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 .

Bovine milk is one of the richest nutrients that contain minerals and vitamins that enhance immunity, especially in children, but because many children do not want to drink the raw milk, therefore this study aimed to enhance the sensory characteristics of raw milk by using hibiscus plant extract, which is characterized by red color and distinctive flavor as well as studying the effect of aqueous extract of Hibiscus sabdariffa on inhibiting the growth of microorganisms, by using three concentrations of the aqueous extract (0.5, 1.0 and 1.5%), where the statistical results showed a significant difference (P≤0.05) between the concentrations in color, texture and general acceptance, and the best results appeared when using

Globalization has occupied a great deal of studies, research and literature, in addition to being a phenomenon that has imposed itself firmly on the ground. Globalization is considered the main feature of the current moment in today's world. The world is now transforming in an unprecedented way under noticeable titles of successive waves of knowledge and technology.The current research aims to identify the effects of globalization on the variables and their political, social, media and cultural dimensions, as well as culture of consumption and cultural identity.The theoretical framework included two sections: the first is the concept of globalization, its history and its dimensions, and the second is the modernity in contemporary Europea

The present study investigates the relation between the biliteral and triliteral roots which is the introduction to comprehend the nature of the Semitic roots during its early stage of development being unconfirmed to a single pattern. The present research is not meant to decide on the question of the biliteral roots in the Semitic languages, rather it is meant to confirm the predominance of the triliteral roots on these languages which refers, partially, to analogy adopted by the majority of linguists. This tendency is frequently seen in the languages which incline to over generalize the triliteral phenomenon, i. e., to transfer the biliteral roots to the triliteral room, that is, to subject it to the predominant pattern regarding the r

Recently, women's rape has been a pervasive problem in the Iraqi society. Thus, it has become necessary to consider the role of language and its influence on the common beliefs and opinions about rape in the Iraqi society. Thus, taking into consideration the critical role of language and its impact on the perception of human reality and the social development based on people's beliefs and principles of life has become highly indispensable. Therefore. The aim of this article is to address this problem critically from legislation and social norms in NGOs' reports (2015; 2019) with reference to some provisions from the Iraqi Panel Code (1969; 2010). Therefore, the researchers examine the discursive strategies and ideological viewpoints in t

This study was conducted to detect the relationship between organic content in the sediment of Rivers Tigris and Diyala, at two locations south of Baghdad, with some environmental factors and the benthic invertebrates and values of diversity indices. Monthly samples collected from the area for the period November 2007 to October 2008. Results showed differences in the physical and chemical characteristics of the two sites, Where the annual average in Tigris and Diyala were respectively for: water temperature (19, 20) C°, pH (8, 8), dissolved oxygen (4, 8) mg / l , Biochemical oxygen Demand BOD5 (3,44 ) mg/l, TDS (632,1585) mg / l, TSS (42, 44) mg / l, turbidity (28,74) NTU, and total hardness as CaCO3 (485,823) mg / l ,Sulfat

Introduction and Aim: Pseudomonas aeruginosa is a nosocomial infection with an ability to develop high levels of antibiotic resistance. The efflux pump system is one of the mechanisms that is linked to multidrug resistance in P. aeruginosa. In this study, we employed siRNA loaded on gold nanoparticles against the MexA efflux pump gene to decrease the MexA gene expression in P. aeruginosa and estimated antibiotic resistance after gene silencing.   Materials and Methods: This study examined four strains of P. aeruginosa isolated from patients in various hospitals in Baghdad. Bacteria isolated were identified by biochemical tests and Vitek compact 2 system.  Single-stranded siRNA (33bp) designed in this study was loaded onto gold

The addition of new reactive sites on the surface area of the inert sand, which are represented by layered double hydroxide nanoparticles, is the primary goal of this work, which aims to transform the sand into a reactive material. Cetyltrimethylammonium bromide (CTAB) surfactant is used in the reaction of calcium extracted from solid waste-chicken eggshells with aluminum prepared from the cheapest coagulant-alum. By separating amoxicillin from wastewater, the performance of coated sand named as "sand coated with (Ca/Al-CTAB)-LDH" was evaluated. Measurements demonstrated that pH of 12 from 8, 9, 10, 11, and 12, CTAB dosage of 0.05 g from 0, 0.03, 0.05, and 0.1 g, ratio of Ca/Al of 2 from 1, 2, 3, and 4, and mass of sand of 1 g/50 mL from

In this work we study the influence of the laser pulse energy and ablation time on the aluminum nanoparticles productivity during nanosecond laser ablation of bulk aluminum immersed in liquid.
Aluminum nanoparticles were synthesized by pulsed laser ablation of Al targets in ethanol for 3-8 minutes using the 1064 nm wavelength of a Nd:YAG laser with energies of 300-500 mJ per pulse.The laser energy was varied between 300 and 500 mJ/pulse, whereas the ablation time was set to 5 minutes. UV-Visible absorption spectra was used for the characterization and comparison of products.

The aim of this work is oriented to increase film cooling effectiveness value through numerical investigations for flow of Mach number not more than 0.3 around vane surface, to find the effects of inclination and compounds angles of round holes in staggered rows on adiabatic film cooling effectiveness of vane suction side. Multi cylindrical film cooling hole cases were studied with pitch ratio P/d =2 and 3, local blowing ratios M=0.382, 0.77 and 1.14,  inclination angles a=30° and 45°, compound angles β= 0°, 15°, 30° and 45° and local momentum ratios I= 0.084, 0.34 and 0.756  for better cooling process.

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