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Solvability of a class of PT-symmetric non-hermitian hamiltonians：Bethe ansatz method

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Chinese Physics B 2017年第6期26卷 14-21页

作者： m Baradaran h Panahi Department of Physics University of Guilan Rasht 41635-1914Iran

We use the Bethe ansatz method to investigate the Schrdinger equation for a class of PT-symmetric non-hermitian hamiltonians. Elementary exact solutions for the eigenvalues and the corresponding wave functions are obtained in terms of the roots of a set of algebraic equations. Also, it is shown that the problems possess sl（2） hidden symmetry and then the exact solutions of the problems are obtained by employing the representation theory of sl（2） Lie algebra. It is found that the results of the two methods are the same.

关键词： PT-symmetry Bethe ansatz method Lie algebraic approach quasi-exactly solvable

A STABILITY ThEOREm FOR CONSTRAINED OPTImAL CONTROL PROBLEmS

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Journal of Computational mathematics 2004年第5期22卷 633-640页

作者： m.h.Farag DepartmentofmathematicsandComputerScienceFacultyofEducation lbriSultanateofOman

This paper presents the stability of difference approximations of an optimal control problem for a quasilinear parabolic equation with controls in the coefficients, boundary conditions and additional restrictions. The optimal control problem has been convered to one of the optimization problem using a penalty function technique. The difference approximations problem for the considered problem is obtained. The estimations of stability of the solution of difference approximations problem are proved. The stability estimation of the solution of difference approximations problem by the controls is obtained.

关键词： Finite difference method Penalty function methods Quasilinear Parabolic equations Stability estimations

Influence of Zn^(2+)or Cu^(2+) on Reduction and Recalcination Behavior of Fe_2TiO_5

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Journal of materials Science & Technology 2007年第5期23卷 697-702页

作者： m.Bahgat m.h.Khedr h.S.Abdelmaksoud CmRDI P.O.Box 87-HelwanCairoEgypt chemistry Department Faculty of ScienceBenisuef UniversityEgypt

Fe2O3, TiO2, CuO and ZnO powders were mixed according to the formula of （1-x）TiO2 xCuO-Fe2O3 or （1-x）TiO2 xZnO-Fe2O3 （x=0, 0.2 0.4, 0.6, 0.8, 1）, and well ball-milled with h2O for 3 h to ensure homogeneity of the powdered solids, then fired at 1200℃ for 4 h. The fired samples were reduced at 500℃ with hydrogen gas. The reduced samples were subjected to recalcination at 500℃ in CO2 atmosphere. Both of fired, reduced and calcined samples were characterized by X-ray diffraction, vibrating sample magnetometry, reflected light microscopy and scanning electron microscopy. Different phases were formed after firing of Cu^＋2 or Zn^2＋ substituted Fe2TiO5. magnetization （Bs） of the formed phases after firing are very low corresponding to diluted magnetic semiconductors （DmS） and increases with increasing the substituted cations （Cu^＋2 or Zn^2＋）. The reduction of the fired samples enhanced the Bs values whereas the reducibility increases with increasing the Cu^＋2 or Zn^2＋ content. Samples show different tendency toward CO2 decomposition which is very important for environmental minimization for CO2.

关键词： Nanosized ferrite Titanate Reduction magnetic properties Reduction-recalcin-ation CO2 decomposition

Experimental study of electro-optical-switched pulsed Nd:YAG laser

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Chinese Physics B 2016年第3期25卷 210-214页

作者： A maleki m Kavosh Tehrani h Saghafifar m h moghtader Dindarlu Optic & Laser Science & Technoltogy Research Center Malek-Ashtar University of Technology Isfahan Iran

We report the specification of a compact and stable side diode-pumped Q-switched pulsed Nd：YAG laser. We ex- perimentally study and compare the performance of the pulsed Nd：YAG laser in the free-running and Q-switched modes at different pulse repetition rates from 1 hz to 100 hz. The laser output energy is stabilized by using a special configu- ration of the optical resonator. In this laser, an unsymmetrical concave-concave resonator is used and this structure helps the mode volume to be nearly fixed when the pulse repetition rate is increased. According to the experimental results in the Q-switched operation, the laser output energy is nearly constant around 70 mJ with an FWhm pulse width of 7 ns at 100 hz. The optical-to-optical conversion efficiency in the Q-switched regime is 17.5%.

关键词： side diode-pumped Nd:YAG laser concave-concave resonator electro-optical Q-switched laser

magnetic field induction and magnetic force distribution profiles in plasma focus discharge device

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Plasma Science and Technology 2021年第7期23卷 110-120页

作者： A A LAShIN T m ALLAm h A EL-SAYED Kamal m AhmED S A WARD h m SOLImANand m A ABOUELATTA Plasma and Nuclear Fusion Department Nuclear Research CentreEgyptian Atomic Energy AuthorityInshas 13759Egypt Faculty of Engineering Delta University for Science and TechnologyGamasa 11152Egypt Electrical Engineering Department Faculty of Engineering at ShoubraBenha UniversityCairo 11629Egypt

We report a simple-to-perform technique to investigate the distribution of the azimuthal magnetic field induction,Bθ,and the induced magnetic force acting on the plasma current sheath(PCS)in a plasma focus(PF)*** in situ measurement technique can undoubtedly be beneficial when other fast-imaging techniques are not *** are not *** work was conducted in the low-energy mather-type EAEA-PF1 device operated in *** axial distribution(Bθ)z along the coaxial electrodes system was measured with a four magnetic-probe set technique at different radial distances(r=2.625×10^(−2) to 4.125×10^(−2) m)within the annular space between the coaxial electrodes during the 1st and 2nd half cycles of the discharge current waveform,where inner electrode of coaxial electrode system has a+ve polarity and−ve polarity,***,radial and total magnetic force distribution profiles were estimated from Bθ*** of PCS shape in terms of its inclination(curvature)angle,θ,along the axial rundown phase and the correlation between the magnetic forces per unit volume acting on the PCS,the inclination angleθof the PCS,and the formation of a powerful PF action during the 1st and 2nd half cycles is carried *** of inclination angle,θ,on total magnetic force per unit volume acting on PCS axial motion was studied,separately,during the 1st and 2nd half cycles.

关键词： plasma focus azimuthal magnetic field magnetic force inclination angle plasma current sheath

Approximate energies and thermal properties of a position-dependent mass charged particle under external magnetic fields

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Chinese Physics B 2017年第6期26卷 22-30页

作者： m Eshghi h mehraban S m Ikhdair Young Researchers and Elite Club Central Tehran BranchIslamic Azad UniversityTehranIran Faculty of Physics Semnan UniversitySemnanIran Department of Physics Faculty of ScienceAn-Najah National UniversityNablusWest BankPalestine Department of Electrical Engineering Near East UniversityNicosiaNorthern CyprusMersin 10Turkey

We solve the Schrodinger equation with a position-dependent mass（PDm） charged particle interacted via the superposition of the morse-plus-Coulomb potentials and is under the influence of external magnetic and Aharonov–Bohm（AB） flux fields. The nonrelativistic bound state energies together with their wave functions are calculated for two spatially-dependent mass distribution functions. We also study the thermal quantities of such a system. Further, the canonical formalism is used to compute various thermodynamic variables for second choosing mass by using the Gibbs formalism. We give plots for energy states as a function of various physical parameters. The behavior of the internal energy, specific heat, and entropy as functions of temperature and mass density parameter in the inverse-square mass case for different values of magnetic field are shown.

关键词： Schr?dinger equation morse-plus-Coulomb potentials position-dependent mass distribution functions perpendicular magnetic and Aharonov–Bohm flux fields

WEYL'S TYPE ThEOREmS AND hYPERCYCLIC OPERATORS

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Acta mathematica Scientia 2012年第2期32卷 539-551页

作者： m.h.m.Rashid Department of mathematics and Statistics Faculty of ScienceP.O.Box(7)Mu'tah UniversityMu'tah-Jordan

For a bounded operator T acting on an infinite dimensional separable hilbert space h, we prove the following assertions：（i） If T or T＊ ∈ SC, then generalized a- Browder＇s theorem holds for f（T） for every f ∈ hol（σ（T））. （ii） If T or T＊ ∈ hC has topological uniform descent at all λ ∈ iso（a（T））, then generalized Weyl＇s theorem holds for f（T） for every f ∈ hol（σ（T））. （iii） If T ∈ hC has topological uniform descent at all λ ∈（T）, then T satisfies generalized Weyl＇s theorem. （iv） Let T ∈ hC. If T satisfies the growth condition Gd（d 〉 1）, then generalized Weyl＇s theorem holds for f（T） for every f ∈ hol（σ（T））. （v） If T ∈ SC, then, f（OssF＋（T）） = aSBF＋（f（T）） for all f ∈ hol（σ（T））. （vi） Let T be a-isoloid such that T＊ ∈ hC. If T - AI has finite ascent at every A ∈ Eσ（T） and if F is of finite rank on hsuch that TF = FT, then T ∈ F obeys generalized a-Weyl＇s theorem.

关键词： Weyl's theorem hypercyclic operators supercyclic operators

Effect of Ni^(+2)-substituted Fe_2TiO_5 on the h_2-reduction and CO_2 Catalytic Decomposition Reactions at 500℃

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Journal of materials Science & Technology 2006年第6期22卷 846-850页

作者： m.h.Khedr chemistry Department Faculty of ScienceBenisuef UniversityEgypt

CO2 is a major component of the greenhouse gases, which causes the global warming. To reduce CO2 gas, high activity nanosized Ni＋2 substituted Fe2TiO5 samples were synthesized by conventional ceramic method. The effect of the composition of the synthesized ferrite on the h2-reduction and CO2-catalytic decomposition was investigated. Fe2TiO5 （iron titanate） phase that has a nanocrystallite size of -80 nm is formed as a result of heating Fe2O3 and TiO2 while the addition of NiO leads to the formation of new phases （-80 nm） NiTiO3 and NiFe2O4, but the mixed solid of NiO and Fe2O3 results in the formation of NiFe2O4 only. Samples with Ni^＋2=0 shows the lowest reduction extent （20%）; as the extent of Ni＋2 increases, the extent of reduction increases. The increase in the reduction percent is attributed to the presence of NiTiO3 and NiFe2O4 phases, which are more reducible phases than Fe2TiO5. The CO2 decomposition reactions were monitored by thermogravimetric analysis （TGA） experiments. The oxidation of the h2-reduced Ni＋2 substituted Fe2TiO5 at 500℃ was investigated. As Ni^＋2 increases, the rate of reoxidation increases. Samples with the highest reduction extents gave the highest reoxidation extent, which is attributed to the highly porous nature and deficiency in oxygen due to the presence of metallic Fe, Ni and/or FeNi alloy. X-ray diffraction （XRD） and transmission electron microscopy （TEm） of oxidized samples show also the presence of carbon in the sample containing Ni＋2〉0, which appears in the form of nanotubes （25 nm）.

关键词： Nanocrystallite Ferrite Titanate Reduction CO2 decomposition Carbon nanotubes

Synthesis and Crystal Structure of Glycin·3,5-Dihydroxybenzoic Acid

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Chinese Journal of Structural chemistry 2006年第2期25卷 229-231页

作者： cheN hao XUE Lin che Yun-Xia ZhENG Ji-min Department of chemistry Nankai University Tianjin 300071 China

The title compound glycin.3,5-dihydroxybenzoic acid （GDB） has been synthesized and characterized by single-crystal X-ray analysis. It crystallizes in orthorhombic, space group Pca21 with a = 25.513（10）, b = 4.668（2）, c = 9.150（4） A°, Z= 4, V= 1089.8（8） A°^3, C9h13NO7, mr= 247.20, Dc = 1.507 g/m^3,/z（moKa） = 0.132 mm^-1, F（000） = 520, R1 = 0.0322 and wR2 = 0.0611 for 885 observed reflections （I 〉 2σ（I））. The title compound is a 1：1 molecular complex of glycin and 3,5-dihydroxybenzoic acid, which is linked by O-h…O and N-h…O hydrogen bonds to form a three-dimensional framework. Test of ShG （second harmonic generation） indicates that NLO generation of the crystal is higher than that of KDP.

关键词： crystal structure synthesis glycin-3,5-dihydroxybenzoic acid