This work is devoted to define new generalized gamma and beta functions involving the recently suggested seven-parameter Mittag-Leffler function, followed by a review of all related special cases. In addition, necessary investigations are affirmed for the new generalized beta function, including, Mellin transform, differential formulas, integral representations, and essential summation relations. Furthermore, crucial statistical application has been realized for the new generalized beta function.  

Lead selenide PbSe thin films of different thicknesses (300, 500, and 700 nm) were deposited under vacuum using thermal evaporation method on glass substrates. X-ray diffraction measurements showed that increasing of thickness lead to well crystallize the prepared samples, such that the crystallite size increases while the dislocation density decreases with thickness increasing. A.C conductivity, dielectric constants, and loss tangent are studied as function to thickness, frequency (10kHz-10MHz) and temperatures (293K-493K). The conductivity measurements confirm confirmed that hopping is the mechanism responsible for the conduction process. Increasing of thickness decreases the thermal activation energy estimated from Arhinus equation is

In the present work the Buildup factor for gamma rays were studied in shields from epoxy reinforced by lead powder and by aluminum powder, for NaI(Tl) scintillation detector size ( ×? ), using two radioactive sources (Co-60 and Cs-137). The shields which are used (epoxy reinforced by lead powder with concentration (10-60)% and epoxy reinforced by aluminum powder with concentration (10-50)% by thick (6mm) and epoxy reinforced by lead powder with concentration (50%) with thick (2,4,6,8,10)mm. The experimental results show that: The linear absorption factor and Buildup factor increase with increase the concentration for the powders which used in reinforcement and high for aluminum powder than the lead powder and decrease with inc

The study effect irradiation on optical properties of film (PVA: CuCL2) prepared by casting method, with thickness of (30±1) μm. And used Cs137 to obtained Gamma ray with energy (662)keV and time irradiation(5,6 and 7) weeks and affectivity (4.3) ci. The spectra absorbance and transmittance register in range (300-1100) nm .
Results show that the optical band gap for (PVA: CuCl2) decreasing after irradiation with gamma ray from (3.2,3.1,3 and 2.7)eV, urbach energy values increase with the increasing time radiation. And the absorption constants (α,k,n,) and the optical conductivity are changing after irradiated with gamma ray .

The effect of 0.662MeV gamma radiation on the optical properties of the CdTe thin films was studied. 300nm thickness of CdTe samples were irradiated with doses (10, 20, 30,60krad) in room temperature. The absorption spectra for all the samples were recorded using UV- Visible spectrometer in order to calculate the energy gap, width of localized states and optical constants(refractive index, extinction coefficient, real and imaginary parts of dielectric constant). The optical energy gap was found to decrease from (1.53 to 1.48 eV), while the width of localized states increased from (1.34 to 1.49 eV) with the increasing of radiation dose. The behavior of energy gap with the irradiation dose makes the material a good candidate for dosimetry

The shale volume is one of the most important properties that can be computed depending on gamma ray log. The shale volume of Mishrif Formation (carbonate formation from middle Cenomanian- early Turonian) was studied for the regional area of the middle and southern parts of Iraq. The gamma ray log data from seventeen  wells ( Kf-3,Kf-4, Ad-1,Ad -2,Dh-1, Bu-47, Ns-2, Ns-4, Am-1,Am-2,Hf-2,Hf-115,Mj-3,Mj-15, Su-7,Wq-15 and  Lu-7) distributed in the study area were used to compute the shale volume of Mishrif Formation. From the available data of the considered wells, a regional isopach map of Mishrif Formation was obtained. The isopach map indicates that the maximum thickness of Mishrif Formation is located at the eastern part of t

     In this paper, the structure of  and  have  been introduced and studied. We also obtain that a is  of a  if and only if there exists an  on such that . In addition, we obtain  that  of if and only if there is an   on  such that  , where  are subspaces of  with eigenvalues 1 and  −1, respectively. We also find  t that the existence of  on  implies that there exists a compatible  under appropriate condition.