43,193 research outputs found
Applications of Hilbert Module Approach to Multivariable Operator Theory
A commuting -tuple of bounded linear operators on a
Hilbert space \clh associate a Hilbert module over
in the following sense: where and
. A companion survey provides an introduction to the theory
of Hilbert modules and some (Hilbert) module point of view to multivariable
operator theory. The purpose of this survey is to emphasize algebraic and
geometric aspects of Hilbert module approach to operator theory and to survey
several applications of the theory of Hilbert modules in multivariable operator
theory. The topics which are studied include: generalized canonical models and
Cowen-Douglas class, dilations and factorization of reproducing kernel Hilbert
spaces, a class of simple submodules and quotient modules of the Hardy modules
over polydisc, commutant lifting theorem, similarity and free Hilbert modules,
left invertible multipliers, inner resolutions, essentially normal Hilbert
modules, localizations of free resolutions and rigidity phenomenon.
This article is a companion paper to "An Introduction to Hilbert Module
Approach to Multivariable Operator Theory".Comment: 46 pages. This is a companion paper to arXiv:1308.6103. To appear in
Handbook of Operator Theory, Springe
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The pupillary response of cephalopods
This paper provides the first detailed description of the time courses of light-evoked pupillary constriction for two species of cephalopods, Sepia officinalis (a cuttlefish) and Eledone cirrhosa (an octopus). The responses are much faster than hitherto reported, full contraction in Sepia taking less than 1 s, indicating it is among the most rapid pupillary responses in the animal kingdom. We also describe the dependence of the degree of pupil constriction on the level of ambient illumination and show considerable variability between animals. Furthermore, both Sepia and Eledone lack a consensual light-evoked pupil response. Pupil dilation following darkness in Sepia is shown to be very variable, often occurring within a second but at other times taking considerably longer. This may be the result of extensive light-independent variations in pupil diameter in low levels of illumination
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The eyes of suckermouth armoured catfish (Loricariidae, subfamily Hypostomus): pupil response, lenticular longitudinal spherical aberration and retinal topography
The dilated, round pupils of a species of suckermouth armoured catfish (Liposarcus pardalis) constrict slowly on illumination (over 35-40 min) to form crescent-shaped apertures. Ray tracing of He-Ne laser beams shows that the lenses of a related species (Pterygoplichthys etentaculus), which also has a crescent-shaped pupil, are well corrected for longitudinal spherical aberration, suggesting that the primary purpose of the irregular pupil in armoured catfish is not to correct such aberration. It is suggested that the iris operculum may serve to camouflage the pupil of these substrate-dwelling species. An examination of the catfish retina shows the photoreceptors to be exclusively single cones interspersed with elongate rods and demonstrates the presence of multiple optic nerve head papillae. Two areas of high ganglion cell density, each side of a vertically oriented falciform process, provide increased spatial resolving power along the axes examining the substrate in front of and behind the animal
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