basically full ideals in local rings abstract let a be a finitely generated module over a noetherian local ring r m we say that a nonzero submodule b of a is basically full in a if no minimal basis for b can be extended to a minimal basis of any submodule of a properly containing b we prove that a basically full submodule of a is m primary and that the following properties of a nonzero m primary submodule b of a are equivalent a b is basically full in a b b mb a m c mb is the irredundant intersection of b irreducible ideals d c b for each cover c of b moreover if b is an m primary submodule of a then b mb a m is the smallest basically full submodule of a containing b and b b is a semiprime operation on the set of nonzero m primary submodules b of a we prove that all nonzero m primary ideals are closed with respect to this operation if and only if m is principal in relation to the closure operation b b we define and study the bf reductions of an m primary submodule d of a that is the m primary submodules c of d such that c d c if g m denotes the form ring of r with respect to m and g m its maximal homogeneous ideal we prove that m n m n for all resp for all large positive integers n if and only if grade g m 0 resp grade m 0 for a regular local ring r m we consider the m primary monomial ideals with respect to a fixed regular system of parameters and determine necessary and sufficient conditions for such an ideal to be basically full

integral closedness of complete intersection ideals the aim of this paper is to give some structure theorem of certain integrally closed ideals in noetherian rings let a be a noetherian ring and i an ideal of a then an element x of a is said to be integral over z if x satisfies an equation x c x c 0 in a with ci e i the integral closure i of z is by definition the set of elements in a which are integral over z and the ideal z is called integrally closed if f i let ua z resp ht i denote the smallest number of elements in systems of generators for z resp the height of i let min a z be the set of minimal prime divisors of i in this paper we shall study the problem when the ideals z of a such that ua z ht z are integrally closed and our result is stated as follows

monoidal extensions of a locally quasi unmixed ufd abstract let r be a locally quasi unmixed domain a b 1 b n an asymptotic sequence in r i a b 1 b n r and s r b 1 a b n a r i a the monoidal transform of r with respect to i it is shown that s is a locally quasi unmixed domain a b 1 a b n a is an asymptotic sequence in s and there is a one to one correspondence between the asymptotic primes a i of i and the asymptotic primes a a s of a s i s moreover if a b 1 b n is an r sequence this extends to a one to one correspondence between ass r r i and ass s s a s in the case that r is a unique factorization domain the height one prime ideals of s are examined to determine how far s is from being a ufd a complete description is given of which height one prime ideals p of s are principal or have a principal primary ideal in the case that p r has height 1 if the prime divisors of a satisfy a mild condition a similar description is given in the case that p r has height 1 these are applied to give similar results for the rees ring r 1 t i t where t is an indeterminate

computational complexity of relating time points with interval abstract several algebras have been proposed for reasoning about qualitative constraints over the time line one of these algebras is vilain s point interval algebra which can relate time points with time intervals apart from being a stand alone qualitative algebra it is also used as a subalgebra in meiri s approach to temporal reasoning which combines reasoning about metric and qualitative temporal constraints over both time points and time intervals while the satisfiability problem for the full point interval algebra is known to be np complete not much is known about its 4 294 967 296 subclasses this article completely determines the computational complexity of these subclasses and it identifies all of the maximal tractable subalgebras five in total

efficient algorithms for fuzzy qualitative temporal reasoning fuzzy qualitative temporal relations have been proposed to reason about events whose temporal boundaries are ill defined although the corresponding reasoning tasks are in the same complexity class as their crisp counterparts in practice the scalability of fuzzy temporal reasoners may be insufficient for applications that require a high expressivity and deal with a large number of events on the other hand transitivity rules can be used to make sound but incomplete inferences in polynomial time utilizing a variant of allen s path consistency algorithm the aim of this paper is to investigate how this polynomial time algorithm can be improved without altering its time complexity to this end we establish a characterization of 2 consistency of fuzzy temporal relations and provide transitivity rules that are significantly stronger than those resulting from straightforwardly generalizing transitivity rules for crisp temporal relations we furthermore provide experimental evidence for the effectiveness of our improved algorithm

point algebras for temporal reasoning algorithms and complexity we investigate the computational complexity of temporal reasoning in different time models such as totally ordered partially ordered and branching time our main result concerns the satisfiability problem for point algebras and point algebras extended with disjunctions for these problems we identify all tractable subclasses we also provide a number of additional results for instance we present a new time model suitable for reasoning about systems with a bounded number of unsynchronized clocks we investigate connections with spatial reasoning and we present improved algorithms for deciding satisfiability of the tractable point algebras

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

chern coefficients and cohen macaulay rings abstract in this study we investigate the relationship between the index of reducibility and chern coefficients for primary ideals therefore the main result of this study provides a characterization of a cohen macaulay ring in terms of its index of reducibility cohen macaulay type and the chern coefficients for parameter ideals as corollaries to the main theorem we obtain characterizations of a gorenstein ring in terms of its chern coefficients for parameter ideals

almost gorenstein rings abstract barucci and froberg 1997 2 introduced the notion of an almost gorenstein ring in the case of an analytically unramified local ring r m in this work we provide a framework that allows us to generalize this notion to include the analytically ramified case as a consequence for any cohen macaulay local ring r m of dimension one we solve in full generality the problem of determining when the endomorphism algebra m m is gorenstein we also provide characterizations for rings to be almost gorenstein in connection with the principle of idealization several examples are explored as well

reasoning about temporal relations a maximal tractable subclass of allen s interval algebra we introduce a new subclass of allen s interval algebra we call ord horn subclass which is a strict superset of the pointisable subclass we prove that reasoning in the ord horn subclass is a polynomial time problem and show that the path consistency method is sufficient for deciding satisfiability further using an extensive machine generated case analysis we show that the ord horn subclass is a maximal tractable subclass of the full algebra assuming p np in fact it is the unique greatest tractable subclass amongst the subclasses that contain all basic relations

solution estimates for linear differential equations with delay abstract in this paper we give explicit exponential estimates x t m e t t 0 where t t0 m 0 for solutions of a linear scalar delay differential equation x t k 1 m b k t x h k t f t t t 0 x t t t t 0 we consider two different cases when 0 corresponding to exponential stability and the case of in the first case together with the exponential estimate we also obtain an exponential stability test in the second case we get estimation for solution growth here both the coefficients and the delays are measurable not necessarily continuous

integrally closed and componentwise linear ideals in a two dimensional regular local ring integrally closed ideals have a unique factorization property and their associated graded ring is cohen macaulay in higher dimension these properties do not hold and the goal of the paper is to identify a subclass of integrally closed ideals for which they do we restrict our attention to 0 dimensional homogeneous ideals in polynomial rings r of arbitrary dimension we identify a class of integrally closed ideals the goto class mathcal g which is closed under product and it has a suitable unique factorization property ideals in mathcal g have a cohen macaulay associated graded ring if either they are monomial or dim r 3 our approach is based on the study of the relationship between the notions of integrally closed contracted full and componentwise linear ideals

invariants of cohen macaulay rings associated to their canonical ideals abstract the purpose of this paper is to introduce new invariants of cohen macaulay local rings our focus is the class of cohen macaulay local rings that admit a canonical ideal attached to each such ring r with a canonical ideal c there are integers the type of r the reduction number of c that provide valuable metrics to express the deviation of r from being a gorenstein ring we enlarge this list with other integers the roots of r and several canonical degrees the latter are multiplicity based functions of the rees algebra of c

asymptotic lech s inequality abstract we explore the classical lech s inequality relating the hilbert samuel multiplicity and colength of an m primary ideal in a noetherian local ring r m we prove optimal versions of lech s inequality for sufficiently deep ideals in characteristic p 0 and we conjecture that they hold in all characteristics our main technical result shows that if r m has characteristic p 0 and r is reduced equidimensional and has an isolated singularity then for any sufficiently deep m primary ideal i the colength and hilbert kunz multiplicity of i are sufficiently close to each other more precisely for all e 0 there exists n 0 such that for any i r with l r i n we have 1 e l r i e hk i 1 e l r i

the goto numbers of parameter ideals abstract let q be a parameter ideal of a noetherian local ring r m the goto number g q of q is the largest integer g such that q m g is integral over q we examine the values of g q as q varies over the parameter ideals of r we concentrate mainly on the case where dim r 1 and many of our results concern parameter ideals of a numerical semigroup ring

resoning about action in polynomial time abstract although many formalisms for reasoning about action exist surprisingly few approaches have taken computational complexity into consideration the contributions of this article are the following a temporal logic with a restriction for which deciding satisfiability is tractable a tractable extension for reasoning about action and np completeness results for the unrestricted problems many interesting reasoning problems can be modelled involving nondeterminism concurrency and memory of actions the reasoning process is proved to be sound and complete

buchsbaumness in rees modules associated to ideals of minimal multiplicity in the equi i invariant case abstract the present article gives certain conditions for rees modules to obtain buchsbaumness suppose a given m primary ideal is of minimal multiplicity in the equi i invariant case then it is shown that the positively graded submodule of the rees module must be buchsbaum and moreover that the rees module itself is also buchsbaum if the dimension of a given module is greater than one

complexity classification in qualitative temporal constraint reasoning we study the computational complexity of the qualitative algebra which is a temporal constraint formalism that combines the point algebra the point interval algebra and allen s interval algebra we identify all tractable fragments and show that every other fragment is np complete

complexity and algorithms for reasoning about time a graph theoretic approach temporal events are regarded here as intervals on a time line this paper deals with problems in reasoning about such intervals when the precise topological relationship between them is unknown or only partially specified this work unifies notions of interval algebras in artificial intelligence with those of interval orders and interval graphs in combinatorics the satisfiability minimal labeling all solutions and all realizations problems are considered for temporal internal data several versions are investigated by restricting the possible interval relationships yielding different complexity results we show that even when the temporal data comprises of subsets of relations based on intersection and precedence only the satisfiability question is np complete

a variant of wangʼs theorem in this paper we give a new formula of j j for any parameter ideal j in a gorenstein local ring r of positive characteristic in terms of test ideals j j j jd 1 where jd 1 denotes the jd 1 test ideal of r as an application we give a variant of wang s theorem namely we prove that if j is a parameter ideal in a cohen macaulay local ring r m of dimension d 2 with j ms then j m d 1 s 1 resp j m d 1 s 1 1 is integral over j resp if r is not regular moreover we prove that after reduction to characteristic p 0 a similar assertion holds true for cohen macaulay q gorenstein normal local domain essentially of finite type over a field of characteristic zero under some extra assumption

on asymptotically autonomous retarded functional differential equations the aim of the present paper is to investigate the asymptotic behavior of the solutions of the asymptotically autonomous retarded functional differential equation t lxt m t xt we obtain a convergence result without assuming that m t is in lp 1 p moreover we give bounds on the rate of convergence as well

linkage and the koszul homology of ideals 0 introduction let r be a local ring and i an ideal of r associated to i are several graded algebras the symmetric algebra of the module i sym i the rees algebra of i defined to be the algebra r i gn o inf and the associated graded algebra of i gr1 r rii g ii 2 in in 1 i i i our purpose in this paper is to study the behavior of these graded algebras when we change i through linkage recall the definition of linkage found in the paper of peskine and szpiro 22

projectively full ideals in noetherian rings ii abstract let r be a noetherian commutative ring with unit 1 0 and let i be a regular proper ideal of r the set p i of integrally closed ideals projectively equivalent to i is linearly ordered by inclusion and discrete there is naturally associated to p i a numerical semigroup s i we have s i n if and only if every element of p i is the integral closure of a power of the largest element j of p i if this holds the ideal j and the set p i are said to be projectively full if i is invertible and r is integrally closed we prove that p i is projectively full we investigate the behavior of projectively full ideals in various types of ring extensions we prove that a normal ideal i of a local ring r m is projectively full if i m 2 and both the associated graded ring g m and the fiber cone ring f i are reduced we present examples of normal local domains r m of altitude two for which the maximal ideal m is not projectively full

the almost gorenstein rees algebras of parameters abstract there is given a characterization for the rees algebras of parameters in a gorenstein local ring to be almost gorenstein graded rings a characterization is also given for the rees algebras of socle ideals of parameters the latter one shows almost gorenstein rees algebras rather rarely exist for socle ideals if the dimension of the base local ring is greater than two

quasi socle ideals in gorenstein numerical semigroup rings quasi socle ideals that is the ideals i of the form i q m q in goren stein numerical semigroup rings over fields are explored where q is a parameter ideal and m is the maximal ideal in the base local ring and q 1 is an integer the problems of when i is integral over q and of when the associated graded ring g i l n 0 i n i n 1 of i is cohen macaulay are studied the problems are rather wild examples are given

an initial study of time complexity in infinite domain constraint satisfaction abstract the constraint satisfaction problem csp is a widely studied problem with numerous applications in computer science and artificial intelligence for infinite domain csps there are many results separating tractable and np hard cases while upper and lower bounds on the time complexity of hard cases are virtually unexplored hence we initiate a study of the worst case time complexity of such csps we analyze backtracking algorithms and determine upper bounds on their time complexity we present asymptotically faster algorithms based on enumeration techniques and we show that these algorithms are applicable to well studied problems in for instance temporal reasoning finally we prove non trivial lower bounds applicable to many interesting csps under the assumption that certain complexity theoretic assumptions hold the gap between upper and lower bounds is in many cases surprisingly small which suggests that our upper bounds cannot be significantly improved

the hartman wintner theorem for functional differential equations abstract in this paper we present a generalization of the hartman wintner theorem about the asymptotic behavior of the solutions of linear ordinary differential equations to functional differential equations

reasoning about temporal relations the tractable subalgebras of allen s interval algebra allen s interval algebra is one of the best established formalisms for temporal reasoning this article provides the final step in the classification of complexity for satisfiability problems over constraints expressed in this algebra when the constraints are chosen from the full allen s algebra this form of satisfiability problem is known to be np complete however eighteen tractable subalgebras have previously been identified we show here that these subalgebras include all possible tractable subsets of allen s algebra in other words we show that this algebra contains exactly eighteen maximal tractable subalgebras and reasoning in any fragment not entirely contained in one of these subalgebras is np complete we obtain this dichotomy result by giving a new uniform description of the known maximal tractable subalgebras and then systematically using a general algebraic technique for identifying maximal subalgebras with a given property

tractable disjunctions of linear constraints basic results and applications to temporal reasoning we study the problems of deciding consistency and performing variable elimination for disjunctions of linear inequalities and disequations with at most one inequality per disjunction this new class of constraints extends the class of generalized linear constraints originally studied by lassez and mcaloon we show that deciding consistency of a set of constraints in this class can be done in polynomial time we also present a variable elimination algorithm which is similar to fourier s algorithm for linear inequalities finally we use these results to provide new temporal reasoning algorithms for the ord horn subclass of allen s interval formalism we also show that there is no low level of local consistency that can guarantee global consistency for the ord horn subclass this property distinguishes the ord horn subclass from the pointizable subclass for which strong 5 consistency is sufficient to guarantee global consistency and the continuous endpoint subclass for which strong 3 consistency is sufficient to guarantee global consistency copyright 2001 elsevier science b v

monoidal extensions of a cohen macaulay unique factorization domain let a be a noetherian cohen macaulay domain b c 1 c g an a sequence j b c 1 c g a and b a j b then b is cohen macaulay there is a natural one to one correspondence between the sets ass b b bb and ass a a j and each q ass a a j has height g 1 if b does not have unique factorization then some height one prime ideals p of b are not principal these primes are identified in terms of j and p a and we consider the question of how far from principal they can be if a is integrally closed necessary and sufficient conditions are given for b to be integrally closed and sufficient conditions are given for b to be a ufd or a krull domain whose class group is torsion finite or finite cyclic it is shown that if p is a height one prime ideal of b then p a also has height one if and only if b p and thus p a has height one for all but finitely many of the height one primes p of b if a has unique factorization a description is given of whether or not such a prime p is a principal prime ideal or has a principal primary ideal in terms of properties of p n a a similar description is also given for the height one prime ideals p of b with p a of height greater than one if the prime factors of b satisfy a mild condition if a is a ufd and b is a power of a prime element then b is a krull domain with torsion class group if and only if j is primary and integrally closed and if this holds then b has finite cyclic class group also if j j is not primary then for each height one prime ideal p contained in at least one but not all prime divisors of j it holds that the height one prime pa 1 b b has no principal primary ideals this applies in particular to the rees ring r a 1 t tj as an application of these results it is shown how to construct for any finitely generated abelian group g a monoidal transform b a j b such that a is a ufd b is cohen macaulay and integrally closed and g cl b the divisor class group of b

koszul homology and the structure of low codimension cohen macaulay ideals the relationship between the properties of the koszul homology modules of two ideals connected by linkage is studied if the ideal i is either i a cohen macaulay ideal of codimension 3 or ii a gorenstein ideal of codimension 4 the one dimensional koszul module carries considerable information on the struct ural nature of the linkage class of i in case i or on the conormal module of i in case ii emphasis is given to the verification of the properties by computation introduction the aim of this paper is to examine the structure of cohen macaulay ideals of low i e 3 and 4 codimension as it is expressed by the koszul homology modules more specifically given a perfect ideal i of a gorenstein nng r we are interested in how i its numerical data e g betti numbers and degrees of its generating syzygies in the case of a homogeneous ideal ii properties of the full linkage class of i and iii whether i is suitably generated e g generated by a d sequence are mirrored on the module and the algebra structures of the homology of the koszul complex build on a generating set of i the man result theorem 2 4 is the proof that for a perfect ideal i of codimension threes the condition that the 1 dimensional koszul homology module h1 i r be cohen macaulay is an invanant of the full linkage class of i the framework for this result is provided by several facts first the classical descnptions of cohen macaulay ideals of codimension two and of gorenstein ideals of heit ht three as belonging to the linkage classes of complete intersections a be ga w then a theorem of huneke hu1 asserting that the property hi i r is cohen macaulay for i ms is an invariant of the eren linkage class of i finally in case of ideals of polynomial rings data on the koszul homology has the advantage of being in principle known at the outset that is hypotheses on them can be venfied once the ideal has been specified by a set of generators in the last section we indicate how symbolic computation packages may be used to obtain this informa tion to contrast already in the case of codimension four gorenstein ideals the depths of the koszul homology modules of directly linked ideals may differ sharply furthermore in codimension three we show that this invanance does not extend to the next koszul module to further enhance the role of h1 i r as a carrier of

on the divisor class group of rees algebras let r be a normal noetherian domain and let i be an ideal whose associated graded ring gr r is reduced barshay 2 showed that under these conditions the rees algebra s r it r 0 it 0 izt2 a e r t is normal a much simpler proof was given later by huneke 111 let p r it t be the extended rees algebra then pt e r t t 1 is normal and p tp e gr r is reduced it follows that p itself is normal this implies easily the normality of s as well we are interested in the class group cl s of s to obtain a neat result we strengthen our hypothesis and assume that gr r is a domain hochster 6 showed in this case that p is factorial if r is so the only tool needed to prove this is the following elementary but powerful theorem of nagata

building tractable disjunctive constraints many combinatorial search problems can be expressed as constraint satisfaction problems this class of problems is known to be np hard in general but a number of restricted constraint classes have been identified which ensure tractability this paper presents the first general results on combining tractable constraint classes to obtain larger more general tractable classes we give examples to show that many known examples of tractable constraint classes from a wide variety of different contexts can be constructed from simpler tractable classes using a general method we also construct several new tractable classes that have not previously been identified

integral closure and generic elements abstract let r m be a formally equidimensional local ring with depth r 2 and i a 1 a n an m primary ideal in r the main result of this paper shows that if i is integrally closed then so is its image modulo a generic element that is if t r x 1 x n a 1 x 1 a n x n then i t i t

on the complexity of qualitative spatial reasoning a maximal tractable fragment of the region connection calculus the computational properties of qualitative spatial reasoning have been investigated to some degree however the question for the boundary between polynomial and np hard reasoning problems has not been addressed yet in this paper we explore this boundary in the region connection calculus rcc 8 we extend bennett s encoding of rcc 8 in modal logic based on this encoding we prove that reasoning is np complete in general and identify a maximal tractable subset of the relations in rcc 8 that contains all base relations further we show that for this subset path consistency is sufficient for deciding consistency

reasoning about partially ordered events abstract this paper describes a class of temporal reasoning problems involving events whose order is not completely known we examine the complexity of such problems and show that for all but trivial cases these problems are likely to be intractable as an alternative to a complete but potentially exponential time decision procedure we provide a partial decision procedure that reports useful results and runs in polynomial time

on the canonical module of the rees algebra and the associated graded ring of an ideal the investigations of this paper originate in the following question suppose i is an ideal of a local gorenstein ring r m whose associated graded ring gr r is cohenmacaulay under which extra conditions is gr r actually a gorenstein ring hochster shows in 151 that gr r is a gorenstein ring if r is factorial and gr r is a domain hochster s arguments work as well if one only requires r to be a gorenstein ring however the condition that gr r is a domain cannot be weakened much in fact we given an example of a local complete intersection r m whose associated graded ring gr r is a reduced cohen macaulay ring but not a gorenstein ring the question when gr r is a gorenstein ring has a more satisfying answer for ideals i generated by a d sequence for which r i is a cohen macaulay ring d sequences were introduced and studied by huneke their relevance in the study of powers of ideals was shown by huneke in 161 for further investigations on d sequences the reader is referred to 111 now given an ideal i generated by a d sequence and such that r i is cohenmacaulay we show that gr r is a gorenstein ring if and only if i is strongly cohen macaulay again the notion strongly cohen macaulay was introduced by huneke it means that the koszul homology of a system of generators of i is cohen macaulay huneke showed in 191 that any ideal in the linkage class of a complete intersection is strongly cohen macaulay this result provides us with plenty of interesting examples the main subject of the paper however is the study of the canonical module of gr r and of the rees algebra r if r zr 12t2 sr t in 14 the canonical class os of the rees algebra s r zr was determined under the assumption that i is

asymptotically exponential solutions in nonlinear integral and differential equations abstract in this paper we investigate the growth decay rate of solutions of an abstract integral equation which frequently arises in quasilinear differential equations applying a variation of constants formula these results are applicable to some abstract equations which appear in the theory of age dependent population models and also to some quasilinear delay differential equations with bounded and unbounded delays examples are given to illustrate the sharpness of the results

asymptotic behavior in volterra difference systems with unbounded delay we show that under certain conditions there is a one to one correspondence between weighted bounded solutions of a linear volterra difference equation with unbounded delay and its perturbation this correspondence is elevated to asymptotic equivalence under suitable conditions

bounds related to projective equivalence classes of ideals let z be a regular ideal in noetherian ring r and let i denote the integral closure of i a situation which is often of interest is when there is an integer b z 2 0 such that i b a e i for all n 2 1 for instance in an analytically unramified local ring such a b z exists for all i now recall that the ideal h is projectively equivalent to i if there are positive integers r and s with h i in section 1 we make the easy observation that the existence of b z as above is an invariant of the projective equivalence class of i that is if such a b z exists and if the ideal h is projectively equivalent to z then there is a b h with h bch n c h for all n 2 1 of course it may happen that b h b z the main purpose of section 1 is to study the stronger condition that there exist a fixed integer b 3 0 such that for all ideals h projectively equivalent to z h c h for all n 1 we make use of a key result namely that given z there exists an integer d such that for any ideal h projectively equivalent to z one can write hd p for some s let s 2 1 be an integer and let the ideal k be a reduction of i this means there is an integer e 20 depending on s and k with k z z in section 2 we discuss a situation in which e can in fact

a unifying approach to temporal constraint reasoning abstract we present a formalism disjunctive linear relations dlrs for reasoning about temporal constraints dlrs subsume most of the formalisms for temporal constraint reasoning proposed in the literature and is therefore computationally expensive we also present a restricted type of dlrs horn dlrs which have a polynomial time satisfiability problem we prove that most approaches to tractable temporal constraint reasoning can be encoded as horn dlrs including the ord horn algebra by nebel and burckert and the simple temporal constraints by dechter et al thus dlrs is a suitable unifying formalism for reasoning about temporal constraints

the complexity of temporal constraint satisfaction problems a temporal constraint language is a set of relations that has a first order definition in q an extended abstract of this article appeared in the proceedings of stoc 08

effective normality criteria for algebras of linear type abstract the algebras studied here are subalgebras of rings of polynomials generated by 1 forms so called rees algebras with coefficients in a noetherian ring given a normal domain r and a torsionfree module e with a free resolution f 2 f 1 f 0 e 0 we study the role of the matrices of syzygies in the normality of the rees algebra of e when the rees algebra r e and the symmetric algebra s e coincide the main results characterize normality in terms of the ideal ic s e and of the completeness of the first s symmetric powers of e where c rank and s rankf0 ranke it requires that r be a regular domain special results under broader conditions on r are still more effective

asymptotic integration of nonautonomous delay differential systems we prove existence theorems and asymptotic formulas for the solutions of a class of delay differential equations with time state dependent lag

normal sally modules of rank one in this paper we explore the structure of the normal sally modules of rank one with respect to an m m primary ideal in a nagata reduced local ring r which is not necessary cohen macaulay as an application of this result when the base ring is cohen macaulay analytically unramified the extremal bound on the first normal hilbert coefficient leads to the depth of the associated graded rings g with respect to a normal filtration is at least dim r 1 dim r 1 and g turns in to cohen macaulay when the third normal hilbert coefficient is vanished

disjunctions independence refinements an important question in constraint satisfaction is how to restrict the problem to ensure tractability since the general problem is np hard the use of disjunctions has proven to be a useful method for constructing tractable constraint classes from existing classes the well known max closed and ord horn constraints are examples of tractable classes that can be constructed this way three sufficient conditions the guaranteed satisfaction property 1 independence and 2 independence that each ensure the tractability of constraints combined by disjunctions have been proposed in the literature we show that these conditions are both necessary and sufficient for tractability in three different natural classes of disjunctive constraints this suggests that deciding this kind of property is a very important task when dealing with disjunctive constraints we provide a simple automatic method for checking the 1 independence property this method is applicable whenever the consistency of the constraints under consideration can be decided by path consistency our method builds on a connection between independence and refinements which is a way of reducing one constraint satisfaction problem to another

asymptotic behavior of parameter ideals in generalized cohen macaulay modules abstract the purpose of this paper is to give affirmative answers to two open questions as follows let r m be a generalized cohen macaulay noetherian local ring both questions the first question was raised by m rogers m rogers the index of reducibility for parameter ideals in low dimension j algebra 278 2004 571 584 and the second one is due to s goto and h sakurai s goto h sakurai the equality i 2 q i in buchsbaum rings rend sem mat univ padova 110 2003 25 56 ask whether for every parameter ideal q contained in a high enough power of the maximal ideal m the following statements are true 1 the index of reducibility n r q r is independent of the choice of q and 2 i 2 q i where i q r m

links of symbolic powers of prime ideals in this paper we prove the following let r frak m be a cohen macaulay local ring of dimension d 2 suppose that either r is not regular or if r is regular assume that d 3 let t 2 be a positive integer if alpha 1 dots alpha d is a regular sequence contained in frak m t then alpha 1 dots alpha d frak m t subseteq frak m t this result gives an affirmative answer to a conjecture raised by polini and ulrich

the index of reducibility of parameter ideals in low dimension in this paper we present results concerning the following ques tion if m is a finitely generated module with finite local cohomologies over a noetherian local ring a m does there exist an integer l such that every parameter ideal for m contained in m l has the same index of reducibility we show that the answer is yes if dim m 1 or if dim m 2 and depth m 0 this research is closely related to work of goto suzuki and goto sakurai goto sakurai have supplied an answer of yes in case m is buchsbaum

integrally closed almost complete intersection ideals abstract let a m be a local ring we study the existence and structure of the m primary integrally closed ideals generated by dim a 1 elements

qualitative constraint satisfaction problems an extended framework with landmarks dealing with spatial and temporal knowledge is an indispensable part of almost all aspects of human activity the qualitative approach to spatial and temporal reasoning known as qualitative spatial and temporal reasoning qstr typically represents spatial temporal knowledge in terms of qualitative relations e g to the east of after and reasons with spatial temporal knowledge by solving qualitative constraints when formulating qualitative constraint satisfaction problems csps it is usually assumed that each variable could be here there and everywhere practical applications such as urban planning however often require a variable to take its value from a certain finite domain i e it is required to be here or there but not everywhere entities in such a finite domain often act as reference objects and are called landmarks in this paper the paper extends the classical framework of qualitative csps by allowing variables to take values from finite domains the computational complexity of the consistency problem in this extended framework is examined for the five most important qualitative calculi viz point algebra interval algebra cardinal relation algebra rcc5 and rcc8 we show that all these consistency problems remain in np and provide under practical assumptions efficient algorithms for solving basic constraints involving landmarks for all these calculi

the equality i2 qi in sequentially cohen macaulay rings let r be a sequentially cohen macaulay local ring and assume that dimr 2 or that dimr 1 and e r 1 then the equality i2 qi holds true for every good parameter ideal q of r contained in a sufficiently high power of the maximal ideal m where i q rm the structure of the graded rings gr i n 0in in 1 r i n 0in and r i n zin associated to i is explored in connection to their sequential cohen macaulayness

rees algebras of f regular type abstract we study the f regularity of rees algebras r i a it in terms of the global f regularity of the blowing up x proj r i of spec a as it reads global f regularity is a global analog of strong f regularity defined via splitting of frobenius maps in prime characteristic and these notions are extended to characteristic zero by reduction modulo p 0 we study in detail the case where a m is a two dimensional local ring and i is an m primary ideal in characteristic zero the condition for r i to have f regular type is described in terms of the dual graph of a resolution x on which i o x is invertible we also prove some miscellaneous results concerning singularities of rees algebras and extended rees algebras of higher dimension

an asymptotic theory for nonlinear functional differential equations abstract the hartman wintner theorem on asymptotic integration is established for a certain class of functional differential equations with nonlinear perturbations by looking them as abstract ordinary differential equations results for delay differential equations are included in this study consequences and applications are also shown

sums of linked ideals it is shown that the sum of two geometrically linked ideals in the linkage class of a complete intersection is again an ideal in the linkage class of a complete intersection conversely every gorenstein ideal of height at least two in the linkage class of a complete intersection can be obtained as a generalized localization of a sum of two geometrically linked ideals in the linkage class of a complete intersection we also investigate sums of doubly linked gorenstein ideals as an application we construct a perfect prime ideal which is strongly nonobstructed but not strongly cohen macaulay and a perfect prime ideal which is not strongly nonobstructed but whose entire linkage class is strongly cohen macaulay

links of prime ideals and their rees algebras abstract in a previous paper we exhibited the somewhat surprising property that most direct links of prime ideals in gorenstein rings are equimultiple ideals with reduction number 1 this led to the construction of large families of cohen macaulay rees algebras the first goal of this paper is to extend this result to arbitrary cohen macaulay rings the means of the proof are changed since one cannot depend so heavily on linkage theory we then study the structure of the rees algebra of these links more specifically we describe their canonical module in sufficient detail to be able to characterize self linked prime ideals in the last section multiplicity estimates for classes of such ideals are established