We present an algorithm for efficient computation of the constant term of a power of a multivariate Laurent polynomial. The algorithm is based on univariate interpolation, does not require the storage of intermediate data and can be easily parallelized. As an application we compute the power series expansion of the principal period of some toric Calabi-Yau varieties and find previously unknown ...

For the anisotropic [u( ∑N i=1 φ 2 i ) 2+v ∑N i=1 φ 4 i ]-theory with N = 2, 3 we calculate the imaginary parts of the renormalization-group functions in the form of a series expansion in v, i. e., around the isotropic case. Dimensional regularization is used to evaluate the fluctuation determinants for the isotropic instanton near the space dimension 4. The vertex functions in the presence of ...

In this chapter, we summarize the results of the five-loop calculations for the power series expansions of the renormalization constants governing the relations between bare and renormalized parameters. These expansions were first calculated more than 15 years ago [1]. Several errors were corrected in a more recent recalculation [2]. An essential error had occurred in diagram No.116 (see page 4...

The generalised Madelung problem, that of finding the spatial electric potential within a crystal lattice, is often approached via analytic function theory. But new results can be achieved through careful application of standard theorems from classical electro-statics. In this way we show that the celebrated Madelung constant for the NaCl crystal can be rigorously bounded through symmetry argum...

We study cluster algebras with principal and arbitrary coefficient systems that are associated to unpunctured surfaces. We give a direct formula for the Laurent polynomial expansion of cluster variables in these cluster algebras in terms of certain paths on a triangulation of the surface. As an immediate consequence, we prove the positivity conjecture of Fomin and Zelevinsky for these cluster a...

It is shown that the ten generators of the Poincaré group acting in the Fock space of nucleons and mesons and based on standard Lagrangians can be blockdiagonalized by one and the same unitary transformation such that the space of a fixed number of nucleons is separated from the rest of the Fock space. The existence proof is carried through in a formal power series expansion in the coupling con...

This paper is a continuation of the paper [De Bie H., Ørsted B., Somberg P., Souček V., Trans. Amer. Math. Soc. 364 (2012), 3875–3902], investigating a natural radial deformation of the Fourier transform in the setting of Clifford analysis. At the same time, it gives extensions of many results obtained in [Ben Säıd S., Kobayashi T., Ørsted B., Compos. Math. 148 (2012), 1265–1336]. We establish ...

This paper studies anchored expansion, a non-uniform version of the strong isoperimetric inequality. We show that every graph with i-anchored expansion contains a subgraph with isoperimetric (Cheeger) constant at least i. We prove a conjecture by Benjamini, Lyons and Schramm (1999) that in such graphs the random walk escapes with a positive lim inf speed. We also show that anchored expansion im...