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The Ultimate Challenge
The $3x+1$ problem, or Collatz problem, concerns the following seemingly innocent arithmetic procedure applied to integers: If an integer $x$ is odd then “multiply by three and add one”, while if it is even then “divide by two”. The $3x+1$ problem asks whether, starting from any positive integer, repeating this procedure over and over will eventually reach the number 1. Despite its simple appearance, this problem is unsolved. Generalizations of the problem are known to be undecidable, and the problem itself is believed to be extraordinarily difficult. This book reports on what is known on this problem. It consists of a collection of papers, which can be read independently of each oth...
Optimization Problems
The German edition of this book, first published in 1966, has been quite popular; we did not, however, consider publishing an English edition because a number of excellent textbooks in this field already exist. In recent years, how ever, the wish was frequently expressed that, especially, the description of the relationships between optimization and other subfields of mathematics, which is not to be found in this form in other texts, might be made available to a wider readership; so it was with this in mind that, be latedly, a translation was undertaken after all. Since the appearance of the German edition, the field of optimization has continued to develop at an unabated rate. A completely ...
Numerical Solution of Elliptic Problems
A study of the art and science of solving elliptic problems numerically, with an emphasis on problems that have important scientific and engineering applications, and that are solvable at moderate cost on computing machines.
Collected Mathematical Papers
This publication was made possible through a bequest from my beloved late wife. United together in this present collection are those works by the author which have not previously appeared in book form. The following are excepted: Vorlesungen uber Differential und Integralrechnung (Lectures on Differential and Integral Calculus) Vols 1-3, Birkhauser Verlag, Basel (1965-1968); Aufgabensammlung zur Infinitesimalrechnung (Exercises in Infinitesimal Calculus) Vols 1, 2a, 2b, and 3, Birkhauser Verlag, Basel (1967-1977); two issues from Memorial des Sciences on Conformal Mapping (written together with C. Gattegno), Gauthier-Villars, Paris (1949); Solution of Equations in Euc1idean and Banach Spaces...
Some Successive Approximation Methods in Control and Oscillation Theory by Peter L Falb and Jan L de Jong
In this book, we study theoretical and practical aspects of computing methods for mathematical modelling of nonlinear systems. A number of computing techniques are considered, such as methods of operator approximation with any given accuracy; operator interpolation techniques including a non-Lagrange interpolation; methods of system representation subject to constraints associated with concepts of causality, memory and stationarity; methods of system representation with an accuracy that is the best within a given class of models; methods of covariance matrix estimation;methods for low-rank matrix approximations; hybrid methods based on a combination of iterative procedures and best operator ...
Differential Equations
Practical, concise text covers the existence and uniqueness theorem, characteristics of first-order equations, boundary problems for second-order linear equations, asymptotic methods, and differential equations in the complex field. 1961 edition.
Forest Ecosystems
This revision maintains the position of Forest Ecosystems as the one source for the latest information on the advanced methods that have enhanced our understating of forest ecosystems. Further understanding is given to techniques to explore the changes in climatic cycles, the implications of wide-scale pollution, fire and other ecological disturbances that have a global effect. The inclusion of models, equations, graphs, and tabular examples provides readers with a full understanding of the methods and techniques. - Includes a revised section on important advances in regional scale analyses - Features an update to global scale analyses including revised color images - Provides a detailed comparison of predicted vs. observed tree diversity across 65 eco-regions
