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

Convolvulus arvensis is a species of bindweed that is rhizomatous and is in the morning glory family (Convolvulaceae) native to Europe and Asia. The plant is naturally grown in Iraq. The plant was reported to be used in traditional medicine from as early as 1730s.

The Aerial parts of Convolvulus arvensis were macerated in 80% ethanol for 6 days. The concentrated extract was partitioned with n-hexane, chloroform, ethyl acetate- and n-butanol successively. The n-hexane and ethyl acetate, fractions were examined for the presence of phytochemicals by thin l

A real method of predication brake pad wear ,could lead to substantiol economies of time and money. This paper describes how such a procedure has been used and gives the results to establish is reliability by comparing the predicted wear with that which actually occurs in an existing service. The experimental work was carried out on three different commercial samples ,tested under different operation conditions (speed,load,time...etc)using a test ring especially modified for this purpose. Abrasive wear is mainly studied , since it is the type of wear that takes place in such arrangements. Samples wear tested in presences of sand or mud between the mating surfaces under different operational conditions of speed, load and braking time .Mec

We have studied theoretically the response of atomic three- level cascade scheme
of rubidium vapor to a strong laser under conditions in which electromagnetically
induced transparency would be induced on a weak probe beam. We show that the
medium that is an opaque to a probe laser can, by applying both lasers
simultaneously, be made transparent.

        In this work, an anti-reflection coating was prepared in the region (400-1000) nm of wavelength, with a double layer of silicon dioxide (SiO₂) as an inner layer and the second layer of the mixture (SiO₂) and titanium dioxide (TiO₂) with certain ratios, as an outer layer using the chemical spraying method with a number of 6 sprays of layer SiO₂ and 12 sprays of layer SiO₂ - TiO₂. Using the method of chemical spraying deposited on the glass as a substrate with a different number of sprays of SiO₂, and a fixed number of TiO₂-SiO₂. The optical and structural properties were determined using UV-Vis spectroscopy and atomic force mi

Micro-perforated panel (MPP) absorber is increasingly gaining popularity as an alternative sound absorber in buildings compared to the well-known synthetic porous materials. A single MPP has a typical feature of a Helmholtz resonator with a high amplitude of absorption but a narrow absorption frequency bandwidth. To improve the bandwidth, a single MPP can be cascaded with another single MPP to form a double-layer MPP. This paper proposes the introduction of inhomogeneous perforation in the double-layer MPP system (DL-iMPP) to enhance the absorption bandwidth of a double-layer MPP. Mathematical models are proposed using the equivalent electrical circuit model and are validated with experiments with good agreement. It is revealed that the DL-

Background: Sealers should demonstrate adhesive properties to dentin, decreasing the chance of endodontic treatment failure. Increased adhesive properties to dentin may lead to greater strength of the restored tooth, which may provide greater resistance to tooth fracture and clinical longevity of an endodontically treated tooth. The aim of this study was to evaluate the shear bond strength of Bioceramic iRoot SP sealer, AH plus sealer and Apexit plus sealer in absence or presence of smear layer using push out bond strength test. Materials and Methods: Sixty straight single roots of the mandibular premolars were selected for this study. All canals were instrumented using ProTaper rotary instruments to achieve tapered canal walls, instrumenta

The primary components of successful engineering projects are time, cost, and quality. The use of the ring footing ensures the presence of these elements. This investigation aims to find the optimum number of geogrid reinforcement layers under ring footing subjected to inclined loading. For this purpose, experimental models were used. The parameters were studied to find the optimum geogrid layers number, including the optimum geogrid layers spacing and the optimum geogrid layers number. The optimum geogrid layers spacing value is 0.5B. And as the load inclination angle increased, the tilting and the tilting improvement percent for the load inclination angles (5°,10°,15°) are (40%,28%, and 5%) respectively. The reduction percent o