A. B. Vistelius

Principles of Mathematical Geology

• Gebundenes Buch

Produktbeschreibung

This volume, which is based on the Russian edition published in 1980, presents the fundamentals of mathematical geology. New developments which have taken place in the last ten years or so have been taken into account as far as possible, and this English edition contains two completely new chapters devoted, respectively, to random diffusion processes and a survey of future geological problems. The book has eight chapters. Chapter I deals with the basic question `What is mathematical geology?' Chapter II considers the concept of probability. Chapter III relates this fundamental tool to geological problems with the help of specific examples. Chapters IV-VI cover the theory of random sequence and concentrates on the form which is the most useful to geologists. Chapter VII is dedicated to continuous Markov processes which occur frequently in geological phenomena. The volume concludes with an overview of ideas which have been generated by mathematical geology and which pave the way for the further development of the subject.
Many examples are included throughout the text and the volume has a comprehensive subject index.

Produktdetails

• Verlag: Springer Netherlands
• 1992.
• Seitenzahl: 504
• Erscheinungstermin: 30. Juni 1992
• Englisch
• Abmessung: 241mm x 160mm x 33mm
• Gewicht: 1015g
• ISBN-13: 9780792300762
• ISBN-10: 0792300769
• Artikelnr.: 27656198

Inhaltsangabe

Preface. Preface to the English Edition. Basic Notations. Introduction. I: Mathematical Geology and the Development of Geological Sciencies. II: Probability Space and Random Variables. III: Basic Statistical Concepts -- Problems of Estimation and Testing of Hypotheses. IV: Random Sequences and their Markov Chains. V: Transformations of Markov Chains. VI: Statistical Inferences on Properties of Random Sequences and Markov Hypotheses. VII: Random Diffusion Processes. VIII: Coming Problems and Paradigm of Geological Sciences of the 21st Century. Authors' Index. Geographical Index. Subject Index.

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I. Mathematical Geology and the Development of Geological Sciences.- I.1 Introduction.- I.2 Development of geology and the change of paradigms.- I.3 Organization of the medium and typical structures.- I.4 Statement of the problem: the role of models in the search for solutions.- I.5 Mathematical geology and its development.- References.- II. Probability Space and Random Variables.- II. 1 Introduction.- II.2 Discrete space of elementary events.- II.3 Kolmogorov's axiom; The Lebesgue integral.- II.4 Exanples of distributions of random variables.- II.5 Vector random variables.- II.6 Transformations of random variables.- II.7 Sequences of independent random variables and limit theorems.- II.8 Random processes and geometric probabilities.- References.- III. Basic Statistical Concepts - Problems of Estimation and Testing of Hypotheses.- III.1 Introductory remarks.- III.2 Point estimation.- III.3 Testing of statistical hypotheses.- III.4 On confidence intervals.- III.5 On robustness.- References.- IV. Randan Sequences and their Markov Chains.- IV. 1 Introduction.- IV.2 Probabilistic structures of Markov sequences.- IV.3 Matrix methods in the study of Markov chains.- IV. 4 Some generalizations of the Markov property.- IV. 5 Three-dimensional packing and Markov sequences.- References.- V. Transformations of Markov chains.- V. 1 Introduction.- V.2 Lumping over a set of states.- V.3 Concentration and rarefaction.- V.5 Sequences of packets.- References.- VI. Statistical Inferences on Properties of Randan Sequences and Markov Hypotheses.- VI. 1 Introduction.- VI. 2 Test of homogeneity.- VI.3 Test of reversibility.- VI.4 Likelihood ratio criterion ? for testing proportionality of transition probabilities.- VI.5 Markov hypotheses.- VI. 6 Partial Markov.- VI.7 Experimental checkof consistency of statistical tests on Markov order.- References.- VII. Randan Diffusion Processes.- VII. 1 Introduction.- VII.2 The general model.- VII.3 Particular models of diffusion.- References.- VIII. Coming Problems and Paradigm of Geological Sciences of the 21st Century.- VIII.1 Introduction.- VIII.2 Time and Compositional data.- VIII.3 Models.- References.- Authors Index.- Geographical Index.

Rezensionen

` The most outstanding feature of this book is the clear, rigorous, and comprehensive presentation of Vistelius' concept of what mathematical geology is and where it should be heading in the future. It summarizes more than fifty years of experience, work, and understanding. ... this book should be mandatory reading for all those interested and working in mathematical geology because it presents much food for thought. '
Mathematical Geology, 26:3 (1994)

` The most outstanding feature of this book is the clear, rigorous, and comprehensive presentation of Vistelius' concept of what mathematical geology is and where it should be heading in the future. It summarizes more than fifty years of experience, work, and understanding. ... this book should be mandatory reading for all those interested and working in mathematical geology because it presents much food for thought. ' Mathematical Geology, 26:3 (1994)