32,123 research outputs found
A Note On Asymptotic Smoothness Of The Extensions Of Zadeh
The concept of asymptotic smooth transformation was introduced by J. Hale [10]. It is a very important property for a transformation between complete metric spaces to have a global attractor. This property has also consequences on asymptotic stability of attractors. In our work we study the conditions under which the Zadeh's extension of a continuous map f : R n → R n is asymptotically smooth in the complete metric space JF(R n) of normal fuzzy sets with the induced Hausdorff metric d ∞ (see Kloeden and Diamond [8]).212141153Barros, L.C., Bassanezi, R.C., Tonelli, P.A., On the continuity of Zadeh's extension (1997) Proceedings Seventh IFSA World Congress, 2, pp. 3-8. , PragueBarros, L.C., Bassanezi, R.C., Tonelli, P.A., Fuzzy modeling in populations dynamics (2000) Ecological Modeling, 128, pp. 27-33Brumley, W.E., On the asymptotic behavior of solutions of differential difference equations of neutral type (1970) J. of Differential Equations, 7, pp. 175-188Cabrelli, C.A., Forte, B., Molter, U., Vrscay, E., Iterated Fuzzy Sets Systems: A new approach to the inverse for fractals and other sets (1992) J. of Math. Anal, and Appl., 171, pp. 79-100Cooperman, G., (1978) α-Condensing Maps and Dissipative Processes, , Ph. D. Thesis, Brown University, Providence, R. IDiamond, P., Chaos in iterated fuzzy systems (1994) J. of Mathematical Analysis and Applications, 184, pp. 472-484Diamond, P., Time Dependent Differential Inclusions, Cocycle Attractors and Fuzzy Differential Equations (1999) IEEE Trans. on Fuzzy Systems, 7, pp. 734-740Diamond, P., Kloeden, P., (1994) Metric Spaces of Fuzzy Sets: Theory and Applications, , World Scientific PubFriedmann, M., Ma, M., Kandel, A., Numerical solutions of fuzzy differential and integral equations (1999) Fuzzy Sets and Systems, 106, pp. 35-48Hale, J.K., Asymptotic Behavior of Dissipative Systems (1988) Math. Surveys and Monographs, 25. , American Mathematical Society, ProvidenceHüllermeier, E., An Approach to Modeling and Simulation of Uncertain Dynamical Systems (1997) J. Uncertainty, Fuzziness, Know Ledge-Bases Syst., 5, pp. 117-137Kloeden, P.E., Fuzzy dynamical systems (1982) Fuzzy Sets and Systems, 7, pp. 275-296Kloeden, P.E., Chaotic iterations of fuzzy sets (1991) Fuzzy Sets and Systems, 42, pp. 37-42Nguyen, H.T., A note on thé extension principle for fuzzy sets (1978) J. Math. Anal. Appl., 64, pp. 369-380Puri, M.L., Ralescu, D.A., Fuzzy Random Variables (1986) J. of Mathematical Analysis and Applications, 114, pp. 409-422Roman-Flores, H., Barros, L.C., Bassanezzi, R., A note on Zadeh's Extensions (2001) Fuzzy Sets and Systems, 117, pp. 327-331Roman-Flores, H., On the Compactness of E(X) (1998) Appl. Math. Lett., 11, pp. 13-17Zadeh, L.A., Fuzzy sets (1965) Inform. Control, 8, pp. 338-35
The Phase Diagram of Scalar Field Theory on the Fuzzy Disc
Using a recently developed bootstrapping method, we compute the phase diagram
of scalar field theory on the fuzzy disc with quartic even potential. We find
three distinct phases with second and third order phase transitions between
them. In particular, we find that the second order phase transition happens
approximately at a fixed ratio of the two coupling constants defining the
potential. We compute this ratio analytically in the limit of large coupling
constants. Our results qualitatively agree with previously obtained numerical
results.Comment: 1+17 pages, v2: typos fixed, published versio
Relating branes and matrices
We construct a general map between a Dp-brane with magnetic flux and a matrix
configuration of D0-branes, by showing how one can rewrite the boundary state
of the Dp-brane in terms of its D0-brane constituents. This map gives a simple
prescription for constructing the matrices of fuzzy spaces corresponding to
branes of arbitrary shape and topology. Since we explicitly identify the
D0-brane degrees of freedom on the brane, we also derive the D0-brane charge of
the brane in a very direct way including the A-genus term. As a check on our
formalism, we use our map to derive the abelian-Born-Infeld equations of motion
from the action of the D0-brane matrices.Comment: 28 pages, Late
Classical dynamics on three dimensional fuzzy space: Connecting the short and long length scales
We derive the path integral action for a particle moving in three dimensional
fuzzy space. From this we extract the classical equations of motion. These
equations have rather surprising and unconventional features: They predict a
cut-off in energy, a generally spatial dependent limiting speed, orbital
precession remarkably similar to the general relativistic result, flat velocity
curves below a length scale determined by the limiting velocity and included
mass, displaced planar motion and the existence of two dynamical branches of
which only one reduces to Newtonian dynamics in the commutative limit. These
features place strong constraints on the non-commutative parameter and
coordinate algebra to avoid conflict with observation and may provide a
stringent observational test for this scenario of non-commutativity.Comment: 21 pages, 4 figure
A survey on fuzzy fractional differential and optimal control nonlocal evolution equations
We survey some representative results on fuzzy fractional differential
equations, controllability, approximate controllability, optimal control, and
optimal feedback control for several different kinds of fractional evolution
equations. Optimality and relaxation of multiple control problems, described by
nonlinear fractional differential equations with nonlocal control conditions in
Banach spaces, are considered.Comment: This is a preprint of a paper whose final and definite form is with
'Journal of Computational and Applied Mathematics', ISSN: 0377-0427.
Submitted 17-July-2017; Revised 18-Sept-2017; Accepted for publication
20-Sept-2017. arXiv admin note: text overlap with arXiv:1504.0515
Large-small dualities between periodic collapsing/expanding branes and brane funnels
We consider space and time dependent fuzzy spheres arising in
intersections in IIB string theory and collapsing D(2p)-branes in
IIA string theory.
In the case of , where the periodic space and time-dependent solutions
can be described by Jacobi elliptic functions, there is a duality of the form
to which relates the space and time dependent solutions.
This duality is related to complex multiplication properties of the Jacobi
elliptic functions. For funnels, the description of the periodic space
and time dependent solutions involves the Jacobi Inversion problem on a
hyper-elliptic Riemann surface of genus 3. Special symmetries of the Riemann
surface allow the reduction of the problem to one involving a product of genus
one surfaces. The symmetries also allow a generalisation of the to duality. Some of these considerations extend to the case of the
fuzzy .Comment: Latex, 50 pages, 2 figures ; v2 : a systematic typographical error
corrected + minor change
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