相关论文: A topological proof of Terao's generalized Arrow's…

We prove a general factorization theorem for maps with hereditarily indecomposable fibers and apply it to reprove a theorem of Mackoviak on the existence of universal hereditarily indecomposable continua.

In this paper, we generalize the existence result in [14] and prove convergence theorems of the iterative scheme in [12, 16] for monotone generalized alpa-nonexpansive mappings in uniformly convex partially ordered hyperbolic metric spaces.…

We generalise gauge theory on a graph so that the gauge group becomes a finite-dimensional ribbon Hopf algebra, the graph becomes a ribbon graph, and gauge-theoretic concepts such as connections, gauge transformations and observables are…

We present proofs of the basic isopermetric structure theory, obtaining some new simplified proofs. As an application, we obtain simple descriptions for subsets $S$ of an abelian group with $|kS|\le k|S|-k+1$ or $|kS-rS|- (k+r)|S|,$ where…

We consider the problem of the observability of positively expansive maps by the time series associated to continuous real functions. For this purpose we prove a general result on the generic observability of a locally injective map of a…

Ultrafilters are very useful and versatile objects with applications throughout mathematics: in topology, analysis, combinarotics, model theory, and even theory of social choice. Proofs based on ultrafilters tend to be shorter and more…

This note is purely expository. The statement of the Gauss theorem on the constructibility of regular polygons by means of compass and ruler is simple and well-known. However, its proofs given in most textbooks rely upon much unmotivated…

The generalized composition graph is used by Cardoso and some researchers for factorization of the adjacency spectrum and Laplacian of a simple graph. Because the generalized composition graph is an example of a set-theoretic linear operad,…

Heuristic functions are central to the performance of search algorithms such as A-star, where admissibility - the property of never overestimating the true shortest-path cost - guarantees solution optimality. Recent deep learning approaches…

A generic method for combinatorial constructions of intrinsic geometrical spaces is presented. It is based on the well known inverse sequences of finite graphs that determine (in the limit) topological spaces. If a pattern of the…

We consider random arrays indexed by the leaves of an infinitary rooted tree of finite depth, with the distribution invariant under the rearrangements that preserve the tree structure. We call such arrays hierarchically exchangeable and…

The global homeomorphism theorem for quasiconformal maps describes the following specifically higher-dimensional phenomenon: {\em Locally invertible quasiconformal mapping $f: {\R}^{n} \to {\R}^{n}$ is globally invertible provided $n > 2$.}…

Kapranov Theorem is a well known generalization of Newton-Puiseux theorem for the case of several variables. This theorem is stated mainly in the context of tropical geometry. We present a new, constructive proof, that also characterizes…

It is well understood that the structure of a social network is critical to whether or not agents can aggregate information correctly. In this paper, we study social networks that support information aggregation when rational agents act…

A barrier to the wider adoption of neural networks is their lack of interpretability. While local explanation methods exist for one prediction, most global attributions still reduce neural network decisions to a single set of features. In…

B\'ar\'any's colorful generalization of Carath\'eodory's Theorem combines geometrical and combinatorial constraints. Kalai-Meshulam (2005) and Holmsen (2016) generalized B\'ar\'any's theorem by replacing color classes with matroid…

In a many-to-many matching model in which agents' preferences satisfy substitutability and the law of aggregate demand, we proof the General Manipulability Theorem. We result generalizes the presented in Sotomayor (1996 and 2012) for the…

In 2016, Hou and Wang introduced the concept of multiple mappings based on iterated function system, which is an important branch of fractal theory. In this paper, we introduce the definitions of sensitivity, accessibility, and Kato's chaos…

On Zariski Main Theorem in Algebraic Geometry and Analytic Geometry. We fill a surprising gap of Complex Analytic Geometry by proving the analogue of Zariski Main Theorem in this geometry, i.e. proving that an holomorphic map from an…

Let $k$ be a field of arbitrary characteristic. Nakai (1978) proved a structure theorem for $k$-domains admitting a nontrivial locally finite iterative higher derivation when $k$ is algebraically closed. In this paper, we generalize Nakai's…