基于集群创新合作网络的知识创新与扩散过程建模及仿真研究

基于集群创新合作网络的知识创新和知识扩散过程是集群企业实现创新的关键。为了揭示集群创新合作网络中知识增长绩效的演化规律,探讨不同网络中知识增长绩效的差异及其形成原因,论文构建了知识创新与扩散的过程模型,以东北三省新能源汽车集群创新合作网络为例,运用复杂网络理论和仿真方法进行分析。研究发现,集群创新合作网络的整体知识水平呈现先递增后递减的演化规律;知识增长的演化过程存在突变点,突变时期不同网络中企业知识水平分化的情况决定不同网络知识增长绩效的差异性;知识扩散约束条件是知识创新与扩散过程的关键;实际网络并非知识创新与扩散的最优网络,无标度网络具有知识增长的绩效优势;hub结构和适度的节点度值分布差异性有利于提升知识增长绩效。     

Extremal Behavior of Diffusion Models in Finance

We investigate the extremal behavior of a diffusion X _t given by the SDE , where W is standard Brownian motion, μ is the drift term and σ is the diffusion coefficient. Under some appropriate conditions on X _t we prove that the point process of ε -upcrossings converges in distribution to a homogeneous Poisson process. As examples we study the extremal behavior of term structure models or asset price processes such as the Vasicek model, the Cox–Ingersoll–Ross model and the generalized hyperbolic diffusion. We also show how to construct a diffusion with pre-determined stationary density which captures any extremal behavior. As an example we introduce a new model, the generalized inverse Gaussian diffusion. This revised version was published online in July 2006 with corrections to the Cover Date.     

Diffusion Approximation in Overloaded Switching Queueing Models

The asymptotic behavior of a queueing process in overloaded state-dependent queueing models (systems and networks) of a switching structure is investigated. A new approach to study fluid and diffusion approximation type theorems (without reflection) in transient and quasi-stationary regimes is suggested. The approach is based on functional limit theorems of averaging principle and diffusion approximation types for so-called Switching processes. Some classes of state-dependent Markov and non-Markov overloaded queueing systems and networks with different types of calls, batch arrival and service, unreliable servers, networks (M _SM,Q /M _SM,Q /1/) ^r switched by a semi-Markov environment and state-dependent polling systems are considered.     

Performance of Organizational Design Models and Their Impact on Organization Learning

The performance of various organizational structures is an essential parameter in the reengineering of organizations, particularly in the current rapidly changing, competitive and information technology-dependent environment. This situation has generally resulted in a smaller workforce confronted with voluminous information-processing requirements. Naturally, the focus has been on the design of organzations that will support effective and efficient learning processes. This specific study is on the contingency modely by Ouksel et al. (1997) on the impact of organizational structure on organizational learning and performance. It expands the empirical evaluation of the model to test its robustness. This is done by conducting extensive simulations with (a) a larger number of variables in the decision tasks, and (b) a larger set of numbers for each of the numeric variables, than has been used in the past. Overall, the validity of previous results achieved has been confirmed, but the selection of the most appropriate design, that which will indeed improve learning, is even more nuanced than past studies have concluded.     

Dynamic Strategic Pricing and Speed of Diffusion

Defining speed of diffusion as the amount of time it takes to get from one penetration level to a higher one, we introduce a dynamic model in which we study the link between pricing policy, speed of diffusion, and number of competitors in the market. Our analysis shows that, in the case of strategic (oligopolistic) competition, the speed of diffusion has an important influence on the optimal pricing policy. In particular, we find that higher speeds of diffusion create an incentive to strategically interacting firms to lower their prices.     

A Nonlinear Drift - Diffusion System with Electric Convection Arising in Electrophoretic and Semiconductor Modeling

A multi-dimensional transient drift-diffusion model for (at most) three charged particles, consisting of the continuity equations for the concentrations of the species and the Poisson equation for the electric potential, is considered. The diffusion terms depend on the concentrations. Such a system arises in electrophoretic modeling of three species (neutrally, positively and negatively charged) and in semiconductor theory for two species (positively charged holes and negatively charged electrons). Diffusion terms of degenerate type are also possible in semiconductor modeling. For the initial boundary value problem with mixed Dirichlet - Neumann boundary conditions and general reaction rates, a global existence result is proved. Uniqueness of solutions follows in the Dirichlet boundary case if the diffusion terms are uniformly parabolic or if the initial and boundary densities are strictly positive. Finally, we prove that solutions exist which are positive uniformly in time and globally bounded if the reaction rates satisfy appropriate growth conditions.     

风险分析中的信息扩散及其参数优化

在进行风险分析和评估过程中,经常遇到样本信息不充分,数据不完备,即小样本问题．本文一,用信息扩散方法对两个具体项目进行分析处理,由于篇幅有限文中仅介绍一个．二在黄崇福教授提出的信息扩散基础上,提出两个优化准则,即波动最小准则和有限偏离度准则,应用优化方法,求得参数最优解,结果是十分理想的．     

空气中PM2.5的扩散衰减与预测分析

以西安市2013年1月1日-9月19日的空气污染监测数据为例,采用非稳态的二维多箱模型,综合考虑了风向、季节等因素的影响,对西安市PM2.5的面源污染扩散和衰减规律进行模拟预测,计算模型相对误差;再选用高斯模型对某一天西安市突发情况下PM2.5浓度扩散情况进行点源污染扩散预测,并评价模型的有效性.     

应用拉普拉斯变换和留数法求解常见非稳态扩散情况下的菲克定律

介绍了三维和一维扩散下的菲克定律,以及两类涉及到扩散的实际问题,即求扩散粒子通过曲面的扩散通量和求解扩散粒子的浓度分布.通过拉普拉斯变换和复变函数相关数学理论,求解了菲克扩散定律在无限长介质和有限长介质两种非稳态扩散情况下的解.粒子在无限长介质中的非稳态扩散和浓度分布可通过方程φ(z,t)=Φ·erfc(z/2DT~(1/2))表示.方程为余补高斯误差函数.粒子在有限长介质中的非稳态扩散和浓度分布可通过方程φ(z,t)=Φ+Φ·4/π∑_(n=1)~(+∞)((-1)~n)/(2n-1)cos[z/L(n-1/2)π]e~((D_t)/(L~2)(n-1/2)~2π~2)表示.该方程为无限加和形式,当n≥100000时,φ可以精确到小数点后6位,在方程的图像上不再能观察出由n的取值造成的误差.从方程的图像可得到粒子在扩散介质中达到饱和的时间或粒子扩散到z=0处的时间等具有重要物理意义的参数.     

水质中放射性核素瞬态三维扩散模型的建立及求解

在一维扩散模型的基础上,建立了放射性核素在水质中的瞬态三维扩散模型,并给出了瞬态排放模式下模型的计算公式,实现了水质中放射性核素扩散浓度的快速估算.在MATLAB程序下,利用该方法对一个实例进行了仿真分析,得出相关结论,对于核泄漏事故下放射性核素扩散浓度预测评估及制定安全措施具有指导意义.     

Weak Convergence of a Sequence of Semimartingales to a Diffusion with Discontinuous Drift and Diffusion Coefficients

This paper presents a set of sufficient conditions for a sequence of semimartingales to converge weakly to a solution of a stochastic differential equation (SDE) with discontinuous drift and diffusion coefficients. This result is closely related to a well-known weak-convergence theorem due to Liptser and Shiryayev (see [27]) which proves the weak convergence to a solution of a SDE with continuous drift and diffusion coefficients in the Skorokhod–Lindvall J ₁-topology.The goal of this paper is to obtain a stronger result in order to solve outstanding problems in the area of large-scale queueing networks – in which the weak convergence of normalized queueing length is a solution of a SDE with discontinuous coefficients. To do this we need to make the stronger assumptions: (1) replacing the convergence in probability of the triplets of a sequence of semimartingales in the original Liptser and Shiryayev's theorem by stronger convergence in L ₂, (2) assuming the diffusion coefficient is coercive, and (3) assuming the discontinuity sets of the coefficients of the limit diffusion processs are of Lebesgue measure zero.     

一类反应扩散系统的分歧与斑图

本文研究了一类发生在密闭容器中的不可激活的高次自催化反应扩散系统．在适当的条件下,用渐进近似的方法讨论了系统平衡态的稳定范围;用多重尺度的方法证明了当扩散系数λ充分小时,系统出现两种类型的斑图,一类是由Hopf分歧引出的驻波斑图;另一类是由 Pitchfork分歧引出的定波斑图．进一步还讨论了,在分歧点附近,对于大于空间或等于空间波数的小扰动,斑图是局部稳定的,而小于自身空间波数的小扰动,斑图是不稳定的．     

Semiparametric Modeling and Estimation of Instrumental Variable Models

We apply Bayesian methods to a model involving a binary nonrandom treatment intake variable and an instrumental variable in which the functional forms of some of the covariates in both the treatment intake and outcome distributions are unknown. Continuous and binary response variables are considered. Under the assumption that the functional form is additive in the covariates, we develop efficient Markov chain Monte Carlo-based approaches for summarizing the posterior distribution and for comparing various alternative models via marginal likelihoods and Bayes factors. We show in a simulation experiment that the methods are capable of recovering the unknown functions and are sensitive neither to the sample size nor to the degree of confounding as measured by the correlation between the errors in the treatment and response equations. In the binary response case, however, estimation of the average treatment effect requires larger sample sizes, especially when the degree of confounding is high. The methods are applied to an example dealing with the effect on wages of more than 12 years of education.     

A Priori and A Posteriori Error Estimates of Streamline Diffusion Finite Element Method for Optimal Control Problem Governed by Convection Dominated Diffusion Equation

In this paper,we investigate a streamline diffusion finite element approxi- mation scheme for the constrained optimal control problem governed by linear con- vection dominated diffusion equations.We prove the existence and uniqueness of the discretized scheme.Then a priori and a posteriori error estimates are derived for the state,the co-state and the control.Three numerical examples are presented to illustrate our theoretical results.     

Optimal Dynamics of Innovation in Models of Economic Growth

A nonlinear model of economic growth which involves production, technology stock, and their rates as the main variables is considered. Two trends (growth and decline) in the interaction between the production and R&D investment are examined in the balanced dynamics. The optimal control problem of R&D investment is studied for the balanced dynamics and the utility function with the discounted consumption. The Pontryagin optimality principle is applied for designing the optimal nonlinear dynamics. An existence and uniqueness result is proved for an equilibrium of the saddle type and the convergence property of the optimal trajectories is shown. Quasioptimal feedbacks of the rational type for balancing the dynamical system are proposed. The growth properties of the production rate, R&D, and technology intensities are examined on the generated trajectories.     

电厂冷却水在湖泊和水库中热扩散过程的数学模拟

本文对电厂冷却水排入湖泊和水库后的热扩散过程进行了数学模拟,建立了三维扩散方程,给出了一维、二维和三维计算湖泊和水库中任意点任意时刻水温上升量的计算公式,并通过实例对一维情形的计算公式进行了验证,结果很好.     

Necessary Maximum Principle of Stochastic Optimal Control with Delay and Jump Diffusion

In this paper, we have studied the necessary maximum principle of stochastic optimal control problem with delay and jump diffusion.