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.

هدفت هذه الدراسة إلى تحليل نتائج الاختبار الوطني الموحد الذي تطبقه وزارة التربية والتعليم الفلسطينية في مادة الرياضيات لطلبة الصف الثامن الأساسي في المدارس الحكومية في محافظة طولكرم، وذلك لمعرفة مستوى الطلبة على هذا الاختبار في ضوء متغيرات الجنس والمنطقة التعليمية ونوع المدرسة، ومعرفة علاقة التحصيل على هذا الاختبار بتحصيل الطلبة المدرسي والمعدل العام. ولتحقيق ذلك تم تحليل درجات (3218) طالباً وطالبة؛ وهم ي

Since the beginning of 21^st century, the prices of Agricultural crops have increased. This Increases is accompanied with that increases of crude oil prices and fluctuation of a dollar exchange rate as a dominant currency used in the global trade. The paper aimed to analysis the short run and long run cointegration relationships between prices of some of Agricultural crops imported by Iraq such as wheat and rice crops and both the crude oil prices and the Iraq dinar exchange rate a gained America dollar using ARDL model. The results show the long run equilibrium between they three variable throng the error correction mechanizem. The results also show the significant and economically sound effects of cru

Background: Polymethyl methacrylate (PMMA) is the most commonly used material in denture fabrication. The material is far from ideal in fulfilling the mechanical requirements, like low impact and transverse strength, poor thermal conductivity. The purpose of this study was to evaluate the effect of addition a composite of surface treated Nano Aluminum oxide (Al2O3) filler and plasma treated polypropylene fiber (PP) on some properties of denture base material. Materials and methods: One hundred fifty prepared specimens were divided into 5 groups according to the tests, each group consisted of 30 specimens and these were subdivided into 3 groups (unreinforced heat cured acrylic resin as control group),reinforced acrylic resin with( 0.5%wt Nan

The tourism industry has undergone exponential transformation, reshaped by online travel agencies (OTAs), shifting consumer preferences, and technological advancements. Established OTAs like TripAdvisor and Travelocity face pressures to adapt their strategies to capitalize on these disruptive landscape changes. This research involves a comparative analysis examining the key challenges confronting TripAdvisor and Travelocity, with a focus on opportunities to leverage artificial intelligence (AI) in enhancing personalization and the traveler experience. The study utilizes publicly available data on the companies and academic literature on AI innovation diffusion. Findings reveal that while TripAdvisor has actively developed AI-based trip plan

In this paper, a subspace identification method for bilinear systems is used . Wherein a " three-block " and " four-block " subspace algorithms are used. In this algorithms the input signal to the system does not have to be white . Simulation of these algorithms shows that the " four-block " gives fast convergence and the dimensions of the matrices involved are significantly smaller so that the computational complexity is lower as a comparison with " three-block " algorithm .

The objective of this work is to design and implement a cryptography system that enables the sender to send message through any channel (even if this channel is insecure) and the receiver to decrypt the received message without allowing any intruder to break the system and extracting the secret information. In this work, we implement an interaction between the feedforward neural network and the stream cipher, so the secret message will be encrypted by unsupervised neural network method in addition to the first encryption process which is performed by the stream cipher method. The security of any cipher system depends on the security of the related keys (that are used by the encryption and the decryption processes) and their corresponding le