Related papers: Relative parametrization of linear multidimensiona…
In this paper, we construct indecomposable integrally closed modules of arbitrary rank over a two-dimensional regular local ring. The modules are quite explicitly constructed from a given complete monomial ideal. We also give structural and…
The problem of minimizing a polynomial over a set of polynomial inequalities is an NP-hard non-convex problem. Thanks to powerful results from real algebraic geometry, one can convert this problem into a nested sequence of…
In this paper, an algebraic theory for local rings of finite embedding dimension is developed. Several extensions of (Krull) dimension are proposed, which are then used to generalize singularity notions from commutative algebra. Finally,…
In the Inverse Matroid problem, we are given a matroid, a fixed basis $B$, and an initial weight function, and the goal is to minimally modify the weights -- measured by some function -- so that $B$ becomes a maximum-weight basis. The…
This article concerns linear parts of minimal resolutions of finitely generated modules over commutative local, or graded rings. The focus is on the linearity defect of a module, which marks the point after which the linear part of its…
We construct a complex entire function with arbitrary number of variables which has the following property: The infinite set consisting of all the values of all its partial derivatives of any orders at all algebraic points, including zero…
In this paper, we introduce a topology on the set of isomorphism classes of finitely generated modules over an associative algebra. Then we focus on the relative topology on the set of isomorphism classes of maximal Cohen--Macaulay modules…
This paper investigates model-order reduction methods for geometrically nonlinear structures. The parametrisation method of invariant manifolds is used and adapted to the case of mechanical systems expressed in the physical basis, so that…
Regularization is a critical technique for ensuring well-posedness in solving inverse problems with incomplete measurement data. Traditionally, the regularization term is designed based on prior knowledge of the unknown signal's…
Recently, we introduced Relative Resolution as a hybrid formalism for fluid mixtures [1]. The essence of this approach is that it switches molecular resolution in terms or relative separation: While nearest neighbors are characterized by a…
Ideals in the ring of power series in three variables can be classified based on algebra structures on their minimal free resolutions. The classification is incomplete in the sense that it remains open which algebra structures actually…
Incorporating a non-Euclidean variable metric to first-order algorithms is known to bring enhancement. However, due to the lack of an optimal choice, such an enhancement appears significantly underestimated. In this work, we establish a…
In this article, we recover singularly-perturbed linear differential systems from their turning points and reduce the rank of the singularity in the parameter to its minimal integer value. Our treatment is Moser-based; that is to say it is…
We present an approach for variational regularization of inverse and imaging problems for recovering functions with values in a set of vectors. We introduce regularization functionals, which are derivative-free double integrals of such…
All current investigations to analyze the derivational complexity of term rewrite systems are based on a single termination method, possibly preceded by transformations. However, the exclusive use of direct criteria is problematic due to…
A matrix optimization problem over an uncertain linear system on finite horizon (abbreviated as MOPUL) is studied, in which the uncertain transition matrix is regarded as a decision variable. This problem is in general NP-hard. By using the…
In this paper we study the finitely generated bigraded modules over a standard bigraded polynomial ring which are relative Cohen-Macaulay or relative unmixed with respect to one of the irrelevant bigraded ideals. A generalization of…
For an ill-posed inverse problem, particularly with incomplete and limited measurement data, regularization is an essential tool for stabilizing the inverse problem. Among various forms of regularization, the lp penalty term provides a…
Differential-elimination algorithms apply a finite number of differentiations and eliminations to systems of partial differential equations. For systems that are polynomially nonlinear with rational number coefficients, they guarantee the…
Primal-dual interior-point methods solve constrained convex optimization problems to tight tolerances with speed and robustness. Their solutions are also efficiently differentiable with respect to the problem data through the implicit…