Related papers: Orthogonal Frames of Translates
Vertex operator superalgebras are studied and various results on rational Vertex operator superalgebras are obtained. In particular, the vertex operator super subalgebras generated by the weight 1/2 and weight 1 subspaces are determined. It…
BGG-sequences offer a uniform construction for invariant differential operators for a large class of geometric structures called parabolic geometries. For locally flat geometries, the resulting sequences are complexes, but in general the…
Using simultaneously two operator identities, we consider the inversion of the convolution operators on a rectangular. The structure of the inverse operators and of some corresponding forms, which are important in signal processing, is…
Vertex operators, being families of birational transformations of infinite-dimensional algebraic ``varieties'' M, act on appropriate line bundles on M. However, they act on (meromorphic) sections only as_partial operators_: they are defined…
A contraction sequence of a graph consists of iteratively merging two of its vertices until only one vertex remains. The recently introduced twin-width graph invariant is based on contraction sequences. More precisely, if one puts red edges…
Multidimensional contractions of irreducible representations of Cayley--Klein orthogonal algebras in Gel'fand--Zetlin basis are considered. Contracted over different parameters, algebras can turn out to be isomorphic. In this case method of…
We provide a pipeline for generating syntax diagrams (also called railroad diagrams) from context free grammars. Syntax diagrams are a graphical representation of a context free language, which we formalize abstractly as a set of mutually…
Finite element codes typically use data structures that represent unstructured meshes as collections of cells, faces, and edges, each of which require associated coordinate systems. One then needs to store how the coordinate system of each…
This paper extends the existing theory of perfect reconstruction two-channel filter banks from bipartite graphs to non-bipartite graphs. By generalizing the concept of downsampling/upsampling we establish the frame of two-channel filter…
For a vertex operator algebra $V$ with conformal vector $\omega$, we consider a class of vertex operator subalgebras and their conformal vectors. They are called semi-conformal vertex operator subalgebras and semi-conformal vectors of…
We investigate the descriptional complexity of operations on semilinear sets. Roughly speaking, a semilinear set is the finite union of linear sets, which are built by constant and period vectors. The interesting parameters of a semilinear…
This article gives a procedure to convert a frame which is not a tight frame into a Parseval frame for the same space, with the requirement that each element in the resulting Parseval frame can be explicitly written as a linear combination…
We provide a criterion for a vertex operator superalgebra homomorphism from an affine vertex algebra to another vertex superalgebra to be conformal, and an additional criterion that guarantees that this homomorphism is surjective. This…
Frames in finite-dimensional vector spaces are spanning sets of vectors which provide redundant representations of signals. The Parseval frames are particularly useful and important, since they provide a simple reconstruction scheme and are…
We associate to every central simple algebra with involution of orthogonal type in characteristic two a totally singular quadratic form which reflects certain anisotropy properties of the involution. It is shown that this quadratic form can…
A congruence $\varepsilon$ on a semigroup $S$ is perfect if for any congruence classes $x\varepsilon$ and $y\varepsilon$ their product as subsets of $S$ coincides (as a set) with the congruence class $(xy)\varepsilon$. Perfect congruences…
In a simple picture, a Bessel beam is viewed as a transverse standing wave formed in the interference region between incoming and outgoing conical waves. Based on this interpretation we propose an optical resonator that supports modes that…
We investigate the class of bisymmetric and quasitrivial binary operations on a given set $X$ and provide various characterizations of this class as well as the subclass of bisymmetric, quasitrivial, and order-preserving binary operations.…
This paper is concerned with the convergence of power sequences and stability of Hilbert space operators, where "convergence" and "stability" refer to weak, strong and norm topologies. It is proved that an operator has a convergent power…
This paper deals with algorithms for producing and ordering lexical and nonlexical sequences of a given degree. The notion of "elementary operations" on positive integral sequences is introduced. Our main theorem answers the question of…