No Gap Second-Order Optimality Conditions for Circular Conic Programs

In this article, we study the second-order optimality conditions for a class of circular conic optimization problem. First, the explicit expressions of the tangent cone and the second-order tangent set for a given circular cone are derived. Then, we establish the closed-form formulation of critical cone and calculate the “sigma” term of the aforementioned optimization problem. At last, in light of tools of variational analysis, we present the associated no gap second-order optimality conditions. Compared to analogous results in the literature, our approach is intuitive and straightforward, which can be manipulated and verified. An example is illustrated to this end.     

光学薄膜特性的锥角效应数值分析

建立非平行光入射多层膜的模型,给出了在圆形光束锥角入射时的薄膜特性表达式,对三类典型光学薄膜即多腔滤光片、非偏振分光薄膜和非偏振截止滤光薄膜的特性进行了数值实验。研究结果表明:随着光束入射锥角的增加,多腔滤光片的影响是中心波长向短波方向移动,透射率下降和通带形状退化;非偏振分光薄膜的s和p偏振透射率增加,宽带波纹度增加;非偏振截止滤光薄膜的通带透射率出现周期振荡,s偏振的通带波纹度大于p偏振,通带波纹度总体具有增加的趋势,过渡区的陡度具有变大的趋势。     

光锥角对窄带滤光片透射率的影响及补偿方法

全介质膜窄带滤光片因具有优良的光学性能、较强的工艺性和空间环境适应性被广泛应用于空间多光谱遥感仪器中,但锥光束入射导致的中心波长漂移问题严重影响此类窄带滤光片的光谱选择性能。为了研究光锥角对窄带滤光片透射率特性的影响,设计了非规整型全介质膜窄带滤光片,分析了高斯光束倾斜入射窄带滤光片导致透射率的变化,建立了非均匀照度下锥光束正入射时窄带滤光片等效透射率的求解模型,定量求解了等效透射率及中心波长漂移量,并对理论模型进行了实验验证。结果表明,锥光束正入射对窄带滤光片透射率的影响主要表现为中心波长的蓝移;在镀膜工艺相对稳定的基础上,理论模型的等效透射率预测精度优于中心波长的0.15%。所以,可以使用等效透射率求解模型定量计算锥光束正入射导致窄带滤光片透射率的变化,并利用中心波长漂移量修正后的设计数据指导滤光片镀膜,进而实现窄带滤光片的高精度光谱选择,这为解决介质膜窄带滤光片因锥光束入射导致的中心波长漂移问题提供了新的技术途径。     

直接辐射式扬声器系统的低频效率计算公式*

效率是扬声器系统的重要性能指标,然而常用的标称效率在低频范围并不适用。本文研究直接辐射式扬声器系统的低频效率,推导了基于TS参数的低频效率计算公式。针对封闭式扬声器系统和倒相式扬声器系统,开展实验验证,结果表明本文提出的计算公式得到的低频效率与实验测量得到的低频效率较为相符。进一步对比分析低频效率和标称效率,结果表明低频效率能够适用于低频,能准确地展示扬声器系统参数对效率的影响。利用本文提出的计算公式,有助于进一步优化提升扬声器系统的低频效率。     

Toric Rigid Spaces

This paper gives a method to construct rigid spaces, which is similar to the method used to construct toric schemes.     

一类二阶三点边值问题单调正解的存在性

利用范数形式的锥上不动点定理,研究了一类二阶微分方程三点边值问题单调正解的存在性．分别给出了齐次和非齐次边界条件下的三点边值问题单调正解存在的充分条件,确定了解曲线的凹凸性,并且给出了一个应用实例．     

四阶微分方程奇异边值问题的正解

本文利用锥上的不动点指数理论,在更一般的边界条件下讨论了一类四阶奇异边值问题正解的存在性并给出了应用．     

Robust supergain beamforming for circular array via second-order cone programming

The phenomenon of supergain for a circular array and its robust beamforming are presented. The coplanar superdirective array gain of the circular array, although it is not so extreme as an endfire line array, outperforms a lot over that of a conventional delay-and-sum beamformer in isotropic noise fields when the inter-element spacings are much smaller than one-half wavelength. However, optimum beamforming algorithms can be extremely sensitive to slight errors in array characteristics. The performance are known to degrade significantly if some of underlying assumptions on the sensor array is violated. Therefore, white noise gain constraint is used to improve the robustness of the supergain beamformer against random errors. We show that the design of the weight vector of robust supergain beamformer can be reformulated as a form of second-order cone programming and resolved efficiently via the well-established interior point method. Results of computer simulation for a 24-element circular array confirm satisfactory performance of the approach proposed in this paper.     

Features of the Motion of a Gas-Liquid Medium in a Compound Shell (Sphere and Truncated Cone) Subject to Vibration

The results from an experimental study into the dynamic behavior of a gas-liquid medium and solid particles in a compound shell (sphere-truncated cone) are reported on. The following processes are studied: formation of gas bubbles and their clusters, strong macroflows, and intensive chaotic motion of the medium in the truncated cone as a nonlinear vibrating liquid-gas system__________Translated from Prikladnaya Mekhanika, Vol. 41, No. 1, pp. 112–118, January 2005.     

Indefinite preference structures and decision analysis

It always takes time for people to digest information and make judgments. The decision maker's preference is not always clear and stable when decision analysis and decision making are performed. In this paper, we introduce a generalized preference structure to cope with indefinite preferences. We describe its general properties, its implication on value function representation, its solution concepts, and methods for obtaining the solutions.This research has been partially supported by NSF Grant No. IST-84-18863. The authors are grateful to Dr. D. J. White for his helpful comments on a previous draft.