一类非线性人口偏微分模型整体解的存在惟一性

讨论了一类非线性人口偏微分模型整体经典解的存在惟一性,并研究了解的C1光滑性和解关于初值的连续依赖性.

基于数学偏微分算法的水稻插秧机控制系统优化

为进一步提升我国水稻插秧机的综合作业效率,以数学偏微分应用思维为改善切入点,针对整机控制系统展开优化研究。以充分分析插秧机各功能实现为基点,搭建数学偏微分模型,进行系统控制优化与整机部件改进,设计出全新的功能提升型水稻插秧机,实施插秧作业。试验结果表明:经数学偏微分算法及控制思维导入,水稻插秧机的整机核心作业参数得到显著提升,秧深精度与系统稳定度均可保持在93.00%以上,插秧合格率相对提升了8.58%,秧苗损失率可降低至0.45%,整机作业效率可达91.12%,符合水稻插秧机的设计标准及预期优化目标,具有较强的应用推广价值。

金融深化、空间溢出与经济增长——基于空间回归模型偏微分效应分解方法及中国的实证

利用中国2000～2011年分省面板数据，采用LeSageandPace（2009）提出的空间回归模型偏微分方法，衡量了金融深化对经济增长的区域内溢出、区域间溢出及总体空间溢出效应。研究发现，中国的区域经济增长存在显著的空间依赖性和空间异质性。金融深化对经济增长均存在正向的区域内溢出效应、区域问溢出效应和空间溢出效应，但在邻接和经济空间权重下其显著性并不高，且在地理距离权重下没有通过显著性检验。金融深化对经济增长的区域内溢出效应远大于区域间溢出效应。控制变量中。投资、外商直接投资对经济增长存在显著的正向空间溢出效应；而财政支出对经济增长的空间溢出效应为负。

具潜伏期的无免疫型传染病动力学的微分模型

对具潜伏期的无免疫型传染病进行讨论,给出一个常微分模型和一个偏微分模型．

带扩散种群模型的分析

考虑允许种群自身在其生存空间存在扩散的情况下,建立一个统一的偏微分模型来描述种群之间的三种关系。分别讨论了三类种群模型的动态变化过程。(1)如果捕食者疯狂猎杀被捕食者,则随着时间的推移,被捕食者因为过度被捕杀而灭绝,捕食者也由于食物的灭绝而灭绝。(2)很好地解释了生态学中的竞争排斥原理:若两种群的单个成员消耗的差不多相同,而环境能承受的种群u的最大容量比种群v大,那么种群v终将灭绝。(3)在强合作的情况下,种群数量会随着时间的增加急剧增加以致环境所允许的容量破坏生态系统的平衡,所以弱合作(相互之间的促进不是很强)比强合作更有利于保持生态系统的平衡.

一类改进的PDE模型在图像去噪和分割中的应用

利用变分原理研究了图像能量泛函的极小值问题所对应的一类改进的偏微分(PDE)模型.通过对偏微分方程的研究,从形式上分析得到方程的解即结果图像,在去噪后与初始图像有较小的偏差,很好地保持了初始图像所具有的特征.实验结果验证了这种分析结果的正确性,并且得到在去噪时间相同的条件下,结果图像要比以往的模型较好.在分割处理上,结果图像也有较好的分割效果.

城镇化、空间溢出与区域经济增长——基于空间回归模型偏微分方法及中国的实证

本文利用中国1995—2011年的分省数据,采用空间计量建模及估计技术,设置三种空间权重矩阵,构建多样化的空间面板数据模型,运用空间回归模型偏微分方法实证测度了城镇化对经济增长的空间溢出效应。研究发现:在不同的空间关联模式下,中国区域经济增长均具有显著的空间依赖性和空间异质性。在控制了资本、财政支出、国有化程度等变量后,城镇化对经济增长的区域内溢出为正,但在统计上不显著。城镇化的区域间溢出效应在不同的空间关联模式下不同,其中:在经济空间的关联模式下为正,在邻接、地理距离空间关联模式下为负。但在不同的空间关联模式下,城镇化对区域经济增长总体上具有正向的空间溢出效应。

长江经济带城市绿色经济绩效的溢出效应及其分解

生态文明视域下提升绿色经济绩效已经成为经济发展的根本要求和必然选择。本文基于长江经济带108个城市2003—2013年数据,使用非期望产出-超效率SBM模型对绿色经济绩效进行了测度,并进行了分区域比较;依据经济空间权重构建多种空间计量模型实证检验了长江经济带绿色经济绩效的空间溢出效应;运用空间回归模型偏微分方法对绿色经济绩效的影响因素及其溢出效应进行了检验与分解。研究结论表明:长江经济带绿色经济绩效的空间分布并不均衡,具有显著的空间依赖和空间集聚特征。经济发展水平越高的地区绿色经济绩效越高,经济发展水平越低的地区绿色经济绩效越低,而且具有高者愈高、低者愈低的演变趋势。长江经济带绿色经济绩效存在显著的空间溢出效应。区域内环境污染与经济发展水平之间存在"U"型关系,即"环境库兹涅茨假说"并不存在。资源禀赋对区域内绿色经济绩效提升具有显著的正向影响效应。产业结构升级的经济示范效应有助于增强绿色经济绩效的区域间正向溢出。技术进步对区域内绿色经济绩效提升没有起到应有的促进作用,但对区域间绿色经济绩效提升却起到了显著的抑制作用。外商直接投资对区域内、区域间绿色经济绩效提升都具有显著的负向溢出效应,即区域内、区域间均存在"污染天堂假说"。长江经济带"共抓大保护,不搞大开发",充分发挥地区间、城市间经济增长的空间溢出效应,努力提升技术进步、产业结构、外商直接投资等因素对绿色经济绩效的正向影响作用,有助于促进长江经济带绿色经济绩效的协同提升。

不良贷款、空间溢出与区域经济增长

利用2008-2016年的分省数据,构建多样化空间关联模式,运用空间回归模型偏微分方法实证测度不良贷款对经济增长的空间溢出效应。研究发现,基于区域间金融关联、投资者非理性行为的传染效应会放大不良贷款对宏观经济的冲击,并且在不同的区域空间关联模式下,银行不良贷款对经济增长的空间溢出效应均为负。结果表明,空间关联在不良贷款对经济增长的传导过程中起着重要作用,因此政府政策的实施应充分考虑地区之间的空间关联,防止决策偏误。

中国旅游产业集聚的空间计量分析——基于2000-2013年中国省际数据的实证研究

建立基于生产函数的动态空间面板计量模型,采用空间回归模型偏微分方法,考察2000-2013年中国30个省份旅游产业集聚的区域内溢出、区域间溢出以及总体空间溢出效应。研究发现,(1)中国旅游产业集聚呈现出显著的时空差异特征。东部沿海经济发达省份旅游产业集聚随时间呈下降趋势,而中西部省份旅游产业集聚呈上升趋势。(2)旅游产业集聚对区域内旅游经济增长的贡献度,约是资本要素和劳动要素的3.5倍和7倍。(3)产业集聚、资本要素和劳动要素对旅游经济增长具有显著正向区域内和总体空间溢出效应,但产业集聚具有负向区域间空间溢出效应,而劳动对地理或经济邻近省份的旅游经济增长起到负向空间溢出效应。这表明资本驱动的旅游产业集聚是推动中国区域旅游经济增长的重要因素。

我国四部门金融杠杆对系统性金融风险的影响——基于空间溢出视角

基于金融杠杆对系统性金融风险的区域内和区域间作用机制的理论分析,运用空间偏微分方法,依据测算出的2010—2019年我国各省(区、市)四部门金融杠杆和系统性金融风险数据,考量我国四部门金融杠杆对系统性金融风险的空间溢出。结果显示:我国系统性金融风险具有较强的空间趋同性特征;由于金融杠杆部门结构和所在区域的不同,其对系统性金融风险的区域内溢出存在显著差异;此外,金融杠杆对系统性金融风险的区域间外溢效应明显,忽视该区域间溢出,将不利于准确评估金融杠杆对系统性金融风险的冲击。

空间溢出效应与产业全要素生产率增长——基于轻工业影响因素的空间计量分析

为揭示产业发展的制约因素对其全要素生产率的影响及空间溢出效应,以轻工业为研究对象,利用中国轻工业省际面板数据,通过基于DEA的Malmquist指数方法计算出省际轻工业全要素生产率,再运用空间回归模型偏微分方法衡量了各影响因素对轻工业全要素生产率的总空间溢出效应、区域间溢出效应和区域内溢出效应。研究发现,中国轻工业全要素生产率增长存在显著的空间依赖性和空间联动性。在影响因素中,信息化、外商直接投资和基础设施对轻工业全要素生产率增长存在正向空间溢出效应,金融扶持、城镇化、对外需求和对内需求对轻工业全要素生产率增长存在负向空间溢出效应。

Getting pre-stack time migration travel times from the single square root operator

Improving the focusing capability of pre-stack time migration allows the imaged section to reflect structural characteristics, depth, and interface shape and it is a key step for the preparation of the initial depth migration velocity model. The traditional symmetrical travel time equation is derived based on the assumption of a layered model. It is difficult to achieve the desired effect of focusing in media with strong lateral variation. The nonsymmetrical travel time equation based on Lie algebra and a pseudo-differential operator contains a lateral velocity derivative which can improve the focusing capability even in strongly lateral variable media and also the computation precision of the weight coefficients for relative amplitude preservation. Compared with the symmetrical methods, the nonsymmetrical method is more effective. In this paper, we describe several key steps of nonsymmetric pre-stack travel time calculation and present some test results using synthetic and real data.

Stochastic Differential Game Model for Decentralized Power Control with Wisdom Regulation Factor in Wearable Audio-Oriented BodyNets

In this study, aiming at the characteristics of randomness and dynamics in Wearable Audiooriented BodyNets （WA-BodyNets）, stochastic differential game theory is applied to the investigation of the problem of transmitted power control inconsumer electronic devices. First, astochastic differential game model is proposed for non-cooperative decentralized uplink power control with a wisdom regulation factor over WA-BodyNets with a onehop star topology.This model aims to minimize the cost associated with the novel payoff function of a player, for which two cost functions are defined： functions of inherent power radiation and accumulated power radiation darmge. Second, the feedback Nash equilibrium solution of the proposed model and the constraint of the Quality of Service （QoS） requirement of the player based on the SIR threshold are derived by solving the Fleming-Bellman-Isaacs partial differential equations. Furthermore, the Markov property of the optimal feedback strategies in this model is verified.The simulation results show that the proposed game model is effective and feasible for controlling the transmitted power of WA-BodyNets.

The Partition of Unity Method for High-Order Finite Volume Schemes Using Radial Basis Functions Reconstruction

This paper introduces the use of partition of unity method for the development of a high order finite volume discretization scheme on unstructured grids for solving diffusion models based on partial differential equations.The unknown function and its gradient can be accurately reconstructed using high order optimal recovery based on radial basis functions.The methodology proposed is applied to the noise removal problem in functional surfaces and images.Numerical results demonstrate the effectiveness of the new numerical approach and provide experimental order of convergence.

Numerical modeling airflow in soil with impact of groundwater

In order to simulate the airflow in anhydrous case and the water-air flow in groundwater case, a numerical model of airflow in soil was developed. For the nonlinearity of the governing partial differential equation, the corresponding discretization and linearization methods were given. Due to the mass transfer between air-phase and water-phase, phase states of the model elements were constantly changing. Thus, parameters of the model were divided into primary ones and secondary ones, and the primary variables changing with phase states and the secondary variables can be obtained by their functional relationship with the primary variables. Additionally, the special definite condition of this numerical model was illustrated. Two examples were given to simulate the airflow in soil whether there was groundwater or not, and the effectiveness of the numerical model is verified by comparing the results of simulation with that of exoeriment.

A Comparison Results of Some Analytical Solutions of Model in Double Phase Flow through Porous Media

In this paper, we consider Variational Iteration Method （VIM） and q-Homotopy Analysis Method （q-HAM） to sotve me partial differential equation resulted from Fingero Imbibition phenomena in double phase flow through porous media. We further compare the results obtained here with the solution obtained in [ 12] using Adomian Decomposition Method. Numerical results are obtained, using Mathematica 9, to show the effectiveness of these methods to our choice of problem especially for suitable values ofh and n.

On Some Bending Problems of Prismatic Shell with the Thickness Vanishing at Infinity

The present work is devoted to the bending problems of prismatic shell with the thickness vanishing at infinity as an exponential function. The bending equation in the zero approximation of Vekua＇s hierarchical models is considered. The problem is reduced to the Dirichlet boundary value problem for elliptic type partial differential equations on half-plane. The solution of the problem under consideration is constructed in the integral form.

Damage and progressive failure of concrete structures using non-local peridynamic modeling

Peridynamics (PD), a recently developed theory of solid mechanics, which employs a non-local model of force interaction and makes use of integral formulation rather than the spatial partial differential equations used in the classical continuum mechanics theory, has shown effectiveness and promise in solving discontinuous problems at both macro and micro scales. In this paper, the peridynamics theory is used to analyze damage and progressive failure of concrete structures. A non-local peridynamic model for a rectangular concrete plate is developed, and a central pairwise force function is introduced to describe the interior interactions between particles within some definite distance. Damage initiation, evolution and crack propagation in the concrete model subject to in-plane uni-axial tension, in-plane uni-axial compression and out-of-plane impact load are investigated respectively. The numerical results show that discontinuities appear and grow spontaneously as part of the solution to the peridynamic equations of motion, and no special failure criteria or re-meshing techniques are required, which proves the potential of peridynamic modeling as a promising technique for analyzing the progressive failure of concrete materials and structures.

OPTIMAL BIRTH CONTROL FOR AN AGE-DEPENDENT COMPETITION SYSTEM OF N SPECIES

In this paper, we investigate optimal policies for an age-dependent n-dimensional competition system, which is controlled by fertility. By using Dubovitskii-Milyutin＇s general theory, the maximum principles are obtained for the problems with free terminal states, infinite horizon, and target sets, respectively.