Related papers: On Camina pairs and the Fitting subgroup
We address the conjectures left by the recent article by Ferreira et al. titled ``Commuting maps and identities with inverses on alternative division rings.'' We also present an example showing the necessity of the conditions of the results…
In this short note we present a set of interesting and useful properties of a one-parameter family of sequences including factorial and subfactorial, and their relations to the Gamma function and the incomplete Gamma function.
The aim of this paper is to define the structure of a ring on a graded cohomology group of a precubical set in coefficients in a ring with unit.
In this study, we propose a Kernel-PCA model designed to capture structure-function relationships in a protein. This model also enables ranking of reaction coordinates according to their impact on protein properties. By leveraging machine…
We consider the problem of improving kernel approximation via randomized feature maps. These maps arise as Monte Carlo approximation to integral representations of kernel functions and scale up kernel methods for larger datasets. Based on…
We introduce the concept of directional coupling, i.e., the selective transfer of a state between adjacent quantum wires, in the context of quantum computing and short-distance communication. Our analysis rests upon a mathematical analogy…
PPI network alignment aims to find topological and functional similarities between networks of different species. Several alignment approaches have been proposed. Each of these approaches relies on a different alignment method and uses…
This is a short survey paper, partly meant as a research announcement. Its purpose is to highlight some aspects of the interplay between quantales, inverse semigroups, and groupoids. Many of the results mentioned have not yet been presented…
Model misspecification can create significant challenges for the implementation of probabilistic models, and this has led to development of a range of robust methods which directly account for this issue. However, whether these more…
We address the non-binary coupling of identical angular momenta based upon the representation theory for the symmetric group. A correspondence is pointed out between the complete set of commuting operators and the reference-frame-free…
We study relationships between certain algebraic properties of groups and rings definable in a first order structure or $*$-closed in a compact $G$-space. As a consequence, we obtain a few structural results about $\omega$-categorical rings…
Kernel-based learning algorithms are widely used in machine learning for problems that make use of the similarity between object pairs. Such algorithms first embed all data points into an alternative space, where the inner product between…
The geometry of spaces with indefinite inner product, known also as Krein spaces, is a basic tool for developing Operator Theory therein. In the present paper we establish a link between this geometry and the algebraic theory of…
The integral cohomology ring of the Hilbert scheme of n-tuples on the affine plane is shown to be isomorphic to the graded ring associated to a filtration of the ring of integral class functions on the symmetric group.
In generalization of knot quandles we introduce similar algebraic structures associated with arbitrary pairs consisting of a path-connected topological space and its path-connected subspace.
We introduce the concept of a partial abstract kernel associated to a group G and a semilattice of groups A and relate the partial cohomology group H^3(G,C(A)) with the obstructions to the existence of admissible extensions of A by G which…
Sequences with good correlation properties are widely used in engineering applications, especially in the area of communications. Among the known sequences, cyclotomic families have the optimal autocorrelation property. In this paper, we…
E. Bunch, P. Lofgren, A. Rapp and D. N. Yetter [J. Knot theory Ramifications (2010)] pointed out that by considering inner automorphism groups of quandles, one have a functor from the category of quandles with surjective homomorphisms to…
In this paper we continue to investigate a certain class of Hankel-like positive definite kernels using their associated orthogonal polynomials. The main result of this paper is about the structure of this kind of kernels.
In this article we survey, and make a few new observations about, the surprising connection between sub-monoids of mapping class groups and interesting geometry and topology in low-dimensions.