In this paper,we consider the stochastic differential equations with piecewise continuous arguments(SDEPCAs)in which the drift coefficient satisfies the generalized one-sided Lipschitz condition and the diffusion coef...In this paper,we consider the stochastic differential equations with piecewise continuous arguments(SDEPCAs)in which the drift coefficient satisfies the generalized one-sided Lipschitz condition and the diffusion coefficient satisfies the linear growth condition.Since the delay term t-[t]of SDEPCAs is not continuous and differentiable,the variable substitution method is not suitable.To overcome this dificulty,we adopt new techniques to prove the boundedness of the exact solution and the numerical solution.It is proved that the truncated Euler-Maruyama method is strongly convergent to SDEPCAs in the sense of L'(q≥2).We obtain the convergence order with some additional conditions.An example is presented to illustrate the analytical theory.展开更多
In this paper,we develop the truncated Euler-Maruyama(EM)method for stochastic differential equations with piecewise continuous arguments(SDEPCAs),and consider the strong convergence theory under the local Lipschitz c...In this paper,we develop the truncated Euler-Maruyama(EM)method for stochastic differential equations with piecewise continuous arguments(SDEPCAs),and consider the strong convergence theory under the local Lipschitz condition plus the Khasminskii-type condition.The order of convergence is obtained.Moreover,we show that the truncated EM method can preserve the exponential mean square stability of SDEPCAs.Numerical examples are provided to support our conclusions.展开更多
Surface-enhanced Raman spectroscopy(SERS)-based bioanalytical technique involves the interaction of SERS-active substrate with complex environment,which has aroused intensive research interests.Compared to the commonl...Surface-enhanced Raman spectroscopy(SERS)-based bioanalytical technique involves the interaction of SERS-active substrate with complex environment,which has aroused intensive research interests.Compared to the commonly used Au SERS substrates,Ag nanocrystals have larger optical absorption cross section and acceptable price,but they possess poor oxidation resistance and potential biotoxicity,and the occurrence of unnecessary chemical reactions is inevitable due to the direct contact with probe molecules.Herein,we report a graphene-isolated AuAg nanocrystal(GIAAN)with the SERS-active AuAg core confined in a nanospace of few-layer graphene shell,which possesses unique Raman peaks,high SERS activity,excellent stability,superior fluorescence quenching performance and good biocompatibility.Based on the limited solubility of GIAAN in water and organic solvents,it is able to spontaneously generate interfacial self-assembled GIAAN(ISA-GIAAN)film at immiscible two-phase interfaces without any inducer,and multiphase Raman analysis of both water-and lipid-soluble drug model molecules is further achieved.Moreover,the GIAAN is further non-covalently functionalized with polyoxyethylenestearyl ether(C18-PEG)to acquire GIAAN@PEG with good water-solubility for SERS quantitative analysis in homogeneous system and multimodal Raman imaging of MCF-7 cells.We expect the versatile GIAAN holds great potential to monitor drug metabolism and guide intended drug delivery in clinic trials.展开更多
基金supported by the National Natural Science Foundation of China(Nos.11671113,12071101).
文摘In this paper,we consider the stochastic differential equations with piecewise continuous arguments(SDEPCAs)in which the drift coefficient satisfies the generalized one-sided Lipschitz condition and the diffusion coefficient satisfies the linear growth condition.Since the delay term t-[t]of SDEPCAs is not continuous and differentiable,the variable substitution method is not suitable.To overcome this dificulty,we adopt new techniques to prove the boundedness of the exact solution and the numerical solution.It is proved that the truncated Euler-Maruyama method is strongly convergent to SDEPCAs in the sense of L'(q≥2).We obtain the convergence order with some additional conditions.An example is presented to illustrate the analytical theory.
基金This work is supported by the National Natural Science Foundation of China(No.11671113)the National Postdoctoral Program for Innovative Talents(No.BX20180347).
文摘In this paper,we develop the truncated Euler-Maruyama(EM)method for stochastic differential equations with piecewise continuous arguments(SDEPCAs),and consider the strong convergence theory under the local Lipschitz condition plus the Khasminskii-type condition.The order of convergence is obtained.Moreover,we show that the truncated EM method can preserve the exponential mean square stability of SDEPCAs.Numerical examples are provided to support our conclusions.
基金the Hunan Provincial Natural Science Foundation of China(Nos.2020RC4017,2018JJ1007)the Science and Technology Development Fund,Macao(No.196/2017/A3).
文摘Surface-enhanced Raman spectroscopy(SERS)-based bioanalytical technique involves the interaction of SERS-active substrate with complex environment,which has aroused intensive research interests.Compared to the commonly used Au SERS substrates,Ag nanocrystals have larger optical absorption cross section and acceptable price,but they possess poor oxidation resistance and potential biotoxicity,and the occurrence of unnecessary chemical reactions is inevitable due to the direct contact with probe molecules.Herein,we report a graphene-isolated AuAg nanocrystal(GIAAN)with the SERS-active AuAg core confined in a nanospace of few-layer graphene shell,which possesses unique Raman peaks,high SERS activity,excellent stability,superior fluorescence quenching performance and good biocompatibility.Based on the limited solubility of GIAAN in water and organic solvents,it is able to spontaneously generate interfacial self-assembled GIAAN(ISA-GIAAN)film at immiscible two-phase interfaces without any inducer,and multiphase Raman analysis of both water-and lipid-soluble drug model molecules is further achieved.Moreover,the GIAAN is further non-covalently functionalized with polyoxyethylenestearyl ether(C18-PEG)to acquire GIAAN@PEG with good water-solubility for SERS quantitative analysis in homogeneous system and multimodal Raman imaging of MCF-7 cells.We expect the versatile GIAAN holds great potential to monitor drug metabolism and guide intended drug delivery in clinic trials.
