Related papers: Parametric linearization of skew products
We consider a generalisation of the baker's transformation, consisting of a skew-product of contractions and a $\beta$-transformation. The Hausdorff dimension and Lebesgue measure of the attractor is calculated for a set of parameters with…
We compute an upper bound for the dimension of the tangent spaces at classical points of certain eigenvarieties associated with definite unitary groups, especially including the so-called critically refined cases. Our bound is given in…
The shear rheology of dense colloidal and granular suspensions is strongly nonlinear, as these materials exhibit shear-thinning and shear-thickening, depending on multiple physical parameters. We numerically study the rheology of a simple…
Given a parabolic map in one dimension $f(z) = z+O(z^2)$, $f \neq Id$, it is known that there exists the analogous of stable and unstable domains. That is, domains in which every point is attracted by $f$ (and by the inverse $f^{-1}$)…
We derive a linearized version of the monotonicity method for shape reconstruction using time harmonic elastic waves. The linearized method provides an efficient version of the method, drastically reducing computation time. Here we show…
A general method for the reduction of coupled spherical harmonic products is presented. When the total angular coupling is zero, the reduction leads to an explicitly real expression in the scalar products within the unit vector arguments of…
A study is made of linear isometries on Fr\'echet spaces for which the metric is given in terms of a sequence of seminorms. This establishes sufficient conditions on the growth of the function that defines the metric in terms of the…
We develop a constitutive model allowing for the description of the rheology of two-dimensional soft dense suspensions above jamming. Starting from a statistical description of the particle dynamics, we derive, using a set of…
This work is devoted to the development and analysis of a linearization algorithm for microscopic elliptic equations, with scaled degenerate production, posed in a perforated medium and constrained by the homogeneous Neumann-Dirichlet…
We study integration and $L_2$-approximation on countable tensor products of function spaces of increasing smoothness. We obtain upper and lower bounds for the minimal errors, which are sharp in many cases including, e.g., Korobov, Walsh,…
The present paper provides a general formula for the dimension of spline space over T-meshes using smoothing cofactor-conformality method. And we introduce a new notion, Diagonalizable T-mesh, over which the dimension formula is only…
We study the approximation of high-dimensional rank one tensors using point evaluations and consider deterministic as well as randomized algorithms. We prove that for certain parameters (smoothness and norm of the $r$th derivative) this…
The paper considers functional linear regression, where scalar responses $Y_1,...,Y_n$ are modeled in dependence of random functions $X_1,...,X_n$. We propose a smoothing splines estimator for the functional slope parameter based on a…
Uni- and bivariate data smoothing with spline functions is a well established method in nonparametric regression analysis. The extension to multivariate data is straightforward, but suffers from exponentially increasing memory and…
Several characterizations are given for a square matrix that can be written as the product of two positive (semidefinite) projections. Based on one of these characterizations, and the theory of alternating projections, a Matlab program is…
We present an approach to defining Hilbert spaces of functions depending on infinitely many variables or parameters, with emphasis on a weighted tensor product construction based on stable space splittings, The construction has been used in…
In this dissertation, we concentrate on the challenging research issue of developing a spline-based modeling framework, which converts the conventional data (e.g., surface meshes) to tensor-product trivariate splines. This methodology can…
We prove that we can always construct strongly minimal linearizations of an arbitrary rational matrix from its Laurent expansion around the point at infinity, which happens to be the case for polynomial matrices expressed in the monomial…
We investigate properties of tempered distributions with discrete or countable supports such that their Fourier transforms are distributions with discrete or countable supports as well. We find sufficient conditions for support of the…
In this paper we generalize the canonical positive scaling of rows and columns of a matrix to the scaling of selected-rank subtensors of an arbitrary tensor. We expect our results and framework will prove useful for sparse-tensor completion…