This paper including a gravitational lens time delays study for a general family of lensing potentials, the popular singular isothermal elliptical potential (SIEP), and singular isothermal elliptical density distribution (SIED) but allows general angular structure. At first section there is an introduction for the selected observations from the gravitationally lensed systems. Then section two shows that the time delays for singular isothermal elliptical potential (SIEP) and singular isothermal elliptical density distributions (SIED) have a remarkably simple and elegant form, and that the result for Hubble constant estimations actually holds for a general family of potentials by combining the analytic results with data for the time dela

Age and BMI may be used to diagnosis of thyroid autoimmune disease. One hundred Iraqi women with age ranged from 18 to 60 years participate in this research, 50 of them were hypothyroidism patients, 30 were hyperthyroidism patients and the other 20 were euthyroidism served as controls. Blood samples were collected from the studied subjects to determine thyroid profile [free triiodothyronine (FT3), free tetraiodothyronine (FT4) and thyroid stimulating hormone (TSH)], thyroid antibodies [anti-thyroid peroxidase (anti-TPO), anti-thyroglobulin (anti-Tg), and anti-thyroid stimulating hormone receptor (anti-TSHR)], and levels of vitamin D (vit D), calcium (Ca), and phosphorus (P) using different analysis techniques. When the effect of age

The present study was performed to evaluate the level of some risk factors (biochemical and immunological) in hypothyroid Iraqi patients considering the different thyroid functional states (hypothyroidism and subclinical hypothyroidism).The study includes 82 patients clinically diagnosed with hypothyroidism. Three study groups have been investigated: (47 clinical hypothyroid patients, 12 subclinical hypothyroid patients 23 healthy individuals) of different ages. This study, show that the proportion of females (83.3 %), (87.2%) in subclinical and clinical hypothyroidisim respectively higher than the proportion of males (16.7%),(12.8%) in subclinical and clinical hypothyrodism respectively of the total patients.The majority of subclinical hyp

In this study forty mature albino rats were used wich were randomly divided into five groups ,four groups were adminstrated Phoenix dactylifera pollen grains suspension at concertenrations (18,54,108,and 216)mg/ kg body weight by oral administration while the fifth group was considered as a control group.Experiment continued for 40 days then rats were sacrificed and samples of blood were collected for determination of some biochemical parameters (total protein ,total cholesterol ,LDLc and HDLc).Testis were removed for preparation histological sections to measures the diameters of seminferous tubules ,thickness of seminiferous epithelium and the numbers of spermatogenic cells.

The aim of this research is to prepare a set of complexes with the general formula [M(HMB)n] , where M=VO (II) , Cr(III) and Cu(II) while  n=2,3,2 respectively resulting from the reaction of anew ligand [N'-(2-hydroxy-3-methoxybenzyl)-4-methylbenzohydrazide] (HMB) derived from the reaction of the tow substances (4-methylbenzohydrazide  and 2-hydroxy-3-methoxy benzaldehyde) with metal ions. The prepared compounds were identified by several spectroscopic methods such as Infrared, Nuclear Magnetic Resonance and Electronic Spectra. From the results of the measurements, it was suggested that the prepared complexes have different geometries such as square planar (Cu), square pyramidal (VO) and octahedral (Cr). DFT simulations backed up

The recent emergence of sophisticated Large Language Models (LLMs) such as GPT-4, Bard, and Bing has revolutionized the domain of scientific inquiry, particularly in the realm of large pre-trained vision-language models. This pivotal transformation is driving new frontiers in various fields, including image processing and digital media verification. In the heart of this evolution, our research focuses on the rapidly growing area of image authenticity verification, a field gaining immense relevance in the digital era. The study is specifically geared towards addressing the emerging challenge of distinguishing between authentic images and deep fakes – a task that has become critically important in a world increasingly reliant on digital med

One of the most important problems in the statistical inference is estimating parameters and Reliability parameter and also interval estimation , and testing hypothesis . estimating two parameters of exponential distribution and also reliability parameter in a stress-strength model.

This parameter deals with estimating the scale parameter and the Location parameter µ , of two exponential distribution   ,using moments estimator and maximum likelihood estimator , also we estimate the parameter R=pr(x>y), where x,y are two- parameter independent exponential random variables .

Statistical properties of this distribution and its properti

Abstract

The Classical Normal Linear Regression Model Based on Several hypotheses, one of them is Heteroscedasticity as it is known that the wing of least squares method (OLS), under the existence of these two problems make the estimators, lose their desirable properties, in addition the statistical inference becomes unaccepted table. According that we put tow alternative,  the first one is  (Generalized Least Square) Which is denoted by (GLS), and the second alternative is to (Robust covariance matrix estimation) the estimated parameters method(OLS), and that the way (GLS) method neat and certified, if the capabilities (Efficient) and the statistical inference Thread on the basis of an acceptable