In this article,we consider the following coupled fractional nonlinear Schrödinger system in R^{(−Δ)su+P(x)u=μ1|u|^2p−2u+β|u|p|u|p−2u,x∈RN,(−Δ)sv+Q(x)v=μ2|v|^2p−2v+β|v|p|v|p−2v,x∈RN,u,v∈Hs(RN),where N≥2...In this article,we consider the following coupled fractional nonlinear Schrödinger system in R^{(−Δ)su+P(x)u=μ1|u|^2p−2u+β|u|p|u|p−2u,x∈RN,(−Δ)sv+Q(x)v=μ2|v|^2p−2v+β|v|p|v|p−2v,x∈RN,u,v∈Hs(RN),where N≥2,0<s<1,1<p<NN−2s,μ1>0,μ2>0 andβ∈R is a coupling constant.We prove that it has infinitely many non-radial positive solutions under some additional conditions on P(x),Q(x),p andβ.More precisely,we will show that for the attractive case,it has infinitely many non-radial positive synchronized vector solutions,and for the repulsive case,infinitely many non-radial positive segregated vector solutions can be found,where we assume that P(x)and Q(x)satisfy some algebraic decay at infinity.展开更多
Near infrared(NIR)assignment of Isopsoralen was performed using deuterated chloroform solvent and two-dimensional correlation spectroscopy(2D-COS)technology.Yunkang Oral Liquid was applied to study Isopsoralen,the cha...Near infrared(NIR)assignment of Isopsoralen was performed using deuterated chloroform solvent and two-dimensional correlation spectroscopy(2D-COS)technology.Yunkang Oral Liquid was applied to study Isopsoralen,the characteristic bands by spectral assignment as well as the bands by interval partial least squares(iPLS)and synergy interval partial least squares(siPLS)were used to establish partial least squares(PLS)model.The coefficient of determination in calibration(R^(2)_(cal))were 0.9987,0.9970 and 0.9982.The coefficient of determination in cross validation(R^(2)_(val)) T were 0.9985,0.9921 and 0.9982.The coe±cient of determination in prediction(R^(2)_(pre)) T were 0.9987,0.9955 and 0.9988.The root mean square error of calibration(RMSEC)were 0.27,0.40 and 0.31 ppm.The root mean square error of cross validation(RMSECV)were 0.30,0.67 and 0.32 ppm.The root mean square error of prediction(RMSEP)were 0.23,0.43 and 0.22 ppm.The residual predictive deviation(RPD)were 31.00,16.58 and 32.41.It turned out that the characteristic bands by spectral assignment had the same results with the chemometrics methods in PLS model.It provided guidance for NIR spectral assignment of chemical compositions in Chinese Materia Medica(CMM).展开更多
基金supported by NSF of China(11701107)NSF of Guangxi Province (2017GXNSFBA198190)+1 种基金the second author is supported by NSF of China (11501143)the PhD launch scientific research projects of Guizhou Normal University (2014)
文摘In this article,we consider the following coupled fractional nonlinear Schrödinger system in R^{(−Δ)su+P(x)u=μ1|u|^2p−2u+β|u|p|u|p−2u,x∈RN,(−Δ)sv+Q(x)v=μ2|v|^2p−2v+β|v|p|v|p−2v,x∈RN,u,v∈Hs(RN),where N≥2,0<s<1,1<p<NN−2s,μ1>0,μ2>0 andβ∈R is a coupling constant.We prove that it has infinitely many non-radial positive solutions under some additional conditions on P(x),Q(x),p andβ.More precisely,we will show that for the attractive case,it has infinitely many non-radial positive synchronized vector solutions,and for the repulsive case,infinitely many non-radial positive segregated vector solutions can be found,where we assume that P(x)and Q(x)satisfy some algebraic decay at infinity.
基金This work was financially supported by the National Natural Science Foundation of China (81303218)Doctoral Fund of Ministry of Education of China (20130013120006)Independent project topics of Beijing University of Chinese Medicine (2014-JYBZZ-XS-082).
文摘Near infrared(NIR)assignment of Isopsoralen was performed using deuterated chloroform solvent and two-dimensional correlation spectroscopy(2D-COS)technology.Yunkang Oral Liquid was applied to study Isopsoralen,the characteristic bands by spectral assignment as well as the bands by interval partial least squares(iPLS)and synergy interval partial least squares(siPLS)were used to establish partial least squares(PLS)model.The coefficient of determination in calibration(R^(2)_(cal))were 0.9987,0.9970 and 0.9982.The coefficient of determination in cross validation(R^(2)_(val)) T were 0.9985,0.9921 and 0.9982.The coe±cient of determination in prediction(R^(2)_(pre)) T were 0.9987,0.9955 and 0.9988.The root mean square error of calibration(RMSEC)were 0.27,0.40 and 0.31 ppm.The root mean square error of cross validation(RMSECV)were 0.30,0.67 and 0.32 ppm.The root mean square error of prediction(RMSEP)were 0.23,0.43 and 0.22 ppm.The residual predictive deviation(RPD)were 31.00,16.58 and 32.41.It turned out that the characteristic bands by spectral assignment had the same results with the chemometrics methods in PLS model.It provided guidance for NIR spectral assignment of chemical compositions in Chinese Materia Medica(CMM).
