Related papers: Almost discrete valuation domains

As in Zariski's Uniformization Theorem we show that a valuation ring $V$ of characteristic $p>0$ of dimension one is a filtered direct limit of smooth ${\bf F}_p$-algebras under some conditions of transcendence degree. Under mild…

In a locally $\lambda$-presentable category, with $\lambda$ a regular cardinal, classes of objects that are injective with respect to a family of morphisms whose domains and codomains are $\lambda$-presentable, are known to be characterized…

AAA rational approximation has normally been carried out on a discrete set, typically hundreds or thousands of points in a real interval or complex domain. Here we introduce a continuum AAA algorithm that discretizes a domain adaptively as…

In this note, we show that the algebraic K-theory of generalized archimedean valuation rings occurring in Durov's compactification of the spectrum of a number ring is given by stable homotopy groups of certain classifying spaces. We also…

Let $D$ be an integral domain and $\star$ a semistar operation stable and of finite type on it. In this paper we define the semistar dimension (inequality) formula and discover their relations with $\star$-universally catenarian domains and…

A deductive system is structurally complete if its admissible inference rules are derivable. For several important systems, like modal logic S5, failure of structural completeness is caused only by the underivability of passive rules, i.e.…

Suppose that $k$ is an arbitrary field. Consider the field $k((x_1,...,x_n))$, which is the quotient field of the ring $k[[x_1,...,x_n]]$ of formal power series in the variables $x_1,...,x_n$, with coefficients in $k$. Suppose that $\sigma$…

The spectrum of the Dirichlet Laplacian on any quasi-conical open set coincides with the non-negative semi-axis. We show that there is a connected quasi-conical open set such that the respective Dirichlet Laplacian has a positive (embedded)…

We prove almost sure invariance principle, a strong form of approximation by Brownian motion, for non-autonomous holomorphic dynamical systems on complex projective space $\Bbb{P}^k$ for H\"{o}lder continuous and DSH observables.

We consider Steklov eigenvalues of nearly hyperspherical domains in $\mathbb{R}^{d + 1}$ with $d\ge 3$. In previous work, treating such domains as perturbations of the ball, we proved that the Steklov eigenvalues are analytic functions of…

An integral domain $R$ is \emph{perinormal} if every local going-down overring is a localization of $R$ and \emph{globally perinormal} if every going-down overring is a localization of $R$. In this paper, I introduce notions of graded…

We call a right module $M$ (strongly) virtually regular if every (finitely generated) cyclic submodule is isomorphic to a direct summand. $M$ is said to be completely virtually regular if every submodule is virtually regular. In this paper,…

We classify the cosmological behaviors of the domain wall under junctions between two spacetimes in terms of various parameters: cosmological constants of bulk spacetime, a tension of a domain wall, and mass parameters of the black…

Let $D$ be a bounded domain in $\mathbb R^n,$ with smooth boundary. Denote $V_D(\omega,t), \ \omega \in S^{n-1}, t \in \mathbb R,$ the Radon transform of the characteristic function $\chi_{D}$ of the domain $D,$ i.e., the $(n-1)-$…

Let $G$ be a random $d$-regular graph. We prove that for every constant $\alpha > 0$, with high probability every eigenvector of the adjacency matrix of $G$ with eigenvalue less than $-2\sqrt{d-2}-\alpha$ has $\Omega(n/$polylog$(n))$ nodal…

This paper focuses on investigating generalized relative interior notions for sets in locally convex topological vector spaces with particular attentions to graphs of set-valued mappings and epigraphs of extended-real-valued functions. We…

Continuity of set-valued maps is hereby revisited: after recalling some basic concepts of variational analysis and a short description of the State-of-the-Art, we obtain as by-product two Sard type results concerning local minima of scalar…

It is shown that a local ring R of bounded module type is an almost maximal valuation ring if there exists a non-maximal prime ideal J such that R/J is a maximal valuation domain.

In this paper, we introduce a new homological invariant called quasi-projective dimension, which is a generalization of projective dimension. We discuss various properties of quasi-projective dimension. Among other things, we prove the…

Vector-valued learning, where the output space admits a vector-valued structure, is an important problem that covers a broad family of important domains, e.g. multi-task learning and transfer learning. Using local Rademacher complexity and…