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A Short Note on Emergence of Computational Robot Consciousness
Jozef Kelemen
Acta Polytechnica Hungarica , 2008,
Abstract: A way is sketched how to answer the question about the computational powersupposed behind the consciousness, esp. the computational robot consciousness. It isillustrated that a formal model of the possible functional architecture of certain type ofrobot enables to satisfy the test of emergence proposed earlier.
A note on the fractional logistic equation  [PDF]
I. Area,J. Losada,J. J. Nieto
Mathematics , 2015,
Abstract: In this short note, we show that the real function recently proposed by Bruce J. West [Exact solution to fractional logistic equation, Physica A 429 (2015) 103--108] is not an exact solution for the fractional logistic equation.
Fractional stochastic active scalar equations generalizing the multi-D-Quasi-Geostrophic & 2D-Navier-Stokes equations. -Short note-  [PDF]
Latifa Debbi
Mathematics , 2012,
Abstract: We prove the well posedness: global existence, uniqueness and regularity of the solutions, of a class of d-dimensional fractional stochastic active scalar equations. This class includes the stochastic, dD-quasi-geostrophic equation, $ d\geq 1$, fractional Burgers equation on the circle, fractional nonlocal transport equation and the 2D-fractional vorticity Navier-Stokes equation. We consider the multiplicative noise with locally Lipschitz diffusion term in both, the free and no free divergence modes. The random noise is given by an $Q-$Wiener process with the covariance $Q$ being either of finite or infinite trace. In particular, we prove the existence and uniqueness of a global mild solution for the free divergence mode in the subcritical regime ($\alpha>\alpha_0(d)\geq 1$), martingale solutions in the general regime ($\alpha\in (0, 2)$) and free divergence mode, and a local mild solution for the general mode and subcritical regime. Different kinds of regularity are also established for these solutions. The method used here is also valid for other equations like fractional stochastic velocity Navier-Stokes equations (work is in progress). The full paper will be published in Arxiv after a sufficient progress for these equations.
A short note on short pants  [PDF]
Hugo Parlier
Mathematics , 2013,
Abstract: It is a theorem of Bers that any closed hyperbolic surface admits a pants decomposition consisting of curves of bounded length where the bound only depends on the topology of the surface. The question of the quantification of the optimal constants has been well studied and the best upper bounds to date are linear in genus, a theorem of Buser and Sepp\"al\"a. The goal of this note is to give a short proof of an linear upper bound which slightly improves the best known bounds.
Variational principle for fractional kinetics and the Lévy Ansatz  [PDF]
Sumiyoshi Abe
Physics , 2013, DOI: 10.1103/PhysRevE.88.022142
Abstract: A variational principle is developed for fractional kinetics based on the auxiliary-field formalism. It is applied to the Fokker-Planck equation with spatio-temporal fractionality, and a variational solution is obtained with the help of the L\'evy Ansatz. It is shown how the whole range from subdiffusion to superdiffusion is realized by the variational solution, as a competing effect between the long waiting time and the long jump. The motion of the center of the probability distribution is also analyzed in the case of a periodic drift.
Distributed-Order Fractional Kinetics  [PDF]
I. M. Sokolov,A. V. Chechkin,J. Klafter
Physics , 2004,
Abstract: Fractional diffusion equations are widely used to describe anomalous diffusion processes where the characteristic displacement scales as a power of time. For processes lacking such scaling the corresponding description may be given by distributed-order equations. In the present paper we consider different forms of distributed-order fractional kinetic equations and investigate the effects described by different classes of such equations. In particular, the equations describing accelerating and decelerating subdiffusion, as well as the those describing accelerating and decelerating superdiffusion are presented.
A short introduction to local fractional complex analysis  [PDF]
Xiao-Jun Yang
Mathematics , 2011,
Abstract: This paper presents a short introduction to local fractional complex analysis. The generalized local fractional complex integral formulas, Yang-Taylor series and local fractional Laurent's series of complex functions in complex fractal space, and generalized residue theorems are investigated.
Ergodicity breaking in random media and the foundation of fractional kinetics  [PDF]
Gianni Pagnini,Daniel Molina-García,Tuan Minh Pham,Carlo Manzo,Paolo Paradisi
Physics , 2015,
Abstract: We show that when diffusion takes place in a medium characterized by a random quantity depending on a parameter $\beta$, e.g. the lengthscale $\ell_\beta$, then all ergodic processes realized in such random medium display Ergodicity Breaking (EB) for any distribution of $\ell_\beta$ verifying the inequality $\langle \ell_\beta^4 \rangle \ne \langle \ell_\beta^2 \rangle^2$. Exploiting the result above, we investigate the connections of EB with fractional kinetics by considering the important case of a Gaussian process with long-range correlation, i.e. the fractional Brownian motion (fBm), in a complex medium, where the statistical distribution of $\ell_\beta$ is a one-side M-Wright/Mainardi density function with $0 < \beta < 1$. In this alternative framework we find that the analysis of the EB leads to the same result obtained for a Continuos Time Random Walk (CTRW) with a power-law distribution of waiting times, whereas the calculation of the p-variation test differs from the CTRW and shows the same behaviour of the fBm. Moreover, when non-stationarity is considered, i.e. $\ell_\beta=\ell_\beta(t)$, also ageing occurs. Due to the coexistence of aging with characteristic features of fBm and CTRW, the proposed approach is a promising modeling framework to describe the nonergodic behaviour observed in some biological systems. Further, the same parameter $\beta$, governing the randomness of $\ell_\beta$ and driving the transition ergodic/nonergodic also controls the transition classical/fractional kinetics. In summary, the derivation of fractional kinetics from a complex medium is in agreement with EB, similarly to what happens in the CTRW picture, but it also preserves the p-variation outcome of fBm, which is a feature qualitatively similar to that found in experimental biological data.
A note on linear fractional set packing problem  [PDF]
Pooja Pandey
Computer Science , 2015,
Abstract: In this note we point out various errors in the paper by Rashmi Gupta and R. R. Saxena, Set packing problem with linear fractional objective function, International Journal of Mathematics and Computer Applications Research (IJMCAR), 4 (2014) 9 - 18. We also provide some additional results.
A Note on Fractional Evolutionary Equations  [PDF]
Rainer Picard
Mathematics , 2013,
Abstract: A class of linear evolutionary equations with material laws involving fractional time-derivatives is considered. The main result is well-posedness and causality for this problem class. The approach is illustrated with two examples: a fractional Fokker-Planck type equation and a class of visco-elastic materials described via fractional derivatives. In conclusion the possibility of imposing initial conditions is discussed.
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