Related papers: Seminormalization package for Macaulay2
A program package, which facilitates computations in the framework of Analytic approach to QCD, is developed and described in details. The package includes the explicit expressions for relevant spectral functions calculated up to the…
The semiclassical trace formula provides the basic construction from which one derives the semiclassical approximation for the spectrum of quantum systems which are chaotic in the classical limit. When the dimensionality of the system…
We characterize when the monomial maximal ideal of a simplicial affine semigroup ring has a monomial minimal reduction. When this is the case, we study the Cohen-Macaulay and Gorenstein properties of the associated graded ring and provide…
In this article, we describe the theoretical foundations of the Macaulay2 package ConnectionMatrices and explain how to use it. For a left ideal in the Weyl algebra that is of finite holonomic rank, we implement the computation of the…
This is a survey paper on applications of mathematics of semirings to numerical analysis and computing. Concepts of universal algorithm and generic program are discussed. Relations between these concepts and mathematics of semirings are…
We present an approach for the semiclassical treatment of open quantum systems. An expansion into localized states allows restriction of a simulation to a fraction of the environment that is located within a predefined vicinity of the…
Macaulay Duality, between quotients of a polynomial ring over a field, annihilated by powers of the variables, and finitely generated submodules of the ring's graded dual, is generalized over any Noetherian ring, and used to provide…
Reduze is a computer program for reducing Feynman integrals to master integrals employing a variant of Laporta's reduction algorithm. This article describes version 2 of the program. New features include the distributed reduction of single…
We present a renormalization scheme which simplifies the dynamics of an important class of interacting multi-qubit systems. We show that a wide class of M+1 qubit systems can be reduced to an equivalent n+1 qubit system with n equal to, or…
We establish system of equations for single function normalized tight frame wavelets with compact supports associated with $2\times 2$ expansive integral matrices in $L^2(\R^2)$.
The aim of this manuscript is to give some basic notions related to numerical semigroups, and from these on the one hand describe a classical application to the study of singularities of plane algebraic curves, and on the other, show how…
In this note, we give several characterizations of left pure-semisimple in terms of the (pre)envelope, (pre)cover, direct limits, direct sums, inverse limits and direct products properties of pure-projective modules or pure-injective…
In this paper, we proceed with the analysis started in \cite{bib:braga-mor-souza} and, using the Renormalization Group method, we obtain logarithmic corrections to the decay of solutions for a class of nonlinear integral equations whenever…
This is an up-to-date introduction to, and overview of, marginal likelihood computation for model selection and hypothesis testing. Computing normalizing constants of probability models (or ratio of constants) is a fundamental issue in many…
Zhou defined $\delta$-semiperfect rings as a proper generalization of semiperfect rings. The purpose of this paper is to discuss relative notions of supplemented modules and to show that the semiperfect rings are precisely the semilocal…
This paper describes the generation of initial conditions for numerical simulations in cosmology with multiple levels of resolution, or multiscale simulations. We present the theory of adaptive mesh refinement of Gaussian random fields…
The purpose of this paper is to characterize one-dimensional local domains, or more in general reduced, in terms of its Macaulay's inverse system. This leads to study almost finitely generated modules in the divided power ring. We…
This paper explores the use of 2-categorical technology for describing and reasoning about complex quantum procedures. We give syntactic definitions of a family of complementary measurements, and of quantum key distribution, and show that…
These course notes are about computing modular forms and some of their arithmetic properties. Their aim is to explain and prove the modular symbols algorithm in as elementary and as explicit terms as possible, and to enable the devoted…
We propose a Semi-Lagrangian scheme coupled with Radial Basis Function interpolation for approximating a curvature-related level set model, which has been proposed by Zhao et al. in \cite{ZOMK} to reconstruct unknown surfaces from sparse,…