The Mathematics and Topology of Fullerenes

The Mathematics and Topology of Fullerenes

This multi-author volume is targeted at advanced graduates and researchers working in carbon materials, chemistry and physics.

Author: Franco Cataldo

Publisher: Springer Science & Business Media

ISBN: 9400702213

Category: Science

Page: 289

View: 219

The Mathematics and Topology of Fullerenes presents a comprehensive overview of scientific and technical innovations in theoretical and experimental studies. Topics included in this multi-author volume are: Clar structures for conjugated nanostructures; counting polynomials of fullerenes; topological indices of fullerenes; the wiener index of nanotubes; toroidal fullerenes and nanostars; C60 Structural relatives: a topological study; local combinatorial characterization of fullerenes; computation of selected topological indices of C60 and C80 Fullerenes via the Gap Program; 4valent- analogues of fullerenes; a detailed atlas of Kekule structures of C60. The Mathematics and Topology of Fullerenes is targeted at advanced graduates and researchers working in carbon materials, chemistry and physics.
Categories: Science

Topological Modelling of Nanostructures and Extended Systems

Topological Modelling of Nanostructures and Extended Systems

Topological Modelling of Nanostructures and Extended Systems completes and expands upon the previously published title within this series: The Mathematics and Topology of Fullerenes (Vol. 4, 2011) by gathering the latest research and ...

Author: Ali Reza Ashrafi

Publisher: Springer Science & Business Media

ISBN: 9789400764132

Category: Science

Page: 575

View: 729

Topological Modelling of Nanostructures and Extended Systems completes and expands upon the previously published title within this series: The Mathematics and Topology of Fullerenes (Vol. 4, 2011) by gathering the latest research and advances in materials science at nanoscale. It introduces a new speculative area and novel concepts like topochemical reactions and colored reactive topological indices and provides a better understanding of the physical-chemical behaviors of extended systems. Moreover, a charming new family of space-filling fullerenic crystals is here analyzed for the first time. Particular attention is given to the fundamental influences exercised by long-range connectivity topological mechanisms on the chemical and physical properties of carbon nanostructures. Systems consisting in graphenic layers with structural and topological defects are investigated in their electronic and magnetic behaviors also in presence of metallic particles. More specifically, the book focuses on: - Electronic Properties of low dimensional nanostructures including negatively-curved carbon surfaces; Pariser-Parr-Pople model hamiltonian approach to graphene studies; - Topochemistry and Toporeactcivity of extended sp2-nanocarbons: PAH, fullerenes, nanoribbons, Moebius-like nanoribbons, nanotubes and grapheme; - Novel class of crystal networks arising from spanning fullerenes; - Nanostructures and eigenvectors of matrices and an extended treatise of topological invariants; - Enumeration hetero-fullerenes by Polya theory. Topological Modelling of Nanostructures and Extended Systems represents a valuable resource to advances graduates and researchers working in mathematics, chemistry, physics and material science.
Categories: Science

Advances in Mathematical Chemistry and Applications

Advances in Mathematical Chemistry and Applications

Cataldo, F.; Ori, O.; Graovac A. Graphene topological modifications. Int. J. Chem. Modeling, 2011, 3(1-2), 45–63. Cataldo, F.; Ori, O.; Iglesias-Groth S. Topological lattice descriptors of graphene sheets with fullerene-like ...

Author: Subhash C. Basak

Publisher: Elsevier

ISBN: 9781681080529

Category: Science

Page: 354

View: 103

Advances in Mathematical Chemistry and Applications highlights the recent progress in the emerging discipline of discrete mathematical chemistry. Editors Subhash C. Basak, Guillermo Restrepo, and Jose Luis Villaveces have brought together 27 chapters written by 68 internationally renowned experts in these two volumes. Each volume comprises a wise integration of mathematical and chemical concepts and covers numerous applications in the field of drug discovery, bioinformatics, chemoinformatics, computational biology, mathematical proteomics, and ecotoxicology. Volume 2 explores deeper the topics introduced in Volume 1, with numerous additional topics such as topological approaches for classifying fullerene isomers; chemical reaction networks; discrimination of small molecules using topological molecular descriptors; GRANCH methods for the mathematical characterization of DNA, RNA and protein sequences; linear regression methods and Bayesian techniques; in silico toxicity prediction methods; drug design; integration of bioinformatics and systems biology, molecular docking, and molecular dynamics; metalloenzyme models; protein folding models; molecular periodicity; generalized topologies and their applications; and many more. Brings together both the theoretical and practical aspects of the fundamental concepts of mathematical chemistry Covers applications in diverse areas of physics, chemistry, drug discovery, predictive toxicology, systems biology, chemoinformatics, and bioinformatics About half of the book focuses primarily on current work, new applications, and emerging approaches for the mathematical characterization of essential aspects of molecular structure, while the other half describes applications of structural approach to new drug discovery, virtual screening, protein folding, predictive toxicology, DNA structure, and systems biology
Categories: Science

Distance Symmetry and Topology in Carbon Nanomaterials

Distance  Symmetry  and Topology in Carbon Nanomaterials

Ashrafi AR, Koorepazan-Moftakhar F (2014) Fullerenes and capped nanotubes: applications and geometry. In: Aliofkhazraei M (ed) Handbook of ... (2011) The mathematics and topology of fullerenes. Carbon materials: chemistry and physics, ...

Author: Ali Reza Ashrafi

Publisher: Springer

ISBN: 9783319315843

Category: Technology & Engineering

Page: 477

View: 464

This contributed volume is inspired by the seminal discovery and identification of C60. Starting with a comprehensive discussion featuring graphene based nanostructures, subsequent chapters include topological descriptions of matrices, polynomials and indices, and an extended analysis of the symmetry and topology of nanostructures. Carbon allotropes such as diamond and its connection to higher-dimensional spaces is explored along with important mathematical and topological considerations. Further topics covered include spontaneous symmetry breaking in graphene, polyhedral carbon structures, nanotube junction energetics, and cyclic polyines as relatives of nanotubes and fullerenes. This book is aimed at researchers active in the study of carbon materials science and technology.
Categories: Technology & Engineering

New Frontiers in Nanochemistry Concepts Theories and Trends

New Frontiers in Nanochemistry  Concepts  Theories  and Trends

Chemical thermodynamics applied to the Diels–Alder reaction of C60 fullerene with polyacenes. Fullerenes, Nanotubes and Carbon Nanostructures, 23, 760–768. Cataldo, F., Graovac, A., & Ori, O., (2011). The Mathematics and Topology of ...

Author: Mihai V. Putz

Publisher: CRC Press

ISBN: 9780429663154

Category: Science

Page: 548

View: 101

New Frontiers in Nanochemistry: Concepts, Theories, and Trends, Volume 2: Topological Nanochemistry is the second of the new three-volume set that explains and explores the important basic and advanced modern concepts in multidisciplinary chemistry. Under the broad expertise of the editor, this second volume explores the rich research areas of nanochemistry with a specific focus on the design and control of nanotechnology by structural and reactive topology. The objective of this particular volume is to emphasize the application of nanochemistry. With 46 entries from eminent international scientists and scholars, the content in this volume spans concepts from A-to-Z—from entries on the atom-bond connectivity index to the Zagreb indices, from connectivity to vapor phase epitaxy, and from fullerenes to topological reactivity—and much more. The definitions within the text are accompanied by brief but comprehensive explicative essays as well as figures, tables, etc., providing a holistic understanding of the concepts presented.
Categories: Science

Geometric Structure of Chemistry Relevant Graphs

Geometric Structure of Chemistry Relevant Graphs

Math. Co. 61,589–602 (2009) Deza, M., Dutour, M., Shtogrin, M.: 4-valent plane graphs with 2-, 3- and 4-gonal faces. ... M., Deza, M.: 4-regular and self-dual analogs of fullerenes, mathematics and topology of fullerenes, pp. 103–116.

Author: Michel-Marie Deza

Publisher: Springer

ISBN: 9788132224495

Category: Mathematics

Page: 211

View: 527

The central theme of the present book is zigzags and central-circuits of three- or four-regular plane graphs, which allow a double covering or covering of the edgeset to be obtained. The book presents zigzag and central circuit structures of geometric fullerenes and several other classes of graph of interest in the fields of chemistry and mathematics. It also discusses the symmetries, parameterization and the Goldberg–Coxeter construction for those graphs. It is the first book on this subject, presenting full structure theory of such graphs. While many previous publications only addressed particular questions about selected graphs, this book is based on numerous computations and presents extensive data (tables and figures), as well as algorithmic and computational information. It will be of interest to researchers and students of discrete geometry, mathematical chemistry and combinatorics, as well as to lay mathematicians.
Categories: Mathematics

Diamond and Related Nanostructures

Diamond and Related Nanostructures

Philos Mag 91 :2671—2679 Baake M, Moody RV (2000) Directions in mathematical quasicrystals. American Mathematical Society, Providence ... Graovac A, Ori O (eds) The mathematics and topology of fullerenes. Springer, Dordrecht, pp 217—247 ...

Author: Mircea Vasile Diudea

Publisher: Springer Science & Business Media

ISBN: 9789400763715

Category: Technology & Engineering

Page: 393

View: 781

Over the past twenty years, the field of carbon structures has been invigorated by the discovery of fullerenes and carbon nanotubes. These nano-structured carbons have attracted a tremendous interest in the fundamental properties of discrete carbon molecules, leading to the discovery of novel complex crystalline and quasi-crystalline materials. As a consequence, a variety of applications have been developed, including technical and bio-medical materials and miniaturized tools. Diamond and Related Nanostructures focuses on the advances in the area of diamond-like carbon nanostructures (hyper-structures built from fullerenes and/or carbon nanotube junctions) and other related carbon nanostructures. Each chapter contributes to the topic from different fields, ranging from theory to synthesis and properties investigation of these new materials. This volume brings together the major findings in the field and provides a source of inspiration and understanding to advanced undergraduates, graduates, and researchers in the fields of Physics, Graph Theory, Crystallography, Computational and Synthetic Chemistry.
Categories: Technology & Engineering

Spin Chemical Physics of Graphene

Spin Chemical Physics of Graphene

The Mathematics and Topology of Fullerenes, Springer Science+Business Media B.V. 46. Ashrafi, A.R., Cataldo, F., Iranmanesh, A., and Ori, O. (Eds.) (2013). Topological Modelling of Nanostructures and Extended Systems, Carbon Materials: ...

Author: Elena Sheka

Publisher: CRC Press

ISBN: 9781351858601

Category: Science

Page: 468

View: 866

Graphene’s nickname ‘miracle material’ normally means the material superior properties. However, all these characteristics are only the outward manifestation of the wonderful nature of graphene. The real miracle of graphene is that the specie is a union of two entities: a physical - and a chemical one, each of which is unique in its own way. The book concerns a very close interrelationship between graphene physics and chemistry as expressed via typical spin effects of a chemical physics origin. Based on quantum-chemical computations, the book is nevertheless addressed to the reflection of physical reality and it is aimed at an understanding of what constitutes graphene as an object of material science – sci graphene – on the one hand, and as a working material- high tech graphene - for a variety of attractive applications largely discussed and debated in the press, on the other. The book is written by a user of quantum chemistry, sufficiently experienced in material science, and the chemical physics of graphene is presented as the user view based on results of extended computational experiments in tight connection with their relevance to physical and chemical realities. The experiments have been carried out at the same theoretical platform, which allows considering different sides of the graphene life at the same level in light of its chemical peculiarity.
Categories: Science

Quantum Nanochemistry Volume Five

Quantum Nanochemistry  Volume Five

... Graovac, A., Ori, O. (Eds.) The Mathematics and Topology of Fullerenes, Springer Science+Business Media, B. V., Dordrecht, Carbon Materials: Chemistry and Physics Series, Vol. 4, pp. 205–216. Ori, O., D'Mello, M. (1992).

Author: Mihai V. Putz

Publisher: CRC Press

ISBN: 9781498729574

Category: Medical

Page: 622

View: 660

Volume 5 of the 5-volume Quantum Nanochemistry focuses on modeling and predicting of the enzyme kinetics and quantitative structure-activity relationships. It reveals the quantum implications to bio-organic and bio-inorganic systems, to enzyme kinetics, and to pharmacophore binding sites of chemical-biological interaction of molecules through cell membranes in targeting specific bindings modeled by celebrated QSARs (Quantitative Structure-Activity Relationships) here reshaped as Qu-SAR (Quantum Structure-Activity Relationships).
Categories: Medical

Nanocomposites Nanophotonics Nanobiotechnology and Applications

Nanocomposites  Nanophotonics  Nanobiotechnology  and Applications

Endohedral fullerene complexes are fascinating objects promising at long-run numerous applications. The results presented in this mini review indicate ... In: Graovac A, Ori O, Cataldo F (eds) Mathematics and topology of fullerenes.

Author: Olena Fesenko

Publisher: Springer

ISBN: 9783319066110

Category: Science

Page: 403

View: 207

This book presents some of the latest achievements in nanotechnology and nanomaterials from leading researchers in Ukraine, Europe, and beyond. It features contributions from participants in the 2nd International Summer School “Nanotechnology: From Fundamental Research to Innovations” and International Research and Practice Conference “Nanotechnology and Nanomaterials”, NANO-2013, which were held in Bukovel, Ukraine on August 25-September 1, 2013. These events took place within the framework of the European Commission FP7 project Nanotwinning, and were organized jointly by the Institute of Physics of the National Academy of Sciences of Ukraine, University of Tartu (Estonia), University of Turin (Italy), and Pierre and Marie Curie University (France). Internationally recognized experts from a wide range of universities and research institutions share their knowledge and key results on topics ranging from nanooptics, nanoplasmonics, and interface studies to energy storage and biomedical applications.
Categories: Science

21st Century Nanoscience A Handbook

21st Century Nanoscience     A Handbook

Canadian Journal of Chemistry, 93(10):1157–1160, 2015. M. Bača, J. Horváthová, M. Mokrišová, and A. Suhányiová. On topological indices of fullerenes. Applied Mathematics and Computation, 251:154– 161, 2015. B. Bollobás and P. Erdos.

Author: Klaus D. Sattler

Publisher: CRC Press

ISBN: 9781000497427

Category: Technology & Engineering

Page: 360

View: 383

This up-to-date reference is the most comprehensive summary of the field of nanoscience and its applications. It begins with fundamental properties at the nanoscale and then goes well beyond into the practical aspects of the design, synthesis, and use of nanomaterials in various industries. It emphasizes the vast strides made in the field over the past decade – the chapters focus on new, promising directions as well as emerging theoretical and experimental methods. The contents incorporate experimental data and graphs where appropriate, as well as supporting tables and figures with a tutorial approach.
Categories: Technology & Engineering

Combinatorial And Toric Homotopy Introductory Lectures

Combinatorial And Toric Homotopy  Introductory Lectures

Introduction These lecture notes are devoted to results on the crossroads of classical polytope theory, toric topology, and the mathematical theory of fullerenes. Toric topology is a new area of mathematics that emerged at the end of ...

Author: Darby Alastair

Publisher: World Scientific

ISBN: 9789813226586

Category: Mathematics

Page: 448

View: 898

This volume consists of introductory lectures on the topics in the new and rapidly developing area of toric homotopy theory, and its applications to the current research in configuration spaces and braids, as well as to more applicable mathematics such as fr-codes and robot motion planning. The book starts intertwining homotopy theoretical and combinatorial ideas within the remits of toric topology and illustrates an attempt to classify in a combinatorial way polytopes known as fullerenes, which are important objects in quantum physics, quantum chemistry and nanotechnology. Toric homotopy theory is then introduced as a further development of toric topology, which describes properties of Davis–Januszkiewicz spaces, moment-angle complexes and their generalizations to polyhedral products. The book also displays the current research on configuration spaces, braids, the theory of limits over the category of presentations and the theory of fr-codes. As an application to robotics, the book surveys topological problems relevant to the motion planning problem of robotics and includes new results and constructions, which enrich the emerging area of topological robotics. The book is at research entry level addressing the core components in homotopy theory and their important applications in the sciences and thus suitable for advanced undergraduate and graduate students. Contents: Toric Homotopy Theory (Stephen Theriault)Fullerenes, Polytopes and Toric Topology (Victor M Buchstaber and Nikolay Yu Erokhovets)Around Braids (Vladimir Vershinin)Higher Limits, Homology Theories and fr-Codes (Sergei O Ivanov and Roman Mikhailov)Configuration Spaces and Robot Motion Planning Algorithms (Michael Farber)Cellular Stratified Spaces (Dai Tamaki) Readership: Advanced undergraduate and graduate students as well as researchers interested in homotopy theory and its applications in the sciences. Keywords: Toric Topology;Toric Homotopy;Configuration Space;Stratified Spaces;Braid Group;Fullerene;Polytope;Virtual Braid Group;Thompson Group;Robotics;Motion PlanningReview: Key Features: The first book in the area of toric homotopy theory consisting of introductory lectures on the topics and their applications to fr-codes and robot motion planning
Categories: Mathematics

Advances in Quantum Methods and Applications in Chemistry Physics and Biology

Advances in Quantum Methods and Applications in Chemistry  Physics  and Biology

... topology of fullerenes. Springer Science+Business Media BV, Berlin 2. Merrifield RE, Simmons HE (1989) Topological methods in chemistry. Wiley, New York 3. Schmidt GMJ (1971) Photodimerization in the solid state.

Author: Matti Hotokka

Publisher: Springer Science & Business Media

ISBN: 9783319015293

Category: Science

Page: 379

View: 445

Advances in Quantum Methods and Applications in Chemistry, Physics, and Biology includes peer-reviewed contributions based on carefully selected presentations given at the 17th International Workshop on Quantum Systems in Chemistry, Physics, and Biology. New trends and state-of-the-art developments in the quantum theory of atomic and molecular systems, and condensed matter (including biological systems and nanostructures) are described by academics of international distinction.
Categories: Science

Scientific Papers of Ettore Majorana

Scientific Papers of Ettore Majorana

Mathematics and topology of fullerenes, Springer series on carbon materials chemistry and physics, vol. 4. Springer, Heidelberg/Berlin (2011) Benedek, G.: When topology matters: the Nobel prize in physics 2016. Revue Quest. Sci.

Author: Luisa Cifarelli

Publisher: Springer Nature

ISBN: 9783030235093

Category: Science

Page: 188

View: 771

This book presents in full the work of the Italian theoretical physicist Ettore Majorana and explains its impacts, which are still being felt. It opens with a contribution by A. Zichichi that considers in depth the scientific genius of Majorana. This introductory chapter is followed, in chronological order, by the eleven scientific papers by this great scientist, in most cases translated into English for the first time. Each paper is accompanied by a comment from an expert in the field in question. Although very few in number, Majorana's papers constitute a heritage of undeniable value and extraordinary scientific meaning, since they laid the foundations for research fields that remain topical today. With this in mind, two additional contributions on ongoing developments in these research fields are included: one on neutrino physics and the other on Majorana fermions in condensed matter. The volume closes with a note on Majorana's life until his ill-fated disappearance.
Categories: Science

Graphene for Defense and Security

Graphene for Defense and Security

Ed.) “The Mathematics and topology of fullerenes” 04 “Carbon materials: Chemistry and physics”, Springer (2011) Boukhalov, D.W., Katsnelson, M.I., and Son, Y.W., “Origin of anomalous water permeation through graphene oxide membrane”, ...

Author: Andre U. Sokolnikov

Publisher: CRC Press

ISBN: 9781351646680

Category: Science

Page: 270

View: 997

Graphene is giving new impetus to the electronics industry because its band structure allows its properties to be dramatically altered and modified by chemical or electrochemical doping methods. This book provides a comprehensive source of information about graphene as a phenomenon, its physics and its mechanical and chemical properties in the light of the latest scientific and technological discoveries. The major focus of the book is on military and special applications since that is where the biggest investments are made.
Categories: Science

Epioptics 11

Epioptics 11

G. Benedek, M. Bernasconi, E. Cinquanta, L. D'Alessio, and M. De Corato, in Mathematics and Topology of Fullerenes, ed. by F. Cataldo, A. Graovac, and O. Ori, Springer Series on Carbon Materials Chemistry and Physics, Vol.

Author: Antonio Cricenti

Publisher: World Scientific

ISBN: 9789814417129

Category: Electronic books

Page: 140

View: 883

The book is aimed at assessing the capabilities of state-of-the-art optical techniques in elucidating the fundamental electronic and structural properties of semiconductor and metal surfaces, interfaces, thin layers, and layer structures, and assessing the usefulness of these techniques for optimization of high quality multilayer samples through feedback control during materials growth and processing. Particular emphasis is dedicated to the theory of nonlinear optics and to dynamical processes through the use of pumpOCoprobe techniques together with the search for new optical sources. Some new applications of Scanning Probe Microscopy to Material Science and biological samples, dried and in vivo, with the use of different laser sources are also presented. Materials of particular interest are silicon, semiconductorOCometal interfaces, semiconductor and magnetic multi-layers and III-V compound semiconductors.
Categories: Electronic books

Epioptics 11

Epioptics 11

G. Benedek, M. Bernasconi, E. Cinquanta, L. D'Alessio, and M. De Corato, in Mathematics and Topology of Fullerenes, ed. by F. Cataldo, A. Graovac, and O. Ori, Springer Series on Carbon Materials Chemistry and Physics, Vol.

Author: Antonio Cricenti

Publisher: World Scientific

ISBN: 9789814417136

Category: Science

Page: 140

View: 224

The book is aimed at assessing the capabilities of state-of-the-art optical techniques in elucidating the fundamental electronic and structural properties of semiconductor and metal surfaces, interfaces, thin layers, and layer structures, and assessing the usefulness of these techniques for optimization of high quality multilayer samples through feedback control during materials growth and processing. Particular emphasis is dedicated to the theory of nonlinear optics and to dynamical processes through the use of pump–probe techniques together with the search for new optical sources. Some new applications of Scanning Probe Microscopy to Material Science and biological samples, dried and in vivo, with the use of different laser sources are also presented. Materials of particular interest are silicon, semiconductor–metal interfaces, semiconductor and magnetic multi-layers and III-V compound semiconductors. Contents:Epitaxial-Like Growth of Lead Phthalocyanine Layers on GaAs(001) Surfaces (L Riele, B Buick, E Speiser, B-O Fimland, P Vogt and W Richter)Optical Properties of Nanostructured Metamaterials (E Cortes, B S Mendoza, W L Mochan and G Ortiz)Ab Initio Long-Wavelength Properties of Metallic Systems: Iron and Magnesium (M Cazzaniga, L Caramella, N Manini, P Salvestrini and G Onida)Magnetic Second-Harmonic Generation from Interfaces and Nanostructures (J F McGilp)Optical Investigations of the Interface Formation between Organic Molecules and Semiconductor Surfaces (T Bruhn, L Riele, B-O Fimland, N Esser and P Vogt)Reflection Anisotropic Spectroscopy Studies of Thiolate/Metal Interfaces (D S Martin)The Physics of X-ray Free Electron Lasers (X-FELs): An Elementary Approach (P Rebernik Ribic and G Margaritondo)The Decisive Role of Interface Phonons in Polaron State Formation in Quantum Nanostructures (A Yu Maslov and O V Proshina)Dielectric Analysis on Optical Properties of Silver Nano Particles in ZrO2 Thin Film Prepared by Sol–Gel Method (M Wakaki and E Yokoyama)Towards Ab Initio Calculation of the Circular Dichroism of Peptides (E Molteni, G Onida and G Tiana)Dynamics and Spectral Properties of Free-Standing Negatively-Curved Carbon Surfaces (M De Corato and G Benedek) Readership: The book is a good reference for researchers that want to be involved in optical spectroscopy as a tool to study surfaces and interfaces. Keywords:Optics;Spectroscopy;Surfaces;Semiconductors;Reflectivity
Categories: Science

Mathematical Challenges from Theoretical Computational Chemistry

Mathematical Challenges from Theoretical Computational Chemistry

MATHEMATICS AND FULLERENES The structures and properties of the fullerene molecules—"buckyballs" (see Figure 3.1) and ... areas of mathematics.1 Topology can provide insights into the types of such structures that can and cannot exist; ...

Author: National Research Council

Publisher: National Academies Press

ISBN: 9780309050975

Category: Mathematics

Page: 144

View: 260

Computational methods are rapidly becoming major tools of theoretical, pharmaceutical, materials, and biological chemists. Accordingly, the mathematical models and numerical analysis that underlie these methods have an increasingly important and direct role to play in the progress of many areas of chemistry. This book explores the research interface between computational chemistry and the mathematical sciences. In language that is aimed at non-specialists, it documents some prominent examples of past successful cross-fertilizations between the fields and explores the mathematical research opportunities in a broad cross-section of chemical research frontiers. It also discusses cultural differences between the two fields and makes recommendations for overcoming those differences and generally promoting this interdisciplinary work.
Categories: Mathematics

Mathematical Challenges from Theoretical Computational Chemistry

Mathematical Challenges from Theoretical Computational Chemistry

MATHEMATICS AND FULLERENES The structures and properties of the fullerene molecules—"buckyballs" (see Figure 3.1) and ... areas of mathematics.1 Topology can provide insights into the types of such structures that can and cannot exist; ...

Author: Committee on Mathematical Challenges from Computational Chemistry

Publisher: National Academies Press

ISBN: 9780309560641

Category: Mathematics

Page: 126

View: 792

Computational methods are rapidly becoming major tools of theoretical, pharmaceutical, materials, and biological chemists. Accordingly, the mathematical models and numerical analysis that underlie these methods have an increasingly important and direct role to play in the progress of many areas of chemistry. This book explores the research interface between computational chemistry and the mathematical sciences. In language that is aimed at non-specialists, it documents some prominent examples of past successful cross-fertilizations between the fields and explores the mathematical research opportunities in a broad cross-section of chemical research frontiers. It also discusses cultural differences between the two fields and makes recommendations for overcoming those differences and generally promoting this interdisciplinary work.
Categories: Mathematics

Topology Geometry and Dynamics V A Rokhlin Memorial

Topology  Geometry  and Dynamics  V  A  Rokhlin Memorial

Toric topology assigns to each n-dimensional combinatorial simple convex polytope P with m facets an (m+n)-dimensional moment-angle manifold ZP with an action of the compact torus Tm such that ZP /Tm is a convex polytope of ...

Author: Anatoly M. Vershik

Publisher: American Mathematical Soc.

ISBN: 9781470456641

Category: Education

Page: 345

View: 108

Vladimir Abramovich Rokhlin (8/23/1919–12/03/1984) was one of the leading Russian mathematicians of the second part of the twentieth century. His main achievements were in algebraic topology, real algebraic geometry, and ergodic theory. The volume contains the proceedings of the Conference on Topology, Geometry, and Dynamics: V. A. Rokhlin-100, held from August 19–23, 2019, at The Euler International Mathematics Institute and the Steklov Institute of Mathematics, St. Petersburg, Russia. The articles deal with topology of manifolds, theory of cobordisms, knot theory, geometry of real algebraic manifolds and dynamical systems and related topics. The book also contains Rokhlin's biography supplemented with copies of actual very interesting documents.
Categories: Education