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 Phenomenon of Extremism of Values ​​(Maximum or Rare Value) an important phenomenon is the use of two techniques of sampling techniques to deal with this Extremism: the technique of the peak sample and the maximum annual sampling technique (AM) (Extreme values, Gumbel) for sample (AM) and (general Pareto, exponential) distribution of the POT sample. The cross-entropy algorithm was applied in two of its methods to the first estimate using the statistical order and the second using the statistical order and likelihood ratio. The third method is proposed by the researcher. The MSE comparison coefficient of the estimated parameters and the probability density function for each of the distributions were

The use of non-parametric models and subsequent estimation methods requires that many of the initial conditions that must be met to represent those models of society under study are appropriate, prompting researchers to look for more flexible models, which are represented by non-parametric models                  

          In this study, the most important and most widespread estimations of the estimation of the nonlinear regression function were investigated using Nadaraya-Watson and Regression Local Ploynomial, which are one of the types of non-linear

In this paper, the process for finding an approximate solution of nonlinear three-dimensional (3D) Volterra type integral operator equation (N3D-VIOE) in R³ is introduced. The modelling of the majorant function (MF) with the modified Newton method (MNM) is employed to convert N3D-VIOE to the linear 3D Volterra type integral operator equation (L3D-VIOE). The method of trapezoidal rule (TR) and collocation points are utilized to determine the approximate solution of L3D-VIOE by dealing with the linear form of the algebraic system. The existence of the approximate solution and its uniqueness are proved, and illustrative examples are provided to show the accuracy and efficiency of the model.

Mathematical Subject Classificat

At present, numerous novel chemical compounds face challenges related to their limited solubility in aqueous environments. These compounds are classified under the Biopharmaceutical Classification System (BCS) as either class II or class IV substances. Different carriers were used to increase their solubility. Candesartan cilexetil (CC) is one of the most widely used antihypertensive drugs, which belongs to class II drugs. The aim of this research was to enhance the solubility and dissolution rate of CC through a complexation approach involving β-cyclodextrin and its derivatives, specifically hydroxypropyl beta cyclodextrin (HP-β-CD), methyl beta cyclodextrin (M-β-CD), and sulfonyl ether beta-cyclodextrin (SBE-β-CD), serving as

This work aimed PVA nanofibers in a range of concentrations were successfully manufactured via electrospinning. PVA NFs/Si was effectively prepared using the electrospinning process. The structural, morphological, optical and electrical properties of the prepared PVA were studied using XRD, FE-SEM, UV-Vis spectrophotometer and I-V characteristics, respectively. The amorphous structure of PVA nanofibers was observed. The optical energy gap from ultraviolet to visible was between (2.75 and 2.41) eV, making this compound highly sensitive to visible orange light at 610 nm, with a photosensitivity of 66%. The optical energy gap of PVA/Si heterojunction was utilized to modify this film from the UV to the visible spectrum. As show in the results,

Thin films of vanadium oxide nanoparticles doped with different concentrations of europium oxide (2, 4, 6, and 8) wt % are deposited on glass and Si substrates with orientation (111) utilizing by pulsed laser deposition technique using Nd:YAG laser that has a wavelength of 1064 nm, average frequency of 6 Hz and pulse duration of 10 ns. The films were annealed in air at 300 °C for two hours, then the structural, morphological and optical properties are characterized using x-ray diffraction (XRD), Field emission scanning electron microscopy (FESEM) and UV-Vis spectroscopy respectively. The X-ray diffraction results of V2O5:Eu2O3 exhibit that the film has apolycrystalline monoclinic V2O5 and triclinic V4O7 phases. The FESEM image shows a h