In a recent article [Physics Letters A 372 （2008） 417], Wang et al. proposed a method, which is called the （G′/G）-expansion method, to look for travelling wave solutions of nonlinear evolution equations. The trav...In a recent article [Physics Letters A 372 （2008） 417], Wang et al. proposed a method, which is called the （G′/G）-expansion method, to look for travelling wave solutions of nonlinear evolution equations. The travelling wave solutions involving parameters of the KdV equation, the mKdV equation, the variant Boussinesq equations, and the Hirota-Satsuma equations are obtained by using this method. They think the （G′/G）-expansion method is a new method and more travelling wave solutions of many nonlinear evolution equations can be obtained. In this paper, we will show that the （G′/G）-expansion method is equivalent to the extended tanh function method.展开更多
In this paper a generalized tanh-function type method is proposed by using the idea of the transformed rational function method. We show that the (G'/G)?-expansion method is a special case of the generalized tanh-...In this paper a generalized tanh-function type method is proposed by using the idea of the transformed rational function method. We show that the (G'/G)?-expansion method is a special case of the generalized tanh-function type method, so the (G'/G)?-expansion method is considered as a special deformation application of the transformed rational function method. We demonstrate that all solutions obtained by the (G'/G)?-expansion method were found by the generalized tanh-function type method. As applications, we consider mKdV equation. Compared with the (G'/G) -expansion method, the generalized tanh-function type method gives new and more abundant solutions.展开更多
Recently the （G′/G）-expansion method was proposed to find the traveling wave solutions of nonlinear evolution equations. This paper shows that the （G′/G）-expansion method is a special form of the truncated Pain...Recently the （G′/G）-expansion method was proposed to find the traveling wave solutions of nonlinear evolution equations. This paper shows that the （G′/G）-expansion method is a special form of the truncated Painlev＇e expansion method by introducing an intermediate expansion method. Then the generalized （G′/G）-（G/G′） expansion method is naturally derived from the standpoint of the nonstandard truncated Painlev＇e expansion. The application of the generalized method to the mKdV equation shows that it extends the range of exact solutions obtained by using the （ G′/ G）-expansion method.展开更多
In this work, the (G'/G)-expansion method is proposed for constructing more general exact solutions of two general form of Burgers type equation arising in fluid mechanics namely, Burgers-Korteweg-de Vries (Burger...In this work, the (G'/G)-expansion method is proposed for constructing more general exact solutions of two general form of Burgers type equation arising in fluid mechanics namely, Burgers-Korteweg-de Vries (Burgers-KdV) and Burger-Fisher equations. Our work is motivated by the fact that the (G'/G)-expansion method provides not only more general forms of solutions but also periodic and solitary waves. If we set the parameters in the obtained wider set of solutions as special values, then some previously known solutions can be recovered. The method appears to be easier and faster by means of a symbolic computation system.展开更多
Ginkgo biloba resources in China are enormous. With the demand of the market, the preparation and application of flavonoids have become a current research hotspot. The main active substances in G. biloba leaves, flavo...Ginkgo biloba resources in China are enormous. With the demand of the market, the preparation and application of flavonoids have become a current research hotspot. The main active substances in G. biloba leaves, flavonoids, have various functional activities and are widely used in fields such as food, medicine, cosmetics, feed, etc. In this paper, the introduction, functional activity, extraction methods, and application research of flavonoids from G. biloba leaves are reviewed, and the development prospects of flavonoids from G. biloba leaves are expected.展开更多
The extended F-expansion method or mapping method is used to construct exact solutions for the coupled KleinGordon Schr/Sdinger equations （K-G-S equations） by the aid of the symbolic computation system Mathematica. ...The extended F-expansion method or mapping method is used to construct exact solutions for the coupled KleinGordon Schr/Sdinger equations （K-G-S equations） by the aid of the symbolic computation system Mathematica. More solutions in the Jacobi elliptic function form are obtained, including the single Jacobi elliptic function solutions, combined Jacobi elliptic function solutions, rational solutions, triangular solutions, soliton solutions and combined soliton solutions.展开更多
Since the room-temperature detector CdZnTe(CZT) has advantages in terms of detection efficiency,energy resolution, and size, it has been extensively used to detect X-rays and gamma-rays. So far, nuclear radiation dete...Since the room-temperature detector CdZnTe(CZT) has advantages in terms of detection efficiency,energy resolution, and size, it has been extensively used to detect X-rays and gamma-rays. So far, nuclear radiation detectors such as cerium chloride doped with lanthanum bromide(LaBr_3(Ce)), thallium doped with cesium iodide(sI(Tl)), thallium doped with sodium iodide(NaI(Tl)),and high-purity germanium(HPGe) primarily use the spectroscopy-dose rate function(G(E)) to achieve the accurate measurement of air kerma rate(K_a) and ambient dose equivalent rate(H*(10)). However, the spectroscopy-dose rate function has been rarely measured for a CZT detector. In this study, we performed spectrum measurement using a hemispherical CZT detector in a radiation protection standards laboratory. The spectroscopy-dose rate function G(E) of the CZT detector was calculated using the least-squares method combined with the standard dose rate at the measurement position. The results showed that the hemispherical CZT detector could complete the measurement of air kerma rate(K_a) and ambient dose equivalent rate(H*(10)) by using the G(E) function at energies between 48 keV and 1.25 MeV, and the relative intrinsic errors were, respectively, controlled within ± 2. 3 and ± 2. 1%.展开更多
In this paper,we construct exact solutions for the (2+1)-dimensional Boiti-Leon-Pempinelle equation byusing the (G'/G)-expansion method,and with the help of Maple.As a result,non-travelling wave solutions with thr...In this paper,we construct exact solutions for the (2+1)-dimensional Boiti-Leon-Pempinelle equation byusing the (G'/G)-expansion method,and with the help of Maple.As a result,non-travelling wave solutions with threearbitrary functions are obtained including hyperbolic function solutions,trigonometric function solutions,and rationalsolutions.This method can be applied to other higher-dimensional nonlinear partial differential equations.展开更多
In this work, the (G,/G)- --expansion method is proposed for constructing more general exact solutions of the (2 + 1)--dimensional Kadomtsev-Petviashvili (KP) equation and its generalized forms. Our work is motivated ...In this work, the (G,/G)- --expansion method is proposed for constructing more general exact solutions of the (2 + 1)--dimensional Kadomtsev-Petviashvili (KP) equation and its generalized forms. Our work is motivated by the fact that the (G,/G)---expansion method provides not only more general forms of solutions but also periodic and solitary waves. If we set the parameters in the obtained wider set of solutions as special values, then some previously known solutions can be recovered. The method appears to be easier and faster by means of a symbolic computation system.展开更多
基于Φ75 mm×75 mm NaI(Tl)多道能谱仪实验测量结果,采用全谱法测定空气吸收剂量率,从理论和实验入手建立能谱剂量转换函数G(E)。选取铀、钍、钾模型和铀、钍、钾混合模型,以及人工放射性核素60Co、137Cs获取标准能谱N(E),用最小...基于Φ75 mm×75 mm NaI(Tl)多道能谱仪实验测量结果,采用全谱法测定空气吸收剂量率,从理论和实验入手建立能谱剂量转换函数G(E)。选取铀、钍、钾模型和铀、钍、钾混合模型,以及人工放射性核素60Co、137Cs获取标准能谱N(E),用最小二乘法拟合得到G(E)函数的系数,并用G(E)函数法和贝克公式法估算剂量率结果与实测数据进行比对,前者的偏差小于后者。利用模型站和野外实地测量数据对该函数的准确性进行验证,误差均<10%。展开更多
基金Supported by National Natural Science Foundation of China under Grant No. 10671172
文摘In a recent article [Physics Letters A 372 （2008） 417], Wang et al. proposed a method, which is called the （G′/G）-expansion method, to look for travelling wave solutions of nonlinear evolution equations. The travelling wave solutions involving parameters of the KdV equation, the mKdV equation, the variant Boussinesq equations, and the Hirota-Satsuma equations are obtained by using this method. They think the （G′/G）-expansion method is a new method and more travelling wave solutions of many nonlinear evolution equations can be obtained. In this paper, we will show that the （G′/G）-expansion method is equivalent to the extended tanh function method.
文摘In this paper a generalized tanh-function type method is proposed by using the idea of the transformed rational function method. We show that the (G'/G)?-expansion method is a special case of the generalized tanh-function type method, so the (G'/G)?-expansion method is considered as a special deformation application of the transformed rational function method. We demonstrate that all solutions obtained by the (G'/G)?-expansion method were found by the generalized tanh-function type method. As applications, we consider mKdV equation. Compared with the (G'/G) -expansion method, the generalized tanh-function type method gives new and more abundant solutions.
基金Project supported by the National Key Basic Research Project of China (Grant No. 2004CB318000)the National Natural Science Foundation of China (Grant No. 10771072)
文摘Recently the （G′/G）-expansion method was proposed to find the traveling wave solutions of nonlinear evolution equations. This paper shows that the （G′/G）-expansion method is a special form of the truncated Painlev＇e expansion method by introducing an intermediate expansion method. Then the generalized （G′/G）-（G/G′） expansion method is naturally derived from the standpoint of the nonstandard truncated Painlev＇e expansion. The application of the generalized method to the mKdV equation shows that it extends the range of exact solutions obtained by using the （ G′/ G）-expansion method.
文摘In this work, the (G'/G)-expansion method is proposed for constructing more general exact solutions of two general form of Burgers type equation arising in fluid mechanics namely, Burgers-Korteweg-de Vries (Burgers-KdV) and Burger-Fisher equations. Our work is motivated by the fact that the (G'/G)-expansion method provides not only more general forms of solutions but also periodic and solitary waves. If we set the parameters in the obtained wider set of solutions as special values, then some previously known solutions can be recovered. The method appears to be easier and faster by means of a symbolic computation system.
基金Supported by Science and Technology Research Project of Hebei Provincial Department of Education (ZC2021206)。
文摘Ginkgo biloba resources in China are enormous. With the demand of the market, the preparation and application of flavonoids have become a current research hotspot. The main active substances in G. biloba leaves, flavonoids, have various functional activities and are widely used in fields such as food, medicine, cosmetics, feed, etc. In this paper, the introduction, functional activity, extraction methods, and application research of flavonoids from G. biloba leaves are reviewed, and the development prospects of flavonoids from G. biloba leaves are expected.
基金Project supported by the National Nature Science Foundation of China （Grant No 49894190） of the Chinese Academy of Science （Grant No KZCXI-sw-18）, and Knowledge Innovation Program.
文摘The extended F-expansion method or mapping method is used to construct exact solutions for the coupled KleinGordon Schr/Sdinger equations （K-G-S equations） by the aid of the symbolic computation system Mathematica. More solutions in the Jacobi elliptic function form are obtained, including the single Jacobi elliptic function solutions, combined Jacobi elliptic function solutions, rational solutions, triangular solutions, soliton solutions and combined soliton solutions.
基金supported by the National Key Scientific Instruments to Develop Dedicated(Nos.2013YQ090811 and 2016YFF0103800)
文摘Since the room-temperature detector CdZnTe(CZT) has advantages in terms of detection efficiency,energy resolution, and size, it has been extensively used to detect X-rays and gamma-rays. So far, nuclear radiation detectors such as cerium chloride doped with lanthanum bromide(LaBr_3(Ce)), thallium doped with cesium iodide(sI(Tl)), thallium doped with sodium iodide(NaI(Tl)),and high-purity germanium(HPGe) primarily use the spectroscopy-dose rate function(G(E)) to achieve the accurate measurement of air kerma rate(K_a) and ambient dose equivalent rate(H*(10)). However, the spectroscopy-dose rate function has been rarely measured for a CZT detector. In this study, we performed spectrum measurement using a hemispherical CZT detector in a radiation protection standards laboratory. The spectroscopy-dose rate function G(E) of the CZT detector was calculated using the least-squares method combined with the standard dose rate at the measurement position. The results showed that the hemispherical CZT detector could complete the measurement of air kerma rate(K_a) and ambient dose equivalent rate(H*(10)) by using the G(E) function at energies between 48 keV and 1.25 MeV, and the relative intrinsic errors were, respectively, controlled within ± 2. 3 and ± 2. 1%.
基金Supported by the Natural Science Foundation of Shanghai under Grant No.09ZR1410800the Science Foundation of Key Laboratory of Mathematics Mechanization under Grant No.KLMM0806+1 种基金the Shanghai Leading Academic Discipline Project under Grant No.J50101Key Disciplines of Shanghai Municipality under Grant No.S30104
文摘In this paper,we construct exact solutions for the (2+1)-dimensional Boiti-Leon-Pempinelle equation byusing the (G'/G)-expansion method,and with the help of Maple.As a result,non-travelling wave solutions with threearbitrary functions are obtained including hyperbolic function solutions,trigonometric function solutions,and rationalsolutions.This method can be applied to other higher-dimensional nonlinear partial differential equations.
文摘In this work, the (G,/G)- --expansion method is proposed for constructing more general exact solutions of the (2 + 1)--dimensional Kadomtsev-Petviashvili (KP) equation and its generalized forms. Our work is motivated by the fact that the (G,/G)---expansion method provides not only more general forms of solutions but also periodic and solitary waves. If we set the parameters in the obtained wider set of solutions as special values, then some previously known solutions can be recovered. The method appears to be easier and faster by means of a symbolic computation system.
文摘基于Φ75 mm×75 mm NaI(Tl)多道能谱仪实验测量结果,采用全谱法测定空气吸收剂量率,从理论和实验入手建立能谱剂量转换函数G(E)。选取铀、钍、钾模型和铀、钍、钾混合模型,以及人工放射性核素60Co、137Cs获取标准能谱N(E),用最小二乘法拟合得到G(E)函数的系数,并用G(E)函数法和贝克公式法估算剂量率结果与实测数据进行比对,前者的偏差小于后者。利用模型站和野外实地测量数据对该函数的准确性进行验证,误差均<10%。
