A Survey on Explicit Representation Formulae for Fundamental Solutions of Linear Partial Differential Operators

In the present article, we aim at treating the existence of fundamental solutions of linear partial differential operators with constant coefficients from the viewpoint of setting up explicit formulae yielding fundamental solutions.     

Sets of sampling and interpolation in Bergman spaces

Properties of the unions of sampling and interpolation sets for Bergman spaces are discussed in conjunction with the examples given by Seip (1993). Their relationship to the classical interpolation sequences is explored. In addition, the role played by canonical divisors in the study of these sets is examined and an example of a sampling set is constructed in the disk.

     

红外遥感用低温制冷器的进展

低温制冷器与红外探测器配套，是军事现代化、高新技术等急需发展的关键产品。国内研制技术也已接近国际先进水平，基本掌握了小型化、低振动、长寿命、细方形漆包线制作、间隙密封、消除电磁干扰等相关关键技术。本文列出了已研制过的直线电机谐振压缩机的主要技术性能。希望主管、用户、研制、生产各方通力合作，应用－改进－再应用－再改进，实现我国低温制冷器的产业化。     

A Note on Geometric Structures of Linear Ordered Orthogonal Arrays and (T,M,S)-Nets of Low Strength

The equivalent geometrical configurations of linear ordered orthogonal arrays are determined when their strengths are 3 and 4. Existence of such geometrical configurations is investigated. They are also useful in the study of (T, M, S)-nets.     

Disparity field and depth map coding for multiview 3D image generation

In the present paper techniques are examined for the coding of the depth map and disparity fields for stereo or multiview image communication applications. It is assumed that both the left and right channels of the multiview image sequence are coded using block- or object-based methods. A dynamic programming algorithm is used to estimate a disparity field between each stereo image pair. Depth is then estimated and occlusions are optionally detected, based on the estimated disparity fields. Spatial interpolation techniques are examined based on the disparity/depth information and the detection of occluded regions using either stereoscopic or trinocular camera configurations. It is seen that the presence of a third camera at the transmitter site improves the estimation of disparities, the detection of occlusions and the accuracy of the resulting spatial interpolation at the receiver. Various disparity field and depth map coding techniques are then proposed and evaluated, with emphasis given to the quality of the resulting intermediate images at the receiver site. Block-based and wireframe modeling techniques are examined for the coding of isolated depth or disparity map information. Further, 2D and 3D motion compensation techniques are evaluated for the coding of sequences of depth or disparity maps. The motion fields needed may be available as a byproduct of block-based or object-based coding of the intensity images. Experimental results are given for the evaluation of the performance of the proposed coding and spatial interpolation methods.     

An 8-bit, 200 MSPS Folding and Interpolating ADC

An 8-bit, 200 MSPS folding and interpolating analog-to-digitalconverter, ADC, has been implemented in a 1.2 µmBiCMOS-process. It achieves 7.5 effective bits with a power dissipationof 575mW. The active area is 4mm². The implementationand measured results are presented. A simple analytical modelfor the interpolation-induced nonlinearity in a folding and interpolatingADC using sinusoidal folding is presented. The bowing of thereference ladder due to interaction with the input stages isanalyzed, and analytical models are derived.     

Balance constraints reduction of large-scale linear programming problems

This paper describes a method and the corresponding algorithms for simplification of large-scale linear programming models. It consists of the elimination of the balance constraints (i.e. constraints with zero RHS term). The idea is to apply some linear transformations to the original problem in order to nullify the balance constraints. These transformations are able to simultaneously eliminate more balance rows. The core of this contribution is the introduction of the reduction matrix and the associated theorems on the equivalent linear programs (original and reduced). The numerical experiments with this method of simplification proved this approach to be beneficial for a large class of LP problems.This research work was done while the first author was at Duisburg University, Mess-, Steuer und Regelungstechnik, Germany, under the greatly appreciated financial assistance given by the Alexander-von-Humboldt Foundation.     

Extended convergence results for the method of multipliers for nonstrictly binding inequality constraints

In this paper, we extend the classical convergence and rate of convergence results for the method of multipliers for equality constrained problems to general inequality constrained problems, without assuming the strict complementarity hypothesis at the local optimal solution. Instead, we consider an alternative second-order sufficient condition for a strict local minimum, which coincides with the standard one in the case of strict complementary slackness. As a consequence, new stopping rules are derived in order to guarantee a local linear rate of convergence for the method, even if the current Lagrangian is only asymptotically minimized in this more general setting. These extended results allow us to broaden the scope of applicability of the method of multipliers, in order to cover all those problems admitting loosely binding constraints at some optimal solution. This fact is not meaningless, since in practice this kind of problem seems to be more the rule rather than the exception.In proving the different results, we follow the classical primaldual approach to the method of multipliers, considering the approximate minimizers for the original augmented Lagrangian as the exact solutions for some adequate approximate augmented Lagrangian. In particular, we prove a general uniform continuity property concerning both their primal and their dual optimal solution set maps, a property that could be useful beyond the scope of this paper. This approach leads to very simple proofs of the preliminary results and to a straight-forward proof of the main results.The author gratefully acknowledges the referees for their helpful comments and remarks. This research was supported by FONDECYT (Fondo Nacional de Desarrollo Científico y Technológico de Chile).     

谐振子薛定谔方程的简单解法

物质的许多物理与化学性质都可以用线性谐振子模型解释，本文用简单的数学运算求解线性谐振子的薛定谔方程，避免了特殊函数等复杂的数学运算，得出了量子力学教材完全相同的结果。     

Hermite Interpolation of Data Sets by Minimal Spline Spaces

Hermite interpolation of 2n + k data by spline spaces of order k with n variable knots counting multiplicities is studied. A characterization of the minimal spline spaces which admit a solution of the interpolation problem is obtained. A sufficient condition on uniqueness of interpolating spline functions is given.