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1.
This is the second of two papers in which we study a group which is the quotient of a free product of groups by the normal closure of a single word that is contained in a subgroup which has the form of a free product of two cyclic groups. We use known properties of generalized triangle groups, together with detailed analysis of pictures and of words in free monoids, to prove a number of results such as a Freiheitssatz and the existence of Mayer-Vietoris sequences for such groups under suitable hypotheses. The results generalize those in an earlier article of the second author and Shwartz.  相似文献   
2.
A protein Pascal triangle has been constructed as new type of supramolecular architecture by using the inducing ligand strategy that we previously developed for protein assemblies. Although mathematical studies on this famous geometry have a long history, no work on such Pascal triangles fabricated from native proteins has been reported so far due to their structural complexity. In this work, by carefully tuning the specific interactions between the native protein building block WGA and the inducing ligand R-SL , a 2D Pascal-triangle lattice with three types of triangular voids has been assembled. Moreover, a 3D crystal structure was obtained based on the 2D Pascal triangles. The distinctive carbohydrate binding sites of WGA and the intralayer as well as interlayer dimerization of RhB was the key to facilitate nanofabrication in solution. This strategy may be applied to prepare and explore various sophisticated assemblies based on native proteins.  相似文献   
3.
We prove two distinct and natural refinements of a recent breakthrough result of Molloy (and a follow‐up work of Bernshteyn) on the (list) chromatic number of triangle‐free graphs. In both our results, we permit the amount of color made available to vertices of lower degree to be accordingly lower. One result concerns list coloring and correspondence coloring, while the other concerns fractional coloring. Our proof of the second illustrates the use of the hard‐core model to prove a Johansson‐type result, which may be of independent interest.  相似文献   
4.
刘志刚  刘伟龙  赵海军 《物理学报》2015,64(16):163202-163202
用传统量子力学方法研究了横截面为正三角形的腔内氢负离子光剥离, 得到了光剥离截面随能量变化的解析表达公式. 该公式还给出了剥离截面的阈值行为. 进一步研究发现, 当氢负离子处于正三角形一角附近时, 用量子力学方法得到的结果与氢负离子处于60°角域内时使用闭合轨道理论得到的结果一致.  相似文献   
5.
The rank of a graph is defined to be the rank of its adjacency matrix. A graph is called reduced if it has no isolated vertices and no two vertices with the same set of neighbors. We determine the maximum order of reduced triangle‐free graphs with a given rank and characterize all such graphs achieving the maximum order.  相似文献   
6.
To date, supramolecular chemistry is an ever growing research field owing to its crucial role in molecular catalysis, recognition, medicine, data storage and processing as well as artificial photosynthetic devices.Different isolated supramolecules were prepared by molecular self-assembly on surfaces. This review mainly focuses on supramolecular aggregations on noble metal surfaces studied by scanning tunneling microscopy, including dimers, trimers, tetramers, pentamers, wire-like assemblies and Sierpin′ ski triangular fractals. The variety of self-assembled structures reflects the subtle balance between intermolecular and molecule–substrate interactions, which to some extent may be controlled by molecules, substrates and the molecular coverage. The comparative study of different architectures helps identifying the operative mechanisms that lead to the structural motifs. The application of these mechanisms may lead to novel assemblies with tailored physicochemical properties.  相似文献   
7.
基于特征基函数的球面共形微带天线阵列分析   总被引:1,自引:0,他引:1       下载免费PDF全文
于涛  尹成友  刘汉 《物理学报》2014,63(23):230701-230701
采用全波分析法对球面共形微带天线阵列进行了分析.相比体-面积分方程,采用球并矢格林函数的面积分方程法可以大幅减少未知量的数目,进而缓解计算机内存压力.微带天线阵列表面采用曲面三角形剖分,可较精确地模拟球面特性.首先,引入边界电荷以及半Rao-Wilton-Glisson基函数,成功实现了探针馈电,并采用镜像法解决了馈电边处线积分奇异问题.然后,采用特征基函数法降低了阻抗矩阵的阶数,并采取有效措施进一步节省内存和计算时间.最后,分析计算了不同尺寸的球面共形微带天线阵列的输入阻抗及远区场特性.与文献和仿真软件结果进行比较,证明了所提出的处理方法的正确性和有效性.  相似文献   
8.
对基于工业CT图像重构的网格模型进行网格简化时,大多数现有网格模型简化算法会丢失特征,出现网格质量不好的问题。因此提出一种网格模型保特征简化方法,该方法用三角形折叠法对原始模型进行简化,当简化后模型的平均二面角角度误差达到允许误差后,再使用边折叠法对模型进行简化。在三角形折叠法中提出了利用被折叠三角形的法向量、各个顶点的高斯曲率及其在周边三角形上的投影确定该三角形的折叠点,利用局部体积误差与二面角角度误差的无因次化和确定折叠代价的方法;在边折叠法中提出了将二面角角度误差引入到二次误差测度(QEM)法的折叠代价中的改进QEM法。实验结果表明:与其他算法相比,该方法能够生成保特征、高质量、低几何误差的网格模型。  相似文献   
9.
Students use GeoGebra to explore the mathematical relations among different radii of circles in a triangle (circumcircle, incircle, excircles) and the sides and other segments in the triangle. The more formal mathematical development of the relations that follows the explorations is based on known geometrical properties, different formulas relating the radii to the sides and the inequalities between the different averages. The activities described were conducted with pre-service teachers of mathematics, with empirical investigation of the relations using dynamical geometry software, and formal presentation of proofs.  相似文献   
10.
鞠生宏  梁新刚 《物理学报》2013,62(2):26101-026101
本文基于非平衡的分子动力学模拟方法计算了带有三角形孔的硅纳米薄膜的界面热阻特性,结果表明300-1100 K范围内随着热流方向的改变,在含有三角形孔的硅纳米薄膜中存在热整流效应,热整流系数达28%.同时借助于声子波包动力学模拟方法,获得了不同频率下的纵波声子在三角形孔处的散射特性,结果表明纵波声子在散射过程中产生了横波声子,并且从三角形底部向顶部入射的声子能量透射系数比反向时平均低22%.不对称结构引起的声子透射率的差异是引起热整流效应的主要因素.  相似文献   
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