The aim of the paper is to study the properties of positive classical solutions to the fractional Laplace equation with the singular term.Using the extension method,we prove the nonexistence and symmetric of solutions...The aim of the paper is to study the properties of positive classical solutions to the fractional Laplace equation with the singular term.Using the extension method,we prove the nonexistence and symmetric of solutions to the singular fractional equation.展开更多
In this paper we study the critical fractional equation with a parameter λ and establish uniform lower bounds for Λ, which is the supremum of the set of λ, related to the existence of positive solutions of the crit...In this paper we study the critical fractional equation with a parameter λ and establish uniform lower bounds for Λ, which is the supremum of the set of λ, related to the existence of positive solutions of the critical fractional equation.展开更多
The present work aims to establish a fractional-order generalized themoelastic diffusion theory for anisotropic and linearly thermoelastic diffusive media. To numerically handle the multi-physics problems expressed by...The present work aims to establish a fractional-order generalized themoelastic diffusion theory for anisotropic and linearly thermoelastic diffusive media. To numerically handle the multi-physics problems expressed by a sequence of incomplete differential equations, particularly by a fractional equation, a generalized variational principle is obtained for the unified theory using a semi-inverse method. In numerical implementation, the dynamic response of a semi-infinite medium with one end subjected to a thermal shock and a chemical potential shock is investigated using the Laplace transform. Numerical results, i.e., non-dimensional temperature, chemical potential, and displacement, are presented graphically. The influence of the fractional order parameter on them is evaluated and discussed.展开更多
As the theory of the fractional order differential equation becomes mature gradually, the fractional order neural networks become a new hotspot.The robust stability of a class of fractional order Hopfield neural netwo...As the theory of the fractional order differential equation becomes mature gradually, the fractional order neural networks become a new hotspot.The robust stability of a class of fractional order Hopfield neural network with the Caputo derivative is investigated in this paper. The sufficient conditions to guarantee the robust stability of the fractional order Hopfield neural networks are derived by making use of the property of the Mittag-Leffler function, comparison theorem for the fractional order system, and method of the Laplace integral transform. Furthermore, a numerical simulation example is given to illustrate the correctness and effectiveness of our results.展开更多
We give the direct method of moving planes for solutions to the conformally invariant fractional power sub Laplace equation on the Heisenberg group.The method is based on four maximum principles derived here.Then symm...We give the direct method of moving planes for solutions to the conformally invariant fractional power sub Laplace equation on the Heisenberg group.The method is based on four maximum principles derived here.Then symmetry and nonexistence of positive cylindrical solutions are proved.展开更多
In cancer clinical trials and other medical studies, both longitudinal measurements and data on a time to an event(survival time) are often collected from the same patients. Joint analyses of these data would improve ...In cancer clinical trials and other medical studies, both longitudinal measurements and data on a time to an event(survival time) are often collected from the same patients. Joint analyses of these data would improve the efficiency of the statistical inferences. We propose a new joint model for the longitudinal proportional measurements which are restricted in a finite interval and survival times with a potential cure fraction. A penalized joint likelihood is derived based on the Laplace approximation and a semiparametric procedure based on this likelihood is developed to estimate the parameters in the joint model. A simulation study is performed to evaluate the statistical properties of the proposed procedures. The proposed model is applied to data from a clinical trial on early breast cancer.展开更多
基金supported by the Key Scientific Research Project of the Colleges and Universities in Henan Province(No.22A110013)the Key Specialized Research and Development Breakthrough Program in Henan Province(No.222102310265)+1 种基金the Natural Science Foundation of Henan Province of China(No.222300420499)the Cultivation Foundation of National Natural Science Foundation of Huanghuai University(No.XKPY-202008).
文摘The aim of the paper is to study the properties of positive classical solutions to the fractional Laplace equation with the singular term.Using the extension method,we prove the nonexistence and symmetric of solutions to the singular fractional equation.
基金supported by National Natural Science Foundation of China(11871315)Natural Science Foundation of Shanxi Province of China(201901D111021)。
文摘In this paper we study the critical fractional equation with a parameter λ and establish uniform lower bounds for Λ, which is the supremum of the set of λ, related to the existence of positive solutions of the critical fractional equation.
文摘The present work aims to establish a fractional-order generalized themoelastic diffusion theory for anisotropic and linearly thermoelastic diffusive media. To numerically handle the multi-physics problems expressed by a sequence of incomplete differential equations, particularly by a fractional equation, a generalized variational principle is obtained for the unified theory using a semi-inverse method. In numerical implementation, the dynamic response of a semi-infinite medium with one end subjected to a thermal shock and a chemical potential shock is investigated using the Laplace transform. Numerical results, i.e., non-dimensional temperature, chemical potential, and displacement, are presented graphically. The influence of the fractional order parameter on them is evaluated and discussed.
基金supported by the Natural Science Foundation of Shandong Province under Grant No.ZR2014AM006
文摘As the theory of the fractional order differential equation becomes mature gradually, the fractional order neural networks become a new hotspot.The robust stability of a class of fractional order Hopfield neural network with the Caputo derivative is investigated in this paper. The sufficient conditions to guarantee the robust stability of the fractional order Hopfield neural networks are derived by making use of the property of the Mittag-Leffler function, comparison theorem for the fractional order system, and method of the Laplace integral transform. Furthermore, a numerical simulation example is given to illustrate the correctness and effectiveness of our results.
基金supported by the National Natural Science Foundation of China(No.11771354)。
文摘We give the direct method of moving planes for solutions to the conformally invariant fractional power sub Laplace equation on the Heisenberg group.The method is based on four maximum principles derived here.Then symmetry and nonexistence of positive cylindrical solutions are proved.
基金supported by the Fundamental Research Funds for the Central Universities of ChinaNational Natural Science Foundation of China (Grant No. 11601060)+1 种基金Dalian High Level Talent Innovation Programme (Grant No.2015R051)Research Grants from Natural Sciences and Engineering Research Council of Canada
文摘In cancer clinical trials and other medical studies, both longitudinal measurements and data on a time to an event(survival time) are often collected from the same patients. Joint analyses of these data would improve the efficiency of the statistical inferences. We propose a new joint model for the longitudinal proportional measurements which are restricted in a finite interval and survival times with a potential cure fraction. A penalized joint likelihood is derived based on the Laplace approximation and a semiparametric procedure based on this likelihood is developed to estimate the parameters in the joint model. A simulation study is performed to evaluate the statistical properties of the proposed procedures. The proposed model is applied to data from a clinical trial on early breast cancer.
