Evans-Selberg potential on planar domains

We provide explicit formulas of Evans kernels, Evans-Selberg potentials and fundamental metrics on potential-theoretically parabolic planar domains

Suita Conjecture for a Complex Torus

The author proves that the generalized Suita conjecture holds for any complex torus, which means that $\alpha\pi K \geq c^2(\alpha\in\mathbb R)$, $c$ being the modified logarithmic capacity and $K$ being the Bergman kernel on the diagonal. The open problems for general compact Riemann surfaces with genus $\geq2$ is also elaborated. The proof relies in part on elliptic function theories.Comment: 6 pages, 3 figure

Stock market development and financial deepening in developing countries : some correlation patterns

Programs to develop securities markets are now a common feature of World Bank financial sector loans. Stock market development in particular is receiving considerable attention, especially the legal and institutional underpinnings required for successful stock market development. The financial underpinnings needed have received less study. The authors contribute to such a study by exploring the relationship between the degrees of financial depth and stock market development in an economy. Using a simple indicator of stock market development and several indicators of financial depth, and using cross-sectional data from 32 developing countries for 1984-90, they find a strong correlation between the two factors. Time-series data from 19 of these countries (for 1978-90) show similar correlations for most Asian countries, but not for other countries in the sample. Also, the correlations of the Asian data are strongest after the mid-1980s. They test a"threshold hypothesis"that a certain level of financial depth may be necessary to allow stock market development to take off. They find that available data do not support the hypothesis. The results suggest that financial depth is a significant factor in stock market development in most developing countries, but that country specific factors (such as industrial policy and structure, foreign investment controls, and stock market regulatory and operational infrastructure) have an equally strong influence on stock market growth. Case studies of economies in which stock market development has been successful would help elucidate the interplay between these factors.Economic Theory&Research,Financial Economics,Environmental Economics&Policies,Banks&Banking Reform,Statistical&Mathematical Sciences

Rank one lattice type vertex operator algebras and their automorphism groups, II: E-series

Let L be the A_1 root lattice and G a finite subgroup of Aut(V_L), where $V_L$ is the associated lattice VOA (in this case, Aut(V) is isomorphic to PSL(2,\Bbb C)). The fixed point subVOA, V^G was studied in q-alg/9710017, which finds a set of generators and determines the automorphism group when G is cyclic (from the "A-series") or dihedral (from the "D-series"). In the present article, we obtain analogous results for the remaining possibilities for G, that it belong to the "E-series": G\cong Alt_4, Alt_5 or Sym_4.Comment: Latex, 10 page