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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.
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.
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
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 ...
Here is a variant of this construction isolated by Stephen Smale as an example of an expanding attractor in the theory of smooth dynamical systems. Denote the angular coordinate on the circle S 1 by t (it is defined mod 2π) and consider the complex coordinate z on the two-dimensional unit disk D .
It argues that human motivation is largely intrinsic and that the aspects of this motivation can be divided into autonomy, mastery, and purpose. [1] He argues against old models of motivation driven by rewards and fear of punishment, dominated by extrinsic factors such as money. [2] [3]
Initially, the 3C-model was published as the "compensatory model of work motivation and volition". [9] The original title referred to one of the central assumptions of the model, namely that volition compensates for insufficient motivation. Because of the potential confusion with "worker compensation", however, the name was changed to "3C-model."
The first example was exhibited through the efforts of several mathematicians, including Arnold S. Shapiro and Bernard Morin, who was blind. On the other hand, it is much easier to prove that such a "turning" exists, and that is what Smale did. Smale's graduate adviser Raoul Bott at first told Smale that the result was obviously wrong .