Self-similar factor approximants.

@article{Gluzman2003SelfsimilarFA,
  title={Self-similar factor approximants.},
  author={Simon Gluzman and Vyacheslav I. Yukalov and Didier Sornette},
  journal={Physical review. E, Statistical, nonlinear, and soft matter physics},
  year={2003},
  volume={67 2 Pt 2},
  pages={
          026109
        }
}
  • S. Gluzman, V. Yukalov, D. Sornette
  • Published 26 August 2002
  • Mathematics, Computer Science
  • Physical review. E, Statistical, nonlinear, and soft matter physics
The problem of reconstructing functions from their asymptotic expansions in powers of a small variable is addressed by deriving an improved type of approximants. The derivation is based on the self-similar approximation theory, which presents the passage from one approximant to another as the motion realized by a dynamical system with the property of group self-similarity. The derived approximants, because of their form, are called self-similar factor approximants. These complement the obtained… 
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References

SHOWING 1-10 OF 71 REFERENCES
Quantum Field Theory and Critical Phenomena
Algebraic preliminaries Euclidean path integrals in quantum mechanics Path integrals in quantum mechanics - generalizations stochastic differential equations - Langevin, Fokker-Planck equations
Algorithmic Information Theory
This paper reviews algorithmic information theory, which is an attempt to apply information-theoretic and probabilistic ideas to recursive function theory. Typical concerns in this approach are, for
Fractal Geometry of Nature
TLDR
This book is a blend of erudition, popularization, and exposition, and the illustrations include many superb examples of computer graphics that are works of art in their own right.
Ann
Aaron Beck’s cognitive therapy model has been used repeatedly to treat depression and anxiety. The case presented here is a 34-year-old female law student with an adjustment disorder with mixed
Phys
  • 80, 5839
  • 1984
Physica 22
  • 932
  • 1956
Phys
  • Rev. E in press
  • 2002
Phys. Rev. E in press
  • Phys. Rev. E in press
  • 2002
Slider-Block Friction Model for Landslides : Implication for Prediction of Mountain Collapse
Accelerating displacements preceding some catastrophic landslides has been found empirically to follow a time-to-failure power law, corresponding to a finite-time singularity of the velocity v ∼
Laser Phys
  • 11, 659
  • 2001
...
1
2
3
4
5
...