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.

Hamiltonians, momentum operators, and other quantum-mechanical perceptible take the form of self-adjoint operators when understood in quantized physical schemes. Unbounded and self-adjoint recognition are required in the situation of positive measurements. The selection of the proper Hilbert space(s) and the selection of the self-adjoint extension must be made in order for this to operate. In this effort, we define a new extension positive measure depending on the measurable field of nonzero positive self-adjoint operator in unbounded Hilbert space of analytic functions of complex variables. Consequently, we define an extension norm in the same space. We show several new properties of the suggested operator and its adjoin operator. These pr

In this paper we use Bernstein polynomials for deriving the modified Simpson's 3/8 , and the composite modified Simpson's 3/8 to solve one dimensional linear Volterra integral equations of the second kind , and we find that the solution computed by this procedure is very close to exact solution.

The research aims to find approximate solutions for two dimensions Fredholm linear integral equation. Using the two-variables of the Bernstein polynomials we find a solution to the approximate linear integral equation of the type two dimensions. Two examples have been discussed in detail.

This article studies the nonlocal inverse boundary value problem for a rectangular domain, a second-order, elliptic equation and a two-dimensional equation. The main objective of the article is to find the unidentified coefficient and provide a solution to the problem. The two-dimensional second-order, convection equation is solved directly using the finite difference method (FDM). However, the inverse problem was successfully solved the MATLAB subroutine lsqnonlin from the optimization toolbox after reformulating it as a nonlinear regularized least-square optimization problem with a simple bound on the unknown quantity. Considering that the problem under study is often ill-posed and that even a small error in the input data can hav

Klebsiella pneumoniae has been found in the urinary tract of some bladder cancer patients. Bacterial presence within tumor tissue may affect the tumor-microenvironment and consequently influence cancer behavior, development, and treatment response. This study investigated mesenchymal and stemness transdifferentiation of bladder cancer cell line due to environmental stress of K. pneumoniae. Cultures of urothelial bladder cancer cell line (T24) were infected with K. pneumoniae with different multiplicity of infection (MOI) for two and four days. Transdifferentiation-associated features were morphologically assessed.

Moreover, transdifferentiation markers were estimated using Q-PCR and immunohistoc

Schiff base derived from PVA and Erythroascorbic acid derivative (pentulosono-ɣ-lactone-2, 3-enedianisoate) was synthesized and characterized by Thin Layer Chromatography (TLC) and FTIR spectra, aldehyde was also characterized by (U.V-Vis), 1HNMR, 13CNMR and mass spectra. The inhibitory effect of prepared polymer on the activity of human serum Cholinesrerase has been studied in vitro. The polymer showed a remarkable activity at low concentration (4.5*10-3 – 4.5*10-8 M).

The importance of forecasting has emerged in the economic field in order to achieve economic growth, as forecasting is one of the important topics in the analysis of time series, and accurate forecasting of time series is one of the most important challenges in which we seek to make the best decision. The aim of the research is to suggest the use of hybrid models for forecasting the daily crude oil prices as the hybrid model consists of integrating the linear component, which represents Box Jenkins models and the non-linear component, which represents one of the methods of artificial intelligence, which is long short term memory (LSTM) and the gated recurrent unit (GRU) which represents deep learning models. It was found that the proposed h