A conjectural generating function for numbers of curves on surfaces

I give a conjectural generating function for the numbers of $\delta$-nodal curves in a linear system of dimension $\delta$ on an algebraic surface. It reproduces the results of Vainsencher for the case $\delta\le 6$ and Kleiman-Piene for the case $\delta\le 8$. The numbers of curves are expressed in terms of five universal power series, three of which I give explicitly as quasimodular forms. This gives in particular the numbers of curves of arbitrary genus on a K3 surface and an abelian surface in terms of quasimodular forms, generalizing the formula of Yau-Zaslow for rational curves on K3 surfaces. The coefficients of the other two power series can be determined by comparing with the recursive formulas of Caporaso-Harris for the Severi degrees in $\P_2$. We verify the conjecture for genus 2 curves on an abelian surface. We also discuss a link of this problem with Hilbert schemes of points.Comment: amslatex 13 page

Theoretical Modelling on the Magnetization by Electric Field Through Product Property.

Multilayer composites of piezoelectric and magnetostrictive materials can be designed to exhibit the magnetoelectric (ME) effect. This ME effect can be realised as an electric polarisation induced by a magnetic field (called MEH effect) or a magnetization by an electric field (called MEE effect). Theoretical modelling of the MEE effect for 2-2 connectivity composites has been developed for three different boundary conditions for perfect coupling at the interface. The calculated MEE coefficients using material properties of piezoelectric lead zirconate titanate (PZT) and magnetostrictive Terfenol-D are a few orders of magnitude larger than those of single phase ME materials and the calculated values are compared with experimental results in the literature. Keywords: magnetoelectric, multiferroic, piezoelectric, magnetostrictive, piezomagnetic, laminated composites, modelling

Model-theoretic Approaches to Semantic Integration (Extended Abstract)

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On the Twisted N=2N=2 Superconformal Structure in 2d2d Gravity Coupled to Matter

It is shown that the two dimensional gravity, described either in the conformal gauge (the Liouville theory) or in the light cone gauge, when coupled to matter possesses an infinite number of twisted $N=2$ superconformal symmetries. The central charges of the $N=2$ algebra for the two gauge choices are in general different. Further, it is argued that the physical states in the light cone gauge theory can be obtained from the Liouville theory by a field redefinition.Comment: Plain Tex, 13 pages, IC/93/81, UG-3/9

Neutrinos with Zee-Mass Matrix in Vacuum and Matter

Neutrino mass matrix generated by the Zee (radiative) mechanism has zero (in general, small) diagonal elements and a natural hierarchy of the nondiagonal elements. It can be considered as an alternative (with strong predictive power) to the matrices generated by the see-saw mechanism. The propagation in medium of the neutrinos with the Zee-mass matrix is studied. The flavor neutrino transitions are described analytically. In the physically interesting cases the probabilities of transitions as functions of neutrino energy can be represented as two-neutrino probabilities modulated by the effect of vacuum oscillations related to the small mass splitting. Possible applications of the results to the solar, supernova, atmospheric and relic neutrinos are discussed. A set of the predictions is found which could allow to identify the Zee-mass matrix and therefore the corresponding mechanism of mass generation.Comment: 25 pages (3 figures available upon request), LaTeX, IC/94/4

Out of Equilibrium Phase Transitions and a Toy Model for Disoriented Chiral Condensates

We study the dynamics of a second order phase transition in a situation thatmimics a sudden quench to a temperature below the critical temperature in a model with dynamical symmetry breaking. In particular we show that the domains of correlated values of the condensate grow as $\sqrt{t}$ and that this result seems to be largely model independent.Comment: 17 pages, UR-1315 ER-40685-76

Status of Supersymmetric Grand Unified Theories

We begin with a brief discussion of the building blocks of supersymmetric grand unified theories. We recall some of the compelling theoretical reasons for viewing supersymmetric grand unification as an attractive avenue for physics beyond the standard model. This is followed by a discussion of some of the circumstantial evidence for these ideas.Comment: 12 pages plain LaTeX to be run twice. Invited talk at the XII DAE Symposium on High Energy Physics, Guwahati, India, Dec. 26, 1996 - Jan. 1, 199