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

The experimental proton resonance data for the reaction P+48Ti have been used to calculate and evaluate the level density by employed the Gaussian Orthogonal Ensemble, GOE version of RMT, Constant Temperature, CT and Back Shifted Fermi Gas, BSFG models at certain spin-parity and at different proton energies. The results of GOE model are found in agreement with other, while the level density calculated using the BSFG Model showed less values with spin dependence more than parity, due the limitation in the parameters (level density parameter, a, Energy shift parameter, E1and spin cut off parameter, σc). Also, in the CT Model the level density results depend mainly on two parameters (T and ground state back shift energy, E0), which are app

Due to the urgent need to develop technologies for continuous glucose monitoring in diabetes individuals, poten tial research has been applied by invoking the microwave tech niques. Therefore, this work presents a novel technique based on a single port microwave circuit, antenna structure, based on Metamaterial (MTM) transmission line defected patch for sensing the blood glucose level in noninvasive process. For that, the proposed antenna is invoked to measure the blood glu cose through the field leakages penetrated to the human blood through the skin. The proposed sensor is constructed from a closed loop connected to an interdigital capacitor to magnify the electric field fringing at the patch center. The proposed an tenna sensor i

This research aims to know the effect of the strategy of map bubbles on developing the skills of science operations among 5th grade literary students in the subject of rhetoric and application, and the design of the experimental and control groups with the pre and post-tests was used. The research sample consisted of (50) students divided into two groups, an experimental group of which reached the number of its members is (25) students and studied using the strategy of map bubbles, and a control group of its members reached (25) students and studied in the traditional (standard) method. The researchers prepared a multiple-choice achievement test with several (30) paragraphs, and its validity and consistency were extracted. Then the test was