Properties of Affinely Regular Polygons

Intuitively, one might consider an affinely regular polygon of the Eucidean plane to be the result of applying an affine transformation to a regular polygon. These affinely regular polygons, and their kindred that go by the same name in the Euclidean plane as well as in more general affine planes, have been onjects of investigations at all levels of sophistication and in a remarkable variety of contexts. For example, they arise in linear algebra as a set of vectors that are cyclically permuted by a unimodular matrix. Our purpose is to describe this concept and its attributes in a general setting. The main result is Theorem 1 where we present seven equivalent definitions of affine regularity, one of which appears for the first time. We are careful to distinguish these definitions from the weaker intuitive definition. Our work also features an application of Chebyshev polynomials to describe parameters associated with these polygons.     

物理测量误差与实验数据处理

本论述了大学物理实验中对测量结果的误差与数据处理的要求。     

Lissajous figures in the application of micro-vibration measurement

Based on Michelson interferometer and phase generated carrier (PGC) homodyne demodulation technique, an optical interferometer system is built, and a novel method using the central angles of Lissajous figures to measure micro-vibration displacement is proposed. The Lissajous figures are obtained by synthesizing two interferometric signals that their vibration directions are orthogonal and their intensities are equal. Through theoretical analysis, software simulation and experimental test, it is concluded that the central angles of Lissajous figures have a linear relationship with the phase modulation coefficients and the micro-vibration displacements when the phase modulation coefficients are small. So the micro-vibration displacements can be directly obtained by measuring the central angles of Lissajous figures. The method is simple and convenient. The experimental results indicate that the micro-vibration displacements measuring range can reach 5-775 nm, with a resolution of about 5 nm.     

Preferred orientations in nano-gold/silica/silicon interfaces

Gold in contact with silicon substrates Si(1 0 0), Si(1 1 1), and SiO₂ is studied by thermal evaporation and annealing in N₂ using the modified sphere-plate technique. The final orientation distribution of crystalline Au films grown on Si substrate systems that incorporate a native amorphous oxide layer of silica and Au on amorphous silica (SiO₂ glass) substrates is influenced by preferred orientations and twinning. Experimental evidence suggests that the orientation of Au{1 1 1} close packed planes (multiply twinned) was found to be of low-energy as the annealing temperature was increased to 530 °C and 920 °C. Additional orientations were observed for Au{1 0 0} on Si(1 0 0) substrates and Au{1 0 0}, {1 1 0}, and {3 1 1} on SiO₂ substrates. After annealing at 920 °C the size distribution of the gold particles was determined to be within the range of 20-800 nm while the morphology of gold surface appears spherical to faceted in character. These results show similarities to recent findings for smaller nano-size 1D particles, islands and thin Au films on silicon annealed over lower temperature ranges.     

利用虚拟仪器平台演示李萨如图形

基于Labview平台设计了虚拟仪器。直观的演示了李萨如图形。     

基于无人机近地面多光谱图像的蛇龙珠葡萄成熟度判别

酿酒葡萄一般批量采收,采收期对其品质有较大影响.传统方法主要依靠对样本的酚、糖等各组分含量进行实验室理化指标检测,判定采收成熟度.如果对多个地块进行采摘前的连续监测,则批量大、成本高、采样与分析工作量繁重,且时效性差,难以保证果品的收获品质.以蛇龙珠品种为对象,提出一种利用近地面多光谱图像对种植区葡萄成熟度和批量采收期...     

Twisted Groups and Locally Toroidal Regular Polytopes

In recent years, much work has been done on the classification of abstract regular polytopes by their local and global topological type. Abstract regular polytopes are combinatorial structures which generalize the well-known classical geometric regular polytopes and tessellations. In this context, the classical theory is concerned with those which are of globally or locally spherical type. In a sequence of papers, the authors have studied the corresponding classification of abstract regular polytopes which are globally or locally toroidal. Here, this investigation of locally toroidal regular polytopes is continued, with a particular emphasis on polytopes of ranks and . For large classes of such polytopes, their groups are explicitly identified using twisting operations on quotients of Coxeter groups. In particular, this leads to new classification results which complement those obtained elsewhere. The method is also applied to describe certain regular polytopes with small facets and vertex-figures.

     

丰、枯水年磨刀门水道盐水上溯运动规律对比

通过一维纵向逐时咸界图的方法, 得到了磨刀门水道丰、枯水年的盐水运动规律图.对比分析了不同年份不同上游径流对磨刀门水道盐水上溯运动规律的影响. 分析表明, 丰、枯水年不同的上游径流量将改变磨刀门水道盐水入侵的上溯距离和上溯速度的快慢, 造成程度不同的咸潮灾害. 磨刀门水道中盐水运动的半月及日周期性变化规律不受上游径流的影响,均为小潮期间盐水逐步上溯, 大潮期间盐水逐步退出. 上游径流量的大小只影响磨刀门水道盐水上溯运动的速度和距离远近, 不改变磨刀门水道中盐水上溯运动的半月周期规律.      

All regular polytopes are Ramsey

In this paper it is shown that all regular polytopes are Ramsey. In the course of this proof all convex quasi-regular polyhedra are proved to be Ramsey.     

Study of Properties of Urea and L-α-Alanine Didoped Triglycine Sulfate (UrLATGS) Crystals

In this report, the properties of triglycine sulfate (TGS) crystals doped with urea and L--alanine were studied. Urea and L--alanine have successfully entered into TGS crystal, demonstrated by infrared transmission spectrum and pyroelectric study. Figures of merit and Curie temperature are increased due to these two additions. UrLATGS is more suitable for infrared detectors than pure TGS crystals.