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 .

The Innovation Of Knowledge Is An Important And A Key Element In The Progress And Business Excellence Organizations, Therefore Requires Several Elements To Help Create And Implement And Move The Innovation Process Of Knowledge, Including The Strategic Empowerment Associated With The Element Of The Process Of Strategic Momentum Engine Driven Wheel Continuous Dynamic Innovation, And Focused Research Problem By Measuring The Availability Of Strategic Empowerment When Individuals From By Senior Departments And Ways To Help Organizations To Provide Empowerment Commensurate With The Requirements Of Achieving The Goals Of Time And Place Appropriate For The Individual, And The Importance Of Research Stems From The Importance Of The Varia

Viscosities (η) and densities (ρ) of atenolol and propranolol hydrochloride in water and in concentrations (0.05 M) and (0.1 M) aqueous solution of threonine have been used to reform different important thermodynamic parameters like apparent molal volumes fv partial molal volumes at infinite dilution fvo , transfer volume fvo (tr), the slop Sv , Gibbs free energy of activation for viscous flow of solution ΔG*1,2 and the B-coefficient have been calculated using Jones-Dole equation. These thermodynamic parameters have been predicted in terms of solute-solute and solute-solvent interaction.

Apparent molar volume, V?, and viscosity B-coefficient of nicotinc acid in water and in aqueous NaCl solutions have been determined from density and viscosity measurements at (293.15, 298.15, 303.15 and 308.15) K. The experimental density data were evaluated by Masson equation, and the derived, apparent molar volume at infinite dilution, Vo?, and the slope Sv, were interpreted in term of solute-solvent and solute- solute interactions. Transfer apparent molar volumes at infinite dilution of nicotinic acid from water to NaCl solutions at various temperatures have been calculated.The viscosity data have been analyzed using Jones-Dole equation, and the derived parameters, Jones-Dolecoefficient, B,and Falkenhagen coefficient,A, have been also in

            This paper is interested in certain  subclasses of univalent and bi-univalent functions concerning  to shell- like curves connected with k-Fibonacci numbers involving modified Sigmoid activation function θ(t)=2/(1+e^(-t) ) ,t ≥0 in unit disk |z|<1 . For estimating of the initial coefficients |c_2 | , |c_3 |, Fekete-Szego ̈ inequality and the  second Hankel determinant have been investigated for the functions in our classes. 

The IGRF model is the empirical representation of the Earth magnetic field recommended for scientific use by the International Association of Geomagnetism and Aeronomy(IAGA).

Since  the  Geomagnetic   field   has   the  abi lity  to   change  the orientation of satellite, the strength of Geomagnetic field and its horizontal component have been studied.

This paper discusses the phenomenon of the Geomagnetic field intensity and its horizontal component at diferent altitudes and at certain latitudes, the geomagnetic field data is obtained by using IGRF2000 model at Baghdad (44.7 degree East longitude) .