some properties of borel summable functions classes of borel summable functions are defined and studied some properties of these functions which are useful for high order calculations pertaining to certain physical theories are proved and discussed they include reciprocal watson like theorems sufficient conditions for membership in the classes and asymptotic behaviors of the expansion coefficients after composition of functions

on the 3 sylow subgroup of the class group of quadratic fields in this paper we give a large number of quadratic fields q vd whose class group h d has 3 sylow subgroup h3 d with rank r3 d 1 they include 20 discriminants d 0 with r3 d 5 the associate real fields have r3 d 4 the distribution of the h3 d is studied and its relative frequency is compared with the heuristic conjectures of cohen and lenstra some of the h d are recorded since they are of special interest some related topics are also considered

infinite class field towers this paper studies infinite class field towers of number fields k that are ramified over mathbb q only at one finite prime in particular we show the existence of such towers for a general family of primes including p 2 3 and 5

parallel characteristic mixed element method for saltwater intrusion problem abstract numerical simulation of saltwater intrusion problem has attracted more and more attention in the past decades based on parallel subspace correction method proposed by xu 1992 a new overlapping domain decomposition parallel algorithm is constructed to solve saltwater intrusion problem in this algorithm the splitting positive definite mixed element method is used to discrete head water equation while the characteristic galerkin finite element method is used to approximate concentration equation the relation between the convergence rate and discretization parameters including the overlapping degree of the subspaces is considered furthermore the convergence of this algorithm is analyzed and the corresponding error estimate is given the convergence result suggests that only two iterations are needed to reach the given accuracy at each time level

the reciprocal of a borel summable function is borel summable it is proven that if a functionf is borel summable in some angular region and has a non vanishing derivative at the origin then its reciprocalf 1 is also borel summable in a region which has essentially the same angular extent

borel summability of the 1 n expansion for then vector o n non linear σ models we construct an analytic interpolation in 1 n for then vector o n non linear models withn component fields on a lattice this interpolation valid at sufficiently high temperatures extends over a large domain in the complex plane containing the half plane re 1 n 0 we use this result to show that the 1 n expansion of the free energy density and of the correlation functions is borel summable in the thermodynamic limit and at high temperature

numerical methods for convection dominated diffusion problems based on combining the method of characteristics with finite element or finite difference procedures finite element and finite difference methods are combined with the method of characteristics to treat a parabolic problem of the form cu t bu x au x x f optimal order error estimates in l 2 and w 1 2 are derived for the finite element procedure various error estimates are presented for a variety of finite difference methods the estimates show that for convection dominated problems b gg a these schemes have much smaller time truncation errors than those of standard methods extensions to n space variables and time dependent or nonlinear coefficients are indicated along with applications of the concepts to certain problems described by systems of differential equations

borel summability in the disorder parameter of the averaged green s function for gaussian disorder in this note we prove borel summability in the disorder parameter of the averaged green s function y of tight binding models h v delta v with gaussian disorder d lambda v 2 pi gamma 1 2 exp v 2 2 gamma dv for 0 and fixed large e using this we can reconstruct the density of states e from the borel sums of y with ime 0 and ime 0

borel summability for a nonpolynomial potential we consider the energy levels of a one dimensional quantum system in the rational potential 1 2x 2 gx 4 1 gx 2 their perturbation expansions ing are shown to be borel summable the proof is flexible enough to allow simple extensions to other nonpolynomial interactions

the t hooft reparametrization respects borel summability in a renormalizable field theory with one coupling constant one may redefine the coupling in the sense of formal power series such that the function in the new coupling consists of the first two terms only it is shown that this change of coupling is borel summable if the original function was borel summable

saltwater intrusion in aquifers development and testing of a three dimensional finite element model a three dimensional finite element model is developed for the simulation of saltwater intrusion in single and multiple coastal aquifer systems with either a confined or phreatic top aquifer the model formulation is based on two governing equations one for fluid flow and the other for salt transport density coupling of these equations is accounted for and handled using a picard sequential solution algorithm with special provisions to enhance convergence of the iterative solution flexibility in the formulation allows for either three dimensional simulations or quasi three dimensional simulations where flow and transport in aquitards are treated using one dimensional analytical and or numerical approximations spatial discretization of three dimensional regions is performed using a vertical slicing approach designed to accommodate complex geometry with irregular boundaries layering and or lateral discontinuity this approach is effectively combined with the use of simple linear elements such as rectangular and triangular prisms and composite hexahedra and pentahedra made up of tetrahedra for these elements computation of element matrices can be performed efficiently using influence coefficient formulas that avoid numerical integration new transport influence coefficient formulas are presented for rectangular and triangular prism elements matrix assembly is performed slice by slice and the matrix solution is achieved using a slice successive relaxation scheme this permits a fairly large number of nodal unknowns of the order of five to ten thousand to be handled conveniently on small or medium size minicomputers flexibility of the formulation and matrix handling procedures also allows two dimensional and axisymmetric problems to be solved efficiently using single slice representations four examples are presented to demonstrate the model verification and utility these problems represent a fair range of physical conditions where possible simulation results are compared with previously published solutions

construction and borel summability of planar 4 dimensional euclidean field theory we use the methods of 1 to show that the planar part of the renormalized perturbation theory for 4 4 euclidean field theory is borel summable on the asymptotically free side of the theory the borel sum can therefore be taken as a rigorous definition of then limit of a massiven n matrix model with a trg 4 interaction hence with wrong sign ofg our construction is relevant for a solution of the ultra violet problem for planar qcd we also propose a program for studying the structure of the renormalons singularities within the planar world

unramified subextensions of ray class field towers abstract fix a prime l in this paper we explore various senses in which the ramification in an infinite l extension of number fields can be small in particular 1 we construct infinitely many pairs of primes p q distinct from l such that q admits an infinite l extension unramified outside p q and 2 we explore the possibility of finding infinite unramified subextensions inside infinite ramified l extensions of number fields

parallel domain decomposition procedures of improved d d type for parabolic problems two parallel domain decomposition procedures for solving initial boundary value problems of parabolic partial differential equations are proposed one is the extended d d type algorithm which extends the explicit implicit conservative galerkin domain decomposition procedures given in 5 from a rectangle domain and its decomposition that consisted of a stripe of sub rectangles into a general domain and its general decomposition with a net like structure an almost optimal error estimate without the factor h 1 2 given in dawson dupont s error estimate is proved another is the parallel domain decomposition algorithm of improved d d type in which an additional term is introduced to produce an approximation of an optimal error accuracy in l 2 norm

functional calculus of the borel transform an explicit form is given of the borel transform b of g f where g f z g f z with f borel summable and g analytic in f 0 and a detailed study of the singularities in b in the borel variable is made examples include g 1 log and e the present paper generalizes results of boenkost et al j math phys 29 1118 1987

infinite class field towers of number fields of prime power discriminant abstract for every prime number p we show the existence of a solvable number field l ramified only at p whose p hilbert class field tower is infinite

growth of selmer rank in nonabelian extensions of number fields let p be an odd prime number let e be an elliptic curve over a number field k and let f k be a galois extension of degree twice a power of p we study the zp corank rkp e f of the p power selmer group of e over f we obtain lower bounds for rkp e f generalizing the results in mr which applied to dihedral extensions if k is the unique quadratic extension of k in f if g gal f k if g is the subgroup of elements of g commuting with a choice of involution of f over k and if rkp e k is odd then we show that under mild hypotheses rkp e f g g as a very specific example of this suppose that a is an elliptic curve over q with a rational torsion point of order p and without complex multiplication if e is an elliptic curve over q with good ordinary reduction at p such that every prime where both e and a have bad reduction has odd order in fp and such that the negative of the conductor of e is not a square modulo p then there is a positive constant b depending on a but not on e or n such that rkp e q a pn bp2n for every n

an efficient characteristic finite difference s ddm scheme for convection diffusion equations abstract in this paper an efficient splitting domain decomposition method scheme for solving time dependent convection diffusion reaction equations is analyzed a three step method along each direction is used to solve the solution over each block divided sub domain at every time interval the new solutions are firstly solved by the quadratic interpolation then the intermediate fluxes on the interfaces of sub domains are computed by local multi point weighted average from the new solutions lastly the solutions and fluxes in the interiors of sub domains are computed by the splitting implicit characteristic difference method by some auxiliary lemmas and the defined intermediate exact solution the stability and error estimate are given in discrete l 2 norm we further prove that our scheme is of second order convergence in space and of first order convergence in time numerical experiments are presented to validate theoretical result

the inverse of a borel summable function let b1 be the borel transform of f f 0 0 by means of an integral equation similar to that proposed by t hooft the whys of subnuclear physics edited by a zichichi plenum new york 1979 an explicit representation of the borel transform b2 of 1 f as a series in convolution powers of b1 and its derivative is given it is proved that the singularities of b1 b2 on the circle of convergence coincide and have the same strength when approaching these singularities on a path inside their common analyticity domain but possibly outside the circle of convergence of their power series representation borel circle

construction and borel summability of infrared φ 4 4 by a phase space expansion we construct the thermodynamic limit of the critical massless 4 model in 4 dimensions with an ultraviolet cutoff by means of a partly renormalized phase space expansion this expansion requires in a natural way the introduction of effective or running constants and the infrared asymptotic freedom of the model i e the decay of the running coupling constant plays a crucial role we prove also that the correlation functions of the model are the borel sums of their perturbation expansion

bounds for the continuation of perturbative results to the spectral region the problem of analytic continuation to the boundary of the holomorphy domain from both continuous and discrete interior sets has recently been the subject of detailed analyses this problem is important in phenomenological applications but is also of interest in theoretical calculations e g in attempting to evaluate the parameters of resonances or other nonperturbative effects in qcd because of the inherent instability of the continuation problem it is necessary to introduce additional criteria which should be physically based to select the right continuation function in this paper the results thus obtained for continuation from a continuum are examined for stability and bounds are derived for the errors on the boundary in terms of the uncertainty of the input data the procedure is shown to be stable in the sense that these bounds tend to zero as the data errors go to zero

asymptotics of the cut discontinuity and large order behaviour from the instanton singularity the case of lattice schrodinger operators with exponential disorder we discuss the relation between the singularity structure of the borel transform the asymptotics of the cut discontinuity and the large order behaviour of perturbation theory in an explicit example a tight binding model with exponential disorder we show how to obtain the first instanton singularity from a cluster expansion in the borel variable and as an application we determine the exact decay of the density of states ase the method opens some perspectives for similar problems arising from different models of mathematical physics

borel transform resurgence and the density of states lattice schrodinger operators with exponential disorder the authors study the averaged green function of a tight binding model with exponentially distributed disorder as an explicit example for a resurgent function in the sense of ecalle 1981 as an application one can find the exact asymptotic decay of the density of states and the large order behaviour of the coefficients of the perturbation expansion

multiplicative schwarz methods for parabolic problems the class of multiplicative schwarz methods originated from the classical schwarz alternating method it has been shown to be one of the most powerful methods for solving finite element or finite d

analyticity of the density of states and replica method for random schrodinger operators on a lattice we analyze the density of states and some aspects of the replica method for anderson s tight binding model on a lattice of arbitrary dimension with diagonal disorder we give heuristic arguments for the conjectures that the classical value of the exponent of the localization length is 1 2 and that the upper critical dimension d c loc is bounded by 4 d c loc 6