We study a family of integrals parameterised by N = 2, 3, . . . generalising the Askey-Wilson integral N = 2 which has arisen in the theory of q-analogs of monodromy preserving deformations of linear differential systems and in theory of the Baxter Q operator for the XXZ open quantum spin chain. These integrals are particular examples of moments defined by weights generalising the Askey-Wilson ...

In this work we study overlap degrees expressed in terms of overlap functions. We present the basic properties that from our point of view must satisfy these overlap functions. We study a construction method, we analyze which t-norms are also overlap functions and we prove that if we apply particular aggregations to such functions we recover the overlap index between fuzzy sets as defined by Du...

This paper concerns with analytical integration of trivariate polynomials over linear polyhedra in Euclidean three-dimensional space. The volume integration of trivariate polynomials over linear polyhedra is computed as sum of surface integrals in R3 on application of the well known Gauss’s divergence theorem and by using triangulation of the linear polyhedral boundary. The surface integrals in...

Determination of the high-resolution quaternary structure of oligomeric membrane proteins requires knowledge of both the oligomeric number and intermolecular distances. The centerband-only detection of exchange (CODEX) technique has been shown to enable the extraction of the oligomeric number through the equilibrium exchange intensity at long mixing times. To obtain quantitative distances, we n...

The approach used by Ahlrichs [Phys. Chem. Chem. Phys., 2006, 8, 3072] to derive the Obara-Saika recurrence relation (RR) for two-electron integrals over Gaussian basis functions, is used to derive an 18-term RR for six-dimensional integrals in phase space and 8-term RRs for three-dimensional integrals in position or momentum space. The 18-term RR reduces to a 5-term RR in the special cases of ...

hyperspectral sensors provide a large number of spectral bands. this massive and complex data structure of hyperspectral images presents a challenge to traditional data processing techniques. therefore, reducing the dimensionality of hyperspectral images without losing important information is a very important issue for the remote sensing community. we propose to use overlap-based feature weigh...

In this article, it is shown how to obtain objects called Eichler integrals in the mathematical literature that can be used for calculating scattering amplitudes in String Theory. These Eichler integrals are also new examples of Eichler integrals with poles.

In this paper, two Howland integrals are evaluated to 25D when the index is an odd integer. Those Howland integrals when the index is an even integer have been evaluated to 18D by Nelson. A new method of evaluation is used. The four Howland integrals were first evaluated to 5D by Howland himself, partly with Stevenson, in the papers dealing with a perforated strip [1], [2]. Ling and Nelson in a...

where ψi = c1(Li) is the first Chern class of Li, and λj = cj(E) is the j-th Chern class of the Hodge bundle. Hodge integrals arise in the calculations of Gromov-Witten invariants by localization techniques [14, 7]. The explicit evaluation of Hodge integrals is a difficult problem. The Hodge integrals involving only ψ classes can be computed recursively by Witten’s conjecture [26] proven by Kon...

A fully numerical method to calculate loop integrals, a numerical contour-integration method, is proposed. Loop integrals can be interpreted as a contour integral in a complex plane for an integrand with multi-poles in the plane. Stable and efficient numerical integrations an along appropriate contour can be performed for tensor integrals as well as for scalar ones appearing in loop calculation...