The necessary optimality conditions with Lagrange multipliers  are studied and derived for a new class that includes the system of Caputo–Katugampola fractional derivatives to the optimal control problems with considering the end time free. The formula for the integral by parts has been proven for the left Caputo–Katugampola fractional derivative that contributes to the finding and deriving the necessary optimality conditions. Also, three special cases are obtained, including the study of the necessary optimality conditions when both the final time  and the final state  are fixed. According to convexity assumptions prove that necessary optimality conditions are sufficient optimality conditions.

In this paper we generalize Jacobsons results by proving that any integer  in   is a square-free integer), belong to . All units of  are generated by the fundamental unit  having the forms

Our generalization build on using the conditions

This leads us to classify the real quadratic fields  into the sets  Jacobsons results shows that  and Sliwa confirm that  and  are the only real quadratic fields in .

This research discusses application Artificial Neural Network (ANN) and Geographical InformationSystem (GIS) models on water quality of Diyala River using Water Quality Index (WQI). Fourteen water parameterswere used for estimating WQI: pH, Temperature, Dissolved Oxygen, Orthophosphate, Nitrate, Calcium, Magnesium,Total Hardness, Sodium, Sulphate, Chloride, Total Dissolved Solids, Electrical Conductivity and Total Alkalinity.These parameters were provided from the Water Resources Ministryfrom seven stations along the river for the period2011 to 2016. The results of WQI analysis revealed that Diyala River is good to poor at the north of Diyala provincewhile it is poor to very polluted at the south of Baghdad City. The selected parameters wer

  The research dealt with the design of the cost accounting system for the transport service and its Role in improving the efficiency of pricing decisions through the application of the cost system based on ABC activities. The main activities were defined and cost guides were to measure the cost of each service and to determine the cost of each service for the purpose of providing management with appropriate information and pricing decisions The problem of research in the lack of adoption by some public companies in the service sector on the cost accounting system to calculate the cost of service as well as the lack of identification of productive activities and service activities and therefore cannot make the appropriate decision t

The study aims to demonstrate the importance of instructional methods in teaching Arabic language as a second language or teaching the Arabic language to non-native speakers. The study is in line with the tremendous development in the field of knowledge, especially in the field of technology and communication, and the emergence of many electronic media in education in general and language teaching in particular. It employs an image in teaching vocabulary and presenting the experience of the Arabic Language Institute for Non-Speakers-King Abdul-Aziz University. The study follows the descriptive approach to solve the problem represented by the lack of interest in the educational methods when teaching Arabic as a second language. Accordingl

Gymnastics is one of the most interesting games in terms of organizing various world championships and tournaments. Their basic skills and their technical development, especially those with high difficulty levels that rely on basic and complex skills, are the basic skills of gymnastics are the main pillar to be developed and therefore high-difficulty skills will not depend on basic skills, which should reach the stage of the automatic mechanism. Retention) in order to move on to training and developing another skill for the difficulty of movements as well as the smooth flow of performance, ie the degrees of difficulty of each skill specific to your gym and The researcher used the experimental method and The research community determin

An experiment was carried out in the vegetables field of Horticulture Department / College of Agriculture / Baghdad University , for the three seasons : spring and Autumn of 2005 , and spring of 2007 , to study the type of gene action in some traits of yield and its components in summer squash crosses (4 x 3 = cross 1 , 3 x 7 = cross 2 , 3 x 4 = cross 3 , 3 x 5 = cross 4 , 5 x 1 = cross 5 , 5 x 2 = cross 6). The study followed generation mean analysis method which included to each cross (P1 , P2 , F1 , F2 , Bc1P1 , Bc1P2) , and those populations obtained by hybridization during the first and second seasons. Experimental comparison was performed in the second (Two crosses only) and third seasons , (four crosses) by using RCBD with three repl

The problem of Multicollinearity is one of the most common problems, which deal to a large extent with the internal correlation between explanatory variables. This problem is especially Appear in economics and applied research, The problem of Multicollinearity has a negative effect on the regression model, such as oversized variance degree and estimation of parameters that are unstable when we use the Least Square Method ( OLS), Therefore, other methods were used to estimate the parameters of the negative binomial model, including the estimated Ridge Regression Method and the Liu type estimator, The negative binomial regression model is a nonline

The research study is important since it establishes predicted rates for various nervous system functional indicators.In terms of performing the skill of Dribbling in basketball for young players in Baghdad Governorate in order to reach scientific results that serve researchers, coaches, and players uniformly. The study's goal is to create predictive equations for specific functional indicators of the nervous system in relation to the Dribbling skill performance of young basketball players in Baghdad Governorate. The researchers used a descriptive approach with a survey method on (8) youth basketball league clubs in Baghdad Governorate for the 2022-2023 sports season, totaling (96) players . Three tests were used to measure the nervous sy