Strata of k-differentials on smooth curves parameterize sections of the k-th power of the canonical bundle with prescribed orders of zeros and poles. Define the tautological ring of the projectivized strata using the κ and ψ classes of moduli spaces of pointed smooth curves along with the class η = O(−1) of the Hodge bundle. We show that if there is no pole of order k, then the tautological rin...

Let R = k[x, y] denote the polynomial ring in two variables over an infinite field k. We study the Betti strata of the family G(H) parametrizing graded Artinian quotients of R = k[x, y] having given Hilbert function H . The Betti stratum Gβ(H) parametrizes all quotients A of having the graded Betti numbers determined by H and the minimal relation degrees β, with βi = dimk Tor R 1 (I, k)i. We re...

Using stable log maps, we introduce log twisted differentials extending the notion of abelian differentials to the Deligne-Mumford boundary of stable curves. The moduli stack of log twisted differentials provides a compactification of the strata of abelian differentials. The open strata can have up to three connected components, due to spin and hyperelliptic structures. We prove that the spin p...

This paper describes the functionality required for a development environment that supports stratified programming (SP), a novel software development method that we have proposed recently [1, 2]. In this paper we discuss the case when program strata are controlled outside the programming language and present the main features of the SPIDER environment for strata creation and SP program executio...

Looking for a document in a stack of papers is a difficult job. If the “strata” of the drawer contents is known, then locating will be much easier. Strata Drawer is a camera-enhanced cabinet used for storage. This cabinet has a single, deep drawer equipped with a camera, a depth-sensor and a computer. When a user places an object in the drawer and closes it, a photograph is automatically taken,...

Received: December 18, 2015 Revised: September 29, 2016 Accepted: October 18, 2016 Abstract: Background: Aiming at the challenges in control and perdition of roof strata which caused by the complexity of coal mine roof, the force and vibration characteristics of drill bit have been analyzed considering the coupling vibration between drill bit and coal rock, and the characteristics of coupled vi...