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

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

time exponential splitting technique for the klein gordon equation with hagstrom warburton high order absorbing boundary conditions klein gordon equations on an unbounded domain are considered in one dimensional and two dimensional cases numerical computation is reduced to a finite domain by using the hagstrom warburton h w high order absorbing boundary conditions abcs time integration is made by means of exponential splitting schemes that are efficient and easy to implement in this way it is possible to achieve a negligible error due to the time integration and to study the behavior of the absorption error numerical experiments displaying the accuracy of the numerical solution for the two dimensional case are provided the influence of the dispersion coefficient on the error is also studied

depth and regularity of powers of sums of ideals given arbitrary homogeneous ideals i and j in polynomial rings a and b over a field k we investigate the depth and the castelnuovo mumford regularity of powers of the sum i j in a otimes k b in terms of those of i and j our results can be used to study the behavior of the depth and regularity functions of powers of an ideal for instance we show that such a depth function can take as its values any infinite non increasing sequence of non negative integers

a vanishing theorem and asymptotic regularity of powers of ideal sheaves abstract let i be an ideal sheaf on p n in the first part of this paper we bound the asymptotic regularity of powers of i as s p reg i p s p e where e is a constant and s is the s invariant of i we also give the same upper bound for the asymptotic regularity of symbolic powers of i under some conditions in the second part by using multiplier ideal sheaves we give a vanishing theorem of powers of i when it defines a local complete intersection subvariety with log canonical singularities

using half plane solutions in the context of mm for analyzing large flat structures with or without resistive loadings the size of the scatterers that can be analyzed using the conventional method of moments mm is limited to only a few wavelengths due to large storage requirements in the computer one way to circumvent this problem is to use techniques that temper the growth in the size of the impedance matrix to a reasonable level even as the scatterer becomes large in terms of the wavelength it is shown that this can be done by choosing an appropriate set of entire or semi entire domain basis functions that incorporate the actual physics of the scattering phenomenon the functional forms of the basis functions are obtained either from an exact or an asymptotic solution to certain canonical problems as an example the problems of scattering from perfectly conducting or resistively loaded flat strips and plates are solved by utilizing the exact or asymptotic solutions to half plane problems as basis functions

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

weak ill posedness of spatial discretizations of absorbing boundary conditions for schrodinger type equations when we wish to solve numerically a differential problem defined on an infinite domain it is necessary to consider a finite subdomain and to use artificial boundary conditions in such a way that the solutions in the finite subdomain approximate the original solution these boundary conditions are called absorbing when small reflections to the interior domain are allowed in this paper we develop a general class of absorbing boundary conditions for schrodinger type equations by using rational approximations to the transparent boundary conditions with this approach previous absorbing boundary conditions in the literature are included in this class we use the method of lines for the discretization of the initial boundary value problems obtained this way we show that the ordinary differential systems that arise after the spatial discretization are weakly ill posed explaining a previous conjecture of fevens and jiang the time discretization is carried out with a stable runge kutta methods where the high order ones may be used to compensate for the possible troubles present in the problems semidiscretized in space

electromagnetic scattering from extended wires and two and three dimensional surfaces efficient numerical solutions for the electromagnetic scattering for classes of electrically large one two and three dimensional perfectly conducting scatterers are presented the formulation is based on solution of the electric field integral equation efie using the method of moments mm an entire domain galerkin representation is used for wires and two dimensional surfaces and a combination of entire and subdomain representations is applied to surfaces in three dimensions the analysis is extendable to corrugated surfaces formed from sections of surfaces of translation or rotation numerical results are presented for wires infinite strips and finite strips or plates the behavior of the solutions with the number of terms in the entire domain expansion is examined the reconstruction of the traveling wave contribution to the scattering cross section using various approximations is discussed and representative examples are given

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

asymptotic multiplicities of graded families of ideals and linear series abstract we find simple necessary and sufficient conditions on a local ring r of dimension d for the limit lim n l r r i n n d to exist whenever i n is a graded family of m r primary ideals and give a number of applications we also give simple necessary and sufficient conditions on projective schemes over a field k for asymptotic limits of the growth of all graded linear series of a fixed kodaira iitaka dimension to exist

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

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

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

growth of primary decompositions of frobenius powers of ideals abstract it was previously known by work of smith swanson and of sharp nossem that the linear growth property of primary decompositions of frobenius powers of ideals in rings of prime characteristic has strong connections to the localization problem in tight closure theory the localization problem has recently been settled in negative by brenner and monsky but the linear growth question is still open we study growth of primary decompositions of frobenius powers of dimension one homogeneous ideals in graded rings over fields if the ring is positively graded we prove that the linear growth property holds for non negatively graded rings we are able to show that there is a polynomial growth we present explicit primary decompositions of frobenius powers of an ideal which were known to have infinitely many associated primes having this linear growth property we also discuss some other interesting examples

stability analysis of the numerical method of characteristics applied to a class of energy preserving hyperbolic systems part ii nonreflecting boundary conditions abstract we show that imposition of non periodic in place of periodic boundary conditions bc can alter stability of modes in the method of characteristics moc employing certain ordinary differential equation ode numerical solvers thus using non periodic bc may render some of the moc schemes stable for most practical computations even though they are unstable for periodic bc this fact contradicts a statement found in some textbooks and known as part of the babenko gelfand criterion that an instability detected by the von neumann analysis for a given numerical scheme implies an instability of that scheme with arbitrary i e non periodic bc we explain the mechanism behind this contradiction which lies in a certain property of the scheme s eigenmodes that is assumed by the babenko gelfand criterion but does not hold for eigenmodes of some of the moc based schemes we also show that and explain why for the moc employing some other ode solvers stability of the modes may indeed not be improved by non periodic bc as the babenko gelfand criterion implies

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

minimal free resolutions and asymptotic behavior of multigraded regularity let s be a standard nk graded polynomial ring over a field k let i be a multigraded homogeneous ideal of s and let m be a finitely generated zk graded s module we prove that the resolution regularity a multigraded variant of castelnuovo mumford regularity of inm is asymptotically a linear function this shows that the well known z graded phenomenon carries to the multigraded situation

some results on asymptotic regularity of ideal sheaves abstract let i be an ideal sheaf on p n defining a subscheme x associated to i there are two elementary invariants the invariant s which measures the positivity of i and the minimal number d such that i d is generated by its global sections it is now clear that the asymptotic behavior of reg i t is governed by s but usually not linear in this paper we first describe the linear behavior of the asymptotic regularity by showing that if s d i e s reaches its maximal value then for t large enough reg i t d t e for some positive constant e we then turn to concrete geometric settings to study the asymptotic regularity of i in the case that x is a nonsingular variety embedded by a very ample adjoint line bundle our approach also gives regularity bounds for i t once we know reg i and assume that x is a local complete intersection

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

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

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

cylindrical eigencurrents the eigenvalue problem for the integro differential operator associated with the electromagnetic scattering by conducting surfaces is solved for the case of long finite circular cylinders the approach consists of reducing the eigenvalue equation to matrix form using the galerkin technique expanding the resulting matrix elements in an asymptotic series in inverse powers of the cylinder length and then applying perturbation theory

asymptotic linear bounds for the castelnuovo mumford regularity we prove asymptotic linear bounds for the castelnuovo mumford regularity of certain filtrations of homogeneous ideals whose rees algebras need not be noetherian

time exponential splitting integrator for the klein gordon equation with free parameters in the hagstrom warburton absorbing boundary conditions abstract the klein gordon equation on an infinite two dimensional strip is considered numerical computation is reduced to a finite domain by using the hagstrom warburton h w absorbing boundary conditions abcs with free parameters in the formulation of the auxiliary variables the spatial discretization is achieved by using fourth order finite differences and the time integration is made by means of an efficient and easy to implement fourth order exponential splitting scheme which was used in alonso mallo and portillo 2016 considering the fixed pade parameters in the formulation of the abcs here we generalize the splitting time technique to other choices of the parameters to check the time integrator we consider on one hand four types of fixed parameters the newmann s parameters the chebyshev s parameters the pade s parameters and optimal parameters proposed in hagstrom et al 2007 and on the other hand an adaptive scheme for the dynamic control of the order of absorption and the parameters we study the efficiency of the splitting scheme by comparing with the fourth order four stage runge kutta method

electromagnetic scattering from ducts with irregular edges ii noncircular case a formulation is developed for electromagnetic scattering from finite circular ducts terminated with irregular edges the analysis is based on the solution of the electric field integral equation using an entire domain galerkin expansion for both the axial and the circumferential variation of the currents defined in terms of an edge slope dependent vector field that provides simplifying symmetry properties for the method of moments system matrix comparisons are made with edge slope independent formulations the analysis is general and applicable for cases in which the functional variation of the edge irregularities is specified by either a deterministic or a random process circumferential modal decoupling occurs when the irregularities are specified by a stationary stochastic process having a periodic correlation function numerical results are given for edge irregularities governed by a gaussian random process and are compared for various limiting cases with results for right circular cylindrical ducts

high order full discretization for anisotropic wave equations abstract two dimensional linear wave equation in anisotropic media on a rectangular domain with initial conditions and periodic boundary conditions is considered the energy of the problem is contemplated the space discretization is reached by means of finite differences on a uniform grid paying attention to the mixed derivative of the equation the discrete energy of the semi discrete problem is introduced for the time integration of the system of ordinary differential equations obtained a fourth order exponential splitting method which is a geometric integrator is proposed this time integrator is efficient and easy to implement the stability condition for time step and space step ratio is deduced numerical experiments displaying the good behavior in the long time integration and the efficiency of the numerical solution are provided

natural frequencies and modes of finite open circular cylinders the natural frequencies and natural modes of open circular cylinders of given aspect ratios are calculated by means of a galerkin procedure involving entire domain bases the results are validated by comparison with other calculations of natural frequencies and modes for cylinders and time response current for wires the usefulness of a previously proposed method based on perturbation theory is examined in this context

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

transient excitation of a straight thin wire segment a new look at an old problem the transient excitation of a straight thin wire segment is analyzed with the aid of a one dimensional integral equation for the current along the wire an almost exact derivation of that equation in which only the radial current on the end faces is approximated is given the integral equation obtained turns out to be identical to the reduced version of pocklington s equation on the basis of this derivation existing and new numerical solution techniques are critically reviewed pocklington s equation and hallen s equivalent form are solved directly by marching on in time as well as indirectly via a transformation to the frequency domain for pocklington s equation a conventional moment method discretization leads to a toeplitz matrix that is inverted with levinson s algorithm for hallen s equation the toeplitz structure is disturbed and the frequency domain constituents are determined with the aid of the conjugate gradient fft method illustrative numerical results are presented and discussed

associated points and integral closure of modules abstract let x spec r be an affine noetherian scheme and m n be a pair of finitely generated r modules denote their rees algebras by r m and r n let n n be the nth homogeneous component of r n and let m n be the image of the nth homogeneous component of r m in n n denote by m n be the integral closure of m n in n n we prove that ass x n n m n and ass x n n m n are asymptotically stable generalizing known results for the case where m is an ideal or where n is a free module suppose either that m and n are free at the generic point of each irreducible component of x or n is contained in a free r module when x is universally catenary we prove a generalization of a classical result due to mcadam and obtain a geometric classification of the points appearing in ass x n n m n notably we show that if x ass x n n m n for some n then x is the generic point of a codimension one component of the nonfree locus of n m or x is a generic point of an irreducible set in x where the fiber dimension proj r m x jumps we prove a converse to this result without requiring x to be universally catenary our approach is geometric in spirit also we recover strengthen and prove a sort of converse of an important result of kleiman and thorup about integral dependence of modules

near conserving energy numerical schemes for two dimensional coupled seismic wave equations abstract two dimensional coupled seismic waves satisfying the equations of linear isotropic elasticity on a rectangular domain with initial conditions and periodic boundary conditions are considered a quantity conserved by the solution of the continuous problem is used to check the numerical solution of the problem second order spatial derivatives in the x direction in the y direction and mixed derivative are approximated by finite differences on a uniform grid the ordinary second order in time system obtained is transformed into a first order in time system in the displacement and velocity vectors for the time integration of this system second order and fourth order exponential splitting methods which are geometric integrators are proposed these explicit splitting methods are not unconditionally stable and the stability condition for time step and space step ratio is deduced numerical experiments displaying the good behavior in the long time integration and the efficiency of the numerical solution are provided

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

ideals in a perfect closure linear growth of primary decompositions and tight closure this paper is concerned with tight closure in a commutative noetherian ring r of prime characteristic p and is motivated by an argument of k e smith and i swanson that shows that if the sequence of frobenius powers of a proper ideal a of r has linear growth of primary decompositions then tight closure of a commutes with localization at the powers of a single element it is shown in this paper that provided r has a weak test element linear growth of primary decompositions for other sequences of ideals of r that approximate in a certain sense the sequence of frobenius powers of a would not only be just as good in this context but in the presence of a certain additional finiteness property would actually imply that tight closure of a commutes with localization at an arbitrary multiplicatively closed subset of r work of m katzman on the localization problem for tight closure raised the question as to whether the union of the associated primes of the tight closures of the frobenius powers of a has only finitely many maximal members this paper develops through a careful analysis of the ideal theory of the perfect closure of r strategies for showing that tight closure of a specified ideal a of r commutes with localization at an arbitrary multiplicatively closed subset of r and for showing that the union of the associated primes of the tight closures of the frobenius powers of a is actually a finite set several applications of the strategies are presented in most of them it was already known that tight closure commutes with localization but the resulting affirmative answers to katzman s question in the various situations considered are believed to be new

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

asymptotic linear bounds of castelnuovo mumford regularity in multigraded modules abstract let a be a noetherian standard n graded algebra over an artinian local ring a 0 let i 1 i t be homogeneous ideals of a and m a finitely generated n graded a module we prove that there exist two integers k k such that reg i 1 n 1 i t n t m n 1 n t k k for all n 1 n t n

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

scattering from conducting finite cylinders with thin coatings the surface equivalence principle is used to develop an integral equation formulation for electromagnetic scattering from open circular cylinders with thin material coatings the method of moments with entire domain functions leads to an algebraic system of equations which is solved numerically results of calculations for various cylinder aspect ratios layer thicknesses and material constitutive properties are presented

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

local okounkov bodies and limits in prime characteristic this article is concerned with the asymptotic behavior of certain sequences of ideals in rings of prime characteristic these sequences which we call p families of ideals are ubiquitous in prime characteristic commutative algebra e g they occur naturally in the theories of tight closure hilbert kunz multiplicity and f signature we associate to each p family of ideals an object in euclidean space that is analogous to the newton okounkov body of a graded family of ideals which we call a p body generalizing the methods used to establish volume formulas for the hilbert kunz multiplicity and f signature of semigroup rings we relate the volume of a p body to a certain asymptotic invariant determined by the corresponding p family of ideals we apply these methods to obtain new existence results for limits in positive characteristic an analogue of the brunn minkowski theorem for hilbert kunz multiplicity and a uniformity result concerning the positivity of a p family

scattering from wires and open circular cylinders of finite length using entire domain galerkin expansions electromagnetic em scattering by finite length perfectly conducting open cylinders i e ducts or tubes with circular cross sections is considered the case of a straight wire viewed as a thin cylinder is examined in this context the salient features of this study are a use of the electric field integral equation efie as a starting point b solution of this equation by the galerkin method and c representation of the axial variation of the currents on the scatterer by an entire domain fourier series expansion edge modes are considered in the expansion set and their effect is examined the open cylinder backscatter cross section is computed as a function of aspect angle for various radii and lengths and is compared with measured data

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

numerical comparison of high order absorbing boundary conditions and perfectly matched layers for a dispersive one dimensional medium abstract high order absorbing boundary conditions abc and perfectly matched layers pml are two powerful methods to numerically solve wave problems in unbounded domains the aim of the proposed study is to analyze and compare the performance of these methods in the one dimensional problem governed by the dispersive wave equation the pmls proposed in literature for time harmonic dynamics are applied to time dependent wave problems and linear quadratic and cubic polynomial stretching functions are considered the resulting pmls exhibit a double absorbing action i they reduce the amplitude of the incident waves and ii they delay the wave propagation then the abc proposed by givoli and neta and those proposed by hagstrom mar or and givoli are considered the former are a reformulation of the higdon high order non reflecting boundary conditions the latter improve the higdon conditions and extend them to take into account evanescent waves the accuracy of the pmls and abcs implemented in a finite element code is first investigated with respect to the frequency of the incident wave being it progressive or evanescent then the response to a wave train characterized by a broad frequency spectrum resulting from an impulsive force is studied a detailed analysis is performed to detect the influence of the parameters of both the abcs and the pmls on the absorption of waves the performances of pmls and abcs are compared and merits and drawbacks of the two methods are pointed out