On the relations of graph parameters and its total parameters

In this paper we get some relations between α（G）, α＇（G）, β（G）, β＇（G） and αT（G）, βT（G）. And all bounds in these relations are best possible, where α（G）, α＇（G）,/3（G）, β（G）, αT（G） and βT（G） are the covering number, edge-covering number, independent number, edge-independent number （or matching number）, total covering number and total independent number, respectively.     

Acyclic edge chromatic number of outerplanar graphs

A proper edge coloring of a graph G is called acyclic if there is no 2‐colored cycle in G. The acyclic edge chromatic number of G, denoted by χ(G), is the least number of colors in an acyclic edge coloring of G. In this paper, we determine completely the acyclic edge chromatic number of outerplanar graphs. The proof is constructive and supplies a polynomial time algorithm to acyclically color the edges of any outerplanar graph G using χ(G) colors. © 2009 Wiley Periodicals, Inc. J Graph Theory 64: 22–36, 2010     

光学元件损伤在线检测图像处理技术

针对光学元件损伤图像中损伤区域的高精度检测问题,对内全反射照明下光学元件损伤图像的处理技术进行了研究。根据在线检测图像中损伤区域中心峰值的信号强度高于局部背景的信号强度这一特点,利用高斯滤波器生成待检测图像的局部信号强度比图像,实现了对损伤区域的低漏检率自动定位;根据CCD的成像原理,利用辐射标定的方法建立起损伤区域的尺寸与其在图像中总灰度的关系方程,实现了损伤区域的亚像素高精度尺寸测量。实验结果表明,与传统的光学元件损伤图像处理算法相比,本文提出的算法在保持低漏检率的同时大大提高了损伤区域的测量精度。     

Localization of disordered bosons and magnets in random fields

We study localization properties of disordered bosons and spins in random fields at zero temperature. We focus on two representatives of different symmetry classes, hard-core bosons (XY magnets) and Ising magnets in random transverse fields, and contrast their physical properties. We describe localization properties using a locator expansion on general lattices. For 1d Ising chains, we find non-analytic behavior of the localization length as a function of energy at ω=0$\omega =0$, ξ⁻¹(ω)=ξ⁻¹(0)+A|ω|^α${\xi }^{-1}\left(\omega \right)={\xi }^{-1}\left(0\right)+A{\left|\omega \right|}^{\alpha }$, with α$\alpha$ vanishing at criticality. This contrasts with the much smoother behavior predicted for XY magnets. We use these results to approach the ordering transition on Bethe lattices of large connectivity K$K$, which mimic the limit of high dimensionality. In both models, in the paramagnetic phase with uniform disorder, the localization length is found to have a local maximum at ω=0$\omega =0$. For the Ising model, we find activated scaling at the phase transition, in agreement with infinite randomness studies. In the Ising model long range order is found to arise due to a delocalization and condensation initiated at ω=0$\omega =0$, without a closing mobility gap. We find that Ising systems establish order on much sparser (fractal) subgraphs than XY models. Possible implications of these results for finite-dimensional systems are discussed.     

Experimental Study of Flow Through a Blade Trailing Edge with a Wavy Partition

Abstract

Flow through a blade trailing edge passage has been experimentally investigated in this article. This rectangular passage is divided into two channels by either a straight or a 120° wavy partition. Fluid in the first channel was injected into the second channel via 14 openings (holes) distributed uniformly and in the crests and troughs for the wavy configuration. Particle image velocimetry and a charge coupled device camera were used in experiment, with Reynolds number varying from 1,800 to 6,700. Experimental results show that the wavy configuration produces an oscillation flow in the second channel. The cause for the oscillation may due to the 120° wavy partition causing shear-layer instabilities and the formation of spanwise eddies by the wavy board. Pictures from the charge coupled device camera revealed strong mixing in the trailing edge, and this mixing could enhance heat transfer, which was confirmed in previous research. The amplitude of oscillation depends on Reynolds number and hole positions. It was observed that the injection flow was not symmetric to the openings, and it was skewed to the direction of the first channel main flow. The ratio of flow rate through the outlet and the bleeding holes was from 1:1 to 1:3.     

Binomial Edge Ideals of Complete Multipartite Graphs

In this article, we prove some results about the binomial edge ideal J _G of a complete r-partite graph G = K _{a 1,…, a r} : (1) characterization of unmixedness of J _G and Cohen–Macaulayness of the residue ring S/J _G , (2) F-purity of S/J _G , and (3) the equality of the symbolic and the ordinary powers of J _G .     

求解两类Maxwell方程组棱元离散系统的快速算法和自适应方法

Maxwell方程组棱元离散系统的快速算法和自适应方法是当前计算电磁场中的研究热点和难点. 首先, 针对H(curl)椭圆方程组的棱元离散系统, 通过建立棱元空间的稳定性分解, 设计了相应的快速迭代法和高效预条件子, 并且证明了迭代算法的收敛率和预条件子的条件数均不依赖于模型参数和网格规模. 其次, 针对时谐Maxwell方程组的棱有限元方法, 利用离散的Helmholtz分解, 连续散度为零函数对离散散度为零函数的逼近性和对偶论证, 获得了在L²和H(curl)范数下的拟最优误差估计. 进而设计和分析了相应的两网格法. 最后, 分别针对变系数H(curl)椭圆方程组和不定时谐Maxwell方程组, 考虑了一种不需要标记振荡项和加密单元不需要满足“内节点” 性质的自适应棱有限元法(AEFEM), 并证明了AEFEM的收敛性. 进一步, 当初始网格和Dörfler标记策略参数满足一定的假设条件时, 利用AEFEM的收敛性、误差的整体下界和局部上界估计, 证明了AEFEM的拟最优复杂性.     

On a Variational Model for Selective Image Segmentation of Features with Infinite Perimeter

Variational models provide reliable formulation for segmentation of features and their boundaries in an image, following the seminal work of Mumford-Shah (1989, Commun. Pure Appl. Math.) on dividing a general surface into piecewise smooth sub-surfaces. A central idea of models based on this work is to minimize the length of feature’s boundaries (i.e., H1 Hausdorff measure). However there exist problems with irregular and oscillatory object boundaries, where minimizing such a length is not appropriate, as noted by Barchiesi et al. (2010, SIAM J. Multiscale Model. Simu.) who proposed to miminize L2 Lebesgue measure of the γ-neighborhood of the boundaries. This paper presents a dual level set selective segmentation model based on Barchiesi et al. (2010) to automatically select a local feature instead of all global features. Our model uses two level set functions: a global level set which segments all boundaries, and the local level set which evolves and finds the boundary of the object closest to the geometric constraints. Using real life images with oscillatory boundaries, we show qualitative results demonstrating the effectiveness of the proposed method.     

图的Smarandachely邻点无圈边色数的一个上界

提出了图的Smarandachely邻点无圈边染色的概念,讨论了图的Smarandachely 邻点无圈边染色与邻点可区别无圈边染色之间的关系,并运用概率方法得到了图G的Smarandachely邻点无圈边色数的一个上界,其中G为无孤立边的图.