24,722 research outputs found
Skew convolution semigroups and affine Markov processes
A general affine Markov semigroup is formulated as the convolution of a
homogeneous one with a skew convolution semigroup. We provide some sufficient
conditions for the regularities of the homogeneous affine semigroup and the
skew convolution semigroup. The corresponding affine Markov process is
constructed as the strong solution of a system of stochastic equations with
non-Lipschitz coefficients and Poisson-type integrals over some random sets.
Based on this characterization, it is proved that the affine process arises
naturally in a limit theorem for the difference of a pair of reactant processes
in a catalytic branching system with immigration.Comment: Published at http://dx.doi.org/10.1214/009117905000000747 in the
Annals of Probability (http://www.imstat.org/aop/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Transience and recurrence of random walks on percolation clusters in an ultrametric space
We study existence of percolation in the hierarchical group of order ,
which is an ultrametric space, and transience and recurrence of random walks on
the percolation clusters. The connection probability on the hierarchical group
for two points separated by distance is of the form , with , non-negative constants , and . Percolation was proved in Dawson and Gorostiza
(2013) for , with
. In this paper we improve the result for the critical case by
showing percolation for . We use a renormalization method of the type
in the previous paper in a new way which is more intrinsic to the model. The
proof involves ultrametric random graphs (described in the Introduction). The
results for simple (nearest neighbour) random walks on the percolation clusters
are: in the case the walk is transient, and in the critical case
, there exists a critical
such that the walk is recurrent for and transient for
. The proofs involve graph diameters, path lengths, and
electric circuit theory. Some comparisons are made with behaviours of random
walks on long-range percolation clusters in the one-dimensional Euclidean
lattice.Comment: 27 page
GDL: a model infrastructure for a regional digital library
This brief article describes the early days of the Glasgow Digital Library (GDL), when it was a cross-sectoral and city-wide collaborative initiative involving Strathclyde, Glasgow and Caledonian Universities, as well as Glasgow City Libraries and Archives and the Glasgow Colleges Group
Chiral Corrections to the Hyperon Vector Form Factors
We present the complete calculation of the SU(3)-breaking corrections to the
hyperon vector form factors up to O(p^4) in the Heavy Baryon Chiral
Perturbation Theory. Because of the Ademollo-Gatto theorem, at this order the
results do not depend on unknown low energy constants and allow to test the
convergence of the chiral expansion. We complete and correct previous
calculations and find that O(p^3) and O(1/M_0) corrections are important. We
also study the inclusion of the decuplet degrees of freedom, showing that in
this case the perturbative expansion is jeopardized. These results raise doubts
on the reliability of the chiral expansion for hyperons.Comment: 20 pages, 4 figures, v2: published versio
Hierarchical equilibria of branching populations
The objective of this paper is the study of the equilibrium behavior of a
population on the hierarchical group consisting of families of
individuals undergoing critical branching random walk and in addition these
families also develop according to a critical branching process. Strong
transience of the random walk guarantees existence of an equilibrium for this
two-level branching system. In the limit (called the hierarchical
mean field limit), the equilibrium aggregated populations in a nested sequence
of balls of hierarchical radius converge to a backward
Markov chain on . This limiting Markov chain can be explicitly
represented in terms of a cascade of subordinators which in turn makes possible
a description of the genealogy of the population.Comment: 62 page
Secondary teachers' perceptions of the effectiveness of their pre-service education and strategies to improve pre-service education for teachers: A school based training route in England
This study aims to provide a deeper understanding of the impact of an EBITT course on teachers' early professional development, identify strengths of the course and also the ways in which the training could be improved. Data collected was recorded during individual face- to- face interviews using a structured interview schedule. In devising our approach we utilised the model suggested by Sharon Feiman-Nemser in her article How do Teachers Learn to Teach? in Cochran - Smith et. al. (2008) Handbook of Research on Teacher Education
The data was analysed to explore (after 2-4 years reflection):
• which elements of initial training were valuable and less valuable
• what they have learned since the course
• which aspects of the course the teachers feel should be improved
It was cross referenced against findings from national surveys of teachers in their post qualifying year of teaching (induction year) and early years of teaching conducted by the TDA. These findings were presented as part of a common wider international study on the same theme in four countries (UK, Spain, Australia, and Ireland)
Noro-Frenkel scaling in short-range square well: A Potential Energy Landscape study
We study the statistical properties of the potential energy landscape of a
system of particles interacting via a very short-range square-well potential
(of depth ), as a function of the range of attraction to provide
thermodynamic insights of the Noro and Frenkel [ M.G. Noro and D. Frenkel,
J.Chem.Phys. {\bf 113}, 2941 (2000)] scaling. We exactly evaluate the basin
free energy and show that it can be separated into a {\it vibrational}
(-dependent) and a {\it floppy} (-independent) component. We
also show that the partition function is a function of ,
explaining the equivalence of the thermodynamics for systems characterized by
the same second virial coefficient. An outcome of our approach is the
possibility of counting the number of floppy modes (and their entropy).Comment: 4 pages, 4 figures accepted for publication on PR
Investigation of phase-separated electronic states in 1.5µm GaInNAs/GaAs heterostructures by optical spectroscopy
We report on the comparative electronic state characteristics of particular GaInNAs/GaAs quantum well structures that emit near 1.3 and 1.5 µm wavelength at room temperature. While the electronic structure of the 1.3 µm sample is consistent with a standard quantum well, the 1.5 µm sample demonstrate quite different characteristics. By using photoluminescence sPLd excitation spectroscopy at various detection wavelengths, we demonstrate that the macroscopic electronic states in the 1.5 µm structures originate from phase-separated quantum dots instead of quantum wells. PL measurements with spectrally selective excitation provide further evidence for the existence of composition-separated phases. The evidence is consistent with phase segregation during the growth leading to two phases, one with high In and N content which accounts for the efficient low energy 1.5 µm emission, and the other one having lower In and N content which contributes metastable states and only emits under excitation in a particular wavelength range
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