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The Generalized Weierstrass Approximation Theorem
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This article is published in Mathematics Magazine.The article was published on 1948-04-01. It has received 537 citations till now. The article focuses on the topics: Weierstrass functions & Weierstrass factorization theorem.read more
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The non-linear field theories of mechanics
TL;DR: A theory aiming to describe their mechanical behavior must take heed of their deformability and represent the definite principles it obeys as mentioned in this paper, which is not the case in modern physics, since it concerns solely the small particles of matter.
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Networks and the Best Approximation Property
Federico Girosi,Tomaso Poggio +1 more
TL;DR: The main result of this paper is that multilayer perceptron networks, of the type used in backpropagation, do not have the best approximation property and it is proved that networks derived from regularization theory and including Radial Basis Functions, have a similar property.
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Adaptive cooperative tracking control of higher-order nonlinear systems with unknown dynamics
Hongwei Zhang,Frank L. Lewis +1 more
TL;DR: A practical design method is developed for cooperative tracking control of higher-order nonlinear systems with a dynamic leader using a robust adaptive neural network controller for each follower node such that all follower nodes ultimately synchronize to the leader node with bounded residual errors.
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The elements of real analysis (2nd edition), by Robert G. Bartle. Pp xv, 480. £10. 1976. SBM 0 471 05464 X (Wiley)
TL;DR: A Glimpse at Set Theory: The Topology of Cartesian Spaces and the Functions of One Variable.
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Brief paper: Distributed adaptive control for synchronization of unknown nonlinear networked systems
Abhijit Das,Frank L. Lewis +1 more
TL;DR: A Lyapunov technique is presented for designing a robust adaptive synchronization control protocol for distributed systems having non-identical unknown nonlinear dynamics, and for a target dynamics to be tracked that is also nonlinear and unknown.