This paper presents a new numerical method for the solution of ordinary differential equations (ODE). The linear second-order equations considered herein are solved using operational matrices of Wang-Ball Polynomials. By the improvement of the operational matrix, the singularity of the ODE is removed, hence ensuring that a solution is obtained. In order to show the employability of the method, several problems were considered. The results indicate that the method is suitable to obtain accurate solutions.

     A fuzzy valued diffusion term, which in a fuzzy stochastic differential equation refers to one-dimensional Brownian motion, is defined by the meaning of the stochastic integral of a fuzzy process. In this paper, the existence and uniqueness theorem of fuzzy stochastic ordinary differential equations, based on the mean square convergence of the mathematical induction approximations to the associated stochastic integral equation, are stated and demonstrated.

     In this paper, the propose is to use the xtreme value distribution as the rate of occurrence of the non-homogenous Poisson process, in order to improve the rate of occurrence of the non-homogenous process, which has been called the Extreme value Process. To estimate the parameters of this process, it is proposed to use the Maximum Likelihood method, Method of Moment and a smart method represented by the Artificial Bee Colony:(ABC) algorithm to reach an estimator for this process which represents the best data representation. The results of the three methods are compared through a simulation of the model, and it is concluded that the estimator of (ABC) is better than the estimator of the maximum likelihood method and method of mo

Lovastatin is one of the most important compounds that is produced from some filamentous fungi, being employed in the reduction of hypocholesterolemia. The results of screening, after the collection of seventy-three local fungal isolates from different areas, demonstrated that the local isolate Aspergillus terreus A50 was the best isolate for lovastatin production, with a concentration of 12.66 µg/ml, through the submerged fermentation. Lovastatin produced from A. terreus A50 showed antimicrobial activities against a Candida albicans isolate. Solid state fermentation (SSF) was the best system to produce the highest yield of lovastatin by A. terreus A50 as compared to the submerged fermentation (SmF)

This study explored the development and qualities of the response of electrochemical properties of enrofloxacin-selective electrodes using precipitation based on producing phosphotungstic, after utilizing a matrix of polyvinyl chloride (PVC) and dibutyl phthalate or dibutyl phosphate as a plasticizer. The resulting membrane sensors were an enrofloxacin-phosphotungstic electrode (sensors 1) and an ENR-DOP-PTA electrode (sensors 2). Linear responses of (ENR-DBPH-PTA) and (ENR-DOP-PTA) within the concentration ranges of 2.1×10^-6-10^-1 and 3.0×10^-6-10^-2 mol. L^-1, respectively, for both sensors were observed. Slopes of 51.61±0.24 and 39.40± 0.16 mV/decade and pH ranges equal to 2.5-8.5

This paper focuses on the optimization of drilling parameters by utilizing “Taguchi method” to obtain the minimum surface roughness. Nine drilling experiments were performed on Al 5050 alloy using high speed steel twist drills. Three drilling parameters (feed rates, cutting speeds, and cutting tools) were used as control factors, and L9 (3³) “orthogonal array” was specified for the experimental trials. Signal to Noise (S/N) Ratio and “Analysis of Variance” (ANOVA) were utilized to set the optimum control factors which minimized the surface roughness. The results were tested with the aid of statistical software package MINITAB-17. After the experimental trails, the tool diameter was found as the most important facto

Submerged arc welding (SAW) process is an essential metal joining processes in industry. The quality of weld is a very important working aspect for the manufacturing and construction industries, the challenges are made optimal process environment. Design of experimental using Taguchi method (L9 orthogonal array (OA)) considering three SAW parameter are (welding current, arc voltage and welding speed) and three levels (300-350-400 Amp. , 32-36-40 V and 26-28-30 cm/min). The study was done on SAW process parameters on the mechanical properties of steel type comply with (ASTM A516 grade 70). Signal to Noise ratio (S/N) was computed to calculate the optimal process parameters. Percentage contributions of each parameter are validated by using an

Abstract

       The grey system model GM(1,1) is the model of the prediction of the time series and the basis of the grey theory. This research presents the methods for estimating parameters of the grey model GM(1,1) is the accumulative method (ACC), the exponential method (EXP), modified exponential method (Mod EXP) and the Particle Swarm Optimization method (PSO). These methods were compared based on the Mean square error (MSE) and the Mean Absolute percentage error (MAPE) as a basis comparator and the simulation method was adopted for the best of the four methods, The best method was obtained and then applied to real data. This data represents the consumption rate of two types of oils a he

 A simulation study is used to examine the robustness of some estimators on a multiple linear regression model with problems of multicollinearity and non-normal errors, the Ordinary least Squares (LS) ,Ridge Regression, Ridge Least Absolute Value (RLAV), Weighted Ridge (WRID), MM and a robust ridge regression estimator MM estimator, which denoted as RMM this is the modification of the Ridge regression by incorporating robust MM estimator . finialy, we show that RMM is the best among the other estimators

The derivation of 5^th order diagonal implicit type Runge Kutta methods (DITRKM5) for solving 3^rd special order ordinary differential equations (ODEs) is introduced in the present study. The DITRKM5 techniques are the name of the approach. This approach has three equivalent non-zero diagonal elements. To investigate the current study, a variety of tests for five various initial value problems (IVPs) with different step sizes h were implemented. Then, a comparison was made with the methods indicated in the other literature of the implicit RK techniques. The numerical techniques are elucidated as the qualification regarding the efficiency and number of function evaluations compared with another literature of the implic