efficient tests for top down termination of logical rules considered is the question of whether top down prolog like evaluation of a set of logical rules can be guaranteed to terminate the nail system is designed to process programs consisting of logical rules and to select for each fragment of the program the best from among many possible strategies for its evaluation in the context of such a system it is essential that termination tests be fast thus the uniqueness property of logical rules is introduced this property is satisfied by many of the common examples of rules and is easily recognized for rules with this property a set of inequalities whose satisfaction is sufficient for termination of the rules can be generated in polynomial time then a polynomial test for satisfaction of constraints generated by this process is given

modular forms of weight 8 for γg 1 2 we complete the program indicated by the ansatz of d hoker and phong in genus 4 by proving the uniqueness of the restriction to jacobians of the weight 8 siegel cusp forms satisfying the ansatz we prove dim 4 1 2 8 0 2 and dim 4 1 2 8 7 in each genus we classify the linear relations among the self dual lattices of rank 16 we extend the program to genus 5 by constructing the unique linear combination of theta series that satisfies the ansatz

analytic fields on riemann surfaces ii the properties of analytic fields on a riemann surface represented by a branch covering of 1 are investigated in detail branch points are shown to correspond to the vertex operators with simple conformal properties as applications we compute determinants of bar partial j operators forzn symmetric surfaces and obtain various representations for the two loop measure in the bosonic string theory together with various identities for theta functions of hyperelliptic surfaces we also present an integral representation for the quantum part of the twist field correlation functions which describe propagation of the string on the orbifold background we also calculate the quantum part of the structure constants of the twist field operator algebra generalizing the results of dixon friedan martinec and shenker

superstring scattering amplitudes in higher genus in this paper we continue the program pioneered by d hoker and phong and recently advanced by cacciatori dalla piazza and van geemen of finding the chiral superstring measure by constructing modular forms satisfying certain factorization constraints we give new expressions for their proposed ansatze in genera 2 and 3 respectively which admit a straightforward generalization we then propose an ansatz in genus 4 and verify that it satisfies the factorization constraints and gives a vanishing cosmological constant we further conjecture a possible formula for the superstring amplitudes in any genus subject to the condition that certain modular forms admit holomorphic roots

partiallyu 1 compactified scalar massless field on the compact riemann surface and the bosonic string amplitudes the theory of the partiallyu 1 compactified scalar massless field on the compact riemann surface with nambu goto action is defined the partition function is determined completely by a choice of the finite dimensional approximations the correlation functions are the only correctly defined objects of the theory the averages of the correlation function asymptotic values provide the amplitudes for the compact riemann surfaces of any genus the usual bosonic string amplitudes are the special cases of the above amplitudes

superconformal geometry and string theory we give a formula for the determinant of the super laplace operator in a holomorphic hermitian line bundle over a superconformal manifold this is then used to obtain an expression for the fermion string measure

a quantum group structure in integrable conformal field theories we discuss a quantization prescription of the conformal algebras of a class ofd 2 conformal field theories which are integrable we first give a geometrical construction of certain extensions of the classical virasoro algebra known as classicalw algebras in which these algebras arise as the lie algebra of the second hamiltonian structure of a generalized korteweg de vries hierarchy this fact implies that thew algebras obtained as a reduction with respect to the nilpotent subalgebras of the kac moody algebra describe the integrability of a toda field theory subsequently we determine the coadjoint operators of thew algebras and relate these to classical yang baxter matrices the quantization of these algebras can be carried out using the concept of a so called quantum group we derive the condition under which the representations of these quantum groups admit a hilbert space completion by exploring the relation with the braid group then we consider a modification of the miura transformation which we use to define a quantumw algebra this leads to an alternative interpretation of the coset construction for kac moody algebras in terms of nonlinear integrable hierarchies subsequently we use the connection between the induced braid group representations and the representations of the mapping class group of riemann surfaces to identify an action of thew algebras on the moduli space of stable curves and we give the invariants of this action this provides a generalization of the situation for the virasoro algebra where such as invariant is given by the so called mumford form which describes the partition function of the bosonic string

summations over equilaterally triangulated surfaces and the critical string measure we propose a new approach to the summation over dynamically triangulated riemann surfaces which does not rely on properties of the potential in a matrix model instead we formulate a purely algebraic discretization of critical string path integral this is combined with a technique which assigns to each equilateral triangulation of a two dimensional surface a riemann surface defined over a certain finite extension of the field of rational numbers i e an arthmetic surface thus we establish a new formulation in which the sum over randomly triangulated surfaces defines an invariant measure on the moduli space of arithmetic surfaces it is shown that because of this it is far from obvious that this measure for large genera approximates the measure defined by the continuum theory i e liouville theory or critical string theory in low genus this subtlety does not exist in the case of critical string theory we explicity compute the volume of the moduli space of arithmetic surfaces in terms of the modular height function and show that for low genus it approximates correctly the continuum measure we also discuss a continuum limit which bears some resemblance with a double scaling limit in matrix models

temporal stratification tests for linear and branching time deductive databases we consider the problem of extending temporal deductive databases with stratified negation we argue that the classical stratification test for deductive databases is too restrictive when one shifts attention to the temporal case moreover as we demonstrate the more general local stratification approach is impractical detecting whether a temporal deductive database is locally stratified is shown to be co np hard even if one restricts attention to programs that only use one predicate symbol and two constants for these reasons we define temporal stratification an intermediate notion between stratification and local stratification we demonstrate that for the temporal deductive databases we consider temporal stratification coincides with local stratification in certain important cases in which the latter is polynomial time decidable we then develop two algorithms for detecting temporal stratification the first algorithm applies to linear time temporal deductive databases and it is efficient and more general than existing approaches however the algorithm sacrifices completeness for efficiency since it does not cover the whole class of temporally stratified programs the second algorithm applies to branching time temporal deductive databases which include as a special case the linear time ones this algorithm is more expensive from a computational point of view but it covers the whole class of temporally stratified programs we discuss the relative merits of the two algorithms and compare them with other existing approaches

extremals of determinants of laplacians on etudie le determinant associe au laplacien en fonction de la metrique sur une surface donnee et en particulier ses valeurs extremes quand la metrique est bien restreinte

meromorphic vector fields with single valued solutions on complex surfaces abstract we study ordinary differential equations in the complex domain given by meromorphic vector fields on compact complex kahler surfaces we prove that if such an equation has a maximal single valued solution in particular an entire one whose image is not contained in a proper analytic subset then up to a bimeromorphic transformation either the vector field is holomorphic or it preserves a fibration

new bosonization and conformal field theory over z new formulation of bosonization is given so that it is defined over the ring z of integers the charge zero sector of the new boson fock space is the completion of the coordinate ring of the universal witt scheme by using new bosonization conformal field theory of free fermions over z is given

special values of canonical green s functions we give a precise formula for the value of the canonical green s function at a pair of weierstrass points on a hyperelliptic riemann surface further we express the energy of the weierstrass points in terms of a spectral invariant recently introduced by n kawazumi and s zhang it follows that the energy is strictly larger than log 2 our results generalize known formulas for elliptic curves

calculus on arithmetic surfaces in a2 and a3 arakelov introduces an intersection calculus for arithmetic surfaces that is for stable models of curves over a number field in this paper we intend to show that his intersection product has a lot of useful properties more precisely we show that the following properties from the theory of algebraic surfaces have an analogue in our situation

testing logic programs for local stratification abstract locally stratified programs are a significant class of logic programs with negation for which both declarative and fixpoint semantics are well defined unfortunately in most cases recognizing local stratification is so hard a task that it has been conjectured that the problem is undecidable indeed in this paper a formal proof of this undecidability is presented and rather general sufficient conditions for local stratification are introduced

the mumford form and the polyakov measure in string theory an explicit formula is derived for the mumford form on the moduli space of algebraic curves according to the belavin knizhnik theorem this gives a formula for the polyakov bosonic string measure

automorphism group of k t applications to the bosonic string this paper is concerned with the formulation of a non pertubative theory of the bosonic string we introduce a formal group g which we propose as the universal moduli space for such a formulation this is motivated because g establishes a natural link between representations of the virasoro algebra and the moduli space of curves

a geometric approach to the path integral formalism of p branes the configuration space for a path integral description of a p brane is seen as a vector bundle over moduli spaces the einstein condition applied to such vector bundles over compact kahler manifolds provides the required stability conditions consequently moduli spaces for such extended objects of higher dimensionality are constructed finally a hermitian metric can be introduced in these moduli spaces

the analysis of elliptic families i metrics and connections on determinant bundles in this paper we construct the quillen metric on the determinant bundle associated with a family of elliptic first order differential operators we also introduce a unitary connection on and calculate its curvature our results will be applied to the case of dirac operators in a forthcoming paper

the analysis of elliptic families ii dirac operators eta invariants and the holonomy theorem in this paper we specialize the results obtained in bf1 to the case of a family of dirac operators we first calculate the curvature of the unitary connection on the determinant bundle which we introduced in bf1

geometric realization of conformal field theory on riemann surfaces conformal field theory on a family of riemann surfaces is formulated we derive equations of motion of vacua which are parametrized by moduli of riemann surfaces and show that these vacua are characterized uniquely by these equations our theory has a deep connection with sato s theory of kp equations

linear dependence among siegel modular forms theorems are given which describe when high enough vanishing at the cusps implies that a siegel modular cusp form is zero formerly impractical computations become practical and examples are given in degree four vanishing order is described by kernels a type of polyhedral convex hull

binary forms and the hyperelliptic superstring ansatz we give a hyperelliptic formulation of the ansatz of d hoker and phong we give an explicit family of binary invariants one for each genus that satisfies this hyperelliptic ansatz we also prove that this is the unique family of weight eight binary forms over the theta group on the hyperelliptic locus that satisfies this ansatz furthermore we prove that this solution may also be obtained by applying thomae s map to multivalued siegel modular forms of grushevsky and making certain choices of roots

the superstring cosmological constant and the schottky form in genus 5 combining certain identities for modular forms due to igusa with schottky jung relations we study the cosmological constant for the recently proposed ansatz for the chiral superstring measure in genus 5 the vanishing of this cosmological constant turns out to be equivalent to the long conjectured vanishing of a certain explicit modular form of genus 5 on the moduli of curves m5 and we disprove this conjecture thus showing that the cosmological constant for the proposed ansatz does not vanish identically we exhibit an easy modification of the genus 5 ansatz satisfying factorization constraints and yielding a vanishing cosmological constant we also give an expression for the cosmological constant for the proposed ansatz that should hold for any genus if certain generalized schottky jung identities hold

non archimedean strings and bruhat tits trees it is shown that the bruhat tits tree for thep adic linear groupgl 2 is a natural non archimedean analog of the open string world sheet the boundary of the tree can be identified with the field ofp adic numbers we construct a lattice quantum field theory on the bruhat tits tree with a simple local lagrangian and show that it leads to the freund olson amplitudes for emission processes of the particle states from the boundary

on determinants of laplacians on riemann surfaces determinants of laplacians on tensors and spinors of arbitrary weights on compact hyperbolic riemann surfaces are computed in terms of values of selberg zeta functions at half integer points