Decompositions of spaces of measures

Let M be the Banach space of sigma-additive complex-valued measures on an abstract measurable space. We prove that any closed, with respect to absolute continuity norm-closed, linear subspace L of M is complemented and describe the unique complement, projection onto L along which has norm 1. Using this fact we prove a decomposition theorem, which includes the Jordan decomposition theorem, the generalized Radon-Nikodym theorem and the decomposition of measures into decaying and non-decaying components as particular cases. We also prove an analog of the Jessen-Wintner purity theorem for our decompositions.

Continuity - based and discontinuity - based segmentation in transparent and spatially segregated global motion

The mechanisms underlying the parsing of a spatial distribution of velocity vectors into two adjacent (spatially segregated) or overlapping (transparent) motion surfaces were examined using random dot kinematograms. Parsing might occur using either of two principles. Surfaces might be defined on the basis of similarity of motion vectors and then sharp perceptual boundaries drawn between different surfaces (continuity-based segmentation). Alternatively, detection of a high gradient of direction or speed separating the motion surfaces might drive the process (discontinuity-based segmentation). To establish which method is used, we examined the effect of blurring the motion direction gradient. In the case of a sharp direction gradient, each dot had one of two directions differing by 135°. With a shallow gradient, most dots had one of two directions but the directions of the remainder spanned the range between one motion-defined surface and the other. In the spatial segregation case the gradient defined a central boundary separating two regions. In the transparent version the dots were randomly positioned. In both cases all dots moved with the same speed and existed for only two frames before being randomly replaced. The ability of observers to parse the motion distribution was measured in terms of their ability to discriminate the direction of one of the two surfaces. Performance was hardly affected by spreading the gradient over at least 25% of the dots (corresponding to a 1° strip in the segregation case). We conclude that detection of sharp velocity gradients is not necessary for distinguishing different motion surfaces.

On subspace lattices II. Continuity of Lat

We study the continuity of the map Lat sending an ultraweakly closed operator algebra to its invariant subspace lattice. We provide an example showing that Lat is in general discontinuous and give sufficient conditions for the restricted continuity of this map. As consequences we obtain that Lat is continuous on the classes of von Neumann and Arveson algebras and give a general approximative criterion for reflexivity, which extends Arvesonâ??s theorem on the reflexivity of commutative subspace lattices.

Absolute single and multiple charge exchange cross sections for highly charged C, O, and Ne ions on H2O, CO, and CO2

Reported herein are measured absolute single, double, and triple charge exchange (CE) cross sections for the highly charged ions (HCIs) Cq+ (q=5,6), Oq+ (q=6,7,8), and Neq+ (q=7,8) colliding with the molecular species H2O, CO, and CO2. Present data can be applied to interpreting observations of x-ray emissions from comets as they interact with the solar wind. As such, the ion impact energies of 7.0q keV (1.62–3.06 keV/amu) are representative of the fast solar wind, and data at 1.5q keV for O6+ (0.56 keV/amu) on CO and CO2 and 3.5q keV for O5+ (1.09 keV/amu) on CO provide checks of the energy dependence of the cross sections at intermediate and typical slow solar wind velocities. The HCIs are generated within a 14 GHz electron cyclotron resonance ion source. Absolute CE measurements are made using a retarding potential energy analyzer, with measurement of the target gas cell pressure and incident and final ion currents. Trends in the cross sections are discussed in light of the classical overbarrier model (OBM), extended OBM, and with recent results of the classical trajectory Monte Carlo theory.

Gateaux complex differentiability and continuity

As is known, there are everywhere discontinuous infinitely Frechet differentiable functions on the real locally convex spaces D(R) and V(R) of finitely supported infinitely differentiable functions and, respectively, of generalized functions. In this paper the relationship between the complex differentiability and continuity of a function on a complex locally convex space is considered. We describe a class of complex locally convex spaces, which includes the complex space V(R), such that every Gateaux complex-differentiable function on a space of this class is continuous. We also describe another class of locally convex spaces, which includes the complex space D(R), such that on every space of this class there is an everywhere discontinuous infinitely Frechet complex-differentiable function whose derivatives are continuous.

Determination of absolute configuration of conformationally flexible cis-dihydrodiol metabolites: Effect of diene substitution pattern on the circular dichroism spectra and optical rotations

Absolute configurations of a number of cis-dihydrodiols (cis-1,2-dihydroxy-3,5-cyclohexadienes), synthetically useful products of TDO-catalyzed dihydroxylations of 1,2- and 1,3-disubstituted benzene derivatives, have been determined by a comparison of calculated and experimental CD spectra and optical rotations and by methods involving X-ray crystallography, H-1 NMR spectra of diastereoisomeric derivatives, and by stereochemical correlations. The computations disclosed a significant effect of the substituents on conformational equilibria of cis-dihydrodiols and chiroptical properties of individual conformers. The assigned absolute configurations of cis-dihydrodiols have allowed the validity of a simple predictive model for TDO-catalyzed arene dihydroxylations to be extended.