"Domain truncation" is the simple strategy of solving problems on y E [ o o , oo] by using a large but finite computational interval, [ L , L ] . Since u(y) is not a periodic function, spectral methods have usually employed a basis of Chebyshev polynomials, Tn(y/L). In this note, we show that because u(_+ L) must be very, very small if domain truncation is to succeed, it is always more efficien...

A modification of Katzman’s example is given to produce a two-generated ideal in a two-dimensional Noetherian integral domain for which the set of associated primes of all the Frobenius powers is infinite. A further modification yields a four-dimensional Noetherian integral domain and a five-dimensional Noetherian local integral domain for which an explicit second local cohomology module has in...

The purpose of this note is to present a criterion for an infinite collection of distinct hyperbolic 3-manifolds to be commensurably infinite. (Here, a collection of hyperbolic 3-manifolds is commensurably infinite if it contains representatives from infinitely many commensurability classes.) Namely, such a collection M is commensurably infinite if there is a uniform upper bound on the volumes ...

background: protein-protein interactions do not provide any direct information re­garding the domains within the proteins that mediate the interactions. the majority of proteins are multi domain proteins and the interaction between them is often defined by the pairs of their domains. most of the former studies focus only on interacting do­main pairs. however they do not consider the interaction...

It is shown that every dp-minimal integral domain R a local ring and for non-maximal prime ideal ℘ of R, the localization R℘ valuation ℘R℘ = ℘. Furthermore, if only its residue field infinite or finite maximal principal.

Abstract This paper describes the calculation of eddy currents in a cylindrical conductive rod of finite length due to a coaxial circular coil carrying an alternating current. The coil impedance variation with frequency is determined from the field for an arbitrary coaxial location of the coil. Expressions for electromagnetic field and impedance of a coil encircling an infinite cylindrical rod ...

let $r$ be an infinite ring. here we prove that if $0_r$ belongs to ${x_1x_2cdots x_n ;|; x_1,x_2,dots,x_nin x}$ for every infinite subset $x$ of $r$, then $r$ satisfies the polynomial identity $x^n=0$. also we prove that if $0_r$ belongs to ${x_1x_2cdots x_n-x_{n+1} ;|; x_1,x_2,dots,x_n,x_{n+1}in x}$ for every infinite subset $x$ of $r$, then $x^n=x$ for all $xin r$.

In generalized semi-infinite programming the feasible set is known to be not closed in general. In this paper, under natural and generic assumptions, the closure of the feasible set is described in explicit terms.

We describe a method for learning word embeddings with stochastic dimensionality. Our Infinite Skip-Gram (iSG) model specifies an energy-based joint distribution over a word vector, a context vector, and their dimensionality, which can be defined over a countably infinite domain by employing the same techniques used to make the Infinite Restricted Boltzmann Machine (Côté & Larochelle, 2015) tra...

We have studied the behavior of magnetic coercivity H # , across the geometric percolation in MBE grown epitaxial Ni films. By increasing a Cu buffer layer thickness, the morphology of Ni films changes from a collection of finite clusters to a single infinite cluster, while all other structural parameters remain constant. H # drops rapidly near the geometric percolation threshold. Atomic Force ...