Related papers: A very easy approach to the holomorphic discrete s…
In this paper we investigate the Cauchy problem for Schr\"odinger ultrahyperbolic equations with singular (less than continuous) coefficients. We prove $H^\infty$ well-posedness in the very weak sense under suitable assumptions of the…
In this paper, we study the Cauchy problem of 2d Dirac equation with Hartree type nonlinearity $c(|\cdot|^{-\gamma} * \langle \psi, \beta \psi\rangle)\beta\psi$ with $c\in \mathbb R\setminus\{0\} $, $0 < \gamma < 2$. Our aim is to show the…
Shellings of simplicial complexes have long been a useful tool in topological and algebraic combinatorics. Shellings of a complex expose a large amount of information in a helpful way, but are not easy to construct, often requiring deep…
We prove that a countable simple unidimensional theory that eliminates hyperimaginaries is supersimple. This solves a problem of Shelah in the more general context of simple theories under weak assumptions.
We investigate relative connections on a sheaf of modules. A sufficient condition is given for the existence of a relative holomorphic connection on a holomorphic vector bundle over a complex analytic family. We show that the relative Chern…
We address two problems regarding the structure and representation theory of finite W-algebras associated with the general linear Lie algebras. Finite W-algebras can be defined either via the Whittaker model of Kostant or, equivalently, by…
We show that it is possible to extract useful information from the straightforward perturbation theory in classical mechanics. Although the secular terms make the perturbation series useless for large time, these expansions yield the…
We extend the decomposition theorem for numerically $K$-trivial varieties with log terminal singularities to the K\"ahler setting. Along the way we prove that all such varieties admit a strong locally trivial algebraic approximation, thus…
Some years ago I demonstrated a simulated annealing heuristic for the Hamiltonian cycle problem (Science 273, 413 (1996)). Here I propose an improved version of this heuristic.
We give a survey about the Runge approximation problem for a holomorphic function defined on the unit ball of a complex Banach space.
In this paper, two main results concerning uniformly continuous retractions are proved. First, an $\alpha$-H\"older retraction from any separable Banach space onto a compact convex subset whose closed linear span is the whole space is…
Proofs that a smooth morphism is flat available in the literature are long and difficult. We give a short proof of this fact.
The aim of this article is to study a Cahn-Hilliard model for a multicomponent mixture with cross-diffusion effects, degenerate mobility and where only one of the species does separate from the others. We define a notion of weak solution…
In this note, we present a simple directed graph proof of Sharkovsky's theorem.
We study the well-posedness of the Hele-Shaw-Cahn-Hilliard system modeling binary fluid flow in porous media with arbitrary viscosity contrast but matched density between the components. For initial data in $H^s, s>\frac{d}{2}+1$, the…
Recent work has demonstrated the existence of universal Hamiltonians - simple spin lattice models that can simulate any other quantum many body system to any desired level of accuracy. Until now proofs of universality have relied on…
We show that any simple holomorphic disc admits the annulus property, i.e., each interior point is surrounded by an arbitrary small annulus consisting entirely of injective points. As an application we show that interior singularities of…
We give a rigorous mathematical proof for the validity of the toric sheaf cohomology algorithm conjectured in the recent paper by R. Blumenhagen, B. Jurke, T. Rahn, and H. Roschy (arXiv:1003.5217). We actually prove not only the original…
Localised structures appear in a wide variety of systems, arising from a pinning mechanism due to the presence of a small-scale pattern or an imposed grid. When there is a separation of lengthscales, the width of the pinning region is…
We say a representation V of a group G has stability if its multiplicities m^{G}_{V}(\lambda) is dependent only on some equivalence class of \lambda for a sufficiently large parameter \lambda. In this paper, we prove that the restriction of…