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.  

The -multiple mixing ratios of γ-transitions from levels of  populated in the  are calculated in the present work by using the a2-ratio methods.  We used the experimental coefficient (a2) for two γ -transitions from the same initial state, the statistical tensor, which is related to the a2-coefficient would be the same for the two transitions.  This method was used in a previous work for pure transitions or which can be considered pure. In these cases the multiple mixing ratios for the second transition ( ) equal zero, but in our work we applied this method for mixed γ-transitions and then the multiple mixing ratio ( ) is known for one transition. Then we calculate the ( ) value and versareversa.  The we

In the current research, we investigated the absorption spectrum for R590 and C480 dyes in ethanol solvent for different dye solution concentrations of 10-4, 10-5 and 10-6M. These dyes have been prepared and studied before and after gamma irradiation (first, second ionization) using cesium-137 source with absorbed doses of 18.36 Gy (time exposure of 10 days) and 73.44 Gy (with time exposure of 40 days). We noticed that the absorption intensity was decreased with decreasing concentration, before gamma irradiation while the absorption spectrum peak shifted towards the short wavelength (blue shift). It was also found that the intensity of absorption spectrum increased and shifted the absorption spectrum peak towards the long wavelength (red

Gamma - irradiation effect on polymethylmethacrylate (PMMA) samples has been studied using Positron Annihilation Lifetime (PAL) method. The orthopositronium (o-Ps) lifetime τ₃, hence the o-ps parameters, the volume hole size (V_h) and the free volume fraction (Ꞙ_h) in the irradiated samples were measured as a function of gamma-irradiation dose up to 28.05 kGy. It has been shown that τ ₃, V_h, and Ꞙ_h, are increasing in general with increasing gamma-dose, to reach a maximum percentage increment of 22.42% in τ₃, 60% in V_h and 29.5% in Ꞙ_h, at. 2.55 kGy, whereas τ₂ reaches maximum increment of 119. 7% at 7.65 kGy. The results s

This work aims to study the exploding copper wire plasma parameters by optical emission spectroscopy. The emission spectra of the copper plasma have been recorded and analyzed The plasma electron temperature (Te), was calculated by Boltzmann plot, and the electron density (ne) calculated by using Stark broadening method for different copper wire diameter (0.18, 0.24 and 0.3 mm) and current
of 75A in distilled water. The hydrogen (Hα line) 656.279 nm was used to calculate the electron density for different wire diameters by Stark broadening. It was found that the electron density ne decrease from 22.4×1016 cm-3 to 17×1016 cm-3 with increasing wire diameter from 0.18 mm to 0.3 mm while the electron temperatures increase from 0.741 to

In this work, an optical fiber biomedical sensor for detecting the ratio of the hemoglobin in the blood is presented. A surface plasmon resonance (SPR)-based coreless optical fiber was developed and implemented using single- and multi-mode optical fibers. The sensor is also utilized to evaluate refractive indices and concentrations of hemoglobin in blood samples, with 40 nm thickness of (20 nm Au and 20 nm Ag) to increase the sensitivity. It is found in practice that when the sensitive refractive index increases, the resonant wavelength increases due to the decrease in energy.

Films of pure polystyrene (ps) and doped by bromothymol blue material with percentages(4%) prepared by using casting technique in room temperature , the absorption and transmission spectra has been recorded in the wavelength rang (200-900)nm and calculated refractive index , reflectivity, real and imaginary parts of dielectric constant and extinction coefficient . this study has been done by recording the absorption and transmission spectra by using spectrophotometer .

The 8 - mixing ratios of 7 - transitions from levels of 26 Mg populated in 23 Na (a, py)26Mg reaction are calculated using a2 — ratio method for the first time in the case of two mixed y - transitions from the same initial level. The results obtained have been compared with 8 - values determined by other methods. The comparison shows that the agreement is excellent. This confirms the validity of this method in calculating the 6 - values of such 7 - transitions.

This study investigates the influence of silver oxide (Ag2O) concentration on the optical characteristics of phosphate bioactive glasses (PBGs). PBGs have emerged as promising alternatives to conventional silicate glasses in the medical field due to their excellent bioactivity and chemical resistance. Samples with varying Ag2O concentrations (0, 0.25, 0.5, and 0.75g) were sintered at 780°C for 2 hrs in an electric furnace. The samples were subjected to Fourier transfer infrared spectroscopy (FTIR), ultraviolet-visible (UV-Vis) spectroscopy, and photoluminescence (PL) tests to assess their functional groups and optical properties. By analyzing the FTIR spectrum of phosphate bioactive glass containing different amounts of Ag2O, it is