We investigate relations between the pseudo-orbit-tracing property, topological stability and openness for tree-shifts. We prove that a tree-shift is of finite type if and only if it has the pseudo-orbit-tracing property which implies that the tree-shift is topologically stable and all shift maps are open. We also present an example of a tree-shift for which all shift maps are open but which is not of finite type. It also turns out that if a topologically stable tree-shift does not have isolated points then it is of finite type.
In this paper, we make the first attempt to
Equivariant monoids are very important objects in many branches of mathematics: they combine the notion of multiplication and the concept of a group action. In this paper we will construct categories which encode the structure borne by monoids with a group action by combining the theory of product and permutation categories (PROPs) and product and braid categories (PROBs) with the theory of crossed simplicial groups. PROPs and PROBs are categories used to encode structures borne by objects in symmetric and braided monoidal categories respectively, whilst crossed simplicial groups are categories which encode a unital, associative multiplication and a compatible group action. We will produce PROPs and PROBs whose categories of algebras are equivalent to the categories of monoids, comonoids and bimonoids with group action using extensions of the symmetric and braid crossed simplicial groups. We will extend this theory to balanced braided monoidal categories using the ribbon braid crossed simplicial group. Finally, we will use the hyperoctahedral crossed simplicial group to encode the structure of an involutive monoid with a compatible group action.
This paper studies the combinatorial Calabi flow for circle patterns with obtuse exterior intersection angles on surfaces of finite topological type. By using a Lyapunov function, we show that the flow exists for all time and converges exponentially fast to a circle pattern metric with prescribed attainable curvatures. This provides an algorithm to search for the desired circle patterns.
We establish the local-in-time existence of weak solutions to the kinetic Cucker–Smale model with singular communication weights
The purpose of the present article is to provide an upper bound of the number of the negative eigenvalues of a generalized Schrödinger operator defined on a finite compact metric tree.
In this paper, we prove a vanishing theorem concerning the periods of cuspidal automorphic sheaves for
We show that coarse maps between countable metric spaces of bounded geometry induce natural transformations of sufficiently good endofunctors of
We show that the Gauduchon metric
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：