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.

Takbiratul Ehram "The First Takbeer to Start Prayer" means: the words that the worshiper says to start his prayers, and refrain from anything invalidates it. the findings revealed that the four school jurists agreed that the prayer is not valid without Takbiratul Ehram "The First Takbeer to Start Prayer", and they disagreed on its description, so the majority of jurists said that it is a pillar, and some of them called it an obligatory, but Hanafi made it a condition. Likewise, the four jurists agreed that the one who articulates Takbiratul Ehram "The First Takbeer to Start Prayer" with the word: “Allahu Akbar,”; his Takbeer is correct, and they disagreed about the one who adds a word, or replaced it with another, where the m

In all applications and specially in real time applications, image processing and compression plays in modern life a very important part in both storage and transmission over internet for example, but finding orthogonal matrices as a filter or transform in different sizes is very complex and importance to using in different applications like image processing and communications systems, at present, new method to find orthogonal matrices as transform filter then used for Mixed Transforms Generated by using a technique so-called Tensor Product based for Data Processing, these techniques are developed and utilized. Our aims at this paper are to evaluate and analyze this new mixed technique in Image Compression using the Discrete Wavelet Transfo

ABSTRACT— In primary teeth, root canal treatment is a time consuming and challenging procedure, particularly during the most important step in endodontic treatment which is the preparation of the canal. Pulpectomy is the treatment of choice in all the necrotic primary teeth. For better treatment protocol, advancing technology brought the rotary system to reduce the manual dexterity and improve the quality of treatment for pulpectomy. This study aimed to compare and assess the efficacy of cleaning and the time required for the instrumentation during the preparation of root canals of the primary molars using the rotary and the manual (conventional) systems. Thirty root canals of primary teeth were selected. These teeth submitted to a

     Enterobius vermicularis infection is considered as one of the important causes of anaemia and malnutrition among children. This topic has recently received an increased amount of attention.  The objective of this study is to evaluate the demographical, anthropometrical, nutritional, and  haematological status of E. vermicularis infection among children. This study was conducted in Al Diwaniyah province, south of Iraq, for the period of October 2020 to the end of January 2021. The study included 122 children from both genders (males, n= 61, and females, n=61) and their ages ranged between 1 and 14 years. Nutritional status, body mass index (BMI), BMI percentile, and weight- for- age Z score were evaluated for some particip

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,