Self-similar structures and fractal transforms in approximation theory

Yukalov, V. I.; Yukalova, E. P.

doi:10.1016/s0960-0779(02)00029-2

Cited by 55 publications

(114 citation statements)

References 80 publications

(156 reference statements)

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“…For this, we use the self-similar approximation theory [63][64][65][66][67][68][69]. The idea is to start from an expansion of the discount rate valid for short time, that is believed to be generally valid.…”

Section: First-principle Construction Of Discount Ratementioning

confidence: 99%

Physics of risk and uncertainty in quantum decision making

2009

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The Quantum Decision Theory, developed recently by the authors, is applied to clarify the role of risk and uncertainty in decision making and in particular in relation to the phenomenon of dynamic inconsistency. By formulating this notion in precise mathematical terms, we distinguish three types of inconsistency: time inconsistency, planning paradox, and inconsistency occurring in some discounting effects. While time inconsistency is well accounted for in classical decision theory, the planning paradox is in contradiction with classical utility theory. It finds a natural explanation in the frame of the Quantum Decision Theory. Different types of discounting effects are analyzed and shown to enjoy a straightforward explanation within the suggested theory. We also introduce a general methodology based on self-similar approximation theory for deriving the evolution equations for the probabilities of future prospects. This provides a novel classification of possible discount factors, which include the previously known cases (exponential or hyperbolic discounting), but also predicts a novel class of discount factors that decay to a strictly positive constant for very large future time horizons. This class may be useful to deal with very long-term discounting situations associated with intergenerational public policy choices, encompassing issues such as global warming and nuclear waste disposal.

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Section: First-principle Construction Of Discount Ratementioning

confidence: 99%

Physics of risk and uncertainty in quantum decision making

2009

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“…This approach is nowadays widely used in various applications (see survey in Yukalov and Yukalova, 2002).…”

Section: Appendixmentioning

confidence: 99%

Self-similar law of energy release before materials fracture

Yukalov

Moura

Nechad

2004

Journal of the Mechanics and Physics of Solids

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A general law of energy release is derived for stressed heterogeneous materials, being valid from the starting moment of loading till the moment of materials fracture. This law is obtained by employing the extrapolation technique of the self-similar approximation theory. Experiments are accomplished measuring the energy release for industrial composite samples. The derived analytical law is confronted with these experimental data as well as with the known experimental data for other materials.

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“…Using the analytical expression (18) with the values of 7 Li Condensate [18][19] and considering the ground state, with n = m = l = 0, p = l = 1 and I 000 = 0.063494,we can obtain N c in Figure 1.…”

Section: Resultsmentioning

confidence: 99%

“…interpolating the asymptotic limits (15) and (16) by means of the self-similar root approximants [17][18], that results in the following approximants crossover roots function…”

Section: Modelmentioning

confidence: 99%

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An analytical solution for the critical number of particles for stable bose-einstein condensation under the influence of an anisotropic potential

Sousa¹,

Bagnato²,

Silva³

2008

Braz. J. Phys.

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We have considered a Bose gas in an anisotropic potential. Applying the the Gross-Pitaevskii Equation (GPE) for a confined dilute atomic gas, we have used the methods of optimized perturbation theory and self-similar root approximants, to obtain an analytical formula for the critical number of particles as a function of the anisotropy parameter for the potential. The spectrum of the GPE is also discussed.

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Self-similar structures and fractal transforms in approximation theory

Cited by 55 publications

References 80 publications

Physics of risk and uncertainty in quantum decision making

Physics of risk and uncertainty in quantum decision making

Self-similar law of energy release before materials fracture

An analytical solution for the critical number of particles for stable bose-einstein condensation under the influence of an anisotropic potential

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