一个角平分线猜想不等式的证明

应用三角形一个重要的基本不等式,证明了有关三角形内角平分线之和的一个猜想不等式:设wa,wb,wc与s分别是三角形三条内角平分线和半周长,R,r分别为三角形的外接圆半径,则(wa wb wc)2s2 102Rr/5 66r2/5.指出了一个相关的值得进一步探讨的问题.     

Comparison between a reanalyzed product by 3-dimensional variational assimilation technique and observations in the Ulleung Basin of the East/Japan Sea

Reanalyzed products from a MOM3-based East Sea Regional Ocean Model with a 3-dimentional variational data assimilation module (DA-ESROM), have been compared with the observed hydrographic and current datasets in the Ulleung Basin (UB) of the East/Japan Sea (EJS). Satellite-borne sea surface temperature and sea surface height data, and in-situ temperature profiles have been assimilated into the DA-ESROM. The performance of the DA-ESROM appears to be efficient enough to be used in an operational ocean forecast system.Comparing with the results from Mitchell et al. [Mitchell, D. A., Watts, D. R., Wimbush, M., Teague, W.J., Tracey, K. L., Book, J. W., Chang, K.-I., Suk, M.-S., Yoon, J.-H., 2005a. Upper circulation patterns in the Ulleung Basin. Deep-Sea Res. II, 52, 1617-1638.], the DA-ESROM fairly well simulates the high variability of the Ulleung Warm Eddy and Dok Cold Eddy as well as the branching of the Tsushima Warm Current in the UB. The overall root-mean-square error between 100 m temperature field reproduced by the DA-ESROM and the observed 100-dbar temperature field is 2.1 °C, and the spatially averaged grid-to-grid correlation between the two temperature fields is high with a mean value of 0.79 for the inter-comparison period.The DA-ESROM reproduces the development of strong southward North Korean Cold Current (NKCC) in summer consistent with the observational results, which is thought to be an improvement of the previous numerical models in the EJS. The reanalyzed products show that the NKCC is about 35 km wide, and flows southward along the Korean coast from spring to summer with maximum monthly mean volume transport of about 0.8 Sv in August–September.     

三阶微分差分方程非线性边值问题的存在性与唯一性

利用微分不等式技巧研究了一类三阶微分差分方程的非线性边值问题,以二阶边值问题的已知结果为基础,建立了Volterra型积分微分差分非线性方程解的存在性,利用反证法获得了解的唯一性.同时,构造适当的上下解,得到了三阶微分差分方程解的存在性与唯一性.结果表明：这种技巧为其它边值问题的研究提出了崭新的思路.     

基于离散水平集方法的Chan-Vese模型

采用离散形式的水平集函数代替传统的符号距离函数,提出基于离散水平集方法的Chan-Vese模型。采用变分方法得到水平集函数演化的梯度降方程,对得到的演化方程进行半隐式离散求解和数值算例验证,并与传统的符号距离函数方法进行对比,以验证离散水平集方法在图像分割中的优势。实验结果表明,基于离散水平集方法的Chan-Vese模型分割速度和精度比用符号距离函数实现的Chan-Vese模型有明显提高。     

HVB随机积分的性质及收敛定理

讨论了关于布朗运动的随机积分用Henstock变差逼近的方法所定义的积分(即HVB积分)的一些性质和收敛定理.主要包括积分原过程的绝对连续性,平均收敛定理,一致收敛定理和Vitali收敛定理.     

一个三角形中线不等式猜想的证明

采用三角形不等式中R—r—s方法,证明了作者多年前提出的一个有关三角形的猜想不等式,即有关中线ma,mb,mc与外接圆半径R以及内切圆半径r的不等式：1Ama＋1／mb＋1／mc≤2（1／R＋1／r）／3．     

ATIS 作用下弹性需求混合交通均衡的效率损失

在ATIS 用户和利己用户组成的交通网络中，利己用户遵循用户均衡原则选择出行路径，其目的是最小化自身出行成本；先进出行者信息系统(ATIS)用户遵循系统最优原则选择出行路径，其目的是最小化系统总出行成本. 本文基于ATIS 用户和利己用户路径选择原则的异质性，对弹性需求下该类混合交通均衡分配的效率损失进行探讨. 构建弹性需求下该类混合交通均衡分配的变分不等式模型，界定其效率损失上界. 结果表明，效率损失上界与用户均衡时社会总收益与社会总剩余之比相关，还与用户均衡时路段上ATIS 用户的流量与总流量之比有关.     

A semi-analytical approach for solving the bottleneck model with general user heterogeneity

This paper proposes a novel semi-analytical approach for solving the dynamic user equilibrium (DUE) of a bottleneck model with general heterogeneous users. The proposed approach makes use of the analytical solutions from the bottleneck analysis to create an equivalent assignment problem that admits closed-form commute cost functions. The equivalent problem is a static and asymmetric traffic assignment problem, which can be formulated as a variational inequality problem (VIP). This approach provides a new tool to analyze the properties of the bottleneck model with general heterogeneity, and to design efficient solution methods. In particular, the existence and uniqueness of the DUE solution can be established using the P-property of the Jacobian matrix. Our numerical experiments show that a simple decomposition algorithm is able to quickly solve the equivalent VIP to high precision. The proposed VIP formation is also extended to address simultaneous departure time and route choice in a single O–D origin-destination network with multiple parallel routes.     

Distribution-free travel time reliability assessment with probability inequalities

An assumption that pervades the current transportation system reliability assessment literature is that probability distributions of the sources of uncertainty are known explicitly. However, this distribution may be unavailable (inaccurate) in reality as we may have no (insufficient) data to calibrate the distribution. In this paper we relax this assumption and present a new method to assess travel time reliability that is distribution-free in the sense that the methodology only requires that the first N moments (where N is a user-specified positive integer) of the travel time to be known and that the travel times reside in a set of bounded and known intervals. Because of our modeling approach, all sources of uncertainty are automatically accounted for, as long as they are statistically independent. Instead of deriving exact probabilities on travel times exceeding certain thresholds via computationally intensive methods, we develop semi-analytical probability inequalities to quickly (i.e. within a fraction of a second) obtain upper bounds on the desired probability. Numerical experiments suggest that the inclusion of higher order moments can potentially significantly improve the bounds. The case study also demonstrates that the derived bounds are nontrivial for a large range of travel time values.     

Multi-class percentile user equilibrium with flow-dependent stochasticity

Travelers often reserve a buffer time for trips sensitive to arrival time in order to hedge against the uncertainties in a transportation system. To model the effects of such behavior, travelers are assumed to choose routes to minimize the percentile travel time, i.e. the travel time budget that ensures their preferred probability of on-time arrival; in doing so, they drive the system to a percentile user equilibrium (UE), which can be viewed as an extension of the classic Wardrop equilibrium. The stochasticity in the supply of transportation are incorporated by modeling the service flow rate of each road segment as a random variable. Such stochasticity is flow-dependent in the sense that the probability density functions of these random variables, from which the distribution of link travel time are constructed, are specified endogenously with flow-dependent parameters. The percentile route travel time, obtained by directly convolving the link travel time distributions in this paper, is not available in closed form in general and has to be numerically evaluated. To reveal their structural properties, percentile UE solutions are examined in special cases and verified with numerical results. For the general multi-class percentile UE traffic assignment problem, a variational inequality formulation is given and solved using a route-based algorithm. The algorithm makes use of the diagonal elements in the Jacobian of percentile route travel time, which is approximated through recursive convolution. Preliminary numerical experiments indicate that the algorithm is able to achieve highly precise equilibrium solutions.