Related papers: Primary decomposition of modules: a computational …
Recently, we have endowed various categories of groups with topologies. The purpose of this paper is to introduce on these categories others topologies which are statistically more suitable to study well-known problems in groups theory. We…
Narayanan showed the existence of the principal partition sequence of a submodular function, a structure with numerous applications in areas such as clustering, fast algorithms, and approximation algorithms. In this work, motivated by two…
We consider a general concept of composition and decomposition of objects, and discuss a few natural properties one may expect from a reasonable choice thereof. It will be demonstrated how this leads to multiplication and co- multiplication…
We introduce a framework for online structure theory. Our approach generalises notions arising independently in several areas of computability theory and complexity theory. We suggest a unifying approach using operators where we allow the…
Suppose $\mathbb{K}$ is a large enough field and $\mathcal{P} \subset \mathbb{K}^2$ is a fixed, generic set of points which is available for precomputation. We introduce a technique called \emph{reshaping} which allows us to design…
We study representations of the double affine Lie algebra associated to a simple Lie algebra. We construct a family of indecomposable integrable representations and identify their irreducible quotients. We also give a condition for the…
Submodularity is a fundamental phenomenon in combinatorial optimization. Submodular functions occur in a variety of combinatorial settings such as coverage problems, cut problems, welfare maximization, and many more. Therefore, a lot of…
This paper is a detailed study of finite-dimensional modules defined on bicomplex numbers. A number of results are proved on bicomplex square matrices, linear operators, orthogonal bases, self-adjoint operators and Hilbert spaces, including…
Let $R$ be a polynomial ring over a field. We describe the extremal rays and the facets of the cone of local cohomology tables of finitely generated graded $R$-modules of dimension at most two. Moreover, we show that any point inside the…
Our overall goal is to unify and extend some results in the literature related to the approximation of generating functions of finite and infinite sequences over a field by rational functions. In our approach, numerators play a significant…
In model selection problems for machine learning, the desire for a well-performing model with meaningful structure is typically expressed through a regularized optimization problem. In many scenarios, however, the meaningful structure is…
The structure of octonionic bimodules is formulated in this paper. It turns out that every octonionic bimodule is a tensor product, the category of octonionic bimodules is isomorphic to the category of real vector spaces. We show that there…
We propose a categorical and algebraic study of quantale modules. The results and constructions presented are also applied to abstract algebraic logic and to image processing tasks.
The classical persistence algorithm computes the unique decomposition of a persistence module implicitly given by an input simplicial filtration. Based on matrix reduction, this algorithm is a cornerstone of the emergent area of topological…
We study three fundamental topics in the representation theory of disconnected algebraic groups whose identity component is reductive: (i) the classification of irreducible representations; (ii) the existence and properties of Weyl and dual…
Recent results for rotations expressed as polynomials of spin matrices are derived here by elementary differential equation methods. Structural features of the results are then examined in the framework of biorthogonal systems, to obtain an…
The aim of this paper is to introduce a method for computing Hilbert decompositions (and consequently the Hilbert depth) of a finitely generated multigraded module $M$ over the polynomial ring $K[X_1,..., X_n]$ by reducing the problem to…
This study presents a theoretical model for a self-replicating mechanical system inspired by biological processes within living cells and supported by computer simulations. The model decomposes self-replication into core components, each of…
We first present a filtration on the ring L of Laurent polynomials such that the direct sum decomposition of its associated graded ring gr L agrees with the direct sum decomposition of gr L, as a module over the complex general linear Lie…
It is shown the construction of a module structure [2] with universe over a set of a particular kind of mathematical proofs, the base ring of this module will be built on a maximal consistent extension of a set of propositions, this…