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Operads, homotopy algebra and iterated integrals for double loop spaces
Operads homotopy algebra iterated integrals double loop spaces
2015/3/25
This paper provides some background to the theory of operads, used in the first author's papers on 2d topological field theory (hep-th/921204, CMP 159 (1994), 265-285; hep-th/9305013). It is intended ...
Burkholder integrals, Morrey's problem and quasiconformal mappings
Rank-one-convex Quasi-convex Variational Integrals
2011/1/17
Inspired by Morrey's Problem (on rank-one convex functionals)and the Burkholder integrals (of his martingale theory) we nd that the Burkholder functionals Bp, p > 2.
Vanishing integrals for Hall-Littlewood polynomials
Vanishing integrals Hall-Littlewood polynomials
2010/11/24
It is well known that if one integrates a Schur function indexed by a partition $\lambda$ over the symplectic (resp. orthogonal) group, the integral vanishes unless all parts of $\lambda$ have even m...
We study the integrals of type $I(a)=\int_{O_n}\prod u_{ij}^{a_{ij}}\,du$, depending on a matrix of exponents $a\in M_{p\times q}(\mathbb N)$, whose exact computation is an open problem. Our results a...
A Fuchsian matrix differential equation for Selberg correlation integrals
Fuchsian matrix differential equation Selberg correlation integrals
2010/11/12
We characterize averages of $\prod_{l=1}^N|x - t_l|^{\alpha - 1}$ with respect to the Selberg density, further contrained so that $t_l \in [0,x]$ $(l=1,...,q)$ and $t_l \in [x,1]$ $(l=q+1,...,N)$, in...
In this paper, we established a new Ostrowski-type inequality involving functions of two independent variables.