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

Steps were taken to obtain the Kojic acid crystals from local fungal isolation A. flavus WJF81 by separating the fermentation products from the fungus mycelium from the production plant at the centrifuge at a speed of 5000 cycles for 10 minutes. The extraction was followed by ethyl acetate then supernatant concentrate by using rotary evaporator, and dried with heat oven 37ºC. Long, yellowish, pristine acid crystals were obtained that examined the optical microscope with a magnification force of 10x and 40x. The melting point of kojic acid was determined between 152.9-153.5 °C Results of the diagnosis of Kojic acid by applying High pressure liquid chromatography HPLC technique showed that the acid was at one peak, which was close to the

This paper is attempt to study the nonlinear second order delay multi-value problems. We want to say that the properties of such kind of problems are the same as the properties of those with out delay just more technically involved. Our results discuss several known properties, introduce some notations and definitions. We also give an approximate solution to the coined problems using the Galerkin's method.

This study evaluated the structural changes of enamel treated by the Regenerate system and carbon dioxide (CO2) laser against acid challenge. Thirty human enamel slabs were prepared and assigned into three groups: Group I: untreated (control); Group II: treated with the Regenerate system; and Group III exposed to CO2 laser. All specimens were subjected to an acid challenge (pH 4.5–7.0) for 14 days. Specimens were evaluated and compared at 120 points using five Raman microspectroscopic peaks; the phosphate vibrations ν1, ν2, ν3, and ν4 at 960, 433, 1029, and 579 cm−1, respectively, and the carbonate at 1070 cm−1, followed by Vickers microhardness test. The ratio of carbonate to phosphate was correlated to the equivalent mic

""

A Raman spectroscopy method was optimised to examine the chemical changes of aspirin tablets after interaction with helium temperatures. Several aspirin tablets were exposed to plasma-assisted desorption ionisation flame for different times (10, 30, 50, 60, 180 and 300s) and then analysed by Raman spectroscopy using optimal conditions. The changes in chemistry between exposed and fresh (without exposure to plasma) tablets were compared. The vibrational peaks of the aspirin molecule in the Raman spectrum were identified by checking the peak position. The results showed clear spectra with increases in intensity of vibrational peaks until 30s, whereas no spectra were measured for the exposed tablets to plasma flame after 50s. It can, the

Cadmium sulphide CdS films with 200 nm have been prepared by thermal evaporation technique on glass substrate at substrate room temperature under vacuum of 10^-5mbar.In this paper, the effect of Dielectric Barrier Discharge plasma on the optical properties of the CdS film. The prepared films were exposed to different time intervals (0, 3, 5, 8) min. For every sample, the Absorption A, absorption coefficient α , energy gap Eg ,extinction coefficient K and dielectric constant ε were studied. It is found that the energy gap were decreased with exposure time, and absorption , Absorption coefficient, refractive index, extinction coefficient,  dielectric constant increased with time of exposure to the plasma. Our study conside