a robust double exponential formula for fourier type integrals abstract a double exponential transformation is presented to obtain a quadrature formula for fourier type integrals 0 f x sin x d x or 0 f x cos x d x where f x is a slowly decaying analytic function on 0 it is an improved version of what we previously proposed in 1991 the transformation x t is such that it maps the interval 0 onto and that while the integrand after the transformation decreases double exponentially at large negative t the points of the formula approaches to zeros of sin x or cos x double exponentially at large positive t then the trapezoidal formula with an equal mesh size is applied to the integral over after the transformation which gives an efficient quadrature formula for the fourier type integrals the present transformation is improved in the sense that it can integrate a function f z with singularities in the finite z plane more efficiently than the one previously proposed

imposing boundary conditions in sinc method using highest derivative approximation sinc approximate methods are often used to solve complex boundary value problems such as problems on unbounded domains or problems with endpoint singularities a recent implementation of the sinc method li c and wu x numerical solution of differential equations using sinc method based on the interpolation of the highest derivatives applied mathematical modeling 31 1 2007 1 9 in which sinc basis functions are used to approximate the highest derivative in the governing equation of the boundary value problem is evaluated for structural mechanics applications in which interlaminar stresses are desired we suggest an alternative approach for specifying the boundary conditions and we compare the numerical results for analysis of a laminated composite timoshenko beam implementing both li and wu s approach and our alternative approach for applying the boundary conditions for the timoshenko beam problem we obtain accurate results using both approaches including transverse shear stress by integration of the 3d equilibrium equations of elasticity the beam results indicate our approach is less dependent on the selection of the sinc mesh size than li and wu s sihd we also apply sihd to analyze a classical laminated composite plate for the plate example we experience difficulty in obtaining a complete system of equations using li and wu s approach for our approach we suggest that additional necessary information may be obtained by applying the derivatives of the boundary conditions on each edge using this technique we obtain accurate results for deflection and stresses including interlaminar stresses by integration of the 3d equilibrium equations of elasticity our results for both the beam and the plate problems indicate that this approach is easily implemented has a high level of accuracy and good convergence properties

the double exponential formula for oscillatory functions over the half infinite interval abstract the double exponential formula is known to be very powerful for evaluation of various kinds of integrals in particular integrals with end point singularities or integrals over the half infinite interval it is also known that a weak point of this formula is the inefficiency when applied to a slowly decaying oscillatory integral over the half infinite interval such as i 0 f1 x sin x dx f1 x is an algebraic function in this paper we propose a new type of the double exponential formula which is quite efficient for evaluation of the integral mentioned above it is based on such a transformation that makes the points of the formula after the transformation approach to the zeros of sin x double exponentially for large x

numerical solution of linear volterra integral equations of the second kind with sharp gradients collocation methods are a well developed approach for the numerical solution of smooth and weakly singular volterra integral equations in this paper we extend these methods through the use of partitioned quadrature based on the qualocation framework to allow the efficient numerical solution of linear scalar volterra integral equations of the second kind with smooth kernels containing sharp gradients in this case the standard collocation methods may lose computational efficiency despite the smoothness of the kernel we illustrate how the qualocation framework can allow one to focus computational effort where necessary through improved quadrature approximations while keeping the solution approximation fixed the computational performance improvement introduced by our new method is examined through several test examples the final example we consider is the original problem that motivated this work the problem of calculating the probability density associated with a continuous time random walk in three dimensions that may be killed at a fixed lattice site to demonstrate how separating the solution approximation from quadrature approximation may improve computational performance we also compare our new method to several existing gregory sinc and global spectral methods where quadrature approximation and solution approximation are coupled

integrated local petrov galerkin sinc method for structural mechanics problems an integrated local petrov galerkin sinc method is introduced and applied to static structural mechanics problems the method approximates the highest derivative in the local weak form of the governing equation on a rectangular grid and the lower derivatives and unknown function are found by numerical indenite integration we suggest that the essential boundary conditions may be applied by the traditional penalty method or by a method in which the stiness matrix is reduced to eliminate dependent degrees of freedom we propose and compare the performance of three basis functions in terms of their accuracy and convergence properties for two problems a one dimensional tapered bar and a two dimensional plane stress elasticity problem our results indicate that the present method can provide greater accuracy than the sinc method based on interpolation of highest derivative an integration based collocation method suggested by li and wu li c and wu x numerical solution of dierential equations using sinc method based on

birational extensions in dimension two and integrally closed ideals the aim of this paper is to examine primarily from an algebraic point of view the structure of a 2 dimensional normal local domain s n which birationally dominates a 2 dimensinal regular local ring r m from the geometric point of view the sine qua non is lipman s paper lr on rational singularities for it follows from one of the early results in that paper that s has a rational singularity using elementary algebraic techniques we are able to recover much information concerning the structure of s we have particularly focused on the fact from lipman ll and artin ar that s must have minimal multiplicity we hope this approach will aid in understanding the algebra of rational singularities and in the exploration of many open questions in dimension two and in higher dimensions the framework of the paper is set up as follows in the first section we use basic algebraic techniques such as analytic independence and zariski s main theorem to prove for example that s has a regular height 1 prime if r m is infinite if s is not regular we may assume that r is maximally regular in s and when this is the case we show for instance that the

numerical solution of integral equations by means of the sinc collocation method based on the double exponential transformation numerical solution of linear integral equations by means of the sinc collocation method based on the double exponential transformation abbreviated the de transformation is considered we first apply the method to the volterra integral equation of the second kind and then to the volterra equation of the first kind this method is also applied to the fredholm integral equation of the second kind for the volterra equations we employed a formula for numerical indefinite integration developed by muhammad and mori obtained by applying the de transformation incorporated into the sinc expansion of the integrand while for the fredholm equation we employed the conventional de transformation for definite integrals an error analysis of the method is given and in every case a convergence rate of o exp cn logn for the error is established where n is a parameter representing the number of terms of the sinc expansion also the condition of the matrix of the main system of linear equations is watched through an estimate of the condition number returned by the program numerical examples show the convergence rate mentioned above and confirm the high efficiency of the present method

a novel pricing method for european options based on fourier cosine series expansions here we develop an option pricing method for european options based on the fourier cosine series and call it the cos method the key insight is in the close relation of the characteristic function with the series coefficients of the fourier cosine expansion of the density function in most cases the convergence rate of the cos method is exponential and the computational complexity is linear its range of application covers underlying asset processes for which the characteristic function is known and various types of option contracts we will present the method and its applications in two separate parts the first one is this paper where we deal with european options in particular in a follow up paper we will present its application to options with early exercise features

burgers equation a general nonlinear solution of infiltration and redistribution 1 the general one dimensional solution of burgers equation is developed using a series of transformations and the green s function method the solution gives the distribution of the reduced water content in a semi infinite and in a finite domain for arbitrary initial moisture distributions the boundary condition at the soil surface can be either a time dependent flux or constant water content while the bottom boundary condition for the finite case is a constant water content value explicit results for a uniform discrete hydrostatic and steady state initial moisture profiles are derived an analytical solution that spans the preponding to the postponding period of rainfall is also obtained expressions for the time to ponding and infiltration equations are presented for the various cases of initial moisture profiles and a shallow water table these results allowed the quantification of the error in the various approximations to the time to ponding and the cumulative infiltration in the postponding period

the exponentially convergent trapezoidal rule it is well known that the trapezoidal rule converges geometrically when applied to analytic functions on periodic intervals or the real line the mathematics and history of this phenomenon are reviewed and it is shown that far from being a curiosity it is linked with computational methods all across scientific computing including algorithms related to inverse laplace transforms special functions complex analysis rational approximation integral equations and the computation of functions and eigenvalues of matrices and operators

parameter equivalence for the brooks corey and van genuchten soil characteristics preserving the effective capillary drive this paper provides a simple way to convert brooks corey bc parameters to van genuchten vg parameters and vice versa for use primarily in situations where saturated conditions are likely to be encountered essential in this conversion is the preservation of the maximum value of a physical characteristic the effective capillary drive h morel seytoux and khanji 1974 defined with a good approximation for a soil water and air system as h jg k dh where k is relative permeability or conductivity to water and ii is capillary pressure head a positive quantity with this conversion infiltration calculations are essentially insensitive to the model used to represent the soil hydraulic properties it is strictly a matter of convenience for the user which expression is used on the other hand the paper shows that other equivalences may lead to great variations in predictions of infiltration capacity consequently the choice of the proper equivalence to use in calculations for rainfall runoff modeling or for low level radioactive waste disposal design is a serious matter

hilbert functions for two ideals let r m denote a noetherian local ring r with maximal ideal m let i and j be ideals contained in m and assume i j is m primary then for all non negative integers r and s the r module r i j s has finite length we denote the length of this r module by l r i j s r s the function r s is called the hilbert function of i and j let denote the integers and for p e let p n e n p in this paper we prove the following theorem suppose for some non negative integer p there exist ordered pairs r 1 s 1 r n s n e p p such that i j s i 1 n i r r i j s s i i r i j sus i i r 1 j s 1 for all r s p then there exists a polynomial f x y e of x y the rational numbers such that r s f r s for all r s 0 furthermore x f dim r j y f dim r i and f l i l j here x f y f denotes the degree of f as a polynomial in x y and f denotes the total degree of f dim s is the krull dimension of the ring s and l u is the analytical spread of the ideal u

correspondence of the gardner and van genuchten mualem relative permeability function parameters the gardner and van genuchten models of relativepermeability are widely used in analytical and numerical solutions toflow problems however the applicab ility of the gardner model to realproblems is usually limited because empirical relative permeability datato calibrate the model are not routinely available in contrast vangenuchten parameters can be estimated using more routinely availablematric potential and saturation data however the van genuchten model isnot amenable to analytical solutions in this paper we introducegeneralized conversion formulae that reconcile these two models ingeneral we find that the gardner parameter alpha g is related to the vangenuchten parameters alpha vg and n by alpha g alpha vg 1 3 n thisconversion rule will allow direct recasting of gardner based analyticalsolutions in the van genuchten parameter space the validity of theproposed formulae was tested by comparing the predicted relativepermeability of various porous media with measured values

on the depth of the fiber cone of filtrations preprint enviat per a la seva publicacio en una revista cientifica journal of algebra 15 december 1997 volume 198 issue 2 pages 428 445 https doi org 10 1006 jabr 1997 7147

numerical integration of the three dimensional green kernel for an electromagnetic problem in this paper we present a method for the numerical integration of the three dimensional green kernel over two triangles this method is compared with the results obtained by other algorithms the comparison proves the efficiency of the technique in removing the numerical singularity furthermore we provide a numerical algorithm for increasing the computation accuracy without refining the finite element mesh

integral closures of ideals generated by regular sequences in particular our proposition contains s theorem 1 i as a special case in section 6 we shall make some remarks on theorem 2 in appendix 1 we shall give a proof of lemma 4 see section 1 for the sake of convenience this lemma is basic to our discussion of rees rings and the assertions in the lemma are all found in 9 if the ring a in the lemma is an integral domain in appendix 2 we shall make some remarks on the local cohomology modules of rees rings 390 0021 8693 88 83 00

time to ponding comparison of analytic quasi analytic and approximate predictions an analytic expression for time to ponding is introduced using the nonlinear model of broadbridge and white 1987 the hydraulic properties of this model can encompass properties ranging from those of a highly nonlinear green ampt like soil to those satisfying the weakly nonlinear burgers equation because of its versatility this analytic solution is used as a benchmark against which extant analytic quasi analytic and approximate expressions are compared time to ponding is parameterized here in terms of the readily measured field properties sorptivity and hydraulic conductivity in the limit of green ampt like properties the analytic solution reduces exactly to the parlange and smith 1976 approximation a similar functional dependence of time to ponding on rainfall rate is found from quasi analytic approximations based on this a modified approximation is suggested which should give time to ponding for most soils to within 10 some existing approximations are found to have unacceptable deviations from the analytic solution and their continued use appears unwarranted finally we address the field problem of predicting time to ponding at any antecedent water content given sorptivity measured at only one initial water content

subgroups with the character restriction property suppose he g are finite groups and every ordinary irreducible character 0 irr h is the restriction xh of some x e irr g following 2 we will say that h has property cr character restriction in g when this occurs an obvious sufficient condition for cr to hold is that h has a normal complement in g but this is of course not necessary as for instance a cyclic group g of order 4 shows a number of authors have shown however that property cr together with suitable additional hypotheses on h and g does imply the existence of a normal complement for h for instance sah 6 shows this if h is a hall rc subgroup of g and either h is solvable or g is n separable also hawkes and humphreys 2 prove that cr yields a normal complement if g is solvable and h is an f projector for g where 9 is any saturated formation among the results in the present paper are a few more situations where cr yields a normal complement the first of these generalizes sah s result

constant rate rainfall infiltration a versatile nonlinear model 1 analytic solution analytic solutions are presented for a nonlinear diffusion convection model describing constant rate rainfall infiltration in uniform soils and other porous materials the model is based on the darcy buckingham approach to unsaturated water flow and assumes simple functional forms for the soil water diffusivity d and hydraulic conductivity k which depend on a single free parameter c and readily measured soil hydraulic properties these d and k yield physically reasonable analytic moisture characteristics the relation between this model and other models which give analytic solutions is explored as c the model reduces to the weakly nonlinear burgers equation which has been applied in certain field situations at the other end of the range as c 1 the model approaches a green ampt like model a wide range of realistic soil hydraulic properties is encompassed by varying the c parameter the general features of the analytic solutions are illustrated for selected c values gradual and steep wetting profiles develop during rainfall aspects seen in the laboratory and field in addition the time dependent surface water content and surface water pressure potential are presented explicitly a simple traveling wave approximation is given which agrees closely with the exact solution at comparatively early infiltration times

infiltration models for semi infinite soil profiles 1 infiltration models for hydrological applications are developed for rational forms of the soil hydraulic conductivity and moisture retention functions the models are based on the traveling and kinematic wave solutions of the governing equation that proved to be highly accurate in specific flow conditions the approximate solutions describe the one dimensional infiltration into a semi infinite medium for uniform initial conditions under either a time dependent flux or a constant head boundary condition they capture the profile development from early to late time accurately due to the proper derivation of the wetting front speed in terms of the time varying surface boundary potential and flux rate algebraic expressions of theoretical and practical importance are derived in terms of well defined soil water parameters and include the effect of the antecedent moisture content in a specific fashion practical results include simple expressions for the surface moisture variation for variable rainfall patterns time to ponding expressions and infiltration equations that account explicitly for the initial condition formulas for the depth of the wetting zone and algebraic equations for parameter estimation of the soil hydraulic parameters by inverse analysis

quadrature formulas obtained by variable transformation and the de rule abstract this paper gives a survey of the results known to date about quadrature formulas obtained by variable transformation followed by an application of the trapezoidal rule with an equal mesh size it has been shown that a formula obtained by an appropriate transformation is in general efficient and also robust against the end point singularity various kinds of useful transformations together with the asymptotic error behaviors of the resulting quadrature formulas are summarized in particular special emphasis is placed on an asymptotically optimal formula called the double exponential formula abbreviated as the de rule which is characterized by the double exponential decrease of its weights in the neighborhood of the end points of the transformed interval of integration

de sinc methods have almost the same convergence property as se sinc methods even for a family of functions fitting the se sinc methods in this paper the theoretical convergence rate of the trapezoidal rule combined with the double exponential de transformation is given for a class of functions for which the single exponential se transformation is suitable it is well known that the de transformation enables the rule to achieve a much higher rate of convergence than the se transformation and the convergence rate has been analyzed and justified theoretically under a proper assumption here it should be emphasized that the assumption is more severe than the one for the se transformation and there actually exist some examples such that the trapezoidal rule with the se transformation achieves its usual rate whereas the rule with de does not such cases have been observed numerically but no theoretical analysis has been given thus far this paper reveals the theoretical rate of convergence in such cases and it turns out that the de s rate is almost the same as but slightly lower than that of the se by using the analysis technique developed here the theoretical convergence rate of the sinc approximation with the de transformation is also given for a class of functions for which the se transformation is suitable the result is quite similar to above the convergence rate in the de case is slightly lower than in the se case numerical examples which support those two theoretical results are also given

multidimensional linearized nonsteady infiltration with prescribed boundary conditions at the soil surface the present work explores a class of analytical solutions of moisture movement in unsaturated porous media characterized by an exponential dependence of the hydraulic conductivity and the moisture content on water pressure the green s function method is used to derive a general analytical model pertaining to multidimensional nonsteady infiltration in a semi infinite flow domain with arbitrary initial conditions boundary conditions and root uptake forcing functions and for various simple source geometry the general solution is expressed in integral form from which particular analytical solutions pertaining to cases of surface and subsurface irrigation evaporation root uptake and moisture redistribution can be easily deduced from the general analytical model the model offers the analyst significant flexibility in deriving results and analyzing infiltration phenomena of practical interest new explicit solutions have been obtained for one dimensional infiltration under various prescribed time dependent flux boundary conditions and for two and three dimensional moisture redistribution for constant initial or boundary conditions the multidimensional solution is essentially the product of two or three time dependent terms with each term being a function of only one space variable

on the structure of the fiber cone of ideals with analytic spread one for a given a local ring a m we study the fiber cone of ideals in a with analytic spread one in this case the fiber cone has a structure as a module over its noether normalization which is a polynomial ring in one variable over the residue field one may then apply the structure theorem for modules over a principal domain to get a complete description of the fiber cone as a module we analyze this structure in order to study and characterize in terms of the ideal itself the arithmetical properties and other numerical invariants of the fiber cone as multiplicity reduction number or castelnuovo mumford regularity

parameter tuning and repeated application of the imt type transformation in numerical quadrature the imt rule which is especially suited for the integration of functions with end point singularities is generalized by introducing parameters and also by repeatedly applying the parametrized imt transformation the quadrature formulas thus obtained are improved considerably both in efficiency and in robustness against end point singularities asymptotic error estimates and numerical results are also given

sinc galerkin method based on the de transformation for the boundary value problem of fourth order ode in this paper a sinc galerkin method incorporated with the double exponential transformation abbreviated as the de transformation for the two point boundary value problem of fourth order ordinary differential equation is considered in this method the error bound o exp c n logn c 0 is attained as in the sinc collocation method based on the de transformation where n is a parameter representing the number of terms in the sinc approximation high efficiency of the sinc galerkin method with the de transformation is confirmed by some numerical examples and the numerical results were compared with ones obtained by sinc collocation method based on the de transformation

three notes on the order of ideals defining hypersurfaces let r n be a regular local ring and let i be a proper ideal in r the order of i is defined to be ord z max it i zc tp it is clear that for f en n l the samuel multiplicity of r fr is e r fr ord fr n in this paper we give sufficient conditions on rji and i so that the converse is true more precisely we describe three situations where e r z ord z n implies i fr for some f e n n in the first situation we consider following an idea of ikeda buchsbaum rings r z the second situation is based in a more general frame on the equimultiplicity of i in the third situation we discuss the case of a graded polynomial ring r over an algebraically closed field and a homogeneous ideal zc r here the methods of the proof were outlined by s ikeda and influenced by j l vicente in the light of these results we ask the following question is it true that if r i satisfies serre s condition s then r i is a hypersurface if and only if e r z ord l this question seems to be open even in the special case that r i is a domain satisfying s with dim r i 2 and e r z ord i 2

bivariate hilbert functions for the torsion functor abstract let r p be a commutative local noetherian ring i j ideals m and n finitely generated r modules suppose j ann r m ann r n is p primary the main result of this paper is theorem 6 which gives necessary and sufficient conditions for the length of tori m inm n jmn to agree with a polynomial for m n 0 as a corollary it is shown that the length of tori m inm n inn always agrees with a polynomial in n for n 0 provided i ann r m ann r n is p primary

the double exponential sinc collocation method for singular sturm liouville problems sturm liouville problems are abundant in the numerical treatment of scientific and engineering problems in the present contribution we present an efficient and highly accurate method for computing eigenvalues of singular sturm liouville boundary value problems the proposed method uses the double exponential formula coupled with sinc collocation method this method produces a symmetric positive definite generalized eigenvalue system and has exponential convergence rate numerical examples are presented and comparisons with single exponential sinc collocation method clearly illustrate the advantage of using the double exponential formula

numerical indefinite integration by double exponential sinc method we present a numerical method for approximating an indefinite integral by the double exponential sinc method the approximation error of the proposed method with n integrand function evaluations is o exp c 1 n log c 2 n for a reasonably wide class of integrands including those with endpoint singularities the proposed method compares favorably with the existing formulas based on the ordinary sinc method computational results show the accordance of the actual convergence rates with the theoretical estimate

error estimates with explicit constants for the sinc approximation over infinite intervals abstract the sinc approximation is a function approximation formula that attains exponential convergence for rapidly decaying functions defined on the whole real axis even for other functions the sinc approximation works accurately when combined with a proper variable transformation the convergence rate has been analyzed for typical cases including finite semi infinite and infinite intervals recently for verified numerical computations a more explicit computable error bound has been given in the case of a finite interval in this paper such explicit error bounds are derived for other cases

near optimality of the sinc approximation near optimality of the sinc approximation is established in a variety of spaces of functions analytic in a strip region about the real axis each space being characterized by the decay rate of their elements functions in the neighborhood of the infinity

function classes for double exponential integration formulas the double exponential de formulas for numerical integration are known to be highly efficient more efficient than the single exponential se formulas in many cases function classes suited to the se formulas have already been investigated in the literature through rigorous mathematical analysis whereas this is not the case with the de formulas this paper identifies function classes suited to the de formulas in a way compatible with the existing theoretical results for the se formulas the de formulas are good for more restricted classes of functions but more efficient for such functions two concrete examples demonstrate the subtlety in the behavior of the de formulas that is revealed by our theoretical analysis

on the associated graded modules of canonical modules the canonical modules of cohen macaulay rings give a useful technical tool in commutative algebra algebraic geometry and singularity theory via various duality theorems but not much is known about the canonical modules themselves in this paper we investigate the structure of the canonical moduies expecially their associated graded modules we ask the following two questions let k be a canonical module over a cohenmacaulay local ring r then

the quasilinear approximation for unsaturated porous media flow this paper gives a review of the quasilinear approximation an exponential relationship between hydraulic conductivity and moisture potential and the uses this has been put to since the time of its creation one of the major attractions of this approximation is that under steady regimes the highly nonlinear richards equation governing unsaturated flow can be linearized this simplification has enabled analytic and semianalytic solutions to be found for many unsaturated flow problems these are reviewed and the current research areas in which the quasilinear approximation is being used are discussed

a character theoretic criterion for the existence of normal complements to subgroups of finite groups if h has a normal complement in g then h certainly has the cr property several authors have studied the converse question sah 6 shows for example that if h is a soluble hall subgroup of g and if h has the cr property then h has a normal complement in g and in is schmidt and richen show that the same is true when g is soluble and h is a carter subgroup of g our object is to prove the following generalization of this result of schmidt and richen

infiltration models for soil profiles bounded by a water table 1 approximate solutions of richards equation are developed for rational forms of the soil hydraulic conductivity and moisture retention functions using a perturbation expansion method a novel approach is devised in the perturbation technique whereby a priori introduced parameters are estimated in an optimal context to ensure the accuracy of the perturbation solution at all times and for all flow conditions the perturbation model describes the one dimensional nonlinear nonsteady infiltration for arbitrary initial conditions under either a time dependent surface flux or a constant head boundary condition into either a semi infinite or a finite medium bounded from below by a shallow water table the optimal perturbation approach proved to be an effective method by which closed form linear solutions can be adapted to nonlinear soils through proper scaling factors the results show that the first order linear term of the optimal perturbation solution is sufficiently accurate for practical applications especially for shallow water table conditions they offer the means to analyze the effect of nonuniform initial conditions and the influence of the water table on the infiltration process practical results in terms of well defined soil water parameters and the antecedent moisture content include algebraic expressions for the surface moisture content variation under variable rainfall conditions time to ponding expressions and infiltration equations for deep and shallow water table conditions and a prediction formula for the water table recharge rate

the generalized advancing conformal contact problem with friction pin loads and remote loading case of rigid pin abstract the advancing frictional contact problem for a rigid pin indenting an infinite plate with a circular hole is considered the formulation is general and considers remotely applied plate stresses in addition to pin loads using the theory of generalized functions it is found that the governing equation in full sliding is a singular integro differential equation side partial slip behavior is governed by an implicit coupled singular integral equation sie pair numerical solutions are presented for both types of problems it is found that the contact tractions in monotonic loading become independent of the coefficient of friction above a certain threshold value finally problems involving typical fretting type pin loads with and without remote stresses are also investigated revealing remarkable effects of the degree of conformality and load path on the steady state traction distributions

new quadrature formulas from conformal maps gauss and clenshaw curtis quadrature like legendre and chebyshev spectral methods make use of grids strongly clustered at boundaries from the viewpoint of polynomial approximation this seems necessary and indeed in certain respects optimal nevertheless such methods may waste a factor of pi 2 with respect to each space dimension we propose new nonpolynomial quadrature methods that avoid this effect by conformally mapping the usual ellipse of convergence to an infinite strip or another approximately straight sided domain the new methods are compared with related ideas of bakhvalov kosloff and tal ezer rokhlin and alpert and others an advantage of the conformal mapping approach is that it leads to theorems guaranteeing geometric rates of convergence for analytic integrands for example one of the formulas presented is proved to converge 50 faster than gauss quadrature for functions analytic in an varepsilon neighborhood of 1 1

exact solutions of the richards equation with nonlinear plant root extraction the richards equation commonly used to model water flow in unsaturated soils is highly nonlinear thus making it very challenging to solve analytically for situations meaningful in practical applications the inclusion of realistic forms of root water uptake rates in this equation adds complications in deriving exact solutions this study provides for the first time analytical solutions of the richards equation with a sink term nonlinearly dependent on soil water content these solutions are applied to irrigation furrows using cartesian coordinates and irrigation from a circular plate in cylindrical coordinates

recent developments of the sinc numerical methods abstract this paper gives a survey of recent developments of the sinc numerical methods a variety of sinc numerical methods have been developed by stenger and his school for a certain class of problems the sinc numerical methods have the convergence rates of o exp n with some 0 where n is the number of nodes or bases used in the methods recently it has turned out that the sinc numerical methods can achieve convergence rates of o exp n log n with some 0 for a smaller but still practically meaningful class of problems and that these convergence rates are best possible the present paper demonstrates these facts for two sinc numerical methods the sinc approximation and the sinc collocation method for two point boundary value problems

a note on the time compression approximation in this paper the work by sivapalan and milly 1989 is extended beyond the time of ponding to estimate the errors of the time compression approximation tca when an exact solution exists the diffusion coefficient is set to be constant and gravitational effects are not considered here the largest error of standard tca in calculating cumulative infiltration is about 2 5 while its underestimate of the time to ponding is about 19 a modified tca is also proposed in which the exact time of ponding is used directly instead of the flux to improve the estimate of postponding infiltration the error for the modified tca is about half of the error for the standard tca in predicting cumulative infiltration and thus the modified tca should be preferred wherever ponding time is or can be measured

the double exponential transformation in numerical analysis the double exponential transformation was first proposed by takahasi and mori in 1974 for the efficient evaluation of integrals of an analytic function with end point singularity afterwards this transformation was improved for the evaluation of oscillatory functions like fourier integrals recently it turned out that the double exponential transformation is useful not only for numerical integration but also for various kinds of sinc numerical methods the purpose of the present paper is to review the double exponential transformation in numerical integration and in a variety of sinc numerical methods

multidimensional linearized nonsteady infiltration toward a shallow water table the green s function method is used to derive a general analytical model pertaining to multidimensional nonsteady infiltration toward a shallow water table with arbitrary initial conditions boundary conditions and root uptake forcing functions and for various simple source geometries the general green s function solution allows the derivation of particular analytical solutions pertaining to cases of surface and subsurface irrigation evaporation root uptake and moisture redistribution the model assumes that the hydraulic conductivity function is an exponential function of the water pressure and a linear function of the moisture content one dimensional solutions are obtained for time dependent distributions of the flux at the land surface and of root uptake in the subsurface two and three dimensional solutions are also derived for point and line sources in the domain for a strip a rectangle and a disc source at the land surface and for two and three dimensional moisture redistribution and root uptake most of the solutions are a product of two terms one term is a function of depth while the other term is a function of time and the lateral coordinates numerical results show the effect of the water table and soil type on the two dimensional moisture movement from a strip source

hilbert series of fiber cones of ideals with almost minimal mixed multiplicity abstract let r m be a cohen macaulay local ring and let i be an m primary ideal we introduce ideals of almost minimal mixed multiplicity which are analogues of ideals studied by j sally compositio math 40 1980 167 175 the main theorem describes the hilbert series of fiber cones of these ideals

function classes for successful de sinc approximations the de sinc formulas resulting from a combination of the sinc approximation formula with the double exponential de transformation provide a highly efficient method for function approximation in many cases they are more efficient than the se sinc formulas which are the sinc approximation formulas combined with the single exponential se transformations function classes suited to the se sinc formulas have already been investigated in the literature through rigorous mathematical analysis whereas this is not the case with the de sinc formulas this paper identifies function classes suited to the de sinc formulas in a way compatible with the existing theoretical results for the se sinc formulas furthermore we identify alternative function classes for the de sinc formulas as well as for the se sinc formulas which are more useful in applications in the sense that the conditions imposed on the functions are easier to verify

extension of the heaslet alksne technique to arbitrary soil water diffusivities note 28 2793 2798 reference eflum article 1992 002 record created on 2005 09 08 modified on 2017 02 23

optimality of the double exponential formula functional analysis approach in the light of the functional analysis theory we establish the optimality of the double exponential formula the argument consists of the following three ingredients 1 introduction of a number of spaces of functions analytic in a strip region about the real axis each space being characterized by the decay rate of their elements functions in the neighborhood of the infinity 2 proof of the near optimality of the trapezoidal formula in each space introduced in 1 by showing the near equality between an upper estimate for the error norm of the trapezoidal formula and a lower estimate for the minimum error norm of quadratures 3 nonexistence theorem for the spaces the characterizing decay rate of which is more rapid than the double exponential

the reaction diffusion master equation as an asymptotic approximation of diffusion to a small target the reaction diffusion master equation rdme has recently been used as a model for biological systems in which both noise in the chemical reaction process and diffusion in space of the reacting molecules is important in the rdme space is partitioned by a mesh into a collection of voxels there is an unanswered question as to how solutions depend on the mesh spacing to have confidence in using the rdme to draw conclusions about biological systems we would like to know that it approximates a reasonable physical model for appropriately chosen mesh spacings this issue is investigated by studying the dependence on mesh spacing of solutions to the rdme in mathbb r 3 for the bimolecular reaction mathrm a mathrm b to varnothing with one molecule of species mathrm a and one molecule of species mathrm b present initially we prove that in the continuum limit the molecules never react and simply diffuse relative to each other nevertheless we show that the rdme with nonzero lattice spacin

on a certain quadrature formula traduction anglaise d un article en japonais publie en aout 1970 dans la serie kokyuroku vol 91 pp 82 118

de sinc methods have almost the same convergence property as se sinc methods even for a family of functions fitting the se sinc methods part ii indefinite integration in this paper the theoretical convergence rate of the sinc indefinite integration combined with the double exponential de transformation is given for a class of functions for which the single exponential se transformation is suitable although the de transformation is considered as an enhanced version of the se transformation for sinc related methods the function space for which the de transformation is suitable is smaller than that for se and therefore there exist some examples such that the de transformation is not better than the se transformation even in such cases however some numerical observations in the literature suggest that there is almost no difference in the convergence rates of se and de in fact recently the observations have been theoretically explained for two explicit approximation formulas the sinc quadrature and the sinc approximation the conclusion is that in such cases the de s rate is slightly lower but almost the same as that of the se the contribution of this study is the derivation of the same conclusion for the sinc indefinite integration numerical examples that support the theoretical result are also provided

normal cones of monomial primes we explicitly calculate the normal cones of all monomial primes which define the curves of the form tl tl 1 tl n where n 4 all of these normal cones are reduced and cohen macaulay and their reduction numbers are independent of the reduction these monomial primes are new examples of integrally closed ideals for which the product with the maximal homogeneous ideal is also integrally closed substantial use was made of the computer algebra packages maple and macaulay2