Related papers: On graded Going down domains
The moduli stack of Deligne-Mumford stable curves of genus g admits a stratification, so that the number of nodes of the curves belonging to one stratum is constant. The irreducible components of the stratum corresponding to curves with…
Many problems encountered in science and engineering can be formulated as estimating a low-rank object (e.g., matrices and tensors) from incomplete, and possibly corrupted, linear measurements. Through the lens of matrix and tensor…
We study the graded polynomial identities with a homogeneous involution on the algebra of upper triangular matrices endowed with a fine group grading. We compute their polynomial identities and a basis of the relatively free algebra,…
In a previous article (see \cite{CNP}), we introduced and analyzed ring-theoretic properties of object unital $\mathcal{G}$-graded rings $R$, where $\mathcal{G}$ is a groupoid. In the present article, we analyze the category $\grmod$ of…
We study stable semistar operations defined over a Pr\"ufer domain, showing that, if every ideal of a Pr\"ufer domain $R$ has only finitely many minimal primes, every such closure can be described through semistar operations defined on…
We define a notion of grading of a monoid T in a monoidal category C, relative to a class of morphisms M (which provide a notion of M-subobject). We show that, under reasonable conditions (including that M forms a factorization system),…
In this version small mistakes are corrected and the exposition is changed as suggested by the referee (to appear in Canadian Journal of Mathematics). The first main result of the paper is a criterion for a partially commutative group $\GG$…
In 3+1 space-time dimensions, fourth order derivative gravity is perturbatively renormalizable. Here it is shown that it describes a unitary theory of gravitons (with/without an additional scalar) in a limited coupling parameter space which…
The aim of this article is to introduce the concept of graded $2$-absorbing coprimary submodules as a generalization of graded strongly $2$-absorbing second submodules, and explore some properties of this class. A non-zero graded…
We study the G-centers of G-graded monoidal categories where G is an arbitrary group. We prove that for any spherical G-fusion category C over an algebraically closed field such that the dimension of the neutral component of C is non-zero,…
We introduce and investigate the category of factorization of a multiplicative, commutative, cancellative, pre-ordered monoid $A$, which we denote $\mathcal{F}(A)$. The objects of $\mathcal{F}(A)$ are factorizations of elements of $A$, and…
The main purpose of this paper is to define dynamical degrees for rational maps over an algebraic closed field of characteristic zero and prove some basic properties (such as log-concavity) and give some applications. We also define…
For finite connected graphs $\Gamma$ and $G$, with $\Gamma$ admitting a free involution $\tau$, we characterize the based homotopy classes $\alpha\in[\Gamma,G]$ for which the Borsuk-Ulam property holds in the sense of Gon\c{c}alves, Guaschi…
We prove a homogenization theorem for a class of quadratic convolution energies with random coefficients. Under suitably stated hypotheses of ergodicity and stationarity we prove that the $\Gamma$-limit of such energy is almost surely a…
We study actions of discrete subgroups $\Gamma$ of semi-simple Lie groups $G$ on associated oriented flag manifolds. These are quotients $G/P$, where the subgroup $P$ lies between a parabolic subgroup and its identity component. For Anosov…
Polarized ferrofluids, lipid monolayers and magnetic bubbles form domains with deformable boundaries. Stability analysis of these domains depends on a family of nontrivial integrals. We present a closed form evaluation of these integrals as…
We introduce classes of graphs with bounded expansion as a generalization of both proper minor closed classes and degree bounded classes. Such classes are based on a new invariant, the greatest reduced average density (grad) of G with rank…
We prove that if $R$ is a ring that is object unital and strongly graded by a groupoid $\Gamma$, and if $\Delta$ is a wide subgroupoid of $\Gamma$, then $R/R_\Delta$ is separable if and only if, for each $e \in \Gamma_0$, there exist $f \in…
We study a novel spline-like basis, which we name the "falling factorial basis", bearing many similarities to the classic truncated power basis. The advantage of the falling factorial basis is that it enables rapid, linear-time computations…
The so called generalized down-up algebras are revisited from a viewpoint of Gr\"obner basis theory. Particularly it is shown explicitly that generalized down-up algebras are solvable polynomial algebras (provided $\lambda\omega\ne 0$), and…