In this paper, the continuous classical boundary optimal control problem (CCBOCP) for triple linear partial differential equations of parabolic type (TLPDEPAR) with initial and boundary conditions (ICs & BCs) is studied. The Galerkin method (GM) is used to prove the existence and uniqueness theorem of the state vector solution (SVS) for given continuous classical boundary control vector (CCBCV). The proof of the existence theorem of a continuous classical boundary optimal control vector (CCBOCV) associated with the TLPDEPAR is proved. The derivation of the Fréchet derivative (FrD) for the cost function (CoF) is obtained. At the end, the theorem of the necessary conditions for optimality (NCsThOP) of this problem is stated and prov

We develop the previously published results of Arab by using the function  under certain conditions and using G-α-general admissible and triangular α-general admissible to prove coincidence fixed point and common fixed point theorems for two weakly compatible self –mappings in complete b-metric spaces.

The principal aim of this research is to use the definition of fuzzy normed space
to define fuzzy bounded operator as an introduction to define the fuzzy norm of a
fuzzy bounded linear operator then we proved that the fuzzy normed space FB(X,Y)
consisting of all fuzzy bounded linear operators from a fuzzy norm space X into a
fuzzy norm space Y is fuzzy complete if Y is fuzzy complete. Also we introduce
different types of fuzzy convergence of operators.

    In this paper we introduce a brief review about Box-Jenkins models. The acronym ARIMA stands for “autoregressive integrated moving average”. It is a good method to forecast for stationary and non stationary time series. According to the data which obtained from Baghdad Water Authority, we are modelling two series, the first one about pure water consumption and the second about the number of participants. Then we determine an optimal model by depending on choosing minimum MSE as criterion.

In this paper, the Azzallini’s method used to find a weighted distribution derived from the standard Pareto distribution of type I (SPDTI) by inserting the shape parameter (θ) resulting from the above method to cover the period (0, 1] which was neglected by the standard distribution. Thus, the proposed distribution is a modification to the Pareto distribution of the first type, where the probability of the random variable lies within the period  The properties of the modified weighted Pareto distribution of the type I (MWPDTI) as the probability density function ,cumulative distribution function, Reliability function , Moment and  the hazard function are found. The behaviour of probability density function for MWPDTI distrib

This Book is intended to be textbook studied for undergraduate course in multivariate analysis. This book is designed to be used in semester system. In order to achieve the goals of the book, it is divided into the following chapters (as done in the first edition 2019). Chapter One introduces matrix algebra. Chapter Two devotes to Linear Equation System Solution with quadratic forms, Characteristic roots & vectors. Chapter Three discusses Partitioned Matrices and how to get Inverse, Jacobi and Hessian matrices. Chapter Four deals with Multivariate Normal Distribution (MVN). Chapter Five concern with Joint, Marginal and Conditional Normal Distribution, independency and correlations. While the revised new chapters have been added (as the curr

This Book is intended to be textbook studied for undergraduate course in multivariate analysis. This book is designed to be used in semester system. In order to achieve the goals of the book, it is divided into the following chapters (as done in the first edition 2019). Chapter One introduces matrix algebra. Chapter Two devotes to Linear Equation System Solution with quadratic forms, Characteristic roots & vectors. Chapter Three discusses Partitioned Matrices and how to get Inverse, Jacobi and Hessian matrices. Chapter Four deals with Multivariate Normal Distribution (MVN). Chapter Five concern with Joint, Marginal and Conditional Normal Distribution, independency and correlations. While the revised new chapters have been added (as the curr

In this paper, we define certain subclasses of analytic univalent function associated with quasi-subordination. Some results such as coefficient bounds and Fekete-Szego bounds for the functions belonging to these subclasses are derived.

In this paper the wind data that is measured for 12 months (January to December 2011) at Al-Hay district of Wasit province, southern IRAQ country has been analyzed statistically. The wind speed at heights of 10 m above ground level was measured for every 10 minutes interval. The statistical analysis of wind data was performed using WAsP software which is based on Weibull distributions. The Weibull shape and scale parameters is obtained and used in this paper statistics. The achieved results demonstrated that the study area has Annual Mean Energy Production (AMEP) about 219.002 MWh. The computations have been performed on 70m hub‟s height of the turbine and on Earth surface roughness length (0.0, 0.03, 0.1, 0.4, 1.5) m respectively.

In this research, a new technique is suggested to reduce the long time required by the encoding process by using modified moment features on domain blocks. The modified moment features were used in accelerating the matching step of the Iterated Function System (IFS). The main disadvantage facing the fractal image compression (FIC) method is the over-long encoding time needed for checking all domain blocks and choosing the least error to get the best matched domain for each block of ranges. In this paper, we develop a method that can reduce the encoding time of FIC by reducing the size of the domain pool based on the moment features of domain blocks, followed by a comparison with threshold (the selected  threshold based on experience