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 fluorescence and absorption spectra of Fluoranthene dissolved in
cyclohexane and ethanol were studied and analyzed. The effect of the
concentration of this molecule and the polarity of the solvents on the spectral
shifts and on relative intensity has been investigated. A computational program
was written in order to convert the spectra from grapher to data. Some
photophysical parameters such as oscillator strength and quantum efficiency have
been calculated. Fluorescence quantum efficiency of Fluoranthene was measured
relative to Quinine Sulfate (QS) in 1N H2SO4. The obtained values were (0.5) in
cyclohexane and (0.45) in ethanol

The semiempirical (PM3) and DFT quantum mechanical methods were used to investigate the theoretical degradation of Indigo dye. The chemical reactivity of the Indigo dye was evaluated by comparing the potential energy stability of the mean bonds. Seven transition states were suggested and studied to estimate the actually starting step of the degradation reaction. The bond length and bond angle calculations indicate that the best active site in the Indigo dye molecule is at C10=C11.  The most possible transition states are examined for all suggested paths of Indigo dye degradation predicated on zero-point energy and imaginary frequency. The first starting step of the reaction mechanism is proposed. The change in enthalpy, Gibbs free energ

Polyaniline (PANI) has been prepared by the oxidation method in order to fabricate it with various concentrations of copper nanoparticles (CuNPs) which produced using the reduction method. Various techniques have characterized pure PANI and PANI doped CuNPs composites, such as fourier transform infrared spectroscopy (FT-IR), X-ray diffraction spectroscopy (XRD), field emission scanning electron microscopy (FE-SEM) and energy dispersive X-ray spectroscopy (EDS), which were provided important information about the structure and morphology of the fabricated polymer nanocomposites. The properties of dielectric permittivity (έ), dielectric loss (ἔ) and electrical conductivity (σ_AC) properties were studied at room temperature versus a range

In this present paper, an experimental study of some plasma characteristics in dielectric barrier discharge (DBD) system using several variables, such as different frequencies and using two different electrodes metals(aluminium (Al) and copper (Cu)), is represented. The discharge plasma was produced by an AC power supply source of 6 and 7 kHz frequencies for the nitrogen gas spectrum and for two different electrodes metals(Al and Cu). Optical emission spectrometer was used to study plasma properties (such as electron temperature ( ), electron number density ( ), Debye length ( ), and plasma frequency ( )). In addition, images were analysed for the plasma emission intensity at atmospheric air pressure.

PMMA films of different thickness (0.006, 0.0105, 0.0206, 0.0385 and 0.056cm) were synthesized by casting process. The temperature and frequency dependence of dielectric constant and AC electrical conductivity measurements at various frequencies (10kHz-10MHz) and temperatures (293-373K) were carried out. Few anomalies in dielectric studies were observed near 313 and 373 K respectively. These points were related to glass transitions temperature. The variation of activation energy and conduction behavior was studied .From the AC conduction studies, it is confirmed that the mechanism responsible for the conduction process is hopping of carriers. The variations of the dielectric constant and loss as function of frequency at different tempera

Lead selenide PbSe thin films of different thicknesses (300, 500, and 700 nm) were deposited under vacuum using thermal evaporation method on glass substrates. X-ray diffraction measurements showed that increasing of thickness lead to well crystallize the prepared samples, such that the crystallite size increases while the dislocation density decreases with thickness increasing. A.C conductivity, dielectric constants, and loss tangent are studied as function to thickness, frequency (10kHz-10MHz) and temperatures (293K-493K). The conductivity measurements confirm confirmed that hopping is the mechanism responsible for the conduction process. Increasing of thickness decreases the thermal activation energy estimated from Arhinus equation is

In this work a model of a source generating truly random quadrature phase shift keying (QPSK) signal constellation required for quantum key distribution (QKD) system based on BB84 protocol using phase coding is implemented by using the software package OPTISYSTEM9. The randomness of the sequence generated is achieved by building an optical setup based on a weak laser source, beam splitters and single-photon avalanche photodiodes operating in Geiger mode. The random string obtained from the optical setup is used to generate the quadrature phase shift keying signal constellation required for phase coding in quantum key distribution system based on BB84 protocol with a bit rate of 2GHz/s.

The production function forms one of the techniques used in evaluation the  production the process for any establishment or company, and to explain the importance of contribution of element from the independent variable and it's affect on the dependent variable. Then knowing the elements which are significant or non-significant on the dependent variable.

    So the importance of this study come from estimating the Cobb-Douglas production function for Al- Mansoor General Company for Engineering industries in Iraq during the period (1989-2001)

     To explain the importance which effects the independent variable such as
(N

Classification of imbalanced data is an important issue. Many algorithms have been developed for classification, such as Back Propagation (BP) neural networks, decision tree, Bayesian networks etc., and have been used repeatedly in many fields. These algorithms speak of the problem of imbalanced data, where there are situations that belong to more classes than others. Imbalanced data result in poor performance and bias to a class without other classes. In this paper, we proposed three techniques based on the Over-Sampling (O.S.) technique for processing imbalanced dataset and redistributing it and converting it into balanced dataset. These techniques are (Improved Synthetic Minority Over-Sampling Technique (Improved SMOTE),  Border