ON THE PROBLEMS OF PREVENTING THE BLOWING UP OF THE SOLUTIONS FOR SEMILINEAR PARABOLIC EQUATIONS

§ 1 Introduction The investigating of the existence of globally smooth solutions or the formation of singularities of the solutions for semilinear parabolic equations is of much importance in the theory of partial differential equation as well as in the application. The blowing up of the solutions is an interesting phenomenon and has been pointed out by many authors in various cases, such as by S. Kaplan [1], C. V. pao[2], H. Kawarada[3]etc. In[4], Chen studied the problem of     

THE MAGNETIC POTENTIAL FOR THE ELLIPSOIDAL MEG PROBLEM

In magnetoencephalography （MEG） a primary current is activated within a bounded conductive medium, i.e., the head. The primary current excites an induction current and the total （primary plus induction） current generates a magnetic field which, outside the conductor, is irrotational and solenoidal. Consequently, the exterior magnetic field can be expressed as the gradient of a harmonic function, known as the magnetic potential. We show that for the case of a triaxial ellipsoidal conductor this potential is obtained by using integration along a specific path which is dictated by the geometrical characteristics of the ellipsoidal system as well as by utilizing special properties of ellipsoidal harmonics. The vector potential representation of the magnetic field is also obtained.     

Improving the complexity of chaotic sequence based on the PCA algorithm

The principal component analysis (PCA) is an effective statistical analysis method in statistical data analysis, feature extraction and data compression. The method simplifies multiple related variables into a linear combination of several irrelevant variables, through the less-comprehensive index as far as possible to replace many of the original data, and can reflect the information provided by the original data. This paper studies the signal feature extraction algorithm based on PCA, and extracts sequences’ feature which generated by Logistic mapping. Then we measured the complexity of the reconstructed chaotic sequences by the permutation entropy algorithm. The testing results show that the complexity of the reconstruction sequences is significantly higher than the original sequences.     

Announcement of Journal of Computational Mathematics Best Paper Prize

Guideline The JCM Best Paper Prize will be established by the Journal of Computational Mathematics (JCM) in 2008.The prize will be awarded to the author(s) of the most outstanding paper,as determined by the prize committee,published in JCM during the two calendar years prior to the year of the award.     

Dynamical Behaviors in a Two-dimensional Map

We consider the dynamics of a two-dimensional map proposed by Maynard Smith as a population model. The existence of chaos in the sense of Marotto‘s theorem is first proved, and the bifurcations of periodic points are studied by analytic methods. The numerical simulations not only show the consistence with the theoretical analysis but also exhibi the complex dynamical behaviors.     

Fuzzy Entropy： Axiomatic Definition and Neural Networks Model

The measure of uncertainty is adopted as a measure of information. The measures of fuzziness are known as fuzzy information measures. The measure of a quantity of fuzzy information gained from a fuzzy set or fuzzy system is known as fuzzy entropy. Fuzzy entropy has been focused and studied by many researchers in various fields. In this paper, firstly, the axiomatic definition of fuzzy entropy is discussed. Then, neural networks model of fuzzy entropy is proposed, based on the computing capability of neural networks. In the end, two examples are discussed to show the efficiency of the model.     

DEGREE OF APPROXIMATION ASSOCIATED WITH SOME ELLIPTIC OPERATORS AND ITS APPLICATIONS

The Jackson-type estimates by using some elliptic operators will be achieved. These results will be used to characterize the regularity of some elliptic operators by means of the approximation degree and the saturation class of the multivariate Bernstein operators as well.     

IMPULSIVE VACCINATION OF SIRS EPIDEMIC MODEL WITH STAGE-STRUCTURE

The period of infection is partitioned into the early and later stages according to the development process of infection. The infected individuals in the different stages have the different ability of transmitting disease. The constant recruitment rate and exponential natural death, as well as the disease-related death and pulse vaccination are incorporated into the model. Through the discrete dynamical system determined by the stroboscopic map, we obtain the exact infection-free periodic solution to the sy...     

Flows associated to Cameron-Martin type vector fields on path spaces over a Riemannian manifold

The flow on the Wiener space associated to a tangent process constructed by Cipriano and Cruzeiro, as well as by Gong and Zhang does not allow to recover Driver’s Cameron-Martin theorem on Riemannian path space. The purpose of this work is to refine the method of the modified Picard iteration used in the previous work by Gong and Zhang and to try to recapture and extend the result of Driver. In this paper, we establish the existence and uniqueness of a flow associated to a Cameron-Martin type vector field on the path space over a Riemannian manifold.     

An Improved Hybrid Method for Inverse Obstacle Scattering Problems

An improved hybrid method is introduced in this paper as a numerical method to reconstruct the scatterer by far-field pattern for just one incident direction with unknown physical properties of the scatterer. The improved hybrid method inherits the idea of the hybrid method by Kress and Serranho which is a combination of Newton and decomposition method, and it improves the hybrid method by introducing a general boundary condition. The numerical experiments show the feasibility of this method.     

技术柔性、柔性生产与柔性技术的价值

在产品市场和要素市场存在不确定性的条件下,将企业的生产行为和技术柔性水平的选择纳入一个统一框架进行分析,给出了柔性技术的价值函数及其特征.结果表明,给定技术柔性水平,柔性生产行为价值不会低于非柔性生产行为的价值;给定生产行为,柔性技术的价值不会随着其柔性增加而降低.进一步,在一定条件下,柔性生产行为比非柔性生产行为更具价值,柔性技术的价值随着其柔性水平的增加而增加.     

How real option disinvestment flexibility augments project NPV

In this article we show how a project’s option value increases with incremental levels of investment and disinvestment flexibility. We do this by presenting two NPV and seven option pricing models in a strict sequence of increasing flexibility. We illustrate each with numerical examples and determine the maximum value that a project option could ever support. We show that managerial consideration of exit options at the time of project initiation can add value.     

随机波动率与投资中的q理论

本文将随机波动率引入托宾q模型,讨论生产率冲击的波动率大小对公司价值与投资决策的影响.研究发现,公司托宾q值会受到生产率冲击波动率的显著影响,波动率的增大会降低托宾q值,且该影响会随着波动率的增大而加剧.此外,波动率对托宾q值的影响也会传导到公司的投资决策上来,托宾q降低会使得投资额减小,该影响同样会随波动率的增大而加剧.本文还考虑了波动率对公司在用资产与成长机会价值的影响,更为合理地刻画了公司生产过程中生产率冲击的波动率为随机的假设现实情况,所得结论对公司估值及投资决策均有一定的参考价值.     

A fuzzy approach to R&D project portfolio selection

A major advance in the development of project selection tools came with the application of options reasoning in the field of Research and Development (R&D). The options approach to project evaluation seeks to correct the deficiencies of traditional methods of valuation through the recognition that managerial flexibility can bring significant value to projects. Our main concern is how to deal with non-statistical imprecision we encounter when judging or estimating future cash flows. In this paper, we develop a methodology for valuing options on R&D projects, when future cash flows are estimated by trapezoidal fuzzy numbers. In particular, we present a fuzzy mixed integer programming model for the R&D optimal portfolio selection problem, and discuss how our methodology can be used to build decision support tools for optimal R&D project selection in a corporate environment.     

基于矩匹配的、多标的实物期权估值方法研究

实物期权能够恰当地反映管理的灵活性价值,但是实际应用中往往对应多个标的物,现有的方法不能很好的求解其价值及变量的敏感性,从而限制了其应用.本文将多个标的资产视为一篮子资产组合,通过矩匹配方法求得组合资产的近似分布,从而可求解多标的实物期权的解析解,并通过案例分析了该方法的优势和便利性.     

Strategic investment under uncertainty: A synthesis

Investment is a central theme in economics, finance, and operational research. Traditionally, the focus of analysis has been either on assessing the value of flexibility (investment under uncertainty) or on describing commitment effects in competitive settings (industrial organization). Research contributions addressing the intersection of investment under uncertainty and industrial organization have become numerous in recent years. In this paper, we provide an overview aimed at categorizing and relating these research streams. We highlight managerial insights concerning the nature of competitive advantage (first- versus second-mover advantage), the manner in which information is revealed, firm heterogeneity, capital increment size, and the number of competing firms.     

Short-term work scheduling with job assignment flexibility for a multi-fleet transport system

In recent years, planning and management of operations of transportation companies has become increasingly complex as tighter financial constraints affect the ability to respond to changing demands for travel. This paper investigates how a firm can reduce its total labor cost, enhance the flexibility of its operations and improve worker productivity and utilization by determining the right mix of jobs in work schedules. Using a method we have developed to generate low cost work schedules for bus drivers of an inter-city transport system in India, we study the changes in worker productivity and utilization when a mix of primary and secondary jobs is built in work schedules. We also investigate other factors that can strongly influence worker productivity and utilization such as the amount of overtime in work schedules, the level of job assignment flexibility, and staff size. Test results and discussions of managerial implications are presented.     

Real R&D options and optimal activation of two-dimensional random controls

We value investments under uncertainty with embedded optional costly controls (impulse-type with uncertain outcome) that capture managerial intervention for value enhancement and/or information acquisition (exploration, R&D, advertising, marketing research, etc). Implementing real option models but neglecting such embedded managerial actions can severely underestimate investment opportunities and lead to erroneous investment decisions. Optimal decisions are solutions to a maximization problem where the trade-off between the control's cost and the value added by such actions is explicitly taken into consideration. In this paper, we generalize such a methodology from one dealing with the special case of actions affecting only one state-variable, to one with actions that affect several. Asset values follow geometric Brownian motion or jump-diffusion processes with multiple generating sources of jumps. The Markov-chain numerical methodology we provide can handle sequential controls. Although we report the results with open-loop policies, the approach can be readily extended to accommodate dependency among the controls.     

Formulating dynamic strategies using decision calculus

This paper presents an applied methodology to assist managers in strategically setting prices and allocating resources over the product, brand, or adoption (diffusion) life cycle. While substantial theoretical work has been achieved in this area in the management science and operations research disciplines, approaches which can be implemented as managerial tools are generally lacking. Our methodology, which has been applied as a PC-based decision support tool in the telecommunications industry, marries the dynamic optimization literature with decision calculus approaches offering sufficient flexibility for applied contexts. We discuss the approach and describe its use to derive optimal price and advertising policies. Strategies not commonly suggested using traditional formulations are also presented.     

Discrete time modeling of mean-reverting stochastic processes for real option valuation

In this paper the recombining binomial lattice approach for modeling real options and valuing managerial flexibility is generalized to address a common issue in many practical applications, underlying stochastic processes that are mean-reverting. Binomial lattices were first introduced to approximate stochastic processes for valuation of financial options, and they provide a convenient framework for numerical analysis. Unfortunately, the standard approach to constructing binomial lattices can result in invalid probabilities of up and down moves in the lattice when a mean-reverting stochastic process is to be approximated. There have been several alternative methods introduced for modeling mean-reverting processes, including simulation-based approaches and trinomial trees, however they unfortunately complicate the numerical analysis of valuation problems. The approach developed in this paper utilizes a more general binomial approximation methodology from the existing literature to model simple homoskedastic mean-reverting stochastic processes as recombining lattices. This approach is then extended to model dual correlated one-factor mean-reverting processes. These models facilitate the evaluation of options with early-exercise characteristics, as well as multiple concurrent options.