Harmonic maps between annuli on Riemann surfaces

Let ρ _Σ = h(|z|²) be a metric in a Riemann surface Σ, where h is a positive real function. Let H _{r 1} = {w = f(z)} be the family of a univalent ρ _Σ harmonic mapping of the Euclidean annulus A(r ₁, 1):= {z: r ₁ < |z| < 1} onto a proper annulus A _Σ of the Riemann surface Σ, which is subject to some geometric restrictions. It is shown that if A _Σ is fixed, then sup{r ₁: ℋ _{r 1} ≠ ∅} < 1. This generalizes similar results from the Euclidean case. The cases of Riemann and of hyperbolic harmonic mappings are treated in detail. Using the fact that the Gauss map of a surface with constant mean curvature (CMC) is a Riemann harmonic mapping, an application to the CMC surfaces is given (see Corollary 3.2). In addition, some new examples of hyperbolic and Riemann radial harmonic diffeomorphisms are given, which have inspired some new J. C. C. Nitsche-type conjectures for the class of these mappings.     

On the divisor function in short intervals

Let d(n) denote the number of positive divisors of the natural number n. The aim of this paper is to investigate the validity of the asymptotic formula

$\begin{array}{lll}\sum \limits_{x < n \leq x+h(x)}d(n)\sim h(x)\log x\end{array}$

for \({x \to + \infty,}\) assuming a hypothetical estimate on the mean

$\begin{array}{lll} \int \limits_X^{X+Y}(\Delta(x+h(x))-\Delta (x))^2\,{d}x, \end{array}$

which is a weakened form of a conjecture of M. Jutila.

     

Rotation set for maps of degree 1 on the graph sigma

For a continuous map on a topological graph containing a unique loop S it is possible to define the degree and, for a map of degree 1, rotation numbers. It is known that the set of rotation numbers of points in S is a compact interval and for every rational r in this interval there exists a periodic point of rotation number r. The whole rotation set (i.e., the set of all rotation numbers) may not be connected and it is not known in general whether it is closed.     

On new measures of pseudorandomness of binary lattices

Hubert, Mauduit and Sárközy introduced the pseudorandom measure of order ? of binary lattices. This measure studies the pseudorandomness only on box lattices of very special type. In certain applications one may need measures covering a more general situation. In this paper the line measure and the convex measure are introduced.     

Fabrication of a pure polarization grating in a cross-linked azopolymer by polarization-modulated holography

A cross-linked azopolymer with high optical and thermal stability was prepared. A pure polarization grating without surface topology was fabricated from cross-linked azopolymer by polarization holography by use of orthogonal linearly polarized beams from a He-Cd laser with a power density of 60 mW/cm(-2). The surface relief structure was investigated by atomic-force microscopy, and the polarization grating was observed by polarization optical microscopy. The grating spacing is 1.5 microm. The grating is stable at room temperature and can endure repeated writing-erasing.     

k-space inherited parallel acquisition (KIPA): application on dynamic magnetic resonance imaging thermometry

In this study, a novel method for dynamic parallel image acquisition and reconstruction is presented. In this method, called k-space inherited parallel acquisition (KIPA), localized reconstruction coefficients are used to achieve higher reduction factors, and lower noise and artifact levels compared to that of generalized autocalibrating partially parallel acquisition (GRAPPA) reconstruction. In KIPA, the full k-space for the first frame and the partial k-space for later frames are required to reconstruct a whole series of images. Reconstruction coefficients calculated for different segments of k-space from the first frame data set are used to estimate missing k-space lines in corresponding k-space segments of other frames. The local determination of KIPA reconstruction coefficients is essential to adjusting them according to the local signal-to-noise ratio characteristics of k-space data. The proposed algorithm is applicable to dynamic imaging with arbitrary k-space sampling trajectories. Simulations of magnetic resonance thermometry using the KIPA method with a reduction factor of 6 and using dynamic imaging studies of human subjects with reduction factors of 4 and 6 have been performed to prove the feasibility of our method and to show apparent improvement in image quality in comparison with GRAPPA for dynamic imaging.     

Carbon nanotube emitters and field emission triode

Based on our study on field emission from multi-walled carbon nanotubes (MWNTs), we experimentally manufactured field emission display (FED) triode with a MWNTs cold cathode, and demonstrated an excellent performance of MWNTs as field emitters. The measured luminance of the phosphor screens was 1.8 × 103 cd/m2 for green light. The emission is stable with a fluctuation of only 1.5% at an average current of 260 μA.     

Parameter estimation of an asymmetric vocal-fold system from glottal area time series using chaos synchronization

In this paper, we apply an iterative parameter adaption scheme based on chaos synchronization to estimate system parameters of the asymmetric vocal folds from glottal area time series. The original asymmetric vocal-fold system associated with recurrent laryngeal paralysis shows chaotic vibrations with positive Lyapunov exponents. Aperiodic glottal area time series from the original system will be applied as the feedback variable coupling the simulative and the original vocal-fold systems. The parameter adaption technique based on chaos synchronization is employed to manipulate the simulative system parameters. The chaotic vibrations, system parameters, and the bifurcation diagram of the original vocal-fold system can be exactly reproduced in the simulative system, and the two chaotic systems can be synchronized. Furthermore, the effects of noise, sampling rate, and equation difference due to nonlinear spring terms on vocal-fold parameter estimations are investigated. Despite large noise perturbations, large equation differences, and low sampling rate, the parameter adaption scheme can effectively estimate the original vocal-fold system parameters. This study provides a theoretical base to apply chaos synchronization to estimate the vocal-fold system parameters from the glottal area data and show its potential application in laryngeal physiology.     

Nonlinear ultrasonic nature of organic liquid and organic liquid mixture

Based on Jacobson's molecular free length theory in liquids and the relationship between ultrasonic velocity and the molecular free length in organic liquids, this paper deduces the equations for pressure coefficient and temperature coefficient of ultrasonic velocity and nonlinear acoustic parameter B/A in both of organic liquid and organic liquid binary mixtures. These nonlinear acoustic parameters are evaluated against the measured results and data from other sources. The equations reveal the connections between the nonlinear acoustic parameters and some internal structural of the medium or mixtures e.g. the sizes of molecule, several thermodynamic physical parameters and outside status e.g. condition of pressure and temperature of the liquid or liquid mixture. With the equations the nonlinear acoustic parameter B/A of organic liquid binary mixtures, which is impossible to know without the nonlinear acoustic parameter B/A of the tow components before, can be calculated based on the structural and physical parameters of organic liquid and organic liquid binary mixtures.     

Experimental synchronization of independent entangled photon sources

We report the generation of independent entangled photon pairs from two synchronized but mutually incoherent laser sources. The quality of synchronization is confirmed by observing a violation of Bell's inequality with 3.2 standard deviations in an entanglement swapping experiment. The techniques developed in our experiment are not only important for realistic linear optical quantum-information processing, but also enable new tests of local realism.