Hamiltonians, momentum operators, and other quantum-mechanical perceptible take the form of self-adjoint operators when understood in quantized physical schemes. Unbounded and self-adjoint recognition are required in the situation of positive measurements. The selection of the proper Hilbert space(s) and the selection of the self-adjoint extension must be made in order for this to operate. In this effort, we define a new extension positive measure depending on the measurable field of nonzero positive self-adjoint operator in unbounded Hilbert space of analytic functions of complex variables. Consequently, we define an extension norm in the same space. We show several new properties of the suggested operator and its adjoin operator. These pr

اصبح لمجالس الادارة في الشركات دوراً حاسماً في تعزيز الحوكمة الفاعلة، كونها تتحمل المسؤولية النهائية عن نظم الرقابة الداخلية في شركاتها، ويلعب التدقيق الداخلي دوراً اساسياً في مساعدة تلك المجالس على القيام بمهمات الحوكمة. ولهذا يبذل مجمع المدققين الداخليين الامريكي جهداً كبيراً في توجيه اعضاءه ليكونوا متخصصين في اصول حوكمة الشركات وتحسين وتقوية اخلاقيات العمل وسلامة المنظمة.

لذا فإن ا

The activation and reaction energies of the C-C and C-H bonds cleavage in pyrene molecule are calculated applying the Density Functional Theory and 6-311G Gaussian basis. Different values for the energies result for the different bonds, depending on the location of the bond and the structure of the corresponding transition states. The C-C bond cleavage reactions include H atom migration, in many cases, leading to the formation of CH2 groups and H-C≡C- acetylenic fragments. The activation energy values of the C-C reactions are greater than 190.00 kcal/mol for all bonds, those for the C-H bonds are greater than 160.00 kcal/mol. The reaction energy values for the C-C bonds range between 56.497 to 191.503 kcal/mol. As for the C-H cleavage rea

The performance in the 110-meter hurdles at the sprint hurdles event is determined by several physical and physiological qualities. Nonetheless, relatively little attention has been paid to the predictability of such factors in determining race performance. This study seeks to fill this gap by establishing the most critical physical and physiological characteristics affecting elite hurdlers’ performance and creating a statistical model that predicts race times from the identified measurable characteristics. The study utilized a descriptive research design in-volving six elite male hurdlers, all of whom completed a battery of standardized physical and functional tests to assess their explosive lower-body strength, agility, reaction

         The graphic privacy feature is one of the most important specifications for the existence of any type of design achievements alike, which is one of the graphic products with its multiple data, and from here the current research investigates the graphic privacy of vector graphics design with all its technical descriptions and concepts associated with it and the possibility of achieving it to the best that it should be from Where its formal structure in children's publications, where the structural structure of the current research came from the first chapter, which contained the research problem, which came according to the following question: What is the graphic privacy in the design of vector graphics in children's publ