Carbon star CGCS 673 identified as a semi-regular variable star

This study reports that the carbon star CGCS 673 is a semi-regular(SR)variable star with a period of 135 d and an amplitude of 0.18mag in the V-band.The light curve obtained by this study correlates well with the SR classification as the photometric data obtained show noticeable periodicity in the light changes of CGCS 673 that is occasionally interrupted by a period of irregular variability.The derived period and colour index obtained from our data and those from professional databases indicate that the attributes of this star fall within the parameters of the SR class of variable stars.Following our notification of the discovery that this star is a variable source,CGCS 673 has received the AAVSO Unique Identifier of(AAVSO UID)000-BMZ-492.

Tiling a Plane with Semi-Regular Equilateral Polygons with 2m-Sides

In this paper, tiling a plane with equilateral semi-regular convex polygons is considered, and, that is, tiling with equilateral polygons of the same type. Tiling a plane with semi-regular polygons depends not only on the type of a semi-regular polygon, but also on its interior angles that join at a node. In relation to the interior angles, semi-regular equilateral polygons with the same or different interior angles can be joined in the nodes. Here, we shall first consider tiling a plane with semi-regular equilateral polygons with 2m-sides. The analysis is performed by determining the set of all integer solutions of the corresponding Diophantine equation in the form of , whereare the non-negative integers which are not equal to zero at the same time, and are the interior angles of a semi-regular equilateral polygon from the characteristic angle. It is shown that of all semi-regular equilateral polygons with 2m-sides, a plane can be tiled only with the semi-regular equilateral quadrilaterals and semi-regular equilateral hexagons. Then, the problem of tiling a plane with semi-regular equilateral quadrilaterals is analyzed in detail, and then the one with semi-regular equilateral hexagons. For these semi-regular polygons, all possible solutions of the corresponding Diophantine equations were analyzed and all nodes were determined, and then the problem for different values of characteristic elements was observed. For some of the observed cases of tiling a plane with these semi-regular polygons, some graphical presentations of tiling constructions are also given.

有向图特征向量的映射与S-因子定理

本文利用出、入关联矩阵绘出了有向图(不必正则)与其有向线图的非零特征值的特征向量空间之间的一一映射.又对半正则有向图,指出了它的S-因子与其有向线图的零特征值的特征向量间的对应关系.这些结果推广了H.Sachs 等人对正则无向图与其线图的相应工作。

Delight and Frustration with Number “Seven” in Plane Geometry and the Regular Heptagon

As starting point for patterns with seven-fold symmetry, we investigate the basic possibility to construct the regular heptagon by bicompasses and ruler. To cover the whole plane with elements of sevenfold symmetry is only possible by overlaps and (or) gaps between the building stones. Resecting small parts of overlaps and filling gaps between the heptagons, one may come to simple parqueting with only a few kinds of basic tiles related to sevenfold symmetry. This is appropriate for parqueting with a center of seven-fold symmetry that is illustrated by figures. Choosing from the basic patterns with sevenfold symmetry small parts as elementary stripes or elementary cells, one may form by their discrete translation in one or two different directions periodic bordures or tessellation of the whole plane but the sevenfold point-group symmetry of the whole plane is then lost and there remains only such symmetry in small neighborhoods around one or more centers. From periodic tiling, we make the transition to aperiodic tiling of the plane. This is analogous to Penrose tiling which is mostly demonstrated with basic elements of fivefold symmetry and we show that this is also possible with elements of sevenfold symmetry. The two possible regular star-heptagons and a semi-regular star-heptagon play here a basic role.

Modular responsive facade proposals based on semi-regular and demi-regular tessellation:daylighting and visual comfort

Responsive facades can reduce building energy consumption and control daylight and natural ventilation to improve user comfort.This study aims to develop alternative responsive facade systems based on semi-regular and demi-regular tessellations.For this purpose,first,the tessellation method used to generate responsive facades is introduced.Then,the geometric and parametric design principles and the movement capabilities of the proposed facade systems are presented.Finally,a set of analyses are performed to test and compare the performances of the facade systems based on daylight metrics and indoor glare comfort.This study contributes to the literature with the proposed facade systems that can adapt to changing environmental conditions,provide flexibility in shape control and simplicity in mechanism design,and improve building performance.The analysis results show that all the proposed facade systems provide the desired visual comfort and daylight levels at different configurations.