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It is closely related to the Real RAM model. BSS machines are more powerful than Turing machines , because the latter are by definition restricted to a finite set of symbols. [ 2 ] A Turing machine can represent a countable set (such as the rational numbers) by strings of symbols, but this does not extend to the uncountable real numbers.
Stephen Smale (born July 15, 1930) is an American mathematician, known for his research in topology, dynamical systems and mathematical economics.He was awarded the Fields Medal in 1966 [2] and spent more than three decades on the mathematics faculty of the University of California, Berkeley (1960–1961 and 1964–1995), where he currently is Professor Emeritus, with research interests in ...
Smale's problems is a list of eighteen unsolved problems in mathematics proposed by Steve Smale in 1998 [1] and republished in 1999. [2] Smale composed this list in reply to a request from Vladimir Arnold, then vice-president of the International Mathematical Union, who asked several mathematicians to propose a list of problems for the 21st century.
The introduction of the book reprints the paper "Complexity and real computation: a manifesto", previously published by the same authors. This manifesto explains why classical discrete models of computation such as the Turing machine are inadequate for the study of numerical problems in areas such as scientific computing and computational geometry, motivating the newer model studied in the book.
In mathematics, the mean value problem was posed by Stephen Smale in 1981. [1] This problem is still open in full generality. The problem asks: For a given complex polynomial of degree [2] A and a complex number , is there a critical point of (i.e. ′ =) such that
In 2007 together with Steve Smale he proposed the so-called Cucker-Smale flocking model. This model, which has received extensive attention in mathematics and other fields, [14] plays an important role in the mathematical study of flocking dynamics. [1] [15] In 2011 together with Peter Bürgisser he contributed to the solution of Smale's 17th ...
The Smale horseshoe map f is the composition of three geometrical transformations Mixing in a real ball of colored putty after consecutive iterations of Smale horseshoe map. In the mathematics of chaos theory, a horseshoe map is any member of a class of chaotic maps of the square into itself. It is a core example in the study of dynamical systems.
The Palais-Smale condition is a condition on the functional that one is trying to extremize. In finite-dimensional spaces, the Palais–Smale condition for a continuously differentiable real-valued function is satisfied automatically for proper maps : functions which do not take unbounded sets into bounded sets.