatment. This paper present the possibility of using Ubiquitous Computing aided RFID system to enhance observation treatment on patients with mental illness in mental wards. Chronological Scientific Research Methodology, which comprise of five stages was used to actualise the research goal under study. Problems and challenges posed by existing observation treatment techniques were discussed in detail such as patient with schizophrenia are most likely to abscond from the mental hospital premises and a bridge of patient’s freedom of privacy e t c. A feasible system solution was formulated called “Real Time RFID Monitoring Middleware System” that would resolve the flaws or challenges of the existing observation treatment techniques. Also, comparative analysis was carried out between the feasible system formulated and the existing system in other to determine the validity and reliability of the feasible system solution. Recommendations were sighted persuading mental healthcare practitioners and government agencies to invest in the development of the proposed system due to its great and exciting features and end with a conclusion.

##### Multiple Solutions of Riemann Type of Functional Equations

T. Cao-Huu, D. Ghisa, F. A. Muscutar

Journal of Advances in Mathematics and Computer Science, Page 1-12
DOI: 10.9734/BJMCS/2016/26322

Linearly independent Dirichlet L-functions satisfying the same Riemann type of functional equation have been supposed for a long time to possess off critical line non trivial zeros. We are taking a closser look into this problem and into its connection with the Generalized Riemann Hypothesis.

##### Solving Network Routing Problem Using Artificial Intelligent Techniques

Ameen Oloduowo, Akande Hakeem Babalola, Aruleba Kehinde Daniel

Journal of Advances in Mathematics and Computer Science, Page 1-9
DOI: 10.9734/BJMCS/2016/27033

The rapid revolution of communication networks requires a solution of network routing problem to be addressed in packet switched network. In the recent years, researchers have been solving routing problem in other to maintain continuous network transmission without any loss of packets. Until now research has shown that most routing devices get distorted when new nodes are added, shortest path and new direction need to be determined when connections goes down in between the network nodes, congestion control and delay factor needs to be put in mind when finding solution to the problem so as to ensure smooth network transmission. In other to solve these problems, Ant colony optimization techniques is used and improved. The Algorithm is simulated using Visual Basic.Net 2012 (VB 11.0) object oriented language. Experimental result show that our method allows network to activate new route if there is service time out, congestion or bottleneck in the existing route and shortest path will also be determined. Several Tests are carried out to ensure the efficiency of the algorithm; Mathematical expression is also generated to locate the route path in this study.Network routing

##### Oscillation Criteria for the Solutions of Second Order Half-linear Delay Dynamic Equations on Time Scales

Quanxin Zhang, Shouhua Liu

Journal of Advances in Mathematics and Computer Science, Page 1-10
DOI: 10.9734/BJMCS/2016/27165

In this paper, we are concerned with a class of second-order half-linear delay dynamic equations on time scales. By using the generalized Riccati technique and the integral averaging technique of Grace-type, four new oscillation criteria are obtained for every solutions of the equations to be oscillatory.

##### Matrix Form of the Iterated Binomial Transforms

Sergio Falcor

Journal of Advances in Mathematics and Computer Science, Page 1-7
DOI: 10.9734/BJMCS/2016/25730

In a previous paper, we have estudied the Binomial transforms of the k-Fibonacci sequences and later we have studied the iterated Binomial transforms of these sequences. Now we study the matrix form of these four different binomial transforms of integer sequences in such a way that we can find a relation between the terms of the transformed sequence and the terms of the initial sequence. In this form we do not need to find the initial terms of the transformed sequence to find the following term from the application of the corresponding recurrence equation.
Later we will apply the obtained results to the particular case of the k-Fibonacci sequence.