874 research outputs found
On the algorithmic construction of classifying spaces and the isomorphism problem for biautomatic groups
We show that the isomorphism problem is solvable in the class of central
extensions of word-hyperbolic groups, and that the isomorphism problem for
biautomatic groups reduces to that for biautomatic groups with finite centre.
We describe an algorithm that, given an arbitrary finite presentation of an
automatic group , will construct explicit finite models for the skeleta
of and hence compute the integral homology and cohomology of
.Comment: 21 pages, 4 figure
Primitive Words, Free Factors and Measure Preservation
Let F_k be the free group on k generators. A word w \in F_k is called
primitive if it belongs to some basis of F_k. We investigate two criteria for
primitivity, and consider more generally, subgroups of F_k which are free
factors.
The first criterion is graph-theoretic and uses Stallings core graphs: given
subgroups of finite rank H \le J \le F_k we present a simple procedure to
determine whether H is a free factor of J. This yields, in particular, a
procedure to determine whether a given element in F_k is primitive.
Again let w \in F_k and consider the word map w:G x G x ... x G \to G (from
the direct product of k copies of G to G), where G is an arbitrary finite
group. We call w measure preserving if given uniform measure on G x G x ... x
G, w induces uniform measure on G (for every finite G). This is the second
criterion we investigate: it is not hard to see that primitivity implies
measure preservation and it was conjectured that the two properties are
equivalent. Our combinatorial approach to primitivity allows us to make
progress on this problem and in particular prove the conjecture for k=2.
It was asked whether the primitive elements of F_k form a closed set in the
profinite topology of free groups. Our results provide a positive answer for
F_2.Comment: This is a unified version of two manuscripts: "On Primitive words I:
A New Algorithm", and "On Primitive Words II: Measure Preservation". 42
pages, 14 figures. Some parts of the paper reorganized towards publication in
the Israel J. of Mat
Abelian subgroups of Garside groups
In this paper, we show that for every abelian subgroup of a Garside
group, some conjugate consists of ultra summit elements and the
centralizer of is a finite index subgroup of the normalizer of .
Combining with the results on translation numbers in Garside groups, we obtain
an easy proof of the algebraic flat torus theorem for Garside groups and solve
several algorithmic problems concerning abelian subgroups of Garside groups.Comment: This article replaces our earlier preprint "Stable super summit sets
in Garside groups", arXiv:math.GT/060258
Anomalous spectral scaling of light emission rates in low dimensional metallic nanostructures
The strength of light emission near metallic nanostructures can scale
anomalously with frequency and dimensionality. We find that light-matter
interactions in plasmonic systems confined in two dimensions (e.g., near metal
nanowires) strengthen with decreasing frequency owing to strong mode
confinement away from the surface plasmon frequency. The anomalous scaling also
applies to the modulation speed of plasmonic light sources, including lasers,
with modulation bandwidths growing at lower carrier frequencies. This allows
developing optical devices that exhibit simultaneously femto-second response
times at the nano-meter scale, even at longer wavelengths into the mid IR,
limited only by non-local effects and reversible light-matter coupling
Beat-wave generation of plasmons in semiconductor plasmas
It is shown that in semiconductor plasmas, it is possible to generate large
amplitude plasma waves by the beating of two laser beams with frequency
difference close to the plasma frequency. For narrow gap semiconductors (for
example n-type InSb), the system can simulate the physics underlying beat wave
generation in relativistic gaseous plasmas.Comment: 11 pages, LaTex, no figures, no macro
Electron correlation vs. stabilization: A two-electron model atom in an intense laser pulse
We study numerically stabilization against ionization of a fully correlated
two-electron model atom in an intense laser pulse. We concentrate on two
frequency regimes: very high frequency, where the photon energy exceeds both,
the ionization potential of the outer {\em and} the inner electron, and an
intermediate frequency where, from a ``single active electron''-point of view
the outer electron is expected to stabilize but the inner one is not. Our
results reveal that correlation reduces stabilization when compared to results
from single active electron-calculations. However, despite this destabilizing
effect of electron correlation we still observe a decreasing ionization
probability within a certain intensity domain in the high-frequency case. We
compare our results from the fully correlated simulations with those from
simpler, approximate models. This is useful for future work on ``real''
more-than-one electron atoms, not yet accessible to numerical {\em ab initio}
methods.Comment: 8 pages, 8 figures in an extra ps-file, submitted to Phys. Rev. A,
updated references and shortened introductio
Inversion of Randomly Corrugated Surfaces Structure from Atom Scattering Data
The Sudden Approximation is applied to invert structural data on randomly
corrugated surfaces from inert atom scattering intensities. Several expressions
relating experimental observables to surface statistical features are derived.
The results suggest that atom (and in particular He) scattering can be used
profitably to study hitherto unexplored forms of complex surface disorder.Comment: 10 pages, no figures. Related papers available at
http://neon.cchem.berkeley.edu/~dan
Maxwell Equations in Complex Form of Majorana - Oppenheimer, Solutions with Cylindric Symmetry in Riemann S_{3} and Lobachevsky H_{3} Spaces
Complex formalism of Riemann - Silberstein - Majorana - Oppenheimer in
Maxwell electrodynamics is extended to the case of arbitrary pseudo-Riemannian
space - time in accordance with the tetrad recipe of Tetrode - Weyl - Fock -
Ivanenko. In this approach, the Maxwell equations are solved exactly on the
background of static cosmological Einstein model, parameterized by special
cylindrical coordinates and realized as a Riemann space of constant positive
curvature. A discrete frequency spectrum for electromagnetic modes depending on
the curvature radius of space and three parameters is found, and corresponding
basis electromagnetic solutions have been constructed explicitly. In the case
of elliptical model a part of the constructed solutions should be rejected by
continuity considerations. Similar treatment is given for Maxwell equations in
hyperbolic Lobachevsky model, the complete basis of electromagnetic solutions
in corresponding cylindrical coordinates has been constructed as well, no
quantization of frequencies of electromagnetic modes arises.Comment: 39 page
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Language support for immigrant children: a study of state schools in the UK and US
In recent decades, immigrants, refugees and asylum seekers have sought a new way of life in large numbers, often leaving their countries of origin behind in search of places that offer a better way of life. The purpose of this study was to investigate how elementary and middle school students in state schools in Reading, England (primarily speakers of Asian languages), and Richmond, Virginia (primarily speakers of Spanish), were supported academically, when most children’s first language was not English. The authors were interested in exploring whether or not there were cultural or structural differences in the way each country helped or hindered these students as they progressed through the school systems. Three UK schools in a district of approximately 100,000 and three US schools in a district of approximately 250,000 were the focus of this exploration from 2000 to 2003. Findings indicated that there were cultural and legislative differences and similarities. Teachers and administrators in both countries attempted to provide services with limited and sometimes diminishing resources. Community support varied based on resources, attitudes toward various ethnic groups, and the coping strategies adopted by these groups in their new environments. Marked differences appeared with regard to the manner in which assessments took place and how the results were made available to the public
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