Optimal discrete Morse functions for 2-manifolds

Morse theory is a powerful tool in its applications to computational topology, computer graphics and geometric modeling. It was originally formulated for smooth manifolds. Recently, Robin Forman formulated a version of this theory for discrete structures such as cell complexes. It opens up several categories of interesting objects (particularly meshes) to applications of Morse theory. Once a Morse function has been defined on a manifold, then information about its topology can be deduced from its critical elements. The main objective of this paper is to introduce a linear algorithm to define optimal discrete Morse functions on discrete 2-manifolds, where optimality entails having the least number of critical elements. The algorithm presented is also extended to general finite cell complexes of dimension at most 2, with no guarantee of optimality.     

Application of tomography method in millimeter wavelengths band II. Experimental

Tomographycal methods of image reconstruction of two-dimensional objects, surfaces or subsurface regions in millimeter wavelengths band are suggested and considered. Experimental images obtained using antennas and waveguiding lines of different types and radiation frequencyf≈33÷35GHz are represented. Volumetric dielectric objects and plane-parallel ferrite (or dielectric) plates distributed in free space or in homogeneous dielectric medium have been taken as objects under investigation. It is shown that in the frequency band under consideration, the images of investigated objects with characteristic dimensionA≈2λ÷7λ may be obtained by first-order diffraction tomography method (Born, Rytov or high frequency approximation of the first-order for electromagnetic field).     

物理学从实物到场的发展

概述物理学从实物到场的发展历程及其对发展现代科学技术的重大意义。     

Generalized cluster complexes via quiver representations

We give a quiver representation theoretic interpretation of generalized cluster complexes defined by Fomin and Reading. Using d-cluster categories defined by Keller as triangulated orbit categories of (bounded) derived categories of representations of valued quivers, we define a d-compatibility degree (−∥−) on any pair of “colored” almost positive real Schur roots which generalizes previous definitions on the noncolored case and call two such roots compatible, provided that their d-compatibility degree is zero. Associated to the root system Φ corresponding to the valued quiver, using this compatibility relation, we define a simplicial complex which has colored almost positive real Schur roots as vertices and d-compatible subsets as simplices. If the valued quiver is an alternating quiver of a Dynkin diagram, then this complex is the generalized cluster complex defined by Fomin and Reading. Supported by the NSF of China (Grants 10471071) and by the Leverhulme Trust through the network ‘Algebras, Representations and Applications’.     

The natural numbers in constructive set theory

Constructive set theory started with Myhill's seminal 1975 article [8]. This paper will be concerned with axiomatizations of the natural numbers in constructive set theory discerned in [3], clarifying the deductive relationships between these axiomatizations and the strength of various weak constructive set theories. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

WIN95下DirectX的动画设计技术

利用DirectDraw模块进行快速动画设计，重点对其直接操纵显存的特性和用后缓冲区实现动画中背景擦除和重绘的技巧进行探索，并结合火焰字的实例说明本文提出的方法是Win95下开发动画软件的一种切实可行的方法．     

低频电磁脉冲对复杂电大目标耦合效应

针对复杂电大目标电磁脉冲耦合效应缺乏定量研究的问题,基于时域有限差分方法(FDTD)建立了一套电磁脉冲耦合效应建模与评估分析流程,开展了低频电磁脉冲激励下的仿真试验,获取和分析了特性数据,进而提出了一种表面加载透明导电材料的低频电磁脉冲激励防护方法。试验结果表明:基于功率密度的易损性分析具有良好的工程适用性,而且防护方法对低频电磁脉冲激励具有较好的屏蔽效能。     

快速无参数背景建模的红外目标检测方法研究

针对复杂背景红外图像序列目标检测的难题,给出了一种用于红外监控系统中入侵目标检测的背景建模方法。应用特征样本集为每一个像素建立统计无参数样本集模型,根据核函数估计计算每一个像素值对模型的符合概率。使用双阈值进行目标检测和模型更新,将图像分为三类:可靠背景、感兴趣区域和不可靠背景。通过不可靠背景类提供的信息进一步将感兴趣区域细分为入侵目标和错误检测。对几种红外图像序列仿真实验表明,该算法不仅可以比较精确的检测显著入侵目标,对于容易淹没在噪声中的弱小入侵目标也可以实现准确地检测。     

Theory of Z-scan technique using Gaussian-Bessel beams with a phase object

This paper reports the theoretical study of combining Z-scan technique with Gauss-Bessel (GB) beams beside a phase object (PO) to measure the third-order nonlinear susceptibility components.By using this method,the sign of refractive index which depends on the shape of the close aperture Z-scan curve can be easily determined.Meanwhile,the magnitude of nonlinear coefficients can also be deduced by theoretical fit.The proposed method is advantageous for high sensitivity and imposes a lower stress in the cases of fragile materials,since small pulse energy is enough for the measurement of nonlinear coefficients.Predictions of the models are compared with Gaussian Z-scan measurement and GB Z-scan measurement.By using GB beams with a PO,the sensitivity of Z-scan measurements is found to be a factor of over 60 times greater than for Gaussian beams and 2 times greater than for Gaussian-Bessel beams.     

基于相机标定的双目三维景物重建方法

介绍了一种基于相机标定的双目静止镜头下的三维景物重建方法.方法假设已经通过相机标定的方法得到两个相机的内外投影矩阵参数,通过投影矩阵和几何的方法,配合图像配准技术,恢复感兴趣场景的深度信息,达到三维景物重建的目的.本方法主要是基于几何变换的方法,巧妙避开了三维投影矩阵的计算,直接从真实图像映射为虚拟极平面图像,可以达到比较好的效果.