In this paper,a prey-predator model with infectious disease in predator population
is proposed and studied. Nonlinear incidence rate is used to describe the transition of
disease. The existence, uniqueness and boundedness of the solution are discussed.
The existences and the stability analysis of all possible equilibrium points are
studied. Numerical simulation is carried out to investigate the global dynamical
behavior of the system.

A dynamical system describes the consequence of the current state of an event or particle in future. The models expressed by functions in the dynamical systems are more often deterministic, but these functions might also be stochastic in some cases. The prediction of the system's behavior in future is studied with the analytical solution of the implicit relations (Differential, Difference equations) and simulations. A discrete-time first order system of equations with quadratic nonlinearity is considered for study in this work. Classical approach of stability analysis using Jury's condition is employed to analyze the system's stability. The chaotic nature of the dynamical system is illustrated by the bifurcation theory. The enhancement o

In this paper, we derive and prove the stability bounds of the momentum coefficient µ and the learning rate ? of the back propagation updating rule in Artificial Neural Networks .The theoretical upper bound of learning rate ? is derived and its practical approximation is obtained

    In this paper, we introduce the bi-normality set, denoted by , which is an extension of the normality set, denoted by  for any operators  in the Banach algebra . Furthermore, we show some interesting properties and remarkable results. Finally, we prove that it is not invariant via some transpose linear operators.

This research is concerned with the study of (the aesthetic of constructive relations in linear composition) with what distinguished Arabic calligraphy through the style and artistic method in its construction, and the specifications it carries that enabled it to pay attention to building formations to achieve in its total linear ranges aesthetic values and relationships. Through the research, the models and the exploratory study that he obtained, the researcher was able to raise the research problem in the first chapter according to the following question: What is the aesthetic of constructive relations in linear formation?
The importance of the research in achieving the aesthetics of the formations, which is a wide field according t

in this paper fourth order kutta method has been used to find the numerical solution for different types of first liner

   In this work, a novel technique to obtain an accurate solutions to nonlinear form by multi-step combination with Laplace-variational approach (MSLVIM) is introduced. Compared with the  traditional approach for variational it overcome all difficulties and enable to provide us more an accurate solutions with extended of the convergence region as well as covering to larger intervals which providing us a continuous representation of approximate analytic solution and it give more better information of the solution over the whole time interval. This technique is more easier for obtaining the general Lagrange multiplier with reduces the time and calculations. It converges rapidly to exact formula with simply computable terms wit

     Structure of network, which is known as community detection in networks, has received a great attention in diverse topics, including social sciences, biological studies, politics, etc. There are a large number of studies and practical approaches that were designed to solve the problem of finding the structure of the network. The definition of complex network model based on clustering is a non-deterministic polynomial-time hardness (NP-hard) problem. There are no ideal techniques to define the clustering. Here, we present a statistical approach based on using the likelihood function of a Stochastic Block Model (SBM). The objective is to define the general model and select the best model with high quality. Therefor