Related papers: Complex spherical designs from group orbits
It is shown the construction of a module structure [2] with universe over a set of a particular kind of mathematical proofs, the base ring of this module will be built on a maximal consistent extension of a set of propositions, this…
We consider the basic features of complex dynamical and control systems. Special attention is paid to the problems of synthesis of dynamical models of complex systems, construction of efficient control models, and to the development of…
We introduce a notion of stable spherical variety which includes the spherical varieties under a reductive group $G$ and their flat equivariant degenerations. Given any projective space $\bP$ where $G$ acts linearly, we construct a moduli…
The concept of spherical $t$-design, which is a finite subset of the unit sphere, was introduced by Delsarte-Goethals-Seidel (1977). The concept of Euclidean $t$-design, which is a two step generalization of spherical design in the sense…
Combinatorial optimization can be described as the problem of finding a feasible subset that maximizes a objective function. The paper discusses combinatorial optimization problems, where for each dimension the set of feasible subsets is…
Using tools from computable analysis we develop a notion of effectiveness for general dynamical systems as those group actions on arbitrary spaces that contain a computable representative in their topological conjugacy class. Most natural…
Combinatorial $t$-designs have nice applications in coding theory, finite geometries and several engineering areas. The objective of this paper is to study how to obtain $3$-designs with $2$-transitive permutation groups. The incidence…
A finite spin system invariant under a symmetry group G is a very illustrative example of the finite group action on a set of mappings f:X->Y. In the case of spin systems X is a set of spin carriers and Y contains 2s+1 z-components -s<=m<=s…
We consider the unitary group $\U$ of complex, separable, infinite-dimensional Hilbert space as a discrete group. It is proved that, whenever $\U$ acts by isometries on a metric space, every orbit is bounded. Equivalently, $\U$ is not the…
Suppose that G is a finite, unitary reflection group acting on a complex vector space V and X is the fixed point subspace of an element of G. Define N to be the setwise stabilizer of X in G, Z to be the pointwise stabilizer, and C=N/Z. Then…
Several algorithms have been proposed to compute partitions of networks into communities that score high on a graph clustering index called modularity. While publications on these algorithms typically contain experimental evaluations to…
Let V be a finite dimensional vector space over the two element field. We compute orbits for the linear action of groups generated by transvections with respect to a certain class of bilinear forms on V. In particular, we compute orbits…
We calculate the higher topological complexity TC$_s$ for the complements of reflection arrangements, in other words for the pure Artin type groups of all finite complex reflection groups. In order to do that we introduce a simple…
We introduce and analyze a new geometric structure on topological surfaces generalizing the complex structure. To define this so called higher complex structure we use the punctual Hilbert scheme of the plane. The moduli space of higher…
The general form of the operators commuting with the ground representation (appearing in many physical problems within single particle approximation) of the group is found. With help of the modified group projector technique, this result is…
This exploratory paper considers the notion of a covering of a configuration and $G$-coverings which are coverings that are quotients under a semi-regular group action. We consider prime configurations, those which cannot $G$-cover other…
We extend recent orbit counts for finitely generated semigroups acting on $\mathbb{P}^N$ to certain infinitely generated, polarized semigroups acting on projective varieties. We then apply these results to semigroup orbits generated by some…
For each finite ordinal n, and each locally-finite group G of cardinality aleph-sub-n, we construct an (n+1)-dimensional, contractible CW-complex on which G acts with finite stabilizers. We use the complex to obtain information about…
A unitary t-design is a set of unitaries that is "evenly distributed" in the sense that the average of any t-th order polynomial over the design equals the average over the entire unitary group. In various fields -- e.g. quantum information…
It is argued that the two problems of choosing characterizations and models of complex systems should not be considered independently. A particular criterion for these choices, oriented on the potential usefulness of the results, is…