拟向量变分不等式的存在性

讨论了拟向量变分不等式问题，在适当条件下，针对不连续映射得到了拟向量变分不等式的存在性。     

向量值映射的极大极小不等式

本文讨论了极大极小不等式问题，证明了仿射连续向量值映射的极大极小不等式以及集值映射的一种极大极小不等式。     

自反巴拿赫空间中混合变分不等式的稳定性与Tikhonov正则化

在自反巴拿赫空间中介绍混合变分不等式的Tikhonov正则化并建立其相关理论.首先,建立Minty型混合变分不等式的解集非空有界的等价刻画.利用Minty型混合变分不等式解集非空有界的等价条件讨论映射与非线性项同时被扰动时,Minty型混合变分不等式的稳定性.基于此稳定性结果,研究Tikhonov正则化的Minty型混合变分不等式解集的特征与扰动分析.进而,获得Tikhonov正则化的广义混合变分不等式解集的特征与扰动分析.     

纵连板式无砟轨道热致隆起屈曲解析解

利用能量变分原理，求解了纵连板式轨道在温度荷载作用下隆起屈曲的解析解，建立了纵连板式轨道失稳临界状态的非线性平衡方程，并与数值分析进行对比验证了解析解的正确性。研究结果表明，轨道厚度、重度是影响上拱稳定性的重要因素，在轨道施工和运营过程中应着重养护；而窄接缝对无限长轨道的整体稳定性影响不明显，局部分析时不可忽略。     

论能量变分的三种解法及其应用

能量变分解可分为三种:间接解、直接解和修正解,其中修正解是建立在直接解的基础上,采用拉格朗日乘子对约束条件和位移函数进行了修正,得到了用于变分分析的无约束泛函。对这三种能量变分解进行了探讨,并对这三种能量变分解在高层及大跨度结构分析中的应用作了简要的介绍,得出了一些有益的结论,对工程应用有一定参考价值。     

自反巴拿赫空间中广义变分不等式的稳定性与Tikhonov正则化(英文)

在自反巴拿赫空间中,介绍了广义变分不等式的Tikhonov正则化及其相关理论.首先讨论了映射被扰动变分不等式的稳定性结果.基于稳定性,给出了Tikhonov正则化的变分不等式解集的某些特征.此结果推广了该领域已有的研究结果.     

关于Hilbert空间中一类广义随机非线性变分不等式

介绍并研究了Hilbert空间中的Minty型广义随机非线性变分不等式问题,并在适当的条件和假设下,得到了这类广义非线性随机变分不等式和Stampacchia型广义随机非线性变分不等式的等价的结论;运用该结论,结合随机化的Banach压缩映像原理得到了关于这一类广义随机非线性变分不等式问题的一些新的随机解的存在性结果.     

一阶非线性时滞差分方程的振动准则

在线性差分方程和的基础上,利用分析法和不等式法证明了一阶非线性时滞差分方程的所有解振动的充分条件,进而利用反证法,假设方程有一非振动解,结合均值不等式法,得出与条件矛盾的结果。于是得到了一阶非线性时滞差分方程在不同条件下所有解的振动准则,推广和改进了线性差分方程已有的相关结果。     

一类矩阵不等式的进一步加强

关于Hermite矩阵A和B的v-加权几何均值的相关估计,许多学者进行了深入研究,已经获得了一系列的研究结果.利用双曲函数的性质以及双曲函数对应的泰勒展开式,得到了邹黎敏的文献中标量不等式的改进形式.再利用谱分解定理和改进后的标量不等式,改进了相应的矩阵的v-加权几何均值不等式,使之得到了进一步加强,从而改进了Kittaneh和Manasrah、邹黎敏等学者的文献中的已有结论.     

关于ODE非局部存在性定理的讨论

以无界开区域G内ODE的初值问题解的非局部存在性定理为基础 ,在半闭无界域G′上证明了ODE的初值问题解的三个非局部存在性定理 .     

带有控制参量的向量优化问题研究

在拓扑向量空间中,考虑了带有控制参量的向量优化问题.首先,给出了带有控制参量函数的广义凸概念,并在目标函数和约束函数的广义凸假设下,获得了问题的Benson真有效解与相应的标量化问题的最优解的关系.然后,定义了问题的实Lagrangian函数及Lagrangian函数的鞍点,并在目标函数和约束函数的广义凸假设下,推导了问题的Benson真有效解和鞍点的关系.     

Cosserat弯曲板的增强数学模型

介绍一个可以从非对称应力、偶应力、位移和微转动来假设其物理和数学目标近似值的弯曲板模型。近似值与三维的Cosserat弹性平衡方程、边界条件和本构关系相一致。根据Hellinger-Prange-Reissner变分原理对Cosserat材料和应力-位移关系进行概括,制定Cosserat弯曲板变分原理。通过该原理可获得平衡方程、本构关系和σ33应力组合近似值参数的最小弹性能的最优值。所得出的解被证明是唯一的,与精确的三维解相比较,弯曲板在初步计算中产生了1%的相对误差,而与著名的用于简单受弯弹性板的Reissner模型结果相一致。对于板厚度的标准值来说,这个较低的相对误差是比较稳定的。     

Bifurcation of locally buckled members

The paper presents a general bifurcation analysis of members that are locally buckled in the fundamental state. The members are assumed to be geometrically perfect in the overall sense such that bifurcation of the locally buckled member in an overall mode may occur. The analysis applies to arbitrary types of loads and support conditions. The cross-section, which may be arbitrary in shape, is assumed to be composed of flat plates. The paper derives the general variational equations expressing equilibrium of the fundamental and bifurcated states. The variational equations are applied to doubly symmetric columns and doubly symmetric beam-columns. The differential equations and boundary conditions are derived from the variational equations and solved for the fundamental and bifurcated states, thus providing the bifurcation loads of the members.     

A network traffic assignment model for autonomous vehicles with parking choices

This article is the first in the literature to investigate the network traffic equilibrium for traveling and parking with autonomous vehicles (AVs) under a fully automated traffic environment. Given that AVs can drop off the travelers at their destinations and then drive to the parking spaces by themselves, we introduce the joint equilibrium of AV route choice and parking location choice, and develop a variational inequality (VI)‐based formulation for the proposed equilibrium. We prove the equivalence between the proposed VI model and the defined equilibrium conditions. We also show that the link flow solution at equilibrium is unique, even though both the route choices and parking choices are endogenous when human‐occupied AV trips (from origin to destination) and empty AV trips (from destination to parking) are interacting with each other on the same network. We then develop a solution methodology based on the parking‐route choice structure, where we adjust parking choices in the upper level and route choices in the lower level. Numerical analysis is conducted to explore insights from the introduced modeling framework for AV network equilibrium. The results reveal the significant difference in network equilibrium flows between the AV and non‐AV situations. The results also indicate the sensitivity of the AV traffic pattern to different factors, such as value of time, parking pricing, and supply. The proposed approach provides a critical modeling device for studying the traffic equilibrium under AV behavior patterns, which can be used for the assessment of parking policies and infrastructure development in the future era of AVs.     

两种AR模型模拟空间相关性风场的比较

风场模拟中广泛应用的AR模型主要有标量过程的AR模型和向量过程的AR模型.通过取数学期望的方法,可以得到标量过程AR模型模拟空间相关性风场所采用的参数,但该参数并未考虑时滞的情况.向量过程AR模型建立在联合平稳的假设之上,可以很好地综合考虑各点的空间相关性,且回归系数矩阵包含时滞的影响,可以考虑较长时间范围内各点风速时程的时间相关性,从理论来说,要相对完善一些.本文算例表明,向量过程AR模型所模拟的风场精确度总体上要高于标量过程AR模型所模拟的风场,但也存在所模拟风场各点的自相关函数偏差大和总体运算时间多等缺点.     

Efficiency of scalar and vector intensity measures for seismic slope displacements

Ground motion intensity measures are usually used to predict the earthquake-induced displacements in earth dams, soil slopes and soil structures. In this study, the efficiency of various single ground motion intensity measures (scalar IMs) or a combination of them (vector IMs) are investigated using the PEER-NGA strong motion database and an equivalent-linear sliding-mass model. Although no single intensity measure is efficient enough for all slope conditions, the spectral acceleration at 1.5 times of the initial slope period and Arias intensity of the input motion are found to be the most efficient scalar IMs for flexible slopes and stiff slopes respectively. Vector IMs can incorporate different characteristics of the ground motion and thus significantly improve the efficiency over a wide range of slope conditions. Among various vector IMs considered, the spectral accelerations at multiple spectral periods achieve high efficiency for a wide range of slope conditions. This study provides useful guidance to the development of more efficient empirical prediction models as well as the ground motion selection criteria for time domain analysis of seismic slope displacements.     

线性向量极值问题基最优解的存在性

本文在偏序向量空间中,对线性向量极值问题建立了基的概念,推广了线性规划问题的一些性质和结论,最后得到了基最优解的存在定理。     

A dynamical systems approach for network oligopolies and variational inequalities

The variational inequality problem has been used to formulate and study a plethora of competitive equilibrium problems at the equilibrium state. In this paper, we focus on oligopolistic market network equilibrium problems in which firms are spatially located and seek to determine their profit-maximizing production out-puts and shipments, in the presence of transportation costs. In particular, we utilize the equivalence between the set of stationary points of a dynamical system and the set of solutions to the associated variational inequality problem governing the network oligopoly problem to explore the underlying dynamics both qualitatively and numerically. Although the dynamical system is nonstandard in that the right-hand side is discontinuous, recent theoretical results have shown that the important qualitative and quantitative results of ordinary differential equations are applicable under the standard Lipschitz continuity assumptions. The identification between solutions to dynamical systems and associated variational inequality problems unveils a new tool for addressing the behavior of competitive network systems over time.This paper was presented in draft form at an International Workshop on Trade, Knowledge and the Network Economy, held in December 1992 at Mallacoota, Australia.     

Regional income and wave energy deployment in Ireland

Alongside environmental benefits, renewable energy deployment is often evaluated on grounds of regional development. Focusing on wave energy deployment in Ireland, this paper quantifies employment-related welfare change net of associated subsidy costs. Although the added employment reduces inter-regional inequality, certain subsidies increase total income inequality by a greater extent. Total inequality increases by 0.25% in the preferred scenario. This pattern of incidence persists under an optimistic scenario where all manufacturing activity is carried out locally. This finding highlights that policies of regional development should consider the spatial distribution of associated subsidy costs.