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Plastics, films, and synthetic fibers are among typical examples of polymer materials fabricated industrially in massive quantities as the basis of modern social life. By comparison, polymers from biological resources, including proteins, DNAs, and cotton fibers, are essential in various processes in living systems. Such polymers are molecular substances, constituted by the linking of hundreds to tens of thousands of small chemical unit (monomer) components. Thus, the form of polymer molecules is frequently expressed by line geometries, and their linear and non-linear forms are believed to constitute the fundamental basis for their properties and functions. In the field of polymer chemistry ...
Theoretical tools and insights from discrete mathematics, theoretical computer science, and topology now play essential roles in our understanding of vital biomolecular processes. The related methods are now employed in various fields of mathematical biology as instruments to "zoom in" on processes at a molecular level. This book contains expository chapters on how contemporary models from discrete mathematics – in domains such as algebra, combinatorics, and graph and knot theories – can provide perspective on biomolecular problems ranging from data analysis, molecular and gene arrangements and structures, and knotted DNA embeddings via spatial graph models to the dynamics and kinetics of molecular interactions. The contributing authors are among the leading scientists in this field and the book is a reference for researchers in mathematics and theoretical computer science who are engaged with modeling molecular and biological phenomena using discrete methods. It may also serve as a guide and supplement for graduate courses in mathematical biology or bioinformatics, introducing nontraditional aspects of mathematical biology.
This volume contains the proceedings of a conference celebrating the work of Steven Boyer, held from June 2–6, 2018, at Université du Québec à Montréal, Montréal, Québec, Canada. Boyer's contributions to research in low-dimensional geometry and topology, and to the Canadian mathematical community, were recognized during the conference. The articles cover a broad range of topics related, but not limited, to the topology and geometry of 3-manifolds, properties of their fundamental groups and associated representation varieties.
Propelled by the success of the sequencing of the human and many related genomes, molecular and cellular biology has delivered significant scientific breakthroughs. Mathematics (broadly defined) continues to play a major role in this effort, helping to discover the secrets of life by working collaboratively with bench biologists, chemists and physicists. Because of its outstanding record of interdisciplinary research and training, the IMA was an ideal venue for the 2007-2008 IMA thematic year on Mathematics of Molecular and Cellular Biology. The kickoff event for this thematic year was a tutorial on Mathematics of Nucleic Acids, followed by the workshop Mathematics of Molecular and Cellular ...
This book provides a comprehensive description of topological polymers, an emerging research area in polymer science and polymer materials engineering. The precision polymer topology designing is critical to realizing the unique polymer properties and functions leading to their eventual applications. The prominent contributors are led by Principal Editor Yasuyuki Tezuka and Co-Editor Tetsuo Deguchi. Important ongoing achievements and anticipated breakthroughs in topological polymers are presented with an emphasis on the spectacular diversification of polymer constructions. The book serves readers collectively to acquire comprehensive insights over exciting innovations ongoing in topological ...
This is the proceedings of an international conference on knot theory held in July 1996 at Waseda University Conference Center. It was organised by the International Research Institute of Mathematical Society of Japan. The conference was attended by nearly 180 mathematicians from Japan and 14 other countries. Most of them were specialists in knot theory. The volume contains 43 papers, which deal with significant current research in knot theory, low-dimensional topology and related topics.The volume includes papers by the following invited speakers: G Burde, R Fenn, L H Kauffman, J Levine, J M Montesinos(-A), H R Morton, K Murasugi, T Soma, and D W Sumners.
"Knot theory is a fascinating mathematical subject, with multiple links to theoretical physics. This enyclopedia is filled with valuable information on a rich and fascinating subject." – Ed Witten, Recipient of the Fields Medal "I spent a pleasant afternoon perusing the Encyclopedia of Knot Theory. It’s a comprehensive compilation of clear introductions to both classical and very modern developments in the field. It will be a terrific resource for the accomplished researcher, and will also be an excellent way to lure students, both graduate and undergraduate, into the field." – Abigail Thompson, Distinguished Professor of Mathematics at University of California, Davis Knot theory has p...
This volume provides an excellent introduction of the statement and main ideas in the proof of the orbifold theorem announced by Thurston in late 1981. It is based on the authors' lecture series entitled "Geometric Structures on 3-Dimensional Orbifolds" which was featured in the third MSJ Regional Workshop on "Cone-Manifolds and Hyperbolic Geometry" held on July 1-10, 1998, at Tokyo Institute of Technology. The orbifold theorem shows the existence of geometric structures on many 3-orbifolds and on 3-manifolds with symmetry. The authors develop the basic properties of orbifolds and cone-manifolds, extends many ideas from the differential geometry to the setting of cone-manifolds and outlines a proof of the orbifold theorem.