In this paper, the dynamics of scavenger species predation of both susceptible and infected prey at different rates with prey refuge is mathematically proposed and studied. It is supposed that the disease was spread by direct contact between susceptible prey with infected prey described by Holling type-II infection function. The existence, uniqueness, and boundedness of the solution are investigated. The stability constraints of all equilibrium points are determined. In addition to establishing some sufficient conditions for global stability of them by using suitable Lyapunov functions. Finally, these theoretical results are shown and verified with numerical simulations.

The aim of this research is analysis the effect of the changes in (GDA, g, inflation) at average and standard economic curriculum in composition of the models, depending on SPSS program in analysis, and according to available date from central bank of Iraq and during the period from 2003 to 2018 and by using OLS and estimate of the equation and the results showed a statistical significance relation in incorporeal level 5% and the R² value equal  to 92.1 refer to the changes in independent variables explain 92% of changes of unemployment and the independent variables effect are very limit depend on estimated parameters in the model and respectively (0.986,0.229,-0.060), the research recommended necessity to active the inve

Throughout this paper we study the properties of the composition operator
C
p1  o
p2  o…o
pn  induced by the composition of finite numbers of special
automorphisms of U,
pi  (z)  i
i
p z
1 p z


Such that pi  U, i  1, 2, …, n, and discuss the relation between the product of
finite numbers of automorphic composition operators on Hardy space H2 and some
classes of operators.

The semiconductor ZnO is one of II – VI compound group, it is prepare as thin films by using chemical spray pyrolysis technique; the films are deposited onto glass substrate at 450 °C by using aqueous zinc chloride as a spray solution of molar concentration 0.1 M/L. Sample of the prepared film is irradiating by Gamma ray using CS 137, other sample is annealed at 550°C. The structure of the irradiated and annealed films are analyzed with X-ray diffraction, the results show that the films are polycrystalline in nature with preferred (002) orientation. The general morphology of ZnO films are imaged by using the Atomic Force Microscope (AFM), it constructed from nanostructure with dimensions in order of 77 nm.
The optical properties o

The dynamical behavior of a two-dimensional continuous time dynamical system describing by a prey predator model is investigated. By means of constructing suitable Lyapunov functional, sufficient condition is derived for the global asymptotic stability of the positive equilibrium of the system. The Hopf bifurcation analysis is carried out. The numerical simulations are used to study the effect of periodic forcing in two different parameters. The results of simulations show that the model under the effects of periodic forcing in two different parameters, with or without phase difference, could exhibit chaotic dynamics for realistic and biologically feasible parametric values.

A numerical investigation has been performed to examine the effect of fluorine concentration on the chain reaction mechanisms and parameters of hydrogen fluoride (HF) chemical laser. The practical difficulties associated with this type of lasers impose that an alternative route might be quite useful. Thus, particular attention was paid to develop a computer program to investigate various processes. The results of this computer simulation program proved their credibility when compared with the little published data. This computer program is called Reaction Rate Simulation Model (RRSM). An entirely new approach to emulate the reaction mechanisms has been followed. The effectiveness of reaction rates in the processes of HF lase