a reconstruction theorem for genus zero gromov witten invariants of stacks we generalize the first reconstruction theorem of kontsevich and manin in two respects first we allow the target space to be a deligne mumford stack second under some convergence assumptions we show it suffices to check the hypothesis of h 2 generation not on the cohomology ring but on an any quantum ring in the family given by small quantum cohomology as an example the latter result is used to compute genus zero gromov witten invariants of p 1 b

ehrhart polynomials and stringy betti numbers we study the connection between stringy betti numbers of gorenstein toric varieties and the generating functions of the ehrhart polynomials of certain polyhedral regions we use this point of view to give counterexamples to hibi s conjecture on the unimodality of vectors of reflexive polytopes

the orbifold chow ring of toric deligne mumford stacks the orbifold chow ring of a deligne mumford stack defined by abramovich graber and vistoli 2 is the algebraic version of the orbifold cohomology ring in troduced by w chen and ruan 7 8 by design this ring incorporates numerical invariants such as the orbifold euler characteristic and the orbifold hodge num bers of the underlying variety the product structure is induced by the degree zero part of the quantum product in particular it involves gromov witten invariants inspired by string theory and results in batyrev 3 and yasuda 28 one expects that in nice situations the orbifold chow ring coincides with the chow ring of a resolution of singularities fantechi and g ttsche 14 and uribe 25 verify this conjecture when the orbifold is symn 5 where 5 is a smooth projective surface with ks 0 and the resolution is hilbn the initial motivation for this project was to compare the orbifold chow ring of a simplicial toric variety with the chow ring of a cr pant resolution to achieve this goal we first develop the theory of toric deligne mumford stacks modeled on simplicial toric varieties a toric deligne mumford stack corresponds to a combinatorial object called a stacky fan as a first approximation this object is a simplicial fan with a distinguished lattice point on each ray in the fan more precisely a stacky fan s is a triple consisting of a finitely generated abelian group n a simplicial fan e in q z n with n rays and a map zn n where the image of the standard basis in zn generates the rays in e a rational simplicial fan e produces a canonical stacky fan s n e where n is the distinguished lattice and is the map defined by the minimal lattice points on the rays hence there is a natural toric deligne mumford stack associated to every simplicial toric variety a stacky fan encodes a group action on a quasi affine variety and the toric deligne mumford stack is the quotient if e corresponds to a smooth toric variety x e and s is the canonical stacky fan associated to e then we simply have x z we show that many of the basic concepts such as open and closed toric substacks line bundles and maps between toric deligne mumford stacks correspond to combinatorial notions we expect that many more results about toric varieties lift to the realm of stacks and hope that toric deligne mumford stacks will serve as a useful testing ground for general theories

fast evaluation of transient acoustic fields the efficient computation of transient fields radiated by non harmonic source distributions is a problem relevant in numerous areas of acoustics this paper presents an efficient easily implemented method for the generation of time dependent spherical harmonic expansions for arbitrary sources which can be used to compute the transient radiated field at arbitrary points outside the source domain the method depends on the theory of time domain spherical harmonic expansions and the solution of vandermonde systems results are presented demonstrating the efficiency and accuracy of the method with respect to full evaluation of the field radiated by a randomized source distribution

gorenstein polytopes and their stringy e functions inspired by ideas from algebraic geometry batyrev and the first named author have introduced the stringy e function of a gorenstein polytope we prove that this a priori rational function is actually a polynomial which is part of a conjecture of batyrev and the first named author the proof relies on a comparison result for the lattice point structure of a gorenstein polytope p a face f of p and the face of the dual gorenstein polytope corresponding to f in addition we study joins of gorenstein polytopes and introduce the notion of an irreducible gorenstein polytope we show how these concepts relate to the decomposition of nef partitions

an iterative method for the computation of nonlinear wide angle pulsed acoustic fields of medical diagnostic transducers the development and optimization of medical ultrasound transducers and imaging modalities require a computational method that accurately predicts the nonlinear acoustic pressure field a prospective method should provide the wide angle pulsed field emitted by an arbitrary planar source distribution and propagating in a three dimensional large scale domain holding a nonlinear acoustic medium in this paper a method is presented that is free of any assumed wavefield directionality the nonlinear acoustic wave equation is solved by treating the nonlinear term as a contrast source this formulation leads to an iterative scheme that involves the repetitive solution of a linear wave problem through green s function method it is shown that accurate field predictions may be obtained within a few iterations moreover by employing a dedicated numerical convolution technique the method allows for a discretization down to two points per wavelength or period of the highest frequency of interest the performance of the method is evaluated through a number of nonlinear field predictions for pulsed transducers with various geometries the results demonstrate the directional independence of the method moreover comparison with results from several existing methods shows that the method accurately predicts the nonlinear field for weak to moderate nonlinearity

termination proofs by multiset path orderings imply primitive recursive derivation lengths it is shown that a termination proof for a term rewriting system using multiset path orderings i e recursive path orderings with multiset status only yields a primitive recursive bound on the length of derivations measured in the size of the starting term confirming a conjecture of plaisted pla78 this result holds for a great variety of path orderings including path of subterms ordering recursive decomposition ordering and the path ordering of kapur narendran sivakumar if lexicographic status is not incorporated the result is essentially optimal as such derivation lengths can be found in each level of the grzegorczyk hierarchy even for string rewriting systems

iterative computational techniques in scattering based upon the integrated square error criterion an iterative technique is developed to rigorously compute the electromagnetic time and frequency domain scattering problems the method is based upon a wave function expansion technique this also includes the integral representation techniques in which the electromagnetic field equations and causality conditions are satisfied analytically while the boundary conditions or the constitutive relations have to be satisfied in a computational manner the latter is accomplished by an iterative minimization of the integrated square error for the solution of an integral equation it is shown how to obtain optimum convergence some numerical results pertaining to a number of representative problems illustrate the numerical advantages and disadvantages of the iterative method

global spectra polytopes and stacky invariants given a convex polytope we define its geometric spectrum a stacky version of batyrev s stringy e functions and we prove a stacky version of a formula of libgober and wood about the e polynomial of a smooth projective variety as an application we get a closed formula for the variance of the geometric spectrum and a noether s formula for two dimensional fano polytopes polytopes whose vertices are primitive lattice points a fano polytope is not necessarily smooth we also show that this geometric spectrum is equal to the algebraic spectrum the spectrum at infinity of a tame laurent polynomial whose newton polytope is the polytope alluded to this gives an explanation and some positive answers to hertling s conjecture about the variance of the spectrum of tame regular functions

simple termination of rewrite systems abstract in this paper we investigate the concept of simple termination a term rewriting system is called simply terminating if its termination can be proved by means of a simplification order the basic ingredient of a simplification order is the subterm property but in the literature two different definitions are given one based on strict partial orders and another one based on preorders or quasi orders we argue that there is no reason to choose the second one as the first one has certain advantages simplification orders are known to be well founded orders on terms over a finite signature this important result no longer holds if we consider infinite signatures nevertheless well known simplification orders like the recursive path order are also well founded on terms over infinite signatures provided the underlying precedence is well founded we propose a new definition of simplification order which coincides with the old one based on partial orders in case of finite signatures but which is also well founded over infinite signatures and covers orders like the recursive path order we investigate the properties of the ensuing class of simply terminating systems

a k space method for coupled first order acoustic propagation equations a k space method for large scale simulation of ultrasonic pulse propagation is presented the present method which solves the coupled first order differential equations for wave propagation in inhomogeneous media is derived in a simple form analogous to previous finite difference methods with staggered spatial and temporal grids like k space methods based on second order wave equations the present method is exact for homogeneous media unconditionally stable for slow c r c0 media and highly accurate for general weakly scattering media in addition unlike previous k space methods the form of the method allows straightforward inclusion of relaxation absorption and perfectly matched layer pml nonreflecting boundary conditions numerical examples illustrate the capabilities of the present k space method for weakly inhomogeneous media accurate results are obtained using coarser temporal and spatial steps than possible with comparable finite difference and pseudospectral methods the low dispers

a filtered convolution method for the computation of acoustic wave fields in very large spatiotemporal domains the full wave computation of transient acoustic fields with sizes in the order of 100x100x100 wavelengths by 100 periods requires a numerical method that is extremely efficient in terms of storage and computation iterative integral equation methods offer a good performance on these points provided that the recurring spatiotemporal convolutions are computed with a coarse sampling and relatively few computational operations this paper describes a method for the numerical evaluation of very large scale four dimensional convolutions that employs a fast fourier transformation and that uses a sampling rate close to or at the limit of two points per wavelength and per period to achieve this the functions involved are systematically filtered windowed and zero padded with respect to all relevant coordinates prior to sampling the method is developed in the context of the neumann iterative solution of the acoustic contrast source problem for an inhomogeneous medium the implementation of the method on a parallel computer is discussed the obtained numerical results have a relative root mean square error of a few percent when sampling at two points per wavelength and per period further the results prove that the method enables the computation of transient fields in the order of the indicated size

weighted blowup correspondence of orbifold gromov witten invariants and applications let mathsf x be a compact symplectic orbifold groupoid with mathsf s being a compact symplectic sub orbifold groupoid and underline mathsf x mathfrak a be the weight mathfrak a blowup of mathsf x along mathsf s with mathsf z being the exceptional divisor we show that there is a weighted blowup correspondence between some certain absolute orbifold gromov witten invariants of mathsf x relative to mathsf s and some certain relative orbifold gromov witten invariants of the pair underline mathsf x mathfrak a mathsf z as an application we prove that the symplectic uniruledness of symplectic orbifold groupoids is a weighted blowup invariant

the s eulerian polynomials have only real roots we study the roots of generalized eulerian polynomials via a novel approach we interpret eulerian polynomials as the generating polynomials of a statistic over inversion sequences inversion sequences also known as lehmer codes or subexcedant functions were recently generalized by savage and schuster to arbitrary sequences s of positive integers which they called s inversion sequences our object of study is the generating polynomial of the ascent statistic over the set of s inversion sequences of length n since this ascent statistic over inversion sequences is equidistributed with the descent statistic over permutations we call this generalized polynomial the s eulerian polynomial the main result of this paper is that for any sequence s of positive integers the s eulerian polynomial has only real roots this result is first shown to generalize several existing results about the real rootedness of various eulerian polynomials we then show that it can be used to settle a conjecture of brenti that eulerian polynomials for all finite coxeter groups have only real roots and partially settle a conjecture of dilks petersen stembridge on type b affine eulerian polynomials it is then extended to several q analogs we show that the macmahon carlitz q eulerian polynomial has only real roots whenever q is a positive real number confirming a conjecture of chow and gessel the same holds true for the hyperoctahedral group and the wreath product groups confirming further conjectures of chow and gessel and chow and mansour respectively our results have interesting geometric consequences as well

duality theorems for etale gerbes on orbifolds abstract let g be a finite group and y a g gerbe over an orbifold b a disconnected orbifold y and a flat u 1 gerbe c on y is canonically constructed from y motivated by a proposal in physics we study a mathematical duality between the geometry of the g gerbe y and the geometry of y twisted by c we prove several results verifying this duality in the contexts of non commutative geometry and symplectic topology in particular we prove that the category of sheaves on y is equivalent to the category of c twisted sheaves on y when y is symplectic we show by a combination of techniques from non commutative geometry and symplectic topology that the chen ruan orbifold cohomology of y is isomorphic to the c twisted orbifold cohomology of y as graded algebras

analysing the implicit complexity of programs we study termination proofs in order to i determine computational complexity of programs and ii generate efficient programs from the complexity analysis for this we construct a termination ordering called light multiset path ordering lmpo which is a restriction of the multiset path ordering we establish that the class of first order functional programs on lists which is terminating by lmpo characterises exactly the functions computable in polynomial time

equivariant gw theory of stacky curves we extend okounkov and pandharipande s work on the equivariant gromov witten theory of mathbb p 1 to a class of stacky curves mathcal x our main result uses virtual localization and the orbifold elsv formula to express the tau function tau mathcal x as a vacuum expectation on a fock space

modeling of nonlinear ultrasound propagation in tissue from array transducers a computationally efficient model capable of simulating finite amplitude ultrasound beam propagation in water and in tissue from phased linear arrays and other transducers of arbitrary quasiplanar geometry is described it is based on a second order operator splitting approach tavakkoli et al j acoust soc am 104 2061 2072 1998 with a fractional step marching scheme whereby the effects of diffraction attenuation and nonlinearity can be computed independently over incremental steps this approach is an extension to that of christopher and parker j acoust soc am 90 507 521 90 488 499 1991 wherein linear and nonlinear effects are propagated separately over incremental steps and the computation of the diffractive substeps are based on an angular spectrum technique with a modified sampling scheme for accurate and efficient implementation of diffractive propagation from nonradially symmetric sources results of the model are compared with published data predicted field profiles for nonlinear propagation in tissue from realistic array transducers using the pulse inversion method are presented

the spaces of laurent polynomials gromov witten theory of ℙ1 orbifolds and integrable hierarchies let mk m be the space of laurent polynomials in one variable x t1x tk mx where k m 1 are fixed integers and tk m 6 0 according to b dubrovin 11 mk m can be equipped with a semi simple frobenius structure in this paper we prove that the corresponding descendent and ancestor potentials of mk m defined as in 16 satisfy hirota quadratic equations hqe for short let ck m be the orbifold obtained from p by cutting small discs d1 z and d2 z 1 around z 0 and z and gluing back the orbifolds d1 zk and d2 zm in the obvious way we show that the orbifold quantum cohomology of ck m coincides with mk m as frobenius manifolds modulo some yet to be clarified details this implies that the descendent respectively the ancestor potential of mk m is a generating function for the descendent respectively ancestor orbifold gromov witten invariants of ck m there is a certain similarity between our hqe and the lax operators of the extended bi graded toda hierarchy introduced by g carlet in 7 therefore it is plausible that our hqe characterize the tau functions of this hierarchy and we expect that the extended bi graded toda hierarchy governs the gromov witten theory of ck m

generalization of the k space formulation to elastodynamic scattering problems a generalized k space gks formulation is presented for vectorial elastodynamic scattering problems it represents a generalization of bojarski s scalar k space formulation from the basic second order partial differential equation or its integral representation in the space frequency r f domain a local equation is derived for the displacement field in the spectral frequency k f domain this equation together with the constitutive equation in the r f domain reduces the original scattering problem into two simultaneous local equations with two unknowns displacement field and the induced source which are then solved by the conjugate gradient cg method the connection between the k f domain and r f domain is obtained by the spatial fast fourier transform fft algorithm the number of complex multiply add operations per cg iteration is o n log2 n and the storage requirement is only o n where n is the number of spatial discretization points this is much more efficient than the conventional m

a new equivariant cohomology ring in this paper motivated by chen ruan s stringy orbifold theory on almost complex orbifolds we construct a new equivariant cohomology ring mathscr h g x for an equivariant almost complex pair x g where x is a compact connected almost complex manifold g is a connected compact lie group which acts on x and preserves the almost complex structure

an integral structure in quantum cohomology and mirror symmetry for toric orbifolds abstract we introduce an integral structure in orbifold quantum cohomology associated to the k group and the class in the case of compact toric orbifolds we show that this integral structure matches with the natural integral structure for the landau ginzburg model under mirror symmetry by assuming the existence of an integral structure we give a natural explanation for the specialization to a root of unity in y ruan s crepant resolution conjecture yongbin ruan the cohomology ring of crepant resolutions of orbifolds in contemp math vol 403 amer math soc providence ri 2006 pp 117 126

noncommutative poisson structures on orbifolds author s halbout gilles tang xiang abstract in this paper we compute the gerstenhaber bracket on the hoch schild cohomology of c infty m rtimes g for a finite group g acting on a compact manifold m using this computation we obtain geometric descriptions for all noncommutative poisson structures on c infty m rtimes g when m is a symplectic manifold we also discuss examples of deformation quantizations of these noncommutative poisson structures

quasi interpretations a way to control resources this paper presents in a reasoned way our works on resource analysis by quasi interpretations the controlled resources are typically the runtime the runspace or the size of a result in a program execution quasi interpretations allow the analysis of system complexity a quasi interpretation is a numerical assignment which provides an upper bound on computed functions and which is compatible with the program operational semantics the quasi interpretation method offers several advantages i it provides hints in order to optimize an execution ii it gives resource certificates and iii finding quasi interpretations is decidable for a broad class which is relevant for feasible computations by combining the quasi interpretation method with termination tools here term orderings we obtained several characterizations of complexity classes starting from ptime and pspace

orderings for term rewriting systems abstract methods of proving that a term rewriting system terminates are presented they are based on the intuitive notion of simplification orderings orderings in which any term that is syntactically simpler than another is smaller than the other as a consequence of kruskal s tree theorem any nonterminating system must be self embedding in the sense that it allows for the derivation of some term from a simpler one thus termination is guaranteed if every rule in the system is a reduction in some simplification ordering most of the orderings that have been used for proving termination are indeed simplication orderings using this notion often allows for much easier proofs a particularly useful class of simplification orderings the recursive path orderings is defined examples of the use of simplication orderings in termination proofs are given

a new cohomology theory of orbifold based on the orbifold string theory model in physics we construct a new cohomology ring for any almost complex orbifold the key theorem is the associativity of this new ring some examples are computed

the derivational complexity of string rewriting systems we study the derivational complexities of string rewriting systems we discuss the following fundamental question which functions can be derivational complexities of terminating finite string rewriting systems they are recursive but for any recursive function there is a derivational complexity larger than it we relate them to the time functions of turing machines in particular we show that the functions n a a 2 and a n a 1 for a real number a are equivalent to the derivational complexity of some finite string rewriting systems if the computational complexity of a is relatively low for example a is rational algebraic p or e on the other hand they cannot be equivalent to any derivational complexities if the complexity of a is high

weighted ehrhart theory and orbifold cohomology we introduce the notion of a weighted d vector of a lattice polytope although the definition is motivated by motivic integration we study weighted d vectors from a combinatorial perspective we present a version of ehrhart reciprocity and prove a change of variables formula we deduce a new geometric interpretation of the coefficients of the ehrhart d vector more specifically they are sums of dimensions of orbifold cohomology groups of a toric stack

on permutation polytopes abstract in this paper we lay the foundations for the study of permutation polytopes the convex hull of a group of permutation matrices we clarify the relevant notions of equivalence prove a product theorem and discuss centrally symmetric permutation polytopes we provide a number of combinatorial properties of faces of permutation polytopes as an application we classify 4 dimensional permutation polytopes and the corresponding permutation groups classification results and further examples are made available online we conclude with several questions suggested by a general finiteness result

ideals of the cohomology rings of hilbert schemes and their applications we study the ideals of the rational cohomology ring of the hilbert scheme x n of n points on a smooth projective surface x as an application for a large class of smooth quasi projective surfaces x we show that every cup product structure constant of h x n is independent of n moreover we obtain two sets of ring generators for the cohomology ring h x n similar results are established for the chen ruan orbifold cohomology ring of the symmetric product in particular we prove a ring isomorphism between h x n c and h orb x n sn c for a large class of smooth quasi projective surfaces with numerically trivial canonical class

second quantized frobenius algebras we show that given a frobenius algebra there is a unique notion of its second quantization which is the sum over all symmetric group quotients of nth tensor powers where the quotients are given by symmetric group twisted frobenius algebras to this end we consider the setting of frobenius algebras given by functors from geometric categories whose objects are endowed with geometric group actions and prove structural results which in turn yield a constructive realization in the case of nth tensor powers and the natural permutation action we also show that naturally graded symmetric group twisted frobenius algebras have a unique algebra structure already determined by their underlying additive data together with a choice of super grading furthermore we discuss several notions of discrete torsion and show that indeed a non trivial discrete torsion leads to a non trivial super structure on the second quantization

an upper bound on the derivational complexity of knuth bendix orderings the derivational complexity of a terminating rewrite system is a measure for the maximal length of rewrite sequences we study the influence of certain standard termination criteria on the derivational complexity in this paper we prove a uniform multiple recursive upper bound for knuth bendix orderings this continues work by hofbauer and lautemann 13 where it has been shown that primitive recursive bounds are impossible

inequalities and ehrhart delta vectors for any lattice polytope p we consider an associated polynomial p t and describe its decomposition into a sum of two polynomials satisfying certain symmetry conditions as a consequence we improve upon known inequalities satisfied by the coefficients of the ehrhart vector of a lattice polytope we also provide combinatorial proofs of two results of stanley that were previously established using techniques from commutative algebra finally we give a necessary numerical criterion for the existence of a regular unimodular lattice triangulation of the boundary of a lattice polytope

derivation lengths and order types of knuth bendix orders abstract the derivation length function of a finite term rewriting system terminating via a knuth bendix order is shown to be bounded by the ackermann function applied to a single exponential function this result is essentially optimal as there are rewrite systems with such derivation lengths in a second part the order types of knuth bendix orders over finite signatures are classified within the ordinals up to

computation of nonlinear ultrasound fields using a linearized contrast source method nonlinear ultrasound is important in medical diagnostics because imaging of the higher harmonics improves resolution and reduces scattering artifacts second harmonic imaging is currently standard and higher harmonic imaging is under investigation the efficient development of novel imaging modalities and equipment requires accurate simulations of nonlinear wave fields in large volumes of realistic lossy inhomogeneous media the iterative nonlinear contrast source incs method has been developed to deal with spatiotemporal domains measuring hundreds of wavelengths and periods this full wave method considers the nonlinear term of the westervelt equation as a nonlinear contrast source and solves the equivalent integral equation via the neumann iterative solution recently the method has been extended with a contrast source that accounts for spatially varying attenuation the current paper addresses the problem that the neumann iterative solution converges badly for strong contrast sources the remedy is linearization of the nonlinear contrast source combined with application of more advanced methods for solving the resulting integral equation numerical results show that linearization in combination with a bi conjugate gradient stabilized method allows the incs method to deal with fairly strong inhomogeneous attenuation while the error due to the linearization can be eliminated by restarting the iterative scheme

on the hard lefschetz property of stringy hodge numbers abstract for projective varieties with a certain class of mild isolated singularities and for projective threefolds with arbitrary gorenstein canonical singularities we show that the stringy hodge numbers satisfy the hard lefschetz property i e h s t p q h s t p 1 q 1 for p q d 2 where d is the dimension of the variety this result fits nicely with a 6 dimensional counterexample of musta and payne for the hard lefschetz property for stringy hodge numbers in general we also give such an example ours is a hypersurface singularity

the witten equation mirror symmetry and quantum singularity theory for any nondegenerate quasi homogeneous hypersurface singularity we describe a family of moduli spaces a virtual cycle and a corresponding cohomological eld theory associated to the singularity this theory is analogous to gromov witten theory and generalizes the theory of r spin curves which corresponds to the simple singularity ar 1 we also resolve two outstanding conjectures of witten the rst conjecture is that ade singularities are self dual and the second conjecture is that the total potential functions of ade singularities satisfy corresponding ade integrable hierarchies other cases of integrable hierarchies are also discussed

a non crossing standard monomial theory abstract the second author has introduced non crossing tableaux objects whose non nesting analogues are semi standard young tableaux we relate non crossing tableaux to gelfand tsetlin patterns and develop the non crossing analogue of standard monomial theory leclerc and zelevinsky s weakly separated sets are special cases of non crossing tableaux and we suggest that non crossing tableaux may help illuminate the theory of weakly separated sets

termination proofs for term rewriting systems by lexicographic path orderings imply multiply recursive derivation lengths abstract it is shown that a termination proof for a term rewriting system using a lexicographic path ordering yields a multiply recursive bound on the length of derivations measured in the depth of the starting term this result is essentially optimal since for every multiply recursive function a rewrite system which reduces under the lexicographic path ordering can be found such that its derivation length cannot be bounded by

topological orbifold models and quantum cohomology rings we discuss the topological sigma model on an orbifold target space we describe the moduli space of classical minima for computing correlation functions involving twisted operators and show through a detailed computation of an orbifold ofcp1 by the dihedral groupd4 how to compute the complete ring of observables through this procedure we compute all the rings of dihedralcp1 orbifolds we then considercp2 d4 and show how the techniques of topologicalanti topological fusion might be used to compute twist field correlation functions for nonabelian orbifolds