Adaptive Algorithm for Constrained Least-Squares Problems

This paper is concerned with the implementation and testing of an algorithm for solving constrained least-squares problems. The algorithm is an adaptation to the least-squares case of sequential quadratic programming (SQP) trust-region methods for solving general constrained optimization problems. At each iteration, our local quadratic subproblem includes the use of the Gauss–Newton approximation but also encompasses a structured secant approximation along with tests of when to use this approximation. This method has been tested on a selection of standard problems. The results indicate that, for least-squares problems, the approach taken here is a viable alternative to standard general optimization methods such as the Byrd–Omojokun trust-region method and the Powell damped BFGS line search method.     

The Kissing Triangles: The Aesthetics of Mathematical Discovery

Papert's (1978) appeal to reconsider the power and possibilities of the aesthetic in mathematics learning is often ignored in mathematics education research. This paper begins with the premise, put forth by Dewey (1934), that the aesthetic structures many dimensions of inquiry and experience. In the same way that using particular paintings, musical compositions, or even everyday experiences has been instrumental to attempts by philosophers to understand the aesthetic dimensions of meaning and experience in artistic domains, I propose that analysing a particular encounter with mathematics may help reveal the nature and role of the often nebulous responses of elegance, beauty, and `fit' to which mathematicians lay claim in their mathematical activity. To achieve this, I draw on and adapt the defining features of the aesthetic character of experience set forth by the aesthetician Beardsley (1982). This, in turn, sheds light on the role thataesthetics can play in mathematical inquiry and experience, and provides initial categories and conjectures that can be used to investigate the potential roles of aesthetics in mathematics learning contexts.This revised version was published online in September 2005 with corrections to the Cover Date.     

具有模糊数的模糊多目标群体决策优选模型与方法

多目标群体决策问题是运筹学的一个重要研究领域，目前已经提出了一些有效的决策方法。但对目标值和权重均为模糊数的模糊多目标群体决策问题却研究不多，本对此类模糊多目标群体决策问题进行了探讨，利用相对正理想方案与相对负理想方案概念定义了相对差异距离，进而建立了模糊多目标群体决策优选模型与方法，并通过战役决心方案的评价说明了该方法是可行、有效的，可作为军事决策与决策支持系统的备选方法。     

Two-component model of solar plages

By use of the 2-m Mcmath-Pierce telescope at Kitt Peak, the high-quality spectra of a plage with moderate brightness near the center of solar disk were obtained. The data include seven spectral lines, which are Hα, Hβ, CaII H and K lines and the infrared triplet. With the consideration of fine structures of solar plages, a two-component atmospheric model is constructed by keeping the cool component to be the quiet atmosphere. Three cases of the hot component are given for different filling factors where the temperature and density distribution are adjusted in order to reproduce the seven observed spectral profiles. We also briefly discuss the influence of the column density at the base of the corona, m0, and the macro-turbulent velocity on the required filling factor and computed profiles. The two-component model is compared with precious one-component semi-empirical models. The limitation of the model is pointed out and further improvement is indicated.     

强流脉冲离子束辐照靶及其喷发的数值研究

利用拟合实测的TEMP Ⅱ型加速器磁绝缘二极管(MID)电压波形及其焦点附近束流密度曲线，建立了Gaussian分布模型，据此计算了与靶作用的离子的能量及数量，采用Monte Carlo(MC)方法计算了沉积在靶内的能量.并以此作为热源，与流体动力学(HD)模型相结合，对不同的靶状态采用相应的状态方程，模拟计算了靶内压力演化情况; 同时对烧蚀产生的等离子体采用理想气体状态方程, 结合HD方程组, 模拟计算了喷发过程中压力的空间演化过程. 关键词： 强流脉冲离子束 Gaussian模型 HD方程 数值研究     

Er3+掺杂的Bi2O3-B2O3-SiO2玻璃的光谱性质

测试了Bi₂O₃-B₂O₃-SiO₂玻璃中的Er³⁺离子的吸收光谱、发射光谱、⁴I_13/2的荧光寿命、拉曼光谱,及OH^-的傅里叶红外吸收光谱。应用Judd-Ofelt理论计算了该玻璃中的Er³⁺离子的J-O参数、振子强度、⁴I_13/2能级的寿命,从而利用测得的⁴I_13/2的荧光寿命得出了⁴I_13/2能级的量子效率(15%)。由于较低量子效率可能与OH^-有关,所以计算了玻璃中的OH^-浓度,发现其浓度较高(1.66×10¹⁹cm^-1,相当于Er³⁺浓度的3倍)。应用McCumber理论和四能级模型计算了Er³⁺离子的受激发射截面和荧光发射光谱的半峰全宽,结果与通过吸收光谱计算所得基本吻合。根据透射率和折射率的关系计算了折射率,发现和测量值相差很大,说明有较大的散射,通过拉曼光谱和显微镜测试,认为是玻璃中的微小气泡造成的。     

动态激光衍射法测量细丝直径

基于夫琅禾费衍射理论和巴比涅互补原理,提出了利用激光衍射对细丝直径进行动态测量的方法.该方法具有测量精度高、速度快、非接触、使用方便且易于微机联接实现自动化测量等优点.     

Patterns and Symmetries in the Visual Cortex and in Natural Images

As borders between different entities, lines are an important element of natural images. Indeed, the neurons of the mammalian visual cortex are tuned to respond best to lines of a given orientation. This preferred orientation varies continuously across most of the cortex, but also has vortex-like singularities known as pinwheels. In attempting to describe such patterns of orientation preference, we are led to consider underlying rotation symmetries: Oriented segments in natural images tend to be collinear; neurons are more likely to be connected if their preferred orientations are aligned to their topographic separation. These are indications of a reduced symmetry requiring joint rotations of both orientation preference and the underlying topography. This is verified by direct statistical tests in both natural images and in cortical maps. Using the statistics of natural scenes we construct filters that are best suited to extracting information from such images, and find qualitative similarities to mammalian vision. PACS84.35+i 89.70.+c 87.57.Nk     

Fundamental processes in long air gap discharges

The development of atmospheric lightning is initiated and sustained by the formation in virgin air of ‘streamer corona’ and ‘leader’ discharges, very similar to those observed in laboratory long sparks. Therefore, the experimental and theoretical investigations of these laboratory discharges have become of large interest to improve the physical knowledge of the lightning process and to develop self-consistent models that could be applied to new protection concepts.In the present paper the fundamental processes of the subsequent phases of long air gap discharges are analyzed, from the first corona inception and development to the leader channel formation and propagation. For all these processes simulations models are discussed that have been essentially derived and simplified by the authors, in order to develop sequential time-dependent simulation of the laboratory breakdown, with both positive and negative voltages. The possibility of extending these models to the case of natural lightning is discussed in the companion paper, presented in this same volume. To cite this article: I. Gallimberti et al., C. R. Physique 3 (2002) 1335–1359.