ultraspherical gauss kronrod quadrature is not possible for lambda 3 with the help of a new representation of the stieltjes polynomial it is shown by using bessel functions that the stieltjes polynomial with respect to the ultraspherical weight function with parameter lambda has only few real zeros for lambda 3 and sufficiently large n since the nodes of the gauss kronrod quadrature formulae subdivide into the zeros of the stieltjes polynomial and the gaussian nodes it follows immediately that gauss kronrod quadrature is not possible for lambda 3 on the other hand for lambda 3 and sufficiently large n even partially positive gauss kronrod quadrature is possible

global wave front sets of banach frechet and modulation spacetypes and pseudo differential operators we introduce global wave front sets with respect to suitable banach or frechet spaces an important special case appears when choosing these spaces as modulation spaces we show that the standard p

weyl product algebras and modulation spaces we discuss algebraic properties of the weyl product acting on modulation spaces for a certain class of weight functions omega we prove that m omega p q is an algebra under the weyl product if p epsilon 1 infinity and 1 q min p p for the remaining cases p epsilon 1 infinity and min p p q infinity we show that the unweighted spaces m p m q are not algebras under the weyl product c 2007 elsevier inc all rights reserved

robust numerical algorithm to the european option with illiquid markets abstract in this paper we consider illiquid european call option which is arisen in nonlinear black scholes equation in this respect we apply the newton s method to linearize it based on the obtained linear equation we obtain the approximate solutions recursively in two steps finally based on the conditions of kantorovich theorem we investigate the convergence analysis of the newton s method on the proposed problem finally the positivity of the solution is discussed

the global cauchy problem for the nls and nlkg with small rough data abstract by using the unit cube decomposition to the frequency spaces we study the cauchy problem for the nonlinear schrodinger equation and the nonlinear klein gordon equation some global well posedness results are obtained for the small cauchy data in some modulation spaces m p 1 s

generating alternative mixed integer programming models using variable redefinition dropping the complicating constraints in a mixed integer linear program often yields a special structure subproblem that can be reformulated using a different set of decision variables once the new variables have been identified the entire problem can be reformulated in terms of the new variables we develop a theory of variable redefinition based on relating the two sets of decision variables by a linear transformation and describe methods for reformulating the special structure problem the reformulated models have a more accurate linear relaxation than the problems from which they were derived an important property within the context of linear programming based branch and bound modeling approaches

the splitting of variables and constraints in the formulation of integer programming models the splitting of variables in an integer programming model into the sum of other variables can allow the constraints to be disaggregated leading to a more constrained tighter linear programming relaxation well known examples of such reformulations are quoted from the literature they can be viewed as instances of some general methods of performing such reformulations namely disjunctive formulations partial network reformulations and a method based on the introduction of auxiliary variables

anti gaussian quadrature formulas an anti gaussian quadrature formula is an n 1 point formula of degree 2n 1 which integrates polynomials of degree up to 2n 1 with an error equal in magnitude but of opposite sign to that of the n point gaussian formula its intended application is to estimate the error incurred in gaussian integration by halving the difference between the results obtained from the two formulas we show that an anti gaussian formula has positive weights and that its nodes are in the integration interval and are interlaced by those of the corresponding gaussian formula similar results for gaussian formulas with respect to a positive weight are given except that for some weight functions at most two of the nodes may be outside the integration interval the anti gaussian formula has only interior nodes in many cases when the kronrod extension does not and is as easy to compute as the n 1 point gaussian formula

metaplectic representation on wiener amalgam spaces and applications to the schrodinger equation we study the action of metaplectic operators on wiener amalgam spaces giving upper bounds for their norms as an application we obtain new fixed time estimates in these spaces for schrodinger equations with general quadratic hamiltonians and strichartz estimates for the schrodinger equation with potentials v x x 2

banach spaces related to integrable group representations and their atomic decompositions i abstract we present a general theory of banach spaces which are invariant under the action of an integrable group representation and give their atomic decompositions with respect to coherent states i e the atoms arise from a single element under the group action several well known decomposition theories are contained as special examples and are unified under the aspect of group theory

stopping functionals for gaussian quadrature formulas abstract gaussian formulas are among the most often used quadrature formulas in practice in this survey an overview is given on stopping functionals for gaussian formulas which are of the same type as quadrature formulas i e linear combinations of function evaluations in particular methods based on extended formulas like the important gauss kronrod and patterson schemes and methods which are based on gaussian nodes are presented and compared

gabor frames and time frequency analysis of distributions abstract this paper lays the foundation for a quantitative theory of gabor expansions f x k n c k n e 2 in x g x k in analogy to wavelet expansions of besov triebel lizorkin spaces we show that the correct class of spaces which can be characterized by the magnitude of the coefficients c k n is the class of modulation spaces to analyze the behavior of the coefficients it is necessary to invert the gabor frame operator on these spaces we show that the frame operator is invertible on modulation spaces if and only if it is invertible on l 2 and the atom g is in a suitable space of test functions a similar statement for wavelet theory is false the second part is devoted to gabor analysis on general time frequency lattices

compactness in translation invariant banach spaces of distributions and compact multipliers abstract it is shown that for a comprehensive family of translation invariant banach spaces b b of classes of measurable functions or distributions on a locally compact group including most of the spaces of interest in harmonic analysis the following compactness criterion generalizing the well known results due to kolmogorov riesz weil concerning compact sets in lp g 1 p 0 k k g k b for all m c 0 h k g h b for all m among various applications a characterization of the space of all compact multipliers between suitable pairs of such spaces can be derived

on stratified extensions of gauss laguerre and gauss hermite quadrature formulas for the practical estimation of the error of gauss laguerre and gauss hermite quadrature formulas it is well known that real positive kronrod formulas do not exist among the alternatives which are available in the literature the stratified rules introduced by laurie are of particular interest in this note we determine the degree optimal stratified extensions for the gauss laguerre and gauss hermite formulas and we investigate their properties

internality of generalized averaged gaussian quadrature rules and truncated variants for modified chebyshev measures of the second kind abstract generalized averaged gaussian quadrature rules associated with some measure and truncated variants of these rules can be used to estimate the error in gaussian quadrature rules however the former quadrature rules may have nodes outside the interval of integration and therefore it may not be possible to apply them when the integrand is defined on the interval of integration only this paper investigates whether generalized averaged gaussian quadrature rules associated with modified chebyshev measures of the second kind and truncated variants of these rules are internal i e if all nodes of these quadrature rules are in the interval of integration

on generalized averaged gaussian formulas we present a simple numerical method for constructing the optimal generalized averaged gaussian quadrature formulas which are the optimal stratified extensions of gauss quadrature formulas these extensions exist in many cases in which real positive kronrod formulas do not exist for the jacobi weight functions w x w x 1 x 1 x 1 we give a necessary and sufficient condition on the parameters a and such that the optimal averaged gaussian quadrature formulas are internal

gauss quadrature rules for a generalized hermite weight function abstract in this paper we give an algorithm for finding the coefficients in the three term recurrence relation for the polynomials orthogonal with respect to the weight function w x x b 2 exp x c 2 on r where b c r 2 1 the algorithm is based on the discretization technique proposed by gautschi with the lanczos algorithm using the coefficients obtained by this algorithm we construct the gauss quadrature rules relative to the weight function w x to show the performance of the new algorithm we give some numerical examples

a historical note on gauss kronrod quadrature the idea of gauss kronrod quadrature in a germinal form is traced back to an 1894 paper of r skutsch

continuity properties for modulation spaces with applications to pseudo differential calculus i we discuss continuity for weighted modulation spaces andprove that many such spaces can be obtained in a canonicalway from the corresponding standard modulation spaces we also discussthe trace operator a a 0 acting on modulationspaces the results are used to get inclusions betweenmodulation spaces and besov spaces and proving continuityfor pseudo differential operators and toeplitz operators

polynomial interpolation and cubature over polygons we have implemented a matlab code to compute discrete extremal sets of fekete and leja type on convex or concave polygons together with the corresponding interpolatory cubature formulas the method works by qr and lu factorizations of rectangular vandermonde matrices on weakly admissible meshes wams of polygons constructed by polygon quadrangulation

positive quadrature formulas iii asymptotics of weights first we discuss briefly our former characterization theorem for positive interpolation quadrature formulas abbreviated qf provide an equivalent characterization in terms of jacobi matrices and give links and applications to other qf in particular to gauss kronrod quadratures and recent rediscoveries then for any polynomial t n which generates a positive qf a weight function depending on n is given with respect to which t n is orthogonal to p n 1 with the help of this result an asymptotic representation of the quadrature weights is derived in general the asymptotic behaviour is different from that of the gaussian weights only under additional conditions do the quadrature weights satisfy the so called circle law corresponding results are obtained for positive qf of radau and lobatto type

computation of gauss kronrod of quadrature rules recently laurie presented a new algorithm for the computation of 2n 1 point gauss kronrod quadrature rules with real nodes and positive weights this algorithm first determines a symmetric tridiagonal matrix of order 2n 1 from certain mixed moments and then computes a partial spectral factorization we describe a new algorithm that does not require the entries of the tridiagonal matrix to be determined and thereby avoids computations that can be sensitive to perturbations our algorithm uses the consolidation phase of a divide and conquer algorithm for the symmetric tridiagonal eigenproblem we also discuss how the algorithm can be applied to compute kronrod extensions of gauss radau and gauss lobatto quadrature rules throughout the paper we emphasize how the structure of the algorithm makes efficient implementation on parallel computers possible numerical examples illustrate the performance of the algorithm

stieltjes polynomials and gauss kronrod quadrature for jacobi weight functions let w beta t 1 t 1 t 1 denote the jacobi weight function for 0 5 2 the stieltjes polynomial has only few real zeros and that gauss kronrod quadrature is not possible so far results of the above type have been known only for ultraspherical weight functions w lambda t big 1 t 2 big lambda 1 2 for 0 2 for 3 the impossibility of gauss kronrod quadrature has been proved by the authors recently

solution of second kind fredholm integral equations by means of gauss and anti gauss quadrature rules this paper is concerned with the numerical approximation of fredholm integral equations of the second kind a nystrom method based on the anti gauss quadrature formula is developed and investigated in terms of stability and convergence in appropriate weighted spaces the nystrom interpolants corresponding to the gauss and the anti gauss quadrature rules are proved to furnish upper and lower bounds for the solution of the equation under suitable assumptions which are easily verified for a particular weight function hence an error estimate is available and the accuracy of the solution can be improved by approximating it by an averaged nystrom interpolant the effectiveness of the proposed approach is illustrated through different numerical tests

stratified nested and related quadrature rules the stratified nested quadrature procedure due to laurie is discussed together with an alternative computational procedure which leads to the concept of hybrid gkp rules in the context of the approximation of stratified nested sequences the work of krogh and van snyder on the representation of the gkp rules is considered and a generalisation of this employing hybrid rules of special form is discussed

error estimates of anti gaussian quadrature formulae anti gauss quadrature formulae associated with four classical chebyshev weight functions are considered complex variable methods are used to obtain expansions of the error in anti gaussian quadrature formulae over the interval 1 1 the kernel of the remainder term in anti gaussian quadrature formulae is analyzed the location on the elliptic contours where the modulus of the kernel attains its maximum value is investigated this leads to effective l error bounds of anti gauss quadratures moreover the effective l 1 error estimates are also derived the results obtained here are an analogue of some results of gautschi and varga 1983 11 gautschi et al 1990 9 and hunter 1995 10 concerning gaussian quadratures

discrete characterizations of wave front sets of fourier lebesgue and quasianalytic type abstract we obtain discrete characterizations of wave front sets of fourier lebesgue and quasianalytic type it is shown that the microlocal properties of an ultradistribution can be obtained by sampling the fourier transforms of its localizations over a lattice in r d in particular we prove the following discrete characterization of the analytic wave front set of a distribution f d let be a lattice in r d and let u be an open convex neighborhood of the origin such that u 0 the analytic wave front set w f a f coincides with the complement in r d 0 of the set of points x 0 0 for which there are an open neighborhood v x 0 u of x 0 an open conic neighborhood of 0 and a bounded sequence f p p n in e x 0 u with f p f on v such that for some h 0 sup f p p h p 1 p p n

strong formulations for mixed integer programming a survey we attempt to motivate and survey recent research on the use of strong valid inequalities and reformulation to solve mixed integer programming problems

a note on splitting of variables in integer programming models abstract the splitting of variables in an integer programming model is a tool to obtain a more constrained tighter linear programming relaxation a known general method for knapsack constraints the partial network reformulation method produces an equivalent set of constraints that has only integer solutions we show how to modify this method to reduce substantially the number of split variables and in most cases the number of disaggregated constraints further the modified method can implicitly handle upper bounds on as well as fixed charges for at least two variables of the considered constraint

calculation of gauss kronrod quadrature rules the jacobi matrix of the 2n 1 point gauss kronrod quadrature rule for a given measure is calculated efficiently by a five term recurrence relation the algorithm uses only rational operations and is therefore also useful for obtaining the jacobi kronrod matrix analytically the nodes and weights can then be computed directly by standard software for gaussian quadrature formulas

an evaluation of clenshaw curtis quadrature rule for integration w r t singular measures this work is devoted to the study of quadrature rules for integration with respect to w r t general probability measures with known moments automatic calculation of the clenshaw curtis rules is considered and analyzed it is shown that it is possible to construct these rules in a stable manner for quadrature w r t balanced measures in order to make a comparison gauss rules and their stable implementation for integration w r t balanced measures are recalled convergence rates are tested in the case of binomial measures

solving multi item capacitated lot sizing problems using variable redefinition mixed integer programming models are typically not used to solve realistic sized production scheduling problems because they require exorbitant solution times we impose a useful taxonomy on production scheduling problems and develop alternative formulations for a wide variety of problems within the taxonomy the linear programming relaxation of the new models is very effective in generating bounds we show that these bounds are equal to those that could be generated using lagrangian relaxation or column generation the linear programming bounds increase in effectiveness as the problems become larger perhaps of greatest significance is that practitioners can obtain our results using only standard off the shelf codes such as lindo or mpsx 370 we report computational experience in several computing environments hardware and software on problems with up to 200 products and 10 time periods 2000 0 1 variables