共查询到20条相似文献,搜索用时 21 毫秒
1.
Wenxuan Lu 《中国科学 数学(英文版)》2006,49(1):54-65
Hodge integrals over moduli spaces of curves appear naturally during the localization procedure in computation of Gromov-Witten invariants. A remarkable formula of Marino-Vafa expresses a generation function of Hodge integrals via some combinatorial and algebraic data seemingly unrelated to these apriori algebraic geometric objects. We prove in this paper by directly expanding the formula and estimating the involved terms carefully that except a specific type all the other Hodge integrals involving up to three Hodge classes can be calculated from this formula. This implies that amazingly rich information about moduli spaces and Gromov-Witten invariants is encoded in this complicated formula. We also give some low genus examples which agree with the previous results in literature. Proofs and calculations are elementary as long as one accepts Mumford relations on the reductions of products of Hodge classes. 相似文献
2.
LU Wenxuan Department of Mathematics Tsinghua University Beijing China 《中国科学A辑(英文版)》2006,49(1):54-65
Hodge integrals over moduli spaces of curves appear naturally during the localization procedure in computation of Gromov-Witten invariants. A remarkable formula of Marino-Vafa expresses a generation function of Hodge integrals via some combinatorial and algebraic data seemingly unrelated to these apriori algebraic geometric objects. We prove in this paper by directly expanding the formula and estimating the involved terms carefully that except a specific type all the other Hodge integrals involving up to three Hodge classes can be calculated from this formula. This implies that amazingly rich information about moduli spaces and Gromov-Witten invariants is encoded in this complicated formula. We also give some low genus examples which agree with the previous results in literature. Proofs and calculations are elementary as long as one accepts Mumford relations on the reductions of products of Hodge classes. 相似文献
3.
John T. Conway 《Integral Transforms and Special Functions》2017,28(6):488-503
A method developed recently for obtaining indefinite integrals of functions obeying inhomogeneous second-order linear differential equations has been applied to obtain integrals with respect to the modulus of the complete elliptic integral of the third kind. A formula is derived which gives an integral involving the complete integral of the third kind for every known integral for the complete elliptic integral of the second kind. The formula requires only differentiation and can therefore be applied for any such integral, and it is applied here to almost all such integrals given in the literature. Some additional integrals are derived using the recurrence relations for the complete elliptic integrals. This gives a total of 27 integrals for the complete integral of the third kind, including the single integral given in the literature. Some typographical errors in a previous related paper are corrected. 相似文献
4.
A general framework is constructed for efficiently and stably evaluating the Hadamard finite-part integrals by composite quadrature rules. Firstly, the integrands are assumed to have the Puiseux expansions at the endpoints with arbitrary algebraic and logarithmic singularities. Secondly, the Euler-Maclaurin expansion of a general composite quadrature rule is obtained directly by using the asymptotic expansions of the partial sums of the Hurwitz zeta function and the generalized Stieltjes constant, which shows that the standard numerical integration formula is not convergent for computing the Hadamard finite-part integrals. Thirdly, the standard quadrature formula is recast in two steps. In step one, the singular part of the integrand is integrated analytically and in step two, the regular integral of the remaining part is evaluated using the standard composite quadrature rule. In this stage, a threshold is introduced such that the function evaluations in the vicinity of the singularity are intentionally excluded, where the threshold is determined by analyzing the roundoff errors caused by the singular nature of the integrand. Fourthly, two practical algorithms are designed for evaluating the Hadamard finite-part integrals by applying the Gauss-Legendre and Gauss-Kronrod rules to the proposed framework. Practical error indicator and implementation involved in the Gauss-Legendre rule are addressed. Finally, some typical examples are provided to show that the algorithms can be used to effectively evaluate the Hadamard finite-part integrals over finite or infinite intervals. 相似文献
5.
A general class of infinite dimensional oscillatory integrals with polynomially growing phase functions is studied. A representation formula of the Parseval type is proved, as well as a formula giving the integrals in terms of analytically continued absolutely convergent integrals. These results are applied to provide a rigorous Feynman path integral representation for the solution of the time-dependent Schrödinger equation with a quartic anharmonic potential. The Borel summability of the asymptotic expansion of the solution in power series of the coupling constant is also proved. 相似文献
6.
A general class of (finite dimensional) oscillatory integrals with polynomially growing phase functions is studied. A representation formula of the Parseval type is proven as well as a formula giving the integrals in terms of analytically continued absolutely convergent integrals. Their asymptotic expansion for “strong oscillations” is given. The expansion is in powers of ?1/2M, where ? is a small parameters and 2M is the order of growth of the phase function. Additional assumptions on the integrands are found which are sufficient to yield convergent, resp. Borel summable, expansions. 相似文献
7.
A theorem concerning a product of a general class of polynomials and theH-function of several complex variables is given. Using this theorem certain integrals and expansion formula have been obtained.
This general theorem is capable of giving a number of new, interesting and useful integrals, expansion formulae as its special
cases. 相似文献
8.
Summary. A Galerkin approximation of both strongly and hypersingular boundary integral equation (BIE) is considered for the solution
of a mixed boundary value problem in 3D elasticity leading to a symmetric system of linear equations. The evaluation of Cauchy
principal values (v. p.) and finite parts (p. f.) of double integrals is one of the most difficult parts within the implementation
of such boundary element methods (BEMs). A new integration method, which is strictly derived for the cases of coincident elements
as well as edge-adjacent and vertex-adjacent elements, leads to explicitly given regular integrand functions which can be
integrated by the standard Gauss-Legendre and Gauss-Jacobi quadrature rules. Problems of a wide range of integral kernels
on curved surfaces can be treated by this integration method. We give estimates of the quadrature errors of the singular four-dimensional
integrals.
Received June 25, 1995 / Revised version received January 29, 1996 相似文献
9.
M.L. Kleptsyna A. Le Breton 《Stochastics An International Journal of Probability and Stochastic Processes》2013,85(3-4):229-251
A Cameron-Martin type formula is derived for the Laplace transform of some integrals of the square of a general continuous Gaussian process. The formula involves in particular the variance of the filtering error in some auxiliary optimal filtering problem which is used in the proof. This variance is expressed in terms of the solution of a Riccati-Volterra type integral equation containing the covariance function of the process. In various specific cases this equation is solved and then the formula becomes completely explicit. 相似文献
10.
We prove a novel type of inversion formula for elliptic hypergeometric integrals associated to a pair of root systems. Using the (A,C) inversion formula to invert one of the known C-type elliptic beta integrals, we obtain a new elliptic beta integral for the root system of type A. Validity of this integral is established by a different method as well. 相似文献
11.
《Applied Mathematics Letters》2000,13(6):97-104
In this work, a new class of inverse Laplace transforms of exponential functions involving nested square roots are determined. Using these new inverses and other techniques from Laplace transform theory, a new class of three-parameter definite integrals, that yield to exact evaluation, is generated. It is shown that these integrals evaluate to simple closed-form expressions. These results are then verified using independent analytical techniques. Special and limiting cases of the parameters are investigated, some of which yield well-known expressions from classical analysis. Asymptotic results for these integrals and inverses are also given. In addition, a representation of the complementary error function as a limit is presented. Last, some aspects concerning the numerical implementation of these inverses are discussed and several applications in continuum mechanics are noted. 相似文献
12.
John T. Conway 《Integral Transforms and Special Functions》2018,29(4):269-283
A new method is presented for deriving indefinite integrals involving quotients of special functions. The method combines an integration formula given previously with the recursion relations obeyed by the function. Some additional results are presented using an elementary method, here called reciprocation, which can also be used in combination with the new method to obtain additional quotient integrals. Sample results are given here for Bessel functions, Airy functions, associated Legendre functions and the three complete elliptic integrals. All results given have been numerically checked with Mathematica. 相似文献
13.
Alexander Wasiljeff 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》1969,20(3):389-402
Summary The paper deals with the generalisation of a formula for the Bessel coefficients which has been found byNeumann andLommel.Summation of products of Bessel functions the order of which is given by a linear Diophantine equation is performed with the aid of an integral representation. The obtained integrals can be used for series expansions and axymptotic approximations. The results are applied to the calculation of frequency modulation distortion caused by multipath transmission. 相似文献
14.
Sheehan Olver 《BIT Numerical Mathematics》2010,50(1):149-171
We present a numerically stable way to compute oscillatory integrals. For each additional frequency, only a small, well-conditioned
linear system with a Hessenberg matrix must be solved, and the amount of work needed decreases as the frequency increases.
Moreover, we can modify the method for computing oscillatory integrals with stationary points. This is the first stable algorithm
for oscillatory integrals with stationary points which does not lose accuracy as the frequency increases and does not require
deformation into the complex plane. 相似文献
15.
Yoon Tae Kim 《Journal of Mathematical Analysis and Applications》2009,359(1):106-125
We introduce two types of the Stratonovich stochastic integrals for two-parameter processes, and investigate the relationship of these Stratonovich integrals and various types of Skorohod integrals with respect to a fractional Brownian sheet. By using this relationship, we derive a differentiation formula in the Stratonovich sense for fractional Brownian sheet through Itô formula. Also the relationship between the two types of the Stratonovich integrals will be obtained and used to derive a differentiation formula in the Stratonovich sense. In this case, our proof is based on the repeated applications of differentiation formulas in the Stratonovich form for one-parameter Gaussian processes. 相似文献
16.
Abstract A Wick-Itô formula for Gaussian processes is obtained. This is a change of variables formula, which is to Wick-Itô integrals what the usual Itô formula is to Itô integrals. The conditions are weak enough to allow processes with infinite quadratic variation. They are satisfied by fractional Brownian motion with parameter 1/4 < H < 1. 相似文献
17.
E. N. Dovbnya 《Journal of Mathematical Sciences》2001,103(2):231-234
A quadrature formula for integrals having a logarithmic singularity is investigated. The formula permits the method of mechanical quadratures to be used in solving a system of boundary integral equations with an analogous singularity in problems associated with the theory of perforated shells. 相似文献
18.
Magdalena Zielenkiewicz 《Central European Journal of Mathematics》2014,12(4):574-583
Using the Berline-Vergne integration formula for equivariant cohomology for torus actions, we prove that integrals over Grassmannians (classical, Lagrangian or orthogonal ones) of characteristic classes of the tautological bundle can be expressed as iterated residues at infinity of some holomorphic functions of several variables. The results obtained for these cases can be expressed as special cases of one formula involving the Weyl group action on the characters of the natural representation of the torus. 相似文献
19.
邱春晖 《数学物理学报(B辑英文版)》2003,23(1)
A new Koppelman-Leray-Norguet formula of (p-1,q) differential forms for a strictly pseudoconvex polyhedron with not necessarily smooth boundary on a Stein manifold is obtained, and an integral representation for the solution of (?)-equation on this domain which does not involve integrals on boundary is given, so one can avoid complex estimates of boundary integrals. 相似文献
20.
《Journal of Computational and Applied Mathematics》2005,175(2):265-290
In this paper, a set of boundary integrals are derived based on a radial integration technique to accurately evaluate two dimensional (2D) and three dimensional (3D), regular and singular domain integrals. A self-contained Fortran code is listed and described for numerical implementation of these boundary integrals. The main feature of the theory is that only the boundary of the integration domain needs to be discretized into elements. This feature cannot only save considerable efforts in discretizing the integration domain into internal cells (as in the conventional method), but also make computational results for singular domain integrals more accurate since the integrals have been regularized. Some examples are provided to verify the correctness of the presented formulations and the included code. 相似文献