Embedding some Riemann surfaces into $${\mathbb {C}^2}$$ with interpolation

We prove that several types of open Riemann surfaces, including the finitely connected planar domains, embed properly into such that the values on any given discrete sequence can be arbitrarily prescribed. Kutzschebauch supported by Schweizerische Nationalfonds grant 200021-107477/1.     

Projection-Iterative Methods for a Class of Difference Equations

We develop a theoretical framework for projection-iterative methods to solve operator equations of the form Au + Bu = f, where A is a Toeplitz operator in a Banach space , B is considered as a perturbation (of general form) of A, and f is a given element in this space. The methods are adopted for application to general situations, in particular, to the equations in which A need not be a Fredholm operator. The idea to involve iteration procedures and the technique which we apply allow to obtain conditions on perturbations for convergence and effective error estimates in terms of some weighted spaces (without any restrictions on the norms for perturbations). Based on established evaluations we derive further information about decaying properties of the solutions. The obtained results are illustrated by considering concrete classes of equations as, for instance, equations corresponding to Jacobi type operators.      

Embedded Rotational Hypersurfaces with Constant Scalar Curvature in Sn: A Correction to a Statement in M. L. Leite, Manuscripta Math. 67 (1990), 285-304.

We prove that there exist (n − 1)-dimensional compact embedded rotational hypersurfaces with constant scalar curvature (n − 1)(n − 2)S (S > 1) of S ⁿ other than product of spheres for 4 ≤ n ≤ 6. As a result, we prove that Leite’s Assertion was incorrect.The project is supported by the grant No. 10531090 of NSFC.     

Theoretical investigation on the threshold value of stimulated Brillouin scattering in terms of laser intensity

The threshold value of stimulated Brillouin scattering (SBS) was investigated theoretically basing on a new concept of real gain length (RGL). It shows that for ideal steady-state SBS or ideal transient SBS, the threshold values are both constants and the later is five orders of magnitude larger than the former. Under general conditions, whether steady-state SBS or transient SBS will occur is determined by RGL. The SBS occurred in a long material may not be steady-state SBS.     

Application of atmospheric pressure microwave plasma source for production of hydrogen via methane reforming

In this paper, results of hydrogen production via methane pyrolysis in the atmospheric pressure microwave plasma with CH₄ swirl are presented. A waveguide-based nozzleless cylinder-type microwave plasma source (MPS) was used to convert methane into hydrogen. The plasma generation was stabilized by a CH₄ swirl having a flow rate of 87.5 L min^-1. The absorbed microwave power was 1.5–5 kW. The hydrogen production rate and the corresponding energy efficiency were 866 g (H₂) h^-1 and 577 g (H₂) kWh^-1 of microwave energy absorbed by the plasma, respectively. These parameters are better than our previous results when nitrogen was used as a swirl gas and much better than those typical for other plasma methods of hydrogen production (electron beam, gliding arc, plasmatron).     

Oscillator strengths for singly ionized oxygen

The electric dipole oscillator strengths for multiplet and individual lines between some doublet and quartet levels have been calculated using the weakest bound electron potential model theory (WBEPMT) in singly ionized oxygen. We employed both numerical Coulomb approximation (NCA) wave functions and numerical non-relativistic Hartree-Fock (NRHF) wave functions for expectation values of radii in determination of parameters. The calculated oscillator strengths have been compared with available theoretical and experimental results. A good agreement with results in literature has been obtained. Moreover, oscillator strengths not existing in the literature for some highly excited levels have been obtained using this method. Electronic supplementary material  Supplementary Online Material     

Time resolved spectroscopy with femtosecond soft-x-ray pulses

The most challenging application of time resolved spectroscopy is to directly observe the structural and electronic dynamics. Here we present the combination of x-ray absorption spectroscopy with laser driven x-ray sources, offering atomic spatial and temporal resolution. Our new approaches for optimization of laser driven x-ray sources resulted in the demonstration of spatially coherent sub-20 fs x-ray pulses in a range up to several keV. We excited polycrystalline silicon with an ultrashort laser pulse and characterized the collective motion of atoms with time resolved x-ray absorption spectroscopy at a temporal resolution of less than 20 fs. Finally, we have shown the feasibility of probing the dynamics of the electronic structure of silicon and carbon with near edge x-ray absorption spectroscopy.     

Hydrothermal preparation and photoluminescence of bundle-like structure of ZnWO4 nanorods

ZnWO₄ nanorods with a bundle-like structure were synthesized at 180°C for 12 h by a hydrothermal technology from Na₂WO₄⋅2H₂O and ZnSO₄⋅7H₂O in the presence of sodium dodecyl sulfate (SDS). The as-synthesized bundle-like structure of ZnWO₄ nanorods was characterized by various techniques: TEM, XRD and EDS. The luminescence properties of the bundle-like structure of the ZnWO₄ nanorods were investigated by photoluminescence (PL) spectroscopy.     

Formation of hexagonal shaped wurtzite zinc sulphide nano rods

Zinc sulfide nanorods with good photoluminescence have been successfully fabricated using a simple sol-gel process via ultrasonication, with mercaptoethanol as capping agent. The formation of ZnS nucleation, followed by subsequent growth, is significant in obtaining highly oriented ZnS nanorods. Temperature, time, and capping agent also proved to be significant factors in the growth of ZnS nanorods and greatly affect their photo luminescent properties. X-ray diffraction (XRD) analysis, low and high-resolution transmission electron microscopy (TEM & HRTEM), selected-area electron diffraction (SAED) pattern, and scanning electron microscopy (SEM) indicated that the ZnS nanorods were single crystal in nature and that they had grown up preferentially along the [0001] direction. This simple method of nucleation, followed by their successive growth, resulted in the development of an effective and low-cost fabrication process for high-quality ZnS nanorods with good photo luminescent properties that can be applied to luminescent sensors and optoelectronic devices.     

Metastable state and macroscopic quantum tunneling of binary mixtures

We provide a mixing model to explore the metastable state and the macroscopic quantum tunneling (MQT) of binary mixtures. For , we first observe the two condensates form the symmetry-breaking state (SBS) and then suddenly transfer to the symmetry-preserving state (SPS) through the MQT. The SBS is shown to be the metastable state in our system. We find the MQT does not spontaneously arise. The inducement mechanism is the damping but not the excitations. The damping mechanism can also control the lifetime and the tunneling decay rate of the SBS. Finally, we further present the origin of these phenomena by examining the energy of the system.