delay independent stability test for systems with multiple time delays delay independent stability dis of a general class of linear time invariant lti multiple time delay system mtds is investigated in the entire delay parameter space stability of such systems may be lost only if their spectrum lies on the imaginary axis for some delays we build an analytical approach that requires the inspection of the roots of finite number of single variable polynomials in order to detect if the spectrum ever lies on the imaginary axis for some delays excluding infinite delays the approach enables to test the necessary and sufficient conditions of dis of lti mtds technically known as weak dis as well as the robust stability of single delay systems against all variations in delay ratios the proposed approach which does not require any parameter sweeping and graphical display becomes possible by establishing a link between the infinite spectrum and algebraic geometry case studies are provided to show the effectiveness of the approach

elimination and nonlinear equations of rees algebra abstract a new approach is established to computing the image of a rational map whereby the use of approximation complexes is complemented with a detailed analysis of the torsion of the symmetric algebra in certain degrees in the case the map is everywhere defined this analysis provides free resolutions of graded parts of the rees algebra of the base ideal in degrees where it does not coincide with the corresponding symmetric algebra a surprising fact is that the torsion in those degrees only contributes to the first free module in the resolution of the symmetric algebra modulo torsion an additional point is that this contribution which of course corresponds to nonlinear equations of the rees algebra can be described in these degrees in terms of non koszul syzygies via certain upgrading maps in the vein of the ones introduced earlier by j herzog the third named author and w vasconcelos as a measure of the reach of this torsion analysis we could say that in the case of a general everywhere defined map half of the degrees where the torsion does not vanish are understood

degree and birationality of multi graded rational maps we give formulas and effective sharp bounds for the degree of multi graded rational maps and provide some effective and computable criteria for birationality in terms of their algebraic and geometric properties we also extend the jacobian dual criterion to the multi graded setting our approach is based on the study of blow up algebras including syzygies of the ideal generated by the defining polynomials of the rational map a key ingredient is a new algebra that we call thesaturated special fiber ring which turns out to be a fundamental tool to analyze the degree of a rational map we also provide a very effective birationality criterion and a complete description of the equations of the associated rees algebra of a particular class of plane rational maps

the moving curve ideal and the rees algebra the rees algebra of an ideal in a commutative ring is the quotient of a polynomial ring by its ideal of defining relations for a polynomial ring in two variables this ideal was discovered independently by the geometric modeling community where it is called the moving curve ideal we review some properties of the rees algebra and discuss one result and one conjecture concerning the structure of the moving curve ideal and its relation to adjoint curves some parts of the paper are purely expository

the explicit minimal resolution constructed from a macaulay inverse system abstract let a be a standard graded artinian gorenstein algebra of embedding codimension three over a field k in the generic case the minimal homogeneous resolution g of a by free sym k a 1 modules is gorenstein linear fix a basis x y z for the k vector space a 1 if g is gorenstein linear then the socle degree of a is necessarily even and if n is the least index with dim k a n less than dim k sym n k a 1 then the socle degree of a is 2 n 2 let m m as m roams over the monomials in x y z of degree 2 n 2 with m k be an arbitrary homogeneous element of degree 2 n 2 in the divided power module d k a 1 the annihilator of denoted ann is the ideal of elements f in sym k a 1 with f 0 the element of d k a 1 is the macaulay inverse system for the ring sym k a 1 ann which is necessarily gorenstein and artinian consider the matrix m m as m and m roam over the monomials in x y z of degree n 1 the ring sym k a 1 ann has a gorenstein linear resolution if and only if det m m 0 if det m m 0 then we give explicit formulas for the minimal homogeneous resolution of sym k a 1 ann in terms the m s and x y z

constrained optimization for average cost continuous time markov decision processes to the best of our knowledge this note is a first study on a multiconstrained optimization problem for average cost continuous time markov decision processes in polish spaces the optimality criterion is the long run expected average cost and the constraints are imposed on similar average costs we give suitable conditions under which the existence of a constrained optimal stationary policy is shown by introducing occupation measures and using a martingale technique also we illustrate our conditions with controlled potlach processes

optimal risk probability for first passage models in semi markov decision processes this paper studies the risk minimization problem in semi markov decision processes with denumerable states the criterion to be optimized is the risk probability or risk function that a first passage time to some target set doesn t exceed a threshold value we first characterize such risk functions and the corresponding optimal value function and prove that the optimal value function satisfies the optimality equation by using a successive approximation technique then we present some properties of optimal policies and further give conditions for the existence of optimal policies in addition a value iteration algorithm and a policy improvement method for obtaining respectively the optimal value function and optimal policies are developed finally two examples are given to illustrate the value iteration procedure and essential characterization of the risk function

fitting ideals and multiple points of surface parameterizations given a birational parameterization f of an algebraic surface s the purpose of this paper is toinvestigate the sets of points on s whose preimage consists in kor more points counting multiplicities these points are described explicitly interms of fitting ideals of some graded parts of the symmetric algebraassociated to the parameterization f to obtain this description weshow that the degree and dimension of a fiber could be computed bycomparing the drop of rank of two explicit representation matrices associated to f

cohen macaulay rees algebras and degrees of polynomial relations e mail aron sunrnp vfba br 2 department of mathematics michigan state university east lansing mi 48824 usa e mail 21144bfu msu edu 3 department of mathematics rutgers university new brunswick nj 08903 usa e mail vasconce rings rutgers edu received 5 october 1993

on some nonlinear elliptic equations involving derivatives of the nonlinearity the existence of weak solutions of the dirichlet problem for nonlinear elliptic equations of the type x j a ij x u x i b j u a x u f is proved for nonlinearities b j which are only continuous the proof is based on the observation that an l a priori estimate is valid which is independent of b j the second part contains several uniqueness results and counterexamples showing that uniqueness may fail in general

artinian gorenstein algebras with linear resolutions for each pair of positive integers n d we construct a complex g n of modules over the bi graded polynomial ring r z x1 xd tm where m roams over all monomials of degree 2n 2 in x1 xd the complex g n has the following universal property let p be the polynomial ring k x1 xd where k is a field and let in d k be the set of homogeneous ideals i in p which are generated by forms of degree n and for which p i is an artinian gorenstein algebra with a linear resolution if i is an ideal from in d k then there exists a homomorphism r p so that p r g n is a minimal homogeneous resolution of p i by free p modules the construction of g n is equivariant and explicit we give the differentials of g n as well as the modules on the other hand the homology of g n is unknown as are the properties of the modules that comprise g n nonetheless there is an ideal i of r and an element of r so that i r is a gorenstein ideal of r and g n is a resolution of r i r by projective r modules the complex g n is obtained from a less complicated complex g n which is built directly and in a polynomial manner from the coefficients of a generic macaulay inverse system furthermore i is the ideal of r determined by the modules of g n are schur and weyl modules corresponding to hooks the complex g n is bi homogeneous and every entry of every matrix in g n is a monomial if m1 mn is a list of the monomials in x1 xd of degree n 1 then is the determinant of the n n matrix tmimj the previously listed results exhibit a flat family of k algebras parameterized by in d k k tm k zr i every algebra p i with i in d k is a fiber of we simultaneously resolve all of these algebras p i the natural action of gld k on p induces an action of gld k on in d k we prove that if d 3 n 3 and the characteristic of k is zero then in d k decomposes into at least four disjoint non empty orbits under this group action

compressed algebras artin algebras having given socle degrees and maximal length j emsalem and the author showed in 18 that a general polynomialf of degree j in the ring sp k yl yr has jr rl 1 linearly independent partial derivates of order i for i 0 1 t j 2 here we generalize the proof to show that the various partial derivates of s polynomials of specified degrees are as independent as possible given the room available using this result we construct and describe the varieties g e and z e parametrizing the graded and nongraded compressed algebra quotients a r i of the power series ring r k xl sxr having given socle type e these algebras are artin algebras having maximal length dimk a possible given the embedding degree r and given the socle type sequence e els s es where ei is the number of generators of the dual module a of a having degree i the variety z e is locally closed irreducible and is a bundle over g e fibred by affine spaces an whose dimension is known we consider the compressed algebras a new class of interesting algebras and a source of examples many of them are nonsmoothable have no deformation to k k for dimension reasons for some choices of the sequence e d buchsbaum d eisenbud and the author have shown that the graded compressed algebras of socle type e have almost linear minimal resolutions over r with ranks and degrees determined by e other examples have given type e dimk socle a and are defined by an ideal i with certain given numbers of generators in r

existence uniqueness and homogenization of the second order slip reynolds equation the decreasing of the distance between the head and the magnetic disk surface leads to a model of the behaviour of the air by using a modified reynolds equation the existence and the uniqueness of this stationary equation is under some conditions on the data proved using both fixed point and monotonicity techniques double scale analysis allows us to obtain the associated homogenized equation

cayley bacharach theorems and conjectures a theorem of pappus of alexandria proved in the fourth century a d began a long development in algebraic geometry in its changing expressions one can see reflected the changing concerns of the field from synthetic geometry to projective plane curves to riemann surfaces to the modern development of schemes and duality we survey this development historically and use it to motivate a brief treatment of a part of duality theory we then explain one of the modern developments arising from it a series of conjectures about the linear conditions imposed by a set of points in projective space on the forms that vanish on them we give a proof of the conjectures in a new

initial complexes of prime ideals abstract the simplicial complex defined by any initial ideal of a prime ideal is pure and strongly connected this proves a conjecture of kredel and weispfenning 12 p 234

the regularity of tor and graded betti numbers let s k x1 xn let a b be finitely generated graded s modules and let m x1 xn s we give bounds for the regularity of the local cohomology of tork a b in terms of the graded betti numbers of a and b under the assumption that dim tor1 a b 1 we apply the results to syzygies grobner bases products and powers of ideals and to the relationship of the rees and symmetric algebras for example we show that any homogeneous linearly presented m primary ideal has some power equal to a power of m and if the first n 1 2 steps of the resolution of i are linear then i 2 is a power of m

singular factors of rational plane curves we give a complete factorization of the invariant factors of resultant matrices built from birational parameterizations of rational plane curves in terms of the singular points of the curve and their multiplicity graph this allows us to prove the validity of some conjectures about these invariants stated by chen wang and liu as a byproduct we also give a complete factorization of the d resultant for rational functions in terms of the similar data extracted from the multiplicities

macaulay style formulas for sparse resultants we present formulas for computing the resultant of sparse polynomials as a quotient of two determinants the denominator being a minor of the numerator these formulas extend the original formulation given by macaulay for homogeneous polynomials

the structure of gorenstein linear resolutions of artinian algebras abstract let k be a field a a standard graded artinian gorenstein k algebra s the standard graded polynomial ring sym k a 1 i the kernel of the natural map d the vector space dimension dim k a 1 and n the least index with i n 0 assume that 3 d and 2 n in this paper we give the structure of the minimal homogeneous resolution b of a by free s modules provided b is gorenstein linear keep in mind that if a has even socle degree and is generic then a has a gorenstein linear minimal resolution our description of b depends on a fixed but arbitrary decomposition of a 1 of the form k x 1 v 0 for some non zero element x 1 and some d 1 dimensional subspace v 0 of a 1 much information about b is already contained in the complex b b x 1 b which we call the skeleton of b one striking feature of b is the fact that the skeleton of b is completely determined by the data d n no other information about a is used in the construction of b the skeleton b is the mapping cone of zero k l where l is a well known resolution of buchsbaum and eisenbud k is the dual of l and l and k are comprised of schur and weyl modules associated to hooks respectively the decomposition of b into schur and weyl modules lifts to a decomposition of b furthermore b inherits the natural self duality of b the differentials of b are explicitly given in a polynomial manner in terms of the coefficients of a macaulay inverse system for a in light of the properties of b the description of the differentials of b amounts to giving a minimal generating set of i and for the interior differentials giving the coefficients of x 1 as an application we observe that every non zero element of a 1 is a weak lefschetz element for a

finite horizon semi markov decision processes with application to maintenance systems abstract this paper investigates finite horizon semi markov decision processes with denumerable states the optimality is over the class of all randomized history dependent policies which include states and also planning horizons and the cost rate function is assumed to be bounded below under suitable conditions we show that the value function is a minimum nonnegative solution to the optimality equation and there exists an optimal policy moreover we develop an effective algorithm for computing optimal policies derive some properties of optimal policies and in addition illustrate our main results with a maintenance system

rees algebras of modules we study rees algebras of modules within a fairly general framework we introduce an approach through the notion of bourbaki ideals that allows the use of deformation theory one can talk about the essentially unique generic bourbaki ideal i e of a module e which in many situations allows one to reduce the nature of the rees algebra of e to that of its bourbaki ideal i e properties such as cohen macaulayness normality and being of linear type are viewed from this perspective the known numerical invariants such as the analytic spread the reduction number and the analytic deviation of an ideal and its associated algebras are considered in the case of modules corresponding notions of complete intersection almost complete intersection and equimultiple modules are examined in some detail special consideration is given to certain modules which are fairly ubiquitous because interesting vector bundles appear in this way for these modules one is able to estimate the reduction number and other invariants in terms of the buchsbaum rim multiplicity

optimal control of ergodic continuous time markov chains with average sample path rewards in this paper we study continuous time markov decision processes with the average sample path reward aspr criterion and possibly unbounded transition and reward rates we propose conditions on the system s primitive data for the existence of epsilon aspr optimal deterministic stationary policies in a class of randomized markov policies satisfying some additional continuity assumptions the proof of this fact is based on the time discretization technique the martingale stability theory and the concept of potential we also provide both policy and value iteration algorithms for computing or at least approximating the epsilon aspr optimal stationary policies we illustrate with examples our main results as well as the difference between the aspr and the average expected reward criteria

on the equations of the moving curve ideal of a rational algebraic plane curve given a parametrization of a rational plane algebraic curve c some explicit adjoint pencils on c are described in terms of determinants moreover some generators of the rees algebra associated to this parametrization are presented the main ingredient developed in this paper is a detailed study of the elimination ideal of two homogeneous polynomials in two homogeneous variables that form a regular sequence

divisors on rational normal scrolls let a be the homogeneous coordinate ring of a rational normal scroll the ring a is equal to the quotient of a polynomial ring s by the ideal generated by the two by two minors of a scroll matrix with two rows and l catalecticant blocks the class group of a is cyclic and is infinite provided l is at least two one generator of the class group is j where j is the ideal of a generated by the entries of the first column of the positive powers of j are well understood if l is at least two then the nth ordinary power the nth symmetric power and the nth symbolic power coincide and therefore all three nth powers are resolved by a generalized eagon northcott complex the inverse of j in the class group of a is k where k is the ideal generated by the entries of the first row of we study the positive powers of k we obtain a minimal generating set and a grobner basis for the preimage in s of the symbolic power k n we describe a filtration of k n in which all of the factors are cohen macaulay s modules resolved by generalized eagon northcott complexes we use this filtration to describe the modules in a finely graded resolution of k n by free s modules we calculate the regularity of the graded s module k n and we show that the symbolic rees ring of k is noetherian

the implicit equation of a multigraded hypersurface in this article we analyze the implicitization problem of the image of a rational map x pn with x a toric variety of dimension n 1 defined by its cox ring r let i f0 fn be n 1 homogeneous elements of r we blow up the base locus of v i and we approximate the rees algebra reesr i of this blow up by the symmetric algebra symr i we provide under suitable assumptions resolutions z for symr i graded by the divisor group of x cl x such that the determinant of a graded strand det z gives a multiple of the implicit equation for suitable cl x indeed we compute a region in cl x which depends on the regularity of symr i where to choose we also give a geometrical interpretation of the possible other factors appearing in det z a very detailed description is given when x is a multiprojective space

rees algebras of truncations of complete intersections abstract in this paper we describe the defining equations of the rees algebra and the special fiber ring of a truncation i of a complete intersection ideal in a polynomial ring over a field with homogeneous maximal ideal m to describe explicitly the rees algebra r i in terms of generators and relations we map another rees ring r m onto it where m is the direct sum of powers of m we compute a grobner basis of the ideal defining r m it turns out that the normal domain r m is a koszul algebra and from this we deduce that in many instances r i is a koszul algebra as well

optimal policy for minimizing risk models in markov decision processes we consider the minimizing risk problems in discounted markov decisions processes with countable state space and bounded general rewards we characterize optimal values for finite and infinite horizon cases and give two sufficient conditions for the existence of an optimal policy in an infinite horizon case these conditions are closely connected with lemma 3 in white 1993 which is not correct as wu and lin 1999 point out we obtain a condition for the lemma to be true under which we show that there is an optimal policy under another condition we show that an optimal value is a unique solution to some optimality equation and there is an optimal policy on a transient set

asymptotic behaviour of arithmetically cohen macaulay blow ups this paper addresses problems related to the existence of arithmetic macaulayfications of projective schemes let y be the blow up of a projective scheme x projr along the ideal sheaf of i r it is known that there are embeddings y projk i e c for c d i e 1 where d i denotes the maximal generating degree of i and that there exists a cohen macaulay ring of the form k i e c if and only if h 0 y oy k h i y oy 0 for i 1 dimy 1 y is equidimensional and cohen macaulay cutkosky and herzog asked when there is a linear bound on c and e ensuring that k i e c is a cohen macaulay ring we obtain a surprising compelte answer to this question namely that under the above conditions there are well determined invariants and e0 such that k i e c is cohen macaulay for all c d i e and e e0 our approach is based on recent results on the asymptotic linearity of the castelnuovo mumford regularity of ideal powers we also investigate the existence of a cohen macaulay rees algebra of the form r i e ct which provides an arithmetic macaulayfication for x if r has negative a invariant we prove that such a cohen macaulay rees algebra exists if and only if oy ox r i oy 0 for i 0 y is equidimensional and cohen macaulay especially these conditions imply the cohen macaulayness of r i e ct for all c d i e and e e0 the above results can be applied to obtain several new classes of cohen macaulay algebras

rational plane curves parameterizable by conics abstract we introduce the class of rational plane curves parameterizable by conics as an extension of the family of curves parameterizable by lines also known as monoid curves we show that they are the image of monoid curves via suitable quadratic transformations in projective plane we also describe all the possible proper parameterizations of them and a set of minimal generators of the rees algebra associated to these parameterizations extending well known results for curves parameterizable by lines

linearly presented perfect ideals of codimension 2 in three variables abstract the goal of this paper is the fine structure of the ideals in the title with emphasis on the properties of the associated rees algebra and the special fiber the watershed between the present approach and some of the previous work in the literature is that here one does not assume that the ideals in question satisfy the usual generic properties one exception is a recent work of n p h lan which inspired the present work here we recover and extend his work we strongly focus on the behavior of the ideals of minors of the corresponding so called hilbert burch matrix and on conjugation features of the latter we apply the results to three important models linearly presented ideals of plane fat points reciprocal ideals of hyperplane arrangements and linearly presented monomial ideals

bound for the number of one dimensional fibers of a projective morphism abstract given a parameterization p k 2 p k 3 of an algebraic surface s p k 3 we bound the number of one dimensional fibers of the canonical projection of the graph of onto its image

existence and uniqueness for several non linear elliptic problems arising in lubrication theory we consider the non linear elliptic equation a x p p b x p with positive dirichlet boundary data the coefficients a and b are taken from models used in lubrication theory andin particular are not d negative values of p we prove some general existence anduniqueness results for a family of mod els which extendrelatedresults in the literature these results allow us to prove existence uniqueness andpositivity of the solution to advanced compressible lubrication models such as the kinetic based fukui kaneko model and the second order slip model we also consider a spring like model of compliant foil compressible bearing andweaken some hypotheses of previous results on more classical mod els such as the standard reynolds model and the first order slip model

existence of optimal policies for semi markov decision processes using duality for infinite linear programming semi markov decision processes on borel spaces with deterministic kernels have many practical applications particularly in inventory theory most of the results from general semi markov decision processes do not carry over to a deterministic kernel since such a kernel does not provide smoothness we develop infinite dimensional linear programming theory for a general stochastic semi markov decision process we give conditions general enough to allow deterministic kernels for solvability and strong duality of the resulting linear programs by using the developed linear programming theory we give conditions for the existence of a stationary deterministic policy for deterministic kernels which is optimal among all possible policies

minimum risk probability for finite horizon semi markov decision processes abstract this paper studies the risk probability criteria for finite horizon semi markov decision processes the goal is to find an optimal policy with the minimum risk probability that the total reward produced by a system during a finite horizon does not exceed a reward level where the optimality is over the class of all randomized historic policies which include states planning horizons and also reward levels under mild conditions the optimality equation and the existence of optimal policies are established and in addition an iteration algorithm for solving optimal policies is developed our main results are applied to a manufacturing system

explicit factors of some iterated resultants and discriminants in this paper the result of applying iterative univariate resultant constructions to multivariate polynomials is analyzed we consider the input polynomials as generic polynomials of a given degree and exhibit explicit decompositions into irreducible factors of several constructions involving two times iterated univariate resultants and discriminants over the integer universal ring of coefficients of the entry polynomials cases involving from two to four generic polynomials and resultants or discriminants in one of their variables are treated the decompositions into irreducible factors we get are obtained by exploiting fundamental properties of the univariate resultants and discriminants and induction on the degree of the polynomials as a consequence each irreducible factor can be separately and explicitly computed in terms of a certain multivariate resultant with this approach we also obtain as direct corollaries some results conjectured by collins and mccallum which correspond to the case of polynomials whose coefficients are themselves generic polynomials in other variables finally a geometric interpretation of the algebraic factorization of the iterated discriminant of a single polynomial is detailled

the bi graded structure of symmetric algebras with applications to rees rings abstract consider a rational projective plane curve c parameterized by three homogeneous forms of the same degree in the polynomial ring r k x y over a field k the ideal i generated by these forms is presented by a homogeneous 3 2 matrix with column degrees d 1 d 2 the rees algebra r r i t of i is the bi homogeneous coordinate ring of the graph of the parameterization of c and accordingly there is a dictionary that translates between the singularities of c and algebraic properties of the ring r and its defining ideal finding the defining equations of rees rings is a classical problem in elimination theory that amounts to determining the kernel a of the natural map from the symmetric algebra sym i onto r the ideal a d 2 1 which is an approximation of a can be obtained using linkage we exploit the bi graded structure of sym i in order to describe the structure of an improved approximation a d 1 1 when d 1 d 2 and has a generalized zero in its first column the latter condition is equivalent to assuming that c has a singularity of multiplicity d 2 in particular we give the bi degrees of a minimal bi homogeneous generating set for this ideal when 2 d 1 d 2 and has a generalized zero in its first column then we record explicit generators for a when d 1 d 2 we provide a translation between the bi degrees of a bi homogeneous minimal generating set for a d 1 2 and the number of singularities of multiplicity d 1 that are on or infinitely near c we conclude with a table that translates between the bi degrees of a bi homogeneous minimal generating set for a and the configuration of singularities of c when the curve c has degree six

optimal threshold probability in undiscounted markov decision processes with a target set we consider risk minimizing problems in undiscounted markov decisions processes with a target set we formulate the problem as an infinite horizon case with a recurrent class we show that an optimal value function is a unique solution to an optimality equation and there exists an stationary optimal policy also we give several value iteration methods and a policy improvement method

regularity of prime ideals we answer several natural questions which arise from a recent paper of mccullough and peeva providing counterexamples to the eisenbud goto regularity conjecture we give counterexamples using rees algebras and also construct counterexamples that do not rely on the mayr meyer construction furthermore examples of prime ideals for which the difference between the maximal degree of a minimal generator and the maximal degree of a minimal first syzygy can be made arbitrarily large are given using a result of ananyan hochster we show that there exists an upper bound on regularity of prime ideals in terms of the multiplicity alone

survey on the theory and applications of μ bases for rational curves and surfaces abstract bases are new representations for rational curves and surfaces which serve as a bridge between their parametric forms and implicit forms geometrically bases are represented by moving lines or moving planes while their algebraic counterparts are special syzygies of the parametric equations of rational curves or surfaces bases have been proven to be significant in solving many important problems in geometric modeling such as fast implicitization singularity computation reparametrization as well as providing easy inversion formulas for points we review the state of the art results in bases theory and applications for rational curves and surfaces and raise unsolved problems for future research

on the closed image of a rational map and the implicitization problem in this paper we investigate some topics around the closed image s of a rational map lambda given by some homogeneous elements f 1 ldots f n of the same degree in a graded algebra a we first compute the degree of this closed image in case lambda is generically finite and f 1 ldots f n define isolated base points in proj a we then relate the definition ideal of s to the symmetric and the rees algebras of the ideal i f 1 ldots f n subset a and prove some new acyclicity criteria for the associated approximation complexes finally we use these results to obtain the implicit equation of s in case s is a hypersurface proj a pp n 2 k with k a field and base points are either absent or local complete intersection isolated points

syzygies of canonical curves and special linear series 0 introduction 105 1 line bundles on scrolls 109 2 scrolls and pencils 113 3 syzygies of a subvariety of a scroll 115 4 canonical curves 118 5 on the equation of rational surfaces 121 6 d gonal curves for d 5 126 7 proof of the main result 131 references 136

rees algebras and almost linearly presented ideals abstract consider a grade 2 perfect ideal i in r k x 1 x d which is generated by forms of the same degree assume that the presentation matrix is almost linear that is all but the last column of consist of entries which are linear for such ideals we find explicit forms of the defining ideal of the rees algebra r i we also introduce the notion of iterated jacobian duals

the implicitization problem for ϕ pn p1 n 1 abstract we develop in this paper methods for studying the implicitization problem for a rational map p n p 1 n 1 defining a hypersurface in p 1 n 1 based on computing the determinant of a graded strand of a koszul complex we show that the classical study of macaulay resultants and koszul complexes coincides in this case with the approach of approximation complexes and we study and give a geometric interpretation for the acyclicity conditions under suitable hypotheses these techniques enable us to obtain the implicit equation up to a power and up to some extra factor we give algebraic and geometric conditions for determining when the computed equation defines the scheme theoretic image of and what are the extra varieties that appear we also give some applications to the problem of computing sparse discriminants

rational normal scrolls and the defining equations of rees algebras consider a height two ideal i which is minimally generated by m homogeneous forms of degree d in the polynomial ring r k x y suppose that one column in the homogeneous presenting matrix of i has entries of degree n and all of the other entries of are linear we identify an explicit generating set for the ideal a which defines the rees ring r r it so r s a for the polynomial ring s r t1 tm we resolve r as an s module and is as an r module for all powers s the proof uses a rational normal scroll ring a s h with aa isomorphic to the nth symbolic power of a height one prime ideal k of a the ideal k n is generated by monomials whenever possible we study a k n in place of a aa because the generators of k n are much less complicated then the generators of aa we obtain a filtration of k n in which the factors are polynomial rings hypersurface rings or modules resolved by eagon northcott complexes the generators of i give rise to an algebraic curve c in projective m 1 space the defining equations of the fiber ring r x y r yield a solution of the implicitization problem for c introduction let i be a height two ideal in the polynomial ring r k x y with i minimally generated by m forms of degree d we consider the following questions what is the defining ideal a of the rees ring r r it r it it what is the hilbert function of r the rees ring r is equal to r t1 tm a what is the minimal resolution of r what are the defining equations of the fiber 1supported in part by the national security agency 2supported in part by the national science foundation and the national security agency 3supported in part by the national science foundation 2000 mathematics subject classification primary 14q05 secondary 13c20 13d02 14e05 14m12 68w30

continuous time discounted jump markov decision processes a discrete event approach this paper introduces and develops a new approach to the theory of continuous time jump markov decision processes ctjmdp this approach reduces discounted ctjmdps to discounted semi markov decision processes smdps and eventually to discrete time markov decision processes mdps the reduction is based on the equivalence of strategies that change actions between jumps and the randomized strategies that change actions only at jump epochs this holds both for one criterion problems and for multiple objective problems with constraints in particular this paper introduces the theory for multiple objective problems with expected total discounted rewards and constraints if a problem is feasible there exist three types of optimal policies i nonrandomized switching stationary policies ii randomized stationary policies for the ctjmdp and iii randomized stationary policies for the corresponding smdp with exponentially distributed sojourn times and these policies can be implemented as randomized strategies in the ctjmdp

approximation complexes of blowing up rings ii this paper is a sequel to 111 where we studied the relationships that hold between the arithmetical properties of the rees ring 9 i and the symmetric algebra sym l of an ideal i and some of their fibers and the depth properties of the koszul homology modules h i r on a set of generators of i the connection between these objects is realized by certain differential graded algebras the so called approximation complexes that are built out of ordinary koszul complexes these compiexes show however different sensitivities being acyclic in situations much broader than the usual context of regular sequences it has been found that certain extensions thereof d sequences and proper sequences play here that role of acyclic sequence the interplay between sequences and approximation complexes will be a basic point of view here where we give

poincare series of modules over compressed gorenstein local rings abstract given two positive integers e and s we consider gorenstein artinian local rings r whose maximal ideal m satisfies m s 0 m s 1 and rank r m m m 2 e we say that r is a compressed gorenstein local ring when it has maximal length among such rings it is known that generic gorenstein artinian algebras are compressed if s 3 we prove that the poincare series of all finitely generated modules over a compressed gorenstein local ring are rational sharing a common denominator a formula for the denominator is given when s is even this formula depends only on the integers e and s note that for s 3 examples of compressed gorenstein local rings with transcendental poincare series exist due to bogvad

syzygies and singularities of tensor product surfaces of bidegree 2 1 let u h op1 p1 2 1 be a basepoint free four dimensional vector space the sections corresponding to u determine a regular map u p1 p1 p3 we study the associated bigraded ideal iu k s t u v from the standpoint of commutative algebra proving that there are exactly six numerical types of possible bigraded minimal free resolution these resolutions play a key role in determining the implicit equation for u p1 p1 via work of buse jouanolou 5 buse chardin 6 botbol 2 and botbol dickensteindohm 3 on the approximation complex z in four of the six cases iu has a linear first syzygy remarkably from this we obtain all differentials in the minimal free resolution in particular this allows us to explicitly describe the implicit equation and singular locus of the image

minimizing risk models in markov decision processes with policies depending on target values abstract this paper studies the minimizing risk problems in markov decision processes with countable state space and reward set the objective is to find a policy which minimizes the probability risk that the total discounted rewards do not exceed a specified value target in this sort of model the decision made by the decision maker depends not only on system s states but also on his target values by introducing the decision maker s state we formulate a framework for minimizing risk models the policies discussed depend on target values and the rewards may be arbitrary real numbers for the finite horizon model the main results obtained are i the optimal value functions are distribution functions of the target ii there exists an optimal deterministic markov policy and iii a policy is optimal if and only if at each realizable state it always takes optimal action in addition we obtain a sufficient condition and a necessary condition for the existence of finite horizon optimal policy independent of targets and we give an algorithm computing finite horizon optimal policies and optimal value functions for an infinite horizon model we establish the optimality equation and we obtain the structure property of optimal policy we prove that the optimal value function is a distribution function of target and we present a new approximation formula which is the generalization of the nonnegative rewards cases an example which illustrates the mistakes of previous literature shows that the existence of optimal policy has not been proved really in this paper we give an existence condition which is a sufficient and necessary condition for the existence of an infinite horizon optimal policy independent of targets and we point out that whether there exists an optimal policy remains an open problem in the general case