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.

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

Background: White spot lesions (WSLs) are subsurface enamel demineralization manifested as white opacities which had an esthetic problem. The purpose of this in-vitro study was to evaluate the lesion depth improvement of WSLs following application of fluoride varnish, tooth mousse and resin infiltration (ICON). Materials and methods: Artificial WSLs were created on 120 premolar teeth using demineralization solution with pH (4-4.5). Samples randomly allocated into four groups; fluoride varnish, tooth mousse, ICON and untreated group. Groups were discolored in Cola and orange juice for 24 hours. Teeth were ground sectioned by longitudinal cutting then these sections examined and photographed under stereomicroscope at 12X magnification then an

Phoenix dactylifera l. pinnae (the green leaves of dates palm) were used as natural reinforcing (strengthening) fibers to improve the mechanical properties of polyester as a matrix material, the fibers of the green leaves of dates palm were used in two lengths, 10 and 20mm with five rates of 0, 2.5, 5, 10, and 20% , where the reinforcing with the leaves fibers increases the hardness strength from 76.5 to be about 86.55 , the Impact value raised from about 0.313 to 0.461 , in addition to that the flexural strength from 2.66 to be about 55 , and the thermal conductivity increases from 2.54 𝑤∕𝑚.℃ to 5.41 𝑤∕𝑚.℃. The results of the present search explains that the composite samples reinforced at rate 20% and 10mm fiber length

A Laced Reinforced Concrete (LRC) structural element comprises continuously inclined shear reinforcement in the form of lacing that connects the longitudinal reinforcements on both faces of the structural element. This study conducted a theoretical investigation of LRC deep beams to predict their behavior after exposure to fire and high temperatures. Four simply supported reinforced concrete beams of 1500 mm, 200 mm, and 240 mm length, width, and depth, respectively, were considered. The specimens were identical in terms of compressive strength (  40 MPa) and steel reinforcement details. The same laced steel reinforcement ratio of 0.0035 was used. Three specimens were burned at variable durations and steady-state temperatures (one

The effect of short range correlations on the inelastic Coulomb form factors for excited +2 states (1.982, 3.919, 5.250 and 8.210MeV) and +4 states (3.553, 7.114, 8.960 and 10.310 MeV) in O18 is analyzed. This effect (which depends on the correlation parameterβ) is inserted into the ground state charge density distribution through the Jastrow type correlation function. The single particle harmonic oscillator wave function is used with an oscillator size parameter .b The parameters β and b are adjusted for each excited state separately so as to reproduce the experimental root mean square charge radius of .18O The nucleusO18 is considered as an inert core of C12 with two protons and four neutrons distributed over 212521211sdp−− activ

When sites of new communication occurs which represents the merit of the development of communication technology which is characterized by the services of ( facebook-twiter-corapora-youtube-mass space-friendster-flicker-willnecked in addition to the direct services for viber-whatsup-telgram-and chat on) play important role in changing the infrastructure of Arabic societies which are consideredas closed and not changeable societies during near period and the significance of this study comes from the importounce of this subject which is considered as anew trend of the age on the field of media and public response and acceptance inspite of what is known about Arabic society-it doesn’t accept change-this occurance is associated with terms