相关论文: Diagonal bases in Orlik-Solomon type algebras
A matroid is a combinatorial structure that captures and generalizes the algebraic concept of linear independence under a broader and more abstract framework. Matroids are closely related with many other topics in discrete mathematics, such…
We give conditions for local diagonalization of an analytic operator family to a diagonal operator polynomial. The families are acting between real or complex Banach spaces. The basic assumption is given by stabilization of the Jordan…
The Orlik-Solomon algebra of a matroid can be considered as a quotient ring over the exterior algebra E. At first we study homological properties of E-modules as e.g. complexity, depth and regularity. In particular, we consider modules with…
The Orlik-Solomon algebra is the cohomology ring of the complement of a hyperplane arrangement A in C^n; it is the quotient of an exterior algebra E(V) on |A| generators. Orlik and Terao introduced a commutative analog S(V)/I of the…
An explicit algorithmic construction is given for orthogonal bases for spaces of homogeneous polynomials, in the context of Hermitean Clifford analysis, which is a higher dimensional function theory centred around the simultaneous null…
This paper completes a series devoted to explicit constructions of finite-dimensional irreducible representations of the classical Lie algebras. Here the case of odd orthogonal Lie algebras (of type B) is considered (two previous papers…
In this work we will treat the spurious eigenvalues obstacle that appears in the computation of the radial Dirac eigenvalue problem using numerical methods. The treatment of the spurious solution is based on applying Petrov-Galerkin finite…
Closure system on a finite set is a unifying concept in logic programming, relational data bases and knowledge systems. It can also be presented in the terms of finite lattices, and the tools of economic description of a finite lattice have…
Zernike polynomials are widely used in optics and ophthalmology due to their direct connection to classical optical aberrations. While orthogonal on the unit disk, their application to discrete data or non-circular domains--such as…
The invariants of solvable Lie algebras with nilradicals isomorphic to the algebra of strongly upper triangular matrices and diagonal nilindependent elements are studied exhaustively. Bases of the invariant sets of all such algebras are…
In La G\'eom\'etrie, Descartes proposed a balance between geometric constructions and symbolic manipulation with the introduction of suitable ideal machines. In modern terms, that is a balance between analog and symbolic computation.…
Orbital semilattices are introduced as bounded semilattices that are, in addition, equipped with an outer multiplication (a semigroup action) and diagonals (a concept borrowed from cylindric algebra), where each semilattice element has a…
We investigate the representation of diffeomorphisms in Connes' Spectral Triples formalism. By encoding the metric and spin structure in a moving frame, it is shown on the paradigmatic example of spin semi-Riemannian manifolds that the…
A deformation of the Orlik-Solomon algebra of a matroid M is defined as a quotient of the free associative algebra over a commutative ring R with 1. It is shown that the given generators form a Groebner basis and that after suitable…
Sets of orthogonal basis functions over two-dimensional circular areas--most often representing pupils in optical applications--are known in the literature for the full circle (Zernike or Jacobi polynomials) and the annulus. This work…
We recall a numerical criteria for Cohen--Macaulayness related to system of parameters, and introduce monomial ideals of K\"onig type which include the edge ideals of K\"onig graphs. We show that a monomial ideal is of K\"onig type if and…
In this paper we determine the facets of the polyhedral cone generated by the exponent set of the monomials defining the base ring associated to some transversal polymatroid. We need the description of these facets to find the canonical…
The construction of the Varchenko matrix for hyperplane arrangements, first introduced by Alexandre Varchenko, extends naturally to oriented matroids. In this paper, we generalize the theorem of Gao and Zhang by proving that the Varchenko…
The invariants of solvable triangular Lie algebras with one nilindependent diagonal element are studied exhaustively. Bases of the invariant sets of all such algebras are constructed using an original algebraic algorithm based on Cartan's…
A decomposition of a higher order linear differential operator with polynomial coefficients into a direct sum of two factor operators is obtained. This leads to a lower echelon matrix representation for operators of the above mentioned type…