### i-manager's Journal on Mathematics (JMAT)

Research Paper

#### Abstract

The main purpose of the present paper is to analyze the processes in a lossy transmission line terminated by in-series connected nonlinear RCL-loads. The distortion less propagation of the TEM-waves along the line under the Heaviside's condition has been investigated in a previous paper. Here we assume that the Heaviside condition is not satisfied. This leads to difficulties which can be overcome by a different type operator presentation of the mixed problem for the lossy transmission line. First, we formulate boundary conditions using the Kirchhoff's law, then transform the system in an operator form, and apply the fixed point method to obtain an existence-uniqueness theorem for a generalized solution. The uniqueness of solution is lost along the whole length of the line. Finally, we demonstrate the conditions of the main theorem on a typical example.

Research Paper

#### Abstract

The Johnson-Segalman model is a viscoelastic fluid model for non-affine deformations. However, non-Newtonian fluid is a fluid with properties that differ in any way from Newtonian fluids. The focus of this paper is deriving of Johnson-Segalman model in cylindrical co-ordinates (r, q, z). The continuity equation, momentum equation were derived from vector form to differential form. The Johnson-Segalman model was derived in cylindrical co-ordinates and system of partial differential equations were obtained.

Research Paper

#### Abstract

In this paper, the authors analyze the stability analysis of directly transmitted viral microparasite model, which includes susceptible (x), infective (y), and immune (z) populations. The total population N is given by the sum of three populations (N=x + y +z). A distributed type of delay is incorporated in the interaction of susceptible (x) and infective (y) populations. The model is represented by the system of nonlinear integro-differential differential equations. It is observed that the model possessed a unique endemic equilibrium point and studied the system dynamics at this point using two delay kernels. The system is asymptotically stable if . Numerical simulation is carried out using MATLAB with two delay kernels in support of stability analysis.

Research Paper

#### Abstract

The circular models based on the Rising Sun function are motivated by purely mathematical considerations as a smoothing function and possible application. This work takes a further step in this direction using several mathematical tools such as Real Analysis along with MATLAB and is applied to enlarge the horizon of Mathematical Statistics. All the available circular / angular models are continuous distributions. Scant attention was made on construction and applications of discrete circular / angular models. Circular model using the Rising Sun function on continuous Wrapped Cauchy distribution is available in literature. Here an attempt is made to construct new discrete circular model by applying the methodology of discretization on the Rising Sun Wrapped Cauchy distribution and the population characteristics are evaluated using MATLAB.

Review Paper

#### Abstract

This paper reviews the literature related to reliability modeling and analysis of complex industrial systems. The types of systems analyzed, various operating conditions and assumptions considered, different methodologies employed by the researchers, and the outcomes of the analysis, have been reviewed. The existing literature has been classified on the basis of significant system parameters. Behavior of important reliability indicators with respect to various system parameters has also been discussed. Tabular and graphical study is carried out to demonstrate crucial results. An up-to-date bibliography is presented systematically.