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.

Abstract:

The aim of the research is to demonstrate the impact of the professional specialization of the audit companies in the detection of fraud in the financial statements of the economic units listed in the Iraqi market for securities for the period 2014-2015 through the application of the model (Carcello) to test the hypothesis of research on the impact of professional specialization of audit companies in the detection of fraud in lists The effect of the variables was revealed through the use of statistical models of logistic regression model and correlation coefficient. After testing the hypotheses of the research, a number of conclusions were reached. The most important was the existence of a signi

Abstract: Microfluidic devices present unique advantages for the development of efficient drug assay and screening. The microfluidic platforms might offer a more rapid and cost-effective alternative. Fluids are confined in devices that have a significant dimension on the micrometer scale. Due to this extreme confinement, the volumes used for drug assays are tiny (milliliters to femtoliters).

 In this research, a microfluidic chip consists of micro-channels carved on substrate materials built by using Acrylic (Polymethyl Methacrylate, PMMA) chip was designed using a Carbon Dioxide (CO₂) laser machine. The CO2 parameters have influence on the width, depth, roughness of the chip. In order to have regular

This study discussed a biased estimator of the Negative Binomial Regression model known as (Liu Estimator), This estimate was used to reduce variance and overcome the problem Multicollinearity between explanatory variables, Some estimates were used such as Ridge Regression and Maximum Likelihood Estimators, This research aims at the theoretical comparisons between the new estimator (Liu Estimator) and the estimators

Some metal ions (Mn+2, Co+2, Ni+2, Cu+2, Zn+2, Cd+2 and Hg+2) complexes of quinaldic acid (QuinH) and α-picoline (α-Pic) have been synthesized and characterized on the basis of their , FTIR, (U.V-Vis) spectroscopy, conductivity measurements, magnetic susceptibility and atomic absorption. From the results obtained the following general formula has suggested for the prepared complexes [M(Quin)2( α-Pic)2].XH2O where M+2 = (Mn, Co, Ni, Cu, Zn, Cd and Hg), X = 2, X = zero for (Co+2 and Hg+2) complexes, (Quin-) = quinaldate ion, (α-Pic) = α-picoline. The results showed that the deprotonated ligand (QuinH) by using (KOH) coordinated to metal ions as bidentate ligand through the oxygen atom of the carboxylate group (-COO-) and the nitrogen ato

A new ligand N-((4-(phenylamino) phenyl) carbamothioyl) acetamide (PCA) was synthesized by reaction of (4-amino di phenyl amine) with (acetyl isothiocyante) by using acetone as a solvent. The prepared ligand(PCA) has been characterization by elemental analysis (CHNS), infrared(FT-IR),electronic spectral (UV-Vis)&1H,13C- NMR spectra. Some Divalent Metal ion complexes of ligand (PCA) were prepared and spectroscopic studies by infrared(FT-IR), electronic spectral (UV-Vis), molar conductance, magnetic susceptibility and atomic absorption. The results measured showed the formula ofFall prepared complexes were [M (PCA)2 Cl2] (M+2 = Mn, Co, Ni, CU, Zn, Cd &Hg),the proposed geometrical structure for all complexes wereeoctahedral.

The aim of this research is to prepare a set of complexes with the general formula [M(HMB)n] , where M=VO (II) , Cr(III) and Cu(II) while  n=2,3,2 respectively resulting from the reaction of anew ligand [N'-(2-hydroxy-3-methoxybenzyl)-4-methylbenzohydrazide] (HMB) derived from the reaction of the tow substances (4-methylbenzohydrazide  and 2-hydroxy-3-methoxy benzaldehyde) with metal ions. The prepared compounds were identified by several spectroscopic methods such as Infrared, Nuclear Magnetic Resonance and Electronic Spectra. From the results of the measurements, it was suggested that the prepared complexes have different geometries such as square planar (Cu), square pyramidal (VO) and octahedral (Cr). DFT simulations backed up