Revisiting the Equivalence Problem for Finite Multitape Automata

The decidability of determining equivalence of deterministic multitape automata (or transducers) was a longstanding open problem until it was resolved by Harju and Karhum\"{a}ki in the early 1990s. Their proof of decidability yields a co_NP upper bound, but apparently not much more is known about the complexity of the problem. In this paper we give an alternative proof of decidability, which follows the basic strategy of Harju and Karhumaki but replaces their use of group theory with results on matrix algebras. From our proof we obtain a simple randomised algorithm for deciding language equivalence of deterministic multitape automata and, more generally, multiplicity equivalence of nondeterministic multitape automata. The algorithm involves only matrix exponentiation and runs in polynomial time for each fixed number of tapes. If the two input automata are inequivalent then the algorithm outputs a word on which they differ

Room temperature ferromagnetism in chemically synthesized ZnO rods

We report structural and magnetic properties of pure ZnO rods using X-ray diffraction (XRD), magnetization hysteresis (M-H) loop and near edge x-ray fine structure spectroscopy (NEXAFS) study at O K edge. Sample of ZnO was prepared by co-precipitation method. XRD and selective area electron diffraction measurements infer that ZnO rods exhibit a single phase polycrystalline nature with wurtzite lattice. Field emission transmission electron microscopy, field emission scanning electron microscopy micrographs infers that ZnO have rod type microstructures with dimension 200 nm in diameter and 550 nm in length. M-H loop studies performed at room temperature display room temperature ferromagnetism in ZnO rods. NEXAFS study reflects absence of the oxygen vacancies in pure ZnO rods.Comment: 8 Pages, 3 Figure

Tverberg-type theorems for intersecting by rays

In this paper we consider some results on intersection between rays and a given family of convex, compact sets. These results are similar to the center point theorem, and Tverberg's theorem on partitions of a point set

Tests of the random phase approximation for transition strengths

We investigate the reliability of transition strengths computed in the random-phase approximation (RPA), comparing with exact results from diagonalization in full $0\hbar\omega$ shell-model spaces. The RPA and shell-model results are in reasonable agreement for most transitions; however some very low-lying collective transitions, such as isoscalar quadrupole, are in serious disagreement. We suggest the failure lies with incomplete restoration of broken symmetries in the RPA. Furthermore we prove, analytically and numerically, that standard statements regarding the energy-weighted sum rule in the RPA do not hold if an exact symmetry is broken.Comment: 11 pages, 7 figures; Appendix added with new proof regarding violation of energy-weighted sum rul

Centrality dependence of charged-particle pseudorapidity distributions from d+Au collisions at sqrt(s_{NN})=200 GeV

Charged-particle pseudorapidity densities are presented for the d+Au reaction at sqrt{s_{NN}}=200 GeV with -4.2 <= eta <= 4.2$. The results, from the BRAHMS experiment at RHIC, are shown for minimum-bias events and 0-30%, 30-60%, and 60-80% centrality classes. Models incorporating both soft physics and hard, perturbative QCD-based scattering physics agree well with the experimental results. The data do not support predictions based on strong-coupling, semi-classical QCD. In the deuteron-fragmentation region the central 200 GeV data show behavior similar to full-overlap d+Au results at sqrt{s_{NN}}=19.4 GeV.Comment: 4 pages, 3figures; expanded discussion of uncertainties; added 60-80% centrality range; added additional discussion on centrality selection bia

Scanning the phases of QCD with BRAHMS

BRAHMS has the ability to study relativistic heavy ion collisions from the final freeze-out of hadrons all the way back to the initial wave-function of the gold nuclei. This is accomplished by studying hadrons with a very wide range of momenta and angles. In doing so we can scan various phases of QCD, from a hadron gas, to a quark gluon plasma and perhaps to a color glass condensate.Comment: 8 pages, 6 figures, proceedings of plenary talk at Quark Matter 2004 conferenc

High Pt Hadron Spectra at High Rapidity

We report the measurement of charged hadron production at different pseudo-rapidity values in deuteron+gold as well as proton+proton collisions at $sqrt{s_{NN}}$ = 200GeV at RHIC. The nuclear modification factors $R_{dAu}$ and $R_{cp}$ are used to investigate new behaviors in the deuteron+gold system as function of rapidity and the centrality of the collisions respectively.Comment: Nine pages 4 figures to be published in the QM2004 Proceedings, typos corrected and one reference adde

Letters from William Burnside to Robert Fricke: Automorphic Functions, and the Emergence of the Burnside Problem

Two letters from William Burnside have recently been found in the Nachlass of Robert Fricke that contain instances of Burnside's Problem prior to its first publication. We present these letters as a whole to the public for the first time. We draw a picture of these two mathematicians and describe their activities leading to their correspondence. We thus gain an insight into their respective motivations, reactions, and attitudes, which may sharpen the current understanding of professional and social interactions of the mathematical community at the turn of the 20th century.Comment: documentclass amsart, 17 page

Meeresatlas: Daten und Fakten über unseren Umgang mit dem Ozean

Ohne das Meer gäbe es kein Leben auf unserem Planeten. Es regelt weitgehend das Klima, gibt uns Nahrung und liefert Energie. Darüber hinaus ist es ein wichtiger Verkehrsweg, ein Erholungsraum und ein Quell ästhetischen Vergnügens. Aber das Meer steht unter Stress, denn das alte Prinzip von der „Freiheit der Meere“ hat zu Überfischung, Artenverlust und einer immensen Verschmutzung der Ozeane geführt. Deshalb muss der Umgang mit dem Meer auf nachhaltige und gerechte Grundlagen gestellt werden. Der Meeresatlas 2017 liefert dazu die Daten, Fakten und Zusammenhänge. Er zeigt in zahlreichen Beiträgen und über 50 Grafiken, in welch schlechtem Zustand sich die Weltmeere befinden, warum das so ist und was man tun muss, um die Situation der Ozeane zu verbessern

Quark Gluon Plasma an Color Glass Condensate at RHIC? The perspective from the BRAHMS experiment

We review the main results obtained by the BRAHMS collaboration on the properties of hot and dense hadronic and partonic matter produced in ultrarelativistic heavy ion collisions at RHIC. A particular focus of this paper is to discuss to what extent the results collected so far by BRAHMS, and by the other three experiments at RHIC, can be taken as evidence for the formation of a state of deconfined partonic matter, the so called quark-gluon-plasma (QGP). We also discuss evidence for a possible precursor state to the QGP, i.e. the proposed Color Glass Condensate.Comment: 32 pages, 18 figure