Fresnel operator, squeezed state and Wigner function for Caldirola-Kanai Hamiltonian

Based on the technique of integration within an ordered product (IWOP) of operators we introduce the Fresnel operator for converting Caldirola-Kanai Hamiltonian into time-independent harmonic oscillator Hamiltonian. The Fresnel operator with the parameters A,B,C,D corresponds to classical optical Fresnel transformation, these parameters are the solution to a set of partial differential equations set up in the above mentioned converting process. In this way the exact wavefunction solution of the Schr\"odinger equation governed by the Caldirola-Kanai Hamiltonian is obtained, which represents a squeezed number state. The corresponding Wigner function is derived by virtue of the Weyl ordered form of the Wigner operator and the order-invariance of Weyl ordered operators under similar transformations. The method used here can be suitable for solving Schr\"odinger equation of other time-dependent oscillators.Comment: 6 pages, 2 figure

The Radio and Gamma-Ray Luminosities of Blazars

Based on the $\gamma$-ray data of blazars in the third EGRET catalog and radio data at 5 GHz, we studied the correlation between the radio and $\gamma$-ray luminosities using two statistical methods. The first method was the partial correlation analysis method, which indicates that there exist correlations between the radio and $\gamma$-ray luminosities in both high and low states as well as in the average case. The second method involved a comparison of expected $\gamma$-ray luminosity distribution with the observed data using the Kolmogorov-- Smirnov (KS) test. In the second method, we assumed that there is a correlation between the radio and $\gamma$-ray luminosities and that the $\gamma$-ray luminosity function is proportional to the radio luminosity function. The KS test indicates that the expected gamma-ray luminosity distributions are consistent with the observed data in a reasonable parameter range. Finally, we used different $\gamma$-ray luminosity functions to estimate the possible 'observed' $\gamma$-ray luminosity distributions by GLAST.Comment: 8 pages, 4 figures, one table, PASJ, 53 (2001

Adaptive Optimal Scaling of Metropolis-Hastings Algorithms Using the Robbins-Monro Process

We present an adaptive method for the automatic scaling of Random-Walk Metropolis-Hastings algorithms, which quickly and robustly identifies the scaling factor that yields a specified overall sampler acceptance probability. Our method relies on the use of the Robbins-Monro search process, whose performance is determined by an unknown steplength constant. We give a very simple estimator of this constant for proposal distributions that are univariate or multivariate normal, together with a sampling algorithm for automating the method. The effectiveness of the algorithm is demonstrated with both simulated and real data examples. This approach could be implemented as a useful component in more complex adaptive Markov chain Monte Carlo algorithms, or as part of automated software packages

Polarization and Variations of BL Lacertae Objects

BL Lacertae objects are an extreme subclass of AGNs showing rapid and large-amplitude variability, high and variable polarization, and core-dominated radio emissions. If a strong beaming effect is the cause of the extreme observation properties, one would expect that these properties would be correlated with each other. Based on the relativistic beaming model, relationships between the polarization and the magnitude variation in brightness, as well as the core- dominance parameter are derived and used statistically to compare with the observational data of a BL Lacertae object sample. The statistical results are consistent with these correlations, which suggests that the polarization, the variation, and the core-dominance parameter are possible indications of the beaming effect.Comment: 6 pages, two figures, one table, some revisions. PASJ, 53 (2001

Inversion formula and Parsval theorem for complex continuous wavelet transforms studied by entangled state representation

In a preceding Letter (Opt. Lett. 32, 554 (2007)) we have proposed complex continuous wavelet transforms (CCWTs) and found Laguerre--Gaussian mother wavelets family. In this work we present the inversion formula and Parsval theorem for CCWT by virtue of the entangled state representation, which makes the CCWT theory complete. A new orthogonal property of mother wavelet in parameter space is revealed.Comment: 4 pages no figur

Basic properties of Gamma-ray loud blazars

In this paper, a method is proposed to determine the basic properties of $\gamma$-ray loud blazars, among them the central black hole mass, M, the Doppler factor, $\delta$, the propagation angle of the $\gamma$-rays with respect to the symmetric axis of a two-temperature accretion disk, $\Phi$, and the distance (i.e. the height above the accretion disk), d at which the $\gamma$-rays are created, for seven $\gamma$-ray loud blazars with available GeV variability timescales and in which the absorption effect of a $\gamma$-ray and the beaming effect have been taken into account. Our results indicate that, if we take the intrinsic $\gamma$-ray luminosity to be $\lambda$ times the Eddington luminosity, $L_{\gamma}^{in} = \lambda L_{Edd.}$, the masses of the blazars are in the range of $(4 \sim 131)\times 10^{7}M_{\odot}$, the Doppler factors ($\delta$) lie in the range of 0.57 to 5.33 the angle ($\Phi$) is in the range of $13^{\circ}$ to 43$^{\circ}$ and the distance (d) is in the range of 26R_{g} to 411R_{g}. Our model results are independent of $\gamma$-ray emission mechanisms but they do depend on the X-ray emission mechanism of the accretion disk.Comment: 14 pages, 3 tables, A&A accepte