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     

一种风险型决策的决策方法

本文阐明了方案益损值和自然状态概率无准确估计的风险型决策问题的决策方法。证明了在期望值决策准则下，用等概率分层随机抽样得到的方案收益期望值的均值，与用简单随机抽样得到的相同。用正交表进行分层随机抽样，得到方案收益期望值服从正态分布的均值和方差。再根据统计推断理论对方案作出选择，并给出决策的风险估计。     

状态迁移下系统适应性改造成本研究

为了解系统为适应在不同环境中安全运行采取改造措施的成本,借鉴王培庄先生的因素空间理论与笔者提出的空间事故树理论,构造了一套确定系统适应工作环境迁移所需措施成本的方法.首先按照元件或子系统X_i的划分将系统T使用事故树结构化,确定由状态c_(j1)迁移到c_(j2),使X_i适应该迁移所采取的措施f_(ni),得到适应状态迁移的措施表Γ(X_i),从而得到系统T的由状态c_(j1)迁移到c_(j2)的适应措施集合δ(T,c_1→c_2),化简得γ(T,c_(j1)→c_(j2)).根据不同X_i与措施f_n组成成本对应表,最终得到了X_i的迁移改造措施成本Ψ(X_i,c_(j1)→c_(j2))和系统措施成本Ψ(T,c_(j1)→c_(j2)).研究可为系统在不同的环境下的安全运行改造措施的成本提供事先确定方法.     

类比迁移优化数学认知结构

类比是根据两个对象或两类事物的一些属性相同或相似，猜测另一些属性也可能相同或相似的方法．迁移是一种学习对另一种学习的影响．凡是一种学习对另一种学习起到促进作用的就称为正迁移；反之起干扰或抑制作用的称为负迁移．从教学目的上看，数学教学应该努力促进一种学习对另一种学习的正迁移，正迁移量越大，说明学生通过学习产生的适应新学习情境或解决新问题的能力越强，在学习中，经常会出现负迁移的情况，关注负迁移发生的可能，防止其负面影响非常重要．数学学习既有知识技能和思维方法的迁移，又有学习态度的迁移，而类比可以成为其相互迁移的桥梁和纽带．     

一般非均匀凸介质的迁移算子广义本征函数系统的完整性

该文讨论一般非均匀凸介质所确定的迁移算子的广义本征函数系统的完整性问题，利用我们探索的相对收敛方法，完整地刻划了一般非均匀凸介质中迁移问题的广义本征函数系统的完整性问题，我们证明了，对迁移半群E（t），当0∈Pσ（E（t）），迁移算子广义本征函数系统不完整，当0∈Pσ（E（t））时，仅当满足相对收敛条件时，迁移算子的广义本征函数系统完整．     

迁移在数学教学中的运用

迁移是心理学上的一个概念．迁移是指已经学过的东西在新情境中的应用，也就是已有的经验对解决新课题的影响．迁移一般可分为两种类型，一种是正迁移，表现为一种知识、技能的掌握促进另一种知识、技能的掌握；另一种负迁移，表现为一种知识、技能的掌握干扰了另一种知识...     

重整之路

弱肉强食的市场丛林，总有企业陷于困境，当前期债务无法清偿，重整还是清算，就是上市公司不得不面对的生死题。     

工科复变函数中的迁移教学

迁移是指一种学习对另一种学习的影响.影响学生学习迁移的主要因素有:学生原有知识的准备状态、概括水平、认知结构变量、学习材料的性质、学习的指导.为了能有效促进学生学习正迁移的发生,同时防止学生学习负迁移的发生,在工科复变函数教学中针对其特点采取以下教学策略:注意加强工科复变函数与高等数学的衔接;突出转化和类比的数学思想方法的教学;加强复变函数学习方法的指导.     

路牌上的字

这里是石炭纪时期的泥炭沼泽，如果你是邪恶的入侵者，就赶紧止步吧!丛林里的动物可异常凶险!     

模糊综合决策模型在FMS加工单元状态监测与故障诊断中的应用

由于对柔性加工单元建立状态监测与故障诊断模型时存在设备与过程复杂多变，联动等特点，独模糊综合决策模型不能有效地利用，本文以铣削加工单元为对象，基于多传感器状态监测信息，提出模糊关联矩阵权值总和不变且流动分配的方案与原则来建立加工设备故障诊断的模糊多级综合决策模型，从而较有效地实现了诊断决策功能。     

On the uniqueness and reconstruction for an inverse problem of the fractional diffusion process

Consider an inverse problem for the time-fractional diffusion equation in one dimensional spatial space. The aim is to determine the initial status and heat flux on the boundary simultaneously from heat measurement data given on the other boundary. Using the Laplace transform and the unique extension technique, the uniqueness for this inverse problem is proven. Then we construct a regularizing scheme for the reconstruction of boundary flux for known initial status. The convergence rate of the regularizing solution is established under some a priori information about the exact solution. Moreover, the initial distribution can also be recovered approximately from our regularizing scheme. Finally we present some numerical examples, which show the validity of the proposed reconstruction scheme.     

TAILORING POINT COUNTS FOR INFERENCE ABOUT AVIAN DENSITY: DEALING WITH NONDETECTION AND AVAILABILITY

Point counts are commonly used for bird surveys, but interpretation is ambiguous unless there is an accounting for the imperfect detection of individuals. We show how repeated point counts, supplemented by observation distances, can account for two aspects of the counting process: (1) detection of birds conditional on being available for observation and (2) the availability of birds for detection given presence. We propose a hierarchical model that permits the radius in which birds are available for detection to vary with forest stand age (or other relevant habitat features), so that the number of birds available at each location is described by a Poisson‐gamma mixture. Conditional on availability, the number of birds detected at each location is modeled by a beta‐binomial distribution. We fit this model to repeated point count data of Florida scrub‐jays and found evidence that the area in which birds were available for detection decreased with increasing stand age. Estimated density was 0.083 (95%CI: 0.060–0.113) scrub‐jays/ha. Point counts of birds have a number of appealing features. Based on our findings, however, an accounting for both components of the counting process may be necessary to ensure that abundance estimates are comparable across time and space. Our approach could easily be adapted to other species and habitats.     

Solving a final value fractional diffusion problem by boundary condition regularization

The evolution process of fractional order describes some phenomenon of anomalous diffusion and transport dynamics in complex system. The equation containing fractional derivatives provides a suitable mathematical model for describing such a process. The initial boundary value problem is hard to solve due to the nonlocal property of the fractional order derivative. We consider a final value problem in a bounded domain for fractional evolution process with respect to time, which means to recover the initial state for some slow diffusion process from its present status. For this ill-posed problem, we construct a regularizing solution using quasi-reversible method. The well-posedness of the regularizing solution as well as the convergence property is rigorously analyzed. The advantage of the proposed scheme is that the regularizing solution is of the explicit analytic solution and therefore is easy to be implemented. Numerical examples are presented to show the validity of the proposed scheme.     

Temporally adaptive estimation of logistic classifiers on data streams

Modern technology has allowed real-time data collection in a variety of domains, ranging from environmental monitoring to healthcare. Consequently, there is a growing need for algorithms capable of performing inferential tasks in an online manner, continuously revising their estimates to reflect the current status of the underlying process. In particular, we are interested in constructing online and temporally adaptive classifiers capable of handling the possibly drifting decision boundaries arising in streaming environments. We first make a quadratic approximation to the log-likelihood that yields a recursive algorithm for fitting logistic regression online. We then suggest a novel way of equipping this framework with self-tuning forgetting factors. The resulting scheme is capable of tracking changes in the underlying probability distribution, adapting the decision boundary appropriately and hence maintaining high classification accuracy in dynamic or unstable environments. We demonstrate the scheme’s effectiveness in both real and simulated streaming environments.     

A deterministic Lagrangian particle separation-based method for advective-diffusion problems

A simple and robust Lagrangian particle scheme is proposed to solve the advective-diffusion transport problem. The scheme is based on relative diffusion concepts and simulates diffusion by regulating particle separation. This new approach generates a deterministic result and requires far less number of particles than the random walk method. For the advection process, particles are simply moved according to their velocity. The general scheme is mass conservative and is free from numerical diffusion. It can be applied to a wide variety of advective-diffusion problems, but is particularly suited for ecological and water quality modelling when definition of particle attributes (e.g., cell status for modelling algal blooms or red tides) is a necessity. The basic derivation, numerical stability and practical implementation of the NEighborhood Separation Technique (NEST) are presented. The accuracy of the method is demonstrated through a series of test cases which embrace realistic features of coastal environmental transport problems. Two field application examples on the tidal flushing of a fish farm and the dynamics of vertically migrating marine algae are also presented.     

Cooperative dispatching – exploiting the flexibility of an FMS by means of incremental optimization

We present a new control scheme for releasing parts into a flexible manufacturing system (FMS) that is based on incremental optimization. Our objective is to exploit the available routing flexibility of parts in an enhanced manner by viewing part release as an assignment problem using system status information. In particular, we propose an “intelligent” part release mechanism with some look-ahead and optimization features in order to allow for optimization-based “cooperation” of workcenters. The cooperative dispatching concept is implemented in an object-oriented computer simulation model, and experiments with a varying degree of average routing flexibility are performed. The experimental results are used for a statistical analysis of the benefits of cooperative dispatching versus the common approach of standard dispatching. Finally, we investigate the robustness of the presented FMS control scheme in the case of random machine breakdowns.     

Fourier regularization for a final value time-fractional diffusion problem

The evolution process of fractional order describes some phenomenon of anomalous diffusion and transport dynamics in complex system. The equation containing time-fractional derivative provides a suitable mathematical model for describing such a process. The backward problem for this system, which means to recover the initial state for some slow diffusion process from its present status, is very hard to solve due to the nonlocal property of fractional derivative and the irreversibility of time. For this ill-posed problem, we construct a regularizing solution using the Fourier transform method. Both the a-priori choice strategy and the a-posteriori choice strategy for the regularizing parameter are given, with the convergence analysis on the regularizing solution. Numerical implementations are presented to show the validity of the proposed scheme.     

Numerical solutions of diffusion mathematical models with delay

In this paper an explicit numerical difference scheme for mixed problems for the delay diffusion equation is proposed, as a generalization of the classic difference scheme for the diffusion problem. A sufficient condition for the asymptotic stability of the new scheme is proved. Consistence, convergence and some properties of stability for this scheme are studied. Illustrative examples of numerical results are also included.     

二维半线性反应扩散方程的交替方向隐格式

本文研究一类二维半线性反应扩散方程的差分方法.构造了一个二层线性化交替方向隐格式.利用离散能量估计方法证明了差分格式解的存在唯一性、差分格式在离散H~1模下的二阶收敛性和稳定性.最后给出两个数值例子验证了理论分析结果.     

A non‐standard finite difference scheme for an advection‐diffusion‐reaction equation

In this note, a non‐standard finite difference (NSFD) scheme is proposed for an advection‐diffusion‐reaction equation with nonlinear reaction term. We first study the diffusion‐free case of this equation, that is, an advection‐reaction equation. Two exact finite difference schemes are constructed for the advection‐reaction equation by the method of characteristics. As these exact schemes are complicated and are not convenient to use, an NSFD scheme is derived from the exact scheme. Then, the NSFD scheme for the advection‐reaction equation is combined with a finite difference space‐approximation of the diffusion term to provide a NSFD scheme for the advection‐diffusion‐reaction equation. This new scheme could preserve the fixed points, the positivity, and the boundedness of the solution of the original equation. Numerical experiments verify the validity of our analytical results. Copyright © 2014 JohnWiley & Sons, Ltd.