Chomsky (1959a) presented an algorithm for constructing a finite transducer that is strongly equivalent to a Chomsky-normal-form context-free grammar for all sentences generated by that grammar with up to any specified finite degree of center embedding. This article presents a new solution using a variety of COORDINATE GRAMMAR to assign nonembedding (paratactic) structures strongly equivalent t...

In this article we consider a generalization of Donkon-Koppinen filtrations for coordinate superalgebras of general linear supergroups. More precisely, if G = GL(m|n) is a general linear supergroup of (super)degree (m|n), then its coordinate superalgebra K[G] is a natural G × G-supermodule. For any finitely generated ideal Γ ⊆ Λ × Λ the largest supersubmodule OΓ(K[G]), whose all composition fac...

Harmonic slicing has in recent years become a standard way of prescribing the lapse function in numerical simulations of general relativity. However, as was first noticed by Alcubierre [Phys. Rev. D 55, 5981 (1997)], numerical solutions generated using this slicing condition can show pathological behaviour. In this paper, analytic and numerical methods are used to examine harmonic slicings of K...

Alan Newell famously asserted that "You can't play 20 questions with nature and win" (Newell, A. (1973). You can't play 20 questions with nature and win. In W.G. Chase (Ed.), Visual information processing. New York: Academic Press.), and specifically focused on the futility of studying binary distinctions. However, the distinction between categorical and coordinate spatial relations representat...

This paper provides auxiliary results for our general scheme of computed tomography. In 3D parallel-beam geometry, we first demonstrate that the inverse Fourier transform in different coordinate systems leads to different reconstruction formulas and explain why the Radon formula cannot directly work with truncated projection data. Also, we introduce a gamma coordinate system, analyze its proper...