In this paper new methods were presented based on technique of differences which is the difference- based modified jackknifed generalized ridge regression estimator(DMJGR) and difference-based generalized  jackknifed ridge regression estimator(DGJR), in estimating the parameters of linear part of the partially linear model. As for the nonlinear part represented by the nonparametric function, it was estimated using Nadaraya Watson smoother. The partially linear model was compared using these proposed methods with other estimators based on differencing technique through the MSE comparison criterion in simulation study.

The current work is characterized by simplicity, accuracy and high sensitivity Dispersive liquid - Liquid Micro Extraction (DLLME). The method was developed to determine Telmesartan (TEL) and Irbesartan (IRB) in the standard and pharmaceutical composition. Telmesartan and Irbesartan are separated prior to treatment with Eriochrom black T as a reagent and formation ion pair reaction dye. The analytical results of DLLME method for linearity range (0.2- 6.0) mg /L for both drugs, molar absorptivity were (1.67 × 105-    5.6 × 105) L/ mole. cm, limit of detection were (0.0242and0.0238), Limit of quantification were (0.0821and0.0711), the Distribution coefficient were

This paper presents a grey model GM(1,1) of the first rank and a variable one and is the basis of the grey system theory , This research dealt  properties of grey model and a set of methods to estimate parameters of the grey model GM(1,1)  is the least square Method (LS) , weighted least square method (WLS), total least square method (TLS) and gradient descent method  (DS). These methods were compared based on two types of standards: Mean square error (MSE), mean absolute percentage error (MAPE), and after comparison using simulation the best method was applied to real data represented by the rate of consumption of the two types of oils a Heavy fuel (HFO) and diesel fuel (D.O) and has been applied several tests to

An efficient modification and a novel technique combining the homotopy concept with  Adomian decomposition method (ADM) to obtain an accurate analytical solution for Riccati matrix delay differential equation (RMDDE) is introduced  in this paper  . Both methods are very efficient and effective. The whole integral part of ADM is used instead of the integral part of homotopy technique. The major feature in current technique gives us a large convergence region of iterative approximate solutions .The results acquired by this technique give better approximations for a larger region as well as previously. Finally, the results conducted via suggesting an efficient and easy technique, and may be addressed to other non-linear problems.

Electromechanical actuators are used in a wide variety of aerospace applications such as missiles, aircrafts and spy-fly etc. In this work a linear and nonlinear fin actuator mathematical model has been developed and its response is investigated by developing an algorithm for the system using MATLAB. The algorithm used to the linear model is the state space algorithm while the algorithm used to the nonlinear model is the discrete algorithm. The huge moment constant is varied from (-3000 to 3000) and the damping ratio is varied from (0.4 to 0.8).        

 The comparison between linear and nonlinear fin actuator response results shows that for linear model, the maximum overshoot is about 10%,

 In this paper, we introduce and discuss an algorithm for the numerical solution of some kinds of fractional integral and fractional integrodifferential equations. The algorithm for the numerical solution of these equations is based on iterative approach. The stability and convergence of the fractional order numerical method are described. Finally, some numerical examples are provided to show that the numerical method for solving the fractional integral and fractional integrodifferential equations is an effective solution method.

This study includes the application of non-parametric methods in estimating the conditional survival function of the Beran method using both the Nadaraya-Waston and the Priestley-chao weights and using data for Interval censored and Right censored of breast cancer and two types of treatment, Chemotherapy and radiation therapy Considering age is continuous variable, through using (MATLAB)  use of the (MSE) To compare weights The results showed a superior weight (Nadaraya-Waston) in estimating the survival function and condition of Both for chemotherapy and radiation therapy.

Pareto distribution is used in many economic, financial and social applications. This distribution is used for the study of income and wealth and the study of settlement in cities and villages and the study of the sizes of oil wells as well as in the field of communication through the speed of downloading files from the Internet according to their sizes. This distribution is used in mechanical engineering as one of the distributions of models of failure, stress and durability. Given the practical importance of this distribution on the one hand, and the scarcity of sources and statistical research that deal with it, this research touched on some statistical characteristics such as derivation of its mathematical function , probability density