Some Results on the Problems of Block Theory

In this paper, we obtain two results on Brauer‘s k (B) - problem about finite groups under some conditions. Furthermore, we obtain that Olsson‘s conjecture holds under the same conditions on the finite groups.     

一类推广的中曲率水平集的运动

研究了根据一个光滑曲面的主曲率函数的经典运动短时存在及唯一性,推广了Evans和Spruck的结果。     

Quantum quasi-cyclic low-density parity-check error-correcting codes

Due to the fault of the author(s) of the article entitled “Quantum quasi-cyclic low-density parity-check error-correcting codes”, published inChinese PhysicsB, 2009, Vol. 18, Issue 10, pp 4154--4160, has been found to partly copy from the articlearXiv:quant-ph/0701020v2on the arXiv preprint. So the above article inChinese PhysicsB has been withdrawn from the publication. [2 February 2010]     

彩色组合编码条纹光栅轮廓术

研究了一种新的编码光栅投影三维轮廓术。其中投影光栅利用彩色空间红、绿、蓝三基色相互独立的特性,用彩色条纹对光栅进行编码,以白色条纹为起始位,后接红、绿、蓝（R、G、B）三种颜色的条纺组成一组。改变红、绿、蓝的排列顺序可使各组有不同的编码。根据排列组合原理,红、绿、蓝三色可有6种不同的排列方式。经过编码处理的光栅在保证测量精度不变的前提下,加大了高度测量的范围。由于每条纹只采用0和255两个状态,因此具有较强的抗干扰能力。测量的精度主要取决于图像的分辨率。     

Spectra edited by relative signs of homonuclear couplings of low abundance nuclei

The proposed homonuclear coupling sign edited (HCSE) experiment can detect signed homonuclear couplings between low abundant nuclei like ¹³C, ²⁹Si and ¹⁵N in linear spin systems, that is, in systems where two nuclei are coupled by the measured coupling, and one of them is coupled by a second coupling to a nucleus of different kind. The third nucleus is usually high abundant hydrogen. Two spectra are measured during the HCSE experiment. Their weighed sum and difference yield two other spectra, one containing peaks coupled only by positive measured couplings and the other having peaks coupled by negative measured couplings. The usual E.COSY‐type experiment requires all three couplings in the three spin system (triangular spin system) and not only two couplings as the HCSE experiment. The experiment was successfully tested on known carbon–carbon and silicon–silicon two bond couplings. A set of six simple siloxanes with |²J(Si‐O‐Si)| couplings ranging from 0.5 to 9.0 Hz was measured for the first time, and all the couplings were found to be positive. Copyright © 2012 John Wiley & Sons, Ltd.     

一类仿射型本原非同步置换群的构造

同步置换群的研究是置换群理论中的一个前沿课题.通过在有限域上定义广义Paley图,来讨论这类图的团数(clique number)和色数(chromatic number)相等的条件.然后证明构造的广义Paley图和一类仿射群的轨道图同构,进而讨论这类仿射群的同步性.在此基础上给出一类本原非同步群的构造.     

Nonorientable regular embeddings of graphs of order pq

In [J. Algeb. Combin. 19(2004), 123-141], Du et al. classified the orientable regular embeddings of connected simple graphs of order pq for any two primes p and q. In this paper, we shall classify the nonorientable regular embeddings of these graphs, where p ≠ q. Our classification depends on the classification of primitive permutation groups of degree p and degree pq but is independent of the classification of the arc-transitive graphs of order pq.     

两类特殊图的逆符号边控制数

设G=(V,E)是一个图,对于图G的一个函数f:E→{-1,1},如果对任意e∈E(G),均有Σe′∈N[e]f(e′)≤1,则称f为图G的一个逆符号边控制函数.图G的逆符号边控制数γ′s(G)=max{Σe∈E(G)f(e)|f为图G的一个逆符号边控制函数}.在逆符号边控制数定义基础上,得到了所有轮图和扇图的逆符号边控制数.     

An image encryption scheme based on rotation matrix bit-level permutation and block diffusion

This paper proposes a novel image encryption scheme based on rotation matrix bit-level permutation and block diffusion. Firstly, divide plain image into non-overlapping 8 × 8 pixels blocks with a random matrix, then transform each block into an 8 × 8 × 8 three-dimensional (3-D) binary matrix, which has six directions just as a cube. Permutation is performed by multiplying the 3-D matrix by the rotation matrix that relies on plain image according to different direction. Secondly, use block diffusion to further change the statistical characteristics of the image after confusion. Experiment results and analysis show that the scheme can not only achieve a satisfactory security performance, but also have the suitability for a parallel mode and the robustness against noise in communication system.