Related papers: Chirality and Racemization on Isotopy Classes of L…
Let $G$ be a finite group and $H$ a subgroup of $G$. Each left transversal (with identity) of $H$ in $G$ has a left loop (left quasigroup with identity) structure induced by the binary operation of $G$. We say two left transversals are…
An answer to the question investigated in this paper brings a new characterization of internal groupoids such that: (a) it holds even when finite limits are not assumed to exist; (b) it is a full subcategory of the category of…
The Isomorphism Conjecture is a conceptional approach towards a calculation of the algebraic K-theory of a group ring RG, where G is an infinite group. In this paper we prove the conjecture in dimensions n<2 for fundamental groups of closed…
Using an algebraic point of view we present an introduction to the groupoid theory, that is, we give fundamental properties of groupoids as, uniqueness of inverses and properties of the identities, and study subgroupoids, wide subgroupoids…
Chirality is a pervasive form of symmetry that is intimately connected to the physical properties of solids, as well as the chemical and biological activity of molecular systems. However, its control with light is challenging, because…
We present a generalized Landau-Brazovskii theory for the solidification of chiral molecules on a spherical surface. With increasing sphere radius one encounters first intervals where robust achiral density modulations appear with…
The paper is devoted to study the behavior of quasitopological homotopy groups on inverse limit spaces. More precisely, we present some conditions under which the quasitopological homotopy group of an inverse limit space and especially a…
According to our previous results, the conjugacy class of the involution induced by the complex conjugation in the homology of a real non-singular cubic fourfold determines the fourfold up to projective equivalence and deformation. Here, we…
The isotopic invariance or universality of types and varieties of quasigroups and loops described by one or more equivalent identities has been of interest to researchers in loop theory in the recent past. A variety of quasigroups(loops)…
In \cite{Oh22}, the second author defined a complex of groups decomposition of the fundamental group of a finitely generated 2-dimensional special group, called an \emph{intersection complex}, which is a quasi-isometry invariant. In this…
We suggest that electromagnetic chirality, generally displayed by 3D or 2D complex chiral structures, can occur in 1D patterned composites whose components are achiral. This feature is highly unexpected in a 1D system which is geometrically…
This paper presents a first-principle and global perspective of electromagnetic chirality. It follows for this purpose a bottom-up construction, from the description of chiral particles or metaparticles (microscopic scale), through the…
Chirality, either of light or matter, has proved to be very practical in biosensing and nanophotonics. However, the fundamental understanding of its temporal dynamics still needs to be discovered. A realistic setup for this are the…
We show, using exact lattice chirality, that partition functions of lattice gauge theories with vectorlike fermion representations can be split into "light" and "mirror" parts, such that the "light" and "mirror" representations are chiral.…
Using the theory of group action, we first introduce the concept of the automorphism group of an exponential family or a graphical model, thus formalizing the general notion of symmetry of a probabilistic model. This automorphism group…
Using samples of structures identified by a multi-scale decomposition from numerical simulation, we analyze the scale-dependence of the virialization of clusters. We find that beyond the scale of full virialization there exists a radius…
We consider Lie groups equipped with arbitrary distances. We only assume that the distance is left-invariant and induces the manifold topology. For brevity, we call such object metric Lie groups. Apart from Riemannian Lie groups,…
We present a new method for regularizing chiral theories on the lattice. The arbitrariness in the regularization is used in order to decouple massless replica fermions. A continuum limit with only one fermion is obtained in perturbation…
We develop realizability models of intensional type theory, based on groupoids, wherein realizers themselves carry non-trivial (non-discrete) homotopical structure. In the spirit of realizability, this is intended to formalize a homotopical…
A quasi-isometry between two connected graphs is measure-scaling if one can control precisely the sizes of pre-images of finite subsets. Such a notion is motivated by the work of Eskin-Fisher-Whyte on lamplighters over $\mathbb{Z}$ and the…