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.

Achieving the Book of Return to the End of the Book of Alimony from the Manuscript of the Forum of the Abhar of the Sheikh (Abraham Bin
Muhammad ibn Ibrahim al-Halabi (d. 956 AH), who was a member of the Hanafi sect, was a long man
Fiqh, interpretation, modernity, Arab sciences, and readings
Hanafi as well as that he was Abid Zahid and the reason for his claim to this book that asked him some
He asked him to take advantage of it
Al-Hanafiya said, mentioning the sources from which he was taken, and presented his opinion and evidence on the correct
He mentioned the issues of the Hanafi jurisprudence in his book according to the chapters of the jurisprudence
Reaction is done to what you have achieved previously in the h

The research aims to get acquainted with the evaluation of the reality of the application of the curriculum axis from among the eight Iraqi academic accreditation standards in a sample of governmental and private universities and colleges in Iraq and to identify the main and secondary reasons for it as well as to provide proposed mechanisms and procedures to help reduce gaps, If the research problem is represented in the weak availability of the requirements of the curriculum axis in universities and colleges (the study sample) due to the weak documentation and successful implementation of them and interest in them is still below the level of ambition, In order to arrive at scientific facts, the researchers adopted the comparativ

هدفت الدراسة الحالية الى التعرف ما اذا كان هناك تقبل اجتماعي للتلاميذ بطيئي من قبل اقرانهم العاديين؟ وكذلك معرفة ما اذا كان هناك فروق ذات دلالة في التقبل الاجتماعي بين افراد عينة الدراسة على وفق المتغيرات الاتية:

أ- العمر (9-13)

ب- الجنس (ذكور –اناث)

ج- المرحلة الدراسية

د- الحالة الاقتصادية (جيدة –متوسطة –جيدة جدا)

    ولغرض تحقيق اه

This study focuses on the phenomenon of child labour, which is regarded as a problem not only in Iraq or in developing countries but also in many other countries around the world .In fact, this problem is ignored and not given enough attention for there are millions of children working and doing different works in economically poor societies. Those children often work for long hours and are being exploited, doing works incompatible with their abilities and energy, preventing them from enjoying their childhood, developing both mentally and physically and joining school. The research introduced some suggestions aiming at preventing children from all forms of harmful and unhealthy works are presented. In fact, this is the very aim that most

Abstract: This research was performed to study the effect of some amino acids and vitamins on the growth of bacteria Staphylococcus aureas and its sensitivity against UV light. The results showed low inhibition in bacterial growth because amino acids repairs the damges caused by UV light. Besides the effect of two groups of antibiotics (β-lactame and tetracycline) on the growth of S. aureus and the possible interference of amino acids and vitamins in the activity of the antibiotics against this bacteria in the presence of UV light were studied. The result show increase in the sensitivity towards these antibiotics and provided protection against the antibiotics.

In this paper, a discretization of a three-dimensional fractional-order prey-predator model has been investigated with Holling type III functional response. All its fixed points are determined; also, their local stability is investigated. We extend the discretized system to an optimal control problem to get the optimal harvesting amount. For this, the discrete-time Pontryagin’s maximum principle is used. Finally, numerical simulation results are given to confirm the theoretical outputs as well as to solve the optimality problem.

The Antimicrobial activity of Probiotic Bifidobacterium sp and Prebiotics : chicory roots ( Hot water extract ) and Inulin ( 10 % ) against some Pathogenic bacteria (Esherichia coli , Proteus mirabilis , Klebsiella sp , Pseudomonas aeruginosa , Serratia marcescens was studied . The combination of Probiotic and Prebiotics (Synbiotic) (Bifidobacterium sp + chicory ) and (Bifidobacterium sp + Inulin ) also tested for their antimicrobial activity against Pathogenic bacteria . Results showed that Bifidobacterium sp had good antimicrobial activity against all the Pathogenic bacteria tested , followed by chicory and inulin . The synergistic inhibitory effect of Synbiotic (Bifidobacterium sp + chicory ) and ( Bifidobacterium sp + inuli