The approach we follow consists in transforming the numerical evaluation of hypersingular integrals into the calculation of a nearly singular integral whose mass is distributed according to a positive parameter ε. To evaluate the latter we apply a Gauss quadrature formula associated with a nearly singular weight function. It is estimated the error in terms of ε. Some numerical results are prese...

We generalize purity of the Newton stratification to purity for a single break point of the Newton point in the context of local G-shtukas respectively of elements of the loop group of a reductive group. As an application we prove that elements of the loop group bounded by a given dominant coweight satisfy a generalization of Grothendieck’s conjecture on deformations of p-divisible groups with ...

In this article we thoroughly investigate the possibility of employing the exact computation of the free rigid body motion as a component of splitting methods for problems of rigid bodies subject to external forces. We review various matrix and quaternion representations of the solution of the free rigid body equation, which involve Jacobi ellipic functions and elliptic integrals, and are amena...

This paper is devoted to prove the unbounded divergence on superdense sets, with respect to product quadrature formulas of interpolatory type on Jacobi nodes. Mathematics Subject Classification (2010): 41A10, 41A55, 65D32.

An iterative definition of any n variable mean function is given in this article, which iteratively uses the two-variable form of the corresponding two-variable mean function. This extension method omits recursivity which is an important improvement compared with certain recursive formulas given before by Ando-Li-Mathias, PetzTemesi. Furthermore it is conjectured here that this iterative algori...

We present a new numerical method, based on a coupling of finite elements and boundary elements, to solve a fluid–solid interaction problem posed in the plane. The boundary unknowns involved in our formulation are approximated by a spectral method. We provide error estimates for the Galerkin method, propose fully discrete schemes based on elementary quadrature formulas and show that the perturb...

Solving systems of nonlinear equations is perhaps one of the most difficult problems in all numerical computation. Although numerous methods have been developed to attack this class of numerical problems, one of the simplest and oldest methods, Newton’s method is arguably the most commonly used. As is well known, the convergence and performance characteristics of Newton’s method can be highly s...

We treat the time discretization of an initial-value problem for a homogeneous abstract parabolic equation by first using a representation of the solution as an integral along the boundary of a sector in the right half of the complex plane, then transforming this into a real integral on the finite interval [0, 1], and finally applying a standard quadrature formula to this integral. The method r...

We report on an observation of the Anomalous X– ray Pulsar 1E 1048.1–5937 performed with the XMM-Newton satellite. The phase averaged spectrum of 1E 1048.1–5937 is well described by the sum of a power law with photon index ∼2.9 and a blackbody with temperature ∼0.6 keV, without evidence for significant absorption or emission lines. The above spectral parameters do not vary during the phases cor...