In this paper, we made comparison among different parametric ,nonparametric and semiparametric estimators for partial linear regression model users parametric represented by ols and nonparametric methods represented by cubic smoothing spline estimator and Nadaraya-Watson estimator, we study three nonparametric regression models and samples sizes  n=40,60,100,variances used σ²=0.5,1,1.5 the results  for the first model show that N.W estimator for partial linear regression model(PLM) is the best followed the cubic smoothing spline estimator for (PLM),and the results of the second and the third model show that the best estimator is C.S.S.followed by N.W estimator for (PLM) ,the

  This work discusses the beginning of fractional calculus and how the Sumudu and Elzaki transforms are applied to fractional derivatives. This approach combines a double Sumudu-Elzaki transform strategy to discover analytic solutions to space-time fractional partial differential equations in Mittag-Leffler functions subject to initial and boundary conditions. Where this method gets closer and closer to the correct answer, and the technique's efficacy is demonstrated using numerical examples performed with Matlab R2015a.

Back ground: Glass ionomer materials lack resistance to wear and pressure and are susceptible to moisture during the initial stages of setting and dehydration. So this study was done to assess diametral tensile strength and microhardness of glass ionomer reinforced by different amounts of hydroxyapatite. Materials and methods: In this study a hydroxyapatite material was added to glass monomer cement at different ratios: 10%, 15%, 20%, 25% and 30% (by weight). The diametral tensile strength test described by the British standard specification for zinc polycarboxylate cement was used in this study and the microhardness test was performed using Vickers microhardness testing machine and the microhardness values were calculated and statistical c

The dual nature of asphalt binder necessitates improvements to mitigate rutting and fatigue since it performs as an elastic material under the regime of rapid loading or cold temperatures and as a viscous fluid at elevated temperatures. The present investigation assesses the effectiveness of Nano Alumina (NA), Nano Silica (NS), and Nano Titanium Dioxide (NT) at weight percentages of 0, 2, 4, 6, and 8% in asphalt cement to enhance both asphalt binder and mixture performance. Binder evaluations include tests for consistency, thermal susceptibility, aging, and workability, while mixture assessments focus on Marshall properties, moisture susceptibility, resilient modulus, permanent deformation, and fatigue characteristics. NS notably im

The dual nature of asphalt binder necessitates improvements to mitigate rutting and fatigue since it performs as an elastic material under the regime of rapid loading or cold temperatures and as a viscous fluid at elevated temperatures. The present investigation assesses the effectiveness of Nano Alumina (NA), Nano Silica (NS), and Nano Titanium Dioxide (NT) at weight percentages of 0, 2, 4, 6, and 8% in asphalt cement to enhance both asphalt binder and mixture performance. Binder evaluations include tests for consistency, thermal susceptibility, aging, and workability, while mixture assessments focus on Marshall properties, moisture susceptibility, resilient modulus, permanent deformation, and fatigue characteristics. NS notably im