Studies in Mathematics and Mechanics - 1st Edition - ISBN: 9781483232720, 9781483263564

Studies in Mathematics and Mechanics

1st Edition

Authors: Richard von Mises
eBook ISBN: 9781483263564
Imprint: Academic Press
Published Date: 1st January 1954
Page Count: 364
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Studies in Mathematics and Mechanics is a collection of studies presented to Professor Richard von Mises as a token of reverence and appreciation on the occasion of his seventieth birthday which occurred on April 19, 1953. von Mises’ thought has been a stimulus in many seemingly unconnected fields of mathematics, science, and philosophy, to which he has contributed decisive results and new formulations of fundamental concepts. The book contains 42 chapters organized into five parts. Part I contains papers on algebra, number theory and geometry. These include a study of Poincaré’s representation of a hyperbolic space on an Euclidean half-space and elementary estimates for the least primitive root. Part II on analysis includes papers on a generalization of Green's Formula and its application to the Cauchy problem for a hyperbolic equation, and the fundamental solutions of a singular Beltrami operator. Part III deals with theoretical mechanics and covers topics such as turbulent flow, axially symmetric flow, and oscillating wakes. The papers in Part IV focus on applied mechanics. These include studies on plastic flow under high stresses and the problem of inelastic thermal stresses. Part V presents studies on probability and statistics, including a finite frequency theory of probability and the problem of expansion of clusters of galaxies.

Table of Contents



Algebra and Number Theory; Geometry

1. On Poincaré's Representation of the Hyperbolic Space on an Euclidean Half-Space

2. Elementary Estimates for the Least Primitive Root

3. Image Errors and Diapoint Errors

4. Sur une propriété caractéristique des produits de deux symétries

5. On Two Problems in Abstract Algebra Connected with Horner's Rule

6. On Dedekind Sums and Lattice Points in a Tetrahedron

7. Some Remarks on the Topological Characterization of Algebraic Surfaces

8. On a Theorem of C. Carathéodory

9. Generalized Commutators of Matrices and Permutations of Factors in a Product of Three Matrices


10. On a Generalization of Green's Formula and Its Application to the Cauchy Problem for a Hyperbolic Equation

11. Properties of Solutions of a System of Partial Differential Equations

12. Induced Potentials

13. On the Fundamental Solutions of a Singular Beltrami Operator

14. Sur le contrôle des intégrations numériques

15. On the Biharmonic Green's Function

16. Sul calcolo delle funzioni olomorfe di una variabile complessa

17. Dirichlet's Principle on Manifolds

18. Weak Functions and the "Finite Part" of Divergent Integrals

Theoretical Mechanics

19. Some Considerations on Turbulent Flow with Shear

20. An Example of Axially Symmetric Flow with a Free Surface

21. On a Class of Spherically Symmetric Flows

22. On Periodically Oscillating Wakes in the Oseen Approximation

23. Some Bounds for the Critical Free Stream Mach Number of a Compressible Flow around an Obstacle

24. Two Topics in One-Dimensional Gas Dynamics

25. On the Stroboscopic Method

26. Estimates for Eigenvalues

27. On Slow Visco-Plastic Flow

28. Relativistically Rigid Surfaces

Applied Mechanics

29. Certain Aspects of Plastic Flow under High Stresses

30. Natural Convection Heat Transfer Correlation

31. Der senkrecht zu seiner Ebene belastete, elastisch gebettete Kreisträger

32. On Inelastic Thermal Stresses

33. Torsion of a Circular Cylindrical Body by Means of Tractions Exerted upon the Cylindrical Boundary

34. Una espressiva applicazione delle proprietà di media dello stress comuni a tutti i sistemi continui

Probability and Statistics

35. A Finite Frequency Theory of Probability

36. Interdépendance du centre et du rayon empiriques de variation de n observations indépendantes (Premier mémoire)

37. On Multivariate Normal Probability Distributions

38. Sur la densité de probabilité du produit de variables aléatoires de Pearson du type III

39. On the Statistical Investigation of Transcendental Numbers

40. Estensioni e portata della teoria della dispersione

41. On the Problem of Expansion of Clusters of Galaxies

42. The Asymptotic Development of the Distribution of the Extreme Values of a Sample


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© Academic Press 1954
Academic Press
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About the Author

Richard von Mises

Affiliations and Expertise

Harvard University Cambridge, Massachusetts

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