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Recent Researches and Reviews in Mathematics and Natural Science
Recent Researches and Reviews in Mathematics and Natural Science, Livre de Lyon
Recent Approaches in Mathematics and Natural Science
Recent Approaches in Mathematics and Natural Science, Livre de Lyon
Graphs and Matrices
This new edition illustrates the power of linear algebra in the study of graphs. The emphasis on matrix techniques is greater than in other texts on algebraic graph theory. Important matrices associated with graphs (for example, incidence, adjacency and Laplacian matrices) are treated in detail. Presenting a useful overview of selected topics in algebraic graph theory, early chapters of the text focus on regular graphs, algebraic connectivity, the distance matrix of a tree, and its generalized version for arbitrary graphs, known as the resistance matrix. Coverage of later topics include Laplacian eigenvalues of threshold graphs, the positive definite completion problem and matrix games based...
Analytic Inequalities
The Theory of Inequalities began its development from the time when C. F. GACSS, A. L. CATCHY and P. L. CEBYSEY, to mention only the most important, laid the theoretical foundation for approximative meth ods. Around the end of the 19th and the beginning of the 20th century, numerous inequalities were proyed, some of which became classic, while most remained as isolated and unconnected results. It is almost generally acknowledged that the classic work "Inequali ties" by G. H. HARDY, J. E. LITTLEWOOD and G. POLYA, which appeared in 1934, transformed the field of inequalities from a collection of isolated formulas into a systematic discipline. The modern Theory of Inequalities, as well as the c...
Topological Approach to the Chemistry of Conjugated Molecules
"The second step is to determine constitution, Le. which atoms are bonded to which and by what types of bond. The result is ex pressed by a planar graph (or the corresponding connectivity mat rix) •••• In constitutional formulae, the atoms are represented by letters and the bonds by lines. They describe the topology of the molecule." VLADIMIR PRELOG, Nobel Lecture, December l2;h 1975. In the present notes we describe the topological approach to the che mistry of conjugated molecules using graph-theoretical concepts. Con jugatedstructures may be conveniently studied using planar and connec ted graphs because they reflect in the simple way the connectivity of their pi-centers. Connectivity is important topological property of a molecule which allows a conceptual qualitative understanding, via a non numerical analysis, of many chemical phenomena or at least that part of phenomenon which depends on topology. This would not be possible sole ly by means of numerical (molecular orbital) analysis.
Molecular Orbital Calculations Using Chemical Graph Theory
Professor John D. Roberts published a highly readable book on Molecular Orbital Calculations directed toward chemists in 1962. That timely book is the model for this book. The audience this book is directed toward are senior undergraduate and beginning graduate students as well as practicing bench chemists who have a desire to develop conceptual tools for understanding chemical phenomena. Although, ab initio and more advanced semi-empirical MO methods are regarded as being more reliable than HMO in an absolute sense, there is good evidence that HMO provides reliable relative answers particularly when comparing related molecular species. Thus, HMO can be used to rationalize electronic structu...
Hückel Molecular Orbital Theory
Huckel Molecular Orbital Theory aims to be a simple, descriptive, and non-mathematical introduction to the Huckel molecular orbital theory and its applications in organic chemistry, thus the more basic text found in the book. The book, after an introduction to related concepts such as quantum mechanics and chemical bonding, discusses the Huckel molecular orbital theory and its basic assumptions; the variation principle and the basic Huckel method; and the use of symmetry properties in simplifying Huckel method orbital calculations. The book also covers other related topics such as the extensions and improvements of the simple Huckel method; the quantitative significance Huckel molecular orbital results; and the principle of conservation of orbital symmetry. The text is recommended for undergraduate students of organic chemistry who wish to be acquainted with the basics of the Huckel molecular orbital theory.
Relativity and Quantum Physics for Beginners
As humanity has expanded its horizon to see things vastly smaller, faster, larger and farther than before, it has been forced to confront preconceptions born of the human experience and create wholly new ways of looking at the world. Relativity and Quantum Physics For Beginners describes the revolutionary theories of relativity and quantum physics and shows how these ideas have led to amazing advances in the understanding of the universe.
Computational Line Geometry
From the reviews: " A unique and fascinating blend, which is shown to be useful for a variety of applications, including robotics, geometrical optics, computer animation, and geometric design. The contents of the book are visualized by a wealth of carefully chosen illustrations, making the book a shear pleasure to read, or even to just browse in." Mathematical Reviews
