In this paper, we establish the conditions of the occurrence of the local bifurcations, such as saddle node, transcritical and pitchfork, of all equilibrium points of an eco-epidemiological model consisting of a prey-predator model with SI (susceptible-infected) epidemic diseases in prey population only and a refuge-stage structure in the predators. It is observed that there is a transcritical bifurcation near the axial and free predator equilibrium points, near disease-free equilibrium point is a saddle-node bifurcation and near positive (coexistence) equilibrium point is a saddle-node bifurcation, a transcritical bifurcation and a pitchfork bifurcation. Further investigations for Hopf bifurcation near coexistence equilibrium point

The influence of fear on the dynamics of harvested prey-predator model with intra-specific competition is suggested and studied, where the fear effect from the predation causes decreases of growth rate of prey.  We suppose that the predator attacks the prey under the Holling type IV functional response. he existence of the solution is investigated and the bounded-ness of the solution is studied too. In addition, the dynamical behavior of the system is established locally and globally. Furthermore, the persistence conditions are investigated. Finally, numerical analysis of the system is carried out.

The concept of intertextuality was one of the problems that occupied the attention of critics and critics in targeting the structure of textual intertextuality between texts and their overlap in the process of producing meaning. Until intertextuality became a stable term and it can be monitored in the structure of the theatrical text and determining the mechanisms of this intertextuality between texts through fields and classifications agreed upon by the most important critics who wrote and considered intertextuality. Perhaps our previous research (the approach of exposure in the epistemological hallway to intertextuality) was an attempt to interview a terminology, which the researcher intended to monitor, through the mechanisms of inter

The proton-neutron interacting boson model (IBM-2) has been used to make a schematic study of the Ruthenium ( ) isotopes of mass region around with and . For each isotope of the values of the IBM-2 Hamiltonian parameters, which yield an acceptable results for excitation energies in comparison with those of experimental data, have been determined. Fixed values of the effective charges ( ) and of the proton and neutron g factors ( and ) have been chosen for all isotopes under study. The calculated electric quadrupole moments of state, transitions, the magnetic dipole moments transitions and mixing ratios are in reasonable agreement with the experimental data.

This work describes the enhancement of phenol red decolorization through immobilizing of laccase in chitosan and enzyme recycling. Commercial laccase from white rot fungus, Trametesversicolor (Tvlac), was immobilizedin to freshly prepared chitosan beads by using glutaraldehyde as a cross linker. Characterization of prepared chitosan was confirmed by FTIR and scanning electron microscope (SEM). Tvlac (46.2 U/mL) immobilized into chitosan beads at 0.8 % glutaraldehyde (v/v) within 24 hrs. Synthetic (HBT) and natural (vanillin) mediators were used to enhance dye decolorizoation. It was found that 89 % of phenol red was decolorized by chitosan beads within 180 min. in the absence of enzyme and mediator, while decolorization percenta