This book is a collection of papers presented at the "Forum Math-for-Industry 2015" for which the unifying theme was "The Role and Importance of Mathematics in Innovation", held at the Institute of Mathematics for Industry, Kyushu University, October 26-30, 2015. The theme highlights two key roles that mathematics plays in supporting innovation in science, technology, and daily life, namely, needs-based and idea-based. For the former, mathematics assists with sorting through the possibilities and putting matters on a more rigorous foundation, and for the latter, mathematical models of the possible implementations play a key role. The book gives excellent examples of how mathematics assists with stimulating innovation and, thereby, highlights the importance and relevance of the concept Mathematics_FOR_Industry. The contents of this volume address productive and successful interaction between industry and mathematicians, as well as the cross-fertilization and collaboration that result when mathematics is involved with the advancement of science and technology.

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 researchers both in academia and industry working in interdisciplinary sectors.

This book is a collection of papers presented at the "Forum Math-for-Industry 2015" for which the unifying theme was "The Role and Importance of Mathematics in Innovation", held at the Institute of Mathematics for Industry, Kyushu University, October 26-30, 2015. The theme highlights two key roles that mathematics plays in supporting innovation in science, technology, and daily life, namely, needs-based and idea-based. For the former, mathematics assists with sorting through the possibilities and putting matters on a more rigorous foundation, and for the latter, mathematical models of the possible implementations play a key role. The book gives excellent examples of how mathematics assists with stimulating innovation and, thereby, highlights the importance and relevance of the concept Mathematics_FOR_Industry. The contents of this volume address productive and successful interaction between industry and mathematicians, as well as the cross-fertilization and collaboration that result when mathematics is involved with the advancement of science and technology.

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 topology of manifolds.

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 researchers both in academia and industry working in interdisciplinary sectors.

This volume is a collection of 6 lecture notes presented at the School on Singularity Theory, Sao Carlos, Brazil, July 16-21, 2012, or at the 12th International Workshop on Real and Complex Singularities, Sao Carlos, Brazil, July 22-27, 2012.Topics treated in the 6 lecture notes written by established authors cover, reflecting authors' expertise, a wide range including Topology and Geometry of real singularities, Singularities of holomorphic map-germs, Singularities of complex algebraic sets, Algorithms of the computer algebra 'SINGULAR', Singularities of maps and characteristic classes, Limit cycles of systems of ordinary differential equations.Each lecture note is extremely well-written with plentiful examples and may be considered as one of the most excellent readings in the relevant topic. This book is suitable for being kept at one's desk-side and widely recommended for graduate students studying singularity theory, and researchers in various fields who would like to enjoy the world of singularities.Published by Mathematical Society of Japan and distributed by World Scientific Publishing Co. for all markets except North America

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 survey articles and 12 research articles, whose topics include algebraic curves and varieties, line arrangements, mixed polynomials, algebraic local cohomology classes, stable maps, and mirror symmetry. This book is recommended to any researcher or graduate student interested in singularity theory.Published by Mathematical Society of Japan and distributed by World Scientific Publishing Co. for all markets except North America