splittable ideals and the resolutions of monomial ideals abstract we provide a new combinatorial approach to study the minimal free resolutions of edge ideals that is quadratic square free monomial ideals with this method we can recover most of the known results on resolutions of edge ideals with fuller generality and at the same time obtain new results past investigations on the resolutions of edge ideals usually reduced the problem to computing the dimensions of reduced homology or koszul homology groups our approach circumvents the highly nontrivial problem of computing the dimensions of these groups and turns the problem into combinatorial questions about the associated simple graph we also show that our technique extends successfully to the study of graded betti numbers of arbitrary square free monomial ideals viewed as facet ideals of simplicial complexes

linear free resolutions and minimal multiplicity let s k x x be a polynomial ring over a field and let a4 a m be a finitely generated graded module in the most interesting case a4 is an ideal of s for a given natural number p there is a great interest in the question can m be generated by homogeneous elements of degree p no simple answer say in terms of the local cohomology of m is known but somewhat surprisingly the stronger question can the jth syzygy of m be generated by elements of degree qp j for all j 0 l n does admit a simple response the following is neither new nor difficult to prove though it seems not well known

ideals with stable betti numbers componentwise linear ideals were introduced earlier to generalize the result that the stanley reisner ideal i of a simplicial complex has a linear resolution if and only if its alexander dual is cohen macaulay it turns out that i is componentwise linear if and only if is sequentially cohen macaulay in this paper we discuss betti number properties of componentwise linear ideals let i be a graded ideal of a polynomial ring s and gin i the generic initial ideal of i with respect to the reverse lexicographic term order on s our main result is that i and gin i admit the same graded betti numbers if and only if i is componentwise linear for the proof of this fact we describe some properties of the betti diagram of a generic initial ideal combinatorial implications for shifted complexes will also be discussed

surfaces in p4 with extremal general hyperplane section abstract optimal upper bounds for the cohomology groups of space curves have been derived recently curves attaining all these bounds are called extremal curves this note is a step to analyze the corresponding problems for surfaces we state optimal upper bounds for the second and third cohomology groups of surfaces in p 4 and show that surfaces attaining all these bounds exist and must have an extremal curve as general hyperplane section surprisingly all the first cohomology groups of such surfaces vanish it follows that an extremal curve does not lift to a locally cohen macaulay surface unless the curve is arithmetically cohen macaulay

optimal controllers and output feedback stabilization abstract in this paper the output feedback stabilizability problem is explored in terms of control lyapunov functions sufficient conditions for stabilization are provided for a certain class of systems by means of output feedback stabilizers that can be obtained from an optimization problem our main results extends those developed in 31 and generalize a theorem due to sontag 23

maximal minimal resolutions that is exact everywhere except at f0 where the cokernel is m such a resolution always exists if r is a noetherian n graded ring with r0 a field and m is a finitely generated z graded r module then a resolution may be constructed in a minimal way in which each fi is graded and each differential is homogeneous of degree 0 the rank of the ith free module in a minimal free resolution of m is an invariant of m called the ith betti number of m and denoted i m likewise r ij m the number of elements of degree j in a minimal set of homogeneous generators of fi is also an invariant of m called the i j th graded betti number of m in this paper we study modules with maximal graded betti numbers more precisely consider a set consisting of pairs r m where r is a noetherian n graded ring with r0 a field and m is a finitely generated graded r module is there some r m such that ij m ij m for every i and j and every r m there are trivial examples in which the answer is yes e g has only one element or no e g consists of all such pairs theorems 1 and 2 below give affirmative answers for certain sets defined by conditions on the hilbert series and the depths of r and m theorem 3 allows one to compute the maximal graded betti numbers for the pairs in the sets considered in theorems 1 and 2 throughout this paper k denotes a field and q the polynomial ring k x1 xn with the usual n grading given by degxi 1 the hilbert series of a finitely generated graded q module m is hm s dimk mis we define d lexicographic ideals and submodules in section 2 the poincare series of an r module m is p m s t ij m s t we write 4 for coefficient wise inequality of laurent series with coefficients in z

betti splitting via componentwise linear ideals abstract a monomial ideal i admits a betti splitting i j k if the betti numbers of i can be determined in terms of the betti numbers of the ideals j k and j k given a monomial ideal i we prove that i j k is a betti splitting of i provided j and k are componentwise linear generalizing a result of francisco ha and van tuyl if i has a linear resolution the converse also holds we apply this result recursively to the alexander dual of vertex decomposable shellable and constructible simplicial complexes moreover we determine the graded betti numbers of the defining ideal of three general fat points in the projective space

buchsbaum rim sheaves and their multiple sections abstract this paper begins by introducing and characterizing buchsbaum rim sheaves on z proj r where r is a graded gorenstein k algebra they are reflexive sheaves arising as the sheafification of kernels of sufficiently general maps between free r modules then we study multiple sections of a buchsbaum rim sheaf b i e we consider morphisms p b of sheaves on z dropping rank in the expected codimension where h0 z p is a free r module the main purpose of this paper is to study properties of schemes associated to the degeneracy locus s of it turns out that s is often not equidimensional let x denote the top dimensional part of s in this paper we measure the difference between x and s compute their cohomology modules and describe ring theoretic properties of their coordinate rings moreover we produce graded free resolutions of x and s which are in general minimal among the applications we show how one can embed a subscheme into an arithmetically gorenstein subscheme of the same dimension and prove that zero loci of sections of the dual of a null correlation bundle are arithmetically buchsbaum

distributed robust filtering with h consensus of estimates the paper addresses a problem of design of distributed robust filters using the recent vector dissipativity theory the main result is a sufficient condition which guarantees a suboptimal h level of disagreement of estimates in a network of filters it involves solving a convex optimization feasibility problem subject to lmi constraints the special case of balanced interconnection graphs is also considered a gradient descent type algorithm is presented which allows the nodes to compute their estimator parameters in a decentralized manner the proposed approach is applied to the problem of observer based robust synchronization of a nonlinear network to an isolated node

decentralized measurement feedback stabilization of large scale systems via control vector lyapunov functions abstract this paper studies the problem of decentralized measurement feedback stabilization of nonlinear interconnected systems as a natural extension of the recent development on control vector lyapunov functions the notion of output control vector lyapunov function ocvlf is introduced for investigating decentralized measurement feedback stabilization problems sufficient conditions on local stabilizability are discussed which are based on the proposed notion of ocvlf it is shown that a decentralized controller for a nonlinear interconnected system can be constructed using these conditions under an additional vector dissipation like condition to illustrate the proposed method two examples are given

convex computation of the region of attraction of polynomial control systems we address the long standing problem of computing the region of attraction roa of a target set e g a neighborhood of an equilibrium point of a controlled nonlinear system with polynomial dynamics and semialgebraic state and input constraints we show that the roa can be computed by solving an infinite dimensional convex linear programming lp problem over the space of measures in turn this problem can be solved approximately via a classical converging hierarchy of convex finite dimensional linear matrix inequalities lmis our approach is genuinely primal in the sense that convexity of the problem of computing the roa is an outcome of optimizing directly over system trajectories the dual infinite dimensional lp on nonnegative continuous functions approximated by polynomial sum of squares allows us to generate a hierarchy of semialgebraic outer approximations of the roa at the price of solving a sequence of lmi problems with asymptotically vanishing conservatism this sharply contrasts with the existing literature which follows an exclusively dual lyapunov approach yielding either nonconvex bilinear matrix inequalities or conservative lmi conditions the approach is simple and readily applicable as the outer approximations are the outcome of a single semidefinite program with no additional data required besides the problem description the approach is demonstrated on several numerical examples

stabilization with relaxed controls cannot in general be stabilized using a continuous closed loop control u x even if each state separately can be driven asymptotically to the origin an example is analyzed in section 2 in this paper we examine the possibility of stabilizing such systems with a continuous closed loop relaxed control we find indeed that the family of systems stabilizable with relaxed controls is larger than the family of those stabilizable with ordinary controls an even larger class is obtained if the continuity of the closed loop at the origin is not required the latter class includes all one dimensional systems for which states can be driven asymptotically to the origin this result does not hold in two dimensional systems and we provide a counter example it should be pointed that relaxed control type stabilization is used both in theory and in practice the method is known as dither we shall comment on the similarities lyapunov functions for the system 1 help us in the construction of the continuous closed loop stabilizers in fact we find that the existence of a smooth lyapunov function is equivalent to the existence of a stabilizing closed loop which is continuous except possibly at the origin an additional condition on the lyapunov function implies the continuity at the origin as well we present these results in section 4 after a brief introduction of closed loop relaxed controls notations and terminology in section 3 prior to that in section 2 we discuss an example illustrating the power of relaxed controls in the particular case of systems linear in the controls relaxed controls can be replaced by ordinary controls this is discussed in section 5 the role of lyapunov functions in the stability and stabilization theories is of course well known examples of systems with lyapunov functions are available in the literature we display some in section 6 along with general comments on the construction applications and counterexamples including one which cannot be continuously stabilized yet possesses a nonsmooth lyapunov function closed loop stabilization with ordinary controls is analyzed extensively in the literature see sontag 8 sussmann ll and references therein lyapunov functions techniques in stabil

the general hyperplane section of a curve in this paper we discuss some necessary and sufficient conditions for a curve to be arithmetically cohen macaulay in terms of its general hyperplane section we obtain a characterization of the degree matrices that can occur for points in the plane that are the general plane section of a non arithmetically cohen macaulay curve of p 3 we prove that almost all the degree matrices with positive subdiagonal that occur for the general plane section of a non arithmetically cohen macaulay curve of p 3 arise also as degree matrices of some smooth integral non arithmetically cohen macaulay curve and we characterize the exceptions we give a necessary condition on the graded betti numbers of the general plane section of an arithmetically buchsbaum non arithmetically cohen macaulay curve in p for curves in p 3 we show that any set of betti numbers that satisfies that condition can be realized as the betti numbers of the general plane section of an arithmetically buchsbaum non arithmetically cohen macaulay curve we also show that the matrices that arise as a degree matrix of the general plane section of an arithmetically buchsbaum integral smooth non arithmetically cohen macaulay space curve are exactly those that arise as a degree matrix of the general plane section of an arithmetically buchsbaum non arithmetically cohen macaulay space curve and have positive subdiagonal we also prove some bounds on the dimension of the deficiency module of an arithmetically buchsbaum space curve in terms of the degree matrix of the general plane section of the curve and we prove that they are sharp

generic projections the equations defining projective varieties and castelnuovo regularity for a reduced irreducible projective variety x of degree d and codimension e in mathbb p n the castelnuovo mumford regularity rm reg x is defined as the least k such that x is k regular i e h i mathbb p n mathcal i x k i 0 for i ge1 where mathcal i x subset cal o mathbb p n is the sheaf of ideals of x there is a long standing conjecture about k regularity see 5 rm reg x le d e 1 here we show that rm reg x le d e 1 10 for any smooth fivefold and rm reg x le d e 1 20 for any smooth sixfold by extending methods used in 10 furthermore we give a bound for the regularity of a reduced connected and equidimensional locally cohen macaulay curve or surface in terms of degree d codimension e and an arithmetic genus rho a see theorem 4 1

rank two acm bundles on the del pezzo threefold with picard number 3 abstract a del pezzo threefold f with maximal picard number is isomorphic to p 1 p 1 p 1 in the present paper we completely classify locally free sheaves e of rank 2 such that h i f e t 0 for i 1 2 and t z such a classification extends similar results proved by e arrondo and l costa regarding del pezzo threefolds with picard number 1

artinian level modules and cancellable sequences in order to use dualization to study hilbert functions of artinian level algebras we extend the notion of level sequences and cancellable sequences introduced by geramita and lorenzini to include

families of space curves with large cohomology abstract we investigate space curves with large cohomology to this end we introduce curves of subextremal type this class includes all subextremal curves based on geometric and numerical characterizations of curves of subextremal type we show that if the cohomology is not too small then they can be parameterized by the union of two generically smooth irreducible families one of them corresponds to the subextremal curves for curves of negative genus the general curve of each of these families is also a smooth point of the support of an irreducible component of the hilbert scheme the two components have the same large dimension and meet in a subscheme of codimension one

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

initial ideals veronese subrings and rates of algebras abstract let s be a polynomial ring over an infinite field and let i be a homogeneous ideal of s let t d be a polynomial ring whose variables correspond to the monomials of degree d in s we study the initial ideals of the ideals v d i t d that define the veronese subrings of s i in suitable orders they are easily deduced from the initial ideal of i we show that in v d i is generated in degree max reg i d 2 where reg i is the regularity of the ideal i in other words the d th veronese subrings of any commutative graded ring s i has a grobner basis of degree max i d 2 we also give bounds on the regularity of i in terms of the degrees of the generators of in i and some combinatorial data this implies a version of backelin s theorem that high veronese subrings of any ring are homogeneous koszul algebras in the sense of priddy trans amer math soc 152 1970 39 60 we also give a general obstruction for a homogeneous ideal i s to have an initial ideal in i that is generated by quadrics beyond the obvious requirement that i itself should be generated by quadrics and the stronger statement that s i is koszul we use the obstruction to show that in certain dimensions a generic complete intersection of quadrics cannot have an initial ideal that is generated by quadrics for the application to backelin s theorem we require a result of backelin whose proof has never appeared we give a simple proof of a sharpened version bounding the rate of growth of the degrees of generators for syzygies of any multihomogenous module over a polynomial ring modulo an ideal generated by monomials following a method of bruns and herzog

robust region of attraction estimation we propose a method to compute invariant subsets of the region of attraction for asymptotically stable equilibrium points of polynomial dynamical systems with bounded parametric uncertainty parameter independent lyapunov functions are used to characterize invariant subsets of the robust region of attraction a branch and bound type refinement procedure reduces the conservatism we demonstrate the method on an example from the literature and uncertain controlled short period aircraft dynamics

pruned cellular free resolutions of monomial ideals abstract using discrete morse theory we give an algorithm that prunes the excess of information in the taylor resolution and constructs a new cellular free resolution for an arbitrary monomial ideal the pruned resolution is not simplicial in general but we can slightly modify our algorithm in order to obtain a simplicial resolution we also show that the lyubeznik resolution fits into our pruning strategy the pruned resolution is not always minimal but it is a lot closer to the minimal resolution than the taylor and the lyubeznik resolutions as we will see in some examples we finally use our methods to give a different approach to the theory of splitting of monomial ideals we deduce from this splitting strategy that the pruned resolution is always minimal in the case of edge ideals of paths and cycles

extended degree functions and monomial modules the arithmetic degree the smallest extended degree and the homological degree are invariants that have been proposed as alternatives of the degree of a module if this module is not cohen macaulay we compare these degree functions and study their behavior when passing to the generic initial or the lexicographic submodule this leads to various bounds and to counterexamples to a conjecture of gunston and vasconcelos respectively particular attention is given to the class of sequentially cohen macaulay modules the results in this case lead to an algorithm that computes the smallest extended degree

algebra structures on some canonical resolutions the study of algebra structures on finite free resolutions of cyclic modules begins with buchsbaum and eisenbud b el the classes of cyclic modules whose minimal resolutions are known to admit an algebra structure include the residue field gu complete intersections koszul complex modules of homological dimension atmost 3 b el gorenstein of codimension four k m and herzog algebras k m23 avramov al gave examples to show that there are cyclic modules whose minimal resolutions do not admit an algebra structure let r be a noetherian local ring with maximal ideal m in this paper we construct algebra structures on the minimal resolutions of two classes of cyclic modules r i namely when z is of the form jk where j is an ideal generated by a regular sequence and when z is the ideal of maximal minors of a generic n x m matrix provided r contains the rationals in al avramov defined certain obstructions to the existance of an algebra structure on the minimal resolution of a module and then produced modules with non zero obstructions the general question is whether the vanishing of these obstructions is also sufficient for the existence of a minimal algebra resolution of a cyclic module when z is an ideal generated by a regular sequence in r and m r z for any positive integer k then these obstructions are all zero therefore avramov and schlessinger asked whether the minimal resolutions of r z admit an algebra structure corollary 3 6 of this paper provides an affirmative answer to this question

non degenerate curves with maximal hartshorne rao module extending results for space curves we establish bounds for the cohomology of a non degenerate curve in projective n space as a consequence for any given n we determine all possible pairs d g where d is the degree and g is the arithmetic genus of the curve furthermore we show that curves attaining our bounds always exist and describe properties of these extremal curves in particular we determine the hartshorne rao module the generic initial ideal and the graded betti numbers of an extremal curve

a universal construction of artstein s theorem on nonlinear stabilization abstract this note presents an explicit proof of the theorem due to artstein which states that the existence of a smooth control lyapunov function implies smooth stabilizability moreover the result is extended to the real analytic and rational cases as well the proof uses a universal formula given by an algebraic function of lie derivatives this formula originates in the solution of a simple riccati equation

on a theorem of castelnuovo and the equations defining space curves introduction 491 w notat ion and conventions 493 w a regularity theorem 494 w a rationality theorem 498 w the existence of secant lines 501 w open problems 505 references 506

output feedback stabilization and estimation of the region of attraction for nonlinear systems a vector control lyapunov function perspective this technical note deals with local asymptotic stabilization of uncertain nonlinear systems by output feedback control our study provides a new design technique from a vector control lyapunov function perspective a comparison principle is developed and as a major consequence an effective estimation method of the region of attraction roa is established application to a class of minimum phase strict feedback nonlinear systems gives rise to a constructive stabilization design as well as an estimate of the resulting roa

an iterative construction of gorenstein ideals in this paper we present a method to inductively construct gorenstein ideals of any codimension c we start from a gorenstein ideal i of codimension c contained in a complete intersection ideal j of the same codimension and we prove that under suitable hypotheses there exists a new gorenstein ideal contained in the residual ideal i j we compare some numerical data of the starting and the resulting gorenstein ideals of the construction we compare also the buchsbaum eisenbud matrices of the two ideals in the codimension three case furthermore we show that this construction is independent from the other known geometrical constructions of gorenstein ideals providing examples

reverse lex ideals we study reverse lex ideals in a polynomial ring and compare their properties to those of lex ideals in particular we provide an analogue of green s theorem for reverse lex ideals we also compare the betti numbers of strongly stable and square free strongly stable monomial ideals to those of reverse lex ideals

free resolutions of lex ideals over a koszul toric ring in this paper we study the minimal free resolution of lex ideals over a koszul toric ring in particular we study in which toric ring r all lex ideals are componentwise linear we give a certain necessity and sufficiency condition for this property and show that lex ideals in a strongly koszul toric ring are componentwise linear in addition it is shown that in the toric ring arising from the segre product p p every hilbert function of a graded ideal is attained by a lex ideal and that lex ideals have the greatest graded betti numbers among all ideals having the same hilbert function

vector lyapunov function based input to state stability of stochastic impulsive switched time delay systems in this paper the input to state stability is studied for stochastic impulsive switched time delay systems using the vector lyapunov function average dwell time and the properties of m matrix different types of sufficient conditions are established both the case that the continuous dynamics is stable and the case that the discrete dynamics is stable are addressed and the stability conditions are obtained in the obtained stability conditions different components of the vector lyapunov function are allowed to be coupled the information in consecutive impulsive switching intervals is also allowed to be coupled therefore the magnification on the corresponding coupling items is avoided and the obtained results are more general and less conservative than the existing results furthermore we investigate the relationships among the vector lyapunov function approach the approach based on the comparison principle and the scalar lyapunov function approach according to the vector lyapunov function the comparison system is constructed and the scalar lyapunov function based stability conditions are established finally the applicability of our results is illustrated through two examples from neural systems and the synchronization problem of chaos based secure communication systems

on the genus and hartshorne rao module of projective curves in this paper optimal upper bounds for the genus and the dimension of the graded components of the hartshorne rao module of curves in projective n space are established this generalizes earlier work by hartshorne h and martin deschamps and perrin mdp special emphasis is put on curves in bf p 4 the first main result is a so called restriction theorem it says that a non degenerate curve of degree d geq 4 in bf p 4 over a field of characteristic zero has a non degenerate general hyperplane section if and only if it does not contain a planar curve of degree d 1 see th 1 3 then using methods of brodmann and nagel bounds for the genus and hartshorne rao module of curves in bf p n with non degenerate general hyperplane section are derived it is shown that these bounds are best possible in a very strict sense coupling these bounds with the restriction theorem gives the second main result for curves in bf p 4 then curves of maximal genus are investigated the betti numbers of their minimal free resolutions are computed and a description of all reduced curves of maximal genus in bf p n of degree geq n 2 is given finally all pairs d g of integers which really occur as the degree d and genus g of a non degenerate curve in bf p 4 are described

hilbert schemes and maximal betti numbers over veronese rings macaulay s theorem macaulay in proc lond math soc 26 531 555 1927 characterizes the hilbert functions of graded ideals in a polynomial ring over a field we characterize the hilbert functions of graded ideals in a veronese ring r the coordinate ring of a veronese embedding of pr 1 we also prove that the hilbert scheme which parametrizes all graded ideals in r with a fixed hilbert function is connected this is an analogue of hartshorne s theorem hartshorne in math ihes 29 5 48 1966 that hilbert schemes over a polynomial ring are connected furthermore we prove that each lex ideal in r has the greatest betti numbers among all graded ideals with the same hilbert function

on the resolution of ideals of fat points abstract in this paper we determine the hilbert function and the minimal system of generators of r 1 n 1 general fat points of p n furthermore by looking at the minimal system of generators we can show that the ideal associated to two fat points in p n or the ideal associated to r 1 n general fat points all with the same multiplicities is a splittable ideal and this is the first step in constructing a minimal resolution

a multiple comparison systems method for distributed stability analysis of large scale nonlinear systems lyapunov functions provide a tool to analyze the stability of nonlinear systems without extensively solving the dynamics recent advances in sum of squares methods have enabled the algorithmic computation of lyapunov functions for polynomial systems however for general large scale nonlinear networks it is yet very difficult and often impossible both computationally and analytically to find lyapunov functions in such cases a system decomposition coupled to a vector lyapunov functions approach provides a feasible alternative by analyzing the stability of the nonlinear network through a reduced order comparison system however finding such a comparison system is not trivial and often for a nonlinear network there does not exist a single comparison system in this work we propose a multiple comparison systems approach for the algorithmic stability analysis of nonlinear systems using sum of squares methods we design a scalable and distributed algorithm which enables the computation of comparison systems using only communications between the neighboring subsystems we demonstrate the algorithm by applying it to an arbitrarily generated network of interacting van der pol oscillators

on the stability and control of nonlinear dynamical systems via vector lyapunov functions vector lyapunov theory has been developed to weaken the hypothesis of standard lyapunov theory in order to enlarge the class of lyapunov functions that can be used for analyzing system stability in this paper we extend the theory of vector lyapunov functions by constructing a generalized comparison system whose vector field can be a function of the comparison system states as well as the nonlinear dynamical system states furthermore we present a generalized convergence result which in the case of a scalar comparison system specializes to the classical krasovskii lasalle invariant set theorem in addition we introduce the notion of a control vector lyapunov function as a generalization of control lyapunov functions and show that asymptotic stabilizability of a nonlinear dynamical system is equivalent to the existence of a control vector lyapunov function moreover using control vector lyapunov functions we construct a universal decentralized feedback control law for a decentralized nonlinear dynamical system that possesses guaranteed gain and sector margins in each decentralized input channel furthermore we establish connections between the recently developed notion of vector dissipativity and optimality of the proposed decentralized feedback control law finally the proposed control framework is used to construct decentralized controllers for large scale nonlinear systems with robustness guarantees against full modeling uncertainty

betti numbers of chordal graphs and f vectors of simplicial complexes abstract let g be a chordal graph and i g its edge ideal let i g 0 1 p denote the betti sequence of i g where i stands for the ith total betti number of i g and where p is the projective dimension of i g it will be shown that there exists a simplicial complex of dimension p whose f vector f f 0 f 1 f p coincides with i g

output feedback stabilization the stabilization of control systems using output feedback is addressed necessary and sufficient lyapunov conditions are established generalizing the artstein s stabilization theorem for linear control systems a necessary and sufficient lyapunov condition is provided for stabilization by means of a linear output feedback law

smoothed rank regression with censored data a weighted rank estimating function is proposed to estimate the regression parameter vector in an accelerated failure time model with right censored data in general rank estimating functions are discontinuous in the regression parameter creating difficulties in determining the asymptotic distribution of the estimator a local distribution function is used to create a rank based estimating function that is continuous and monotone in the regression parameter vector a weight is included in the estimating function to produce a bounded influence estimate the asymptotic distribution of the regression estimator is developed and simulations are performed to examine its finite sample properties a lung cancer dataset is used to illustrate the methodology

order ideals and a generalized krull height theorem let n be a finitely generated module over a noetherian local ring r m we give criteria for the height of the order ideal n x of an element x n to be bounded by the rank of n the generalized principal ideal theorem of bruns eisenbud and evans says that this inequality always holds if x mn we show that the inequality even holds if the hypothesis becomes true after first extending scalars to some local domain and then factoring out torsion we give other conditions in terms of residual intersections and integral closures of modules we derive information about order ideals that leads to bounds on the heights of trace ideals of modules even in circumstances where we do not have the expected bounds for the heights of the order ideals

on invariant polyhedra of continuous time linear systems this note presents some conditions of existence of positively invariant polyhedra for linear continuous time systems these conditions are first described algebraically then interpreted on the basis of the system eigenstructure then a simple state feedback placement method is described for solving some linear regulation problems under constraints

resolutions of a stable ideals abstract let a a 1 a 2 a n be a sequence of integers or we introduce a stable ideals in a polynomial ring and study their homological properties our results generalize results on square free monomial ideals by aramova avramov herzog hibi and srinivasan

global stabilization of nonlinear systems based on vector control lyapunov functions this paper studies the use of vector lyapunov functions for the design of globally stabilizing feedback laws for nonlinear systems recent results on vector lyapunov functions are utilized the main result of the paper shows that the existence of a vector control lyapunov function is a necessary and sufficient condition for the existence of a smooth globally stabilizing feedback applications to nonlinear systems are provided practically checkable sufficient conditions are proposed to guarantee the existence of a smooth globally stabilizing feedback law the obtained results are applied to the problem of the stabilization of an equilibrium point of a reaction network taking place in a continuous stirred tank reactor

the weak and strong lefschetz properties for artinian k algebras abstract let a i 0ai be a standard graded artinian k algebra where chark 0 then a has the weak lefschetz property if there is an element l of degree 1 such that the multiplication l a i a i 1 has maximal rank for every i and a has the strong lefschetz property if l d a i a i d has maximal rank for every i and d the main results obtained in this paper are the following 1 every height three complete intersection has the weak lefschetz property our method surprisingly uses rank two vector bundles on p 2 and the grauert mulich theorem 2 we give a complete characterization including a concrete construction of the hilbert functions that can occur for k algebras with the weak or strong lefschetz property and the characterization is the same one 3 we give a sharp bound on the graded betti numbers achieved by our construction of artinian k algebras with the weak or strong lefschetz property and fixed hilbert function this bound is again the same for both properties some hilbert functions in fact force the algebra to have the maximal betti numbers 4 every artinian ideal in k x y possesses the strong lefschetz property this is false in higher codimension

the hilbert function of generic plane sections of curves of ℙ3 a characteristic condition is given on a zero dimensional differentiable 0 sequenceh hi i 0 h1 3 in order to be the hilbert function of a generic plane section of a reduced irreducible curve of 3 hence of points of 2 with the uniform position property in this way an answer is given to some question stated by harris in ha2

lefschetz properties and hyperplane arrangements abstract in this article we study the weak and strong lefschetz properties and the related notion of almost revlex ideal in the non artinian case proving that several results known in the artinian case hold also in this more general setting we then apply the obtained results to the study of the jacobian algebra of hyperplane arrangements

curves of degree two and ropes on a line their ideals and even liaison classes abstract in this paper we investigate degree two curves of arbitrary codimension this requires to study also ropes supported on a line after establishing several characterizations of ropes supported on a line we describe their homogeneous ideals and hartshorne rao modules in particular we characterize the arithmetically buchsbaum ropes then we describe the even gorenstein liaison classes of the non arithmetically buchsbaum non degenerate ropes generalizing a well know result of migliore on double lines of codimension two the result relies on the explicit description of certain arithmetically gorenstein curves with maximal tangent spaces at each point as a consequence we can decide if two curves of degree two belong to the same gorenstein liaison class finally we show as an application how ropes can be used in order to construct quasi extremal curves

canonical curves with low apolarity abstract let k be an algebraically closed field and let c be a non hyperelliptic smooth projective curve of genus g defined over k since the canonical model of c is arithmetically gorenstein macaulay s theory of inverse systems allows us to associate to c a cubic form f in the divided power k algebra r g 3 in g 2 variables the apolarity ap c of c is the minimal number t of linear form l 1 l t r g 3 needed to write f as the sum of their divided power cubes it is easy to see that ap c g 2 and p de poi and f zucconi classified curves with ap c g 2 when k c in this paper we give a complete characteristic free classification of curves c with apolarity g 1 and g 2

sheaves with canonical determinant on cohen macaulay schemes abstract this paper studies the class of sheaves which lie on arithmetically cohen macaulay schemes and which have as determinant a twist of the canonical sheaf special emphasis is placed on finding minimal sufficient cohomological conditions which ensure that the top dimensional component of regular sections of the dual of these sheaves vanish along arithmetically gorenstein schemes duals of odd rank buchsbaum rim sheaves normal sheaves to licci schemes certain sheafified koszul homology modules and various other families are shown to satisfy the requisite conditions

monotone estimating equations for censored data the monotone class rank test based estimating equations for regression models with right censored data is considered we introduce an estimator which is a solution of a monotone estimating equation that is an extension of the gehan test the estimator is easy to derive sqrt n consistent and asymptotically normal under minimal conditions all monotone estimating equations are characterized and a simulation study which shows that our suggested procedure performs well is included

some linear syzygy conjectures in this paper we introduce four conjectures refining a very useful result of mark green s on the linear part of the free resolution of a graded module over a polynomial ring we prove a number of special cases of the conjectures including all cases pertaining to modules over a polynomial ring in at most four variables in a later paper we will give a complete classification of the nets of skew symmetric transformations on a sdimensional vector space over an algebraically closed field from which we deduce that our conjectures are true in five variables as well

a bound on the geometric genus of projective varieties verifying certain flag conditions fix integers n r s1 sl and let s n r s1 sl be the set of all integral projective and nondegenerate varieties v of degree s1 and dimension n in the projective space pr such that for all i 2 l v does not lie on any variety of dimension n i 1 and degree sl we determine an upper bound gh n r s1 sl depending only on n r s1 sl for the number g n r s1 sl max pg v v s n r s1 sl where pg v denotes the geometric genus of v in case n 1 and l 2 the study of an upper bound for the geometric genus has a quite long history and for n 1 l 2 and s2 r n it has been introduced by harris we exhibit sharp results for particular ranges of our numerical data n r s1 sl for instance we extend halphen s theorem for space curves to the case of codimension two and characterize the smooth complete intersections of dimension n in pn 3 as the smooth varieties of maximal geometric genus with respect to appropriate flag condition this result applies to smooth surfaces in p5 next we discuss how far gh n r s1 sl is from g n r s1 sl and show a sort of lifting theorem which states that at least in certain cases the varieties v s n r s1 sl of maximal geometric genus g n r s1 sl must in fact lie on a flag such as v v n s1 v n 1 s2 v n l 1 sl p r where v j s denotes a subvariety of pr of degree s and dimension j we also discuss further generalizations of flag conditions and finally we deduce some bounds for castelnuovo s regularity of varieties verifying flag conditions 0 introduction fix integers n r s1 sl such that 1 n r 2 2 l r n and let s n r s1 sl be the set of all integral projective and nondegenerate varieties v of degree s1 and dimension n in the projective space p such that for all i 2 l v does not lie on any variety of dimension n i 1 and degree sl we determine an upper bound g n r s1 sl depending only on n r s1 sl for the number g n r s1 sl max pg v v s n r s1 sl 0 1 received by the editors october 23 1995 1991 mathematics subject classification primary 14j99 14m07 14m10 secondary 14f17

non degenerate projective curves with very degenerate hyperplane section in this paper we study the hilbert scheme of non degenerate locally cohen macaulay projective curves with general hyperplane section spanning a linear space of dimension 2 and minimal hilbert function the main result is that those curves are almost always the general element of a generically smooth component hn d g of the corresponding hilbert scheme moreover we show that the curves with maximal cohomology almost always correspond to smooth points of hn d g

the minimal free resolution of the migliore peterson rings in the case that the reflexive sheaf has even rank abstract letrbe a commutative noetherian ring and f gbe a homomorphism of freer modules where rank f fand rank g g fix an elementbg 1 g 1fand a generator g for gg the module action of f on fproduces the elementb1 g g bg 1 inf letjdenote the image ofb1 f r assume that gradej f g which is the largest grade possible and is attained in the generic case the idealjmay be interpreted as the defining ideal of the degeneracy locus of a regular section of a rankf greflexive sheaf it may also be interpreted as the order ideal of an element in a second syzygy module of rankf g also jmay be interpreted as the defining ideal for the symmetric algebra of a module of projective dimension two migliore and peterson have studied the idealjunm which is the unmixed part ofj under geometric hypotheses they have shown thatr junmis a cohen macaulay ring and they have resolved this ring furthermore iff gis odd thenjunmis a gorenstein ideal and is not equal toj on the other hand iff gis even thenjunm j in the present paper we produce the resolution ofr jby freer modules in the case thatf gis even and f g 2 is a unit inr our resolution is minimal whenever the data are local or homogeneous our resolution is built from the differential graded algebra f x1 xg d where the restriction ofdto f is the koszul complex associated tob1 f rand the degree two divided power variablesx1 xghave been adjointed in order to kill the cycles g 1f the acyclicity lemma is used to prove exactness ifg 1 then the idealjis equal to the huneke ulrich almost complete intersection ideali1 yx whereyis a 1 fmatrix andxis anf falternating matrix the resolution of this ideal is already known

structural decomposition of monomial resolutions abstract we express the multigraded betti numbers of an arbitrary monomial ideal in terms of the multigraded betti numbers of two basic classes of ideals this decomposition has multiple applications in some concrete cases we use it to construct minimal resolutions of classes of monomial ideals in other cases we use it to compute projective dimensions to illustrate the effectiveness of the structural decomposition we give a new proof of a classic theorem by charalambous that states the following let k be a field and m an artinian monomial ideal in s k x 1 x n then for all i b i s m n i

projective embeddings of projective schemes blown up at subschemes suppose x is a nonsingular projective scheme z a nonsingular closed subscheme of x let x be the blowup of x centered at z e0 the pull back of a general hyperplane in x and e the exceptional divisor in this paper we study projective embeddings of x given by divisors when x satisfies a necessary condition we give explicit values of d and such that for all e 0 and embeds x as a projectively normal and arithmetically cohen macaulay scheme we also give a uniform bound for the regularities of the ideal sheaves of these embeddings and study their asymptotic behaviour as t gets large compared to e when x is a surface and z is a 0 dimensional subscheme we further show that these embeddings possess property np for all t e 0

large sample theory of estimation in biased sampling regression models i biased sampling regression models were introduced by jewell generalizing the truncated regression model studied by bhattacharya chernoff and yang if the independent variable takes on only a finite number of values as does the stratum variable we show 1 that if the slope of the underlying regression model is assumed known then the nonparametric maximum likelihood estimates of the distribution of the independent and dependent variables a can be calculated from ordinary m estimates b are asymptotically efficient 2 how to construct m estimates of the slope which are always sqrt n consistent asymptotically gaussian and are efficient locally for example if the error distribution is gaussian we support our asymptotics with a small simulation

geometric consequences of extremal behavior in a theorem of macaulay f s macaulay gave necessary and sufficient conditions on the growth of a nonnegative integer valued function which determine when such a function can be the hilbert function of a standard graded k algebra we investigate some algebraic and geometric consequences which arise from the extremal cases of macaulay s theorem our work also builds on the fundamental work of g gotzmann our principal applications are to the study of hilbert functions of zeroschemes with uniformity conditions as a consequence we have new strong limitations on the possible hilbert functions of the points which arise as a general hyperplane section of an irreducible curve

poset embeddings of hilbert functions and betti numbers abstract we study inequalities between graded betti numbers of ideals in a standard graded algebra over a field and their images under embedding maps defined earlier by us in caviglia and kummini 2013 5 we show that if graded betti numbers do not decrease when we replace ideals in an algebra by their embedded versions then the same behaviour is carried over to ring extensions as a corollary we give alternative inductive proofs of earlier results of bigatti hulett pardue mermin peeva stillman and murai we extend a hypersurface restriction theorem of herzog and popescu to the situation of embeddings we show that we can obtain the betti table of an ideal in the extension ring from the betti table of its embedded version by a sequence of consecutive cancellations we further show that the lex plus powers conjecture of evans reduces to the artinian situation