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

Background: Lumbar disc degeneration (LDD) is a common musculoskeletal disorder that frequently causes low back pain (LBP). In addition to the discomfort of lower back pain, it can accompany pain in one or both legs. The lumbar spine and sacrum, consisting of five vertebrae and one bone, determine the spine's balance. Microelements are essential in bone metabolism and are associated with the prevention of osteoporosis and the alleviation of musculoskeletal pain. Objectives: To examine the correlation between lumbar spinal surgery and the concentrations of microelements, namely zinc and copper. Methods: A case-control study was conducted in Ghazi Al-Hariri Hospital in Baghdad, Iraq, during the period from October 2023 to January 2024

Visceral leishmaniasis (VL) or kala-azar is one of the worlds most neglected tropical diseases in mortality and fourth in morbidity, rK39 dipstick was used to diagnose the suspected infected patients as cheapest simple technique which can differentiate recent from chronic infection, for disease out-coming, naïve T-lymphocyte cells should be differentiated into pathogen-specific immunity responses, such as T-helper 1(Th-1) or (Th-2). HLA-G is a special protein defined as nonclassical HLA class I molecule can suppress the immune system through prevention of T-cell function by foul all T-cell mechanisms. So, this study aimed to detect and evaluate the level of sHLA-G in the sera of patients infected with VL. The results showed that there was

Aims: The aim of this study was to evaluate the value and accuracy of longitudinal strain in detection of coronary artery disease compared to coronary angiography. Results: The left ventricular longitudinal strain-speckle tracking showed evidence of stenosis of left anterior descending artery, circumflex artery and right coronary artery in (86.1%), (76.4%), and (84.7%) respectively. For the stenosis in left anterior descending artery, the current study showed that the longitudinal strain was a good predictor for presence of significant stenosis with a sensitivity of (93.8%), specificity (75%) and accuracy (91.7%) compared with coronary angiography. For the stenosis in right coronary artery, the left ventricular longitudinal strain had

Stress with all its kinds are the results of a nick development Leading to delinquency burdening the ability of people.. development gas its effect on self and body reflecting on health ( physically, Psychological. And mentally) and finally leading to death (Al emara,2001,2).

Stress refers to he degree of response of the individual to events and environmental changes in his daily life with their physiological effects  such as headaches , backaches, and gastric ulcer that have different effect depending on the personality of the person and his psychological characteristics differences airing individuals ( Al emirs, zool,2  )

The aims:

• knowi

The researcher [1-10] proposed a method for computing the numerical solution to quasi-linear parabolic p.d.e.s using a Chebyshev method. The purpose of this paper is to extend the method to problems with mixed boundary conditions. An error analysis for the linear problem is given and a global element Chebyshev method is described. A comparison of various chebyshev methods is made by applying them to two-point eigenproblems. It is shown by analysis and numerical examples that the approach used to derive the generalized Chebyshev method is comparable, in terms of the accuracy obtained, with existing Chebyshev methods.

The aim of this work is to evaluate the one- electron expectation value from the radial electronic density function D(r1) for different wave function for the 2S state of Be atom . The wave function used were published in 1960,1974and 1993, respectavily. Using Hartree-Fock wave function as a Slater determinant has used the partitioning technique for the analysis open shell system of Be (1s22s2) state, the analyze Be atom for six-pairs electronic wave function , tow of these are for intra-shells (K,L) and the rest for inter-shells(KL) . The results are obtained numerically by using computer programs (Mathcad).

In this research was to use the method of classic dynamic programming (CDP) and the method of fuzzy dynamic programming (FDP) to controlling the inventory in N periods and only one substance ,in order to minimize the total cost and determining the required quantity in warehouse rusafa principal of the ministry of commerce . A comparison was made between the two techniques، We found that the value of fuzzy total cost is less than that the value of classic total cost

Background: urethrocutaneous fistula after hypospadias surgery repair is the most common complication and remains a frustrating problem for surgeon and the patient. The problem is exacerbated because the urethrocutaneous fistula may recur which adds more demands surgery. Objectives: The purpose of this study is to evaluate of the use of oral mucosal graft for management of recurrent urethrocutaneous fistula after hypospadias repair. Patients and Methods: twelfth patients with age ranging from 4 year to 15 years were presented with history of recurrent fistula. Most of fistula were located in proximal penile and penoscrotal region (58.3%) . those patients were repaired by using oral mucosal graft with mean postoperative follow up period up t