On Volume Growth of Gradient Steady Ricci Solitons

In this paper we study volume growth of gradient steady Ricci solitons. We show that if the potential function satisfies a uniform condition, then the soliton has at most Euclidean volume growth.Comment: 8 page

A review of parallel computing for large-scale remote sensing image mosaicking

Interest in image mosaicking has been spurred by a wide variety of research and management needs. However, for large-scale applications, remote sensing image mosaicking usually requires significant computational capabilities. Several studies have attempted to apply parallel computing to improve image mosaicking algorithms and to speed up calculation process. The state of the art of this field has not yet been summarized, which is, however, essential for a better understanding and for further research of image mosaicking parallelism on a large scale. This paper provides a perspective on the current state of image mosaicking parallelization for large scale applications. We firstly introduce the motivation of image mosaicking parallel for large scale application, and analyze the difficulty and problem of parallel image mosaicking at large scale such as scheduling with huge number of dependent tasks, programming with multiple-step procedure, dealing with frequent I/O operation. Then we summarize the existing studies of parallel computing in image mosaicking for large scale applications with respect to problem decomposition and parallel strategy, parallel architecture, task schedule strategy and implementation of image mosaicking parallelization. Finally, the key problems and future potential research directions for image mosaicking are addressed