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This book is a collection of papers presented at the Forum "Applications + Practical Conceptualization + Mathematics = fruitful Innovation" in October 2014. This book illustrates various aspects of this two-way interaction between applications and the association highlighting how the practical conceptualization assists with the linking of the question that encapsulates the current application to the relevant mathematics. The contents of this book 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.