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Page 15
... motion problems , hydro- dynamics , behavior of radiation ... Compared to quantum theory the project work was like applied mathematics as compared with abstract mathe- matics . [ Edward ] Teller , in whose group I was sup- posed to work ...
... motion problems , hydro- dynamics , behavior of radiation ... Compared to quantum theory the project work was like applied mathematics as compared with abstract mathe- matics . [ Edward ] Teller , in whose group I was sup- posed to work ...
Page 19
... motions , had ex- pected . The original objective had been to see at what rate the energy of the string , initially put into a single sine wave ( the note was struck as one tone ) , would gradually develop higher tones with the ...
... motions , had ex- pected . The original objective had been to see at what rate the energy of the string , initially put into a single sine wave ( the note was struck as one tone ) , would gradually develop higher tones with the ...
Page 20
... motions of such stars . Edward Lasker ( International Chess Master ) and Stan , late sixties While such astrophysical calculations were going on , I began in an amateurish way to work on some questions of biology . After reading about ...
... motions of such stars . Edward Lasker ( International Chess Master ) and Stan , late sixties While such astrophysical calculations were going on , I began in an amateurish way to work on some questions of biology . After reading about ...
Page 53
... motions of such a system . ) At present researchers are trying to formulate limit- ing laws governing the long - term dynam- ics of nonlinear systems that are analo- gous to the major limiting theorems in classical probability theory ...
... motions of such a system . ) At present researchers are trying to formulate limit- ing laws governing the long - term dynam- ics of nonlinear systems that are analo- gous to the major limiting theorems in classical probability theory ...
Page 63
... motion maps one onto the other ) , their measures are equal . When dealing with sets of points on a line , in a plane , or in space , one chooses E to be an interval , a square , and a cube , respectively . These choices are dictated by ...
... motion maps one onto the other ) , their measures are equal . When dealing with sets of points on a line , in a plane , or in space , one chooses E to be an interval , a square , and a cube , respectively . These choices are dictated by ...
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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.