In this paper, we characterize normal composition operators induced by holomorphic self-map , when and .Moreover, we study other related classes of operators, and then we generalize these results to polynomials of degree n.

he assignment model represents a mathematical model that aims at expressing an important problem facing enterprises and companies in the public and private sectors, which are characterized by ensuring their activities, in order to take the appropriate decision to get the best allocation of tasks for machines or jobs or workers on the machines that he owns in order to increase profits or reduce costs and time As this model is called multi-objective assignment because it takes into account the factors of time and cost together and hence we have two goals for the assignment problem, so it is not possible to solve by the usual methods and has been resorted to the use of multiple programming The objectives were to solve the problem of

A piezoelectric cantilever beam with a tip mass at its free end is a common energy harvester configuration. This article introduces a new principle of designing such a harvester that increases the generated power without changing the resonance frequency of the harvester: the attraction force between two permanent magnets is used to add stiffness to the system. This magnetic stiffening counters the effect of the tip mass on the efficient operation frequency. Five set-ups incorporating piezoelectric bimorph cantilevers of the same type in different mechanical configurations are compared theoretically and experimentally to investigate the feasibility of this principle: theoretical and experimental results show that magnetically stiffened harve

The research include a pulsed Nd: YAG Laser with (300µs) pulse duration in the TEM00 mode at (1.06µm) wavelength for energies between (0.5-3) J was employed to drill Brass material which is use in industrial applications. The process of drill was assisted by an electric field. This resulted in an increase in the hole aspect ratio by the value (45%) and decrease in the hole taper by the value (25%) of its value under ordinary drilling conditions using the same input energy.

ترك السلطان عبدالحميد الثاني بصماتهُ على أخاديد الزمان وعلى خارطة المشرق العربي الخاضع للسيطرة العثمانية أنذاك ، لكونهُ أهم شخصية أسلامية غير عربية واجهت الخطر الصهيوني ومحاولاتهم الإستيطانية في مشرق الوطن العربي ، على الرغم من صعوبة الظروف التي كانت تمر بها الدولة العثمانية داخليا ً وخارجيا ً، بما فيها من أطماع اقتسامها بين الاوربين ولذا سموها بالرجل المريض .