We define L-contraction mapping in the setting of D-metric spaces analogous to L-contraction mappings [1] in complete metric spaces. Also, give a definition for general D- matric spaces.And then prove the existence of fixed point for more general class of mappings in generalized D-metric spaces.

This study has contributed to understanding a delayed prey-predator system involving cannibalism. The system is assumed to use the Holling type II functional response to describe the consuming process and incorporates the predator’s refuge against the cannibalism process. The characteristics of the solution are discussed. All potential equilibrium points have been identified. All equilibrium points’ local stability analyses for all time delay values are investigated. The system exhibits a Hopf bifurcation at the coexistence equilibrium, which is further demonstrated. The center manifold and normal form theorems for functional differential equations are then used to establish the direction of Hopf bifurcation and the stability of the per

Simulation of free convection heat transfer in a square enclosure induced by heated thin plate is represented numerically. All  the enclosure walls have constant temperature lower than the plate’s temperature. The flow is assumed to be two-dimensional. The discretized equations were solved stream function, vorticity, and energy equations by finite difference method using explicit technique and Successive Over- Relaxation method. The study was performed for different values of Rayleigh number ranging from 10³ to 10⁵ for different angle position of heated thin plate(0°, 45°, 90°). Air was chosen as a working fluid (Pr = 0.71). Aspect ratio of center of plate to the parallel left wall A₂

In this paper, a least squares group finite element method for solving coupled Burgers' problem in   2-D is presented. A fully discrete formulation of least squares finite element method is analyzed, the backward-Euler scheme for the time variable is considered, the discretization with respect to space variable is applied as biquadratic quadrangular elements with nine nodes for each element. The continuity, ellipticity, stability condition and error estimate of least squares group finite element method are proved.  The theoretical results  show that the error estimate of this method is . The numerical results are compared with the exact solution and other available literature when the convection-dominated case to illustrate the effic

A simple, fast, selective of a new flow injection analysis method coupled with potentiometric detection was used to determine vitamin B1 in pharmaceutical formulations via the prepared new selective membranes. Two electrodes were constructed for the determination of vitamin B1 based on the ion-pair vitamin B1-phosphotungestic acid (B1-PTA) in a poly (vinyl chloride) supported with a plasticized di-butyl phthalate (DBPH) and di-butyl phosphate (DBP). Applications of these ion selective electrodes for the determination of vitamin B1 in the pharmaceutical preparations for batch and flow injection systems were described. The ion selective membrane exhibited a near-Nernstian slope values 56.88 and 58.53 mV / decade, with the linear dy

Abstract: Microfluidic devices present unique advantages for the development of efficient drug assay and screening. The microfluidic platforms might offer a more rapid and cost-effective alternative. Fluids are confined in devices that have a significant dimension on the micrometer scale. Due to this extreme confinement, the volumes used for drug assays are tiny (milliliters to femtoliters).

 In this research, a microfluidic chip consists of micro-channels carved on substrate materials built by using Acrylic (Polymethyl Methacrylate, PMMA) chip was designed using a Carbon Dioxide (CO₂) laser machine. The CO2 parameters have influence on the width, depth, roughness of the chip. In order to have regular

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