Beyond all orders: Singular perturbations in a mapping

Summary We consider a family ofq-dimensional (q>1), volume-preserving maps depending on a small parameterε. Asε → 0⁺ these maps asymptote to flows which attain a heteroclinic connection. We show that for smallε the heteroclinic connection breaks up and that the splitting between its components scales withε likeε ^γexp[-β/ε]. We estimateβ using the singularities of theε → 0⁺ heteroclinic orbit in the complex plane. We then estimateγ using linearization about orbits in the complex plane. These estimates, as well as the assertions regarding the behavior of the functions in the complex plane, are supported by our numerical calculations. Deceased.     

关于小伸缩商拟共形群的几个定理

本文研究了单位球Bn上小伸缩商拟共形群的离散性质，给出了一个收敛定理，并且证明了在一定限制条件下任意一个非初等非离散小伸缩商拟共形群含有一个二元生成的非初等非离散子群。     

Optimal complex networks spontaneously emerge when information transfer is maximized at least expense: A design perspective

Complex networks with multiple nodes and diverse interactions among them are ubiquitous. We suggest that optimal networks spontaneously emerge when “information” transfer is maximized at the least expense. We support our hypothesis by evolving optimal topologies for a particle swarm optimizer (PSO), a population‐based stochastic algorithm. Results suggest that (1) an optimum topology emerges at the phase transition when connectivity is high enough to transfer information but low enough to prevent premature convergence, and (2) Small World (SW) networks are a compromise between higher performance and resistance to mutation. The graph characteristics of the optimal PSO networks in the SW regime are similar to that of the visual cortices of cat and macaque, thereby suggesting similar design principles. © 2006 Wiley Periodicals, Inc. Complexity 11:26–35, 2006     

Quantum mechanics as the quadratic Taylor approximation of classical mechanics: The finite-dimensional case

We show that in contrast to a rather common opinion, quantum mechanics can be represented as an approximation of classical statistical mechanics. We consider an approximation based on the ordinary Taylor expansion of physical variables. The quantum contribution is given by the second-order term. To escape technical difficulties related to the infinite dimensionality of the phase space for quantum mechanics, we consider finite-dimensional quantum mechanics. On one hand, this is a simple example with high pedagogical value. On the other hand, quantum information operates in a finite-dimensional state space. Therefore, our investigation can be considered a construction of a classical statistical model for quantum information. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 152, No. 2, pp. 278–291, August, 2007.     

Moser扭转定理在Lagrange稳定性中的应用

本文利用Moser扭转定理证明了一类Duffing方程x″ 9(x)=e(t)的Lagrange稳定性，其中e(t)以1为周期，9：R→R具有下列性质：当x≥d0时，9(x)是超线性的；当x≤-d0时，9(x)是次线性的，其中d0是一正常数．     

小电网故障定位的研究

关于模拟电路故障诊断的多频率法对小型电网的短路故障及开路故障定位的研究表明,选择适当的测试频率及诊断精度,能准确地诊断出故障点,并可用微机迅速地完成诊断。     

高速脱壳穿甲弹三维图象的识别与处理

该文提出了一种新的高速脱壳穿甲弹三维图象的识别与处理方法，通过对ＩＢ－１２中间弹道靶道拍摄的照片进行处理，获得了脱壳过程的三维立体图形。它实现了从不同位置、不同角度来观察、分析和研究弹托的分离过程和干扰因素；实现了用计算机模拟高速脱壳穿甲弹的飞行姿态和脱壳全过程；解决了目前数值模拟技术尚未能解决的问题。该方法形象、直观，能全面、动态、连续地重现高速脱壳穿甲弹的空间飞行姿态及脱壳全过程。     

Short range order of silica particles bound through adsorbed polymer layers

Small angle neutron scattering was used to examine the organization of silica spheres which had been flocculated by various cationic copolymers. When the adsorbed polymers bound the spheres without compensating their surface charge, the resulting aggregates had a liquid-like short range order. When the polymers compensated for the surface charges, we found only tenuous aggregates with self-similar structures.This work used the neutron beams of ILL in Grenoble and LLB in Saclay.     

一种面部图像处理的边缘检测方法

介绍在3×3小矩阵中直接采用中心像素值与周围各像素值分别求差,再分别将各个差值与阈值相比较,最后将各个结果综合起来判断此像素点是否为边缘点的方法。判断过的像素点对当前阈值进行了一定的修改,使之随实际情况上下浮动,更有利于当前像素点的判断。实验证明,该方法检测出的边缘更完整,噪声也能更有效地去除。     

Anomalous small‐angle X‐ray scattering characterization of composites based on sulfonated poly(ether ether ketone), zirconium phosphates,and zirconium oxide

The morphology and distribution of zirconium oxide and zirconium phosphates in a matrix of sulfonated poly(ether ether ketone) (SPEEK) were investigated with anomalous small‐angle X‐ray scattering (ASAXS) and electron microscopy. ASAXS revealed that ZrO₂ was distributed in the SPEEK matrix in the form of nanoparticles smaller than 13 Å. A decrease in the conductivity suggested that the sulfonic groups were bound to the zirconium oxo species at the particle surface. Furthermore, two kinds of membranes containing zirconium phosphate were investigated. In one case, the phosphate was directly dispersed in the polymer solution for the casting of the membrane. In the other case, the phosphate was previously treated with n‐propyl ammonium and polybenzimidazole. From ASAXS data, the fractal dimension could be estimated. Mass‐fractal behavior was confirmed for the SPEEK membrane containing previously exfoliated zirconium phosphate, with aggregates of 6.3–165 Å. Surface‐fractal behavior was detected for membranes with untreated phosphates, with aggregates of 6.4–185 Å. The untreated phosphates caused an increase in the permeability, without changing the proton conductivity much. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 567–575, 2004