The paper is concerned with the state and proof of the existence theorem of a unique solution (state vector) of couple nonlinear hyperbolic equations (CNLHEQS) via the Galerkin method (GM) with the Aubin theorem. When the continuous classical boundary control vector (CCBCV) is known, the theorem of existence a CCBOCV with equality and inequality state vector constraints (EIESVC) is stated and proved, the existence theorem of a unique solution of the adjoint couple equations (ADCEQS) associated with the state equations is studied. The Frcéhet derivative derivation of the "Hamiltonian" is obtained. Finally the necessary theorem (necessary conditions "NCs") and the sufficient theorem (sufficient conditions" SCs") for optimality of the stat

The current paper examines the Arab EFL teacher view on the application of AI-based chatbots as a method of aiding writing instruction. It explores pedagogy, didactic difficulties and ethics. The overall aim is to clarify the perception that teachers have of AI chatbots as a useful tool in the writing process and to find out to what degree these perceptions are reflected in instructional decision-making and classroom behaviors. A quantitative study was conducted using a structured questionnaire that was given to forty Arab EFL teachers, using a sequential explanatory mixed-method design. To elaborate and contextualize the survey results, qualitative enquiry was implemented through semi-structured interviews with twelve teachers. Fin

The current paper examines the Arab EFL teacher view on the application of AI-based chatbots as a method of aiding writing instruction. It explores pedagogy, didactic difficulties and ethics. The overall aim is to clarify the perception that teachers have of AI chatbots as a useful tool in the writing process and to find out to what degree these perceptions are reflected in instructional decision-making and classroom behaviors. A quantitative study was conducted using a structured questionnaire that was given to forty Arab EFL teachers, using a sequential explanatory mixed-method design. To elaborate and contextualize the survey results, qualitative enquiry was implemented through semi-structured interviews with twelve teachers. Fin

The research included five sections containing the first section on the introduction o research and its importance and was addressed to the importance of the game of gymnastic and skilled parallel bars effectiveness and the importance of biochemical variables, either the research problem that there is a difference in learning this skill and difficulty in learning may be one of the most important reasons are falling and injury Has a negative impact on the performance and lack of sense of movement of is one of the obstacles in the completion of the skill and the goal of research to design a device that helps in the development of biochemical changes to skill of rear vault dismount with one-half twist on parallel bars in gymnastics . And the n

Advancements and modernizations introduced into the educational and pedagogical systems have significantly impacted teaching processes and how subjects are presented and explained to students. The focus has shifted to how learners interact with the material they need to learn, providing sufficient opportunities for learning and granting them freedom and self-confidence to achieve learning objectives. The research problem stems from the researcher's experience as a lecturer in the College of Physical Education and Sports Science, particularly in teaching basketball. She observed that some instructors were deficient in using the most effective teaching methods. The researcher formulated her research question based on these observations: "What

ت نايبتسلاا ثحابلا مدختسا دقو ,ةيداصتقلاا تادحولا ةميق ىلع انوروك ةحئاج لظ يف يلخادلا قيقدتلا ريثأت ةيداصتقلاا تادحولا فادها قيقحت يف مهسي يلخادلا قيقدتلا نا ثحبلا تاجاتنتسا مها تناكو , ثحبلا تاريغتم نيب ةقلاعلا نايبل رطاخملا ةرادأو اهتءافكو اهتيلعاف نيسحتو قيقدتلا عقوم زيزعت ىلع لمعلا تايصوتلا مها تناكو امك, ةمكوحلا تايلمعو ةباقرلاو قيقحتل رارمتسأب ئراوطلا ططخ ثيدحتو ةبقارمو ةحضاو تازفحم ءاشناو ةلمتحم

Watermarking operation can be defined as a process of embedding special wanted and reversible information in important secure files to protect the ownership or information of the wanted cover file based on the proposed singular value decomposition (SVD) watermark. The proposed method for digital watermark has very huge domain for constructing final number and this mean protecting watermark from conflict. The cover file is the important image need to be protected. A hidden watermark is a unique number extracted from the cover file by performing proposed related and successive operations, starting by dividing the original image into four various parts with unequal size. Each part of these four treated as a separate matrix and applying SVD