We compute the precise value of measure noncompactness Sobolev embeddings $W_0^{1,p}(D)\hookrightarrow L^p(D)$, $p\in(1,\infty)$, on strip-like domains $D$ form $\mathbb{R}^k\times\prod\limits_{i=1}^{n-k}(a_i,b_i)$. show that such are always maximally noncompact, is, their coincides with norms. Furthermore, we not only but also all strict $s$-numbers in question coincide prove maximal remains v...

We prove that estimating the ground state energy of a translationallyinvariant, nearest-neighbour Hamiltonian on a 1D spin chain is QMAEXPcomplete, even for systems of low local dimension (≈ 40). This is an improvement over the best previously-known result by several orders of magnitude, and it shows that spin-glass-like frustration can occur in translationally-invariant quantum systems with a ...

The laplacian operator applied to the coordinates of a manifold provides the mean curvature vector. Manipulating the metric of the manifold or interpreting its coordinates in various ways provide useful tools for shape and image processing and representation. We will review some of these tools focusing on scale invariant geometry, curvature flow with respect to an embedding of the image manifol...

In this paper we study the heat equation (of Hodge Laplacian) deformation of .p; p/-forms on a Kähler manifold. After identifying the condition and establishing that the positivity of a .p; p/-form solution is preserved under such an invariant condition, we prove the sharp differential Harnack (in the sense of LiYau-Hamilton) estimates for the positive solutions of the Hodge Laplacian heat equa...

A technique for enhancing the perceptual sharpness of an image is described. The enhancement algorithm augments the frequency content of the image using shape-invariant properties of edges across scale by using a nonlinearity that generates phase coherent higher harmonics. The procedure utilizes the Laplacian transform and the Laplacian pyramid image representation. Results are presented depict...

Aalto University, P.O. Box 11000, FI-00076 Aalto www.aalto.fi Author Mathias Masson Name of the doctoral dissertation Regularity for parabolic quasiminimizers in metric measure spaces Publisher School of Science Unit Department of Mathematics and Systems Analysis Series Aalto University publication series DOCTORAL DISSERTATIONS 89/2013 Field of research Mathematical analysis Manuscript submitte...