In this work, we give an identity that leads to establishing the operator . Also, we introduce the polynomials . In addition, we provide Operator proof for the generating function with its extension and the Rogers formula for . The generating function with its extension and the Rogers formula for the bivariate Rogers-Szegö polynomials  are deduced. The Rogers formula for  allows to obtain the inverse linearization formula for , which allows to deduce the inverse linearization formula for . A solution to a q-difference equation is introduced and the solution is expressed in terms of the operators . The q-difference method is used to recover an identity of the operator  and the generating function for the polynomials

Cabrera and Mohammed proved that the right and left bounded algebras of quotients  and  of norm ideal  on a Hilbert space  are equal to  Banach algebra of all bounded linear operators on . In this paper, we prove that  where  is a norm ideal on a complex Banach space .

Abstract

In this work, the plasma parameters (electron temperature (T_e), electron density( n_e), plasma frequency (f_p) and Debye length (λ_D)) have been studied by using the spectrometer that collect the spectrum of Laser produce CdTe_(X):S_(1-X) plasma at X=0.5 with different energies. The results of electron temperature for CdTe range 0.758-0.768 eV also the electron density 3.648 10¹⁸ – 4.560 10¹⁸ cm^-3  have been measured under vacuum reaching 2.5 10^-2 mbar .Optical properties of CdTe:S were determined through the optical transmission method using ultraviolet visible spectrophotometer within the r

This paper aims to identify the approaches used in assessment the credit applications by Iraqi banks, as well as which approach is most used. It also attempted to link these approaches with reduction of credit default and banks’ efficiency particularly for the Gulf Commercial Bank. The paper found that the Gulf Bank widely relies on the method of Judgment Approach for assessment the credit applications in order to select the best of them with low risk of default. In addition, the paper found that the method of Judgment Approach was very important for the Gulf Bank and it driven in reduction the ratio of credit default as percentage of total credit. However, it is important to say that the adoption of statistical approaches for

      Spray pyrolysis technique was subjected to synthesized (SnO₂)_1-x (TiO₂: CuO) _x Thin films on different substrates like glass and single crystal silicon using. The structure of the deposited films was studied using x-ray diffraction. A more pronounced diffraction peaks of SnO₂ while no peaks of (CuO , TiO₂ ) phase appear in the X-ray profiles by increasing of the content of (TiO₂ , CuO) in the sprayed films. Mixing concentration (TiO₂ , CuO) influences on the size of the crystallites of the SnO₂ films ,the size of crystallites of the spray paralyzed oxide films change in regular manner by increasing of (TiO

We have theoretically investigated the in-plane lattice thermal conductivity of Zn4Sb3single quantum well structure taking into account spatial confinement of phonons. The calculations were carried out for free-surface quantum wells with thickness 8.5nm in the room temperature. We show that the lattice thermal conductivity is a significant reduce. The reduction is mostly due to the drop in the average group velocity caused by the spatial confinement of acoustic phonons and the corresponding increase in phonon relaxation rates. The predicted decrease is important for the anticipated applications of Zn4Sb3 nanostructure materials for room-temperature thermoelectric devices. Our theoretical results are in a good agreement with available exp

This paper deals with the preparation of new monomers and polymers which including heterocyclic unit. The diacid chlorides compounds [1-3] were prepared from the reaction of glutaric acid, adipic acid, terephthalic acid with thionyl chloride. Succinic acid reacted with ethanol to produce compound [4]. Compound [4] reacted with hydrazine hydrate to obtain succinic hydrazide [5].Compound [5] reaction with CS2 and KOH in absolute ethanol to produce compound [6].The polymers [7-12] have been created by reacting diacid chlorides compounds [1-3] with compound[5] or [6] in dry pyridine with some drops of DMF. The topology of produced compounds has characterized through their spectral and analytical data as in FT-IR spectra, Thermal analysis [DSC,

The study presents the test results of stabilizing gypseous soil embankment obtained from
Al- Faluja university Campus at Al-Ramady province. The laboratory investigation was divided
into three phases, The physical and chemical properties, the optimum liquid asphalt (emulsion)
requirements (which are manufactured in Iraq) were determined by using one dimensional
unconfined compression strength test.in the first phase , The optimum fluid content was 11%
(6% of emulsion with 5% water content).. At phase two, the effect of Aeration technique was
investigated using both direct shear and permeability test. At phase three for the case of static
load , the pure soil embankment model under dry test condition was investigated