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 Problems (IVPs) compared to other approaches found in the literature, which is verified by the obtained solutions. The determination of the transient solutions for Markov chains is presented using the proposed method. The results show better accuracy in solving the transient distribution in Markov chains, which implies that there is an improved assurance in adopting this approach in future studies of the Markov chain modeling process for predicting future events based on the current state of a process. Future studies on Markov chain modeling could adopt the introduced method to predict future events based on the current state of a process.
The aerodynamic characteristics of general three-dimensional rectangular wings are considered using non-linear interaction between two-dimensional viscous-inviscid panel method and vortex ring method. The potential flow of a two-dimensional airfoil by the pioneering Hess & Smith method was used with viscous laminar, transition and turbulent boundary layer to solve flow about complex configuration of airfoils including stalling effect. Viterna method was used to extend the aerodynamic characteristics of the specified airfoil to high angles of attacks. A modified vortex ring method was used to find the circulation values along span wise direction of the wing and then interacted with sectional circulation obtained by Kutta-Joukowsky theorem of
... Show MoreAn efficient combination of Adomian Decomposition iterative technique coupled with Laplace transformation to solve non-linear Random Integro differential equation (NRIDE) is introduced in a novel way to get an accurate analytical solution. This technique is an elegant combination of theLaplace transform, and the Adomian polynomial. The suggested method will convert differential equations into iterative algebraic equations, thus reducing processing and analytical work. The technique solves the problem of calculating the Adomian polynomials. The method’s efficiency was investigated using some numerical instances, and the findings demonstrate that it is easier to use than many other numerical procedures. It has also been established that (LT
... Show MoreBackground: Congenital club foot is a complex deformity of foot .It is a collection of different abnormalities, with different etiologies. Consequently, Severity varies with difficulties in evaluating treatment strategies with outcome results. The treatment of congenital club foot remains controversial. Usually, the orthopedist's goal is to obtain anatomically and functionally normal feet in all patients. Objective: To asses short term follow up result of conservatively treated club feet in relation to the age of initial casting by Ponseti technique. Methods :A cross sectional observational study with some comparative content done in Al-kindy
... Show MoreAlumina thin films have significant applications in the areas of optoelectronics, optics, electrical insulators, sensors and tribology. The novel aspect of this work is that the homogeneous alumina thin films were prepared in several stages to generate a plasma jet. In this paper, aluminium nanoparticles suspended in vinyl alcohol were prepared using exploding wire plasma. TEM analysis was used to determine the size and shape of particles in aluminium and vinyl alcohol suspensions; the TEM images showed that the particle size is 17.2 nm. Aluminium/poly vinyl alcohol (Al/PVA) thin films were prepared using this suspension on quartz substrate by plasma jet technique at room temperature with an argon gas flow rate of 1 L/min. The Al/PV
... Show MoreManganese-zinc ferrite MnxZn1-xFe2O4 (MnZnF) powder was prepared using the sol-gel method. The morphological, structural, and magnetic properties of MnZnF powder were studied using X-ray diffraction (XRD), atomic force microscopy (AFM), energy dispersive X-ray (EDX), field emission-scanning electron microscopes (FE-SEM), and vibrating sample magnetometers (VSM). The XRD results showed that the MnxZn1-xFe2O4 that was formed had a trigonal crystalline structure. AFM results showed that the average diameter of Manganese-Zinc Ferrite is 55.35 nm, indicating that the sample has a nanostructure dimension. The EDX spectrum revealed the presence of transition metals (Mn, Fe, Zn, and O) in Mang
... Show MoreThis paper is concerned with the numerical solutions of the vorticity transport equation (VTE) in two-dimensional space with homogenous Dirichlet boundary conditions. Namely, for this problem, the Crank-Nicolson finite difference equation is derived. In addition, the consistency and stability of the Crank-Nicolson method are studied. Moreover, a numerical experiment is considered to study the convergence of the Crank-Nicolson scheme and to visualize the discrete graphs for the vorticity and stream functions. The analytical result shows that the proposed scheme is consistent, whereas the numerical results show that the solutions are stable with small space-steps and at any time levels.
Flexure members such as reinforced concrete (RC) simply supported beams subjected to two-point loading were analyzed numerically. The Extended Finite Element Method (XFEM) was employed for the treatment the non-smooth h behaviour such as discontinuities and singularities. This method is a powerful technique used for the analysis of the fracture process and crack propagation in concrete. Concrete is a heterogeneous material that consists of coarse aggregate, cement mortar and air voids distributed in the cement paste. Numerical modeling of concrete comprises a two-scale model, using mesoscale and macroscale numerical models. The effectiveness and validity of the Meso-Scale Approach (MSA) in modeling of the reinforced concrete beams w
... Show MoreThe aim of this investigation is to study and analysis the role of governance in the evaluation of the and social performance of the economic units to be addressed through the concept of corporate governance and then to the social performance and its relationship to corporate governance.
The most important obtained results from this research is that the corporate governance of extreme importance, and derive their importance from being an essential tool to contribute to the transparency and fair disclosure of the financial results of economic units in the fight against financial and administrative corruption in economic units, thus providing protection and confidence of all parties, and the evaluating soci
... Show MoreAbstract:
Rabi’a tribe lived on the land of Euphrates since the first century of the
Christ. Then that land becomes her homeland. The Persians tried many times
to drive her away from that land, but with out result.
In the course of time Rabi’a become more knowledgeable of Persia.
This tribe proved her love and sanctification to the land of Euphrates, in the
battle of Dhyqar.
Rabi’a converted to Islam quickly and helped the Muslims to conquer
Iraq with a big number of fighters in many battles like al- Qadisyyah. That
influenced the anger of Mudriat Arab tribes who were their old enemies.
Mudriat tribes did their efforts to reduce the importance of Rabi’a because of
some its branches were among of t