The present paper investigates the role of fear and predator dependent refuge in the prey-predator system. The system describes the interaction between prey and a stage structure of predator that incorporates Holling II functional response. The predator splits into two compartments immature (juvenile) and mature (adult). The mature predators can hunt and reproduce but this capability is not found in the immature predators, the immature depend on their parents. The growth rate of prey decreases due to the existence of mature predators. The existence, uniqueness, and boundedness of the solution of the system are investigated. Three equilibrium points of the system are determined. The local stability of the system is studied. The global stabil

The necessary optimality conditions with Lagrange multipliers  are studied and derived for a new class that includes the system of Caputo–Katugampola fractional derivatives to the optimal control problems with considering the end time free. The formula for the integral by parts has been proven for the left Caputo–Katugampola fractional derivative that contributes to the finding and deriving the necessary optimality conditions. Also, three special cases are obtained, including the study of the necessary optimality conditions when both the final time  and the final state  are fixed. According to convexity assumptions prove that necessary optimality conditions are sufficient optimality conditions.

Laser is a powerful device that has a wide range of applications in fields ranging from materials science and manufacturing to medicine and fibre optic communications. One remarkable

Experimental study on the effect of cylindrical hollow cathode, working pressure and magnetic field on spatial glow distribution and the characteristics of plasma produced by dc discharge in Argon gas, were investigated by image analyses for the plume within the plasma. It was found that the emission intensity appears as a periodic structure with many peaks appeared between the electrodes. Increasing the pressure leads to increase the number of intensity peaks finally converted to continuous form at high pressure, especially with applied of magnetic field, i.e. the plasma is more stable with the presence of magnetic field. The emission intensity study of plasma showed that the intensity has a maximum value at 1.07 mbar pressure and decre

The cost-effective carbon cross-linked Y zeolite nanocrystals composite (NYC) was prepared using an eco-friendly substrate prepared from bio-waste and organic adhesive at intermediate conditions. The green synthesis method dependent in this study assures using chemically harmless compounds to ensure homogeneous distribution of zeolite over porous carbon. The greenly prepared cross-linked composite was extensively characterized using Fourier transform infrared, nitrogen adsorption/desorption, Field emission scanning electron microscope, Dispersive analysis by X-ray, Thermogravimetric analysis, and X-ray diffraction. NYC had a surface area of 176.44 m2/g, and a pore volume of 0.0573 cm3/g. NYC had a multi-function nature, sustained at a long-

The aim of present study was to develop solid and liquid  self-microemulsifying drug  delivery system of poorly water soluble drug mebendazole using Aerosil 200 as solid carrier.  Microemulsions are clear, stable, isotropic liquid mixtures of oil, water and surfactant, frequently in combination with a co-surfactant having droplet size range usually in the range of 20-250 nm. Oleic acid, tween 80 and polypropylene glycol were selected as oil, surfactant and co-surfactant respectively and for preparation of stable SMEDDS, micro emulsion region was identified by constructing pseudo ternary phase diagram containing different proportion of surfactant: co-surfactant (1:1, 2:1 and 3:1), oil and water. In brief S/ CoS mix means su

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The two-neutron halo-nuclei (¹⁷B, ¹¹Li, ⁸He) was investigated using a two-body nucleon density distribution (2BNDD) with two frequency shell model (TFSM). The structure of valence two-neutron of ¹⁷B  nucleus in a pure (1d_5/2) state and in a pure (1p_1/2) state for  ¹¹L and ⁸He nuclei. For our tested nucleus, an efficient (2BNDD's) operator for point nucleon system folded with two-body correlation operator's functions was used to investigate nuclear matter density distributions, root-mean square (rms) radii, and elastic electron scattering form factors. In the nucleon-nucleon forces the correlation took account of