Applied Mathematics

An Hepatitis B epidemic model with treatment is investigated. The model allows for the some infected individuals to move from the symptomatic phase to the asymptomatic phase by all sorts of treatment methods. The model exhibits two equilibria, namely, the disease-free equilibrium (DFE) and the endemic equilibrium. The stability of these two equilibria is controlled by the basic reproduction number It is shown that if is less than one, the disease-free equilibrium is locally asymptotically stable and is greater than one, the unique endemic equilibrium is locally asymptotically stable. By computer simulation it is found that if the growth rate of pharmacological effect of the lamivadine to the free virus increases, the symptomatic phase decreases. Numerical simulations are also carried out to investigate the influence of certain parameters on the spread of disease, to support the analytical results. Also, sensitivity analysis of the endemic equilibrium point is carried out.

In this paper, we made an attempt to study the algebraic nature of intuitionistic fuzzy subsemiring of a semiring.

The dispersion of a solute in an annulus modeling blood as Herschel-Bulkley fluid is studied by using the generalized dispersion model. The impact of the presence of catheter and the non- Newtonian nature of blood is studied. It is observed that the yield stress and presence of catheter inhibit the rate of dispersion. The dispersion coefficient is found to be dependent on the yield stress of the fluid, the power law index of the fluid and the annular gap. The steady state value of dispersion is found to decrease in the order Newtonian, Bingham, Power law and Herschel-Bulkley fluids consecutively. The results of this model can be applied to understand the role played by the size of the catheter on the process of dispersion in a catheterized artery. A comparison of the dispersion coefficient and concentration has been made in the Newtonian, Bingham, Power law and Herschel-Bulkley fluids

In this paper a new Trigonometric shear deformation theory is developed for the static flexure of thick isotropic beam, considering Trigonometric functions in terms of thickness co-ordinate associated with transverse shear deformation effect. The most important feature of the theory is that the transverse shear stress can be obtained directly from the constitutive relations satisfying the shear stress free surface conditions on the top and bottom of the beam. Hence the theory obviates the need of shear correction factor. Governing equations and boundary conditions of the theory are obtained using the principle of virtual work. Results obtained for static flexure of simply supported isotropic beam subjected to various loading cases are compared with those of other refined theories and exact solution.

In this paper, the dynamics of spatially extended infected phytoplankton with the Holling type II functional response and logistically growing susceptible phytoplankton system and also the phytoplankton dynamics with susceptible and infected class of populations with diffusion is studied. The reaction diffusion system exhibits spatiotemporal chaos and pattern formation in phytoplankton dynamics, which is particularly important role for the spatially extended systems. We obtained the condition of diffusion-driven stability for the spatial dynamical system. Also we obtained the numerical simulation for the chaos and pattern formation for understanding the dynamical behavior of the phytoplankton system.

Energy is the primary need of any society. It is consumed in transportation, in industries and for the heating, lighting and water-pumping etc. To fulfil its energy demand, our society is dependent on fossil fuels such as oil, coal and natural gas. But fossil fuels are conventional resources and are depleting fast. Therefore, it is necessary to find some alternatives sources, so as to fulfil the ever increasing demand for energy. This demand can be fulfilled by utilizing renewable energy sources. This paper studies various types of available non-conventional energy sources. It also includes a brief review of the work done by different researchers on mathematical modeling of solar irradiance.

In this paper, we study Lu’s system, and we study the stability of equilibrium point of Lu’s system. Then, we study chaos synchronization of Lu’s system by using adaptive control methods.

An innovative method for the decomposition of the elastic constant tensor into its irreducible parts is presented. The norm concept of elastic constant tensor, norm ratios and irreducible decomposed parts of elastic constant tensor are used to study the anisotropy of tool steel, rock types and the relationship of their structural properties and other properties with their anisotropy are given. Finally the results are indicated.

The desire to economize time and mental effort in an arithmetical computations and to eliminate human liability to error is probably as old as the science of arithmetic itself. This desire led us to the design of a calculator software to estimate the dominant eigenvalue and the corresponding eigenvectors of an n x n matrix up to the tenth order. The method used in designing the software includes developing a Graphical User Interface (GUI) application with MATLAB (Matrix Laboratory) using the Rapid Application Development (RAD). RAD is a software development methodology that involves methods like iteration development and software prototyping. This RAD is used to refactor our codes and amend the design should there be complaints from the users. The application software was tested to estimate the largest eigenvalue and the corresponding eigenvector of an n x n matrix using the power method with accuracy and reduced time.

In this paper, we introduce and study some new separation axioms using the (1, 2)*-?gb-open sets in bitopological spaces.