In this research, our aim is to study the optimal control problem (OCP) for triple nonlinear elliptic boundary value problem (TNLEBVP). The Mint-Browder theorem is used to prove the existence and uniqueness theorem of the solution of the state vector for fixed control vector. The existence theorem for the triple continuous classical optimal control vector (TCCOCV) related to the TNLEBVP is also proved. After studying the existence of a unique solution for the triple adjoint equations (TAEqs) related to the triple of the state equations, we derive The Fréchet derivative (FD) of the cost function using Hamiltonian function. Then the theorems of necessity conditions and the sufficient condition for optimality of

Multiple linear regressions are concerned with studying and analyzing the relationship between the dependent variable and a set of explanatory variables. From this relationship the values of variables are predicted. In this paper the multiple linear regression model and three covariates were studied in the presence of the problem of auto-correlation of errors when the random error distributed the distribution of exponential. Three methods were compared (general least squares, M robust, and Laplace robust method). We have employed the simulation studies and calculated the statistical standard mean squares error with sample sizes (15, 30, 60, 100). Further we applied the best method on the real experiment data representing the varieties of

Integrating Renewable Energy (RE) into Distribution Power Networks (DPNs) is a choice for efficient and sustainable electricity. Controlling the power factor of these sources is one of the techniques employed to manage the power loss of the grid. Capacitor banks have been employed to control phantom power, improving voltage and reducing power losses for several decades. The voltage sag and the significant power losses in the Iraqi DPN make it good evidence to be a case study proving the efficiency enhancement by adjusting the RE power factor. Therefore, this paper studies a part of the Iraqi network in a windy and sunny region, the Badra-Zurbatya-11 kV feeder, in the Wasit governorate. A substation of hybrid RE sources is connected to this

Background: To investigate the effect of different types of storage media on enamel surface microstructure of avulsed teeth by using atomic force microscope.Materials and methods : Twelve teeth blocks from freshly extracted premolars for orthodontic treatment were selected . The study samples were divided into three groups according to type of storage media :A-egg white , B- probiotic yogurt , and C-bovine milk . All the samples were examined for changes in surface roughness and surface granularity distribution  using atomic force microscope, at two periods: baseline, and after 8 hours of immersing in the three types of storage media. Results: Milk group had showed a significant increase in the mean of the  roughness values at

A group of acceptance sampling to testing the products was designed when the life time of an item follows a log-logistics distribution. The minimum number of groups (k) required for a given group size and acceptance number is determined when various values of Consumer’s Risk and test termination time are specified. All the results about these sampling plan and probability of acceptance were explained with tables.

  This paper is concerned with Double Stage Shrinkage Bayesian (DSSB) Estimator for lowering the mean squared error of classical estimator ˆ q for the scale parameter (q) of an exponential distribution in a region (R) around available prior knowledge (q0) about the actual value (q) as initial estimate as well as to reduce the cost of experimentations.         In situation where the experimentations are time consuming or very costly, a Double Stage procedure can be used to reduce the expected sample size needed to obtain the estimator. This estimator is shown to have smaller mean squared error for certain choice of the shrinkage weight factor y( ) and for acceptance region R. Expression for

A new results for fusion reactivity and slowing-down energy distribution functions for controlled thermonuclear fusion reactions of the hydrogen isotopes are achieved to reach promising results in calculating the factors that covered the design and construction of a given fusion system or reactor. They are strongly depending upon their operating fuels, the reaction rate, which in turn, reflects the physical behavior of all other parameters characterization of the system design

  In this paper, we introduce a new class of sets, namely , s*g--open sets and we show that the family of all s*g--open subsets of a topological space ) ,X(  from a topology on X which is finer than  . Also , we study the characterizations and basic properties of s*g-open sets and s*g--closed sets . Moreover, we use these sets to define and study a new class of functions, namely , s*g-  -continuous functions and s*g-  -irresolute functions in topological spaces . Some properties of these functions have been studied .

This research concentrate on cultivated Iraqi Agave attenuata dried leaves and roots, because of little studies on this plant especially on the root that lead to the eager of study and comparison of phytochemical constituents between leaves and root. Extraction of bioactive constituents was carried out using several solvents with increasing polarity (n-hexane, ethyl acetate and methanol) by soxhlet apparatus. Steroidal saponins in Agave genus is well documented in many species, lightening the minds in this research on extraction method which is specific for steroidal saponins. Phytochemical screening was done by GC/MS for n-hexane fraction, qualitative and quantitative estimation of several bioactive constituents (caffe