Related papers: On computations of Hurwitz-Hodge integrals
This paper proposes an efficient symbolic-numeric method to compute the integrals in the successive Galerkin approximation (SGA) of the Hamilton-Jacobi-Bellman (HJB) equation. A solution of the HJB equation is first approximated with a…
We give an identity which is conjectured and proved by using an implementation in Multi-WZ.
In this article we introduce algorithms which compute iterations of Gauss-Manin connections, Picard-Fuchs equations of Abelian integrals and mixed Hodge structure of affine varieties of dimension $n$ in terms of differential forms. In the…
An approach to constructing an upper bound for the Riemann-Farey sum is described.
We expose (without proofs) a unified computational approach to integrable structures (including recursion, Hamiltonian, and symplectic operators) based on geometrical theory of partial differential equations. We adopt a coordinate based…
We develop a Fourier approach to rough path integration, based on the series decomposition of continuous functions in terms of Schauder functions. Our approach is rather elementary, the main ingredient being a simple commutator estimate,…
This paper develops an efficient iterative method for computing all zeros of solutions of second order ordinary differential equations. A third order Halleys method is first derived by approximating the solution of an associated Riccati…
This paper presents an alternative approach for the computation of trajectory segments on slow manifolds of saddle type. This approach is based on iterative methods rather than collocation-type methods. Compared to collocation methods, that…
We report our experiences with the generalized integration-by-parts algorithm [hep-ph/9609429] in the context of calculations of a realistic one-loop subset of diagrams.
Methods of calculation of loop diagrams in Heavy Quark Effective Theory (HQET) are presented.
We try to understand and justify Schubert Calculus the way Schubert did it.
The central binomial series is a subject that has been extensively studied, for example in the context of the irrationality of Riemann zeta values. In this paper, the Hurwitz version of the central binomial series is defined by adding one…
The cohomology ring of a finite group, with coefficients in a finite field, can be computed by a machine, as Carlson has showed. Here "compute" means to find a presentation in terms of generators and relations, and involves only the…
We calculate a double integral over a product of Legendre polynomials multiplied by a binomial raised to a power.
In this article a new upper bounds for the multiple trigonometrical integrals are found. The method of the work based on a new method of estimation for the areas of algebraic surfaces.
We determine a new technique which allows the computation of the arithmetical rank of certain monomial ideals.
We develop a new method of umbral nature to treat blocks of Hermite and of Hermite like polynomials as independent algebraic quantities. The Calculus we propose allows the formulation of a number of practical rules allowing significant…
In this note a general result is proved that can be used to evaluate exactly a class of highly oscillatory integrals.
In this paper, based on the toric hypergeometric model given in a paper by Beukers--Cohen--Mellit, we provide two other ways to explain why the zig-zag diagram method can be used to compute Hodge numbers for hypergeometric data defined over…
We discuss a progress in calculation of Feynman integrals which has been done with help of the differential equation method and demonstrate the results for a class of two-point two-loop diagrams.