This paper aims to investigate the tamed Euler method for the random periodic solution of semilinear SDEs with one-sided Lipschitz coefficient.We introduce a novel approach to analyze mean-square error bounds of the n...This paper aims to investigate the tamed Euler method for the random periodic solution of semilinear SDEs with one-sided Lipschitz coefficient.We introduce a novel approach to analyze mean-square error bounds of the novel schemes,without relying on a priori high-order moment bound of the numerical approximation.The expected order-one mean square convergence is attained for the proposed scheme.Moreover,a numerical example is presented to verify our theoretical analysis.展开更多
In this paper we study the L^(p)-convergence rate of the tamed Euler scheme for scalar stochastic differential equations(SDEs)with piecewise continuous drift coefficient.More precisely,under the assumptions that the d...In this paper we study the L^(p)-convergence rate of the tamed Euler scheme for scalar stochastic differential equations(SDEs)with piecewise continuous drift coefficient.More precisely,under the assumptions that the drift coefficient is piecewise continuous and polynomially growing and that the diffusion coefficient is Lipschitz continuous and non-zero at the discontinuity points of the drift coefficient,we show that the SDE has a unique strong solution and the L^(p)-convergence order of the tamed Euler scheme is at least 1/2 for all p∈[1,∞).Moreover,a numerical example is provided to support our conclusion.展开更多
The"corridor"constructed jointly by multi-nationalities provides a space of cultural dissemination for the Legend of King Yu Tamed the Flood the in Hexi Corridor.Legend of King Yu Tamed the Flood spreads on ...The"corridor"constructed jointly by multi-nationalities provides a space of cultural dissemination for the Legend of King Yu Tamed the Flood the in Hexi Corridor.Legend of King Yu Tamed the Flood spreads on the flowing cultural"corridor",relying on various narrative forms of cultural media.It deeply promotes the localization of the Legend of King Yu Tamed the Flood.The situation of integration and harmony between ethnic groups and Common value orientation of multi-ethnic humanities and religions are explored and taken through the multicultural elements embedded in the legend so that the"cultural integration"hidden in the legends and stories can emerge.展开更多
In this paper,we introduce a new class of explicit numerical methods called the tamed stochastic Runge-Kutta-Chebyshev(t-SRKC)methods,which apply the idea of taming to the stochastic Runge-Kutta-Chebyshev(SRKC)methods...In this paper,we introduce a new class of explicit numerical methods called the tamed stochastic Runge-Kutta-Chebyshev(t-SRKC)methods,which apply the idea of taming to the stochastic Runge-Kutta-Chebyshev(SRKC)methods.The key advantage of our explicit methods is that they can be suitable for stochastic differential equations with non-globally Lipschitz coefficients and stiffness.Under certain non-globally Lipschitz conditions,we study the strong convergence of our methods and prove that the order of strong convergence is 1/2.To show the advantages of our methods,we compare them with some existing explicit methods(including the Euler-Maruyama method,balanced Euler-Maruyama method and two types of SRKC methods)through several numerical examples.The numerical results show that our t-SRKC methods are efficient,especially for stiff stochastic differential equations.展开更多
In the sweltering heat of summer,a visitor to Nugusitai Town of Tongliao City,Inner Mongolia Autonomous Region,might find it hard to recognise the landscape.Once a desolate expanse of drifting sand,the hillsides are n...In the sweltering heat of summer,a visitor to Nugusitai Town of Tongliao City,Inner Mongolia Autonomous Region,might find it hard to recognise the landscape.Once a desolate expanse of drifting sand,the hillsides are now cloaked in lush forest.Tall wind turbines rotate quietly,and wetlands glimmer between groves of forest,providing a haven for waterfowl.展开更多
In this paper,we will discuss the almost global existence result for d-dimensional fractional nonlinear Schrodinger equation on flat torus,which is based on BNF technique,the tame property and the analysis of the spec...In this paper,we will discuss the almost global existence result for d-dimensional fractional nonlinear Schrodinger equation on flat torus,which is based on BNF technique,the tame property and the analysis of the spectrum of(-Δ)^(s).展开更多
油页岩热解过程中产生大量的高质量浓度含酚废水无法排放,文中采用溶剂萃取法,以甲基叔戊基醚(TAME)为溶剂,针对页岩油含酚废水的处理进行初步研究。通过实验和Aspen P lus软件模拟相结合来考察TAME的萃取脱酚性能,研究了不同温度和相...油页岩热解过程中产生大量的高质量浓度含酚废水无法排放,文中采用溶剂萃取法,以甲基叔戊基醚(TAME)为溶剂,针对页岩油含酚废水的处理进行初步研究。通过实验和Aspen P lus软件模拟相结合来考察TAME的萃取脱酚性能,研究了不同温度和相比条件下错、逆流萃取流程的分离性能。结果表明:TAME的脱酚能力很强,对苯酚的分配系数在40—60之间,pH值在2—10时萃取率达95%以上。此外比较了错、逆流3级萃取工艺,综合考虑萃取效果和溶剂用量,逆流多级萃取远远优于错流多级萃取,塔内3级萃取相比为2时出口废水酚质量浓度可降到1 mg/L以下,且受温度影响不明显。可见TAME的脱酚性能优异,在酸碱性体系中均适用,同时TAME原料易得,成本较低,可以作为含酚废水萃取工艺的萃取剂。展开更多
基金supported by the National Natural Science Foundation of China(Nos.12471394,12371417)Natural Science Foundation of Changsha(No.kq2502101)。
文摘This paper aims to investigate the tamed Euler method for the random periodic solution of semilinear SDEs with one-sided Lipschitz coefficient.We introduce a novel approach to analyze mean-square error bounds of the novel schemes,without relying on a priori high-order moment bound of the numerical approximation.The expected order-one mean square convergence is attained for the proposed scheme.Moreover,a numerical example is presented to verify our theoretical analysis.
基金supported by the National Natural Science Foundation of China(Nos.12371417,11971488)。
文摘In this paper we study the L^(p)-convergence rate of the tamed Euler scheme for scalar stochastic differential equations(SDEs)with piecewise continuous drift coefficient.More precisely,under the assumptions that the drift coefficient is piecewise continuous and polynomially growing and that the diffusion coefficient is Lipschitz continuous and non-zero at the discontinuity points of the drift coefficient,we show that the SDE has a unique strong solution and the L^(p)-convergence order of the tamed Euler scheme is at least 1/2 for all p∈[1,∞).Moreover,a numerical example is provided to support our conclusion.
基金Graduate Project of the Central Universities Basic Research Funds of Northwest Minzu University in 2021(Yxm2021012).
文摘The"corridor"constructed jointly by multi-nationalities provides a space of cultural dissemination for the Legend of King Yu Tamed the Flood the in Hexi Corridor.Legend of King Yu Tamed the Flood spreads on the flowing cultural"corridor",relying on various narrative forms of cultural media.It deeply promotes the localization of the Legend of King Yu Tamed the Flood.The situation of integration and harmony between ethnic groups and Common value orientation of multi-ethnic humanities and religions are explored and taken through the multicultural elements embedded in the legend so that the"cultural integration"hidden in the legends and stories can emerge.
基金supported by the National Natural Science Foundation of China(Grant Nos.12101525,12071403)by the Natural Science Foundation of Hunan Province of China(Grant No.2023JJ40615)+1 种基金by the Research Foundation of Education Department of Hunan Province of China(Grant No.21A0108)by the Research Initiation Fund Project of Xiangtan University(Grant No.21QDZ16).
文摘In this paper,we introduce a new class of explicit numerical methods called the tamed stochastic Runge-Kutta-Chebyshev(t-SRKC)methods,which apply the idea of taming to the stochastic Runge-Kutta-Chebyshev(SRKC)methods.The key advantage of our explicit methods is that they can be suitable for stochastic differential equations with non-globally Lipschitz coefficients and stiffness.Under certain non-globally Lipschitz conditions,we study the strong convergence of our methods and prove that the order of strong convergence is 1/2.To show the advantages of our methods,we compare them with some existing explicit methods(including the Euler-Maruyama method,balanced Euler-Maruyama method and two types of SRKC methods)through several numerical examples.The numerical results show that our t-SRKC methods are efficient,especially for stiff stochastic differential equations.
文摘In the sweltering heat of summer,a visitor to Nugusitai Town of Tongliao City,Inner Mongolia Autonomous Region,might find it hard to recognise the landscape.Once a desolate expanse of drifting sand,the hillsides are now cloaked in lush forest.Tall wind turbines rotate quietly,and wetlands glimmer between groves of forest,providing a haven for waterfowl.
基金Supported by the National Natural Science Foundation of China(12101542,12371189,12371241).
文摘In this paper,we will discuss the almost global existence result for d-dimensional fractional nonlinear Schrodinger equation on flat torus,which is based on BNF technique,the tame property and the analysis of the spectrum of(-Δ)^(s).
文摘油页岩热解过程中产生大量的高质量浓度含酚废水无法排放,文中采用溶剂萃取法,以甲基叔戊基醚(TAME)为溶剂,针对页岩油含酚废水的处理进行初步研究。通过实验和Aspen P lus软件模拟相结合来考察TAME的萃取脱酚性能,研究了不同温度和相比条件下错、逆流萃取流程的分离性能。结果表明:TAME的脱酚能力很强,对苯酚的分配系数在40—60之间,pH值在2—10时萃取率达95%以上。此外比较了错、逆流3级萃取工艺,综合考虑萃取效果和溶剂用量,逆流多级萃取远远优于错流多级萃取,塔内3级萃取相比为2时出口废水酚质量浓度可降到1 mg/L以下,且受温度影响不明显。可见TAME的脱酚性能优异,在酸碱性体系中均适用,同时TAME原料易得,成本较低,可以作为含酚废水萃取工艺的萃取剂。
