This paper is devoted to wavelet analysis on adele ring $bA$ and the theory of pseudo-differential operators. We develop the technique which gives the possibility to generalize finite-dimensional results of wavelet analysis to the case of adeles $bA$
by using infinite tensor products of Hilbert spaces. The adele ring is roughly speaking a subring of the direct product of all possible ($p$-adic and Archimedean) completions $bQ_p$ of the field of rational numbers $bQ$ with some conditions at infinity. Using our technique, we prove that $L^2(bA)=otimes_{e,pin{infty,2,3,5,...}}L^2({bQ}_{p})$ is the infinite tensor product of the spaces $L^2({bQ}_{p})$ with a stabilization $e=(e_p)_p$, where $e_p(x)=Omega(|x|_p)in L^2({bQ}_{p})$, and $Omega$ is a characteristic function of the unit interval $[0,,1]$, $bQ_p$ is the field of $p$-adic numbers, $p=2,3,5,...$; $bQ_infty=bR$. This description allows us to construct an infinite family of Haar wavelet bases on $L^2(bA)$ which can be obtained by shifts and multi-delations. The adelic multiresolution analysis (MRA) in $L^2(bA)$ is also constructed. In the framework of this MRA another infinite family of Haar wavelet bases is constructed. We introduce the adelic Lizorkin spaces of test functions and distributions and give the characterization of these spaces in terms of wavelet functions. One class of pseudo-differential operators (including the fractional operator) is studied on the Lizorkin spaces. A criterion for an adelic wavelet function to be an eigenfunction for a pseudo-differential operator is derived. We prove that any wavelet function is an eigenfunction of the fractional operator. These results allow one to create the necessary prerequisites for intensive using of adelic wavelet bases and pseudo-differential operators in applications.
We consider correlation properties of twophoton polarization states in the parametric down-conversion process. In our description of polarization states we take into account the simultaneous presence of colored and white noise in the density matrix.
Within the considered model we study the dependence of the von Neumann entropy on the noise amount in the system and derive the separability condition for the density matrix of twophoton polarization state, using Perec-Horodecki criterion and majorization criterion. Then the dependence of the Bell operator (in CHSH form) on noise is studied. As a result, we give a condition for determining the presence of quantum correlation states in experimental measurements of the Bell operator. Finally, we compare our calculations with experimental data [doi:10.1103/PhysRevA.73.062110] and give a noise amount estimation in the photon polarization state considered there.
We present photometric and spectroscopic observations of two luminous blue variable (LBV) stars in two extremely metal-deficient blue compact dwarf (BCD) galaxies, DDO 68 with 12+logO/H = 7.15 and PHL 293B with 12+logO/H = 7.72. These two BCDs are th
e lowest-metallicity galaxies where LBV stars have been detected, allowing to study the LBV phenomenon in the extremely low metallicity regime, and shedding light of the evolution of the first generation of massive stars born from primordial gas. We find that the strong outburst of the LBV star in DDO 68 occurred sometime between February 2007 and January 2008. We have compared the properties of the broad line emission in low-metallicity LBVs with those in higher metallicity LBVs. We find that, for the LBV star in DDO 68, broad emission with a P Cygni profile is seen in both H and He I emission lines. On the other hand, for the LBV star in PHL 293B, P Cygni profiles are detected only in H lines. For both LBVs, no heavy element emission line such as Fe II was detected. The Halpha luminosities of LBV stars in both galaxies are comparable to the one obtained for the LBV star in NGC 2363 (Mrk 71) which has a higher metallicity 12+logO/H = 7.89. On the other hand, the terminal velocities of the stellar winds in both low-metallicity LBVs are high, ~800 km/s, a factor of ~4 higher than the terminal velocities of the winds in high-metallicity LBVs. This suggests that stellar winds at low metallicity are driven by a different mechanism than the one operating in high-metallicity winds.
We propose a model for isotropization and corresponding thermalization in a nucleon system created in the collision of two nuclei. The model is based on the assumption: during the fireball evolution, two-particle elastic and inelastic collisions give
rise to the randomization of the nucleon-momentum transfer which is driven by a proper distribution. As a first approximation, we assume a homogeneous distribution where the values of the momentum transfer is bounded from above. These features have been shown to result in a smearing of the particle momenta about their initial values and, as a consequence, in their partial isotropization and thermalization. The nonequilibrium single-particle distribution function and single-particle spectrum which carry a memory about initial state of nuclei have been obtained.
We present 3.5m Apache Point Observatory second-epoch spectra of four low-metallicity emission-line dwarf galaxies discovered serendipitously in the Data Release 5 of the Sloan Digital Sky Survey (SDSS) to have extraordinary large broad Halpha lumino
sities, ranging from 3x10^41 to 2x10^42 erg/s. The oxygen abundance in these galaxies is very low, varying in the range 12+logO/H = 7.36- 7.99. Such extraordinarily high broad Halpha luminosities cannot be accounted for by massive stars at different stages of their evolution. By comparing with the first-epoch SDSS spectra, we find that the broad Halpha luminosities have remained constant over a period of 3-7 years, which probably excludes type IIn supernovae as a possible mechanism of broad emission. The emission most likely comes from accretion disks around intermediate-mass black holes with lower mass limits in the range ~5x10^5 Msun-3x10^6 Msun. If so, these four objects form a new class of very low-metallicity AGN that have been elusive until now. The absence of the strong high-ionization lines [NeV] 3426 and He II 4686 can be understood if the nonthermal radiation contributes less than ~10% of the total ionizing radiation.
The robustness of Bells inequality (in CHSH form) violation by entangled state in the simultaneous presence of colored and white noise in the system is considered. A twophoton polarization state is modeled by twoparameter density matrix. Setting para
meter values one can vary the relative fraction of pure entangled Bells state as well as white and colored noise fractions. Bells operator-parameter dependence analysis is made. Computational results are compared with experimental data [quant-ph/0511265] and with results computed using a oneparameter density matrix [doi: 10.1103/PhysRevA.72.052112], which one can get as a special case of the model considered in this work.
The partition function of nonequilibrium distribution which we recently obtained [arXiv:0802.0259] in the framework of the maximum isotropization model (MIM) is exploited to extract physical information from experimental data on the proton rapidity a
nd transverse mass distributions. We propose to partition all interacting nucleons into ensembles in accordance with the number of collisions. We analyze experimental rapidity distribution and get the number of particles in every collision ensemble. We argue that even a large number of effective nucleon collisions cannot lead to thermalization of nucleon system; the thermal source which describes the proton distribution in central rapidity region arises as a result of fast thermalization of the parton degrees of freedom. The obtained number of nucleons which corresponds to the thermal contribution is treated as a ``nucleon power of the created quark-gluon plasma in a particular experiment.
We present 6.5-meter MMT spectrophotometry of 20 H II regions in 13 extremely metal-poor emission-line galaxies selected from the Data Release 5 of the Sloan Digital Sky Survey to have [O III] 4959/Hbeta < 1 and [N II] 6583/Hbeta < 0.05. The electron
temperature-sensitive emission line [O III] 4363 is detected in 13 H II regions allowing a direct abundance determination. The oxygen abundance in the remaining H II regions is derived using a semi-empirical method. The oxygen abundance of the galaxies in our sample ranges from 12+logO/H ~ 7.1 to ~ 7.8, with 10 H II regions having an oxygen abundance lower than 7.5. The lowest oxygen abundances, 12+logO/H = 7.14+/-0.03 and 7.13+/-0.07, are found in two H II regions of the blue compact dwarf galaxy SDSSJ0956+2849=DDO 68, making it the second most-metal deficient emission-line galaxy known, after SBS 0335-052W.
