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991.
We investigate the zero dissipation limit problem of the one-dimensional compressible isentropic Navier-Stokes equations with Riemann initial data in the case of the composite wave of two shock waves.It is shown that the unique solution to the Navier-Stokes equations exists for all time,and converges to the Riemann solution to the corresponding Euler equations with the same Riemann initial data uniformly on the set away from the shocks,as the viscosity vanishes.In contrast to previous related works,where either the composite wave is absent or the efects of initial layers are ignored,this gives the frst mathematical justifcation of this limit for the compressible isentropic Navier-Stokes equations in the presence of both composite wave and initial layers.Our method of proof consists of a scaling argument,the construction of the approximate solution and delicate energy estimates.  相似文献   
992.
Importance sampling is a classical Monte Carlo technique in which a random sample from one probability density, π1, is used to estimate an expectation with respect to another, π. The importance sampling estimator is strongly consistent and, as long as two simple moment conditions are satisfied, it obeys a central limit theorem (CLT). Moreover, there is a simple consistent estimator for the asymptotic variance in the CLT, which makes for routine computation of standard errors. Importance sampling can also be used in the Markov chain Monte Carlo (MCMC) context. Indeed, if the random sample from π1 is replaced by a Harris ergodic Markov chain with invariant density π1, then the resulting estimator remains strongly consistent. There is a price to be paid, however, as the computation of standard errors becomes more complicated. First, the two simple moment conditions that guarantee a CLT in the iid case are not enough in the MCMC context. Second, even when a CLT does hold, the asymptotic variance has a complex form and is difficult to estimate consistently. In this article, we explain how to use regenerative simulation to overcome these problems. Actually, we consider a more general setup, where we assume that Markov chain samples from several probability densities, π1, …, πk, are available. We construct multiple-chain importance sampling estimators for which we obtain a CLT based on regeneration. We show that if the Markov chains converge to their respective target distributions at a geometric rate, then under moment conditions similar to those required in the iid case, the MCMC-based importance sampling estimator obeys a CLT. Furthermore, because the CLT is based on a regenerative process, there is a simple consistent estimator of the asymptotic variance. We illustrate the method with two applications in Bayesian sensitivity analysis. The first concerns one-way random effect models under different priors. The second involves Bayesian variable selection in linear regression, and for this application, importance sampling based on multiple chains enables an empirical Bayes approach to variable selection.  相似文献   
993.
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.  相似文献   
994.
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].  相似文献   
995.
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.  相似文献   
996.
997.
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.  相似文献   
998.
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.  相似文献   
999.
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.  相似文献   
1000.
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.  相似文献   
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