Entire curves avoiding given sets in C^n

Let $F\subset\Bbb C^n$ be a proper closed subset of $\Bbb C^n$ and $A\subset\Bbb C^n\setminus F$ at most countable ($n\geq 2$). We give conditions of $F$ and $A$, under which there exists a holomorphic immersion (or a proper holomorphic embedding) $\phi:\Bbb C\to\Bbb C^n$ with $A\subset\phi(\Bbb C)\subset\Bbb C^n\setminus F$.Comment: 10 page

A Carleman type theorem for proper holomorphic embeddings

In 1927, Carleman showed that a continuous, complex-valued function on the real line can be approximated in the Whitney topology by an entire function restricted to the real line. In this paper, we prove a similar result for proper holomorphic embeddings. Namely, we show that a proper \cC^r embedding of the real line into \C^n can be approximated in the strong \cC^r topology by a proper holomorphic embedding of \C into \C^n

Abstract basins of attraction

Abstract basins appear naturally in different areas of several complex variables. In this survey we want to describe three different topics in which they play an important role, leading to interesting open problems

Intermolecular Structure Determination of Amyloid Fibrils with 2 Magic-Angle Spinning and Dynamic Nuclear Polarization NMR

We describe magic-angle spinning NMR experiments designed to elucidate the interstrand architecture of amyloid fibrils. Three methods are introduced for this purpose, two being based on the analysis of long-range [superscript 13]C–[superscript 13]C correlation spectra and the third based on the identification of intermolecular interactions in [superscript 13]C–[superscript 15]N spectra. We show, in studies of fibrils formed by the 86-residue SH3 domain of PI3 kinase (PI3-SH3 or PI3K-SH3), that efficient [superscript 13]C–[superscript 13]C correlation spectra display a resonance degeneracy that establishes a parallel, in-register alignment of the proteins in the amyloid fibrils. In addition, this degeneracy can be circumvented to yield direct intermolecular constraints. The [superscript 13]C–[superscript 13]C experiments are corroborated by [superscript 15]N–[superscript 13]C correlation spectra obtained from a mixed [[superscript 15]N,[superscript 12]C]/[[superscript 14]N,[superscript 13]C] sample which directly quantify interstrand distances. Furthermore, when the spectra are recorded with signal enhancement provided by dynamic nuclear polarization (DNP) at 100 K, we demonstrate a dramatic increase (from 23 to 52) in the number of intermolecular [superscript 15]N–[superscript 13]C constraints detectable in the spectra. The increase in the information content is due to the enhanced signal intensities and to the fact that dynamic processes, leading to spectral intensity losses, are quenched at low temperatures. Thus, acquisition of low temperature spectra addresses a problem that is frequently encountered in MAS spectra of proteins. In total, the experiments provide 111 intermolecular [superscript 13]C–[superscript 13]C and [superscript 15]N–[superscript 13]C constraints that establish that the PI3-SH3 protein strands are aligned in a parallel, in-register arrangement within the amyloid fibril.National Institutes of Health (U.S.) (Grant EB-003151)National Institutes of Health (U.S.) (Grant EB-002804)National Institutes of Health (U.S.) (Grant EB-002026

Stein structures and holomorphic mappings

We prove that every continuous map from a Stein manifold X to a complex manifold Y can be made holomorphic by a homotopic deformation of both the map and the Stein structure on X. In the absence of topological obstructions the holomorphic map may be chosen to have pointwise maximal rank. The analogous result holds for any compact Hausdorff family of maps, but it fails in general for a noncompact family. Our main results are actually proved for smooth almost complex source manifolds (X,J) with the correct handlebody structure. The paper contains another proof of Eliashberg's (Int J Math 1:29--46, 1990) homotopy characterization of Stein manifolds and a slightly different explanation of the construction of exotic Stein surfaces due to Gompf (Ann Math 148 (2):619--693, 1998; J Symplectic Geom 3:565--587, 2005). (See also the related preprint math/0509419).Comment: The original publication is available at http://www.springerlink.co

Solid-State Dynamic Nuclear Polarization at 263 GHz: Spectrometer Design and Experimental Results

Dynamic Nuclear Polarization (DNP) experiments transfer polarization from electron spins to nuclear spins with microwave irradiation of the electron spins for enhanced sensitivity in nuclear magnetic resonance (NMR) spectroscopy. Design and testing of a spectrometer for magic angle spinning (MAS) DNP experiments at 263 GHz microwave frequency, 400 MHz 1H frequency is described. Microwaves are generated by a novel continuous-wave gyrotron, transmitted to the NMR probe via a transmission line, and irradiated on a 3.2 mm rotor for MAS DNP experiments. DNP signal enhancements of up to 80 have been measured at 95 K on urea and proline in water–glycerol with the biradical polarizing agent TOTAPOL. We characterize the experimental parameters affecting the DNP efficiency: the magnetic field dependence, temperature dependence and polarization build-up times, microwave power dependence, sample heating effects, and spinning frequency dependence of the DNP signal enhancement. Stable system operation, including DNP performance, is also demonstrated over a 36 h period.National Institutes of Health (U.S.) (NIH grant EB-002804)National Institutes of Health (U.S.) (NIH grant EB-002026

Affine modifications and affine hypersurfaces with a very transitive automorphism group

We study a kind of modification of an affine domain which produces another affine domain. First appeared in passing in the basic paper of O. Zariski (1942), it was further considered by E.D. Davis (1967). The first named author applied its geometric counterpart to construct contractible smooth affine varieties non-isomorphic to Euclidean spaces. Here we provide certain conditions which guarantee preservation of the topology under a modification. As an application, we show that the group of biregular automorphisms of the affine hypersurface $X \subset C^{k+2}$ given by the equation $uv=p(x_1,...,x_k)$ where $p \in C[x_1,...,x_k],$ acts $m-$transitively on the smooth part reg$X$ of $X$ for any $m \in N.$ We present examples of such hypersurfaces diffeomorphic to Euclidean spaces.Comment: 39 Pages, LaTeX; a revised version with minor changes and correction

Assessing the psychometric and ecometric properties of neighborhood scales using adolescent survey data from urban and rural Scotland

This work was supported by NHS Health Scotland and the University of St Andrews.Background:  Despite the well-established need for specific measurement instruments to examine the relationship between neighborhood conditions and adolescent well-being outcomes, few studies have developed scales to measure features of the neighborhoods in which adolescents reside. Moreover, measures of neighborhood features may be operationalised differently by adolescents living in different levels of urban/rurality. This has not been addressed in previous studies. The objectives of this study were to: 1) establish instruments to measure adolescent neighborhood features at both the individual and neighborhood level, 2) assess their psychometric and ecometric properties, 3) test for invariance by urban/rurality, and 4) generate neighborhood level scores for use in further analysis. Methods:  Data were from the Scottish 2010 Health Behaviour in School-aged Children Survey, which included an over-sample of rural adolescents. The survey responses of interest came from questions designed to capture different facets of the local area in which each respondent resided. Intermediate data zones were used as proxies for neighborhoods. Internal consistency was evaluated by Cronbach’s alpha. Invariance was examined using confirmatory factor analysis. Multilevel models were used to estimate ecometric properties and generate neighborhood scores. Results:  Two constructs labeled neighborhood social cohesion and neighborhood disorder were identified. Adjustment was made to the originally specified model to improve model fit and measures of invariance. At the individual level, reliability was .760 for social cohesion and .765 for disorder, and between .524 and .571 for both constructs at the neighborhood level. Individuals in rural areas experienced greater neighborhood social cohesion and lower levels of neighborhood disorder compared with those in urban areas. Conclusions:  The scales are appropriate for measuring neighborhood characteristics experienced by adolescents across urban and rural Scotland, and can be used in future studies of neighborhoods and health. However, trade-offs between neighborhood sample size and reliability must be considered.Publisher PDFPeer reviewe