Related papers: Chemical Examples in Hypergroups

Graph-based signal processing techniques have become essential for handling data in non-Euclidean spaces. However, there is a growing awareness that these graph models might need to be expanded into `higher-order' domains to effectively…

Given a semigroup of local homeomorphisms on a compact space X we consider the corresponding semigroup of *-endomorphisms on C(X) and discuss the possibility of extending it to an interaction group, a concept recently introduced by the…

An interesting question about quasiconvexity in a hyperbolic group concerns finding classes of quasiconvex subsets that are closed under finite intersections. A known example is the class of all quasiconvex subgroups. However, not much is…

We present a novel method for identifying a biochemical reaction network based on multiple sets of estimated reaction rates in the corresponding reaction rate equations arriving from various (possibly different) experiments. The current…

Recently, we have endowed various categories of groups with topologies. The purpose of this paper is to introduce on these categories others topologies which are statistically more suitable to study well-known problems in groups theory. We…

Ordering theorems, characterizing when partial orders of a group extend to total orders, are used to generate hypersequent calculi for varieties of lattice-ordered groups (l-groups). These calculi are then used to provide new proofs of…

Motivated by appearance of multisemigroups in the study of additive $2$-categories, we define and investigate the notion of a multisemigroup with multiplicities. This notion seems to be better suitable for applications in higher…

Sociological research has framed collective action in science, innovation, and culture as tripartite networks connecting teams of actors, lists of prior works, and sets of labels (e.g., keywords, topics). While methods for multipartite…

In this work, we are concerned with hierarchically hyperbolic spaces and hierarchically hyperbolic groups. Our main result is a wide generalization of a combination theorem of Behrstock, Hagen, and Sisto. In particular, as a consequence, we…

Superconductivity, superfluidity, condensation, cluster formation, etc. are phenomena that might occur in many-particle systems. These are due to residual interactions between the particles. To explain these phenomena consistently in a…

We study those group rings whose group of units is hyperbolic.

A directed hypergraph, which consists of nodes and hyperarcs, is a higher-order data structure that naturally models directional group interactions (e.g., chemical reactions of molecules). Although there have been extensive studies on local…

We prove a category equivalence between algebraic supergroups and Harish-Chandra pairs over a commutative ring which is $2$-torsion free. The result is applied to re-construct the Chevalley $\mathbb{Z}$-supergroups constructed by Fioresi…

A hyperbolic reflection group is a discrete group generated by reflections in the faces of an $n$-dimensional hyperbolic polyhedron. This survey article is dedicated to the study of arithmetic hyperbolic reflection groups with an emphasis…

In complex systems research, the study of higher-order interactions has exploded in recent years. Researchers have formalized various types of group interactions, such as public goods games, biological contagion, and information…

We study a new type of sequences whose elements are defined in terms of the position, sign and magnitude of another element of the sequence. The name ultra-recursive comes from the fact that these sequences possess terms that are generated…

We introduce the term "protonormal" to refer to a subgroup H of a group G such that for every x in G the subgroups x^{-1}Hx and H commute as sets. If moreover (G,H) is a Hecke pair we show that the Hecke algebra H(G,H) is generated by the…

Hypergraphs offer a natural modeling language for studying polyadic interactions between sets of entities. Many polyadic interactions are asymmetric, with nodes playing distinctive roles. In an academic collaboration network, for example,…

We study and relate certain actions and extensions involving 2-groups.

In the context of the concordance cosmology, structure formation in the Universe is the result of the amplification, by gravitational effects, of small perturbations in the primeval density field. This results in the formation of structures…