exact closed form representations for the time domain surface impedances of a homogeneous lossy half space in this paper we derive exact closed form representations for the transverse electric and transverse magnetic time domain surface impedances associated with a plane wave that is obliquely incident on a homogeneous lossy half space the time domain surface impedances are expressed in terms of modified bessel functions and incomplete lipschitz hankel integrals the limitations on the validity of a previously published approximate expression are also discussed

seshadri constants and periods of polarized abelian varieties the purpose of this paper is to study the seshadri constants of abelian varieties consider a polarized abelian variety a l of dimension g over the field of complex numbers one can associate to a l a real number e a l its seshadri constant which in effect measures how much of the positivity of l can be concentrated at any given point of a the number e a l can be defined as the rate of growth in k of the number of jets that one can specify in the linear series oa kl alternatively one considers the blow up f x blx x x of x at a point x with exceptional divisor e x over x and defines e a l def sup e r f l ee is nef

seshadri constants on abelian varieties we show that on a complex abelian variety of dimension two or greater the seshadri constant of an ample line bundle is at least one moreover the seshadri constant is equal to one if and only if the polarized abelian variety splits as a product of a principally polarized elliptic curve and a polarized abelian subvariety of codimension one we also examine the case when the seshadri constant is not one and obtain lower bounds when the dimension of the abelian variety is small

seshadri constants in a family of surfaces the aim of this note is to study local and global seshadri constants for a family of smooth surfaces with prescribed polarization

local positivity of principally polarized abelian threefolds in recent years there has been considerable interest in understanding the local positivity of ample line bundles on algebraic varieties seshadri constants introduced by demailly 4 emerged as a natural measure of the local positivity of a line bundle these invariants are very hard to control and their exact value is known only in very few cases let x be a smooth projective variety of dimension n and let l an ample line bundle on x then the real number

transmission of pulsed plane wave into dispersive half space prony s method approximation time domain impulse transmission functions of a dispersive half space due to an obliquely incident pulsed plane wave of either te or tm polarization are presented as inverse fourier transforms the frequency domain transmission functions are approximated by using prony s method as finite series of exponential decaying functions the inverse fourier transform of these exponential decaying functions are evaluated analytically in closed forms time domain response due to a specific pulse shape is obtained by convoluting the impulse transmission functions with the required pulse shape

seshadri constants on jacobian of curves we compute the seshadri constants on the jacobian of hyperelliptic curves as well as of curves with genus three and four for higher genus curves we conclude that if the seshadri constants of their jacobian are less than 2 then the curves must be hyperelliptic

positivity of the diagonal abstract we study how the geometry of a projective variety x is reflected in the positivity properties of the diagonal x considered as a cycle on x x we analyze when the diagonal is big when it is nef and when it is rigid in each case we give several implications for the geometric properties of x for example when the cohomology class of x is big we prove that the hodge groups h k 0 x vanish for k 0 we also classify varieties of low dimension where the diagonal is nef and big

positivity and complexity of ideal sheaves the problem of bounding the complexity of a polynomial ideal in terms of the degrees of its generators has attracted a great deal of interest in recent years results in this direction go back at least as far as the classical work 17 of hermann on the ideal membership problem and the effective nullstellensatz of brownawell 4 and kollar 21 marks a major recent advance with the development of computational algebraic geometry the question has taken on increasing importance and it came into particularly clear focus through the influential paper 3 of bayer andmumford more recently the theorem of 8 and 20 concerning regularity of powers raises the question of bounding the complexity of powers of an ideal and suggests that asymptotically the picture should become very clean the aim of the present paper is to examine some of the results and questions of 3 30 and 7 from a geometric perspective in the spirit of 12 our thesis is that much of this material is clarified and parts rendered transparent when viewed through the lenses of vanishing theorems and intersection theory specifically motivated by thework 25 26 of paolettiwe introduce an invariant s j thatmeasures in effect howmuchonehas to twist an idealj in order tomake

seshadri constants and fano manifolds in memory of meeyoung kim in this paper we give a lower bound of seshadri constants on smooth fano varieties more precisely we show that on a smooth fano manifold of dimension n whose anticanonical system is base point free seshadri constants of ample divisors are bounded from below by one over n 2 as a corollary we recover the earlier result on fano threefolds

numerical computation of the incomplete lipschitz hankel integral je o a z abstract two factorial neumann series expansions are derived for the incomplete lipschitz hankel integral je 0 a z these expansions are used together with the neumann series expansion given by agrest in an algorithm which efficiently computes je 0 a z to a user defined number of significant digits other expansions for je 0 a z which are found in the literature are also discussed but these expansions are found to offer no significant computational advantages when compared with the expansions used in the algorithm

exact solutions of the complex modified korteweg de vries equation firstly some similarity reductions of the complex modified korteweg de vries equation cmkdv which arises in the asymptotic interpretation of one dimensional plane wave propagation in a quadratic micropolar medium are discussed although it is not a soliton equation solvable by inverse scattering transformation its similarity reductions obtained by the use of lie group methods are of mathematical interest secondly the painleve analysis developed by weiss et al 1983 for nonlinear partial differential equations is applied to the cmkdv equation and the data obtained by the truncation technique yield some analytical solutions of the ordinary modified korteweg de vries equation and travelling wave solutions of the cmkdv equation which are also solutions of the similarity reduction obtained by classical lie group analysis

network oriented dyadic time domain green s function for a sequentially excited infinite planar array of dipoles in free space during the past few years we have performed an effective wideband analysis for characterizing the electrodynamic behavior of phased array antennas infinite periodic structures frequency selective surfaces and related applications with emphasis on gaining physical insight into the phenomenology of short pulse radiation the present contribution shows the current status of our network oriented dyadic time domain green s function td gf for a planar array of sequentially excited dipoles that constitutes a prototype study of sequentially short pulsed radiation by infinite periodic arrays the dispersive effects of the td floquet waves fw and the consequences of a te and tm field decomposition are discussed in details in this network formulation the equivalent td transmission line tl voltages and currents excited by equivalent td current generators are determined an expression for the tm voltage tl gf is provided for the first time in terms of incomplete lipschitz hankel integrals and bessel functions together with some remarks for its evaluation as shown in previous publications for the scalar potentials real td physical observables are determined by pairing td floquet waves with positive and negative indices it is shown that the vectorial td radiated field is reconstructed at any time with the superposition of a few td fws

a relation between one point and multi point seshadri constants abstract t szemberg proposed in 2001 a generalization to arbitrary varieties of m nagata s 1959 open conjecture which claims that the seshadri constant of r 9 very general points of the projective plane is maximal here we prove that nagata s original conjecture implies szemberg s for all smooth surfaces x with an ample divisor l generating ns x and such that l2 is a square more generally we prove the inequality e n 1 l r e n 1 l 1 e n 1 o p n 1 r where en 1 l r stands for the n 1 dimensional seshadri constant of the ample divisor l at r very general points of a normal projective variety x and n dimx

primitive higher order embeddings of abelian surfaces the aim of this note is to study higher order embeddings of abelian surfaces de nedby primitive line bundles in recent years several concepts of higher order embeddings have been studied in particular k spannedness k very ampleness and k jet ampleness see 7 for refer ences on this topic recall that a line bundle lon a smooth projective variety xis called k jet ample if for any choice of distinct points x

remarks on seshadri constants which is called the seshadri constant of l at x here the infimum is taken over all irreducible curves c passing through x and mx c is the multiplicity of c at x for example if l is very ample then e l x 1 there has been recant interest in trying to give lower bounds for this invariant at a general point ein and lazarsfeld el show that if x is a surface then e l x 1 for very general x x in higher dimension n 3 ein kuchle and lazarsfeld ekl prove that e l x 1 n for a very general point we say that a point x x is very general if x is in the complement x z of z a countably union of proper subvarieties examples of miranda show that e l x can take arbitrarily small values in codimension two i e codim z 2 even for an ample line bundle one may expect that this general bounds are not optimal an elementary observation see remark 1 below for the proof shows that e l x n ln a natural question is are there conditions which guarantee equality even in relative simple cases it turns out to be hard to give an answer recently xu xu improved the surface bound given by ein and lazarsfeld he showed that if l2 3 4 4 5 for a given integer 1

an accurate and efficient analysis for transient plane waves obliquely incident on a conductive half space te case we develop a method for the analytical evaluation of the inverse laplace transform representations for transient transverse magnetic tm plane wave obliquely incident on a conductive half space we assume that the permittivity and conductivity of the dispersive half space are independent of frequency the time domain expressions for the reflected and transmitted waves are first represented as inverse laplace transforms the transient fields are then shown to consist of two canonical integrals the canonical integrals in turn are solved analytically thereby yielding close form solutions involving incomplete lipschitz hankel integrals ilhis the ilhis are computed numerically using efficient convergent and asymptotic series expansions thus enabling the efficient computation of the transient fields the exact closed form expressions are verified by comparing with previously published results and with results obtained using standard numerical integration and fast fourier transform fft algorithms an asymptotic series representation for the ilhis is also employed to obtain a relatively simple late time approximation for the transient fields this approximate late time expression is shown to accurately model the fields over a large portion of its time history

seshadri exceptional foliations the maximal seshadri number l of an ample line bundle l on a smooth projective variety x measures the local positivity of the line bundle l at a general point of x by refining the method of ein kuchle lazarsfeld lower bounds on l are obtained in terms of ln n dim x for a class of varieties the main idea is to show that if a certain lower bound is violated there exists a non trivial foliation on the variety whose leaves are covered by special curves in a number of examples one can show that such foliations must be trivial and obtain lower bounds for l the examples include the hyperplane line bundle on a smooth surface in 3 and ample line bundles on smooth threefolds of picard number 1

an effective and sharp lower bound on seshadri constants on surfaces with picard number 1 abstract on an algebraic surface with picard number 1 we compute in terms of the generator of the ample ray a lower bound for seshadri constant valid at every point of the surface we show that this bound cannot be improved in general

seshadri constants of quartic surfaces by seshadri s criterion l is ample if and only if e l 0 recent interest in seshadri constants derives on the one hand from their application to adjoint linear systems in fact a lower bound on the seshadri constant of l gives a bound on the number of jets that the adjoint line bundle ox kx l separates see 2 and 3 on the other hand seshadri constants are very interesting invariants of polarized varieties in their own right it is this second aspect that we investigate in the present paper specifically consider a smooth surface x ip and think of the projective embedding as fixed we then simply write

painleve analysis and backlund transformation in the kuramoto sivashinsky equation the authors apply the painleve test to the kuramoto sivashinsky nonlinear partial differential equation which describes many interesting fluid motions the equation passes the test in a weak sense although the painleve analysis does not yield the general solution they perform the backlund transformation in order to obtain new particular solutions the authors find explicitly all the solutions of the set of equations which define the painleve backlund transformation they reduce to only one type namely the already known kink shaped solitary wave