7,016 research outputs found
Almost periodic evolution systems with impulse action at state-dependent moments
We study the existence of almost periodic solutions for semi-linear abstract
parabolic evolution equations with impulse action at state-dependent moments.
In particular, we present conditions excluding the beating phenomenon in these
systems. The main result is illustrated with an example of impulsive diffusive
logistic equation.Comment: 16 pages, minor changes from the previous versio
Almost Automorphic Solutions of Delayed Neutral Dynamic Systems on Hybrid Domains
We study the existence of almost automorphic solutions of the delayed neutral dynamic system on hybrid domains that are additively periodic. We use exponential dichotomy and prove uniqueness of projector of exponential dichotomy to obtain some limit results leading to sufficient conditions for existence of almost automorphic solutions to neutral system. Unlike the existing literature we prove our existence results without assuming boundedness of the coefficient matrices in the system. Hence, we significantly improve the results in the existing literature. Finally, we also provide an existence result for an almost periodic solutions of the system
Large Scale Inhomogeneity Versus Source Evolution -- Can We Distinguish Them Observationally?
We reconsider the issue of proving large scale spatial homogeneity of the
universe, given isotropic observations about us and the possibility of source
evolution both in numbers and luminosities. Two theorems make precise the
freedom available in constructing cosmological models that will fit the
observations. They make quite clear that homogeneity cannot be proven without
either a fully determinate theory of source evolution, or availability of
distance measures that are independent of source evolution. We contrast this
goal with the standard approach that assumes spatial homogeneity a priori, and
determines source evolution functions on the basis of this assumption.Comment: mn style, mn.sty file included, mn.sty file remove
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