2,010 research outputs found
Almost automorphic delayed differential equations and Lasota-Wazewska model
Existence of almost automorphic solutions for abstract delayed differential
equations is established. Using ergodicity, exponential dichotomy and Bi-almost
automorphicity on the homogeneous part, sufficient conditions for the existence
and uniqueness of almost automorphic solutions are given.Comment: 16 page
Fuzzy Solutions to Second Order Three Point Boundary Value Problem
In this manuscript, the proposed work is to study the existence of second-order differential equations with three point boundary conditions. Existence is proved using fuzzy set valued mappings of a real variable whose values are normal, convex, upper semi continuous and compactly supported fuzzy sets. The sufficient conditions are also provided to establish the existence results of fuzzy solutions of second order differential equations for three point boundary value problem. By using Banach fixed point principle, a new existence theorem of solutions for these equations in the metric space of normal fuzzy convex sets with distance given by the maximum of the Hausdorff distance between level sets is obtained. Then to further establish the existence, fixed point theorem for absolute retracts is used by taking consideration that space of fuzzy sets can be embedded isometrically as a cone in Banach space. Finally, an example is provided to illustrate the result
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
Decoherence and wave function collapse
The possibility of consistency between the basic quantum principles of
quantum mechanics and wave function collapse is reexamined. A specific
interpretation of environment is proposed for this aim and applied to
decoherence. When the organization of a measuring apparatus is taken into
account, this approach leads also to an interpretation of wave function
collapse, which would result in principle from the same interactions with
environment as decoherence. This proposal is shown consistent with the
non-separable character of quantum mechanics
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