Pluripolarity of Graphs of Denjoy Quasianalytic Functions of Several Variables

In this paper we prove pluripolarity of graphs of Denjoy quasianalytic functions of several variables on the spanning se

Pluricomplex Green and Lempert functions for equally weighted poles

For $\Omega$ a domain in $\mathbb C^n$, the pluricomplex Green function with poles $a_1, ...,a_N \in \Omega$ is defined as $G(z):=\sup \{u(z): u\in PSH_-(\Omega), u(x)\le \log \|x-a_j\|+C_j \text{when} x \to a_j, j=1,...,N \}$. When there is only one pole, or two poles in the unit ball, it turns out to be equal to the Lempert function defined from analytic disks into $\Omega$ by $L_S (z) :=\inf \{\sum^N_{j=1}\nu_j\log|\zeta_j|: \exists \phi\in \mathcal {O}(\mathbb D,\Omega), \phi(0)=z, \phi(\zeta_j)=a_j, j=1,...,N \}$. It is known that we always have $L_S (z) \ge G_S(z)$. In the more general case where we allow weighted poles, there is a counterexample to equality due to Carlehed and Wiegerinck, with $\Omega$ equal to the bidisk. Here we exhibit a counterexample using only four distinct equally weighted poles in the bidisk. In order to do so, we first define a more general notion of Lempert function "with multiplicities", analogous to the generalized Green functions of Lelong and Rashkovskii, then we show how in some examples this can be realized as a limit of regular Lempert functions when the poles tend to each other. Finally, from an example where $L_S (z) > G_S(z)$ in the case of multiple poles, we deduce that distinct (but close enough) equally weighted poles will provide an example of the same inequality. Open questions are pointed out about the limits of Green and Lempert functions when poles tend to each other.Comment: 25 page

Convergence and multiplicities for the Lempert function

Given a domain $\Omega \subset \mathbb C$, the Lempert function is a functional on the space Hol (\D,\Omega) of analytic disks with values in $\Omega$, depending on a set of poles in $\Omega$. We generalize its definition to the case where poles have multiplicities given by local indicators (in the sense of Rashkovskii's work) to obtain a function which still dominates the corresponding Green function, behaves relatively well under limits, and is monotonic with respect to the indicators. In particular, this is an improvement over the previous generalization used by the same authors to find an example of a set of poles in the bidisk so that the (usual) Green and Lempert functions differ.Comment: 24 pages; many typos corrected thanks to the referee of Arkiv for Matemati

Performance of the Two Aerogel Cherenkov Detectors of the JLab Hall A Hadron Spectrometer

We report on the design and commissioning of two silica aerogel Cherenkov detectors with different refractive indices. In particular, extraordinary performance in terms of the number of detected photoelectrons was achieved through an appropriate choice of PMT type and reflector, along with some design considerations. After four years of operation, the number of detected photoelectrons was found to be noticeably reduced in both detectors as a result of contamination, yellowing, of the aerogel material. Along with the details of the set-up, we illustrate the characteristics of the detectors during different time periods and the probable causes of the contamination. In particular we show that the replacement of the contaminated aerogel and parts of the reflecting material has almost restored the initial performance of the detectors.Comment: 18 pages, 9 Figures, 4 Tables, 44 Reference

Atlas-Based White Matter Analysis in Individuals With Velo-Cardio-Facial Syndrome (22q11.2 Deletion Syndrome) and Unaffected Siblings

Background: Velo-cardio-facial syndrome (VCFS, MIM#192430, 22q11.2 Deletion Syndrome) is a genetic disorder caused by a deletion of about 40 genes at the q11.2 band of one copy of chromosome 22. Individuals with VCFS present with deficits in cognition and social functioning, high risk of psychiatric disorders, volumetric reductions in gray and white matter (WM) and some alterations of the WM microstructure. The goal of the current study was to characterize the WM microstructural differences in individuals with VCFS and unaffected siblings, and the correlation of WM microstructure with neuropsychological performance. We hypothesized that individuals with VCFS would have decreased indices of WM microstructure (fractional anisotropy (FA), axial diffusivity (AD) and radial diffusivity (RD)), particularly in WM tracts to the frontal lobe, and that these measures would be correlated with cognitive functioning. Methods: Thirty-three individuals with VCFS (21 female) and 16 unaffected siblings (8 female) participated in DTI scanning and neuropsychological testing. We performed an atlas-based analysis, extracted FA, AD, and RD measures for 54 WM tracts (27 in each hemisphere) for each participant, and used MANOVAs to compare individuals with VCFS to siblings. For WM tracts that were statistically significantly different between VCFS and siblings (pFDR \u3c 0.05), we assessed the correlations between DTI and neuropsychological measures. Results: In VCFS individuals as compared to unaffected siblings, we found decreased FA in the uncinate fasciculus, and decreased AD in multiple WM tracts (bilateral superior and posterior corona radiata, dorsal cingulum, inferior fronto-occipital fasciculus, superior longitudinal fasciculus, superior cerebellar peduncle, posterior thalamic radiation, and left anterior corona radiata, retrolenticular part of the internal capsule, external capsule, sagittal stratum). We also found significant correlations of AD with measures of executive function, IQ, working memory, and/or social cognition. Conclusions: Our results suggest that individuals with VCFS display abnormal WM connectivity in a widespread cerebro-anatomical network, involving tracts from/to all cerebral lobes and the cerebellum. Future studies could focus on the WM developmental trajectory in VCFS, the association of WM alterations with psychiatric disorders, and the effects of candidate 22q11.2 genes on WM anomalies

Proton Spin Structure in the Resonance Region

We have examined the spin structure of the proton in the region of the nucleon resonances (1.085 GeV < W < 1.910 GeV) at an average four momentum transfer of Q^2 = 1.3 GeV^2. Using the Jefferson Lab polarized electron beam, a spectrometer, and a polarized solid target, we measured the asymmetries A_parallel and A_perp to high precision, and extracted the asymmetries A_1 and A_2, and the spin structure functions g_1 and g_2. We found a notably non-zero A_perp, significant contributions from higher-twist effects, and only weak support for polarized quark--hadron duality.Comment: 6 pages, 4 figures, REVTeX4, similar to PRL submission, plots colorized and appenix added, v3: minor edit, matches PR

Probing Quark-Gluon Interactions with Transverse Polarized Scattering

We have extracted QCD matrix elements from our data on double polarized inelastic scattering of electrons on nuclei. We find the higher twist matrix element \tilde{d_2}, which arises strictly from quark- gluon interactions, to be unambiguously non zero. The data also reveal an isospin dependence of higher twist effects if we assume that the Burkhardt-Cottingham Sum rule is valid. The fundamental Bjorken sum rule obtained from the a0 matrix element is satisfied at our low momentum transfer.Comment: formerly "Nachtmann Moments of the Proton and Deuteron Spin Structure Functions

Cross Section Measurement of Charged Pion Photoproduction from Hydrogen and Deuterium

We have measured the differential cross section for the gamma n --> pi- p and gamma p --> pi+ n reactions at center of mass angle of 90 degree in the photon energy range from 1.1 to 5.5 GeV at Jefferson Lab (JLab). The data at photon energies greater than 3.3 GeV exhibit a global scaling behavior for both pi- and pi+ photoproduction, consistent with the constituent counting rule and the existing pi+ photoproduction data. Possible oscillations around the scaling value are suggested by these new data The data show enhancement in the scaled cross section at a center-of-mass energy near 2.2 GeV. The cross section ratio of exclusive pi- to pi+ photoproduction at high energy is consistent with the prediction based on one-hard-gluon-exchange diagrams

Measurement of the Electric Form Factor of the Neutron at Q^2=0.5 and 1.0 (GeV/c)^2

The electric form factor of the neutron was determined from measurements of the \vec{d}(\vec{e},e' n)p reaction for quasielastic kinematics. Polarized electrons were scattered off a polarized deuterated ammonia target in which the deuteron polarization was perpendicular to the momentum transfer. The scattered electrons were detected in a magnetic spectrometer in coincidence with neutrons in a large solid angle detector. We find G_E^n = 0.0526 +/- 0.0033 (stat) +/- 0.0026 (sys) and 0.0454 +/- 0.0054 +/- 0.0037 at Q^2 = 0.5 and 1.0 (GeV/c)^2, respectively.Comment: 5 pages, 2 figures, as publishe