In this paper, Laplace decomposition method (LDM) and Pade approximant are employed to find approximate solutions for the Whitham-Broer-Kaup shallow water model, the coupled nonlinear reaction diffusion equations and ...In this paper, Laplace decomposition method (LDM) and Pade approximant are employed to find approximate solutions for the Whitham-Broer-Kaup shallow water model, the coupled nonlinear reaction diffusion equations and the system of Hirota-Satsuma coupled KdV. In addition, the results obtained from Laplace decomposition method (LDM) and Pade approximant are compared with corresponding exact analytical solutions.展开更多
A barrier option valuation model with stochastic barrier which was regarded as the main feature of the model was developed under the Hull-White interest rate model.The purpose of this study was to deal with the stocha...A barrier option valuation model with stochastic barrier which was regarded as the main feature of the model was developed under the Hull-White interest rate model.The purpose of this study was to deal with the stochastic barrier by means of partial differential equation methods and then derive the exact analytical solutions of the barrier options.Furthermore,a numerical example was given to show how to apply this model to pricing one structured product in realistic market.Therefore,this model can provide new insight for future research on structured products involving barrier options.展开更多
藏东-川西生态维护水源涵养区位于西南高山峡谷区北部,是中国典型的生态脆弱区,生态系统抗干扰能力差,对气候变化的反应敏感。产水量是生态系统服务中的一项重要功能,研究产水量空间分布特征及其影响因子对该地区水资源保护、涵养,开发...藏东-川西生态维护水源涵养区位于西南高山峡谷区北部,是中国典型的生态脆弱区,生态系统抗干扰能力差,对气候变化的反应敏感。产水量是生态系统服务中的一项重要功能,研究产水量空间分布特征及其影响因子对该地区水资源保护、涵养,开发和利用有重要意义。基于2000—2020年地表覆盖产品、气候、基岩深度、土壤和地形等数据,运用InVEST模型Annual Water Yield模块模拟了藏东-川西地区产水量;结合地理探测器(GDM)分析了造成产水量空间分异的各因子的解释能力;对q>0.1的因子引入多尺度地理加权回归(MGWR)分析它们对研究区不同地理位置产水量的影响程度,并运用Theil-Sen趋势分析、Mann-Kendall显著性检验得到了产水量及其主导因素时空变化特征;同时利用Hurst指数预测了未来短期内产水量上升或下降趋势和评估了研究时段内产水量在不同空间位置的波动水平。结果表明:1)降水量和产水量空间分布在研究区内呈现“东西高,中部低”的分布格局,岷江流域降水量为最大,金沙江流域蒸散水平最高,怒江流域产水量领先其余三个流域;2)除降水量和蒸散发外,藏东-川西地区产水量主要影响因子有气候因子(年均湿度和年均风速)、地形因子(高程)、土壤类型、植被因子(归一化植被指数和净初级生产力)与社会因子(地表覆盖类型和人类活动强度指数);其中降水量、蒸散发、高程、归一化植被指数、净初级生产力和地表覆盖类型是产水量的主导影响因素。3)降水、高程与人类活动强度指数对产水服务的影响有较强的正向作用,而蒸散发、归一化植被指数和净初级生产力展现出较强的负向作用。4)研究区南部区域产水量波动水平高。在未来短期内,研究区95.30%的区域有下降趋势。5)藏东-川西地区不应将盲目提升人工植被覆盖度作为提高产水量首要方案,应注意对天然林的保护和预防石漠化。展开更多
文章以河谷城市甘肃省兰州市为例,在测度“三生”空间冲突强度并揭示多尺度分异机制的基础上提出冲突协调策略。结果显示:①“三生”空间格局演化与地域分异显著。生活空间的增加主要源于对生态空间和生产空间的侵占。②兰州市“三生”...文章以河谷城市甘肃省兰州市为例,在测度“三生”空间冲突强度并揭示多尺度分异机制的基础上提出冲突协调策略。结果显示:①“三生”空间格局演化与地域分异显著。生活空间的增加主要源于对生态空间和生产空间的侵占。②兰州市“三生”空间冲突时空演化与地类分异显著。时序上,“三生”空间冲突强度呈持续上升态势,整体处于基本可控级别;空间上,形成了“一心、两翼、多轴带”的空间冲突格局;就地类而言,城镇的生活空间与生产空间冲突水平较高。③兰州市“三生”空间冲突影响因素尺度效应和异质性明显。高程、坡度、地形起伏度等对“三生”空间冲突具有抑制作用;人口密度、人均G D P、夜间灯光指数等因素加剧了区域“三生”空间冲突程度。展开更多
This paper is concerned with a low-dimensional dynamical system model for analytically solving partial differential equations(PDEs).The model proposed is based on a posterior optimal truncated weighted residue(POT-WR)...This paper is concerned with a low-dimensional dynamical system model for analytically solving partial differential equations(PDEs).The model proposed is based on a posterior optimal truncated weighted residue(POT-WR)method,by which an infinite dimensional PDE is optimally truncated and analytically solved in required condition of accuracy.To end that,a POT-WR condition for PDE under consideration is used as a dynamically optimal control criterion with the solving process.A set of bases needs to be constructed without any reference database in order to establish a space to describe low-dimensional dynamical system that is required.The Lagrangian multiplier is introduced to release the constraints due to the Galerkin projection,and a penalty function is also employed to remove the orthogonal constraints.According to the extreme principle,a set of ordinary differential equations is thus obtained by taking the variational operation of the generalized optimal function.A conjugate gradient algorithm by FORTRAN code is developed to solve the ordinary differential equations.The two examples of one-dimensional heat transfer equation and nonlinear Burgers’equation show that the analytical results on the method proposed are good agreement with the numerical simulations and analytical solutions in references,and the dominant characteristics of the dynamics are well captured in case of few bases used only.展开更多
文摘In this paper, Laplace decomposition method (LDM) and Pade approximant are employed to find approximate solutions for the Whitham-Broer-Kaup shallow water model, the coupled nonlinear reaction diffusion equations and the system of Hirota-Satsuma coupled KdV. In addition, the results obtained from Laplace decomposition method (LDM) and Pade approximant are compared with corresponding exact analytical solutions.
基金National Natural Science Foundations of China(Nos.11471175,11171221)
文摘A barrier option valuation model with stochastic barrier which was regarded as the main feature of the model was developed under the Hull-White interest rate model.The purpose of this study was to deal with the stochastic barrier by means of partial differential equation methods and then derive the exact analytical solutions of the barrier options.Furthermore,a numerical example was given to show how to apply this model to pricing one structured product in realistic market.Therefore,this model can provide new insight for future research on structured products involving barrier options.
文摘藏东-川西生态维护水源涵养区位于西南高山峡谷区北部,是中国典型的生态脆弱区,生态系统抗干扰能力差,对气候变化的反应敏感。产水量是生态系统服务中的一项重要功能,研究产水量空间分布特征及其影响因子对该地区水资源保护、涵养,开发和利用有重要意义。基于2000—2020年地表覆盖产品、气候、基岩深度、土壤和地形等数据,运用InVEST模型Annual Water Yield模块模拟了藏东-川西地区产水量;结合地理探测器(GDM)分析了造成产水量空间分异的各因子的解释能力;对q>0.1的因子引入多尺度地理加权回归(MGWR)分析它们对研究区不同地理位置产水量的影响程度,并运用Theil-Sen趋势分析、Mann-Kendall显著性检验得到了产水量及其主导因素时空变化特征;同时利用Hurst指数预测了未来短期内产水量上升或下降趋势和评估了研究时段内产水量在不同空间位置的波动水平。结果表明:1)降水量和产水量空间分布在研究区内呈现“东西高,中部低”的分布格局,岷江流域降水量为最大,金沙江流域蒸散水平最高,怒江流域产水量领先其余三个流域;2)除降水量和蒸散发外,藏东-川西地区产水量主要影响因子有气候因子(年均湿度和年均风速)、地形因子(高程)、土壤类型、植被因子(归一化植被指数和净初级生产力)与社会因子(地表覆盖类型和人类活动强度指数);其中降水量、蒸散发、高程、归一化植被指数、净初级生产力和地表覆盖类型是产水量的主导影响因素。3)降水、高程与人类活动强度指数对产水服务的影响有较强的正向作用,而蒸散发、归一化植被指数和净初级生产力展现出较强的负向作用。4)研究区南部区域产水量波动水平高。在未来短期内,研究区95.30%的区域有下降趋势。5)藏东-川西地区不应将盲目提升人工植被覆盖度作为提高产水量首要方案,应注意对天然林的保护和预防石漠化。
文摘文章以河谷城市甘肃省兰州市为例,在测度“三生”空间冲突强度并揭示多尺度分异机制的基础上提出冲突协调策略。结果显示:①“三生”空间格局演化与地域分异显著。生活空间的增加主要源于对生态空间和生产空间的侵占。②兰州市“三生”空间冲突时空演化与地类分异显著。时序上,“三生”空间冲突强度呈持续上升态势,整体处于基本可控级别;空间上,形成了“一心、两翼、多轴带”的空间冲突格局;就地类而言,城镇的生活空间与生产空间冲突水平较高。③兰州市“三生”空间冲突影响因素尺度效应和异质性明显。高程、坡度、地形起伏度等对“三生”空间冲突具有抑制作用;人口密度、人均G D P、夜间灯光指数等因素加剧了区域“三生”空间冲突程度。
基金supported by Natural Science Foundation of China under Great Nos.11072053 and 11372068,and the National Basic Research Program of China under Grant No.2014CB74410.
文摘This paper is concerned with a low-dimensional dynamical system model for analytically solving partial differential equations(PDEs).The model proposed is based on a posterior optimal truncated weighted residue(POT-WR)method,by which an infinite dimensional PDE is optimally truncated and analytically solved in required condition of accuracy.To end that,a POT-WR condition for PDE under consideration is used as a dynamically optimal control criterion with the solving process.A set of bases needs to be constructed without any reference database in order to establish a space to describe low-dimensional dynamical system that is required.The Lagrangian multiplier is introduced to release the constraints due to the Galerkin projection,and a penalty function is also employed to remove the orthogonal constraints.According to the extreme principle,a set of ordinary differential equations is thus obtained by taking the variational operation of the generalized optimal function.A conjugate gradient algorithm by FORTRAN code is developed to solve the ordinary differential equations.The two examples of one-dimensional heat transfer equation and nonlinear Burgers’equation show that the analytical results on the method proposed are good agreement with the numerical simulations and analytical solutions in references,and the dominant characteristics of the dynamics are well captured in case of few bases used only.
