Discrete and Embedded Eigenvalues for One-Dimensional Schrödinger Operators

I present an example of a discrete Schrödinger operator that shows that it is possible to have embedded singular spectrum and, at the same time, discrete eigenvalues that approach the edges of the essential spectrum (much) faster than exponentially. This settles a conjecture of Simon (in the negative). The potential is of von Neumann-Wigner type, with careful navigation around a previously identified borderline situation.     

Algebro-Geometric Approach in the Theory of Integrable Hydrodynamic Type Systems

The algebro-geometric approach for integrability of semi-Hamiltonian hydrodynamic type systems is presented. The class of symmetric hydrodynamic type systems is defined and the calculation of the associated Riemann surfaces is greatly simplified for this class. Many interesting and physically motivated examples are investigated.     

Actively mode-locked dual-wavelength fiber laser with close wavelength spacing using a fiber Bragg grating

A simple actively mode-locked fiber ring laser is proposed and successfully demonstrated to generate dual-wavelength picosecond pulses with close wavelength spacing using one Bragg grating in standard single-mode fiber. The proposed laser can be made to operate in stable dual-wavelength at room temperature, due to the birefringence characteristic of the FBG induced by transverse strain. Transverse strain loading on the FBG allows the wavelength spacing to be controlled. Generation of stable dual-wavelength pulses with a pulsewidth of 212–234 ps and a tunable wavelength separation from 0.2 to 0.44 nm at a pulse rate of 1.05 GHz was demonstrated.     

On the Zero-Energy-Limit Solution for the Modified Gross–Pitaevskii Equation

The modified Gross–Pitaevskii equation was derived and solved to obtain the 1D solution in the zero-energy limit. This stationary solution could account for the dominated contributions due to the kinetic effect as well as the chemical potential in inhomogeneous Bose gases.     

Characterization of a pectic polysaccharide from the fruit of <Emphasis Type="Italic">Ziziphus jujuba</Emphasis>

A pectic polysaccharide was isolated from the fruits of Ziziphus jujuba Mill. cv. jinsixiaozao Hort. and its structure was characterized by acid hydrolysis, methylation, and NMR spectroscopies. The purified fraction Ju-B-7 had a molecular mass of over 2000 kDa. Chemical and spectroscopic analyses indicated that Ju-B-7 is composed mainly of α-1,4-linked D-galactopyranosyluronic acid and 1,2-linked L-rhamnose with a molar ratio of 8.1:1. It can significantly stimulate spleen cell proliferation in vitro (P<0.01, 10 μmg/mL). Published in Khimiya Prirodnykh Soedinenii, No. 4, pp. 311–312, July–August, 2007.     

Estimating the Scale Parameter of a Lévy-stable Distribution via the Extreme Value Approach

The characteristic exponent α of a Lévy-stable law S _α (σ, β, μ) was thoroughly studied as the extreme value index of a heavy tailed distribution. For 1 < α < 2, Peng (Statist. Probab. Lett. 52: 255–264, 2001) has proposed, via the extreme value approach, an asymptotically normal estimator for the location parameter μ. In this paper, we derive by the same approach, an estimator for the scale parameter σ and we discuss its limiting behavior.