Download or read book Partitioning of Fibonacci Numbers Representing Kekule Structures written by Sherif El-Basil and published by . This book was released on 1987 with total page 29 pages. Available in PDF, EPUB and Kindle. Book excerpt: When a Kekule structure is transformed into the subspace of its double bonds a factor of graph results. A function called degenerate transformation is defined on the set of factor graphs of a benzenoid system which was demonstrated to be an equivalence relation. For nonbranched catacondensed all-benzenoid, NBCCAB, hydrocarbons, this relation is shown to preserve the Fibonacci-type recursion of the number of their Kekule structures. Keywords: Graph theory, Factor graph, Fibonacci numbers, Equivalence relation.
Download or read book Technical Reports Awareness Circular TRAC written by and published by . This book was released on 1987-10 with total page 544 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Government Reports Announcements Index written by and published by . This book was released on 1987-12 with total page 1642 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Carbon Bonding and Structures written by Mihai V. Putz and published by Springer Science & Business Media. This book was released on 2011-08-27 with total page 445 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Carbon Bonding and Structures: Advances in Physics and Chemistry" features detailed reviews which describe the latest advances in the modeling and characterization of fundamental carbon based materials and recently designed carbon composites. Significant advances are reported and reviewed by globally recognized experts in the field. The quantification, indexing, and interpretation of physical and chemical patterns of carbon atoms in molecules, crystals, and nanosystems is presented. "Carbon Bonding and Structures: Advances in Physics and Chemistry" will be primarily of interest to theoretical physical chemists and computational materials scientists based in academia, government laboratories, and industry.
Download or read book Government Reports Annual Index written by and published by . This book was released on 1987 with total page 1256 pages. Available in PDF, EPUB and Kindle. Book excerpt: Sections 1-2. Keyword Index.--Section 3. Personal author index.--Section 4. Corporate author index.-- Section 5. Contract/grant number index, NTIS order/report number index 1-E.--Section 6. NTIS order/report number index F-Z.
Download or read book Government Reports Annual Index Keyword A L written by and published by . This book was released on 1987 with total page 1260 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Fibonacci and Catalan Numbers written by Ralph Grimaldi and published by John Wiley & Sons. This book was released on 2012-02-21 with total page 380 pages. Available in PDF, EPUB and Kindle. Book excerpt: Discover the properties and real-world applications of the Fibonacci and the Catalan numbers With clear explanations and easy-to-follow examples, Fibonacci and Catalan Numbers: An Introduction offers a fascinating overview of these topics that is accessible to a broad range of readers. Beginning with a historical development of each topic, the book guides readers through the essential properties of the Fibonacci numbers, offering many introductory-level examples. The author explains the relationship of the Fibonacci numbers to compositions and palindromes, tilings, graph theory, and the Lucas numbers. The book proceeds to explore the Catalan numbers, with the author drawing from their history to provide a solid foundation of the underlying properties. The relationship of the Catalan numbers to various concepts is then presented in examples dealing with partial orders, total orders, topological sorting, graph theory, rooted-ordered binary trees, pattern avoidance, and the Narayana numbers. The book features various aids and insights that allow readers to develop a complete understanding of the presented topics, including: Real-world examples that demonstrate the application of the Fibonacci and the Catalan numbers to such fields as sports, botany, chemistry, physics, and computer science More than 300 exercises that enable readers to explore many of the presented examples in greater depth Illustrations that clarify and simplify the concepts Fibonacci and Catalan Numbers is an excellent book for courses on discrete mathematics, combinatorics, and number theory, especially at the undergraduate level. Undergraduates will find the book to be an excellent source for independent study, as well as a source of topics for research. Further, a great deal of the material can also be used for enrichment in high school courses.
Download or read book Government Reports Annual Index Corporate author written by and published by . This book was released on 1987 with total page 1028 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Introduction to the Theory of Benzenoid Hydrocarbons written by Ivan Gutman and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 157 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the last hundred years benzenoid hydrocarbons have constantly attracted the attention of both experimental and theoretical chemists. In spite of the fact that some of the basic concepts of the theory of benzenoid hydrocarbons have their origins in the 19th and early 20th century, research in this area is still in vigorous expansion. The present book provides an outline of the most important current theoretical approaches to benzenoids. Emphasis is laid on the recent developments of these theories, which can certainly be characterized as a significant advance. Em phasis is also laid on practical applications rather than on "pure" theory. The book assumes only some elementary knowledge of organic and physical chemistry and requires no special mathematical training. Therefore we hope that undergraduate students of chemistry will be able to follow the text without any difficulty. Since organic and physical chemists are nowadays not properly acquaint ed lVith the modern theory of benzenoid molecules, we hope that they will find this book both useful and informative. Our book is also aimed at theoretical chemists, especially those concerned with the "topological" features of organic molecules. The authors are indebted to Dr. WERNER SCHMIDT (Ahrensburg, FRG) for valuable discussions. One of the authors (1. G.) thanks the Royal Norwegian Council for Scientific and Industrial Research for financial support during 1988, which enabled him to stay at the University of Trondheim and write the present book. Trondheim, July 1989 Ivan Gutman Sven J. Cyvin Contents Chapter 1 Benzenoid Hydrocarbons .
Download or read book Congressus Numerantium written by and published by . This book was released on 1970 with total page 592 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Mathematical Reviews written by and published by . This book was released on 1997 with total page 1164 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Graph Theoretical Approaches to Chemical Reactivity written by Danail D. Bonchev and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 291 pages. Available in PDF, EPUB and Kindle. Book excerpt: The progress in computer technology during the last 10-15 years has enabled the performance of ever more precise quantum mechanical calculations related to structure and interactions of chemical compounds. However, the qualitative models relating electronic structure to molecular geometry have not progressed at the same pace. There is a continuing need in chemistry for simple concepts and qualitatively clear pictures that are also quantitatively comparable to ab initio quantum chemical calculations. Topological methods and, more specifically, graph theory as a fixed-point topology, provide in principle a chance to fill this gap. With its more than 100 years of applications to chemistry, graph theory has proven to be of vital importance as the most natural language of chemistry. The explosive development of chemical graph theory during the last 20 years has increasingly overlapped with quantum chemistry. Besides contributing to the solution of various problems in theoretical chemistry, this development indicates that topology is an underlying principle that explains the success of quantum mechanics and goes beyond it, thus promising to bear more fruit in the future.
Download or read book Chemistry from First Principles written by Jan C. A. Boeyens and published by Springer Science & Business Media. This book was released on 2008-09-11 with total page 332 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Chemistry from First Principles" examines the appearance of matter in its most primitive form. It features the empirical rules of chemical affinity that regulate the synthesis and properties of molecular matter, analyzes the compatibility of the theories of chemistry with the quantum and relativity theories of physics, formulates a consistent theory based on clear physical pictures and manageable mathematics to account for chemical concepts such as the structure and stability of atoms and molecules. This text also explains the self-similarity between space-time, nuclear structure, covalent assembly, biological growth, planetary systems, and galactic conformation.
Download or read book Resources for Teaching Discrete Mathematics written by Brian Hopkins and published by MAA. This book was released on 2009 with total page 342 pages. Available in PDF, EPUB and Kindle. Book excerpt: Hopkins collects the work of 35 instructors who share their innovations and insights about teaching discrete mathematics at the high school and college level. The book's 9 classroom-tested projects, including building a geodesic dome, come with student handouts, solutions, and notes for the instructor. The 11 history modules presented draw on original sources, such as Pascal's "Treatise on the Arithmetical Triangle," allowing students to explore topics in their original contexts. Three articles address extensions of standard discrete mathematics content. Two other articles explore pedagogy specifically related to discrete mathematics courses: adapting a group discovery method to larger classes, and using logic in encouraging students to construct proofs.
Download or read book Human Accomplishment written by Charles Murray and published by Harper Collins. This book was released on 2009-10-13 with total page 790 pages. Available in PDF, EPUB and Kindle. Book excerpt: A sweeping cultural survey reminiscent of Barzun's From Dawn to Decadence. "At irregular times and in scattered settings, human beings have achieved great things. Human Accomplishment is about those great things, falling in the domains known as the arts and sciences, and the people who did them.' So begins Charles Murray's unique account of human excellence, from the age of Homer to our own time. Employing techniques that historians have developed over the last century but that have rarely been applied to books written for the general public, Murray compiles inventories of the people who have been essential to the stories of literature, music, art, philosophy, and the sciences—a total of 4,002 men and women from around the world, ranked according to their eminence. The heart of Human Accomplishment is a series of enthralling descriptive chapters: on the giants in the arts and what sets them apart from the merely great; on the differences between great achievement in the arts and in the sciences; on the meta-inventions, 14 crucial leaps in human capacity to create great art and science; and on the patterns and trajectories of accomplishment across time and geography. Straightforwardly and undogmatically, Charles Murray takes on some controversial questions. Why has accomplishment been so concentrated in Europe? Among men? Since 1400? He presents evidence that the rate of great accomplishment has been declining in the last century, asks what it means, and offers a rich framework for thinking about the conditions under which the human spirit has expressed itself most gloriously. Eye-opening and humbling, Human Accomplishment is a fascinating work that describes what humans at their best can achieve, provides tools for exploring its wellsprings, and celebrates the continuing common quest of humans everywhere to discover truths, create beauty, and apprehend the good.
Download or read book Recurrence Sequences written by Graham Everest and published by American Mathematical Soc.. This book was released on 2015-09-03 with total page 338 pages. Available in PDF, EPUB and Kindle. Book excerpt: Recurrence sequences are of great intrinsic interest and have been a central part of number theory for many years. Moreover, these sequences appear almost everywhere in mathematics and computer science. This book surveys the modern theory of linear recurrence sequences and their generalizations. Particular emphasis is placed on the dramatic impact that sophisticated methods from Diophantine analysis and transcendence theory have had on the subject. Related work on bilinear recurrences and an emerging connection between recurrences and graph theory are covered. Applications and links to other areas of mathematics are described, including combinatorics, dynamical systems and cryptography, and computer science. The book is suitable for researchers interested in number theory, combinatorics, and graph theory.
