max noether s theorem for integral curves abstract we study a celebrated result of max noether on global sections of the n dualizing sheaf of a smooth nonhyperelliptic curve in the case where the curve is integral we reduce the proof of the statement in such a case to a purely numerical condition which we show that holds if the non gorenstein points are bibranch at worst this is our main result we also extend the notion of a canonical embedding for integral curves with unibranch non gorenstein points at worst in a way that we can express the dimensions of the components of the ideal in terms of the main invariants of the curve as well afterwards we focus on gonality clifford index and koszul cohomology of non gorenstein curves by allowing torsion free sheaves of rank 1 in their definitions we find an upper bound for the gonality which agrees with brill noether s one for a rational and unibranch curve we characterize curves of genus 5 with clifford index 1 and finally we study green s conjecture for a certain class of curves called nearly gorenstein

on the cohen macaulay type of s lines in an 1 abstract let a be the coordinate ring of s lines through the origin in a n 1 k we discuss what it means for these lines to be in sufficiently general position and then with this restriction on the lines we attempt to verify our belief that the cohen macaulay type of a depends only on s and n we characterize those s and n for which a is a gorenstein ring i e of c m type 1 and explicitly calculate the cohen macaulay type in several other cases we then extend some of our results to the case of an arbitrary reduced curve whose tangent cone consists of lines in sufficiently general position finally we calculate the hubert samuel polynomials of the curves we have been considering

atoms of the set of numerical semigroups with fixed frobenius number abstract given a positive integer g we denote by f g the set of all numerical semigroups with frobenius number g the set f g is a semigroup in this paper we study the generators of this semigroup

domain decomposition method using integral equations and adaptive cross approximation ie aca ddm for studying antenna radiation and wave scattering from large metallic platforms in this paper we present a new methodology for a nonoverlapping domain decomposition method using boundary integral equations and adaptive cross approximation in the frequency domain ie aca ddm this paper proposes two main novelties first the ie ddm condition number is improved with the development of a formulation based on electric field integral equation efie implementation over the entire subdomains and on a simplification of the magnetic field integral equation mfie on the interfaces as a consequence the number of matrix vector products is significantly reduced during the iterative resolution then this paper proves that the aca can be applied and efficiently implemented in ie ddm methods moreover a hierarchical lu hlu decomposition is proposed to accelerate the aca solver the ie aca ddm is very suitable for the resolution of multiple excitations and to bypass the low frequency breakdown the flexibility accuracy and efficiency of ie aca ddm are demonstrated by comparing with reference integral equation solutions and scaled mock up measurements

almost gorenstein homogeneous rings and their h vectors abstract in this paper for the development of the study of almost gorenstein graded rings we discuss some relations between almost gorensteinness of cohen macaulay homogeneous rings and their h vectors concretely for a cohen macaulay homogeneous ring r we give a sufficient condition for r to be almost gorenstein in terms of the h vector of r theorem 3 1 and we also characterize almost gorenstein homogeneous domains with small socle degrees in terms of the h vector of r theorem 4 4 moreover we also provide the examples of almost gorenstein homogeneous domains arising from lattice polytopes

on trigonal non gorenstein curves with zero maroni invariant abstract by means of canonical models we answer some questions on trigonal non gorenstein curves with zero maroni invariant the number of non gorenstein points the kind of such singularities possible canonical models uniqueness and number of base points of a g 1 3 on the curve

almost gorenstein monomial curves in affine four space abstract in this paper we classify the almost symmetric semigroups of embedding dimension four and we give minimal systems of generators and minimal free resolutions for the defining ideals of almost gorenstein monomial curves in affine four space finally we conclude that they are set theoretic complete intersections

almost gorenstein rings abstract barucci and froberg 1997 2 introduced the notion of an almost gorenstein ring in the case of an analytically unramified local ring r m in this work we provide a framework that allows us to generalize this notion to include the analytically ramified case as a consequence for any cohen macaulay local ring r m of dimension one we solve in full generality the problem of determining when the endomorphism algebra m m is gorenstein we also provide characterizations for rings to be almost gorenstein in connection with the principle of idealization several examples are explored as well

a pointwise quasi newton method for unconstrained optimal control problems for a class of unconstrained optimal control problems we propose a quasi newton method that exploits the structure of the problem we define a new type of superlinear convergence for sequences in function spaces and prove superlinear convergence of the iterates generated by the quasi newton method in this sense

invariants of cohen macaulay rings associated to their canonical ideals abstract the purpose of this paper is to introduce new invariants of cohen macaulay local rings our focus is the class of cohen macaulay local rings that admit a canonical ideal attached to each such ring r with a canonical ideal c there are integers the type of r the reduction number of c that provide valuable metrics to express the deviation of r from being a gorenstein ring we enlarge this list with other integers the roots of r and several canonical degrees the latter are multiplicity based functions of the rees algebra of c

invariants associated with ideals in one dimensional local domains let r be a one dimensional local noetherian domain with maximal ideal m quotient field k and residue field r m k we assume that the integral closure r of r in its quotient field k is a dvr and a finite r module we assume also that the field k is isomorphic to the residue field of r for i a proper ideal of r denote the inverse of i by i that is i is the set r ki of elements of k that multiply i into r we investigate two numerical invariants associated to a proper ideal i of r that have previously come up in the literature from various points of view the two invariants are 1 the difference between the composition lengths of i r and r i and 2 the difference between the product when the composition length of r i is multiplied by the composition length of m r and the length of i r we show that these two differences can be expressed in terms of the type sequence of r a finite sequence of positive integers related to the natural valuation inherited from r

radial angular singularity cancellation transformations derived by variable separation the variable separation method is utilized to construct new radial angular r n coordinate transformation schemes for the singularity cancellation technique derived from the concept of achieving an ideal jacobian of the transformations and with different parameter settings in the variable separation method a new augmented radial angular r 1 transformation new radial angular r 2 and radial angular r 2 cosh transformations as well as a new radial angular r 3 an augmented radial angular r 3 and an arcsinh r 3 transformation are introduced the proposed r 2 and r 3 transformations are efficient and applicable to all types of near singular kernels occurring in the method of moments mom solution of electromagnetic surface integral equations whereas the r 1 transformation is only suitable for the first order singular integrals the newly proposed transformation schemes are verified and they are also applied to deformed triangles where good performances are still achieved

numerical evaluation via singularity cancellation schemes of near singular integrals involving the gradient of helmholtz type potentials in this paper we present a purely numerical procedure to evaluate strongly near singular integrals involving the gradient of helmholtz type potentials for observation points at finite arbitrarily small distances from the source domain in the proposed approach the source domain is subdivided into a disc plus truncated subtriangles and proper variable transformations are applied in each integration domain to exactly cancel the kernel singularity a novel feature of the proposed angular transform is that required discrete values of the inverse transform which is transcendental are determined via a root finding procedure the same idea can also be applied to other transforms that arise in singularity cancellation methods the resulting integral may then evaluated via a low order gauss legendre quadrature scheme

quadrature over a pyramid or cube of integrands with a singularity at a vertex a simple transformation is introduced which facilitates the evaluation of integrals over certain square based pyramids or cubes in cases where the integrand has a singularity at a vertex

associated graded rings of one dimensional analytically irreducible rings ii abstract lance bryant noticed in his thesis bryant 2009 3 that there was a flaw in our paper barucci and froberg 2006 2 it can be fixed by adding a condition called the bf condition in bryant 2009 3 we discuss some equivalent conditions and show that they are fulfilled for some classes of rings in particular for our motivating example of semigroup rings furthermore we discuss the connection to a similar result stated in more generality by cortadellas and zarzuela in 4 finally we use our result to conclude when a semigroup ring in embedding dimension at most three has an associated graded which is a complete intersection

advanced numerical schemes for the accurate evaluation of 4 d reaction integrals in the method of moments in this paper we present a simple and efficient fully numerical technique for the evaluation of 4 d reaction integrals arising in the method of moments in the proposed approach the accuracy of the source integration which uses a singularity cancellation scheme is retained in the final 4 d reaction integral through the application of an appropriate variable transformation and numerical quadrature scheme to the test integral several numerical results compared to the usual gauss legendre test quadrature demonstrate the accuracy of the method for both planar and curvilinear discretizations moreover the proposed scheme is independent of test basis functions hence it can be used for higher order basis functions as well as curl conforming or buffa christiansen test basis functions

the almost gorenstein rees algebras of parameters abstract there is given a characterization for the rees algebras of parameters in a gorenstein local ring to be almost gorenstein graded rings a characterization is also given for the rees algebras of socle ideals of parameters the latter one shows almost gorenstein rees algebras rather rarely exist for socle ideals if the dimension of the base local ring is greater than two

application of curvilinear basis functions and mlfma for radiation and scattering problems involving curved pec structures the curvilinear surface and wire basis functions have been applied to solve radiation and scattering problems of various shapes of curved metallic structures with the method of moments however a suitable form of junction basis function that can connect the curvilinear wire and the curvilinear rao wilton glisson rwg surface basis functions has not been found we present a novel curvilinear junction basis function that can fill the gap the convergence tests reveal that the curvilinear junction basis function in conjunction with curvilinear wire and surface basis functions can reduce the radar cross section rcs error by one order of magnitude more than their reduced linear forms for a curved structure the curvilinear basis functions are applied to solve the radiation from wire antennas attached to curved surfaces we will demonstrate that the curvilinear basis functions with the multilevel fast multipole algorithm can significantly reduce the computational resources for simulating electrically large objects with curved features

duffy method for evaluation of weakly singular sie potential integrals over curved quadrilaterals with higher order basis functions a duffy method for singularity cancellation is proposed for evaluation of weakly singular potential integrals defined on generalized curved parametric quadrilateral patches with polynomial basis functions such integrals arise in evaluation of galerkin matrix elements in method of moments analysis of antennas and scatterers in cases of coincident source and test elements examples demonstrate that the proposed duffy method is more accurate more rapidly converging with the increase of orders of gauss legendre integration formulas and faster to execute than four other methods for singularity treatment considered in the study

evaluation of potential and impedance integrals in analysis of axially symmetric metallic structures to prescribed accuracy up to machine precision this paper presents a novel method for evaluating potential and impedance integrals appearing in the method of moment analysis of arbitrary axially symmetric metallic structures based on exact wire kernel and higher order bases due to new variable transforms proposed for singularity cancellation and smoothing the integrands high accuracy up to machine precision is achieved using relatively small number of integration points simple formulas are determined for predicting a number of integration points needed for prescribed accuracy benefits of high precision evaluation of impedance integrals are illustrated on a number of numerical examples

on the evaluation of the 4 d reaction integral for the scalar potential in galerkin s method of moments despite the great progress made in the evaluation of the 4 d reaction integrals arising in the method of moments applied to the surface integral equation formulations there are still some aspects that deserve to be explored further the focus in this paper lies in the evaluation of the 4 d reaction integral for the scalar potential we demonstrate that unless this integral is computed to machine precision in the whole impedance matrix it is imperative to maintain the trianglewise balance in the evaluation of the scalar potential part a small imbalance even at very small error results in a loss of degrees of freedom dofs for the charge distribution violating the null space property of the divergence operator and yielding potentially spurious solutions the effect although present may go unnoticed at the conventional frequency regimes where the usual mesh sizes can be applied however it becomes more pronounced as we approach the quasi static limit eventually rendering spurious solutions at the frequencies higher than the classical low frequency breakdown would

sally modules of canonical ideals in dimension one and 2 agl rings abstract the notion of 2 agl ring in dimension one which is a natural generalization of almost gorenstein local ring is posed in terms of the rank of sally modules of canonical ideals the basic theory is developed investigating also the case where the rings considered are numerical semigroup rings over fields examples are explored

pseudo frobenius numbers versus defining ideals in numerical semigroup rings abstract the structure of the defining ideal of the semigroup ring k h of a numerical semigroup h over a field k is described when the pseudo frobenius numbers of h are multiples of a fixed integer

modeling junctions in sharp edge conducting structures with higher order method of moments scattering targets are often made by complex structures constituted by thin metallic plates as wings fins winglets when thin plates are connected together they define surface junctions with the possible presence of sharp edges in this paper we describe a complete procedure to handle junctions in presence of sharp edges in surface integral equation methods by defining the required basis functions and unknowns this approach is based on the use of divergence conforming higher order interpolatory vector basis functions singular vector basis functions and on kirchhoff s current law the paper presents several numerical test cases that show the instability of solutions using classical methods and the full convergence of the proposed numerical scheme

one dimensional local rings of maximal and almost maximal length let a m k denote a one dimensional cohen macaulay local ring with maximal ideal m and residue class field k we assume a is a reduced excellent local ring which has a canonical module a with no loss of generality we can also assume k is infinite let denote the integral closure of a in its total quotient ring q and let b denote the conductor of a in a has maximal length if la aa la ab t a here t a denotes the cohen macaulay type of a and la denotes the length of the a module a has almost maximal length if la aa la ab t a 1 the two main results of this paper are as follows a has maximal length if and only if either a is gorenstein or there exists an x m and a positive integer p such that m x b andba xpa let e a denote the multiplicity of a then a has almost maximal length and 1 t a e a if and only if there exists a transversal x of m such that m x b and la bxpa 1 here p min i xi b these two theorems generalize more specific results for semigroup rings obtained in brown and curtis numerical semigroups of maximal and almost maximal length semigroup forum vol 42 springer verlag berlin new york 1991 219 235

potential integrals for uniform and linear source distributions on polygonal and polyhedral domains formulas for the potentials due to uniform and linearly varying source distributions defined on simply shaped domains are systematically developed and presented domains considered are infinite planar strips infinite cylinders of polygonal cross sections planar surfaces with polygonal boundaries and volumetric regions with polyhedral boundaries the expressions obtained are compact in form and their application in the numerical solution of electromagnetics problems by the method of moments is illustrated

on the type of an almost gorenstein monomial curve abstract we prove that the cohen macaulay type of an almost gorenstein monomial curve c a 4 is at most 3 and make some considerations on the general case

optimized numerical evaluation of singular and near singular potential integrals involving junction basis functions in analyzing conducting bodies composed of surfaces connected to wires via a method of moments discretization of the electric field integral equation junction basis functions are defined at connection points between wires and surfaces to correctly capture the physics of the current flux in the vicinity of the junction in evaluating the associated self term vector potential surface integrals two singularities are present one is related to the green s function and the other is due to the 1 behavior of the junction basis function that models the current near a junction here we present a simple and efficient numerical procedure for evaluating singular and near singular source vector potential integrals involving junction basis functions the approach is based on a double transformation that cancels both singularities and also overcomes some limitations of singularity subtraction methods the proposed scheme is then optimized to obtain at least four correct digits in the evaluation of these integrals essentially arbitrary accuracy is achievable by suitably increasing the quadrature order

ulrich ideals and 2 agl rings abstract the notion of 2 almost gorenstein local ring 2 agl ring for short is a generalization of the notion of almost gorenstein local ring from the point of view of sally modules of canonical ideals in this paper for further developments of the theory we discuss three different topics on 2 agl rings the first one is to clarify the structure of minimal presentations of canonical ideals and the second one is the study of the question of when certain fiber products so called amalgamated duplications are 2 agl rings we also explore ulrich ideals in 2 agl rings mainly two generated ones

on the numerical integration of the linear shape functions times the 3 d green s function or its gradient on a plane triangle formulas for the static and dynamic potentials due to linearly varying source distributions defined on a planar triangle are presented the general linear variation of the source is represented in terms of three linear basis functions each one associated with a different vertex of the triangular domain the singular kernels considered are given by the 3 d green s function and its gradient both for the static and dynamic case in the static case the evaluation of potentials is performed analytically and compact form results are given in the dynamic case the results are given in a form suited for numerical integration

evaluation of galerkin integrals involving triangular type wire to surface junctions in the method of moments the objective of this paper is to provide efficient and reliable numerical procedures for the evaluation of the galerkin testing integrals with the use of the triangular type wire to surface junction function the 1 spl rho singular behavior of the testing integrands is removed before the evaluation leading to two dimensional integrations suited for its numerical implementation compact closed form approximations are also given that allows to speed up the computations while maintaining a high level of accuracy the proposed procedure guarantees the reliable application of the galerkin s formulation to the analysis of arbitrary configurations of wires and surfaces using the rao wilton glisson basis functions for surfaces and its counterparts for wires and wire to surface junctions