Optimal decay rates of the compressible magnetohydrodynamic equations

We use a pure energy method recently developed by Guo and Wang to prove the optimal time decay rates of the solutions to the compressible magnetohydrodynamic equations in the whole space. In particular, the optimal decay rates of the higher-order spatial derivatives of solutions are obtained.     

Variable Exponent Sobolev Spaces for Semilinear Elliptic Systems

In this work, the semilinear elliptic systems with Dirichlet boundary value are considered. We extend the notion of subcritical growth from polynomial growth to variable exponent growth. Under the variable exponent growth, nontrivial solutions are obtained via variable exponent Sobolev spaces and variational methods. In article final, we make a remark to explain that our main result is a extention of a recent result of D. G. de Figueiredo, J. M. do Óand B. Ruf [D. G. de Figueiredo, J. M. do Ó, B. Ruf, An Orlicz-space approach to superlinear elliptic systems, J. Funct. Anal. 224 (2005) 471–496].     

The fine structure levels and spin-singlet contributions to zero-field-splitting parameters of Cr2+ ion in CdGa2S4

A theoretical investigation is reported of the fine structure levels and the spin-singlet contributions to zero-field-splitting (ZFS) parameters for Cr²⁺ ion in CdGa₂S₄ crystals. Firstly, the complete energy matrix including all spin states for a 3d ⁴ ion in tetrahedral D _2d symmetry is constructed according the double-group chain in the strong-field scheme. Then, by diagonalizing the complete energy of electron–electron interactions, the crystal field and the spin–orbit coupling for the Cr²⁺ (3d ⁴) ion in CdGa₂S₄ crystal, the fine structure levels and the spin-singlet contributions to ZFS parameters a, D and F are calculated. The results show that the spin-singlet contribution to D is negligible, but the contributions to a and F are very important. So, to obtain more accurate ZFS parameters for 3d ⁴ ions in the tetrahedral crystals, all spin states should be considered.     

Stable single longitudinal mode erbium-doped silica fiber laser based on an asymmetric linear three-cavity structure

We present a stable linear-cavity single longitudinal mode (SLM) erbium-doped silica fiber laser. It consists of four fiber Bragg gratings (FBGs) directly written in a section of photosensitive erbium-doped fiber (EDF) to form an asymmetric three-cavity structure. The stable SLM operation at a wavelength of 1545.112 nm with a 3-dB bandwidth of 0.012 nm and an optical signal-to-noise ratio (OSNR) of about 60 dB is verified experimentally. Under laboratory conditions, the performance of a power fluctuation of less than 0.05 dB observed from the power meter for 6 h and a wavelength variation of less than 0.01 nm obtained from the optical spectrum analyzer (OSA) for about 1.5 h are demonstrated. The gain fiber length is no longer limited to only several centimeters for SLM operation because of the excellent mode-selecting ability of the asymmetric three-cavity structure. The proposed scheme provides a simple and cost-effective approach to realizing a stable SLM fiber laser.     

A sensitive method of determining optic axis azimuth based on laser feedback

A sensitive method to determine the optic axis azimuth of the birefringence element is presented, which is based on laser feedback. The phase difference between the two intensities in birefringence feedback changes with the angle between the optic axis of the birefringence element and laser original polarization. The phase difference is highly sensitive to the relative position of the optic axis and the laser original polarization. This method is used to highly precisely determine the optic axis azimuth, and is able to distinguish between the fast axis and the slow axis of the birefringence element. Theoretical analysis and experimental results are both demonstrated.     

Experimental study of the temperature and electron-irradiation effect on erbium-doped fiber amplifiers

We study the influence of temperature on the gain of 980 nm pumped erbium-doped fiber amplifier (EDFA) before and after the electron irradiation. Our experimental results indicate that in the irradiation process the EDFA gain at low temperatures is less than that at high temperatures, but after 7 days recovery, the EDFA gain at low temperatures is significantly higher than that at high temperatures. After 200 krad electron irradiation, the EDFA gain is more sensitive to temperature as compared to non-irradiated one.     

Effect of TiO2 addition on the crystallization of quenched glasses in the SiO2–Al2O3–ZrO2 system

The glass formation in the SiO₂-rich region of the ternary oxide system Al₂O₃–ZrO₂–SiO₂ with MgO, CaO, and TiO₂ as melting aids was analyzed. The crystallization of glasses with different content of TiO₂ and phase evolution with the temperature was studied by X-ray diffraction, infrared, laser Raman spectroscopy and transmission electron microscopy. The use of TiO₂ favored formation and crystallization of the glasses due to the decrease of the viscosity of melts and acting as a nucleating agent. The crystalline phase of t-ZrO₂ was developed at temperatures as low as 880°C whereas in as prepared specimens without TiO₂ its presence was not detected. For the specimens with TiO₂, t-ZrO₂ and mullite were the principal phases at 1000°C. TiO₂ addition did not change the crystallization sequence but decreased the formation temperature of the crystalline phases. Most of Ti⁴⁺ ions entered into t-ZrO₂ and only a small portion in mullite, but the surplus was detected in ZrTiO₄.     

A computationally efficient state-space partitioning approach to pricing high-dimensional American options via dimension reduction

This paper studies the problem of pricing high-dimensional American options. We propose a method based on the state-space partitioning algorithm developed by Jin et al. (2007) and a dimension-reduction approach introduced by Li and Wu (2006). By applying the approach in the present paper, the computational efficiency of pricing high-dimensional American options is significantly improved, compared to the extant approaches in the literature, without sacrificing the estimation precision. Various numerical examples are provided to illustrate the accuracy and efficiency of the proposed method. Pseudcode for an implementation of the proposed approach is also included.