A Drawing System for Pole Diagram and Rose Diagram of Rock Mass Structural Surface

The distribution of structural planes is complex and irregular. How to quickly and effectively obtain the occurrence and distribution characteristics of structural planes and improve the efficiency of data processing is a key technical issue in structural plane analysis. The paper combined fuzzy equivalent clustering algorithm, rose diagram drawing method, and C++ language, developed a drawing system for the pole diagram and rose diagram of rock mass structural planes, and verified the practicability of the system through an engineering case analysis. In the article, the fuzzy equivalent clustering of the occurrence of structural planes, the drawing of pole diagram, and the statistical analysis of structural planes were realized based on the fuzzy equivalent clustering algorithm. The rapid drawing of the striking rose diagram, trending rose diagram, and dip rose diagram module were realized based on the rose diagram drawing method. The system integrated the structure plane pole diagram and the occurrence rose diagram together and realized the rapid analysis and drawing of the structure plane.

An enhanced bracket polynomial for knotoids

A multi-variable polynomial invariant for knotoids and linkoids, which is an enhancement of the bracket polynomial for knotoids introduced by Turaev, is given by using the concept of a pole diagram which originates in constructing a virtual link invariant. Several features of the polynomial are revealed.

THE POLE DIAGRAM AND THE MIYAZAWA POLYNOMIAL

We introduce the pole diagram, which helps to retrieve information from a knot diagram when we smooth crossings. By using the notion, we define a bracket polynomial for the Miyazawa polynomial. The bracket polynomial gives a simple definition and evaluation for the Miyazawa polynomial. Then we show that the virtual crossing number of a virtualized alternating link is determined by its diagram. Furthermore, we construct infinitely many virtual link diagrams which attain the minimal real and virtual crossing numbers together.