Let f be a twice continuously differentiable self-mapping of a unit disk satisfying Poisson differential inequality |△f(z)| ≤ B · |Df(z)|^(2) for some B > 0 and f(0) = 0. In this note, we show that f does no...Let f be a twice continuously differentiable self-mapping of a unit disk satisfying Poisson differential inequality |△f(z)| ≤ B · |Df(z)|^(2) for some B > 0 and f(0) = 0. In this note, we show that f does not always satisfy the Schwarz-Pick type inequality (1-|z|^(2))/(1-|f(z)|^(2))≤ C(B),where C(B) is a constant depending only on B. Moreover, a more general Schwarz-Pick type inequality for mapping that satisfies general Poisson differential inequality is established under certain conditions.展开更多
In this article, we introduce some results with respect to the integrality and exact solutions of some 2nd order algebraic DEs. We obtain the sufficient and necessary conditions of integrable and the general meromorph...In this article, we introduce some results with respect to the integrality and exact solutions of some 2nd order algebraic DEs. We obtain the sufficient and necessary conditions of integrable and the general meromorphic solutions of these equations by the complex method, which improves the corresponding results obtained by many authors. Our results show that the complex method provides a powerful mathematical tool for solving a large number of nonlinear partial differential equations in mathematical physics.展开更多
In this paper, we use the complex method to obtain all meromorphic solu- tions of the complex Zakharov-Kuznetsov modified equal width equation, then find the exact traveling wave solutions of the Zakharov-Kuznetsov mo...In this paper, we use the complex method to obtain all meromorphic solu- tions of the complex Zakharov-Kuznetsov modified equal width equation, then find the exact traveling wave solutions of the Zakharov-Kuznetsov modified equal width equation. At last, we give some computer simulations to illustrate our main results.展开更多
Railway passenger flow forecasting is an important basis for scientific dispatching of railway transportation. In order to remedy the shortcomings of one single time series prediction method for passenger flow, a mode...Railway passenger flow forecasting is an important basis for scientific dispatching of railway transportation. In order to remedy the shortcomings of one single time series prediction method for passenger flow, a model of combining autoregressive integrated moving average (ARIMA) with extreme learning machine (ELM) based on wavelet transform, named WAADE is presented in this paper. Firstly, the complex railway passenger flow time series was decomposed into linear and non-linear components by wavelet transform. Then, the decomposed linear and non-linear components were predicted by using ARIMA and ELM respectively. Finally, the final prediction results were obtained through fusing the linear and nonlinear prediction results by wavelet transform once again. At the same time, considering the obvious seasonal and periodic regularity of the railway passenger flow data, a WAADES model was constructed combined the WAADE model with the seasonal model based on the entropy value method. The experimental results show that the prediction accuracy of proposed WAADE and WAADES model is higher than the one of the ARIMA or ELM or seasonal model when used alone. Because of the combination of seasonal characteristics, the prediction accuracy of WAADES model is higher than that of WAADE model. The effectiveness and superiority of the two combined models proposed are proved.展开更多
Let ■:=Hn x C^n be the Siegel-type nilpotent group,which can be identified as the Shilov boundary of Siegel domain of typeⅡ,where Hn denotes the set of all n x n Hermitian matrices.In this article,we use singular co...Let ■:=Hn x C^n be the Siegel-type nilpotent group,which can be identified as the Shilov boundary of Siegel domain of typeⅡ,where Hn denotes the set of all n x n Hermitian matrices.In this article,we use singular convolution operators to define Radon transform on ■ and obtain the inversion formulas of Radon transforms.Moveover,we show that Radon transform on ■ is a unitary operator from Sobolev space W^n,2 into L^2(■).展开更多
Reticular crack is generally found on the surface of ceramic material that has been subjected to a thermal-shock condition. In the present study, a quantitative effect of thermal shock and quench temperature has been ...Reticular crack is generally found on the surface of ceramic material that has been subjected to a thermal-shock condition. In the present study, a quantitative effect of thermal shock and quench temperature has been studied and investigated. Experimental tests were carried out to characterize the reticular crack that has been found in the Ge Kiln, which is a famous art of the ancient Chinese culture. After comparative analysis between thermal-shock cracks and the glaze crack patterns of the Ge Kiln porcelain,it is found that this study is expected to provide a powerful tool for recurrence of the long-lost firing and cooling process of the Ge Kiln porcelain.展开更多
基金supported by NNSF of China(11701111)NNSFs of Guangdong Province (2016A030310257 and 2015A030313346)the Visiting Scholar Program of Chern Institute of Mathematics at Nankai University when the authors worked as visiting scholars。
文摘Let f be a twice continuously differentiable self-mapping of a unit disk satisfying Poisson differential inequality |△f(z)| ≤ B · |Df(z)|^(2) for some B > 0 and f(0) = 0. In this note, we show that f does not always satisfy the Schwarz-Pick type inequality (1-|z|^(2))/(1-|f(z)|^(2))≤ C(B),where C(B) is a constant depending only on B. Moreover, a more general Schwarz-Pick type inequality for mapping that satisfies general Poisson differential inequality is established under certain conditions.
基金supported by the Visiting Scholar Program of Chern Institute of Mathematics at Nankai Universitythe support with the NSF of China (No. 11271090, 11326083)+2 种基金NSF of Guangdong Province (S2012010010121)Shanghai university young teacher training program (ZZSDJ12020)projects 10XKJ01, 12C401 and 12C104 from the Leading Academic Discipline Project of Shanghai Dianji University
文摘In this article, we introduce some results with respect to the integrality and exact solutions of some 2nd order algebraic DEs. We obtain the sufficient and necessary conditions of integrable and the general meromorphic solutions of these equations by the complex method, which improves the corresponding results obtained by many authors. Our results show that the complex method provides a powerful mathematical tool for solving a large number of nonlinear partial differential equations in mathematical physics.
基金supported by NSF of China (11271090)NSF of Guangdong (2016A030310257 and 2015A030313346)
文摘In this paper, we use the complex method to obtain all meromorphic solu- tions of the complex Zakharov-Kuznetsov modified equal width equation, then find the exact traveling wave solutions of the Zakharov-Kuznetsov modified equal width equation. At last, we give some computer simulations to illustrate our main results.
基金the National Natural Science Foundation of China (Grant Nos. 11862003, 81860635, 11462003)the Key Project of Guangxi Natural Science Foundation (Grant No. 2017GXNSFDA198038)+1 种基金the Project of Guangxi Natural Science Foundation (Grant No. 2018JJA110023)the Project for Promotion of Young and Middle-aged Teachers’ Basic Scientific Research Ability in Guangxi Universities (Grant No. 2019KY0084), Guangxi “Bagui Scholar” Teams for Innovation and Research Project.
文摘Railway passenger flow forecasting is an important basis for scientific dispatching of railway transportation. In order to remedy the shortcomings of one single time series prediction method for passenger flow, a model of combining autoregressive integrated moving average (ARIMA) with extreme learning machine (ELM) based on wavelet transform, named WAADE is presented in this paper. Firstly, the complex railway passenger flow time series was decomposed into linear and non-linear components by wavelet transform. Then, the decomposed linear and non-linear components were predicted by using ARIMA and ELM respectively. Finally, the final prediction results were obtained through fusing the linear and nonlinear prediction results by wavelet transform once again. At the same time, considering the obvious seasonal and periodic regularity of the railway passenger flow data, a WAADES model was constructed combined the WAADE model with the seasonal model based on the entropy value method. The experimental results show that the prediction accuracy of proposed WAADE and WAADES model is higher than the one of the ARIMA or ELM or seasonal model when used alone. Because of the combination of seasonal characteristics, the prediction accuracy of WAADES model is higher than that of WAADE model. The effectiveness and superiority of the two combined models proposed are proved.
基金The authors would like to express their deep thanks to the referees for their very careful reading and useful comments which do improve the presentation of this articleThis work was partially supported by the Natural Science Foundation of Xinjiang Uygur Autonomous Region(Grant Nos.2019D01C049,62008031,042312023)the National Natural Science Foundation of China(Grant Nos.11671414,11501131).
文摘Let ■:=Hn x C^n be the Siegel-type nilpotent group,which can be identified as the Shilov boundary of Siegel domain of typeⅡ,where Hn denotes the set of all n x n Hermitian matrices.In this article,we use singular convolution operators to define Radon transform on ■ and obtain the inversion formulas of Radon transforms.Moveover,we show that Radon transform on ■ is a unitary operator from Sobolev space W^n,2 into L^2(■).
基金supported by the National Natural Science Foundation of China(Grant No.11272313)
文摘Reticular crack is generally found on the surface of ceramic material that has been subjected to a thermal-shock condition. In the present study, a quantitative effect of thermal shock and quench temperature has been studied and investigated. Experimental tests were carried out to characterize the reticular crack that has been found in the Ge Kiln, which is a famous art of the ancient Chinese culture. After comparative analysis between thermal-shock cracks and the glaze crack patterns of the Ge Kiln porcelain,it is found that this study is expected to provide a powerful tool for recurrence of the long-lost firing and cooling process of the Ge Kiln porcelain.
