Related papers: Multiplied configurations, series induced by quasi…
Novel geometries can be created by coupling internal states of atoms or molecules to mimic movement in real-space
In this note we observe that the notion of an induced representation has an analog for quasi-actions. We then use induced quasi-actions to refine some earlier rigidity results for product spaces.
We explain why, in a configuration space that is multiply connected, i.e., whose fundamental group is nontrivial, there are several quantum theories, corresponding to different choices of topological factors. We do this in the context of…
This paper defines and examines the basic properties of noncommutative analogues of almost complex structures, integrable almost complex structures, holomorphic curvature, cohomology, and holomorphic sheaves. The starting point is a…
We introduce a theory of multigraded Cayley-Chow forms associated to subvarieties of products of projective spaces. Two new phenomena arise: first, the construction turns out to require certain inequalities on the dimensions of projections;…
A combinatorial object representing schemas of, possibly skew, perspectives, called {\em a configuration of skew perspective} is defined. Some classifications of skew perspectives are presented.
New types of designs called nested space-filling designs have been proposed for conducting multiple computer experiments with different levels of accuracy. In this article, we develop several approaches to constructing such designs. The…
Abstract separation systems are a new unifying framework in which separations of graph, matroids and other combinatorial structures can be expressed and studied. We characterize the abstract separation systems that have representations as…
With the advancement of computer technology, there is a surge of interest in effective mapping methods for objects in higher-dimensional spaces. To establish a one-to-one correspondence between objects, higher-dimensional quasi-conformal…
Gauge invariance in discrete dynamical systems and its connection with quantization are considered. For a complete description of gauge symmetries of a system we construct explicitly a class of groups unifying in a natural way the space and…
The analysis of a timeseries can provide many new perspectives if it is accompanied by the assumption that the timeseries is generated from an underlying dynamical system. For example, statistical properties of the data can be related to…
Quasimetric spaces form a natural framework to study distance problems with an inherent directional asymmetry. We introduce a simple novel class of quasimetrics on probability simplices, inspired by the Chebyshev distance. It is shown that…
We introduce the notions of partial dynamical symmetry (PDS) and quasi dynamical symmetry (QDS) and demonstrate their relevance to nuclear spectroscopy, to quantum phase transitions and to mixed systems with regularity and chaos. The…
Using the concept of mixable shuffles, we formulate explicitly the quantum quasi-shuffle product, as well as the subalgebra generated by primitive elements of the quantum quasi-shuffle bialgebra. We construct a braided coalgebra structure…
Quasi-isometries are mappings on graphs, with distance-distortions parameterized by a multiplicative factor and an additive constant. The distance-distortions of quasi-isometries are in a general form that captures a wide range of…
Four-manifold theory is employed to study the existence of (twisted) generalized complex structures. It is shown that there exist (twisted) generalized complex structures that have more than one type change loci. In an example-driven…
We enumerate graph homomorphisms to quasi-complete graphs, i.e., graphs obtained from complete graphs by removing one edge. The source graphs are complete graphs, quasi-complete graphs, cycles, paths, wheels and broken wheels. These…
A nested coordinate system is a reassigning of independent variables to take advantage of geometric or symmetry properties of a particular application. Polar, cylindrical and spherical coordinate systems are primary examples of such a…
We present a unified theoretical and computational framework that bridges mathematical quasiperiodicity with classical crystallographic models. Based on a rigorous cut-and-projection construction, the proposed proximal coincidence point set…
The theory of quasi-Lie systems, i.e. systems of first order ordinary differential equations which can be related via a generalised flow to Lie systems, is extended to systems of partial differential equations and its applications to…