Related papers: Basis Criteria for Extending Generalized Splines

To every local complete intersection ring one may associate a so-called generic hypersurface. In this paper we introduce rank varieties for modules and complexes over the generic hypersurface. The definition uses extension of scalars,…

This paper generalize the idea of the authors in J. Pure Appl. Algebra 210 (2007) 437--445. Namely, we define and study a particular case of Gorenstein projective modules. We investigate some change of rings results for this new kind of…

The one-skeleton of a G-manifold M is the set of points p in M where $\dim G_p \geq \dim G -1$; and M is a GKM manifold if the dimension of this one-skeleton is 2. Goresky, Kottwitz and MacPherson show that for such a manifold this…

We observe that any regular Lie groupoid G over an manifold M fits into an extension $K \to G \to E$ of a foliation groupoid E by a bundle of connected Lie groups K. If $\FF$ is the foliation on M given by the orbits of E and T is a…

A graph G on n vertices is said to be extendable if G can be modified to form a new graph H on more than n vertices, while preserving the degrees of the vertices common to G and H. The added vertices all have the same degree and we define…

This paper generalizes a result of Lynn on the "degree" of an equivariant cohomology ring $H^*_G(X)$. The degree of a graded module is a certain coefficient of its Poincar\'{e} series, and is closely related to multiplicity. In the present…

A summation is a shift-invariant ${\rm R}$-module homomorphism from a submodule of ${\rm R}[[\sigma]]$ to ${\rm R}$ or another ring. [11] formalized a method for extending a summation to a larger domain by telescoping. In this paper, we…

We generalize Kauffman's famous formula defining the Jones polynomial of an oriented link in 3-space from his bracket and the writhe of an oriented diagram. Our generalization is an epimorphism between skein modules of tangles in compact…

We analyze the space of geometrically continuous piecewise polynomial functions or splines for quadrangular and triangular patches with arbitrary topology and general rational transition maps. To define these spaces of G 1 spline functions,…

Let $H$ be a group and $E$ a set such that $H \subseteq E$. We shall describe and classify up to an isomorphism of groups that stabilizes $H$ the set of all group structures that can be defined on $E$ such that $H$ is a subgroup of $E$. A…

Local properties of the fundamental group of a path-connected topological space can pose obstructions to the applicability of covering space theory. A generalized covering map is a generalization of the classical notion of covering map…

We investigate scalar restriction, scalar extension, and scalar coextension functors for graded modules, including their interplay with coarsening functors, graded tensor products, and graded Hom functors. This leads to several…

For a graph $E$, we introduce the notion of an extended $E$-algebraic branching system, generalising the notion of an $E$-algebraic branching system introduced by Gon\c{c}alves and Royer. We classify the extended $E$-algebraic branching…

The use of topological persistence in contemporary data analysis has provided considerable impetus for investigations into the geometric and functional-analytic structure of the space of persistence modules. In this paper, we isolate a…

In this paper we present a method for direct evaluation of generalized B-splines (GB-splines) via the local representation of these curves as piecewise functions. To accomplish this we introduce a local structure that makes GB-spline curves…

Our interest in this paper is a generalization of the additive Deligne-Simpson problem which is originally defined for Fuchsian differential equations on the Riemann sphere. We shall extend this problem to differential equations having an…

Let G be a Lie goup, let M and N be smooth connected G-manifolds, let f be a smooth G-map from M to N, and let P denote the fiber of f. Given a closed and equivariantly closed relative 2-form for f with integral periods, we construct the…

Let R be a Noetherian standard graded ring, and M and N two finitely generated graded R-modules. We introduce reg_R (M,N) by using the notion of generalized local cohomology instead of local cohomology, in the definition of regularity. We…

Splines come in a variety of flavors that can be characterized in terms of some differential operator L. The simplest piecewise-constant model corresponds to the derivative operator. Likewise, one can extend the traditional notion of total…

An R-algebra A is called E(R)-algebra if the canonical homomorphism from A to the endomorphism algebra End_RA of the R-module {}_R A, taking any a in A to the right multiplication a_r in End_R A by a is an isomorphism of algebras. In this…