Using the (2+1)-dimensional Schwartz dcrivative, the usual (2+1)-dimensional Schwartz Kadomtsev-Petviashvili (KP) equation is extended to (n+1)-dimensional conformal invariance equation. The extension possesses Painlc...Using the (2+1)-dimensional Schwartz dcrivative, the usual (2+1)-dimensional Schwartz Kadomtsev-Petviashvili (KP) equation is extended to (n+1)-dimensional conformal invariance equation. The extension possesses Painlcvc property. Some (3+1)-dimensional examples are given and some single three-dimensional camber soliton and two spatial-plane solitons solutions of a (3+1)-dimensional equation are obtained.展开更多
The compound KdV-Burgers equation and combined KdV-mKdV equation are real physical models concerning many branches in physics.In this paper,applying the improved trigonometric function method to these equations,rich e...The compound KdV-Burgers equation and combined KdV-mKdV equation are real physical models concerning many branches in physics.In this paper,applying the improved trigonometric function method to these equations,rich explicit and exact travelling wave solutions,which contain solitary-wave solutions,periodic solutions,and combined formal solitary-wave solutions,are obtained.展开更多
As a generalization of the Bernstein-Durrmeyer operatora defined on the simplex, a class of general Bernstein-Durrmeyer operators is introduced. With the weighted moduli of smoothness as a metric, we prove a strong di...As a generalization of the Bernstein-Durrmeyer operatora defined on the simplex, a class of general Bernstein-Durrmeyer operators is introduced. With the weighted moduli of smoothness as a metric, we prove a strong direct theorem and an inverse theorem of weak type for these operators by using a decom-position way. From the theorems the characterization of Lp approximation behavior is derived.展开更多
In this letter, a class of reaction-diffusion equations, which arise in chemical reaction or ecology and other fields of physics, are investigated. A more general analytical solution of the equation is obtained by usi...In this letter, a class of reaction-diffusion equations, which arise in chemical reaction or ecology and other fields of physics, are investigated. A more general analytical solution of the equation is obtained by using the first integral method.展开更多
Through Pickering's and extended Painleve nonstandard truncated expansionmethod, this paper solves the phase-separating dynamics equation of diblock copolymer, and obtainsvarious exact solutions. We discuss non-co...Through Pickering's and extended Painleve nonstandard truncated expansionmethod, this paper solves the phase-separating dynamics equation of diblock copolymer, and obtainsvarious exact solutions. We discuss non-complex special solutions which can be made up of hyperbolicfunctions or elliptic functions.展开更多
Poly[styrene(iodosodiacetate)] reacted with diaryl diselenides, followed by sodium azide, giving 1-azido-2-arylselenoalkanes regioselectively. The polymer reagent could be regenerated and reused.
Several polystyrene-supported selenides and selenoxide have been prepared firstly. These novel reagents were treated with LDA to produce selenium stabilized carbanions, which reacted with aldehydes and alkyl halides, ...Several polystyrene-supported selenides and selenoxide have been prepared firstly. These novel reagents were treated with LDA to produce selenium stabilized carbanions, which reacted with aldehydes and alkyl halides, followed by selenoxide syn-elimination and [2,3] sigmatropic rearrangement respectively to give Z-allylic alcohols stereoselectively.展开更多
Polycrystalline ZnO films were prepared on glass wafer using Zn targets by radio frequency(RF)reactive sputtering technique under different deposition conditions.X-ray diffraction (XRD) and optical transmittance spect...Polycrystalline ZnO films were prepared on glass wafer using Zn targets by radio frequency(RF)reactive sputtering technique under different deposition conditions.X-ray diffraction (XRD) and optical transmittance spectrum were employed to analyze the structure and optical character of the films.The strain and stress in films, as well as the packing density are calculated in terms of refractive index of films measured with an elliptic polarization analyzer.It is the deposition conditions that have great effects on the structural and optical properties of ZnO films.Under the optimal conditions,the only evident peak in XRD spectrum was (002) peak with the full width at half maximum (FWHM) of 0.20° showing the grain size of 42.8 nm.The packing density,the stress in (002) plane and the average optical transmittance in the visible region were about 97%,-1.06×10~9 N/m^2 and 92%, respectively.展开更多
We point out that the Meyer-Konig and Zeller operator Mn (f;x) are unbounded in usual Jacobi weighted norm at first, and then we consider the weighted approximation by Mn(f;x) by a new norm and obtain the characteriza...We point out that the Meyer-Konig and Zeller operator Mn (f;x) are unbounded in usual Jacobi weighted norm at first, and then we consider the weighted approximation by Mn(f;x) by a new norm and obtain the characterization of convergence rate in nonoptimal approximation by K-functional.展开更多
文摘Using the (2+1)-dimensional Schwartz dcrivative, the usual (2+1)-dimensional Schwartz Kadomtsev-Petviashvili (KP) equation is extended to (n+1)-dimensional conformal invariance equation. The extension possesses Painlcvc property. Some (3+1)-dimensional examples are given and some single three-dimensional camber soliton and two spatial-plane solitons solutions of a (3+1)-dimensional equation are obtained.
文摘The compound KdV-Burgers equation and combined KdV-mKdV equation are real physical models concerning many branches in physics.In this paper,applying the improved trigonometric function method to these equations,rich explicit and exact travelling wave solutions,which contain solitary-wave solutions,periodic solutions,and combined formal solitary-wave solutions,are obtained.
基金Supported by Foundation of Key Item of Science and Technology of Education Ministry of China (03142)Foundation of Higher School of Ningxia (JY2002107)Nature Science Foundation of Zhejiang Province(102002).
文摘As a generalization of the Bernstein-Durrmeyer operatora defined on the simplex, a class of general Bernstein-Durrmeyer operators is introduced. With the weighted moduli of smoothness as a metric, we prove a strong direct theorem and an inverse theorem of weak type for these operators by using a decom-position way. From the theorems the characterization of Lp approximation behavior is derived.
文摘In this letter, a class of reaction-diffusion equations, which arise in chemical reaction or ecology and other fields of physics, are investigated. A more general analytical solution of the equation is obtained by using the first integral method.
文摘Through Pickering's and extended Painleve nonstandard truncated expansionmethod, this paper solves the phase-separating dynamics equation of diblock copolymer, and obtainsvarious exact solutions. We discuss non-complex special solutions which can be made up of hyperbolicfunctions or elliptic functions.
基金Project 29932020 was supported by the National Natural Science Foundation of China.
文摘Poly[styrene(iodosodiacetate)] reacted with diaryl diselenides, followed by sodium azide, giving 1-azido-2-arylselenoalkanes regioselectively. The polymer reagent could be regenerated and reused.
文摘Several polystyrene-supported selenides and selenoxide have been prepared firstly. These novel reagents were treated with LDA to produce selenium stabilized carbanions, which reacted with aldehydes and alkyl halides, followed by selenoxide syn-elimination and [2,3] sigmatropic rearrangement respectively to give Z-allylic alcohols stereoselectively.
文摘Polycrystalline ZnO films were prepared on glass wafer using Zn targets by radio frequency(RF)reactive sputtering technique under different deposition conditions.X-ray diffraction (XRD) and optical transmittance spectrum were employed to analyze the structure and optical character of the films.The strain and stress in films, as well as the packing density are calculated in terms of refractive index of films measured with an elliptic polarization analyzer.It is the deposition conditions that have great effects on the structural and optical properties of ZnO films.Under the optimal conditions,the only evident peak in XRD spectrum was (002) peak with the full width at half maximum (FWHM) of 0.20° showing the grain size of 42.8 nm.The packing density,the stress in (002) plane and the average optical transmittance in the visible region were about 97%,-1.06×10~9 N/m^2 and 92%, respectively.
基金Supported by the Shanxi Province Youth Foundation of China,Grant 20011005.
文摘We point out that the Meyer-Konig and Zeller operator Mn (f;x) are unbounded in usual Jacobi weighted norm at first, and then we consider the weighted approximation by Mn(f;x) by a new norm and obtain the characterization of convergence rate in nonoptimal approximation by K-functional.
