相关论文: A construction of patterns with many critical poin…
We study the existence of critical points of stable stationary solutions to reaction-diffusion problems on topological tori. Stable nonconstant stationary solutions are often called patterns. We construct topological tori and patterns with…
A general system of several ordinary differential equations coupled with a reaction-diffusion equation in a bounded domain with zero-flux boundary condition is studied in the context of pattern formation. These initial-boundary value…
This paper investigates circle patterns with obtuse exterior intersection angles on surfaces of finite topological type. We characterise the images of the curvature maps and establish several equivalent conditions regarding long time…
Numerical simulations of a simple reaction--diffusion model reveal a surprising variety of irregular spatio--temporal patterns. These patterns arise in response to finite--amplitude perturbations. Some of them resemble the steady irregular…
An asymptotic method for finding instabilities of arbitrary $d$-dimensional large-amplitude patterns in a wide class of reaction-diffusion systems is presented. The complete stability analysis of 2- and 3-dimensional localized patterns is…
A general system of n ordinary differential equations coupled with one reaction-diffusion equation, considered in a bounded N-dimensional domain, with no-flux boundary condition is studied in a context of pattern formation. Such initial…
The tori $T_r = r S^1 \times s S^1 \subset S^3$, where $r^2 + s^2 = 1$, are constrained Willmore surfaces, i.e. critical points of the Willmore functional among tori of the same conformal type. We compute which of the $T_r$ are stable…
On objects of a triangulated category with a stability condition, we construct a topology.
A configuration of points and lines is cyclic if it has an automorphism which permutes its points in a full cycle. A closed formula is derived for the number of non-isomorphic connected cyclic configurations of type (v_3), i.e., which have…
Nonexpansive mappings play a central role in modern optimization and monotone operator theory because their fixed points can describe solutions to optimization or critical point problems. It is known that when the mappings are sufficiently…
Dynamical processes on networks are currently being considered in different domains of cross-disciplinary interest. Reaction-diffusion systems hosted on directed graphs are in particular relevant for their widespread applications, from…
This brief note gives a survey on results relating to existence of closed points on schemes, including an elementary topological characterization of the schemes with (at least one) closed point.
Point-like topological defects are singular configurations that occur in a variety of in and out of equilibrium systems with two-dimensional orientational order. As they are associated with a nonzero circuitation condition, the presence of…
We classify the topological types of surfaces in the 3-dimensional unit sphere that contain both a great and a small circle through each point. In particular, these surfaces are homeomorphic to one of five normal forms and are either the…
We consider functions with isolated critical points on a closed surface. We prove that in a neighborhood of a critical point the function conjugates with Re$z^k$ for the some nonnegative integer k. The full topological invariant of such…
Response surface designs are usually described as being run under complete randomization of the treatment combinations to the experimental units. In practice, however, it is often necessary or beneficial to run them under some kind of…
A new class of patterns for multiplex networks is studied, which consists in a collection of different homogeneous states each referred to a distinct layer. The associated stability diagram exhibits a tricritical point, as a function of the…
We study a p-adic reaction-diffusion system and the associated Turing patterns. We establish an instability criteria and show that the Turing patterns are not classical patterns consisting of alternating domains. Instead of this, a Turing…
We analyze here Hamiltonian stationary surfaces in the complex projective plane as (local) solutions to an integrable system, formulated as a zero curvature on a loop group. As an application, we show in details why such tori are finite…
The purpose of this paper is to present the critical cases of the trace theorems for the restriction of functions to closed surfaces, and to give the asymptotics for the norms of the traces under dilations of the surface. We also discuss…