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 .

Audio classification is the process to classify different audio types according to contents. It is implemented in a large variety of real world problems, all classification applications allowed the target subjects to be viewed as a specific type of audio and hence, there is a variety in the audio types and every type has to be treatedcarefully according to its significant properties.Feature extraction is an important process for audio classification. This workintroduces several sets of features according to the type, two types of audio (datasets) were studied. Two different features sets are proposed: (i) firstorder gradient feature vector, and (ii) Local roughness feature vector, the experimentsshowed that the results are competitive to

Watermarking operation can be defined as a process of embedding special wanted and reversible information in important secure files to protect the ownership or information of the wanted cover file based on the proposed singular value decomposition (SVD) watermark. The proposed method for digital watermark has very huge domain for constructing final number and this mean protecting watermark from conflict. The cover file is the important image need to be protected. A hidden watermark is a unique number extracted from the cover file by performing proposed related and successive operations, starting by dividing the original image into four various parts with unequal size. Each part of these four treated as a separate matrix and applying SVD

4-((2-hydroxy-3,5-dinitrophenyl)diazenyl)-1,5-dimethyl-2-phenyl-1H-pyrazol-3(2H)-one was produced through the reaction of diazonium salt from 4-amino antipyrine with 2,4-dinitrophenol. This ligand is examined by (UV-Vis, FTIR,1H,13CNMR, and LC-Mass) spectral techniques and micro elemental analysis (C.H.N.O). Co(II), Ni(II), Cu(II), and Zn(II) complexes were also performed and depicted. Metal chelates were distinguished by utilizing flame atomic absorption, infrared analysis, and elemental, visible, as well as ultraviolet spectroscopy, in addition to conductivity and magnetic quantification. Methods of mole ratio and continuous contrast have been studied to determine the nature of the compounds. Beer's law was followed throughout a co

This paper presents the synthesis and study of some new mixed-ligand complexes containing anthranilic acid and amino acid phenylalanine (phe) with some metals . The resulting products were found to be solid crystalline complexes which have been characterized by using (FT-IR,UV-Vis) spectra , melting point, elemental analysis (C.H.N) , molar conductivity . The proposed structure of the complexes using program , chem office 3D(2000) . The general formula have been given for the prepared complexes : [M(A-H)(phe-H)] M(II): Hg(II) , Mn(II) ,Co(II) , Ni(II) , Cu(II) , Zn(II) , Cd(II) . A = Anthranilic acid = C7H7NO2 Phe = phenylalanine = C9H11NO2

1-(4-amino-3-(benzo[d]thiazol-2-yldiazenyl)phenyl)ethanone has been synthezied by reaction the diazonium salt of 2-aminobenzothiazole with 4-aminoacetophenone. Specroscopic studies ( FTIR,UV-Vis, 1H and 13CNMR) and microelemental analysis (C.H.N.S.O) are use to identified of the azo ligand. Metal chelates of some transition metals were performed as well depicted. Complexes were identified using atomic absorption of flame, elemental analysis, infrared and UV-Vis spectral process as well conductivity and magnetic quantifications. Nature of compounds produced have been studied followed the mole ratio and continuous contrast methods, Beer's law followed during a concentration scope (1×10-4 - 3×10-4 mol/L). height molar absorbtivity of compoun

Thispaperpresentsthesynthesisandstudyofsomenewmixed-liagnd complexescontainingtowaminoacids[Alanine(Ala)andphenylalanine(phe)]withsome metals .Theresultsproductswerefoundtobesolidcrystallinecomplexeswhichhave been characterized by using (FT-IR,UV-Vis) spectra , melting point, elemental analysis (C.H.N) , molar conductivity and solubiltyThe proposed structure of the complexes using program , chem office 3D(2000) .The general formula have been given for the prepared complexes :[M(A-H)(phe-H)]M(II): Hg , Mn ,Co , Ni , Cu ) , Zn , Cd(II) .Ala = Alanine acid = C3H7NO2Phe = phenylalanine = C9H11NO2

This paper presents the synthesis and study of some new mixed-liagnd complexes containing tow amino acids[Alanine(Ala) and phenylalanine (phe)] with some metals . The results products were found to be solid crystalline complexes which have been characterized by using (FT-IR,UV-Vis) spectra , melting point, elemental analysis (C.H.N) , molar conductivity and solubilty The proposed structure of the complexes using program , chem office 3D(2000) . The general formula have been given for the prepared complexes : [M(A-H)(phe-H)] M(II): Hg , Mn ,Co , Ni , Cu ) , Zn , Cd(II) . Ala = Alanine acid = C3H7NO2 Phe = phenylalanine = C9H11NO2