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Page 30
... structure for electromagnetic theory free of algebraic irrelevancies . The second problem bore on ergodic dynamical systems . Poincaré , and sev- eral others after him , taught us that in such a system every state is visited in ...
... structure for electromagnetic theory free of algebraic irrelevancies . The second problem bore on ergodic dynamical systems . Poincaré , and sev- eral others after him , taught us that in such a system every state is visited in ...
Page 38
... structures that describe never - repeating orbit confined to a finite region of space . These systems exhibit what appears to be chaotic behavior . How would one describe the long - term behavior of such a system ? Dan shows us how to ...
... structures that describe never - repeating orbit confined to a finite region of space . These systems exhibit what appears to be chaotic behavior . How would one describe the long - term behavior of such a system ? Dan shows us how to ...
Page 51
... Structure : Selected Essays on Science , Art , and History . Cambridge , Massachusetts : The MIT Press . Verna Gardiner , R. Lazarus , N. Metropolis , and S. Ulam . 1956. On certain sequences of integers defined by sieves . Mathematics ...
... Structure : Selected Essays on Science , Art , and History . Cambridge , Massachusetts : The MIT Press . Verna Gardiner , R. Lazarus , N. Metropolis , and S. Ulam . 1956. On certain sequences of integers defined by sieves . Mathematics ...
Page 65
... structure , earlier pointed out by Hausdorff , of the group of rigid motions of three - dimensional Euclidean space . We close this section on measure theory with a few comments from Kac and Ulam . " Attempts to generalize the notion of ...
... structure , earlier pointed out by Hausdorff , of the group of rigid motions of three - dimensional Euclidean space . We close this section on measure theory with a few comments from Kac and Ulam . " Attempts to generalize the notion of ...
Page 80
... structure of the surface determines the appropriate measure to use . Since the surface is a manifold , by definition there is a positive integer m such that each point of S lies in a region that is geometrically the same as a piece of ...
... structure of the surface determines the appropriate measure to use . Since the surface is a manifold , by definition there is a positive integer m such that each point of S lies in a region that is geometrically the same as a piece of ...
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Popular passages
Page 299 - Talibus orabat dictis, arasque tenebat, cum sic orsa loqui vates : ' Sate sanguine divom, 125 Tros Anchisiade, facilis descensus Averno ; noctes atque dies patet atri janua Ditis ; sed revocare gradum superasque evadere ad auras, hoc opus, hie labor est.
Page 231 - But it is not always so; it may happen that small differences in the initial conditions produce very great ones in the final phenomena. A small error in the former will produce an enormous error in the latter. Prediction becomes impossible, and we have the fortuitous phenomenon.
Page 210 - The low-velocity equation of state for a lattice gas can be written as p - ^p (l - |v2), where p is the pressure, p is the density, and v is the flow speed.
Page 316 - Southeastern Conference on Combinatorics. Graph Theory, and Computing (Florida Atlantic University, Boca Raton, Florida, April 2-6, 1979), 3-18.
Page 121 - He is a member of the National Academy of Sciences and a Fellow of the American Academy of Arts and Sciences, the American Physical Society and the American Association for the Advancement of Science.
Page 231 - A very small cause which escapes our notice determines a considerable effect that we cannot fail to see, and then we say that the effect is due to chance. If we knew exactly the laws of nature and the situation of the universe at the initial moment, we could predict exactly the situation of that same universe at a succeeding moment. But even if it were the case that the natural laws...
Page 224 - Instead, we conclude by remarking that really efficient high-speed computing devices may, in the field of non-linear partial differential equations as well as in many other fields, which are now difficult or entirely denied of access, provide us with those heuristic hints which are needed in all parts of mathematics for genuine progress.
Page 272 - Let us say here that the results of our computations show features which were, from the beginning, surprising to us. Instead of a gradual, continuous flow of energy from the first mode to the higher modes, all of the problems show an entirely different behavior.
Page 58 - That was dramatized by Bertrand, who considered the problem of finding the probability that a chord of a circle chosen "at random" be longer than the side of an equilateral triangle inscribed in the circle.