The investigation of determining solutions for the Diophantine equation over the Gaussian integer ring for the specific case of is discussed. The discussion includes various preliminary results later used to build the resolvent theory of the Diophantine equation studied. Our findings show the existence of infinitely many solutions. Since the analytical method used here is based on simple algebraic properties, it can be easily generalized to study the behavior and the conditions for the existence of solutions to other Diophantine equations, allowing a deeper understanding, even when no general solution is known.
The Boltzmann equation has been solved using (EEDF) package for a pure sulfur hexafluoride (SF6) gas and its mixtures with buffer Helium (He) gas to study the electron energy distribution function EEDF and then the corresponding transport coefficients for various ratios of SF6 and the mixtures. The calculations are graphically represented and discussed for the sake of comparison between the various mixtures. It is found that the various SF6 – He content mixtures have a considerable effect on EEDF and the transport coefficients of the mixtures
Synthesis of new nucleoside analogues of the type : 3¢ , 3¢ - gem – di – C – nitromethly , expected to have useful application in the chemotherapeutic treatment of AIDS , cancer and microbial infections. The synthesis involved the condensation of the appropriate sugar derivative ( i.e . 3¢ , 3¢ – gem – di – C – nitromethly – 1– ribofuranose ) with nitrogen bases , such as , uracil and theophllin following a multi step scheme starting from diacetone golucose (1) (scheme 1) .The prepared compound were identified by spectroscopic methods ; ir , mass , 1H and 13C nmr.
The Boltzmann transport equation is solved by using two- terms approximation for pure gases and mixtures. This method of solution is used to calculate the electron energy distribution function and electric transport parameters were evaluated in the range of E/N varying from . 172152110./510.VcmENVcm
The electron energy distribution function of CF4 gas is nearly Maxwellian at (1,2)Td, and when E/N increase the distribution function is non Maxwellian. Also, the mixtures are have different energy values depending on transport energy between electron and molecule through the collisions. Behavior of electrons transport parameters is nearly from the experimental results in references. The drift velocity of electron in carbon tetraflouride i
The research includes the preparation of several complexes of the internal transition elements lanthanide (Ln = La, Nd, Er, Gd, and Dy) containing the 4f shell, with Schiff bases resulting from condensation reactions between 4-antipyrinecarboxaldehyde and 2-aminobenzothiazoles. Schiff's base was identified using FTIR spectra, UV-vis spectroscopy, elemental microanalysis CHNSO, nuclear magnetic resonance, mass spectrometry, and TGA thermal analysis. The complexes were studied and identified with elemental microanalysis CHNSO, FTIR spectroscopy, UV-vis spectroscopy, TGA thermal analysis, conductivity measurement, and magnetic sensitivity. The result showed that these complexes were classified as homogeneous bidentate complexes with th
... Show MoreThe paper is devoted to solve nth order linear delay integro-differential equations of convolution type (DIDE's-CT) using collocation method with the aid of B-spline functions. A new algorithm with the aid of Matlab language is derived to treat numerically three types (retarded, neutral and mixed) of nth order linear DIDE's-CT using B-spline functions and Weddle rule for calculating the required integrals for these equations. Comparison between approximated and exact results has been given in test examples with suitable graphing for every example for solving three types of linear DIDE's-CT of different orders for conciliated the accuracy of the results of the proposed method.
In this work a series of fourteen new compounds were synthesized. Compound [1] was formed from the reaction of 2-aminobenzothiazole and p-bromophenacyl bromide. Aldehyde group [2] was obtained from the reaction of compound [1] with pocl3 in presence of DMF and CHCl3 .After that shiff bases have been synthesized from the reaction of compound [2] with different aromatic amine to give new shiff bases [3- 5]. These new shiff bases have been reduced to their corresponding amine [6-8] by means of sodium borohydride. Then reaction of shiff bases [3-5] with phenyl isocyanate gives 3-cyclic lactam derivatives [9-11]. 3-cyclic Oxazepine derivatives [12-14] were obtained by reaction of shiff bases [3-5] with succinic anhydride. These new formed co
... Show MoreIn this work, the fractional damped Burger's equation (FDBE) formula = 0,
In this work a hybrid composite materials were prepared containing matrix of polymer (polyethylene PE) reinforced by different reinforcing materials (Alumina powder + Carbon black powder CB + Silica powder). The hybrid composite materials prepared are: • H1 = PE + Al2O3 + CB • H2 = PE + CB + SiO2 • H3 = PE + Al2O3 + CB + SiO2 All samples related to electrical tests were prepared by injection molding process. Mechanical tests include compression with different temperatures and different chemical solutions at different immersion times The mechanical experimentations results were in favour of the samples (H3) with an obvious weakness of the samples (H1) and a decrease of these properties with a rise in temperature and the increasing
... Show MoreElectrochemical Machining is a term given to one of nontraditional machining that uses a chemical reaction associated with electric current to remove the material. The process is depending on the principle of anodic dissolution theory for evaluating material removal during electrochemical process. In this study, the electrochemical machining was used to remove 1 mm from the length of the a workpiece (stainless steel 316 H) by immersing it in to electrolyte (10, 20 and 30 g) of NaCl and Na2SO4 to every (1 litter of filtered water). The tool used was made from copper. Gap size between the workpiece and electrode is (0.5) mm. This study focuses on the effect of the changing the type and concentration of electroly
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