Collection of papers on geometry, analysis and mathematical physics : in honor of Professor Gu Chaohao

These days, an increasing amount of information can be obtained in graphical forms, such as weather maps, soil samples, locations of nests in a breeding colony, microscopical slices, satellite images, radar or medical scans and X-ray techniques. "High level" image analysis is concerned with the global interpretation of images, attempting to reduce it to a compact description of the salient features of the scene.This book takes a stochastic approach. It studies Markov object processes, showing that they form a flexible class of models for a range of problems involving the interpretation of spatial data. Applications can be found in statistical physics (under the name of "Gibbs processes"), environmental mapping of diseases, forestry, identification of ore structure in materials science, signal analysis, object recognition, robot vision, and interpretation of images from medical scans or confocal microscopy This volume is published in honor of Professor Gu Chaohao, a renowned mathematician and member of the Chinese Academy of Sciences, on the occasion of his 70th birthday and his 50th year of educational work. The subjects covered by this collection are closely related to differential geometry, partial differential equations and mathematical physics — the major areas in which Professor Gu has received notable achievements. Many distinguished mathematicians all over the world contributed their papers to this collection. This collection also consists of “Gu Chaohao and I” written by C N Yang, “The academic career and accomplishment of Professor Gu Chaohao” by T T Li and “List of publications of Professor Gu Chaohao”. It is known that a classical polytropic perfect fluid will in general develop singularities: for 1 dimensional flows see John, Klainerman - Majda, for 3 dimensional flows see Sideris who proves occurrence of singularities for example for flows slightly compressed initially and out going near the wave front (see precise definitions in Sideris's paper). Published in honour of Professor Gu Chaohao, this work covers subjects closely related to differential geometry, partial differential equations and mathematical physics, the major areas in which Professor Gu has received notable achievements.