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

A particulate polymer composite material was prepared by reinforcing with the Aluminum Oxide (Al₂O₃) or Aluminum (Al) metallic particles with a particle size of (30) µm to an unsaturated Polyester Resin with a weight fraction of (5%, 10%, 15%, 20%).

Tensile test results showed the maximum value of elastic modulus reached (2400MPa.)  in the case of reinforcing with (Al) particles with weight fraction (20%) and (1500 MPa.)  in the case of reinforcing with (Al₂O₃) particles of the same weight fraction.

  When the impact and the flexural strength tests were done, the results showed that flexural strength (F.S), maximum shear stress (τ_max), impact strength

Inthisstudy,FourierTransformInfraredSpectrophotometry(FTIR),XRay Diffraction(XRD)andlossonignition(LOI),comparativelyemployedtoprovideaquick,relativelyinexpensiveandefficientmethodforidentifyingandquantifyingcalcitecontentofphosphateoresamplestakenfromAkashatsiteinIraq.Acomprehensivespectroscopicstudyofphosphate-calcitesystemwasreportedfirstintheMid-IRspectra(4004000cm-1)usingShimadzuIRAffinity-1,fordifferentcutsofphosphatefieldgradeswithsamplesbeneficiatedusingcalcinationandleachingwithorganicacidatdifferenttemperatures.Thenusingtheresultedspectratocreateacalibrationcurverelatesmaterialconcentrationstotheintensity(peaks)ofFTIRabsorbanceandappliesthiscalibrationtospecifyphosphate-calcitecontentinIraqicalcareousphosphateore.Theirpeakswereass

Consistent "with the thought of tax talk is unified tax natural evolution for him, as the application leads to the inclusion of tax all branches of income and its sources and through truncated part of this entry through the application of price ascending it, it means the procedures of tax reform. Taxes on total income characterized by giving a clear picture of the total income of the taxpayer and its financial situation and its burden family which allows granting exemptions, downloads, and application of prices that fit this case. This requires reconsideration of the structure of the tax system in force and the transition from a system specific taxes to the tax system on the total income of the integration of income from the rental of re

In this current work, Purpose; to clearly the fundamental idea for constructing a design and
investigation of spur gear made of composite material its comes from the combination of (high
speeds, low noise, oil-les running, light weight, high strength, and more load capability)
encountered in modern engineering applications of the gear drives, when the usual metallic gear
cannot too overwhelming these combinations.
An analyzing of stresses and deformation under static and dynamic loading for spur gear tooth
by finite element method with isoparametric eight-nodded in total of 200 brick element with 340
nods in three degree of freedom per node was selected for this analysis. This is responsible for the
catastropic fa

Polymer films of PEG and PVA and their blend with different
concentrations of MnCl2 (0, 2, 4, 6 and 10 %.wt) were study using
casting technique. The X-ray spectra of pure PEG, PVA and
PVA:PEG films and with addition of 2% concentrations from
(MnCl2) show amorphous structures. The results for FTIR show the
interaction between the filler and polymer blend results in
decreasing crystallinity with rich amorphous phase. This
amorphous nature confirms the complexation between the filler and
the polymer blend. The optical properties of (PVA:PEG/MnCl2)
contain the recording of absorbance (A) and explain that the
absorption coefficient (α), refractive index (n), extinction coefficient
(ko) and the dielectric cons

In this work dithine complexes prepared from dithiol benzil ligand and central ion to the Ni,Pd,Pt, element the ligand and complexes have been investigated using FTIR spectrophotometer and uv-vis-NIR spectral reigns show higher intensity represents the ?-?* transition in the chromopher cycle .These absorption which appear in visible and near IR spectral regions ,According to the complexes of one group ,the spectral shifting due to the change of central ion has been found to be related to atomic number of central ion .This shifting is increased while decreasing the central ion atom number These complexes have been implemented in Nd+2:YAG cavity because each posses resonant absorption band near Nd+2:YAG, Nd+2:Glass emitting at (106

In This research a Spectroscopic complement and Thermodynamic properties for molecule PO2 were studied . That included a calculation of potential energy . From the curve of total energy for molecule at equilibrium distance , for bond (P-O), the degenerated of bond energy was (4.332eV) instate of the vibration modes of ( PO2 ) molecule and frequency that was found active in IR spectra because variable inpolarization and dipole moment for molecule. Also we calculate some thermodynamic parameters of ( PO2 ) such as heat of formation , enthalpy , heat Of capacity , entropy and gibb's free energy Were ( -54.16 kcal/mol , 2366.45 kcal/mol , 10.06 kcal /k/mol , 59.52 k