7,014 research outputs found
Patterns theory and geodesic automatic structure for a class of groups
We introduce a theory of "patterns" in order to study geodesics in a certain
class of group presentations. Using patterns we show that there does not exist
a geodesic automatic structure for certain group presentations, and that
certain group presentations are almost convex.Comment: Appeared in 2003. I am putting all my past papers on arxi
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Does correction for guessing reduce students' performance on multiple-choice examinations? Yes? No? Sometimes?
Multiple-choice (MC) examinations are becoming increasingly popular in higher education because they can be used effectively to assess breadth of knowledge in large cohorts of students. This present research investigated Psychology students' performance on, and experiences of, MC examinations with and without correction for guessing. In Study 1, data were collected from two cohorts of students across three Psychology MC examinations. The results revealed that students scored higher, and left fewer questions unanswered, when there was no correction for guessing. Furthermore, when the correction for guessing was removed from the theory MC examination, students who were told there was no correction for guessing did better than those told there was a correction. In addition, there was limited evidence of gender differences, with female students performing significantly better on one MC examination than males. In Study 2, a further set of first-year Psychology students reported their experiences of correction for guessing on open-book and closed-book MC examinations. Students reported feeling less anxious and more confident on the open-book MC examination. The findings of both of these studies have implications for instructors deciding whether or not correction for guessing is appropriate, and for the advice to be given to students preparing for MC examinations
Morphological instability, evolution, and scaling in strained epitaxial films: An amplitude equation analysis of the phase field crystal model
Morphological properties of strained epitaxial films are examined through a
mesoscopic approach developed to incorporate both the film crystalline
structure and standard continuum theory. Film surface profiles and properties,
such as surface energy, liquid-solid miscibility gap and interface thickness,
are determined as a function of misfit strains and film elastic modulus. We
analyze the stress-driven instability of film surface morphology that leads to
the formation of strained islands. We find a universal scaling relationship
between the island size and misfit strain which shows a crossover from the
well-known continuum elasticity result at the weak strain to a behavior
governed by a "perfect" lattice relaxation condition. The strain at which the
crossover occurs is shown to be a function of liquid-solid interfacial
thickness, and an asymmetry between tensile and compressive strains is
observed. The film instability is found to be accompanied by mode coupling of
the complex amplitudes of the surface morphological profile, a factor
associated with the crystalline nature of the strained film but absent in
conventional continuum theory.Comment: 16 pages, 10 figures; to be published in Phys. Rev.
Phase field crystal dynamics for binary systems: Derivation from dynamical density functional theory, amplitude equation formalism, and applications to alloy heterostructures
The dynamics of phase field crystal (PFC) modeling is derived from dynamical
density functional theory (DDFT), for both single-component and binary systems.
The derivation is based on a truncation up to the three-point direct
correlation functions in DDFT, and the lowest order approximation using scale
analysis. The complete amplitude equation formalism for binary PFC is developed
to describe the coupled dynamics of slowly varying complex amplitudes of
structural profile, zeroth-mode average atomic density, and system
concentration field. Effects of noise (corresponding to stochastic amplitude
equations) and species-dependent atomic mobilities are also incorporated in
this formalism. Results of a sample application to the study of surface
segregation and interface intermixing in alloy heterostructures and strained
layer growth are presented, showing the effects of different atomic sizes and
mobilities of alloy components. A phenomenon of composition overshooting at the
interface is found, which can be connected to the surface segregation and
enrichment of one of the atomic components observed in recent experiments of
alloying heterostructures.Comment: 26 pages, 5 figures; submitted to Phys. Rev.
On trivial words in finitely presented groups
We propose a numerical method for studying the cogrowth of finitely presented
groups. To validate our numerical results we compare them against the
corresponding data from groups whose cogrowth series are known exactly.
Further, we add to the set of such groups by finding the cogrowth series for
Baumslag-Solitar groups and prove
that their cogrowth rates are algebraic numbers.Comment: This article has been rewritten as two separate papers, with improved
exposition. The new papers are arXiv:1309.4184 and arXiv:1312.572
C-graph automatic groups
We generalize the notion of a graph automatic group introduced by Kharlampovich, Khoussainov and Miasnikov by replacing the regular languages in their definition with more powerful language classes. For a fixed language class C, we call the resulting groups C-graph automatic. We prove that the class of C-graph automatic groups is closed under change of generating set, direct and free product for certain classes C. We show that for quasi-realtime counter-graph automatic groups where normal forms have length that is linear in the geodesic length, there is an algorithm to compute normal forms (and therefore solve the word problem) in polynomial time. The class of quasi-realtime counter-graph automatic groups includes all Baumslag-Solitar groups, and the free group of countably infinite rank. Context-sensitive-graph automatic groups are shown to be a very large class, which encompasses, for example, groups with unsolvable conjugacy problem, the Grigorchuk group, and Thompson's groups F, T and V. © 2014 Elsevier Inc
Metric properties of Baumslag-Solitar groups
© 2015 World Scientific Publishing Company. We compute estimates for the word metric of Baumslag-Solitar groups in terms of the Britton's lemma normal form. As a corollary, we find lower bounds for the growth rate for the groups BS(p, q) with 1 < p ≤ q
Thompson's group F is 1-counter graph automatic
© 2016 by De Gruyter. It is not known whether Thompson's group F is automatic. With the recent extensions of the notion of an automatic group to graph automatic by Kharlampovich, Khoussainov and Miasnikov and then to C-graph automatic by the authors, a compelling question is whether F is graph automatic or C-graph automatic for an appropriate language class C. The extended definitions allow the use of a symbol alphabet for the normal form language, replacing the dependence on generating set. In this paper we construct a 1-counter graph automatic structure for F based on the standard infinite normal form for group elements
Dainty Butterfly : Intermezzo-Characteristique
https://digitalcommons.library.umaine.edu/mmb-ps/1470/thumbnail.jp
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