In this paper, we establish a common xed point theorem for two pairs of mappings satisfying an almost generalized contractive condition for comparable elements in a partially ordered metric space. Our results generalize and extend the main results in [2] to multivalued mappings. As corollaries we obtain the results in [8, 9], and many others.

In this paper, we introduce the notion of mixed weakly monotone property for two hybrid pairs and each of them consists of multi-valued mapping and single valued mapping defined on partially ordered metric space and then we prove coincidence and common fixed point theorems for two hybrid pairs under different contractive conditions. These theorems extend and generalize very recent results that can be found in [12] and many others.

An analytical solution for the dissipative system of two charge qubits located in an SC-cavity field is obtained in the dispersive regime. Therefore, the quantum correlation of the trace distance discord, the Bell function and the logarithmic negativity are investigated. The sensitivity of the correlation measures are investigated under the physical parameters of the phase damping and the qubit distribution angle of the initial symmetric/non-symmetric Bell-state, whereby correlation phenomena, such as the oscillatory behavior, disappearance/appearance and the collapses/revivals, are proven to demonstrate noticeable changes and high sensitivity to these physical parameters. It is shown that the unitary cavity-qubit interaction leads to the generation of quantum correlations periodically with different amplitudes and oscillations which depend on the initial two-qubit state and its distribution angle. The increase of the two-qubit phase damping leads to the complete disappearance of the generated trace distance, Bell function and log-negativity correlations.

An analytical solution for the dissipative system of two charge qubits located in an SC-cavity field is obtained in the dispersive regime. Therefore, the quantum correlation of the trace distance discord, the Bell function and the logarithmic negativity are investigated. The sensitivity of the correlation measures are investigated under the physical parameters of the phase damping and the qubit distribution angle of the initial symmetric/non-symmetric Bell-state, whereby correlation phenomena, such as the oscillatory behavior, disappearance/appearance and the collapses/revivals, are proven to demonstrate noticeable changes and high sensitivity to these physical parameters. It is shown that the unitary cavity-qubit interaction leads to the generation of quantum correlations periodically with different amplitudes and oscillations which depend on the initial two-qubit state and its distribution angle. The increase of the two-qubit phase damping leads to the complete disappearance of the generated trace distance, Bell function and log-negativity correlations.

An analytical solution for the dissipative system of two charge qubits located in an SC-cavity field is obtained in the dispersive regime. Therefore, the quantum correlation of the trace distance discord, the Bell function and the logarithmic negativity are investigated. The sensitivity of the correlation measures are investigated under the physical parameters of the phase damping and the qubit distribution angle of the initial symmetric/non-symmetric Bell-state, whereby correlation phenomena, such as the oscillatory behavior, disappearance/appearance and the collapses/revivals, are proven to demonstrate noticeable changes and high sensitivity to these physical parameters. It is shown that the unitary cavity-qubit interaction leads to the generation of quantum correlations periodically with different amplitudes and oscillations which depend on the initial two-qubit state and its distribution angle. The increase of the two-qubit phase damping leads to the complete disappearance of the generated trace distance, Bell function and log-negativity correlations.

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Controlling pore structure, e.g. pore diameter, size and distribution of porous silicon (PS) is highly needed for technological applications such as microfluidic operation and filtration in which the pore size and shape can block the entrance of some species or increase its concentration or purity by separation. In the present study, highly doped p-type silicon is utilized to prepare PS with different pore dimensions by electrochemical etching (anodization) process in HF and C2H5OH mixture. The anodization process was performed under various conditions such as different electrolyte types, temperature, and concentrations, etching potential, current density, and etching duration. This research was to further study the influence of electrochemical etching parameters on pore formation kinetics including pore size, layer thickness and mechanistic aspects of silicon etching. The study offers a fundamental understanding of the fabrication process of porous silicon that may be exploited in nanotechnology applications. The present study confirms that the anodization rate increases with increasing the steady-state current at all the presented conditions. It is demonstrated that adjusting the anodizing potential is very important as it determines whether the anodization will lead to PS formation and/or PS dissolution.