相关论文: Clark measures on polydiscs associated to product …

In a previous work [L.Delle Site, J.Phys.A 40, 2787 (2007)] the derivation of an analytic expression for the kinetic functional of a many-body electron system has been proposed. Though analytical, the formula is still non local…

We investigate a result on convergence of double sequences of numbers and how it extends to measurable functions.

We study representations of inner functions on the bidisc from a fractional linear transformation point of view, and provide sufficient conditions, in terms of colligation matrices, for the existence of two-variable inner functions. Here…

In this article left invariant measures and functionals on locally compact nonassociative fan loops are investigated. For this purpose necessary properties of topological fan loops, estimates and approximations of functions on them are…

We study the dimension of self-similar measures associated to a homogeneous iterated function system of three contracting similarities on $\bf R$ and other more general IFS's. We extend some of the theory recently developed for Bernoulli…

A bilinear quadrature numerically evaluates a continuous bilinear map, such as the $L^2$ inner product, on continuous $f$ and $g$ belonging to known finite-dimensional function spaces. Such maps arise in Galerkin methods for differential…

We introduce a notion of the Euclidean- and the Minkowski rank for arbitrary metric spaces and we study their behaviour with respect to products. We show that the Minkowski rank is additive with respect to metric products, while additivity…

We develop theory and computational methods to investigate particle inclusions embedded within curved lipid bilayer membranes. We consider the case of spherical lipid vesicles where inclusion particles are coupled through (i) intramembrane…

Measuring comodules are defined and shown to provide a useful generalization of the set of maps between modules with a broad range of applications. Three applications are described. Connections on bundles are described in terms of measuring…

Parke-Taylor functions are certain rational functions on the Grassmannian of lines encoding MHV amplitudes in particle physics. For $n$ particles there are $n!$ Parke-Taylor functions, corresponding to all orderings of the particles. Linear…

We reorganize, simplify and expand the theory of contractions or interior products of multivectors, and related topics like Hodge star duality. Many results are generalized and new ones are given, like: geometric characterizations of blade…

We study square integrable functions on the metaplectic group and functions on the space of unitary symmetric matrices. We relate them using the oscillator representations.

The Mullineux map is a combinatorial function on partitions which describes the effect of tensoring a simple module for the symmetric group in characteristic $p$ with the one-dimensional sign representation. It can also be interpreted as an…

Exploiting the explicit bijection between the density of singular values and the density of eigenvalues for bi-unitarily invariant complex random matrix ensembles of finite matrix size, we aim at finding the induced probability measure on…

We consider the one dimensional periodic complex valued mKdV, which corresponds to the first equation above cubic NLS in the associated integrable hierarchy. Our main result is the construction of a sequence of invariant measures supported…

We construct a new operation among representations of the symmetric group that interpolates between the classical internal and external products, which are defined in terms of tensor product and induction of representations. Following…

We study the relationship between the tensor product multiplicities of a compact semisimple Lie algebra $\mathfrak{g}$ and a special function $\mathcal{J}$ associated to $\mathfrak{g}$, called the volume function. The volume function arises…

Let $(X,d)$ be a compact metric space. We consider the behavior of probability measures $\mu$ with the property that $$ \int_{X} d(x, y) d\mu(y) \qquad \mbox{is independent of}~x \in X.$$ It appears that such measures, when they exist,…

Let $P_{\alpha} f(x,t)$ be the Caffarelli-Silvestre extension of a smooth function $f(x): \mathbb{R}^n \rightarrow \mathbb{R}^{n+1}_+:=\mathbb{R}^n\times (0,\infty).$ The purpose of this article is twofold. Firstly, we want to characterize…

In this thesis we study the relationship between the existence of canonical metrics on a complex manifold and stability in the sense of geometric invariant theory. We introduce a modification of K-stability of a polarised variety which we…