The purpose of the present paper is twofold. First, the projective Riccati equations （PREs for short） are resolved by means of a linearized theorem, which was known in the literature. Based on the signs and values o...The purpose of the present paper is twofold. First, the projective Riccati equations （PREs for short） are resolved by means of a linearized theorem, which was known in the literature. Based on the signs and values of coeffcients of PREs, the solutions with two arbitrary parameters of PREs can be expressed by the hyperbolic functions, the trigonometric functions, and the rational functions respectively, at the same time the relation between the components of each solution to PREs is also implemented. Second, more new travelling wave solutions for some nonlinear PDEs, such as the Burgers equation, the mKdV equation, the NLS^＋ equation, new Hamilton amplitude equation, and so on, are obtained by using Sub-ODE method, in which PREs are taken as the Sub-ODEs. The key idea of this method is that the travelling wave solutions of nonlinear PDE can be expressed by a polynomial in two variables, which are the components of each solution to PREs, provided that the homogeneous balance between the higher order derivatives and nonlinear terms in the equation is considered.展开更多
Crystals of CdSxSe1-x alloys have been grown from the vapour phase. Some of the physical properties, such as lattice parameters, crystal structure and x-rays data of CdSxSe1-x alloys were determined using x-ray diffra...Crystals of CdSxSe1-x alloys have been grown from the vapour phase. Some of the physical properties, such as lattice parameters, crystal structure and x-rays data of CdSxSe1-x alloys were determined using x-ray diffractometry. X-ray diffractometry has shown that CdS-CdSe mixed crystals had the wurtzite structure for all compositions between CdS and CdSe. The lattice parameters （both a and c） were found to show a linear dependence with composition. The dependence of the lattice parameters of a and c on composition can be expressed as： a（x） = 4.165 ＋ 0.16x; c（x） = 6.713 ＋ 0.27x. The variation of band gap with composition was determined for these samples from optical absorption measurements, which showed that the band gap varied smoothly and monotonically, but not linearly over the composition range typical results were found between 2.42-1.74 eV at room temperature.展开更多
基金The project supported in part by the Natural Science Foundation of Education Department of Henan Province of China under Grant No. 2006110002 and the Science Foundations of Henan University of Science and Technology under Grant Nos. 2004ZD002 and 2006ZY001
文摘The purpose of the present paper is twofold. First, the projective Riccati equations （PREs for short） are resolved by means of a linearized theorem, which was known in the literature. Based on the signs and values of coeffcients of PREs, the solutions with two arbitrary parameters of PREs can be expressed by the hyperbolic functions, the trigonometric functions, and the rational functions respectively, at the same time the relation between the components of each solution to PREs is also implemented. Second, more new travelling wave solutions for some nonlinear PDEs, such as the Burgers equation, the mKdV equation, the NLS^＋ equation, new Hamilton amplitude equation, and so on, are obtained by using Sub-ODE method, in which PREs are taken as the Sub-ODEs. The key idea of this method is that the travelling wave solutions of nonlinear PDE can be expressed by a polynomial in two variables, which are the components of each solution to PREs, provided that the homogeneous balance between the higher order derivatives and nonlinear terms in the equation is considered.
文摘Crystals of CdSxSe1-x alloys have been grown from the vapour phase. Some of the physical properties, such as lattice parameters, crystal structure and x-rays data of CdSxSe1-x alloys were determined using x-ray diffractometry. X-ray diffractometry has shown that CdS-CdSe mixed crystals had the wurtzite structure for all compositions between CdS and CdSe. The lattice parameters （both a and c） were found to show a linear dependence with composition. The dependence of the lattice parameters of a and c on composition can be expressed as： a（x） = 4.165 ＋ 0.16x; c（x） = 6.713 ＋ 0.27x. The variation of band gap with composition was determined for these samples from optical absorption measurements, which showed that the band gap varied smoothly and monotonically, but not linearly over the composition range typical results were found between 2.42-1.74 eV at room temperature.
