相关论文: Building Mixed Hodge Structures

This paper documents and reviews the state of the art concerning computational models of construction grammar learning. It brings together prior work on the computational learning of form-meaning pairings, which has so far been studied in…

We construct certain monoids, called tied monoids. These monoids result to be semidirect products finitely presented and commonly built from braid groups and their relatives acting on monoids of set partitions. The nature of our monoids…

In this article one builds a class of recursive sets, one establishes properties of these sets, and one proposes applications.

This article summarises a Web-book on "Complexity" that was developed to introduce undergraduate students to interesting complex systems in the biological, physical and social sciences, and the common tools, principles and concepts used for…

The aim of this paper is to transfer the restrictedness theory to Hom-Lie algebras. The concept of restricted Hom-Lie algebras which is introduced in \cite{BM2} will be used in this paper. First, the existence of $p$-structures on a Hom-Lie…

This paper has several purposes. We present through a critical review the results from already published papers on the constructive semigroup theory, and contribute to its further development by giving solutions to open problems. We also…

This short introduction to positive geometries, targeted at a mathematical audience, is based on my talk at OPAC 2022.

This is an exposition of the theory of differentiable structures on metric measures spaces, in the sense of Cheeger and Keith.

The main purpose of this note is to pose a couple of problems which are easily formulated thought some seem to be not yet solved. These problems are of general interest for discrete mathematics including a new twig of a bough of theory of…

These notes aim to give an introduction to a few aspects of noncommutative geometry.

Since the subject of noncommutative geometry is now entering maturity, we felt there is need for presentation of the material at an undergraduate course level. Our review is a zero order approximation to this project. Thus, the present…

The goal of this article is to invite the reader to get to know and to get involved into higher Teichm\"uller theory by describing some of its many facets.

This paper explicitly describes Hodge structures of complete intersections of ample hypersurfaces in compact simplicial toric varieties.

Magnesium and its alloys are intriguing as possible biodegradable biomaterials due to their unique combination of biodegradability and high specific mechanical properties. However, uncontrolled biodegradation of magnesium during…

We consider posets of lattice paths (endowed with a natural order) and begin the study of such structures. We give an algebraic condition to recognize which ones of these posets are lattices. Next we study the class of Dyck lattices (i.e.,…

The main purpose of this article is to pose three problems which are easy to be formulated in an elementary way. These problems which are specifically important also for the new class of partially ordered sets seem to be not yet solved.

This text gives a construction of a differential graded Lie algebra in Nori's category of effective homological motives. In fact the construction works in more a general setting than that of an Abelian category. This allows us to give the…

Artificial gauge fields are currently realized in a wide range of physical settings. This includes solid-state devices but also engineered systems, such as photonic crystals, ultracold gases and mechanical setups. It is the aim of this…

We develop a Hodge theory for relative simple normal crossing varieties over an Artinian base scheme. We introduce the notion of a mixed Hodge structure over an Artin ring, which axiomatizes the structure that is found on the cohomology of…

We discuss a new geometric construction of port-Hamiltonian systems. Using this framework, we revisit the notion of interconnection providing it with an intrinsic description. Special emphasis on theoretical and applied examples is given…