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Web Intelligence (WI)
TLDR
This paper is about a new research field called Web Intelligence (WI for short) for systematic studies on advanced Web related theories and technologies, as well as the design and implementation of Intelligent Web Information Systems (IWIS). Expand
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The Wave Equation with Computable Initial Data Whose Unique Solution Is Nowhere Computable
We give a rough statement of the main result. Let D be a compact subset of ℝ3× ℝ. The propagation u(x, y, z, t) of a wave can be noncomputable in any neighborhood of any point of D even though theExpand
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Computability theory of generalized functions
TLDR
The theory of generalized functions is the foundation of the modern theory of partial differential equations (PDE). Expand
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Computing the solution of the Korteweg-de Vries equation with arbitrary precision on Turing
In this paper we answer an open question raised by Pour-El and Richards: Is the solution operator of the Korteweg-de Vries (KdV) equation computable? The initial value problem of the KdV equationExpand
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Computing Schrödinger propagators on Type-2 Turing machines
TLDR
We study Turing computability of the solution operators of the initial-value problems for the linear Schrodinger equation of the form iu"t=-@Du+mu+|u|^2u. Expand
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A note on sharpness of the local Kato-smoothing property for dispersive wave equations
It is well known that solutions of the Cauchy problem for general dispersive equations wt + iP (D)w = 0, w(x, 0) = q(x), x ∈ R n , t ∈ R, enjoy the local smoothing property q ∈ H s(Rn) =⇒ w ∈ L ( −Expand
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Computable Analysis of a Boundary-Value Problem for the Korteweg-de Vries Equation
  • N. Zhong
  • Mathematics, Computer Science
  • Theory of Computing Systems
  • 1 July 2007
TLDR
We show that the initial-boundary-value problem for the KdV equation is Turing computable for any integer m ≥ 2 and computable real number T > 0. Expand
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Computability and Computational Complexity of the Evolution of Nonlinear Dynamical Systems
Nonlinear dynamical systems abound as models of natural phenomena. They are often characterized by highly unpredictable behaviour which is hard to analyze as it occurs, for example, in chaoticExpand
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An analytic System with a Computable Hyperbolic Sink Whose Basin of Attraction is Non-Computable
  • D. Graça, N. Zhong
  • Mathematics, Computer Science
  • Theory of Computing Systems
  • 3 September 2014
TLDR
In many applications one is interested in finding the stability regions (basins of attraction) of some stationary states (attractors). Expand
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