This work aims to investigate the dependence of gravitational lensing properties on the lens redshift and source redshift.

The angular diameter distance hereafter referred to as ADD has been determined using two different numerical integral methods, Simpson's rule, and definite integral methods. Both of those two methods gave identical results. In addition, observational data of gravitational Lensing systems have been used to find the most probable value of lens redshift and source redshift. The result showed that the lens redshift and source redshift are more likely to occur in the ranges of z_L=0.2-0.6 and z_S=1-3, respectively.

Einstein radius and the critical surface mass density

The assessment of data quality from different sources can be considered as a key challenge in supporting effective geospatial data integration and promoting collaboration in mapping projects. This paper presents a methodology for assessing positional and shape quality for authoritative large-scale data, such as Ordnance Survey (OS) UK data and General Directorate for Survey (GDS) Iraq data, and Volunteered Geographic Information (VGI), such as OpenStreetMap (OSM) data, with the intention of assessing possible integration. It is based on the measurement of discrepancies among the datasets, addressing positional accuracy and shape fidelity, using standard procedures and also directional statistics. Line feature comparison has been und

To learn how the manner of preparation influences film development, this study examined film expansion under a variety of deposition settings. To learn about the membrane’s properties and to ascertain the optimal pretreatment conditions, which are represented by ambient temperature and pressure, Laser pressure of 2.5[Formula: see text]m bar, the laser energy density of 500[Formula: see text]mJ, distortion ratio ([Formula: see text]) as a function of laser pulse count, all achieved with the double-frequency Nd: YAG laser operating in quality-factor mode at 1064[Formula: see text]nm. Mg_xZn[Formula: see text] films of thickness [Formula: see text][Formula: see text]nm were deposited on glass substrates at pulse

The effect of annealing temperature (Ta) on the electrical properties like ,D.C electrical conductivity (σ DC), activation energy (Ea),A.C conductivity σa.c ,real and imaginary (ε1,ε2) of dielectric constants ,relaxation time (τ) has been measured of ZnS thin films (350 nm) in thickness which were prepared at room temperature (R.T) using thermal evaporation under vacuum . The results showed that σD.C increases while the activation energy values(Ea) decreases with increasing of annealing temperature.(Ta) from 303- 423 K .
The density of charge carriers (nH) and Hall mobility (μH) increases also with increasing of annealing temperature Hall effect measurements showed that ZnS films were n-type converted to p-type at high annealin

Through this study, the following has been proven, if  is an algebraically paranormal operator acting on separable Hilbert space, then  satisfies the ( ) property and  is also satisfies the ( ) property for all . These results are also achieved for  ( ) property.    In addition, we prove that for a polaroid operator with finite ascent then after the property ( ) holds for  for all.

     The purpose of this  paper is to show that for a holomorphic and univalent function in class S, an omitted –value transformation  yields a class of starlike functions as a rotation transformation of  the Koebe function, allowing both the image and rotation of the function

   to be connected. Furthermore, these functions have several properties that are not far from a convexity properties. We also show that Pre- Schwarzian derivative is not invariant since the convexity property of the function   is so weak.

 Eight soil samples were selected around Najaf governorate at depth levels 40-50 cm. X-Ray Fluorescence (XRF) was used to determine the concentrations of major and trace elements. Liner and mass attenuation coefficient (µ, µ_ρ) have been determined at gamma energies (662, 1172,1332) keV using NaI (Tl) detector. The range of linear attenuation coefficients for calculated samples were (0.553-1.163) cm^-1, (0.122-0.178) cm^-1 and (0.049-0.105) cm^-1 at (662, 1172,1332) keV respectively. The range of mass attenuation coefficients obtained (0.39-0.76) cm²/gm, (0.087-0.117) cm²/gm and (0.0336-0.074) cm²/gm at (662, 1172,1332) keV respectively. The result

Through this study, the following has been proven, if  is an algebraically paranormal operator acting on separable Hilbert space, then  satisfies the ( ) property and  is also satisfies the ( ) property for all . These results are also achieved for  ( ) property.

   In addition, we prove that for a polaroid operator with finite ascent then after the property ( ) holds for  for all .

GaN thin films were deposited by thermal evaporation onto
glass substrates at substrate temperature of 403 K and a thickness of
385 nm . GaN films have amorphous structure as shown in X-ray
diffraction pattern . From absorbance data within the range ( 200-
900 ) nm direct optical energy gap was calculated . Also the others
optical parameters like transmittance T, reflectance R , refractive
index n , extinction coefficient k , real dielectric constant 1 Î , and
imaginary dielectric constant 2 Î were determined . GaN films
have good absorbance and minimum transmittance in the region of
the visible light .