相关论文: Multiplicity of a space over another space

Using a notation of corner between edges when graph has a fixed rotation, i.e. cyclical order of edges around vertices, we define combinatorial objects - combinatorial maps as pairs of permutations, one for vertices and one for faces.…

A flat membrane with given shape is displayed; two points in the membrane are randomly selected; the probability that the separation between the points have a specified value is sought. A simple method to evaluate the probability density is…

For any length category, we establish a set of rules (necessary and sufficient) that ensure a partial order on the isomorphism classes of simple objects such that the category is equivalent to the category of finite dimensional…

We define the similarity boundary of a self-similar set and use it to analyze the properties of self-similar sets in the general setting of any complete metric space. The similarity boundary is an attempt at extending the concept of the…

We review the basic definition of a stack and apply it to the topological and smooth settings. We then address two subtleties of the theory: the correct definition of a ``stack over a stack'' and the distinction between small stacks (which…

We define four different kinds of multiplicity of an invariant algebraic curve for a given polynomial vector field and investigate their relationships. After taking a closer look at the singularities and at the line of infinity, we improve…

We consider mappings satisfying an upper bound for the distortion of families of curves. We establish lower bounds for the distortion of distances under such mappings. As applications, we obtain theorems on the discreteness of the limit…

Many branches of theoretical and applied mathematics require a quantifiable notion of complexity. One such circumstance is a topological dynamical system - which involves a continuous self-map on a metric space. There are many notions of…

In this paper, we will give a natural definition for morphisms between multiplicative unitaries. We will then discuss some equivalences of this definition and some interesting properties of them. Moreover, we will define normal…

The multiplicity of an algebraic curve $C$ in the complex plane at a point $p$ on that curve is defined as the number of points that occur at the intersection of $C$ with a general complex line that passes close to the point $p$. It is…

Diversity indices are useful single-number metrics for characterizing a complex distribution of a set of attributes across a population of interest. The utility of these different metrics or sets of metrics depend on the context and…

We already saw in [A1] that the space of dynamically marked rational maps can be identified to a subspace of the space of covers between trees of spheres on which there is a notion of convergence that makes it sequentially compact. In the…

We introduce strings in metric spaces and define string complexes of metric spaces. We describe the class of 2-dimensional topological spaces which arise in this way from finite metric spaces.

``An orbifold is a space which is locally modeled on the quotient of a vector space by a finite group.'' This sentence is so easily said or written that more than one person has missed some of the subtleties hidden by orbifolds. Orbifolds…

We classify the metric spaces that can be approximated by finite homogeneous ones.

The level of a module over a differential graded algebra measures the number of steps required to build the module in an appropriate triangulated category. Based on this notion, we introduce a new homotopy invariant of spaces over a fixed…

A `discrete differential manifold' we call a countable set together with an algebraic differential calculus on it. This structure has already been explored in previous work and provides us with a convenient framework for the formulation of…

A differential module is a module equipped with a square-zero endomorphism. This structure underpins complexes of modules over rings, as well as differential graded modules over graded rings. We establish lower bounds on the class--a…

We provide combinatorial/topological formula for the multiplicity of a complex analytic normal surface singularity whenever the analytic structure on the fixed topological type is generic.

We define and study a natural category of graph limits. The objects are pairs $(\pi,\mu)$, where $\pi$ (the distribution of vertices) is an abstract probability measure on some abstract measurable space $(X,\mathcal{A})$ and $\mu$ (the…