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 communication, introduce the split Mersenne and Mersenne-Lucas hybrid quaternions, also obtaining generating functions and Binet formulas for these hybrid quaternions and investigating some properties among them.

  The audience is one of the important practical elements in the theatrical show and its importance is not confined to its static activity as a receiver element only, rather it went beyond that issue as an effective and influential element in the proceedings of the show and the process of meaning construction, that it gains an active role in the construction and production of the connotation that influences and is influenced by the actor, where the communication channels are open between the two sides, consequently a kind of watching and joint interaction happens between them. Thus, it has become necessary for the actor to create a suitable environment for the onlookers in order for it to be an essential part of the show system. The

The culture of theatre performance has a vital role in the process of reading the linguistic and visual signs of the performance. And the process of transforming a theatre performance from its original context into a new hosting cultural context starts from the actual reading of the text. Directors derives their new signs out of his personal culture, depending on the society where they lives and the culture that forms the social conventions, traditions and beliefs. The text is usually written within its own historical and temporal culture. The process of its production usually takes it away from its original culture, when it interprets the codes of the original writer and their visual and linguistic signs and instils new alternative sign

Praise be to God alone, and prayers and peace be upon the one after whom there is no prophet, and after:

This is a regular judicial search for the issuance, validity, and cancellation of regulations in the Saudi system. It came in an introduction and four demands and a conclusion of the most important results, then a list of the most important sources and references, in which I presented: A brief study on the issuance of regulations in the Kingdom of Saudi Arabia and the stages that they pass through, their validity and application, and the rules that govern this system in terms of people, places and times, then canceling and amending regulations And its rulings, I referred to it to the original sources approved in this section,

In an intensive study of the various species of the Euglenophyceae under different environmental conditions, the algal samples were collected monthly in twelve springs and six related streams from September 2019 to August 2020 within Shaglawa district-Erbil Province in virgin areas for phycolimnological study. Twenty species of Euglenophyceaen are identified as a new record for the algal flora. These taxa consist of Colacium vesiculosum, Lepocinclis salina and L.wangi, Eutreptia viridis, Euglena chlamydophora, E. clavata,

Oil recovery could be impacted by the relation between vertical permeability (K_v) and horizontal permeability (K_h) (K_v/K_h). 4816 plugs that have been getting hold of 18 wells of Mishrif formation in the West Qurna oilfield were used. K_v/K_h data provided some scatter, but the mean is ~1. K_v/K_h =1 was used for the Petrel model before upscaling according to the heterogeneity of each layer.

K_v/K_h values for Mishrif Formation in West Qurna Oilfield are 0.8 for relatively homogeneous, 0.4 for heterogeneous rock, and 0.1 for cap rocks (CRII).

   Eclipse ^TM was used for reservoir simulation. PVT and SCAL data e

The study aimed to identify the effect of the ethical perception of a sample of managers in public organizations on responsible behavior in light of the rapid changes taking place in the external environment. To achieve this, the researcher followed the descriptive analytical approach by applying a questionnaire of two parts. The first part dealt with the ethical perception according to the scale of Johnson (2015), which consisted of (22) items. The second part dealt with measuring responsible behavior, which consisted of (20) items based on the scale of Development of Ethical Behavior (Narvaez, 2006) for a sample of (125) respondents randomly chosen. The results showed that the estimation degree of managers in public governmental o