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

enriched finite elements for regions with multiple interacting singular fields enriched two dimensional finite elements are formulated for analysis of solids with interacting singular points these elements contain both the order and the angular variation of all singular stress fields emanating from each singular point so that the possible interaction of stress states present in such regions is represented the order and distribution of the singular fields are determined with a separate finite element eigenanalysis these field characterizations and the subsequent enrichment are carried out numerically rather than analytically for ease of extension of the technique to complex geometries for which analytical solutions would be difficult to obtain generalized stress intensity factors as well as the stresses and displacements result directly from models incorporating enriched elements enriched element models can be applied not only to crack problems but also to singular stress states not involving cracks and crack growth and are thus more versatile than j integral and virtual crack closure techniques used for calculating energy release rates in addition the proper angular distribution of the displacement fields leading to each singular stress state is used in formulating the element an advantage not shared by formulations such as the quarter point elements the advantages of using enriched elements containing information from interacting singular points are demonstrated with an example having two interacting singular points this tensile groove specimen is modeled using these new elements as well as enriched elements that do not take interaction into consideration attention is given to modeling issues when using interactive enriched elements

multigraded castelnuovo mumford regularity we develop a multigraded variant of castelnuovo mumford regularity motivated by toric geometry we work with modules over a polynomial ring graded by a finitely generated abelian group as in the standard graded case our definition of multigraded regularity involves the vanishing of graded components of local cohomology we establish the key properties of regularity its connection with the minimal generators of a module and its behavior in exact sequences for an ideal sheaf on a simplicial toric variety x we prove that its multigraded regularity bounds the equations that cut out the associated subvariety we also provide a criterion for testing if an ample line bundle on x gives a projectively normal embedding

new bounds on the total squared correlation and optimum design of ds cdma binary signature sets the welch lower bound see welch r l ieee trans inform theory vol it 20 p 397 9 1974 on the total squared correlation tsc of signature sets is known to be tight for real valued signatures and loose for binary signatures whose number is not a multiple of four we derive new bounds on the tsc of binary signature sets for any number of signatures k and any signature length l then for almost all k l in 1 2 256 we design optimum binary signature sets that achieve the new bounds the design procedure is based on simple transformations of hadamard matrices

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

iterative construction of optimum signature sequence sets in synchronous cdma systems optimum signature sequence sets that maximize the capacity of single cell synchronous code division multiple access cdma systems have been identified optimum signature sequences minimize the total squared correlation tsc they form a set of orthogonal sequences if the number of users is less than or equal to the processing gain and a set of welch 1994 bound equality wbe sequences otherwise we present an algorithm where users update their transmitter signature sequences sequentially in a distributed fashion by using available receiver measurements we show that each update decreases the tsc of the set and produces better signature sequence sets progressively we prove that the algorithm converges to a set of orthogonal signature sequences when the number of users is less than or equal to the processing gain we observe and conjecture that the algorithm converges to a wbe set when the number of users is greater than the processing gain at each step the algorithm replaces one signature sequence from the set with the normalized minimum mean squared error mmse receiver corresponding to that signature sequence since the mmse filter can be obtained by a distributed algorithm for each user the proposed algorithm is amenable to distributed implementation

asymptotic approach to analyze singular stress state in anisotropic multi material application to the rivets the problem of stress singularities due to multi material junctions is described in this paper a semi analytical approach is proposed based on an asymptotic model in the case of anisotropic linear elasticity in three dimensions the advantage of the present method is the quasi explicit knowledge of the stress and displacement fields around the junctions thus after a brief explanation of the approach leading to the mechanical fields around the singular line at the junction between different materials numerical results are presented concerning various configurations of an assembly with rivets included in a bi layer composite that illustrate this method

generalized castelnuovo mumford regularity for affine kac moody algebras abstract the graded modules over noncommutative algebras often have minimal free resolutions of infinite length resulting in infinite castelnuovo mumford regularity in kang et al 2010 6 we introduced a generalized notion of castelnuovo mumford regularity to overcome this difficulty in this paper we compute the generalized castelnuovo mumford regularity for integrable highest weight representations of all affine kac moody algebras it is shown that the generalized regularity depends only on the type and rank of algebras and the level of representations

rank 2 optimal adaptive design of binary spreading codes over the real complex field the spreading code that maximizes the signal to interference plus noise ratio sinr at the output of the maximum sinr linear filter is the minimum eigenvalue eigenvector of the interference autocovariance matrix in the context of binary spreading codes the maximization problem is np hard with complexity exponential in the code length a new method for the optimization of binary spreading codes under a rank 2 approximation of the inverse interference autocovariance matrix is presented where the rank 2 optimal binary code is obtained in lower than quadratic complexity significant sinr performance improvement is demonstrated over the common binary hard limited eigenvector design which is shown to be equivalent to the rank 1 optimal solution

cdma codeword optimization interference avoidance and convergence via class warfare interference avoidance has been shown to reduce total square correlation tsc for given ensembles of user signature waveforms codewords in a synchronous code division multiple access cdma system in all experiments we have conducted sequential application of interference avoidance produces an optimal codeword set when starting from randomly chosen initial codewords here we provide the first formal proof of convergence to optimal codeword ensembles for greedy interference avoidance algorithms augmented by a technique called class warfare whereby users which reside in more heavily loaded areas of the signal space purposely interfere with attack the reception of users in less crowded areas coordination of deliberate interference by a complete class of aggrieved user is also sometimes necessary such attacks and subsequent codeword adjustment by attacked users are shown to strictly decrease tsc along the way we also show using linear algebra and a variant of stochastic ordering equivalence between minimization of tsc and maximization of sum capacity

a game theoretic framework for interference avoidance various iterative algorithms for interference avoidance ia in networks with co located receivers suitable for distributed implementation have been proposed in the literature in this paper the ia problem is cast in a game theoretic framework and is formulated as a potential game this formulation accommodates previously proposed algorithms and in addition gives us a framework that enables the design of new distributed and convergent algorithms for ia including algorithms with nonidentical utility functions for the users two new convergence results for potential games are then derived the first result establishes the convergence of a class of potential games to the global solution while following best response iterations and when noise is added the second result establishes the convergence of potential games to the nash equilibria of the game while following random better response iterations the first result combined with the potential game formulation allows us to show that for a large class of network scenarios arbitrarily small noise assures the convergence of best response ia algorithms including the eigeniterations to an arbitrarily small neighborhood of the globally optimal signature sequence set the second result enables the design of reduced feedback mechanisms for ia that converge to desirable solutions

a diagonal bound for cohomological postulation numbers of projective schemes abstract let x be a projective scheme over a field k and let f be a coherent sheaf of o x modules we show that the cohomological postulation numbers f i of f e g the ultimate places at which the cohomological hilbert functions n dim k h i x f n h f i n start to be polynomial for n 0 are polynomially bounded in terms of the cohomology diagonal h f i i i 0 dim f of f as a consequence we obtain that there are only finitely many different cohomological hilbert functions h f i if f runs through all coherent sheaves of o x modules with fixed cohomology diagonal in order to prove these results we extend the regularity bound of bayer and mumford computational algebraic geometry and commutative algebra proc cortona 1991 cambridge univ press 1993 pp 1 48 from graded ideals to graded modules moreover we prove that the castelnuovo mumford regularity of the dual f of a coherent sheaf of o p k r modules f is polynomially bounded in terms of the cohomology diagonal of f

the information encoded in initial ideals we consider homogeneous ideals i and the initial ideal in i for the revlex order first we give a sequence of invariants computed from i giving better and better approximations to the initial ideal and ending in an equivalent description then we apply this to different settings in algebraic geometry to understand what information is encoded in the generic initial ideal of the ideal of a projective scheme we also consider the higher initial ideals as defined in a paper by fl0ystad in particular we show that giving the generic higher initial ideal of a space curve is equivalent to giving the generic initial ideal of a linked curve

optimal sequences for cdma under colored noise a schur saddle function property we consider direct sequence code division multiple access ds cdma modeling interference from users communicating with neighboring base stations by additive colored noise we consider two types of receiver structures first we consider the information theoretically optimal receiver and use the sum capacity of the channel as our performance measure second we consider the linear minimum mean square error lmmse receiver and use the signal to interference ratio sir of the estimate of the symbol transmitted as our performance measure our main result is a constructive characterization of the possible performance in both these scenarios a central contribution of this characterization is the derivation of a qualitative feature of the optimal performance measure in both the scenarios studied we show that the sum capacity is a saddle function it is convex in the additive noise covariances and concave in the user received powers in the linear receiver case we show that the mini average power required to meet a set of target performance requirements of the users is a saddle function it is convex in the additive noise covariances and concave in the set of performance requirements

a combinatorial proof of the eisenbud goto conjecture for monomial curves and some simplicial semigroup rings abstract we will give a pure combinatorial proof of the eisenbud goto conjecture for arbitrary monomial curves moreover we will show that the conjecture holds for certain simplicial affine semigroup rings

finite element analysis of anisotropic materials with singular inplane stress fields abstract a finite element formulation is developed for the analysis of singular stress states at material and geometric discontinuities in anisotropic materials loaded inplane the displacement field of the sectorial element is quadratic in the angular coordinate direction and exponential in the radial direction measured from the singular point the formulation of yamada and okumura 1983a b is extended to take into account the anisotropy of the material the stress and displacement fields are obtained when the order of the stress singularity is real as well as complex when the order of the stress singularity is complex it is shown that the angular variation of the stress and displacement fields can be expressed in an infinite number of ways results for the displacement and stress fields obtained when the order of the stress singularity is complex can be made to match already published results once a similarity transformation is applied the simplicity and accuracy of the formulation are demonstrated by comparison to several analytical solutions for both isotropic and anisotropic multi material wedges and junctions with and without disbonds the nature and rate of convergence associated with the element suggests that it could be used in developing enriched elements for use with standard elements to yield accurate and computationally efficient solutions to problems having complex global geometries

enrichment of finite elements with numerical solutions for singular stress fields enriched 2 d and 3 d finite elements are formulated for analysis of solids having multi material junction and wedge configurations that create singular stress fields due to the material and or geometric discontinuities the order and angular variation of the displacements associated with the singular fields are determined from a separate special finite element eigenanalysis and used in the enrichment process the use of these numerically determined singular fields allows enriched elements to be developed for complex configurations for which analytical fields are not available in addition to this added flexibility of application the current formulation applies to elements that may or may not be in direct contact with the singular point this allows multiple layers of enriched elements to be used around the singular point and traditional mesh refinement studies to be carried out in the enriched element region previous enriched formulations have not provided this important capability for cases where analytical fields are available such as cracked solids the performance of elements developed with the current approach is shown to be equivalent to that obtained using analytically enriched elements mesh refinement techniques using enriched elements are described that allow accurate stress distributions and generalized stress intensity factors to be directly determined the importance of high order numerical integration use of multiple layers of enriched elements and proper choice of the size of the enriched region are demonstrated by comparison to existing solutions for solids with cracks application of enriched element modelling to a 2 d bi material wedge and a 3 d stepped thickness anisotropic composite laminate is demonstrated 1997 john wiley sons ltd

recent improvements in the complexity of the effective nullstellensatz we bring up to date the estimates on the complexity of the effective nullstellensatz and the membership problem

optimal sequences and sum capacity of synchronous cdma systems the sum capacity of a multiuser synchronous cdma system is completely characterized in the general case of asymmetric user power constraints this solves the open problem posed by rupf and massey see ibid vol 40 p 1261 6 1994 which had solved the equal power constraint case we identify the signature sequences with real components that achieve sum capacity and indicate a simple recursive algorithm to construct them

stress singularity analysis around the singular point on the stress singularity line in three dimensional joints abstract the characteristics of the stress fields around a singular point on the stress singularity line of dissimilar materials in three dimensional joints are investigated using bem contour for the order of stress singularity around the point is mapped on dundurs parameters plane using eigen value analysis by fem the results in 3d joints are compared with those in 2d joints having the same cross section and material combination the order of stress singularity around the singular point on the stress singularity line in 3d joints is almost identical with that in 2d joints in the singularity region however the zero boundary of singularity in 3d joints is slightly different from that in 2d joints furthermore the multiple root of p 1 exists in the eigen value analysis by fem therefore logarithmic singularity possibly occurs around the singular point on the stress singularity line then the stress distributions around this point are expressed by the combination of the r term and logarithmic singularity terms finally the characteristics of the stress intensity factors of the r term and logarithmic singularity terms around the singular points are investigated

analysis of a three dimensional dissimilar material joint with one real singularity using a conservative integral abstract in the present study a conservative integral based on the betti reciprocal principle is formulated to determine the intensity of singularity at a vertex of the interface in three dimensional dissimilar material joints with one real singularity eigenanalysis formulated using a three dimensional finite element method fem is used to calculate the order of stress singularity angular functions of displacements and stresses models with various element sizes and various integral areas are used to investigate the effect of the integration area on the accuracy of the results the results are compared with those obtained from the boundary element method bem using a curve fitting technique to calculate the intensity of singularity in addition models of various lengths and various material combinations are used to investigate the stress singularity characteristics in three dimensional dissimilar material joints the results of the present study indicate that the conservative integral can be used to determine the intensity of singularity in three dimensional bi material joints the accuracy of the results can be improved by mesh refinement finally the relationships among the intensity of singularity the order of stress singularity and the model geometry are discussed

new bounds and optimal binary signature sets part ii aperiodic total squared correlation we derive new bounds on the aperiodic total squared correlation atsc of binary antipodal signature sets for any number of signatures k and any signature length l we then present optimal designs that achieve the new bounds for several k l cases as interesting arguably side results we show that individual maximal merit factor sequences for example barker sequences are single user atsc optimal while neither the familiar gold nor the kasami set designs are atsc optimal in general the atsc optimal signature set designs provided in this work are in this sense better suited for asynchronous and or multipath code division multiplexing applications

saturation and castelnuovo mumford regularity abstract let i be a homogeneous ideal of the polynomial ring k x 0 x n where k is an arbitrary field avoiding the construction of a minimal graded free resolution of i we provide effective methods for computing the castelnuovo mumford regularity of i that also compute other cohomological invariants of k x 0 x n i

cohomology of projective schemes from annihilators to vanishing we provide bounds on the castelnuovo mumford regularity in terms of defining equations by using elements that annihilates some cohomology modules inspired by works of miyazaki nagel schenzel and vogel the elements in these annihilators are provided either by liaison or by tight closure theories our results hold in any characteristic

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

ensuring convergence of the mmse iteration for interference avoidance to the global optimum viswanath and anantharam 1999 characterize the sum capacity of multiaccess vector channels for a given number of users received powers spreading gain and noise covariance matrix in a code division multiple access cdma system viswanath and anantharam present a combinatorial algorithm to generate a set of signature sequences that achieves the maximum sum capacity these sets also minimize a performance measure called generalized total square correlation tsc sub g ulukus and yates 2001 propose an iterative algorithm suitable for distributed implementation at each step one signature sequence is replaced by its linear minimum mean square error mmse filter this algorithm results in a decrease of tsc sub g at each step the mmse iteration has fixed points not only at the optimal configurations which attain the global minimum tsc sub g but also at other configurations which are suboptimal the authors of claim that simulations show that when starting with random sequences the algorithm converges to optimum sets of sequences but they give no formal proof we show that the tsc sub g function has no local minima in the sense that given any suboptimal set of sequences there exist arbitrarily close sets with lower tsc sub g therefore only the optimal sets are stable fixed points of the mmse iteration we define a noisy version of the mmse iteration as follows after replacing all the signature sequences one at a time by their linear mmse filter we add a bounded random noise to all the sequences using our observation about the tsc sub g function we can prove that if we choose the bound on the noise adequately making it decrease to zero the noisy mmse iteration converges to the set of optimal configurations with probability one for any initial set of sequences

circuit complexity proof complexity and polynomial identity testing the ideal proof system we introduce a new and natural algebraic proof system whose complexity measure is essentially the algebraic circuit size of nullstellensatz certificates this enables us to exhibit close connections between effective nullstellensatze proof complexity and algebraic circuit complexity in particular we show that any super polynomial lower bound on any boolean tautology in our proof system implies that the permanent does not have polynomial size algebraic circuits vnp vp we also show that super polynomial lower bounds on the number of lines in polynomial calculus proofs imply the permanent versus determinant conjecture note that there was no proof system prior to ours for which lower bounds on an arbitrary tautology implied any complexity class lower bound our proof system helps clarify the relationships between previous algebraic proof systems in doing so we highlight the importance of polynomial identity testing pit in proof complexity in particular we use pit to illuminate ac0 p frege lower bounds which have been open for nearly 30 years with no satisfactory explanation as to their apparent difficulty finally we explain the obstacles that must be overcome in any attempt to extend techniques from algebraic circuit complexity to prove lower bounds in proof complexity using the algebraic structure of our proof system we propose a novel route to such lower bounds although such lower bounds remain elusive this proposal should be contrasted with the difficulty of extending ac0 p circuit lower bounds to ac0 p frege lower bounds

almost regular sequences and betti numbers let be a simplicial complex and s the shifted simplicial complex of as defined by kalai it is shown that the stanley reisner ideals i and i s have the same extremal betti numbers this theorem is the squarefree analogue of the corresponding result by bayer charalambous and popescu which asserts that a graded ideal and its generic ideal have the same extremal betti numbers our theorem implies well known results by kalai according to which and s have the same simplicial homology and is cohen macaulay if and only if its shifted complex is cohen macaulay

minimum total squared correlation quaternary signature sets new bounds and optimal designs we derive new bounds on the total squared correlation tsc of quaternary quadriphase signature sequence sets for all lengths l and set sizes k then for all k l we design minimum tsc optimal sets that meet the new bounds with equality direct numerical comparison with the tsc value of the recently obtained optimal binary sets shows under what k l realizations gains are materialized by moving from the binary to the quaternary code division multiplexing alphabet on the other hand comparison with the welch tsc value for real complex field sets shows that arguably not much is to be gained by raising the alphabet size above four for any k l the sum capacity as well as the maximum squared correlation and total asymptotic efficiency of minimum tsc quaternary sets is also evaluated in closed form and contrasted against the sum capacity of minimum tsc optimal binary and real complex sets

bounds for the castelnuovo mumford regularity of modules we establish bounds for the castelnuovo mumford regularity of a finitely generated graded module and its symmetric powers in terms of the degrees of the generators of the module and the degrees of their relations we extend to modules and improve the known bounds for homogeneous ideals in a polynomial ring established by galligo giusti caviglia and sbarra

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

stress singularity analysis in three dimensional bonded structure abstract stress analysis for joints between two isotropic materials is performed using three dimensional boundary element method with rongved s fundamental solution rongved l 1955 force interior to one of two joined semi infinite solids in second midwestern conf on solid mechanics pp 1 13 which satisfies boundary conditions at the interface the stress distribution around the vertex of the joint is precisely examined and the order of stress singularity obtained in three dimensional analysis is compared with that in two dimensional analysis it is shown that the order of the stress singularity along the stress singularity line which is the intersection of the interface with the free surface varies from the value in plane strain to that in plane stress as the opposite side free surface is approached the order of stress singularity in the spherical coordinates centered at the vertex is next investigated when singularity lines with a singularity order meet with each other at the vertex the order of stress singularity is larger than that for plane strain and plane stress when the vertex angle between two side free surfaces is varied the order of stress singularity is also altered in particular a bound at which singularity disappears at the plane for dundurs composite parameters is examined for a cubic dissimilar material it is demonstrated that the bound varies little in comparison with the one obtained from the two dimensional theory

a finite element approach to three dimensional singular stress states in anisotropic multi material wedges and junctions abstract a finite element formulation is developed to determine the order and angular variation of singular stress states due to material and geometric discontinuities in anisotropic materials the formulation applies to any two dimensional geometry that is prismatic in the third direction and has three dimensional displacement fields in some special cases the three dimensional fields become uncoupled antiplane and inplane fields and this formulation yields the uncoupled results the formulation provides for the determination of the asymptotic stress and displacement fields present at interior singular points of three dimensional structures the displacement field of the sectorial finite element is quadratic in the angular coordinate direction and asymptotic in the radial direction measured from the singular point the formulation of yamada and okumura 1983 hybrid and mixed finite element methods pp 325 343 wiley chichester for inplane problems is adapted for this purpose the simplicity and accuracy of the formulation are demonstrated by comparison with several analytical solutions for both isotropic and anisotropic multi material wedges and junctions the nature and speed of convergence associated with the element suggests that it could be employed in developing two dimensional and three dimensional enriched elements for use along with standard elements to yield accurate and computationally efficient solutions to problems having complex global geometries leading to singular stress states

a finite element analysis of the singular stress fields in anisotropic materials loaded in antiplane shear a finite element formulation is developed to determine the order and angular variation of singular stress states at material and geometric discontinuities in anisotropic materials subject to antiplane shear loading the displacement field of the sectorial element is quadratic in the angular co ordinate direction and asymptotic in the radial direction measured from the singular point the formulation of yamada and okumura14 for in plane problems is adapted for this purpose the simplicity and accuracy of the formulation are demonstrated by comparison to several analytical antiplane shear solutions for both isotropic and anisotropic multi material wedges and junctions with and without disbonds the nature and speed of convergence of the eigensolution suggests that the solution presented here could be used in developing enriched elements for accurate and computationally efficient evaluation of stress intensity factors in problems having complex global geometries

application of the finite element iterative method to the eigenvalue problem of a crack between dissimilar media the finite element iterative method is applied to the eigenvalue problem of a crack between dissimilar media in this case the transfer matrix is non symmetric which leads to complex eigenvalues the singularity obtained agrees with the analytical results of r 1 2 ie the method of evaluating the eigenfunctions is general and can be applied to more complex cases of material and geometry which are frequently encountered in composite materials a powerful method for evaluating stress intensities in dissimilar media is given in the appendix the method is also reduced for homogeneous media to give stress intensity factors for modes i ii and iii

sum capacity and tsc bounds in collaborative multibase wireless systems we consider a wireless system with base stations which collaborate and derive bounds on sum capacity and total squared correlation for uniform channels between users and bases the correspondence also investigates structural properties which must be satisfied by user transmit covariance matrices at the optimal sum capacity total squared correlation tsc point and shows that for multibase systems maximizing sum capacity and minimizing tsc are in general not equivalent problems

conditions for generic initial ideals to be almost reverse lexicographic abstract let i be a homogeneous artinian ideal in a polynomial ring r k x 1 x n over a field k of characteristic 0 we study an equivalent condition for the generic initial ideal gin i with respect to reverse lexicographic order to be almost reverse lexicographic as a result we show that the moreno socias conjecture implies the froberg conjecture and the pardue conjecture and for the case codim i 3 we show that r i has the strong lefschetz property if and only if gin i is almost reverse lexicographic finally we give a positive partial answer to the moreno socias conjecture and hence to the pardue conjecture

a stratification of the hilbert scheme of points in the projective plane this result is analogous to a theorem of iarrobino and brian on on the stratification of the punctual hilbert scheme where a different hilbert function defined by initial forms instead is used however cp i l thm 2 9 p 26 the proof essentially makes use of the smoothness of h a cp f p 517 and a general result of bialynicki birula on the action of the multiplicative group on a smooth projective scheme as already was done in a study of the homology of h a by ellingsrud and stromme this method is applied here to a study of h a around points which are invariant under the borel group in the appendix a method for computing the dimension of h is represented which rests on iarrobino s description of the tangent space to certain points of h a and the theorem of bialynicki birula finally i would like to mention that hirschowitz has outlined a general program for studying stratifications including those defined by hilbert functions cp h p 175 but the result obtained here can at best be regarded only as the most simple perhaps non trivial example

on the castelnuovo mumford regularity of connected curves in this paper we prove that the regularity of a connected curve is bounded by its degree minus its codimension plus 1 we also investigate the structure of connected curves for which this bound is optimal in particular we construct connected curves of arbitrarily high degree in p 4 having maximal regularity but no extremal secants we also show that any connected curve in p 3 of degree at least 5 with maximal regularity and no linear components has an extremal secant

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

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

direct methods for primary decomposition leti be an ideal in a polynomial ring over a perfect field we given new methods for computing the equidimensional parts and radical ofi for localizingi with respect to another ideal and thus for finding the primary decomposition ofi our methods rest on modern ideas from commutative algebra and are direct in the sense that they avoid the generic projections used by hermann 1926 and all others until now

finiteness of hilbert functions and bounds for castelnuovo mumford regularity of initial ideals bounds for the castelnuovo mumford regularity and hilbert coefficients are given in terms of the arithmetic degree if the ring is reduced or in terms of the defining degrees from this it follows that there exists only a finite number of hilbert functions associated with reduced algebras over an algebraically closed field with a given arithmetic degree and dimension a good bound is also given for the castelnuovo mumford regularity of initial ideals which depends neither on term orders nor on the coordinates and holds for any field

the ubiquity of smooth hilbert schemes we investigate the geography of hilbert schemes parametrizing closed subschemes of projective space with specified hilbert polynomials we classify hilbert schemes with unique borel fixed points via combinatorial expressions for their hilbert polynomials these expressions naturally lead to an arrangement of nonempty hilbert schemes as the vertices of an infinite full binary tree here we discover regularities in the geometry of hilbert schemes specifically under natural probability distributions on the tree we prove that hilbert schemes are irreducible and nonsingular with probability greater than 0 5

analysis of the stress singularity field at a vertex in 3d bonded structures having a slanted side surface the stress singularity that occurs at a vertex in a joint with a slanted side surface is investigated the orders of stress singularity at a vertex and at a point on stress singularity lines for various material properties are determined using eigenanalysis the stress distribution on an interface and the intensity of stress singularity at the vertex are investigated using bem it is shown that the order of stress singularity at the vertex in the joints can be reduced by slanting a side surface so as to decrease the angle between the interface and the side surface the results of bem analysis reveal that the distribution of stress on the interface is influenced by the slanted side surface finally the 3d intensities of the singularity for stress components which are continuous at the interface are newly defined and determined for various material combinations

a finite element approach for computing edge singularities in piezoelectric materials by using the eigenfunction expansion technique and the weak form of the governing equations for prismatic sectorial domains composed of piezoelectrics and air an one dimensional finite element procedure is formulated for computing the eigensolutions of the electromechanical field problem generalized displacement and electric potential are taken to be the nodal variables the resulting global equation is a second order characteristic matrix equation validity of the formulation is verified by comparing the computed results with the existing solutions for impermeable cracks and interfacial cracks configurations which are of practical interest including conducting cracks permeable and impermeable notches are studied

asymptotic resurgences for ideals of positive dimensional subschemes of projective space abstract recent work of ein lazarsfeld smith and hochster huneke raised the containment problem of determining which symbolic powers of an ideal are contained in a given ordinary power of the ideal bocci harbourne defined a quantity called the resurgence to address this problem for homogeneous ideals in polynomial rings with a focus on zero dimensional subschemes of projective space here we take the first steps toward extending this work to higher dimensional subschemes we introduce new asymptotic versions of the resurgence and obtain upper and lower bounds on them for ideals i of smooth subschemes generalizing what is done in bocci and harbourne 2010 5 we apply these bounds to ideals of unions of general lines in p n we also pose a nagata type conjecture for symbolic powers of ideals of lines in p 3

finite element evaluation of free edge singular stress fields in anisotropic materials a finite element formulation based on the work of yarnada and okumura 14 is presented to determine the order of singularity and angular variation of the stress and displacement fields surrounding a singular point on a free edge of anisotropic materials emphasis is placed on the computational aspects of this method when applied to configurations including fully bonded multi material junctions intersecting a free edge as well as materials containing cracks intersecting a free edge the study shows that the singularity of the three dimensional stress field may be accurately determined with a relatively small number of elements only when a proper level of numerical integration is used the method is applied to isotropic and orthotropic materials with a crack intersecting a free edge and an anisotropic three material junction intersecting a free edge the efficiency and accuracy of the method indicates it could be used to develop a numerical solution for the singular field that could in turn be used to create free edge enriched finite elements

linear normality of general linear sections and some graded betti numbers of 3 regular projective schemes in this paper we study graded betti numbers of any nondegenerate 3 regular algebraic set x in a projective space pn more concretely via generic initial ideals gins method we mainly consider tailing betti numbers whose homological index is at least codim x pn for this purpose we first introduce a key definition nd 1 property which provides a suitable ground where one can generalize the concepts such as being nondegenerate or of minimal degree from the case of varieties to the case of more general closed subschemes and give a clear interpretation on the tailing betti numbers next we recall basic notions and facts on gins theory and we analyze the generation structure of the reverse lexicographic rlex gins of 3 regular nd 1 subschemes as a result we present exact formulae for these tailing betti numbers which connect them with linear normality of general linear sections of x with a linear subspace of dimension at least codim x pn finally we consider some applications and related examples

borel fixed ideals and reduction number abstract the aim of this paper is to study the relationship between the reduction number and borel fixed ideals in all characteristics especially it is shown that r r i r r i lex where i lex denotes the unique lex segment ideal whose hilbert function is equal to that of i this solves a recent question by conca