on the equivalence of constrained and compound optimal designs abstract constrained and compound optimal designs represent two well known methods for dealing with multiple objectives in optimal design as reflected by two functionals 1 and 2 on the space of information matrices a constrained optimal design is constructed by optimizing 2 subject to a constraint on 1 and a compound design is found by optimizing a weighted average of the functionals 1 1 2 0 1 we show that these two approaches to handling multiple objectives are equivalent

on the gauss algebra associated to a rational map pd pn abstract letkbe a field of characteristic zero given a polynomial ringboverkand a finitely generatedk subalgebraa b one associates toaak subalgebra g a bin such a way that whenais generated byn 1 forms of the same degree then so is g a and moreover in this case g a is the homogeneous coordinate ring of the gauss image of proj a p nin the plucker embedding of the grassmannian g d n whered dim proj a the precise structure of g a is established whenais the homogeneous coordinate ring of a veronese embedding of p dor of a projective monomial curve

on the generalized scarf complex of lattice ideals abstract let k be a field l z n be a lattice such that l n n 0 and i l r k x 1 x n the corresponding lattice ideal we present the generalized scarf complex of i l and show that it is indispensable in the sense that it is contained in every minimal free resolution of r i l

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

on birational macaulayfications and cohen macaulay canonical modules abstract the aim of the paper is twofold at first there is a characterization of those local domains admitting a birational macaulayfication it turns out that a local domain a quotient of a gorenstein ring possesses a cohen macaulay birational extension b if and only if its canonical module k a is a cohen macaulay module in this situation it follows that b is isomorphic to the endomorphism ring of k a the second part of the paper is devoted to the question when the canonical module of a local ring is a cohen macaulay module there are applications on sequentially cohen macaulay rings a large class of rings whose canonical module are cohen macaulay is given by the simplicial affine semigroup rings as a technical tool there is a spectral sequence related to the duality with respect to the dualizing complex

a biobjective method for sample allocation in stratified sampling the two main and contradicting criteria guiding sampling design are accuracy of estimators and sampling costs in stratified random sampling the sample size must be allocated to strata in order to optimize both objectives in this note we address following a biobjective methodology this allocation problem a two phase method is proposed to describe the set of pareto optimal solutions of this nonlinear integer biobjective problem in the first phase all supported pareto optimal solutions are described via a closed formula which enables quick computation moreover for the common case in which sampling costs are independent of the strata all pareto optimal solutions are shown to be supported for more general cost structures the non supported pareto optimal solutions are found by solving a parametric knapsack problem bounds on the criteria can also be imposed directing the search towards implementable sampling plans our method provides a deeper insight into the problem than simply solving a scalarized version whereas the computational burden is reasonable

on the depth of the fiber cone of filtrations preprint enviat per a la seva publicacio en una revista cientifica journal of algebra 15 december 1997 volume 198 issue 2 pages 428 445 https doi org 10 1006 jabr 1997 7147

simplicial ideals 2 linear ideals and arithmetical rank abstract in the first part of this paper we study scrollers and linearly joined varieties scrollers were introduced in barile and morales 2004 bm4 linearly joined varieties are an extension of scrollers and were defined in eisenbud et al 2005 eghp there they proved that scrollers are defined by homogeneous ideals having a 2 linear resolution a particular class of varieties of important interest in classical geometry are cohen macaulay varieties of minimal degree they were classified geometrically by the successive contribution of del pezzo 1885 dp bertini 1907 b and xambo 1981 x and algebraically in barile and morales 2000 bm2 they appear naturally studying the fiber cone of a codimension two toric ideals morales 1995 m gimenez et al 1993 1999 gms1 gms2 barile and morales 1998 bm1 ha 2006 h ha and morales 2009 hm let s be a polynomial ring and i s a homogeneous ideal defining a sequence of linearly joined varieties we compute depth s i we prove that c v depth s i 1 where c v is the connectedness dimension of the algebraic set defined by i we characterize sets of generators of i and give an effective algorithm to find equations as an application we prove that ara i projdim s i in the case where v is a union of linear spaces in particular this applies to any square free monomial ideal having a 2 linear resolution in the case where v is a union of linear spaces the ideal i can be characterized by a tableau which is an extension of a ferrer or young tableau all these results are new and extend results in barile and morales 2004 bm4 eisenbud et al 2005 eghp

the regularity of a toric variety abstract we give a method for computing the degrees of the minimal syzygies of a toric variety by means of combinatorial techniques indeed we complete the explicit description of the minimal free resolution of the associated semigroup algebra using the simplicial representation of koszul homology which appeared in a campillo and c marijuan 1991 sem theor nombres bordeaux3 249 260 as an application we obtain an algorithm for computing the castelnuovo mumford regularity of a projective toric variety this regularity is explicitly bounded by means of the semigroup generators which parametrize the variety

a new look at degenerate lagrangian dynamics from the viewpoint of almost product structures singular lagrangian systems are studied in the framework of almost product structures the choice of an appropriate almost product structure permits us to obtain the dynamics the relationship with the dirac bracket is also elucidated

on the structure of the fiber cone of ideals with analytic spread one for a given a local ring a m we study the fiber cone of ideals in a with analytic spread one in this case the fiber cone has a structure as a module over its noether normalization which is a polynomial ring in one variable over the residue field one may then apply the structure theorem for modules over a principal domain to get a complete description of the fiber cone as a module we analyze this structure in order to study and characterize in terms of the ideal itself the arithmetical properties and other numerical invariants of the fiber cone as multiplicity reduction number or castelnuovo mumford regularity

on simplicial toric varieties which are set theoretic complete intersections abstract in this paper we prove in characteristic 0 every simplicial toric affine or projective variety with full parametrization is a set theoretic complete intersection this extends previous results by r hartshorne 1979 380 383 and t t moh 1985 217 220 in any characteristic every simplicial toric affine or projective variety with full parametrization is an almost set theoretic complete intersection this extends previous known results by m barile and m morales 1998 1907 1912 and a thoma to appear in any characteristic every simplicial toric affine or projective variety of codimension two is an almost set theoretic complete intersection moreover the proofs are constructive and the equations we find are binomial ones

computing the feng rao distances for codes from order domains abstract we compute the feng rao distance of a code coming from an order domain with a simplicial value semigroup the main tool is the apery set of a semigroup that can be computed using a grobner basis

the local structure of poisson manifolds varietes de poisson et applications decomposition structures de poisson lineaires approximation lineaire systemes hamiltoniens le probleme de linearisation groupes de fonction realisations et applications impulsion paires duales et groupes de jauge existence des realisations unicite des realisations les problemes des 3 corps restreints et autres exemples

a graphical method for finding maximin efficiency designs we consider the problem of designing an experiment when there are two competing optimality criteria designs that maximize the minimum efficiencies under the two criteria are proposed along with a graphical method for finding these maximin designs

binomial generation of the radical of a lattice ideal abstract let i l be a lattice ideal we provide a necessary and sufficient criterion under which a set of binomials in i l generates the radical of i l up to radical we apply our results to the problem of determining the minimal number of generators of i l or of the rad i l up to radical

set theoretic complete intersection lattice ideals in monoid rings assume that the characteristic of the base field is zero we give a necessary and sufficient condition for the defining ideal of a monomial curve to be generated by one polynomial on another lattice ideal up to radical by applying it we provide two examples of monomial curves in affine 4 space in the first one a monomial curve is set theoretic complete intersection in the second it is never generated by two binomials and one polynomial up to radical

the circuit ideal of a vector configuration abstract given a configuration a a 1 a n z d a basis ideal of a is an ideal j b x u x u u b k x 1 x n where b spans the lattice l a u z n a i u i 0 our main interest is to understand when the toric ideal i a of a equals a basis ideal j b with radical i a the circuit ideal j c a of a is an example of such a basis ideal we study such a j b in relation to i a from various algebraic and combinatorial perspectives with a special focus on j c a we prove that the obstruction to equality of the ideals is the existence of certain polytopes this result is based on a complete characterization of the standard pairs associated primes of a monomial initial ideal of j b and their differences from those for the corresponding toric initial ideal eisenbud and sturmfels proved that the embedded primes of j b are indexed by certain faces of the cone spanned by a we provide a necessary condition for a particular face to index an embedded prime and a partial converse finally we compare various polyhedral fans associated to i a and j c a the grobner fan of j c a is shown to refine that of i a when the codimension of the ideals is at most two

unequal probability sampling from a finite population a multicriteria approach abstract in this note we address the problem of determining selection probabilities for multipurpose surveys when the aim is the simultaneous minimization of variances for each variable under study a characterization of the set of pareto optimal designs is given for designs with replacement and also for a class of designs without replacement namely poisson designs as an application we describe a problem encountered in auditing where both the fraction of misstatements and the average amount of such misstatements are of interest

on the depth of the associated graded ring of an ideal abstract let r be a local cohen macaulay ring let i be an r ideal and let g be the associated graded ring of i we give an estimate for the depth of g when g fails to be cohen macaulay we assume that i has a small reduction number and sufficiently good residual intersection properties and satisfies local conditions on the depth of some powers the main theorem unifies and generalizes several known results we also give conditions that imply the serre properties of the blow up rings

gorenstein graded rings associated to ideals let a be a noetherian local ring with the maximal ideal m and dim a d let i 6 a be an ideal in a and s hta i this article studies the question of when the associated graded ring g i i 0 i i is gorenstein to state our result we set up some notation let be an integer such that d and let j be a reduction of i generated by elements a1 a2 a we denote by rj i the reduction number of i with respect to j the analytic spread of i is i dim a m a g i then s i we always assume that the generating set a1 a2 a of j is a basic generating set for j in the sense of aberbach huneke and trung aht which means that jiaq is a reduction of iaq for all q v i with i hta q here let v i be a set of prime ideals in a containing i and ji a1 a2 ai for 0 i by aht 7 2 there always exists a basic generating set for j if the field a m is infinite let

complete intersection lattice ideals abstract in this paper we completely characterize lattice ideals that are complete intersections or equivalently complete intersections finitely generated semigroups of z n t with no invertible elements where t is a finite abelian group we also characterize the lattice ideals that are set theoretic complete intersections on binomials

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

grobner deformations connectedness and cohomological dimension abstract in this paper we will compare the connectivity dimension c p i of an ideal i in a polynomial ring p with that of any initial ideal of i generalizing a theorem of kalkbrener and sturmfels m kalkbrener b sturmfels initial complex of prime ideals adv math 116 1995 365 376 we prove that c p lt i min c p i dim p i 1 for each monomial order as a corollary we have that every initial complex of a cohen macaulay ideal is strongly connected our approach is based on the study of the cohomological dimension of an ideal a in a noetherian ring r and its relation with the connectivity dimension of r a in particular we prove a generalized version of a theorem of grothendieck a grothendieck cohomologie locale des faisceaux coherents et theoremes de lefschetz locaux et globaux sga 2 in seminaire de geometrie algebrique du bois marie 1962 as consequence of these results we obtain some necessary conditions for an open subscheme of a projective scheme to be affine

gorenstein algebras of veronese type abstract letk t1 t2 tn be the polynomial ring innvariables over a fieldk we fix an integerdand a sequencea a1 a2 an of integers with 1 a1 a2 an dand d i 1 n a i leta a d denote thek subalgebra ofk t1 t2 tn generated by all monomials of the formt1x1t2x2 tnxnwithx1 x2 xn dand withxi aifor each 1 i n in this paper we classify all the sequencesaand integersdfor which the algebraa a d is gorenstein

the equivalence of constrained and weighted designs in multiple objective design problems abstract several competing objectives may be relevant in the design of an experiment the competing objectives may not be easy to characterize in a single optimality criterion one approach to these design problems has been to weight each criterion and find the design that optimizes the weighted average of the criteria an alternative approach has been to optimize one criterion subject to constraints on the other criteria an equivalence theorem is presented for the bayesian constrained design problem equivalence theorems are essential in verifying optimality of proposed designs especially when as in most nonlinear design problems numerical optimization is required this theorem is used to show that the results of cook and wong on the equivalence of the weighted and constrained problems apply much more generally the results are applied to bayesian nonlinear design problems with several objectives

the projector method for regular poisson manifolds degenerate lagrangians have recently been studied through a pair of projection operators induced by an almost product structure we extend the projector method to regular poisson manifolds this approach proves to be useful in the interpretation of the theories of collective motion of n particle systems for applications in nuclear physics

monomial and toric ideals associated to ferrers graphs each partition a 1 2 an determines a so called ferrers tableau or equivalently a ferrers bipartite graph its edge ideal dubbed a ferrers ideal is a squarefree monomial ideal that is generated by quadrics we show that such an ideal has a 2 linear minimal free resolution i e it defines a small subscheme in fact we prove that this property characterizes ferrers graphs among bipartite graphs furthermore using a method of bayer and sturmfels we provide an explicit description of the maps in its minimal free resolution this is obtained by associating a suitable polyhedral cell complex to the ideal graph along the way we also determine the irredundant primary decomposition of any ferrers ideal we conclude our analysis by studying several features of toric rings of ferrers graphs in particular we recover establish formulae for the hilbert series the castelnuovo mumford regularity and the multiplicity of these rings while most of the previous works in this highly investigated area of research involve path counting arguments we offer here a new and self contained approach based on results from gorenstein liaison theory

on a special class of simplicial toric varieties abstract we show that for all n 3 and all primes p there are infinitely many simplicial toric varieties of codimension n in the 2n dimensional affine space whose minimum number of defining equations is equal to n in characteristic p and lies between 2 n 2 and 2n in all other characteristics in particular these are new examples of varieties which are set theoretic complete intersections only in one positive characteristic moreover we show that the minimum number of binomial equations which define these varieties in all characteristics is 4 for n 3 and 2 n 2 n 2 2 whenever n 4

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

minimal free resolutions of monomial curves in p3k abstract minimal free resolutions for prime ideals with generic zero t n 3 t n 3 n 1 0 t n 1 1 t n 3 n 2 0 t n 2 t n 3 1 n 1 n 2 n 3 positive integers n 1 n 2 n 3 1 are determined