Related papers: Uniform sheaves and differential equations

We derive a blow-up formula for the de Rham cohomology of a local system of complex vector spaces on a compact complex manifold. As an application, we obtain the blow-up invariance of $E_{1}$-degeneracy of the Hodge-de Rham spectral…

We consider the dyadic model with viscosity and additive Gaussian noise as a simplified version of the stochastic Navier-Stokes equations, with the purpose of studying uniqueness and emergence of singularities. We prove path-wise uniqueness…

For differential inequalities of the form $$ \sum_{|\alpha| = m} (- 1)^m \partial^\alpha a_\alpha (x, u) \ge b (x) |u|^\lambda \quad \mbox{in } {\mathbb R}^n, \: n \ge 1, $$ where $a_\alpha$ and $b$ are some functions, we obtain conditions…

We classify (up to quasi-isomorphism) the free differential modules whose homology is equal to a given module $M$ by developing a theory for deforming an arbitrary free complex into a differential module. We use an iterative approach to…

The relativistic membrane equation can be rewritten as a first order hyperbolic system. Making use of the characteristic decomposition method, a new blow-up theorem is established. As an application, it demonstrates the formation of…

The present article presents a summarizing view at differential-algebraic equations (DAEs) and analyzes how new application fields and corresponding mathematical models lead to innovations both in theory and in numerical analysis for this…

We study a long-recognised but under-appreciated symmetry called "dynamical similarity" and illustrate its relevance to many important conceptual problems in fundamental physics. Dynamical similarities are general transformations of a…

In this paper we give a necessary combinatorial condition for a negative--definite plumbing tree to be suitable for rational blow--down, or to be the graph of a complex surface singularity which admits a rational homology disk smoothing.…

We show that the global and local constructions of three types of blowup of a smooth manifold along a closed submanifold in differential topology are equivalent.

For a finite dimensional algebra $A$, we prove that the bounded homotopy category of projective $A$-modules and the bounded derived category of $A$-modules are dual to each other via certain categories of locally-finite cohomological…

The notion of $c$-differential uniformity has recently received a lot of attention since its proposal~\cite{Ellingsen}, and recently a characterization of perfect $c$-nonlinear functions in terms of difference sets in some quasigroups was…

This paper gives a uniform-theoretic refinement of classical homotopy theory. Both cubical sets (with connections) and uniform spaces admit classes of weak equivalences, special cases of classical weak equivalences, appropriate for the…

Models which allow an explicit application to structurally modulated substances are reviewed within the frame of a symmetry-based approach starting from discrete lattice theory. Focus is set on models formulated in terms of local variables…

We discuss some finite homogeneous structures, addressing the question of universality of their automorphism groups. We also study the existence of so-called Kat\v{e}tov functors in finite categories of embeddings or homomorphisms.

Does three-dimensional incompressible Euler flow with smooth initial conditions develop a singularity with infinite vorticity after a finite time? This blowup problem is still open. After briefly reviewing what is known and pointing out…

We review the theory of non-commutative deformations of sheaves and describe a versal deformation by using an A-infinity algebra and the change of differentials of an injective resolution. We give some explicit non-trivial examples.

In recent work we have developed a renormalization framework for stabilizing reduced order models for time-dependent partial differential equations. We have applied this framework to the open problem of finite-time singularity formation…

In the category of log schemes, it is unclear how to define the blow-ups for non-strict closed immersions. In this article, we introduce the notion of divided log spaces. We obtain the category of divided log spaces by locally inverting log…

Network dynamics is nowadays of extreme relevance to model and analyze complex systems. From a dynamical systems perspective, understanding the local behavior near equilibria is of utmost importance. In particular, equilibria with at least…

In this paper, we deal with uniform spaces whose diagonal uniformity admits a basis consisting of equivalence relations. Such non-Archimedean uniform spaces are particularly interesting for applications in commutative ring theory, because…