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1.
Ronald E Bruck 《Journal of Mathematical Analysis and Applications》1980,76(1):159-173
We show that if u is a bounded solution on + of u″(t) ?Au(t) + f(t), where A is a maximal monotone operator on a real Hilbert space H and f∈Lloc2(+;H) is periodic, then there exists a periodic solution ω of the differential equation such that u(t) ? ω(t) 0 and u′(t) ? ω′(t) → 0 as t → ∞. We also show that the two-point boundary value problem for this equation has a unique solution for boundary values in and that a smoothing effect takes place. 相似文献
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Ronald E. Bruck 《Israel Journal of Mathematics》1978,29(1):1-16
LetT be a nonexpansive self-mapping of a closed convex subsetC of a real Hilbert space. In this paper we deal with the structure of the weak ω-limit set of iterates {T
nx}, establish conditions under which it is invariant underT, and show that {T
nx} converges weakly iffT has a fixed-point andT
nx-Tn+1x→0 weakly.
Dedicated to the memory of my father
Supported by NSF Grant MCS 76-08217. 相似文献
4.
For a sequence (cn) of complex numbers, the quadratic polynomialsfcn(z) := z2 + cn and the sequence (Fn) of iterates Fn := fcn...fc1areconsidered. The Fatou set F(cn) is by definition the set ofall z C^ such that (Fn) is normal in some neighbourhood ofz, while the complement of F(cn) is called the Julia set J(cn).The aim of this article is to study the connectedness and stabilityof the Julia set J(cn) provided that the sequence (cn) is bounded. 相似文献
5.
Short duration stress pulses are of particular interest in determining the interfacial crack tip instability criteria for
the dynamic fracture behavior of laminated carbon-fiber/epoxy composites. However, the heterogeneous architectures of laminated
composites can alter the characteristics of a stress pulse as it propagates toward a crack tip. This makes it difficult to
use standard dynamic testing techniques for characterizing these materials, since these techniques assume the characteristics
of the stress pulse do not change as a result of propagation and can therefore be unambiguously determined from impact conditions.
This paper presents a novel experimental technique that has been developed for characterizing short duration stress pulse
propagation in laminated composite materials. In this technique, a dynamic moiré interferometer is used to capture fringe
patterns corresponding to displacement fields associated with short duration stress pulses that were generated by impacting
0° and 90°/0°/90° carbon-fiber/epoxy composites with a magnetic flyer plate. Appropriate dynamic testing conditions for capturing
high fidelity fringe patterns were determined using the recently developed dynamic moiré fringe contrast factor. The effects
of the composite architecture on the propagation of short duration stress pulses observed with the dynamic moiré interferometer
were confirmed by transient dynamic finite element analysis. From comparisons of experimental and numerical data, it was determined
that the impact conditions for the magnetic flyer plate and laminated composite will not necessarily be planar, which has
a significant effect on the intensity and duration of the propagating stress pulse. 相似文献
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7.
The mass spectra of 4-(ω-hydroxyalkylamino)-phthalazinone derivatives (I to IV) have been studied. The most important primary fragmentation process is the fission of the alkyl chain β to the amino group, combined with an intramolecular cyclisation reaction. This process results an ion of tricyclic structure, possessing a 4-membered ring, as was established by partial 15N labelling. 相似文献
8.
R. H. Bruck 《Archiv der Mathematik》1959,10(1):419-421
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