Boundedness properties for Sobolev inner products

AbstractSobolev orthogonal polynomials with respect to measures supported on subsets of the complex plane are considered. The connection between the following properties is studied: the multiplication operator Mp(z)=zp(z) defined on the space P of algebraic polynomials with complex coefficients is bounded with respect to the norm defined by the Sobolev inner product, the supports of the measures are compact and the zeros of the orthogonal polynomials lie in a compact subset of the complex plane. In particular, we prove that the boundedness of the multiplication operator M always implies the compactness of the supports

Landau theory of phase separation in cuprates

I discuss the problem of phase separation in cuprates from the point of view of the Landau theory of Fermi liquids. I calculate the rate of growth of unstable regions for the hydrodymanics and collisionless limit and, in presence of long range Coulomb interactions, the size of these regions. These are analytic results valid for any strength of the Landau parameters.Comment: RevteX, preprint ITP (1994

Near Extremal Kerr Entropy from AdS_2 Quantum Gravity

We analyze the asymptotic symmetries of near extremal Kerr black holes in four dimensions using the AdS_2/CFT_1 correspondence. We find a Virasoro algebra with central charge c_R=12J that is independent from the Virasoro algebra (with the same central charge) that acts on the degenerate ground state. The energy of the excitations is computed as well, and we can use Cardy's formula to determine the near extremal entropy. Our result is consistent with the Bekenstein-Hawking area law for near extremal Kerr black holes.Comment: 28 pages. v2: references added, typos correcte

Complete Analysis of Baryon Magnetic Moments in 1/N_c

We generate a complete basis of magnetic moment operators for the N_c = 3 ground-state baryons in the 1/N_c expansion, and compute and tabulate all associated matrix elements. We then compare to previous results derived in the literature and predict additional relations among baryon magnetic moments holding to subleading order in 1/N_c and flavor SU(3) breaking. Finally, we predict all unknown diagonal and transition magnetic moments to <= 0.15 mu_N accuracy, and suggest possible experimental measurements to improve the analysis even further.Comment: 28 pages (including 11 tables), ReVTeX. One reference and grant acknowledgment adde

γ-Radonifying operators and UMD-valued Littlewood–Paley–Stein functions in the Hermite setting on BMO and Hardy spaces

AbstractIn this paper we study Littlewood–Paley–Stein functions associated with the Poisson semigroup for the Hermite operator on functions with values in a UMD Banach space B. If we denote by H the Hilbert space L2((0,∞),dt/t), γ(H,B) represents the space of γ-radonifying operators from H into B. We prove that the Hermite square function defines bounded operators from BMOL(Rn,B) (respectively, HL1(Rn,B)) into BMOL(Rn,γ(H,B)) (respectively, HL1(Rn,γ(H,B))), where BMOL and HL1 denote BMO and Hardy spaces in the Hermite setting. Also, we obtain equivalent norms in BMOL(Rn,B) and HL1(Rn,B) by using Littlewood–Paley–Stein functions. As a consequence of our results, we establish new characterizations of the UMD Banach spaces

Influence of the substrate type on CVD grown homoepitaxial diamond layer quality by cross sectional TEM and CL analysis

To assess diamond-based semiconducting devices, a reduction of point defect levels and an accurate control of doping are required as well as the control of layer thickness. Among the analyses required to improve such parameters, cross sectional studies should take importance in the near future. The present contribution shows how FIB (focused ion beam) preparations followed by electron microscopy related techniques as TEM or CL allowed to performanalysis versus depth in the layer, doping and point defect levels. Three samples grown along the sameweek in the same machinewith identical growth conditions but on different substrates (CVD-IIIa (110) oriented, CVD-optical grade (100) oriented and a HPHT-Ib (100) oriented) are studied. Even though A-band is observed by CL, no dislocation is observed by CTEM. Point defect type and level are shown to substantially change with respect to the substrate type as well as the boron doping levels that vary within an order of magnitude. H3 present in the epilayer grown on HPHT type of substrate is replaced by T1 and NE3 point defects for epilayers grown on the CVD type one. An increase of excitonic transitions through LO phonons is also shown to take place near the surface while only TO ones are detected deeper in the epilayer. Such results highlight the importance of choosing the correct substrate.5 page

Cellular mechanisms underlying Pax3-related neural tube defects and their prevention by folic acid

Neural tube defects (NTDs), including spina bifida and anencephaly, are among the most common birth defects worldwide, but their underlying genetic and cellular causes are not well understood. Some NTDs are preventable by supplemental folic acid. However, despite widespread use of folic acid supplements and implementation of food fortification in many countries, the protective mechanism is unclear. Pax3 mutant (splotch; Sp2H) mice provide a model in which NTDs are preventable by folic acid and exacerbated by maternal folate deficiency. Here, we found that cell proliferation was diminished in the dorsal neuroepithelium of mutant embryos, corresponding to the region of abolished Pax3 function. This was accompanied by premature neuronal differentiation in the prospective midbrain. Contrary to previous reports, we did not find evidence that increased apoptosis could underlie failed neural tube closure in Pax3 mutant embryos, nor that inhibition of apoptosis could prevent NTDs. These findings suggest that Pax3 functions to maintain the neuroepithelium in a proliferative, undifferentiated state, allowing neurulation to proceed. NTDs in Pax3 mutants were not associated with abnormal abundance of specific folates and were not prevented by formate, a one-carbon donor to folate metabolism. Supplemental folic acid restored proliferation in the cranial neuroepithelium. This effect was mediated by enhanced progression of the cell cycle from S to G2 phase, specifically in the Pax3 mutant dorsal neuroepithelium. We propose that the cell-cycle-promoting effect of folic acid compensates for the loss of Pax3 and thereby prevents cranial NTDs

On the nature of the short duration GRB 050906

The definitive version is available at www.blackwell-synergy.com. Copyright Blackwell Publishing DOI : 10.1111/j.1365-2966.2007.11953.xPeer reviewe

ILLUMINATING THE DARKEST GAMMA-RAY BURSTS WITH RADIO OBSERVATIONS

We present X-ray, optical, near-infrared (IR), and radio observations of gamma-ray bursts (GRBs) 110709B and 111215A, as well as optical and near-IR observations of their host galaxies. The combination of X-ray detections and deep optical/near-IR limits establish both bursts as "dark." Sub-arcsecond positions enabled by radio detections lead to robust host galaxy associations, with optical detections that indicate z ≾ 4 (110709B) and z ≈ 1.8-2.9 (111215A). We therefore conclude that both bursts are dark due to substantial rest-frame extinction. Using the radio and X-ray data for each burst we find that GRB 110709B requires A_V^(host) ≳ 5.3 mag and GRB 111215A requires A_V^(host) ≳ 8.5 mag (assuming z = 2). These are among the largest extinction values inferred for dark bursts to date. The two bursts also exhibit large neutral hydrogen column densities of N H, int ≳ 10^(22) cm^(–2) (z = 2) as inferred from their X-ray spectra, in agreement with the trend for dark GRBs. Moreover, the inferred values are in agreement with the Galactic A_V -N_H relation, unlike the bulk of the GRB population. Finally, we find that for both bursts the afterglow emission is best explained by a collimated outflow with a total beaming-corrected energy of E_γ + E_K ≈ (7-9) × 10^(51) erg (z = 2) expanding into a wind medium with a high density, Ṁ ≈ (6-20) x 10^(-5) M_☉ yr^(–1) (n ≈ 100-350 cm^(–3) at ≈ 10^(17) cm). While the energy release is typical of long GRBs, the inferred density may be indicative of larger mass-loss rates for GRB progenitors in dusty (and hence metal rich) environments. This study establishes the critical role of radio observations in demonstrating the origin and properties of dark GRBs. Observations with the JVLA and ALMA will provide a sample with sub-arcsecond positions and robust host associations that will help to shed light on obscured star formation and the role of metallicity in GRB progenitors