On the pre‐metric foundations of wave mechanics I: massless waves

The mechanics of wave motion in a medium are founded in conservation laws for the physical quantities that the waves carry, combined with the constitutive laws of the medium, and define Lorentzian structures only in degenerate cases of the dispersion laws that follow from the field equations. It is suggested that the transition from wave motion to point motion is best factored into an intermediate step of extended matter motion, which then makes the dimension‐codimension duality of waves and trajectories a natural consequence of the bicharacteristic (geodesic) foliation associated with the dispersion law. This process is illustrated in the conventional case of quadratic dispersion laws, as well as quartic ones, which include the Heisenberg–Euler dispersion law. It is suggested that the contributions to geodesic motion from the non‐quadratic nature of a dispersion law might represent another source of quantum fluctuations about classical extremals, in addition to the diffraction effects that are left out by the geometrical optics approximation.     

Guiding functions and periodic solutions for inclusions with causal multioperators

In the present paper, the method of guiding functions is applied to study the periodic problem for a differential inclusion with a causal multioperator. At first we consider the case when the multioperator is closed and convex-valued. Then the case of a non-convex-valued and lower semicontinuous right-hand part is considered. Thereafter, the theory is extended to the case of non-smooth guiding functions.     

Complex crowns of Riemannian symmetric spaces and non-compactly causal symmetric spaces

In this paper we define a distinguished boundary for the complex crowns of non-compact Riemannian symmetric spaces . The basic result is that affine symmetric spaces of can appear as a component of this boundary if and only if they are non-compactly causal symmetric spaces.

     

Constructing Invariant Fairness Measures for Surfaces

The paper proposes a rational method to derive fairness measures for surfaces. It works in cases where isophotes, reflection lines, planar intersection curves, or other curves are used to judge the fairness of the surface. The surface fairness measure is derived by demanding that all the given curves should be fair with respect to an appropriate curve fairness measure. The method is applied to the field of ship hull design where the curves are plane intersections. The method is extended to the case where one considers, not the fairness of one curve, but the fairness of a one parameter family of curves. Six basic third order invariants by which the fairing measures can be expressed are defined. Furthermore, the geometry of a plane intersection curve is studied, and the variation of the total, the normal, and the geodesic curvature and the geodesic torsion is determined.     

利他偏好下供应链效率和公平度动态演进研究

根据零售商利他偏好信息非对称性和动态演进特征,将零供博弈信息结构分为4个演进过程,采用逆向归纳法求解各个过程中供应链主观效率和客观效率、以"公平熵"计算供应链主观公平度和客观公平度,从主观与客观2个维度分析供应链利他偏好行为对供应链效率和公平度动态演进的影响.通过对比分析得出:信息对称下零售商利他偏好行为不改变供应链利润但会改变各个成员在供应链中的利润分配比例,起到"供应链利润分配机制"的作用;供应链主观效率总是不低于客观效率,供应链主观公平度总是不低于客观公平度;从主观评价供应链能够实现协调且供应链能够兼顾效率和公平.     

Invariant smoothness measures for surfaces

Two novel smoothness measures for surfaces are presented in this paper. The second and third order smoothness are defined as the squared normal curvature and the squared variation in normal curvature integrated over all directions in the tangent plane. Both quantities are truly geometric in the sense that they are invariant with respect to the actual parametrization of the surface. All the same, all formulae are derived in terms of an arbitrary parametrization. In addition to providing a basis for variational surface construction, the second and third order smoothness can also be used for evaluation and assessment of the quality of an existing surface. This revised version was published online in August 2006 with corrections to the Cover Date.     

时变系统的稳定化

This paper deals with the stabilization problem for linear time-varying systems within the framework of nest algebras. We give a necessary and sufficient condition for a class of plants to be stabilizable, and we also study the simultaneous and strong stabilization problems.     

Algorithms for fair k-clustering with multiple protected attributes

We study fair center based clustering problems. In an influential paper, Chierichetti, Kumar, Lattanzi and Vassilvitskii (NIPS 2017) consider the problem of finding a good clustering, say of women and men, such that every cluster contains an equal number of women and men. They were able to obtain a constant factor approximation for this problem for most center based k-clustering objectives such as k-median, k-means, and k-center. Despite considerable interest in extending this problem for multiple protected attributes (e.g. women and men, with or without citizenship), so far constant factor approximations for these problems have remained elusive except in special cases. We settle this question in the affirmative by giving the first constant factor approximation for a wide range of center based k-clustering objectives.     

公平偏好下基于批发价契约的供应链 协调研究

文中基于Nash讨价还价博弈思想建立公平偏好框架,构建公平偏好效用体系,以此为基础对采用批发价契约的报童模型展开行为研究,采用数理模型和数值分析方法分析了零售商和供应商的公平偏好行为对零售商和供应链系统最优订货量的影响,即零售商和供应商同时关注公平时,零售商和供应链系统的最优订货量趋于保守;并发现零售商和供应链系统的最优订货量随零售商的公平偏好程度增加而递减,但随着供应商公平偏好程度增加而递增,且供应链系统最优订货量变化趋势比零售商明显．然后,在此基础上分析比较得到,无论供应商和零售商是否偏好公平,批发价契约都不能实现供应链协调．最后,对批发价、零售价、供应商生产成本、零售商缺货成本和供应商缺货成本进行敏感度分析．