Vibrational Spectra of Carbonyl Sulphide by U(2) Lie Algebraic Method

J. Vijayasekhar, M. V. Subba Rao, G. Ananda Rao

Journal of Advances in Mathematics and Computer Science, Page 1-5
DOI: 10.9734/JAMCS/2017/37595

In this paper, we have calculated vibrational frequencies of Carbonyl sulphide (OCS) in fundamental level and at higher overtones by Hamiltonian expression, which is in terms of invariant and Majorana operators, describe stretching vibrations. The Hamiltonian is an algebraic one and so far all the operations in this method, unlike the more well-known differential operators of wave mechanics.

Modelling Influenza Dynamics with Drug Resistance Aspect

Caroline W. Kanyiri, Mark Kimathi, L. S. Luboobi

Journal of Advances in Mathematics and Computer Science, Page 1-19
DOI: 10.9734/JAMCS/2017/37442

Despite improvement in medical and public health standards, influenza continues to plague humankind causing high morbidity,mortality and socio-economic cost. Efforts to effectively combat the spread of influenza can be put in place if its dynamics are well understood. Numerous challenges have been faced in the event of controlling the spread and eradicating this contagious disease, a major impediment being the rise of drug resistance. In light of this, a deterministic model is formulated and used to analyze the transmission dynamics of influenza having incorporated the aspect of drug resistance. A system of differential equations that models the transmission dynamics of influenza is developed. The effective reproduction number (Re) and the basic reproduction number (R0) are calculated.For this model,there exists at least four equilibrium points. The stability of the disease free equilibrium point and endemic equilibrium point is analyzed. Results of the analysis show that there exists a locally stable disease free equilibrium point, E0 when Re < 1 and a unique endemic equilibrium E* , when Re > 1. Sensitivity analysis is carried out to determine parameters that should be targeted by intervention strategies. The effect of drug resistance and transmission rate of the resistant strain on the infected and the recovered is discussed.Results show that development of drug resistance and transmission of the resistant strain result in widespread of the resistant strain. A decrease in either of these two factors leads to a significant reduction in the number of infected individuals,hence, social distancing can be used as an intervention mechanism to curb the spread of the resistant strain.

Some Fixed Point Theorems for Berinde-Type Contraction Mappings on Gp-Metric Spaces

Şeyma Çevik, Hasan Furkan

Journal of Advances in Mathematics and Computer Science, Page 1-18
DOI: 10.9734/JAMCS/2017/37129

In this paper, we define the concepts of (δ, 1 − δ)-weak contraction, (φ , 1 − δ)-weak contraction and Ćirić-type almost contraction in the sense of Berinde in Gp-complete Gp-metric space. Furthermore, we prove the existence of fixed points and common fixed points of mappings satisfying Berinde-type contractions stated above and also provide the conditions which are necessary for the uniqueness of the fixed points and common fixed points. Consequently, we obtain the generalizations of comparable results in the literature. In addition, we introduce a few examples which ensure the existence of these attained results.

Second derivative Hybrid Block Backward Differentiation Formulae for Numerical Solution of Stiff Systems

Y. Skwame, G. M. Kumleng, I. A. Bakari

Journal of Advances in Mathematics and Computer Science, Page 1-11
DOI: 10.9734/JAMCS/2017/36340

In this research work, two and three step second derivative hybrid block backward differentiation formulae (SDHBBDF) method of order 6 and 7 are presented for the numerical solution of stiff initial value problems. The block scheme was obtained through increasing the number k in the multi-step collocation (MC) with the aid of maple software. The stability analysis of the method have shown that the schemes are A-stable and consistent. We compared SDHBBDF methods with exact solutions and have shown that the results obtained using proposed new block methods are excellent for the solution of stiff problems.

Some Stationary Solutions of Schrödinger Map Equation

Yanting Zhou, Hui Yang, Ganshan Yang

Journal of Advances in Mathematics and Computer Science, Page 1-13
DOI: 10.9734/JAMCS/2017/37475

In this paper, we construct a type of plane wave solution of Landau-Lifshitz equation with the model | u | = 1. In addition, we discover the law which when the spin vector u is moving along one direction, the spin vector u approaches the south pole (0, 0, −1) from the north pole (0, 0, 1) with the model | x | from 0 tend to ∞. Landau-Lifshitz equations describe an evolution of spin field in continuous ferromagnetic. Therefore, it is very significant to study the problems about magnetization movement. Many people studied a lot of problems and constructed many solutions about the Landau-Lifshitz equation, but no one to study the linear plane wave solution. So, in this paper, we construct some stationary solutions of Schrodinger Map equation which contains a style of plane wave solutions.