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.

Gangyong Lee, S.Tariq Rizvi, and Cosmin S.Roman studied Rickart modules.

The main purpose of this paper is to develop the properties of Rickart modules .

We prove that each injective and prime module is a Rickart module. And we give characterizations of some kind of rings in term of Rickart modules.

תקציר

     ביטויי אהבה ושנאה קבלה בההגדרות שונות, לפעמים ביניהם לבין עצמם והסכימו בזמנים אחרים מהבחינה הדתית נתפסה לאהוב ביטויים ושנאה במונחים של טוב ורע, או במונחים של חלאל וחראם למעשה, הרגשות של אהבה ושנאה הם רגשות אנושיים המקושרים לאמונות של חברות אנושיות הבנויות על העמדה של דתות מכל נושא או מקרה  , דבר אשר אהוב על ידי הקדושים והכמורה יהיה חלאל, וכל מה שהם שונאים יהיה חראם במילים אח

  Shmuel Yosef Agnon, a well-known Jewish writer, wrote many literary works, including poetry, story, etc. In the field of story, this writer used two areas: the first: a simple exterior, and the second: an inner full of secrets and mysteries. This area is common when Agnon is affected by his symbolic method of purpose. In his productions, we find the political and historical significance embodied in his characters, where there is almost no story without it.

    Agnon and all his productions gave the character a large area, Agnon’s characters often play the center and cornerstone in those productions, where the author dealt deeply and stated the fines details of the external and internal of that ch

The focus of this research lies in the definition of an important aspect of financial development, which is reflected on the alleviation of poverty in Iraq, namely financial inclusion and then taking the path of achieving a sustainable economy, certainly after reviewing one of the important international experiences in this regard and finally measuring the level of financial inclusion in Iraq and its impact on poverty reduction through the absolute poverty line indicator.

In this paper we introduced a new type of integrals based on binary element sets “a generalized integral of Shilkret and Choquet integrals” that combined the two kinds of aggregation functions which are Shilkret and Choquet integrals. Then, we gave some properties of that integral. Finally, we illustrated our integral in a numerical example.
.

           Let R be  commutative Ring , and let T be  unitary left .In this paper ,WAPP-quasi prime submodules are introduced as  new generalization of Weakly quasi prime submodules , where  proper submodule C of an R-module T is called WAPP –quasi prime submodule of T, if whenever 0≠rstϵC, for r, s ϵR , t ϵT, implies that either  r tϵ C +soc   or  s tϵC +soc  .Many examples of characterizations and basic properties are given . Furthermore several characterizations of WAPP-quasi prime submodules in the class of multiplication modules are established.

The current study seeks to evaluate teacher preparation programs in the scientific disciplines at the College of Education in Al-Aqsa University in the light of the requirements of the labor market. It further aims to reveal the significance of the differences in the sample members’ response averages of to the availability of labor market requirements in the program that prepares the teacher of scientific disciplines at the Faculty of Education in Al-Aqsa University taking into account the (gender, program) variables. The study followed the descriptive analytical approach, and so a questionnaire was distributed to a sample of scientific discipline students in the teacher preparation program adopted in Al-Aqsa University, (200) male and

This study aims at identifying the reality of alternative assessment for teachers of the first cycle of the basic education in the Sultanate of Oman with respect to the degree of teachers' use of alternative assessment strategies, level of self-efficacy for alternative assessment strategies, and attitude towards alternative assessment, and their relationship with other variables. To achieve the aims of the study, a descriptive research approach was utilized. A 5-point self-rated questionnaire was developed. It consists of three sections: Actual use of alternative assessment strategies (21 items), self-efficacy for alternative assessment strategies (21 items), and attitude towards alternative assessment (27 items). The psychometric proper

In this article we derive two reliability mathematical expressions of two kinds of s-out of -k stress-strength model systems; and . Both stress and strength are assumed to have an Inverse Lomax distribution with unknown shape parameters and a common known scale parameter. The increase and decrease in the real values of the two reliabilities are studied according to the increase and decrease in the distribution parameters. Two estimation methods are used to estimate the distribution parameters and the reliabilities, which are Maximum Likelihood and Regression. A comparison is made between the estimators based on a simulation study by the mean squared error criteria, which revealed that the maximum likelihood estimator works the best.