combinatorial decompositions of a class of rings in this paper we introduce some combinatorial methods for the study of graded rings and use these methods to analyze a class of rings that are of importance in combinatorics our methods are based on a unique representation theorem which is shown section 2 to hold for any graded algebra and which in a sense is an extension of the direct sum decomposition for cohen macaulay algebras this unique representation is reminiscent of a similar result obtained by rees 20 both results yield a decomposition of the algebra however our result differs from that of rees in that it carries more information about the algebra our main results are concerned with a class of rings see section 3 for the definition associated to simplicial complexes there are several natural operations that can be performed on simplicial complexes to obtain new complexes which in turn have an interpretation for the corresponding rings we show sections 4 5 and 6 that our basic decompositions can be transferred during these operations from the original rings to the newly constructed ones the operations studied here are the chain transform or barycentric subdivision section 4 rank selection both for partially ordered sets and for simplicial complexes section s and localization section 6 as we develop these tools we give some applications in section 5 we give a new topological characterization of the cohen macaulay property for partially ordered sets an immediate consequence of which is the rankselection theorem baclawski 2 this characterization is closely related to those obtained by garsia in 14

castelnuovo mumford regularity of simplicial toric rings abstract bounds for the castelnuovo mumford regularity of simplicial toric rings are given which are close to the bound stated in eisenbud goto s conjecture

zeros of eisenstein series quadratic class numbers and supersingularity for rational function fields the support of the divisor of certain eisenstein series on the modular curve for gl 2 fq t generate a big extension of fq t from this an upper bound for the number of supersingular primes of a xed degree for a given drinfeld module can be deduced in the course of the proof 2 power divisibility of the class number of certain hyperelliptic extensions of fq t is studied

noether resolutions in dimension 2 let r k x 1 ldots x n be a polynomial ring over an infinite field k and let i subset r be a homogeneous ideal with respectto a weight vector omega omega 1 ldots omega n in mathbb z n such that dim r i d in this paper we study the minimal graded free resolution of r i as a module that we call the noether resolution of r i whenever a k x n d 1 ldots x n is a noether normalization of r i when d 2 and i is saturated we give an algorithm for obtaining this resolution that involves the computation of a minimalgr obner basis of i with respect to the weighted degree reverse lexicographic order in the particular case when r i is a 2 dimensional semigroup ring we also describe the multigraded version of this resolution in terms of the underlying semigroup whenever we have the noether resolution of r i or its multigraded version we obtain formulas for the corresponding hilbert series of r i and when i is homogeneous we obtain a formula for the castelnuovo mumford regularity of r i moreover in the more general setting that r i is a simplicial semigroup ring of any dimension we provide its macaulayfication as an application of the results for 2 dimensional semigroup rings we provide a new upper bound for the castelnuovo mumford regularity of the coordinate ring of a projective monomial curve finally we describe the multigraded noether resolution and the macaulayfication of either the coordinate ring of a projective monomial curve mathcal c l subseteq mathbb p k n associated to an arithmetic sequence or the coordinate ring of any canonical projection pi r mathcal c of mathcal c to mathbb p k n 1

kronecker limit formula over global function fields the aim of this paper is to present a function field analogue of the classical kronecker limit formula we first introduce a non holomorphic eisenstein series on the drinfeld half plane and connect its second term with gekeler s discriminant function one application is to express the taguchi height of rank 2 drinfeld modules with complex multiplication in terms of the logarithmic derivative of the corresponding zeta functions moreover from the integral form of the rankin type l function associated to two drinfeld type newforms we then derive a formula for a non central special derivative of the l function in question adapting the classical approach we also obtain a kronecker type solution for pell s equation over function fields

corrigendum to affine semigroups and cohen macaulay rings generated by monomials trans amer math soc 298 1986 no 1 145 167 mr0857437 87j 13032

a generalized mazur s theorem and its applications we generalize a theorem of mazur concerning the universal norms of an abelian variety over a d p extension of a complete local field then we apply it to the proof of a control theorem for abelian varieties over global function fields

abelian subvarieties of drinfeld jacobians and congruences modulo the characteristic we relate the existence of frobenius morphisms into the jacobians of drinfeld modular curves to the existence of congruences between cusp forms

design of experiments for eigenvalue identification in distributed parameter systems the problem of optimal design of experiments for identification of distributed systems described by a linear parabolic partial differential equation is considered conditions of an experiment which consists of the spectral density of a stochastic input signal and a probability measure corresponding to positions of sensors are chosen such as to maximize the accuracy of a finite number of the system s eigenvalue estimates conditions for optimality of the experiment design are derived in particular it is shown that the optimal input consists of a finite number sinusoids and optimal positions of the sensors can be found analytically in some eases application of the results is illustrated in case of a vibrating system

optimal measurement trajectories for distributed parameter systems abstract the paper deals with the optimal sensor location problem associated with minimax filtering for linear distributed parameter systems under the moving sensors the problem of optimal choice of a measurement trajectory is treated here as an h optimal control one under phase constraints with the objective to minimize a given weak performance index under worst possible disturbances existence of a solution to such a problem is established for the case of quadratic constraints on the disturbances and necessary conditions for optimally are derived on the basis of constructing a sequence of suboptimal solutions associated in turn with a sequence of finite dimensional maximum principles

proof of an exceptional zero conjecture for elliptic curves over function fields based on the analogy between number fields and function fields of one variable over finite fields we formulate and prove an analogue of the exceptional zero conjecture of mazur tate and teitelbaum for elliptic curves defined over function fields the proof uses modular parametrization by drinfeld modular curves and the theory of non archimedean integration as an application we prove a refinement of the birch swinnerton dyer conjecture if the analytic rank of the elliptic curve is zero

diagonal subalgebras of bigraded algebras and embeddings of blow ups of projective spaces let v be closed subscheme of inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 01i defined by a homogeneous ideal i a k x 1 x n and let x be the n 1 fold obtained by blowing up inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 02i along v if one embeds x in some projective space one is led to consider the subalgebra k i e c of a for some positive integers c and e the aim of this paper is to study ring theoretic properties of k i e c this is achieved by developing a theory which enables us to describe the local cohomology of certain modules over generalized segre products of bigraded algebras these results are applied to the study of the cohen macaulay property of the homogeneous coordinate ring of the blow up of the projective space along a complete intersection we also study the koszul property of diagonal subalgebras of bigraded standard k algebras

analogue of the degree conjecture over function fields under a certain assumption similar to manin s conjecture we prove an upper bound on the degree of modular parametrizations of elliptic curves by drinfeld modular curves which is the function field analogue of the conjectured bound over the rational numbers

continuous observability for parabolic system under observations of discrete type for the linear partial differential equation of parabolic type the problem of continuous observability under observations of discrete type received from the moving or stationary sensors is considered the techniques exploit the knowledge about observability of an associated system with observations that are continuous in time on the basis of sensitivity points of the latter a method of constructing discrete observations that preserve the property of continuous observability at final time is developed

green s functions on mumford curves we study an analogue of a green s function on mumford curves the meromorphic continuation of this green s function comes from a differential equation and we interpret the special value at s 0 as a volume of the corresponding curve using harmonic analysis on bruhat tits trees we derive a kronecker limit formula for the green s functions in question which connects the derivative at s 0 with the manin drinfeld theta functions following gross description of neron s local height pairing on mumford curves the special derivative here then equals twice of the neron s local height with sign changed

elliptic points of the drinfeld modular groups let k be an algebraic function field with constant field mathbb f q fix a place infty of k of degree delta and let a be the ring of elements of k that are integral outside infty we give an explicit description of the elliptic points for the action of the drinfeld modular group g gl 2 a on the drinfeld s upper half plane omega and on the drinfeld modular curve g setminus omega it is known that under the building map elliptic points are mapped onto vertices of the bruhat tits tree of g we show how such vertices can be determined by a simple condition on their stabilizers finally for the special case delta 1 we obtain from this a surprising free product decomposition for pgl 2 a

finite generation of rings of differential operators of semigroup algebras we prove that the ring of differential operators of any semigroup algebra is finitely generated in contrast we also show that the graded ring of the order filtration on the ring of differential operators of a semigroup algebra is finitely generated if and only if the semigroup is scored

on metaplectic forms over function fields we propose a concept of half integral weight in the global function field context and construct natural families of functions with given weight an analogue of shimura correspondence between weight 2 functions and weight frac 3 2 functions via theta series from definite quaternion algebras over function fields is then established from the study of fourier coefficients of these theta series we arrive at a waldspurger type formula this formula is then applied to l series coming from elliptic curves over function fields

a combinatorial li yau inequality and rational points on curves we present a method to control gonality of nonarchimedean curves based on graph theory let k denote a complete nonarchimedean valued field we first prove a lower bound for the gonality of a curve over the algebraic closure of k in terms of the minimal degree of a class of graph maps namely one should minimize over all so called finite harmonic graph morphisms to trees that originate from any refinement of the dual graph of the stable model of the curve next comes our main result we prove a lower bound for the degree of such a graph morphism in terms of the first eigenvalue of the laplacian and some volume of the original graph this can be seen as a substitute for graphs of the li yau inequality from differential geometry although we also prove that the strict analogue of the original inequality fails for general graphs finally we apply the results to give a lower bound for the gonality of arbitrary drinfeld modular curves over finite fields and for general congruence subgroups vargamma of vargamma 1 that is linear in the index vargamma 1 vargamma with a constant that only depends on the residue field degree and the degree of the chosen infinite place this is a function field analogue of a theorem of abramovich for classical modular curves we present applications to uniform boundedness of torsion of rank two drinfeld modules that improve upon existing results and to lower bounds on the modular degree of certain elliptic curves over function fields that solve a problem of papikian

on the uniform boundedness conjecture for drinfeld modules in analogy with the famous theorems of mazur and merel on the torsion subgroups of elliptic curves one can formulate similar conjectures for the torsion points of drinfeld modules we prove some partial results for rank 2 drinfeld q t modules for example the uniform boundedness of the primary torsion

on seminormal monoid rings given a seminormal affine monoid m we consider several monoid properties of m and their connections to ring properties of the associated affine monoid ring k m over a field k we characterize when k m satisfies serre s condition s2 and analyze the local cohomology of k m a s an application we present criteria which imply that k m is cohen macaulay and we give lower bounds for the depth of k m finally the seminormality of an arbitrary affine monoid m is studied with characteristic p methods

the a hypergeometric system associated with a monomial curve introduction inthis paper we make a detailed analysis of the hypergeometric system or gkz system associated with a monomial curve and integral hence resonant exponents we describe all rational solutions and show in theorem 1 10 that they are in fact laurent polynomials we also show that for any exponent there are at most two linearly independent laurent solutions and that the upper bound is reached if and only if the curve is not arithmetically cohen macaulay we then construct for all integral parameters a basis of local solutions in terms of the roots of the generic univariate polynomial 0 5 associated with we also determine in theorem 3 7 the holonomic rank r for all z 2 and show that d r d 1 where d is the degree of the curve moreover the value d 1 is attained only for those exponents for which there are two linearly independent rational solutions and therefore r d for all if and only if the curve is arithmetically cohen macaulay inorder to place these results intheir appropriate con text we recall the defin ition

toric singularities revisited abstract in k kato toric singularities amer j math 116 5 1994 1073 1099 kato defined his notion of a log regular scheme and studied the local behavior of such schemes a toric variety equipped with its canonical logarithmic structure is log regular and these schemes allow one to generalize toric geometry to a theory that does not require a base field this paper will extend this theory by removing normality requirements

on rankin triple product l functions over function fields central critical values the aim of this article is to study the special values of rankin triple product l functions associated to drinfeld type newforms of equal square free levels the functional equation of these l functions is deduced from a garrett type integral representation and the functional equation of eisenstein series on the group of similitudes of a symplectic vector space of dimension 6 when the associated root number is positive we present a function field analogue of gross kudla formula for the central critical value this formula is then applied to the non vanishing of l functions coming from elliptic curves over function fields

local cohomology of modules of covariants abstract let g be a connected reductive algebraic group over an algebraically closed field of characteristic zero and let w u be two finite dimensional representations of g in this paper we compute the local cohomology of u sw g provided a certain relatively weak technical condition is true

development of objective oriented groundwater models 2 robust experimental design 1 this paper continues the discussion in part 1 by considering the data collection strategy problem when the existing data are judged to be insufficient for constructing a reliable model designing an experiment for identifying a distributed parameter is very difficult because the identification of a more complex parameter structure requires more data moreover without knowing the sufficiency of a design finding an optimal design becomes meaningless these difficulties can be avoided if we turn to the construction of objective oriented models the identifiability of a distributed parameter as defined in this paper contains the reducibility of parameter structure sufficient conditions for this kind of identifiability are given when the structure error associated with a structure reduction is too large these conditions may not be satisfied no matter how much data are collected in this paper we formulate a new experimental design problem that consists of two objectives minimizing the cost and maximizing the information content with robustness and feasibility as constraints we develop an algorithm that can find a cost effective robust design for objective oriented parameter identification we also present a heuristic algorithm that can find a suboptimal design with less computational effort for real case studies the proposed methodology is used to design a pumping test for identifying a distributed hydraulic conductivity we verify the robustness of the obtained design by assuming that the true parameter may have continuous discrete random and fractured structures finally the presented procedure of constructing objective oriented models is described step by step

syzygies of affine toric varieties we give a method for computing the syzygies of the coordinate ring r of an affine toric variety we show how the method works for dimension one and two cases cohen macaulay semigroups and for computing minimal generators of the defining ideal we show how to compute the depth of r and generalize a criterion for cohen macaulayness

castelnuovo mumford regularity of seminormal simplicial affine semigroup rings abstract we show that the eisenbud goto conjecture holds for homogeneous seminormal simplicial affine semigroup rings moreover we prove an upper bound for the castelnuovo mumford regularity in terms of the dimension which is similar as in the normal case finally we compute explicitly the regularity of full veronese rings

on kronecker terms over global function fields we establish a general kronecker limit formula of arbitrary rank over global function fields with drinfeld period domains playing the role of upper half plane the drinfeld siegel units come up as equal characteristic modular forms replacing the classical delta this leads to analytic means of deriving a colmez type formula for stable taguchi height of cm drinfeld modules having arbitrary rank a lerch type formula for totally real function fields is also obtained with the heegner cycle on the bruhat tits buildings intervene also our limit formula is naturally applied to the special values of both the rankin selberg l functions and the godement jacquet l functions associated to automorphic cuspidal representations over global function fields

optimum choice of moving sensor trajectories for distributed parameter system identification the problem is considered of the optimal choice of moving sensor trajectories from the viewpoint of distributed parameter system identification accuracy the determinant of the information matrix of parameter estimates is taken as a measure of identification accuracy necessary and sufficient conditions for the trajectories to be optimal are derived it is shown that the optimum trajectories can be found by solving a sequence of optimal sensor allocation problems a number of examples illustrates the proposed approach

une base explicite de symboles modulaires sur les corps de fonctions modular symbols for the congruence subgroup gamma 0 mathfrak n of gl 2 mathbf f q t have been defined by teitelbaum they have a presentation given by a finite number of generators and relations in a formalism similar to manin s for classical modular symbols we completely solve the relations and get an explicit basis of generators when mathfrak n is a prime ideal of odd degree as an application we give a non vanishing statement for l functions of certain automorphic cusp forms for mathbf f q t the main statement also provides a key step for a result towards the uniform boundedness conjecture for drinfeld modules of rank 2

defining ideals of affine semigroup rings of codimension 2 let s be an affine semigroup i e a finitely generated submonoid of the additive monoid n where n is the set of nonnegative integers and r is w x some number and let k s denote the semigroup ring over s where k is a w x field then k s is a homomorphic image of some polynomial ring over k let i be an ideal of a such that the ring ari is canonically isomorphic to w x w x k s it is natural to examine i to investigate the properties of k s for example cohen macaulay and buchsbaum properties kamoi proved that under the conditions that s is simplicial and that the height of i is 2 w x k s is cohen macaulay if and only if m i f 3 where m denotes the w x least number of generators 10 independently there are many results w x concerning the relationship between the properties of k s and m i 3 w x when it is the coordinate ring of the monomial curve in p e g 1 4 9 in this paper we will generalize these results uniformly we only set the assumption that the height of i is 2 in section 1 we will prepare the notation of monoid rings monoid rings are defined for submodules of z where z is the ring of integers and w x studied in 7 an affine semigroup ring is a monoid ring in section 2 we will find a minimal generating system of the defining ideal of the monoid ring associated with the submodule of z r of rank 2 when it is positively graded and we will give a minimal free resolution of it consequently we can prove that

reduction of distributed system identification complexity using intelligent sensors abstract the identification problems of distributed parameter systems dps is dealt with a special method of data collection by using moving sensors is proposed the sensors are intelligent in the sense that they are able to track the positions of the exiremum values of a system state at each time instant it is shown how to reduce the identification problem for dps to that of identifying a certain system described by ordinary differential equations ode the proposed approach is applicable to the dps described by quasi linear partial differential equations of the hyperbolic type attention is focused on the problem of reduction while the identification of the resulting ode is not considered in detail since it is an easier task

the rational torsion subgroups of drinfeld modular jacobians and eisenstein pseudo harmonic cochains let mathfrak n be a square free ideal of mathbb f q t we study the rational torsion subgroup of the jacobian variety j 0 mathfrak n of the drinfeld modular curve x 0 mathfrak n we prove that for any prime number ell not dividing q q 1 the ell primary part of this group coincides with that of the cuspidal divisor class group we further determine the structure of the ell primary part of the cuspidal divisor class group for any prime ell not dividing q 1

graded rings associated with contracted ideals the study of the ideals in a regular local ring r m of dimension 2 has a long and important tradition dating back to the fundamental work of zariski zs more recent contributions are due to several authors including cutkosky huneke lipman rees sally and teissier among others see c1 c2 h hs l lt r one of the main result in this setting is the unique factorization theorem for complete i e integrally closed ideals proved originally by zariski zs theorem 3 appendix 5 it asserts that any complete ideal can be factorized as a product of simple complete ideals in a unique way up to the order of the factors by definition an ideal is simple if it cannot be written as a product of two proper ideals another important property of a complete ideal i is that its reduction number is 1 which in turns implies that the associated graded ring gri r is cohen macaulay and its hilbert series is well understood this is due to lipman and teissier lt see also hs the class of contracted ideals plays an important role in the original work of zariski as well as in the work of huneke h an ideal i of r is contracted if i r ir m x for some x m m2 any complete ideal is contracted but not the other way round the associated graded ring gri r of a contracted ideal i need not be cohen macaulay and its hilbert series can be very complicated

dualizing complexes of affine semigroup rings for an affine semigroup ring we construct the dualizing complex in terms of the semigroup and the homology of the face lattice of the polyhedral cone spanned by the semigroup as a consequence there are characterizations of locally cohen macaulay rings buchsbaum rings and cohen macaulay rings as well as serre s condition 9 introduction let s denote a finitely generated submonoid of the additive monoid n n being a positive integer by the affine semigroup ring i s of s over a field x let us denote the subring of x xl xn generated by all monomials xs s e s so one has up to isomorphisms a one to one correspondence between affine semigroup rings and affine varieties given parametrically by monomials now it is of some interest to characterize ring theoretic properties as cohenmacaulay gorenstein etc in terms of the semigroup s a first breakthrough in this direction was done by kempf et al kkms and hochster hol who showed that x s is a cohen macaulay ring provided it is normal moreover the normality of x s is described in terms of s see hol another particular case if s is a simplicial semigroup is treated by goto suzuki and watanabe gsw resp stanley st2 who showed that x s is a cohen macaulay ring if it satisfies the 22 condition of serre note that normality is equivalent to 5y2 and r1 moreover there is a description of the 5 condition in terms of s see theorem 6 3 in general the 52 condition is not sufficient for i s to be a cohen macaulay ring as follows by examples in hol resp th 1 2 on the other side grobner g posed the problem to classify cohen macaulay affine semigroup rings the solution of this problem was done by hoa and trung th related to structural properties of graded rings is a technical tool of the duality theory this is the dualizing complex introduced by grothendieck see ha in recent years it became a helpful tool in commutative algebra in particular its knowledge allows characterizations of cohen macaulay rings locally cohenmacaulay rings buchsbaum rings gorenstein rings and the 5 conditions of received by the editors december 18 1988 1980 mathematics subject classification 1985 revision primary 13h10 secondary 14m05 06a99 1990 american mathematical society 0002 9947 90 1 q0 25 per page

cm points on products of drinfeld modular curves let x be a product of drinfeld modular curves over a general base ring a of odd characteristic we classify those subvarieties of x which contain a zariski dense subset of cm points this is an analogue of the andre oort conjecture as an application we construct non trivial families of higher heegner points on modular elliptic curves over global function fields