多群迁移与临界问题

在中子迁移理论中，用多群逼近来探讨原迁移问题不仅对原迁移方程的计算，而且对     

具积分边界条件的中子迁移方程的适定性及谱分布

该文在Ｌｐ（ｐ＞２）空间中讨论一类带积分边界条件的中子迁移方程的适定性．首先，利用预解式正算子理论和积分半群理论证明了该方程正解的存在唯一性；其次，我们还讨论了相应的迁移算子的谱性质，证明了迁移算子包含在右半平面的谱由最多可数多个具有限代数重数的本值征组成．     

一类具Rotenberg模型解的存在性

迁移方程是研究物质中的粒子运动所产生的微观效应综合所致的宏观迁移现象规律的一种模型,研究这类迁移方程对数学基础理论的发展有着非常重要的意义.在L_1空间中,运用线性算子理论,研究了种群细胞增生中具Rotenberg模型的迁移方程,采用所谓的豫解算子等法证明了种群细胞增生中具Rotenberg模型解的存在性.     

迁移方程多群逼近的一致收敛性

在核反应堆的近似计算中,多群方法是一很重要的方法,由于讨论问题是在L~p(G)(1≤P<∞)空间中进行的(如[1,2]),因而多群迁移方程的解对原方程的解的收敛性不是一致的。本文运用有界线性算子的积分半群理论[3-5],在L~∞(G)中讨论了这个问题,证明了迁移方程在L~∞(G)中非负解的存在唯一性以及多群迁移方程的解逼近原方程的解的一致收敛性。     

例谈学生学习不等式时易产生的错误

例谈学生学习不等式时易产生的错误高保中（湖北应城市一中４３２４００）在不等式学习中，许多知识和能力都依赖于以前所学的代数等知识的迁移，且更直接地依赖于等式、方程中的运算方式和思想方法的迁移，而等与不等毕竟本质不同，负迁移也就应运而生．另一方面，不等式...     

L~1空间中迁移方程的解对边界参数的连续依赖性

在L~1空间研究平板几何中具有不完全反射边界条件的迁移方程,证明了迁移算子的共轭算子的定义域的正锥在共轭空间的正锥中共尾,得到迁移算子的谱界等于增长界.利用主算子的预解式对边界参数连续依赖最终证明了迁移方程的解对边界参数连续依赖.     

迁移方程的扩散近似的收敛性

导出了迁移方程的扩散近似方程．说明了它的离散纵标方法在区间内和边界上都有扩散极限，它的解关于一致地收敛于迁移方程的解．其收敛性的证明是依据其渐近扩散展开式，在边界层上得到的误差估计逼近其离散纵标方法的解．     

板几何中一类具完全反射边界条件的奇异迁移算子的谱

在L1空间上研究了板几何中一类具完全反射边界条件下各向异性、连续能量、均匀介质的奇异迁移方程.证明了这类方程相应的奇异迁移算子产生C0半群和该半群的Dyson-Phillips展开式的二阶余项是弱紧的,从而得到了该迁移算子的谱在区域Γ中仅由至多有限个具有限代数重数的离散本征值组成等结果.     

一类增生扩散型种群细胞中迁移方程的谱问题

在Lp(1≤p＜+∞)空间上,研究了一类具年龄结构的增生扩散型种群细胞中具无限周长的迁移方程,讨论了这类方程相应的迁移算子的谱,证明了在某个半平面该迁移算子的谱仅由可数个具有限代数重数的离散本征值组成等结果.     

矿区土壤中含水率及重金属迁移转化的数值模拟

本文基于由连续性方程和达西定律所推出的土壤中水分运动基本方程,以一维垂向水分方程为研究对象,构造稳定收敛的有限差分格式,运用MATLAB数学工具,对地面饱水情况下土壤水分运动的一维垂向方程进行了数值模拟,得到了土壤中水分的迁移规律;同时,综合考虑对流扩散作用以及土壤对重金属的吸附解吸作用,利用非饱和土壤中重金属离子迁移转化模型,对锌离子在矿区土壤中的迁移转化进行了数值模拟,展示了锌离子在矿区土壤中的浓度分布规律．     

Non-classical regimes of colloid-facilitated impurity transport in statistically homogeneous double porosity media

In the context of impurity transport study it is shown how complexity of the system leads to emergence of anomalous transport regimes, moreover the power-law behavior of which changes with time. Specifically, a model of nonequillibrium colloid-facilitated transport in statistically homogeneous double porosity media is presented and possible transport regimes are simulated. Depending on the medium and colloids characteristics different sequences of transport regimes can realize. Temporal interval exists where anomalous transport regimes (sub-diffusion and quasi-diffusion) occur. At asymptotically large times the transport is described by the classical advection-diffusion with modified parameters.     

公路客运市场建设项目的系统评价研究

本文通过对公路客运市场的生产和经营状况、所处的经营环境以及运力和客运需求进行了分析 ,提出了客运市场建设项目的评价指标体系 ,并且利用系统评价模型进行评价 ,得出了满意的结果     

各种运输方式客运质量的综合评价研究

在建立各种运输方式客运质量综合评价指标体系的基础上,提出了用于各种运输方式客运质量综合评价的方法——"专家法—信息熵—灰色关联投影法"相结合的组合评价模型,该模型将专家法、信息熵理论和灰色关联决策法有机结合起来.最后根据实际数据对各种运输方式的客运质量加以综合评价并排序比较,验证该方法的合理性和有效可行性.     

交通运输系统协调发展理论与模型研究

提出了交通运输系统协调度的评价分析模型.从系统论的观点出发,提出了交通运输系统协调理论的概念,探讨了交通运输系统随时间而不断演化变迁的规律,给出了交通运输系统协调发展基本步骤;并根据协调学原理,讨论了交通运输系统的协调性问题,提出了系统协调发展模型,对交通运输子系统内部及子系统之间及系统整体的协调发展问题进行了研究,探讨了交通运输可持续发展的系统协调管理过程,为进一步研究交通运输系统的可持续发展奠定了基础.     

An adaptive characteristics method for advective-diffusive transport

An adaptive characteristics method is presented for the solution of advective-diffusive groundwater transport problems. The method decomposes the transport processes into advective and diffusive transport components. Advective flows are defined by using a streamtube incrementing procedure, based on the method of characteristics, to define the position of advective front. Diffusive transport orthogonal to the front is represented by an array of propagating streamtube elements, with dimension determined from analytical solution of the one-dimensional diffusion equation. Adaptive time scaling is used to moderate the dimensions and aspect ratios of the advective and diffusive streamtube elements as appropriate to the dominant transport mechanism. Finite differences are used to solve for transport ahead of the advancing front. The distribution of streamtubes are predetermined from a direct boundary element algorithm. Comparison with analytical results for a one-dimensional transport geometry indicates agreement for Peclet numbers between zero and infinity. Solution for transport in two-dimensional domains illustrates excellent agreement for Peclet numbers from zero to 25.     

Peacock geodesics in Wasserstein space

Martingale optimal transport has attracted much attention due to its application in pricing and hedging in mathematical finance. The essential notion which makes martingale optimal transport different from optimal transport is peacock. A peacock is a sequence of measures which satisfies convex order property. In this paper we study peacock geodesics in Wasserstain space, and we hope this paper can provide some geometrical points of view to look at martingale optimal transport.     

On the Optimal Design of Wall-to-Wall Heat Transport

We consider the problem of optimizing heat transport through an incompressible fluid layer. Modeling passive scalar transport by advection-diffusion, we maximize the mean rate of total transport by a divergence-free velocity field. Subject to various boundary conditions and intensity constraints, we prove that the maximal rate of transport scales linearly in the r.m.s. kinetic energy and, up to possible logarithmic corrections, as the one-third power of the mean enstrophy in the advective regime. This makes rigorous a previous prediction on the near optimality of convection rolls for energy-constrained transport. On the other hand, optimal designs for enstrophy-constrained transport are significantly more difficult to describe: we introduce a “branching” flow design with an unbounded number of degrees of freedom and prove it achieves nearly optimal transport. The main technical tool behind these results is a variational principle for evaluating the transport of candidate designs. The principle admits dual formulations for bounding transport from above and below. While the upper bound is closely related to the “background method,” the lower bound reveals a connection between the optimal design problems considered herein and other apparently related model problems from mathematical materials science. These connections serve to motivate designs. © 2019 Wiley Periodicals, Inc.     

Magnetohydrodynamics in laser fusion: Fluid modeling of energy transport in laser targets

Fluid models for two-dimensional, electron energy transport are examined. It is shown that enhanced lateral transport due to particle drifts in self-generated magnetic fields occurs when certain transport terms are flux-limited by artificially enhancing collisions. With flux limiting, fluid models reproduce the essential features of numerical simulations of transport in CO₂ laser target experiments.     

最优传输理论在图像处理中的应用

最优传输问题是寻找概率测度间的最优传输变换的一类特殊的优化问题,近年来在众多领域得到了广泛的关注.针对传统最优传输问题存在的计算量过大、正则性缺失等问题,学者们提出了多种改进的最优传输模型和算法,用于处理实际中的各种问题.简述最优传输问题的基本理论和方法,介绍Wasserstein距离的概念及其衍生出的Wasserstein重心,探讨离散化最优传输模型及其在正则化等方面的改进,讨论求解最优传输问题的算法进展,综述Wasserstein距离在图像处理领域的简单应用,并展望有待进一步研究的工作.     

客运问题的进化博弈分析

构建了客运车主群体之间以及客运车主群体与客运管理部门之间的博弈模型及其复制动态方程,并对复制动态方程做了分析与讨论,得出了博弈模型中各博弈方的进化稳定策略,并根据所提出的博弈模型,提出了合理性建议.