In this paper we generalize Jacobsons results by proving that any integer  in   is a square-free integer), belong to . All units of  are generated by the fundamental unit  having the forms

Our generalization build on using the conditions

This leads us to classify the real quadratic fields  into the sets  Jacobsons results shows that  and Sliwa confirm that  and  are the only real quadratic fields in .

Background: The hybrid compounds hold promise for developing novel pharmaceuticals, potentially exhibiting greater activity, mainly against viruses and cancer diseases, than their components.

Objective: In this study, researchers explored the potential synergistic effects of hybrid molecules by designing and synthesizing a series of isatin-gallate hybrids, denoted as N’-(5-substituted-2-oxoindolin-3-ylidene)-3,4,5-trihydroxybenzohydrazide (3a–d).

Methods: Isatin-gallate hybrids (3a–d) were synthesized by reacting gallic hydrazide with each of the isatin analogs (2a–d). The structures of all produced comp

This study investigates the impacts of climate change (CC) on the emergence and proliferation of fungal pathogens, with a particular focus on global food security and the potential of medicinal plants and their by-products as sustainable mitigation strategies. Through a systematic literature review of articles published up to 2024, we analyze how CC exacerbates the spread and severity of fungal diseases in crops, leading to significant agricultural losses and threats to food availability. The findings highlight that, alongside conventional approaches such as genetic resistance and precision farming, bioactive compounds derived from medicinal plants and their by-products offer promising, eco-friendly alternatives for the management of fungal

In this work , an effective procedure of Box-Behnken based-ANN (Artificial Neural Network) and GA (Genetic Algorithm) has been utilized for finding the optimum conditions of wt.% of doping elements (Ce,Y, and Ge) doped-aluminizing-chromizing of Incoloy 800H . ANN and Box-Behnken design method have been implanted for minimizing hot corrosion rate k_p (10^-12g².cm^-4.s^-1) in Incoloy 800H at 900^oC . ANN was used for estimating the predicted values of hot corrosion rate k_p (10^-12g².cm^-4.s^-1) . The optimal wt.% of doping elements combination to obtain minimum hot corrosion rate was calculated using genetic alg

A sensitivity-turbidimetric method at (0-180^o) was used for detⁿ. of mebeverine in drugs by two solar cell and six source  with C.F.I.A.. The method was based on the formation  of  ion pair for the pinkish banana color  precipitate by the reaction of Mebeverine hydrochloride with Phosphotungstic acid. Turbidity was measured via the reflection of incident light that collides on the surface particles of   precipitated at 0-180^o. All variables were optimized. The linearity ranged of Mebeverine hydrochloride was 0.05-12.5mmol.L^-1, the L.D. (S/N= 3)(3S_B) was 521.92 ng/sample depending on dilution for the minimum concentration , with correlation coefficient r = 0.9966while was R.S.D%

The differential cross section for the Rhodium and Tantalum has been calculated by using the Cross Section Calculations (CSC) in range of energy(1keV-1MeV) . This calculations based on the programming of the Klein-Nashina and Rayleigh Equations. Atomic form factors as well as the coherent functions in Fortran90 language Machine proved very fast an accurate results and the possibility of application of such model to obtain the total coefficient for any elements or compounds.

The research aims to: Preparing rehabilitative exercises with accompanying tools to rehabilitate those with shoulder dislocation. Knowing the effect of rehabilitative exercises and accompanying aids in improving the muscular strength and motor range of those with dislocations in the shoulder joint. The two researchers used the experimental design with the same experimental group with the pre and post tests, so the researcher chose a sample appropriate to the nature of his research problem, its goals and its hypotheses, as a sample of the injured was chosen to remove the shoulder joint, who completed the treatment, who were not practicing sports, and those who went to the Physiotherapy Center at Al-Was

This study focuses on the biodegradation of oxymatrine insecticide by some soil fungi isolated from four agriculture stations. The results showed that the highest degradation rate 94.66% was recorded by Ulocladium sp. at 10 days and A. niger recorded the lowest degradation rate 45.86%, while at 20 days Ulocladium sp. also showed the highest degradation rate 94.98% and the lowest degradation rate reached to 82.49% with A.niger. The mix (Exerohilum sp.+Ulocladium sp.) recorded the highest degradation rate of oxymatrine insecticide 90.22%, 88.51%, 85.34%  at 4, 8 and 12 ppm.The use of mixed isolates enhanced the biodegradation process. There is no study of oxymatrine biodegradation

Mammals are under threat worldwide due to deforestation, hunting, and other human activities. In Iraq, a total of 93 species of wild mammals have been recorded including species with global conservation concern. Bamo Mountain is situated within the Zagros Mountains in northern Iraq which is a suitable habitat for wild mammals. Due to scarcity of the field survey efforts and cryptic behavior, monitoring of the wild mammals fauna in Zagros Mountain seems challenging. Therefore, we used a camera trap which seems to be an ideal way to determine species diversity of wild mammals in Bamo Mountain. Moreover, interviews with local villagers were performed. The mammalian diversity of Bamo Mountain is not fully explored but seemed threatened by lo