In this paper, we introduce an exponential of an operator defined on a Hilbert space H, and we study its properties and find some of properties of T inherited to exponential operator, so we study the spectrum of exponential operator e^T according to the operator T.

This paper proposes a new method to tune a fractional order PID controller. This method utilizes both the analytic and numeric approach to determine the controller parameters. The control design specifications that must be achieved by the control system are gain crossover frequency, phase margin, and peak magnitude at the resonant frequency, where the latter is a new design specification suggested by this paper. These specifications results in three equations in five unknown variables. Assuming that certain relations exist between two variables and discretizing one of them, a performance index can be evaluated and the optimal controller parameters that minimize this performance index are selected. As a case study, a third order linear time

Econazole nitrate (EN) is considered as the most effective agent for the treatment of all forms of dermatomycosis caused by dernatophytes. It was formulated as a topical solution in our laboratories. This study was designed to evaluate the effectiveness of Econazol Nitrate in the prepared formula and compared with that of commercial brand, Pevaryl®. A total of 104 patient suffering from dermatomycoses were involved in this investigation. Both formula were applied to the affected skin region in the morning and evening from week to 16 weeks with light massage until complete healing effect was achieved. The data revealed that the percentage of cured patient treated with the prepared formula and reference formula of Ecanozol Nitrate 1% so

This review paper examines the crucial impact of YouTube on learning English as a Foreign Language. Recently, learners’ interaction and development of their skills have been improved due to the integration of digital platforms into language education. YouTube is regarded as one of the most prevalent platforms due to its accessibility, multimodal content, and capacity to simulate real-life communication. This study tackles thirty selected research articles from various cultural and institutional backgrounds to identify the pedagogical benefits and challenges associated with using YouTube in teaching English. Conventional methods of teaching English as a foreign language encounter difficulties in improving students’ engagement and

This paper proposes a new method to tune a fractional order PID controller. This method utilizes both the analytic and numeric approach to determine the controller parameters. The control design specifications that must be achieved by the control system are gain crossover frequency, phase margin, and peak magnitude at the resonant frequency, where the latter is a new design specification suggested by this paper. These specifications results in three equations in five unknown variables. Assuming that certain relations exist between two variables and discretizing one of them, a performance index can be evaluated and the optimal controller parameters that minimize this performance index are selected. As a case study, a thir

Using an electrochemical polymerization technique at room temperature, poly nicotine amide (PNA) was produced from the monomer nicotine amide (NA) in aqueous solution. The structure of polymer layer generated on the stainless steel surface (316 L) (working electrode) is investigated by Fourier Transmission Infrared Region (FT-IR). The anti-corrosion activity of polymer coating on the stainless steel (SS 316 L) is investigated by electrochemical polarization in 0.20M solution of HCl at 293-323K. The graphene -modified polymer film-coated SS had greater protection efficiency (PE percent) when compared to Nano ZnO -modified polymer film-coated SS. For the corrosion process of SS 316 L, kinetic and thermo-dynamic parameters of activatio

Never the less, banking compliance function became one of the most important functions in banking sector according to its characteristics that considered as an interior control tools to control (executive management, departments, subsidiaries…etc) in any bank; and their compliance towards applying rules, recommendations and legislations. In addition to, estimating the risks and limited them; and controlling the anti-money laundering. Thus, these functions that covered the main concept of (Banking Compliance) would avoid the bank to be under the control of any sanctions.

Marketing plays a role in the transfer of consumer desires through research, studies and satisfy the needs process, and with the technical development has evolved and marketing departments in the world of commerce has made great strides since the expansion of the trade deal, especially in light of spread of the Internet and the culture of use where he became a lot as individuals or institutions are dealings via electronic shopping . In all cases, we find that the consumer is important party, and that the legal rules did not leave the shopping process or contracting E without protection and I've dealt with so many studies through the civil protection for the consumer in electronic contracts legally with an analytical study of the