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.

The problem of this research lies in the fact that there is a lack of accurate scientific perceptions about the size of the use of Iraqi women’s social networking sites and the motives behind this use and the expectations generated by them.
The goals of the research are as follows:
1- Determine the extent of Iraqi women’s use of social networking sites (Facebook, YouTube, twitter, and Instagram).
2- Investigative the motives behind the use of social networking sites by Iraqi women.
3- Detecting the repercussions of Iraqi women’s use of social networking sites (Facebook, you tube, twitter, and Instagram).
The research is classified as a descriptive one. The researchers use the survey methodology. The research commu

The selection of proper field survey parameters of electrical resistivity can significantly provide efficient results within a reasonable time and cost. Four electrode arrays of 2D Electric Resistivity Imaging (ERI) surveys were applied to characterize and detect subsurface archaeological bodies and to determine the appropriate array type that should be applied in the field survey. This research is to identify the subsurface features of the Borsippa archaeological site, Babylon Governorate, Middle Iraq. Synthetic modeling studies were conducted to determine the proper array and parameters for imaging the shallow subsurface features or targets. The efficiency of many array types has been tested for the detection the buried archaeolog

: The Aluminium (Al) material emerged as a plasmonic material in the wavelength ranges from the ultraviolet to the visible bands in different on-chip plasmonic applications. In this paper, we demonstrate the effect of using Al on the electromagnetic (EM) field distribution of a compact hybrid plasmonic waveguide (HPW) acting as a polarization rotator. We compare the performance of Al with other familiar metals that are widely used as plasmonic materials, which are Silver (Ag) and Gold (Au). Furthermore, we study the effect of reducing the geometrical dimensions of the used materials on the EM field distributions inside the HPW and, consequently, on the efficiency of the polarization rotation. We perform the study based o

In this paper, the computational method (CM) based on the standard polynomials has been implemented to solve some nonlinear differential equations arising in engineering and applied sciences. Moreover, novel computational methods have been developed in this study by orthogonal base functions, namely Hermite, Legendre, and Bernstein polynomials. The nonlinear problem is successfully converted into a nonlinear algebraic system of equations, which are then solved by Mathematica®12. The developed computational methods (D-CMs) have been applied to solve three applications involving well-known nonlinear problems: the Darcy-Brinkman-Forchheimer equation, the Blasius equation, and the Falkner-Skan equation, and a comparison between the met

الوصف In this time, most researchers toward about preparation of compounds according to green chemistry. This research describes the preparation of 2-fluoro-5-(substituted benzylideneamino) benzonitrile under reflux and microwave methods. Six azomethine compounds (B1-6) were synthesized by two methods under reflux and assisted microwave with the comparison between the two methods. Reflux method was prepared of azomethine (B1-6) by reaction of 5-amino-2-fluorobenzonitrile with some aldehyde derivatives with (50–100) mL of absolute ethanol and some quantity of GAA and time is limited between (2–5) hours with a yield between (60–70) percent with recrystallization for appropriate solvents. But the microwave-assisted method was synthe