On the Tanaka formula for the derivative of self-intersection local time of fractional Brownian motion

The derivative of self-intersection local time (DSLT) for Brownian motion was introduced by Rosen (2005) and subsequently used by others to study the L²$L^2$ and L³$L^3$ moduli of continuity of Brownian local time. A version of the DSLT for fractional Brownian motion (fBm) was introduced in Yan et al. (2008); however, the definition given there presents difficulties, since it is motivated by an incorrect application of the fractional Itô formula. To rectify this, we introduce a modified DSLT for fBm and prove existence using an explicit Wiener chaos expansion. We will then argue that our modification is the natural version of the DSLT by rigorously proving the corresponding Tanaka formula. This formula corrects a formal identity given in both Rosen (2005) and Yan et al. (2008). In the course of this endeavor we prove a Fubini theorem for integrals with respect to fBm. The Fubini theorem may be of independent interest, as it generalizes (to Hida distributions) similar results previously seen in the literature. As a further byproduct of our investigation, we also provide a small correction to an important technical second-moment bound for fBm which has appeared in the literature many times.     

A semilocal convergence result for Newton’s method under generalized conditions of Kantorovich

From Kantorovich’s theory we establish a general semilocal convergence result for Newton’s method based fundamentally on a generalization required to the second derivative of the operator involved. As a consequence, we obtain a modification of the domain of starting points for Newton’s method and improve the a priori error estimates. Finally, we illustrate our study with an application to a special case of conservative problems.     

绿色建筑项目管理综合均衡优化研究

绿色建筑凭借其诸多优点,已然成为我国未来建筑发展的新方向,而对绿色建筑的工期、成本和功能进行全面系统研究并进行综合均衡优化,对于促进绿色建筑的发展具有深远影响.在描述各工程活动的成本和持续时间之间、功能和持续时间之间的非线性关系基础上,运用多属性效用函数理论构建了绿色建筑项目的功能一工期一成本综合均衡优化模型,并用遗传算法进行求解,可以得到最佳均衡解.最后通过一个实例验证了优化模型具有良好的科学性和实用性.     

On a nonlocal problem modelling Ohmic heating in planar domains

In this paper, we consider the nonlocal problem of the form ut-Δu = (λe-u)/(∫Ωe-udx)2,x ∈Ω, t0 and the associated nonlocal stationary problem -Δv = (λe-v)/(∫Ωe-vdx)2, x ∈Ω,where λ is a positive parameter. For Ω to be an annulus, we prove that the nonlocal stationary problemhas a unique solution if and only if λ 2| Ω| 2 , and for λ = 2|Ω|2, the solution of the nonlocal parabolic problem grows up globally to infinity as t →∞.     

分式布朗运动的加权局部时

本文研究了Hurst参数H∈(0,1)的分式布朗运动的加权局部时.利用多重Wiener-It(o)积分,得到了分式布朗运动的加权局部时的展开式,推广了布朗运动的加权局部时问题.     

The fractal dimensions of the level sets of the generalized iterated Brownian motion

Let{W1(t), t∈R+} and {W2(t), t∈R+} be two independent Brownian motions with W1(0) = W2(0) = 0. {H (t) = W1(|W2(t)|), t ∈R+} is called a generalized iterated Brownian motion. In this paper, the Hausdorff dimension and packing dimension of the level sets {t ∈[0, T ], H(t) = x} are established for any 0 < T ≤ 1.     

一类带时间窗车辆分配问题的贪婪算法

本文对一类带时间窗的车辆分配问题进行了分析,引入了车辆任务的概念,并将问题转化为车辆与车辆任务的匹配问题,同时制订了运输任务选择和车辆选择的贪婪策略,并在此基础上设计了车辆分配问题的贪婪算法,最后通过实例验证了算法的有效性。     

基于Rosenbrock型指数积分的一维间断Galerkin有限元方法

提出基于Rosenbrock型指数积分的一维间断Galerkin有限元方法.该方法在空间上使用间断有限元方法离散,在时间上采用Rosenbrock型指数积分方法.这样不仅可以保持空间离散上的高精度,而且继承了指数时间积分方法具有显式大步长时间推进的优点.数值试验的结果表明,对于一维双曲守恒律问题,这种方法是一种有效的数值算法.     

基于均线交易系统的非特定时间动态VaR研究

为使交易产生稳定持续的收益, 使用基于一定交易规则的交易系统进行交易成为越来越多的投资者和投资机构使用的方法。如能把VaR引入交易系统,进行风险管理,将具有重要的意义。本文以5-60日均线交易系统为研究对象,建立了非特定时间动态VaR模型。经过检验,验证了模型的准确性。在基于模型进行交易策略优化后,得出了有意义的结果。本文使VaR在非特定时间度量方面实现了应用,研究结果对交易系统的风险控制,具有较大的应用价值。