The purpose of this paper is to introduce and prove some coupled coincidence fixed point theorems for self mappings satisfying -contractive condition with rational expressions on complete partially ordered metric spaces involving altering distance functions with mixed monotone property of the mapping. Our results improve and unify a multitude of coupled fixed point theorems and generalize some recent results in partially ordered metric space. An example is given to show the validity of our main result. 

It is through a review of conversion of vegetable oils into glycidyl ethers focusing on their roles in achieving sustainability and improved epoxy resin performance. It involves functionalization of triglycerides in the form of epoxidation followed by glycidylation and yields bio-based monomers having improved mechanical as well as thermal properties. The review covers the underlying chemistry, production drivers, industrial applications, and future issues, supported by quantitative data and comparative studies. In addition, it integrates recent data on catalyst choice, feedstock flexibility, and environmental performance factors of bio-based resins, indicating their suitability for replacing traditional petroleum-based components.<

Markov chains are an application of stochastic models in operation research, helping the analysis and optimization of processes with random events and transitions. The method that will be deployed to obtain the transient solution to a Markov chain problem is an important part of this process. The present paper introduces a novel Ordinary Differential Equation (ODE) approach to solve the Markov chain problem. The probability distribution of a continuous-time Markov chain with an infinitesimal generator at a given time is considered, which is a resulting solution of the Chapman-Kolmogorov differential equation. This study presents a one-step second-derivative method with better accuracy in solving the first-order Initial Value Problem

In this paper, a theoretical analysis of optimum bed thickness operates under mass transfer control for realizing a high efficiency and reaction conversion of an electrochemical reactor has been made based on flowthrough porous electrode (FTPE) configuration. Many models have been used to represent the optimum bed thickness by taking a look into previous works concerned and collecting all related information, data, and models. The parameters that affect the optimum bed thickness have been visualized and reviewed, and almost all of them have been examined by experimental data from different sources and based on the various models. It has been found that the increase in electrolyte flow rate, concentration, limiting current density, and sp

   The kinetics of removing cadmium from aqueous solutions was studied using a bio-electrochemical reactor with a packed bed rotating cylindrical cathode. The effect of applied voltage, initial concentration of cadmium, cathode rotation speed, and pH on the reaction rate constant (k) was studied. The results showed that the cathodic deposition occurred under the control of mass transfer for all applied voltage values ​​used in this research. Accordingly, the relationship between logarithmic concentration gradient with time can be represented by a first-order kinetic rate equation. It was found that the rate constant (k) depends on the applied voltage, the initial cadmium concentration, the pH and the rotational speed of cathode. It

This research is addressing the effect of different ferrocene concentration (0.00, 2.15x10-3, 4.30x10-3, 8.60x10-3, and 12.9x10-3) on the bulk free radical polymerization of methyl methacrylate monomer in benzene using benzoyl peroxide as initiator. The polymerization was conducted at 60º C under free oxygen atmosphere. The resulting polymers were characterized by FTIR. The results were compared with the presence and absence of ferrocene at 10% conversion. The %conversion was 3.04% with no ferrocene present in the polymerization medium and its increase to 9.06 with a first lowest ferrocene concentration added, i.e. 2.15 x10-3mol/l. This was positively reflected on the poly(methyl methacrylate) molecular weight measured by viscosity techniq

A theoretical and experimental investigation was carried out to study the behavior of a two-phase closed thermosyphon loop (TPCTL) during steady-state operation using different working fluids. Three working fluids were investigated, i.e., distilled water, methanol, and ethanol. The TPCTL was constructed from an evaporator, condenser, and two pipelines (riser and downcomer). The driving force is the difference in pressure between the evaporator and condenser sections and the fluid returns to the heating section by gravity. In this study, the significant parameters used in the experiments were filling ratios (FR%) of 50%, 75%, and 100% and heat-input range at the evaporator section of 215-860.2 W. When the loop reached to