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

This study evaluates the flexural behavior of ultra-thin (50 mm) one‑way reinforced‑concrete (RC) slabs retrofitted with near‑surface mounted (NSM) carbon‑fiber‑reinforced polymer (CFRP) rods under quasi‑static loading. T300‑grade CFRP rods (≈4 mm diameter) were bonded in pre‑cut 7 mm × 7 mm grooves using a two‑part epoxy. As a proof-of-concept experimental baseline, three simply‑supported specimens (1000 mm × 500 mm × 50 mm) were tested in a six‑point bending configuration (four applied loads + two reactions): two conventional controls and one strengthened slab. A load‑control rate of ~15 kN/min was applied; the controls were cycled twice and the strengthened slab four times. Relative to the average of

The Current Research Seeks To Identify The Possibility Of Unifying The Private Drinking Stations In The Session In A Single Station In Order To Prevent Pollution. In Order To Achieve The Goal Of The Current Research, The Researcher Followed The Descriptive Survey Approach. The Researcher Identified The Research Community As Working In Institutions Related To Drinking Water Filtering In The Governorate Of Baghdad, And In Order To Collect Data And Information Necessary To Answer The Study's Question (Is It Possible To Supply Private Drinking Stations With One Station?) Researcher Designed A Questionnaire Consisting Of (10) Paragraphs Measuring Aspects Of This Topic, And Applied It To A Sample Of Employees And Workers Amounted To (200) People,

The inhibition of 3-Benzyl -2-mercaptoquinoizoline -4 (3H)-one (BMQ) on the corrosion of carbon steel in 0.5 M HCl studied by potentionstat polarization methods at 303–333 K. Results obtained show that BMQ act as inhibitor for carbon steel in HCl solution. The inhibition efficiency increase with increase in BMQ concentration. Activation parameters and Gibbs free energy for the adsorption process using Statistical Physics calculated and discussed. Quantum chemical calculations using DFT at the B3LYP/6-31G level of theory were used to calculate some electronic properties of the molecule to verify any correlation between the inhibitive effect and molecular structure of BMQ. The quantum calculations were proceeded to get data around correlati

One male specimen of the species Metapenaeus stebbingi Nobili, 1904 was first recorded in November 2021 from the Iraqi territorial waters, Northwest of the Arabian Gulf. Therefore, the investigated shrimp species nominally corresponds to the original description of M. stebbing through the main diagnostic features. It must be adopted in the spread and expansion of species, a new record of the area, and a distinctive addition to the species of commercial shrimp within the Iraqi marine waters.

The analysis of time series considers one of the mathematical and statistical methods in explanation of the nature phenomena and its manner in a specific time period.

Because the studying of time series can get by building, analysis the models and then forecasting gives the priority for the practicing in different fields, therefore the identification and selection of the model is of great importance in spite of its difficulties.

The selection of a standard methods has the ability for estimation the errors in the estimated the parameters for the model, and there will be a balance between the suitability and the simplicity of the model.

In the analysis of d

Background: During acrylic resin processing, the mold must be separated from the surface of the gypsum to prevent liquid resin from penetrating into the gypsum, and water from the gypsum seeping into the acrylic resin. For many years, tin foil was the most acceptable separating medium, and because it's difficult to apply, a tin-foil substitute is used. In this study, olive oil is used as an alternative to tin foil separating medium for first time, and evaluating its effect as a separating medium on some mechanical properties such as (indentation hardness and transverse strength) of acrylic resins denture base comparing it with those processed using tin-foil and tin foil substitute such as (cold mold seal) separating medium. Materials and M

The research emphasizes importance of preliminary drawings in design of any product. Therefore, using of simulation as tools for visual thinking in developing drawing and design skills. So that practice of drawing by hand, considering shape of ideas in first stage of visualizations, and practice of its techniques and continuous training.
Hence, the research problem arose with the role of simulation method for developing preliminary sketches in the sample of students of the Product Design Department at the College of Design and Art, PNU, as it is important tool for visual thinking that helps the designer in designing and producing innovative artistic works.
Therefore, the research axes, a number of findings and recommendations were

The study showed a significant rise in the proportion of the labor force in agriculture
activity among the detailed economic activities in 1997 with a rate (%28.9), and then
decreased to (%18.8) in 2011, and this belong to the deterioration of agriculture and the
transition to the other economic activities.
2- The highest percentage of male's participation in year 1997 obtained by the activity (A),
which is represented by agriculture , where was (%30.0) while the highest percentage of
female's participation has been brought by the activity (M) which is represented education
with a rate (% 47.9). while in 2011 that the highest proportion of males' concentration
obtained by the activity (L) with a rate (%23.1) while