The transportation problem (TP) is employed in many different situations, such as scheduling, performance, spending, plant placement, inventory control, and employee scheduling. When all variables, including supply, demand, and unit transportation costs (TC), are precisely known, effective solutions to the transportation problem can be provided. However, understanding how to investigate the transportation problem in an uncertain environment is essential. Additionally, businesses and organizations should seek the most economical and environmentally friendly forms of transportation, considering the significance of environmental issues and strict environmental legislation. This research employs a novel ranking function to solve the transpor

Background: Assessment of function of the right side of the heart in cases of left ventricular dysfunction has been widely studied but the sensitive and specific echocardiographic parameter to be tested is still a matter of controversy. Right ventricular function is related to left ventricular function by ventricular independence so function of both should be assessed carefully. The objective of this study was to evaluate the effects of left ventricular systolic dysfunction on right ventricular systolic and diastolic functions and pulmonary pressure using conventional and tissue Doppler echocardiography. Patients and Methods: Sixty patients (39 males and 21 females) with heart failure due to left ventricular systolic dysfunction

In this research, we find the Bayesian formulas and the estimation of Bayesian expectation for product system of Atlas Company.  The units of the system have been examined by helping the technical staff at the company and by providing a real data the company which manufacturer the system.  This real data include the failed units for each drawn sample, which represents the total number of the manufacturer units by the company system.  We calculate the range for each estimator by using the Maximum Likelihood estimator.  We obtain that the expectation-Bayesian estimation is better than the Bayesian estimator of the different partially samples which were drawn from the product system after  it checked by the

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The primary aim of this paper, is to introduce the rough probability from topological view. We used the Gm-topological spaces which result from the digraph on the stochastic approximation spaces to upper and lower distribution functions, the upper and lower mathematical expectations, the upper and lower variances, the upper and lower standard deviation and the upper and lower r th moment. Different levels for those concepts are introduced, also we introduced some results based upon those concepts.

The 3-parameter Weibull distribution is used as a model for failure since this distribution is proper when the failure rate somewhat high in starting operation and these rates will be decreased with increasing time .

In practical side a comparison was made between (Shrinkage and Maximum likelihood) Estimators for parameter and reliability function using simulation , we conclude that the Shrinkage estimators for parameters are better than maximum likelihood estimators but the maximum likelihood estimator for reliability function is the better using statistical measures (MAPE)and (MSE) and for different sample sizes.

Note:- n_s : small sample ; n_m=median sample

 A computational investigation has been carried out to describe synthesis optimization procedure of magnetic lenses. The research is concentrated on the determination of the inverse design of the symmetrical double polepiece magnetic lenses whose magnetic field distribution is already defined. Magnetic lenses field model well known in electron optics have been used as the axial magnetic field distribution. This field has been studied when the halfwidth is variable and the maximum magnetic flux density is kept constant. The importance of this research lies in the possibility of using the present synthesis optimization procedure for finding the polepieces design of symmetrical double polepiece magnetic lenses which have the best proje

Objective: The aim of this study was to evaluate the effect of pumice, burning investment material
and black sand on the surface roughness of heat cure acrylic resin.
Methodology: Sixty specimens were prepared from pink heat cure acrylic resin, the specimens
where grouped into; 20 specimens which polished with pumice and water (control group); 20
specimens which polished with investment material (after burning it) and water; and 20 specimens
which polished with black sand and water. The average surface roughness of specimens after
polishing procedure had been determined by profilometer (surface roughness tester).
Results: Through the application of ANOVA and LSD tests, the result of this study showed that there
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