Spectral Energy Distributions of Active Galactic Nuclei from an Accretion Disk with Advective Coronal Flow

To explain the broad-band spectral energy distributions (SED) of Seyfert nuclei and QSOs, we study the emission spectrum emerging from a vertical disk-corona structure composed of a two-temperature plasma by solving hydrostatic equilibrium and radiative transfer self-consistently. Our model can nicely reproduce the soft X-ray excess with alpha (L_frequency proportional to the frequency to the power of -alpha) of about 1.5 and the hard tail extending to about 50 keV with alpha about 0.5. The different spectral slopes (alpha about 1.5 below 2 keV and about 0.5 above) are the results of different emission mechanisms: unsaturated Comptonization in the former and a combination of Comptonization, bremsstrahlung, and reflection of the coronal radiation at the disk-corona boundary in the latter.Comment: Contributed talk presented at the Joint MPE,AIP,ESO workshop on NLS1s, Bad Honnef, Dec. 1999, to appear in New Astronomy Reviews; also available at http://wave.xray.mpe.mpg.de/conferences/nls1-worksho

Point counting on reductions of CM elliptic curves

We give explicit formulas for the number of points on reductions of elliptic curves with complex multiplication by any imaginary quadratic field. We also find models for CM $\mathbf{Q}$-curves in certain cases. This generalizes earlier results of Gross, Stark, and others.Comment: Minor corrections. To appear in Journal of Number Theor

The Shimura-Taniyama Conjecture and Conformal Field Theory

The Shimura-Taniyama conjecture states that the Mellin transform of the Hasse-Weil L-function of any elliptic curve defined over the rational numbers is a modular form. Recent work of Wiles, Taylor-Wiles and Breuil-Conrad-Diamond-Taylor has provided a proof of this longstanding conjecture. Elliptic curves provide the simplest framework for a class of Calabi-Yau manifolds which have been conjectured to be exactly solvable. It is shown that the Hasse-Weil modular form determined by the arithmetic structure of the Fermat type elliptic curve is related in a natural way to a modular form arising from the character of a conformal field theory derived from an affine Kac-Moody algebra

Complex Multiplication Symmetry of Black Hole Attractors

We show how Moore's observation, in the context of toroidal compactifications in type IIB string theory, concerning the complex multiplication structure of black hole attractor varieties, can be generalized to Calabi-Yau compactifications with finite fundamental groups. This generalization leads to an alternative general framework in terms of motives associated to a Calabi-Yau variety in which it is possible to address the arithmetic nature of the attractor varieties in a universal way via Deligne's period conjecture.Comment: 28 page

Solar cells of metal-free phthalocyanine dispersed in polyvinyl carbazole. 1: Effects of the recrystallization of H2PC on cell characteristics

The development of an organic semiconductor solar cell and the effects of the recrystallization of metal free phthalocyanine (H2PC) on the characteristics of NESA/H2PC-PVK/Au sandwich cells were investigated. Alfa-H2PC sandwich cells showed photovoltage and photocurrent in a two direction opposite to that shown y as supplied H2PC cells, which consists mainly of beta-H2PC. Some difference was observed in the response times of the two cells. It is suggested that photocharacteristics change with the specific resistance of the H2PC, which is related to its crystal forms. In the cells with low resistance H2PC carriers are generated in H2PC by illumination, while in high resistance H2PC cells, carriers are generated in PVK which is sensitized with H2PC

Design requirements for group-IV laser based on fully strained Ge1-xSnx embedded in partially relaxed Si1-y-zGeySnz buffer layers

Theoretical calculation using the model solid theory is performed to design the stack of a group-IV laser based on a fully strained Ge1-xSnx active layer grown on a strain relaxed Si1-y-zGeySnz buffer/barrier layer. The degree of strain relaxation is taken into account for the calculation for the first time. The transition between the indirect and the direct band material for the active Ge1-xSnx layer is calculated as function of Sn content and strain. The required Sn content in the buffer layer needed to apply the required strain in the active layer in order to obtain a direct bandgap material is calculated. Besides, the band offset between the (partly) strain relaxed Si1-y-zGeySnz buffer layer and the Ge1-xSnx pseudomorphically grown on it is calculated. We conclude that an 80% relaxed buffer layer needs to contain 13.8% Si and 14% Sn in order to provide sufficiently high band offsets with respect to the active Ge1-xSnx layer which contains at least 6% Sn in order to obtain a direct bandgap

Tate twists of Hodge structures arising from abelian varieties of type IV

We show that certain abelian varieties A have the property that for every Hodge structure V in the cohomology of A, every effective Tate twist of V occurs in the cohomology of some abelian variety. We deduce the general Hodge conjecture for certain non-simple abelian varieties of type IV

Hilbert modular forms of weight 1/2 and theta functions

Serre and Stark found a basis for the space of modular forms of weight 1/2 in terms of theta series. In this paper, we generalize their result - under certain mild restrictions on the level and character - to the case of weight 1/2 Hilbert modular forms over a totally real field of narrow class number 1. The methods broadly follow those of Serre-Stark; however we are forced to overcome technical difficulties which arise when we move out of Q.Comment: 23 page

Complex multiplication, rationality and mirror symmetry for abelian varieties

We show that complex multiplication on abelian varieties is equivalent to the existence of a constant rational K\"ahler metric. We give a sufficient condition for a mirror of an abelian variety of CM-type to be of CM-type as well. We also study the relationship between complex multiplication and rationality of a toroidal lattice vertex algebra.Comment: 22 pages, introduction and exposition of results rewritten, references adde