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 .

This experiment was conducted to study the effect of injecting hatching eggs into a flock of broiler aged mothers with different concentrations of the alcoholic extract of Moringa oleifera powder on productive performance of broilers during the period of rearing of 35 days. The study included two experiments for a period at 2/10/2021 to 28/11/2021, where eggs were injected into the Mustafa Poultry Hatchery/ Wasit Governorate- Aziziyah District. A 400 hatching eggs of 308 Ross  mothers of modern broilers used at age  of 48  week, eggs of average weight  66 ± 1 g/egg were collected in same day then stored for two days. A quarter of treatments were randomly distributed with 100 eggs for each treatment.

Background: Suppression of quorum sensing (QS) that regulates many virulence factors, including antimicrobial resistance, in bacteria may subject the pathogenic microbes to the harmful consequences of the antibiotics, increasing their susceptibility to such drugs. Aim: The current study aimed to make an aqueous crude extract from the soil Proteus mirabilis isolate with the use of the gas chromatography-mass spectrometry (GC-MS) technique for its analysis, and then, study the impact of the extract on clinical isolates of Pseudomonas aeruginosa. Methods: Preparation of crude extracts from P. mirabilis (both organic and aqueous), which were then analyzed by GC-MS to detect the bioactive ingredients. Furthermore, the extract’s capability to i

The current study was designed to evaluate the anti-inflammatory effect of GKB in the rat model of granulomatous inflammation. Thirty rats were distributed into five groups:  The first group served as negative control group that received distilled water (DW) only without inducting inflammation, positive control group; treated with DW with the induction of inflammation and they were assigned to cotton pellet-induced granuloma, ginkgo biloba (GKB) treated group (200mg/kg/day), dexamethasone-treated group (1mg/kg), and Prednisolone treated group (5mg/kg). All the treatments were given orally for seven consecutive days.  On day eight, the rats were anesthetized and the pellets together with granulation tissue were carefully removed

The tetradentate N2O2 Schiff base ligand, which is produced via the condensation reaction of 2-hydroxynaphthaldehyde with phthalohydrazide, is prepared in this work with a fair yield. The prepared ligand was characterized using a microanalysis technique (C.H.N), UV-vis, FTIR, 1H-,13C-NMR, mass spectrometry, and thermal gravimetric analysis (TGA). New complexes were synthesized by a reaction between ligand (N'1E,N'2Z)-N'1,N'2-bis((1-hydroxynaphthalen-2yl)methylene)phthalohydrazide and metal chloride of Co+2, Ni+2, and Zn+2 ions in absolute ethanol. The present complexes are also characterized by techniques such as C.H.N, UV-vis, FTIR, TGA, molar conductivity, atomic absorption, and magnetic moment measurements. The in vitro antimicro

Studied the effect of foliar fertilizers Alaongrin results showed that spraying fertilizer Alaongrin and Fertilizers and Ministry of Agriculture and rack licorice extract every three weeks after thirty days from planting seedlings

Plantation of humic acid nanoparticles on the inert sand through simple impregnation to obtain the permeable reactive barrier (PRB) for treating of groundwater contaminated with copper and cadmium ions. The humic acid was extracted from sewage sludge which is byproduct of the wastewater treatment plant; so, this considers an application of sustainable development. Batch tests signified that the coated sand by humic acid (CSHA) had removal efficiencies exceeded 98 % at contact time, sorbent dosage, and initial pH of 1 h, 0.25 g/50 mL and 7, respectively for 10 mg/L initial concentration and 200 rpm agitation speed. Results proved that physicosorption was the predominant mechanism for metals-CSHA interaction because the sorption data followed

This study discussed a biased estimator of the Negative Binomial Regression model known as (Liu Estimator), This estimate was used to reduce variance and overcome the problem Multicollinearity between explanatory variables, Some estimates were used such as Ridge Regression and Maximum Likelihood Estimators, This research aims at the theoretical comparisons between the new estimator (Liu Estimator) and the estimators

The process of evaluating data (age and the gender structure) is one of the important factors that help any country to draw plans and programs for the future. Discussed the errors in population data for the census of Iraqi population of 1997. targeted correct and revised to serve the purposes of planning. which will be smoothing the population databy using nonparametric regression estimator (Nadaraya-Watson estimator) This estimator depends on bandwidth (h) which can be calculate it by two ways of using Bayesian method, the first when observations distribution is Lognormal Kernel and the second is when observations distribution is Normal Kernel

The efficiency evaluation of the railway lines performance is done through a set of indicators and criteria, the most important are transport density, the productivity of enrollee, passenger vehicle production, the productivity of freight wagon, and the productivity of locomotives. This study includes an attempt to calculate the most important of these indicators which transport density index from productivity during the four indicators, using artificial neural network technology. Two neural networks software are used in this study, (Simulnet) and (Neuframe), the results of second program has been adopted. Training results and test to the neural network data used in the study, which are obtained from the international in