An Optimal Control Derivation of Nonlinear Smoothing Equations

The purpose of this paper is to review and highlight some connections between the problem of nonlinear smoothing and optimal control of the Liouville equation. The latter has been an active area of recent research interest owing to work in mean-field games and optimal transportation theory. The nonlinear smoothing problem is considered here for continuous-time Markov processes. The observation process is modeled as a nonlinear function of a hidden state with an additive Gaussian measurement noise. A variational formulation is described based upon the relative entropy formula introduced by Newton and Mitter. The resulting optimal control problem is formulated on the space of probability distributions. The Hamilton's equation of the optimal control are related to the Zakai equation of nonlinear smoothing via the log transformation. The overall procedure is shown to generalize the classical Mortensen's minimum energy estimator for the linear Gaussian problem.Comment: 7 pages, 0 figures, under peer reviewin

Visible light driven photocatalysis mediated via ligand-to-metal charge transfer (LMCT): An alternative approach to solar activation of titania

Visible light harvesting or utilization through semiconductor photocatalysis is a key technology for solar chemical conversion processes. Although titania nanoparticles are popular as a base material of photocatalysis, the lack of visible light activity needs to be overcome. This mini-review is focused on an uncommon approach to visible light activation of titania: the ligand-to-metal charge transfer (LMCT) that takes place between TiO2 nanoparticles and surface adsorbates under visible light irradiation. We discuss a basic concept of photoinduced LMCT and the recent advances in LMCT-mediated visible light photocatalysis which has been applied in environmental remediation and solar energy conversion. Although the LMCT processes have been less investigated and limited in photocatalytic applications compared with other popular visible light activation methods such as impurity doping and dye sensitization, they provide lots of possibilities and flexibility in that a wide variety of organic or inorganic compounds can form surface complexes with TiO2 and introduce a new absorption band in the visible light region. The LMCT complexes may serve as a visible light sensitizer that initiates the photocatalytic conversion of various substrates or the self-degradation of the ligand complexes (usually pollutants) themselves. We summarized and discussed various LMCT photocatalytic systems and their characteristics. The LMCT-mediated activation of titania and other wide bandgap semiconductors has great potential to be developed as a more general method of solar energy utilization in photocatalytic systems. More systematic design and utilization of LMCT complexes on semiconductors are warranted to advance the solar-driven chemical conversion processes.open11144136Ysciescopu

Deep ROSAT-HRI observation of the elliptical galaxy NGC 1399

We present the preliminary results of a deep (167 ks) ROSAT HRI observation of the cD galaxy NGC1399 in the Fornax cluster. We find, in agreement with previous observations, an extended (41 Kpc adopting a distance of 19 Mpc) gaseous halo with a luminosity of L_X=(4.41\pm 0.04)x10^{41} erg/s. The 5 arcsec resolution of the data allows us to detect a very complex and asymmetric structure of the halo with respect to the optical galaxy. Moreover the analysis of the radial structure reveals the presence of a multi-component profile not consistent with a simple King model over the whole 40 Kpc. We do not detect the presence of a central source and pose an upper limit to the luminosity of a possible active nucleus. Due to the length of the observation, comparable to that of a deep survey, we detect a large number of sources within the HRI FOV, in slight excess with respect to the estimates based on previous surveys. We study the flux distribution of the sources, their temporal behaviour and their spatial distribution with respect to the central galaxy.Comment: 15 pages, 10 figures (6 in color), 1 table; uses subfigure.sty, supertabular.sty, lscape.sty, color.sty; To be published in the proceeding of "X-ray Astronomy 2000" (Mondello (Palermo), September 2000

Pion form factors with improved infrared factorization

We calculate electromagnetic pion form factors with an analytic model for $\alpha_{\rm s}(Q^2)$ which is infrared (IR) finite without invoking a ``freezing'' hypothesis. We show that for the asymptotic pion distribution amplitude, $F_{\pi ^{0}\gamma ^{*}\gamma}$ agrees well with the data, whereas the IR-enhanced hard contribution to $F_{\pi}$ and the soft (nonfactorizing) part can jointly account for the data.Comment: 12 pages; 3 figures as PS files (1 figure added); modified text; added references. To appear in Phys. Lett.