We prove that if X is an infinite dimensional Banach lattice with a weak unit then there exists a probability space (Ω,Σ,/i) so that the unit sphere of (Li(Ω,Σ,/i)) is uniformly homeomorphic to the unit sphere S(X) if and only if X does not contain Z^'s uniformly.
Background: In this paper, the impact of the dispersion effect, due to atmospheric pressure and temperature, on NRZ-OOK terrestrial free-space optical transmission system is investigated. An expression for the dispersion parameter in FSO atmospheric channel is derived. Results: The results show that the variation of the refractive index along the transmission path induces fluctuations of group velocity dispersion of the optical pulse resulting in broadening of the pulse duration. Simulation results show that at a propagation distance of 7.5 km, the broadening ratio for input pulse duration of 300 fs is approximately 2.39. Further, at a propagation distance of 7.5 km, the remaining fraction of energy is approximately 40 % for a 300 fs input pulse duration. However, by increasing the transmitter input power, the effect of dispersion could be reduced. Namely, for a reference BER of 10 -9 , the maximum distance that it could be achieved is about 1. 461 km for an input power of 1 mW, while it is about 2.694 km for an input power of 4 mW.
Conclusions:The results indicate that the effect of dispersion resulting from pressure and temperature increases with the propagation distance, which induces a high BER. However, the results show that it is possible to reach longer propagation distances with a lower BER by increasing the input power.
It is proved that every function of finite Baire index on a separable metric space K is a D-function, i.e., a difference of bounded semi-continuous functions on K. In fact it is a strong D-function, meaning it can be approximated arbitrarily closely in D-norm, by simple D-functions. It is shown that if the n th derived set of K is non-empty for all finite n, there exist D-functions on K which are not strong D-functions. Further structural results for the classes of finite index functions and strong D-functions are also given.
We show that any separable stable Banach space can be represented as a group of isometries on a separable reflexive Banach space, which extends a result of S. Guerre and M. Levy. As a consequence, we can then represent homeomorphically its space of types.
Abstract. Extrinsic and intrinsic characterizations are given for the class DSC(K) of differences of semi-continuous functions on a Polish space K, and also decomposition characterizations of DSC(K) and the class PS(K) of pointwise stabilizing functions on K are obtained in terms of behavior restricted to ambiguous sets. The main, extrinsic characterization is given in terms of behavior restricted to some subsets of second category in any closed subset of K. The concept of a strong continuity point is introduced, using the transfinite oscillations oscα f of a function f previously defined by the second named author. The main intrinsic characterization yields the following DSC analogue of Baire's characterization of first Baire class functions: a function belongs to DSC(K) iff its restriction to any closed non-empty set L has a strong continuity point. The characterizations yield as a corollary that a locally uniformly converging series ϕ j of DSC functions on K converges to a DSC function provided oscα ϕ j converges locally uniformly for all countable ordinals α.
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