bi-gyrogroup: the group-like structure induced by bi-decomposition of groups

Bi-Gyrogroup: The Group-Like Structure Induced by Bi-Decomposition of Groups

‎The decomposition $Gamma=BH$ of a group $Gamma$ into a subset B ‎and a subgroup $H$ of $Gamma$ induces‎, ‎under general conditions‎, ‎a ‎group-like structure for B‎, ‎known as a gyrogroup‎. ‎The famous‎ concrete realization of a gyrogroup‎, ‎which motivated the emergence ‎of gyrogroups into the mainstream‎, ‎is the space of all ‎relativistically admissible velocities along with a binary ‎mbox{...

Timing-driven logic bi-decomposition

An approach for logic decomposition that produces circuits with reduced logic depth is presented. It combines two strategies: logic bi-decomposition of Boolean functions and tree-height reduction of Boolean expressions. It is a technology-independent approach that enables one to find tree-like expressions with smaller depths than the ones obtained by state-of-the-art techniques. The approach ca...

Bi-extensions of Formal Groups

Bi-harmonic Functions on Groups

| Two natural deenitions of bi-harmonic functions on countable groups are shown to essentially coincide. Criteria of absence of non-constant bounded bi-harmonic functions are formulated. A description of these functions for free groups is given. Fonctions bi-harmoniques sur les groupes R esum e R esum e | Nous montrons l' equivalence essentielle de deux d eenitions naturelles des fonctions bi-h...

Investigating the Longitudinal Optical Conductivity in Three-Layer Graphene Systems with Composes Mono-Bi-Bi and Bi-Mono-Bi and Bi-Bi-Mono

The longitudinal optical conductivity is the most important property for graphene-baseddevices. So investigating this property for spatially separated few-layer graphene systems analytically and numerically is the main purpose of our study. Each layer can be mono- or bi-layer graphene. The density-density correlation function has been screened by the dielectric function using the random p...

Bi-Decomposition of Multi-Valued Relations

This paper discusses an approach to decomposition of multivalued functions and relations into networks of two-input gates implementing multi-valued MIN and MAX operations. The algorithm exploits both the incompleteness of the initial specification and the flexibilities generated in the process of decomposition. Experimental results over a set of multi-valued benchmarks show that this approach o...