We show that there are hyperbolic tunnel-number one knots with arbitrarily high bridge number and that “most” tunnelnumber one knots are not one-bridge with respect to an unknotted torus. The proof relies on a connection between bridge number and a certain distance in the curve complex of a genus-two surface.

A geometric invariant of a space curve, the writhing number, is defined and studied. For the central curve of a twisted cord the writhing number measures the extent to which coiling of the central curve has relieved local twisting of the cord. This study originated in response to questions that arise in the study of supercoiled double-stranded DNA rings.

The rainfall and runoff relationship becomes an intriguing issue as urbanization continues to evolve worldwide. In this paper, we developed a simulation model based on the soil conservation service curve number (SCS-CN) method to analyze the rainfall-runoff relationship in Guangzhou, a rapid growing metropolitan area in southern China. The SCS-CN method was initially developed by the Natural Re...

Runoff assessment and estimation is crucial for watershed management as it provides information that is needed to expedite the course of watershed planning and development. The most commonly used model due to its simplicity and versatility in runoff estimation is the soil conservation service curve number developed by the United States Department of Agriculture. The study estimates the surface ...