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

Doppler broadening of the 511 keV positron annihilation ??? ? was used to estimate the concentration of defects ?? different deformation levels of pure alnminum samples. These samples were compressed at room temperature to 15, 22, 28, 38,40, and 75 % thickness reduction. The two-state ^sitron-trapping model has been employed. 'I he s and w lineshape parameters were measured using high-resolution gamma spectrometer with high pure germanium detector of 2.1 keV resolution at 1.33 MeV of 60Co. The change of defects concentration (Co) with the deformation level (e) is found to obey an empirical formula of the form Cd - A £ B where A and ? are positive constants that depend mainly on the deformation procedure and the temperature at which the def

The corrosion behavior of bare and chemical conversion coated (through anodizing) aluminum ASA 606 I in stagnant chromic acid solutions . Solutions of 2, 6 & J O wt. % Cr03 at 45°C, have been investigated using polarization technique. The anodizing experiments were conducted under fixed conditions of 35 minute exposure time and 30 volt supplied voltage. The most important feature achieved was the great difference in behavior between the anodic polarization curves for bare and anodized aluminum in different concentrations of chromic acid solutions.

On of the direct causes which led to the global financial crisis 2008 is decrease or collapse in liquidity of large financial institutions which is reflected on investments of a considerable number of institutions and persons.

This study aim's through out its three sections to explain the disclosure level of financial institutions which affected by Financial Crisis from liquidity information which explained in the statement of cash flow according to Timeliness and Completeness.

The study concluded an important result the company of research sample was disclosure in Timeliness and Completeness from all of accounting information is related in liquidity or that related in result of operations and financial position. The more

Background: Orthodontic mini-implants are increasingly used in orthodontics and the bone density is a very important factor in stabilization and success of mini-implant. The aim of this study was to observe the relationship among maximum bite force (MBF); body mass index (BMI); face width, height and type; and bone density in an attempt to predict bone density from these variables to eliminate the need for CT scan which have a highly hazard on patient. Materials and Methods: Computed tomographic (CT) images were obtained for 70 patients (24 males and 46 females) with age range 18-30 years. The maxillary and mandibular buccal cortical and cancellous bone densities were measured between 2nd premolar and 1st molar at two levels from the alveol

Aluminum alloy 5052 had been anodized by sulfuric acid as an electrolyte under constant voltage and the anodic oxide film produce will be testing by potentiostatic anodic polarization .Two variables, which were considered as important variables, were studied. These variables are anodizing time 15,30 min. and sealing time 10,20 min., and the test by potentiostatic anodic polarization through electro chemical polarization measurements in solutions of 1N na2so4 ( PH= 1 ). The results are discussed in light of the rate of ionic current flow through the coating during anodic polarization measurements.

The aim of present work is to improve mechanical and fatigue properties for Aluminum alloy7049 by using Nano composites technique. The ZrO₂ with an average grain diameter of 30-40 nm, was selected as Nano particles, to reinforce Aluminum alloy7049 with different percentage as, 2, 4, 6 and 7 %. The Stir casting method was used to fabricate the Nano composites materials due to economical route for improvement and processing of metal matrix composites. The experimental results were shown that the adding of zirconium oxide (ZrO₂) as reinforced material leads to improve mechanical properties. The best percentage of improvement of mechanical properties of 7049 AA was with 4% wt. of ZrO₂ about (7.76% ) for ultim