Splitting of liftings in products of probability spaces

We prove that if (X,\mathfrakA,P) is an arbitrary probability space with countably generated \sigma-algebra \mathfrakA, (Y,\mathfrakB,Q) is an arbitrary complete probability space with a lifting \rho and \hat R is a complete probability measure on \mathfrakA \hat \otimes_R \mathfrakB determined by a regular conditional probability {S_y:y\in Y} on \mathfrakA with respect to \mathfrakB, then there exist a lifting \pi on (X\times Y,\mathfrakA \hat \otimes_R \mathfrakB,\hat R) and liftings \sigma_y on (X,\hat \mathfrakA_y,\hat S_y), y\in Y, such that, for every E\in\mathfrakA \hat \otimes_R \mathfrakB and every y\in Y, [\pi(E)]^y=\sigma_y\bigl([\pi(E)]^y\bigr). Assuming the absolute continuity of R with respect to P\otimes Q, we prove the existence of a regular conditional probability {T_y:y\in Y} and liftings \varpi on (X\times Y,\mathfrakA \hat \otimes_R \mathfrakB,\hat R), \rho' on (Y,\mathfrakB,\hat Q) and \sigma_y on (X,\hat \mathfrakA_y,\hat S_y), y\in Y, such that, for every E\in\mathfrakA \hat \otimes_R \mathfrakB and every y\in Y, [\varpi(E)]^y=\sigma_y\bigl([\varpi(E)]^y\bigr) and \varpi(A\times B)=\bigcup_{y\in\rho'(B)}\sigma_y(A)\times{y}\qquadif A\times B\in\mathfrakA\times\mathfrakB. Both results are generalizations of Musia\l, Strauss and Macheras [Fund. Math. 166 (2000) 281-303] to the case of measures which are not necessarily products of marginal measures. We prove also that liftings obtained in this paper always convert \hat R-measurable stochastic processes into their \hat R-measurable modifications.Comment: Published at http://dx.doi.org/10.1214/009117904000000018 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org

Fluorescein angiography compared to three-dimensional measurements by the retinal thickness analyzer in classic choroidal neovascularization

Purpose: To compare and correlate imaging of classic subfoveal choroidal neovascularization (CNV) with noninvasive 3-dimensional imaging by the retinal thickness analyzer (RTA) to conventional fluorescein angiography (FA). Methods: A total of 29 eyes of 29 consecutive patients with predominantly classic CNV eligible for photodynamic therapy underwent FA and RTA imaging. The FA dimensions of the CNV were measured independently by two graders. With the RTA, masked to FA the size of the CNV itself as imaged in 3-dimensional reconstruction, the size of significantly thickened retina overlying the CNV and the maximum retinal thickness were measured. Results: The mean diameter of the CNV determined from 3-dimensional RTA reconstructions showed an excellent correlation with measurements from FA (r = 0.91, p < 0.001). The area of retinal thickening was by a mean of 0.7 mm in diameter larger and correlated moderately well with the size of the CNV on FA (r = 0.65, p < 0.001). In contrast, there was no correlation between the absolute retinal thickness and the CNV size on FA. Conclusions: Noninvasive quantitative mapping of predominantly classic CNV by RTA is feasible and also allows 3-dimensional measurement of the lesion itself. The results correlate well with FA assessment but visualize different properties of the disease. Copyright (c) 2007 S. Karger AG, Basel

Very Long Baseline Array Imaging of Type-2 Seyferts with Double-Peaked Narrow Emission Lines: Searches for Sub-kpc Dual AGNs and Jet-Powered Outflows

This paper presents Very Long Baseline Array (VLBA) observations of 13 double-peaked [O III] emission-line type-2 Active Galactic Nuclei (AGNs) at redshifts 0.06 < z < 0.41 (with a median redshift of z~0.15) identified in the Sloan Digital Sky Survey. Such double-peaked emission-line objects may result from jets or outflows from the central engine or from a dual AGN. The VLBA provides an angular resolution of <~10 pc at the distance of many of these galaxies, sufficient to resolve the radio emission from extremely close dual AGNs and to contribute to understanding the origin of double-peaked [O III] emission lines. Of the 13 galaxies observed at 3.6 cm (8.4 GHz), we detect six at a 1\sigma\ sensitivity level of ~0.15 mJy/beam, two of which show clear jet structures on scales ranging from a few milliarcseconds to tens of milliarcseconds (corresponding to a few pc to tens of pc at a median redshift of 0.15). We suggest that radio-loud double-peaked emission-line type-2 AGNs may be indicative of jet produced structures, but a larger sample of double-peaked [O III] AGNs with high angular resolution radio observations will be required to confirm this suggestion.Comment: 14 pages, 7 figures; ApJ in pres

Power assist EVA glove development

Structural modeling of the EVA glove indicates that flexibility in the metacarpophalangeal (MCP) joint can be improved by selectively lowering the elasticity of the glove fabric. Two strategies are used to accomplish this. One method uses coil springs on the back of the glove to carry the tension in the glove skin due to pressurization. These springs carry the loads normally borne by the glove fabric, but are more easily deformed. An active system was also designed for the same purpose and uses gas filled bladders attached to the back of the EVA glove that change the dimensions of the back of the glove and allow the glove to bend at the MCP joint, thus providing greater flexibility at this joint. A threshold control scheme was devised to control the action of the joint actuators. Input to the controller was provided by thin resistive pressure sensors placed between the hand and the pressurized glove. The pressure sensors consist of a layer of polyester film that has a thin layer of ink screened on the surface. The resistivity of the ink is pressure dependent, so an extremely thin pressure sensor can be fabricated by covering the ink patch with another layer of polyester film and measuring the changing resistance of the ink with a bridge circuit. In order to sense the force between the hand and the glove at the MCP joint, a sensor was placed on the palmar face of the middle finger. The resultant signal was used by the controller to decide whether to fill or exhaust the bladder actuators on the back of the glove. The information from the sensor can also be used to evaluate the effectiveness of a given control scheme or glove design since the magnitude of the measured pressures gives some idea of the torque required to bend a glove finger at the MCP joint. Tests of this actuator, sensor, and control system were conducted in an 57.2 kPa glove box by performing a series of 90 degree finger bends with a glove without an MCP joint assembly, a glove with the coil spring assembly, and with the four fingered actuated glove. The tests of these three glove designs confirm the validity of the model

A preliminary structural analysis of space-based inflatable tubular frame structures

The use of inflatable structures has often been proposed for aerospace and planetary applications. The advantages of such structures include low launch weight and easy assembly. The use of inflatables for applications requiring very large frame structures intended for aerospace use are proposed. In order to consider using an inflated truss, the structural behavior of the inflated frame must be examined. The statics of inflated tubes as beams was discussed in the literature, but the dynamics of these elements has not received much attention. In an effort to evaluate the vibration characteristics of the inflated beam a series of free vibration tests of an inflated fabric cantilevers were performed. Results of the tests are presented and models for system behavior posed

Asymptotics from scaling for nonlinear wave equations

We present a scaling technique which transforms the evolution problem for a nonlinear wave equation with small initial data to a linear wave equation with a distributional source. The exact solution of the latter uniformly approximates the late-time behavior of solutions of the nonlinear problem in timelike and null directions.Comment: 14 pages; minor changes (notation, typos

Linear and nonlinear tails II: exact decay rates in spherical symmetry

We derive the exact late-time asymptotics for small spherically symmetric solutions of nonlinear wave equations with a potential. The dominant tail is shown to result from the competition between linear and nonlinear effects.Comment: 17 pages, 3 figures, 2 table

Global pointwise decay estimates for defocusing radial nonlinear wave equations

We prove global pointwise decay estimates for a class of defocusing semilinear wave equations in $n=3$ dimensions restricted to spherical symmetry. The technique is based on a conformal transformation and a suitable choice of the mapping adjusted to the nonlinearity. As a result we obtain a pointwise bound on the solutions for arbitrarily large Cauchy data, provided the solutions exist globally. The decay rates are identical with those for small data and hence seem to be optimal. A generalization beyond the spherical symmetry is suggested.Comment: 9 pages, 1 figur