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The volume develops a thorough theory of singular fibers of generic differentiable maps. This is the first work that establishes the foundational framework of the global study of singular differentiable maps of negative codimension from the viewpoint of differential topology. The book contains not only a general theory, but also some explicit examples together with a number of very concrete applications.

This is a very interesting subject in differential topology, since it shows a beautiful interplay between the usual theory of singularities of differentiable maps and the geometric...

This volume includes selected technical papers presented at the Forum “Math-for-Industry” 2018. The papers written by eminent researchers and academics working in the area of industrial mathematics from the viewpoint of financial mathematics, machine learning, neural networks, inverse problems, stochastic modelling, etc., discuss how the ingenuity of science, technology, engineering and mathematics are and will be expected to be utilized. This volume focuses on the role that mathematics-for-industry can play in interdisciplinary research to develop new methods. The contents are useful for...

This book collects original and survey papers on Singularities in Geometry and Topology, which resulted from the 6th Franco-Japanese Symposium on Singularities, held in Fukuoka, during September 5-10, 2011. Though singularity theory was born in the XIXth century, this field of research became more popular in France after Prof. Heisuke Hironaka came to Paris. Then, a lot of collaborations between Japanese and French mathematicians started, and the conferences on Singularities in Geometry and Topology continue to develop this collaboration between France and Japan. This volume consists of 2...