双边截断型分布族参数的经验Bayes估计

在Linex损失函数下,讨论一类双边截断型分布族参数的经验Bayes（EB）估计问题,构造了参数的EB估计,在适当的条件下给出了该估计的收敛速度,最后给出例子,说明定理条件的合理性。     

多维线性模型均值矩阵的线性Minimax估计

本研究多维线性模型中均值矩阵在不同损失函数下的线性Ｍｉｎｉｍａｘ估计,得到了具体的表达式。     

乙醇在Mn薄膜／Rh（100）上吸附和分解的研究

应用高分辨电子能量损失谱（HREELS）和热脱附谱（TDS）,研究了Mn薄膜／Rh(100)上乙醇的吸附和分解,提出了表面吸附和分解的反应工,在300K时,蒸镀的Mn在清洁Rh(100)表面上以层层模式生长;在130－300K间,在25mLMn/Rh(100)表面上吸附20L乙醇的TDS结果与乙醇在Rh(100)表面上的结果一致在155K处,脱附出多层凝聚态吸附的乙醇;升温到255K,脱附出H2和CH4,继续升温,出现了与乙醇在R (100)表面上不一致的现象,在470K,同时出现了第2个H2和CH4的脱附峰,在500K,脱附极少量的CO;在950K附近,脱附出大量CO。     

A catenary element for the analysis of cable structures

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奇异值函数的二阶方向导数

本文用一个直接的方法给出了奇异值函数的二阶方向导数公式. 作为应用, 利用这一公式建立了谱范数的上图集合与核范数的上图集合的切锥和二阶切集的具体表达式, 这些表达式在矩阵优化的一阶和二阶最优条件的研究中起着重要作用.     

A Framework for Four-Dimensional Variational Data Assimilation Based on Machine Learning

The initial field has a crucial influence on numerical weather prediction (NWP). Data assimilation (DA) is a reliable method to obtain the initial field of the forecast model. At the same time, data are the carriers of information. Observational data are a concrete representation of information. DA is also the process of sorting observation data, during which entropy gradually decreases. Four-dimensional variational assimilation (4D-Var) is the most popular approach. However, due to the complexity of the physical model, the tangent linear and adjoint models, and other processes, the realization of a 4D-Var system is complicated, and the computational efficiency is expensive. Machine learning (ML) is a method of gaining simulation results by training a large amount of data. It achieves remarkable success in various applications, and operational NWP and DA are no exception. In this work, we synthesize insights and techniques from previous studies to design a pure data-driven 4D-Var implementation framework named ML-4DVAR based on the bilinear neural network (BNN). The framework replaces the traditional physical model with the BNN model for prediction. Moreover, it directly makes use of the ML model obtained from the simulation data to implement the primary process of 4D-Var, including the realization of the short-term forecast process and the tangent linear and adjoint models. We test a strong-constraint 4D-Var system with the Lorenz-96 model, and we compared the traditional 4D-Var system with ML-4DVAR. The experimental results demonstrate that the ML-4DVAR framework can achieve better assimilation results and significantly improve computational efficiency.     

通信用低损耗蜘蛛网结构包层空芯塑料布喇格光纤

提出并分析了利用蜘蛛网结构包层空芯布喇格光纤在0.65 μm~1.55 μm和200 μm ~500 μm波长范围得到低损耗传输的可能性.采用渐近转移矩阵公式所做的分析结果表明：这种光纤的传输损耗远低于构成光纤所用塑料的吸收损耗.在0.65 μm ~1.54 μm的可见至近红外波段,这种光纤结构可把构成光纤所用塑料的吸收损耗抑制为1/237 000,甚至可抑制为1/1 300 000;在200 μm ~500 μm的太赫兹波段,这种光纤结构可把构成光纤所用塑料的吸收损耗抑制为1/8 962,甚至可抑制为1/83 390.因此用便宜的塑料,可以在可见至太赫兹波段用这种光纤构成较长距离、较高带宽的光纤通信系统,并实现波分复用（WDM）.     

Contingent cone to a set defined by equality and inequality constraints at a Fréchet differentiable point

In this paper, we prove equality expression for the contingent cone and the strict normal cone to a set determined by equality and/or inequality constraints at a Fréchet differentiable point. A similar result has appeared before in the literature under the assumption that all the constraint functions are of classC or under the assumption that the functions are strictly differentiable at the point in question. Our result has applications to the calculation of various kinds of tangent cones and normal cones.This research was supported, in part by the National Science and Engineering Research Council of Canada under Grant No. OGP-41983.The authors would like to thank D. E. Ward for his many helpful comments.     

Optimality conditions in mathematical programming and composite optimization

New second order optimality conditions for mathematical programming problems and for the minimization of composite functions are presented. They are derived from a general second order Fermat's rule for the minimization of a function over an arbitrary subset of a Banach space. The necessary conditions are more accurate than the recent results of Kawasaki (1988) and Cominetti (1989); but, more importantly, in the finite dimensional case they are twinned with sufficient conditions which differ by the replacement of an inequality by a strict inequality. We point out the equivalence of the mathematical programming problem with the problem of minimizing a composite function. Our conditions are especially important when one deals with functional constraints. When the cone defining the constraints is polyhedral we recover the classical conditions of Ben-Tal—Zowe (1982) and Cominetti (1990).     

Quasi-optical measurement of complex dielectric constant at 300 GHz

A two beam interferometer in the Martin-Puplett configuration is used to determine the complex dielectric constant at 300 GHz of teflon, TPX-plastics, SPECTRALON and paraffin waxes with melting temperatures of 48° C and 72° C, respectively. The design of the quasi-optical system leads to a constant beam diameter at the power detector independent of path delay and frequency. The power detector signal is recorded not only along one period but over about 50 periods. A spectrum estimation routine allows to determine more exactly amplitude and phase angle of the signal. A basic problem is noticed: imperfect detector and source match cause harmonic distortion of the power detector signal. The effects on processing the loss tangent and the invalidation are shown. Finally loss tangent and dielectric constant are determined indirectly by optimizing an equivalent microwave circuit using a commercial available microwave design system to take multiple reflections and losses in consideration.