Abstract We establish the local Lipschitz continuity and higher differentiability of vector-valued minimizers a class energy integrals Calculus Variations. The main novelty is that we deal with possibly degenerate densities respect to

A bstract We identify two families of ten-point Feynman diagrams that generalize the elliptic double box, and show they can be expressed in terms same class multiple polylogarithms to all loop orders. Interestingly, one these also written as a d log form. For both diagrams, we provide new 2ℓ-fold integral representations are linearly reducible but variable make above properties manifest. illust...

No. title/pages date update file name 1 A note on the elliptic integrals and elliptic functions ellipsoid-may04.tex 3 A note on " Potential flow of a second order fluid over a sphere or an ellipse " ellipse-wang-joseph-apr27.tex 4 A note on flows of a second order fluid around an ellipsoid ellipse-may31a.tex 5 A note on flows of a second order fluid around an ellipsoid of revolution/11pages

In a series of papers, B. C. Carlson produced tables of elliptic integrals, evaluating them in terms of easily computed symmetrical functions, using a group of multivariate recurrence relations. These relations are, however, cumbersome to use by hand and, in the absence of a specific reductive algorithm, difficult to use with computer algebra. This paper presents such an algorithm, guaranteed t...

We study the elliptic C n and BC n Ruijsenaars-Schneider models which is elliptic generalization of system given in [1]. The Lax pairs for these models are constructed by Hamiltonian reduction technology. We show that the spectral curves can be parameter-ized by the involutive integrals of motion for these models. Taking nonrelativistic limit and scaling limit, we verify that they lead to the s...

The GKZ system for the Hesse pencil of elliptic curves has more solutions than the period integrals. In this work we give different realizations and interpretations of the extra solution, in terms of oscillating integral, Eichler integral, chain integral on the elliptic curve, limit of a period of a certain compact Calabi–Yau threefold geometry, etc. We also highlight the role played by the orb...

We work out finite-dimensional integral formulae for the scalar product of genus one states of the group G Chern-Simons theory with insertions of Wilson lines. Assuming convergence of the integrals, we show that unitarity of the elliptic KnizhnikZamolodchikov-Bernard connection with respect to the scalar product of CS states is closely related to the Bethe Ansatz for the commuting Hamiltonians ...

In this paper we describe numerical investigations of definite integrals that arise by considering the moments of multi-step uniform random walks in the plane, together with a closely related class of integrals involving the elliptic functions K,K ′, E and E′. We find that in many cases such integrals can be “experimentally” evaluated in closed form or that intriguing linear relations exist wit...