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The efficacy of the psychodrama technique of doubling in increasing self-acceptance
The influence of the strength of bone on the deformation of acetabular shells : a laboratory experiment in cadavers
Date of Acceptance: 24/08/2014 ©2015 The British Editorial Society of Bone & Joint Surgery. The authors would like to thank N. Taylor (3D Measurement Company) for his work with regard to data acquisition and processing of experimental data. We would also like to thank Dr A. Blain of Newcastle University for performing the statistical analysis The research was supported by the NIHR Newcastle Biomedical Research Centre. The authors P. Dold, M. Flohr and R. Preuss are employed by Ceramtec GmbH. Martin Bone received a salary from the joint fund. The author or one or more of the authors have received or will receive benefits for personal or professional use from a commercial party related directly or indirectly to the subject of this article. This article was primary edited by G. Scott and first proof edited by J. Scott.Peer reviewedPostprin
Stability of a spherical flame ball in a porous medium
Gaseous flame balls and their stability to symmetric disturbances are studied numerically and asymptotically, for large activation temperature, within a porous medium that serves only to exchange heat with the gas. Heat losses to a distant ambient environment, affecting only the gas, are taken to be radiative in nature and are represented using two alternative models. One of these treats the heat loss as being constant in the burnt gases and linearizes the radiative law in the unburnt gas (as has been studied elsewhere without the presence of a solid). The other does not distinguish between burnt and unburnt gas and is a continuous dimensionless form of Stefan's law, having a linear part that dominates close to ambient temperatures and a fourth power that dominates at higher temperatures.Numerical results are found to require unusually large activation temperatures in order to approach the asymptotic results. The latter involve two branches of solution, a smaller and a larger flame ball, provided heat losses are not too high. The two radiative heat loss models give completely analogous steady asymptotic solutions, to leading order, that are also unaffected by the presence of the solid which therefore only influences their stability. For moderate values of the dimensionless heat-transfer time between the solid and gas all flame balls are unstable for Lewis numbers greater than unity. At Lewis numbers less than unity, part of the branch of larger flame balls becomes stable, solutions with the continuous radiative law being stable over a narrower range of parameters. In both cases, for moderate heat-transfer times, the stable region is increased by the heat capacity of the solid in a way that amounts, simply, to decreasing an effective Lewis number for determining stability, just as if the heat-transfer time was zero
A Tverberg type theorem for matroids
Let b(M) denote the maximal number of disjoint bases in a matroid M. It is
shown that if M is a matroid of rank d+1, then for any continuous map f from
the matroidal complex M into the d-dimensional Euclidean space there exist t
\geq \sqrt{b(M)}/4 disjoint independent sets \sigma_1,\ldots,\sigma_t \in M
such that \bigcap_{i=1}^t f(\sigma_i) \neq \emptyset.Comment: This article is due to be published in the collection of papers "A
Journey through Discrete Mathematics. A Tribute to Jiri Matousek" edited by
Martin Loebl, Jaroslav Nesetril and Robin Thomas, due to be published by
Springe
Kappia lobulata (Apocynaceae, Periplocoideae), a new genus from South Africa
Kappia, a new genus from the Fish River Valley in the Eastern Cape Province, South Africa is presented. At first described as Raphionacme lobulata Venter and R.L.Verh. [Venter, H.J.T., Verhoeven, R.L. 1988. Raphionacme lobulata (Periplocaceae), a new species from the eastern Cape Province, South Africa. South African Journal of Botany 54, 603–606.] based on a single specimen collected in 1936, recently discovered plants of this species proved it to be a new genus. In habit Kappia resembles Baseonema Schltr. and Rendle, Batesanthus N.E.Br., Mondia Skeels and Stomatostemma N.E.Br. However, as far as floral structure is concerned, Kappia reveals more affinity with Raphionacme Harv. DNA sequence data show Kappia to be distinct from Batesanthus, Mondia and Raphionacme Harv. and weakly supported as a sister to Stomatostemma
Combustion waves in a model with chain branching reaction and their stability
In this paper the travelling wave solutions in the adiabatic model with
two-step chain branching reaction mechanism are investigated both numerically
and analytically in the limit of equal diffusivity of reactant, radicals and
heat. The properties of these solutions and their stability are investigated in
detail. The behaviour of combustion waves are demonstrated to have similarities
with the properties of nonadiabatic one-step combustion waves in that there is
a residual amount of fuel left behind the travelling waves and the solutions
can exhibit extinction. The difference between the nonadiabatic one-step and
adiabatic two-step models is found in the behaviour of the combustion waves
near the extinction condition. It is shown that the flame velocity drops down
to zero and a standing combustion wave is formed as the extinction condition is
reached. Prospects of further work are also discussed.Comment: pages 32, figures 2
Shadows and traces in bicategories
Traces in symmetric monoidal categories are well-known and have many
applications; for instance, their functoriality directly implies the Lefschetz
fixed point theorem. However, for some applications, such as generalizations of
the Lefschetz theorem, one needs "noncommutative" traces, such as the
Hattori-Stallings trace for modules over noncommutative rings. In this paper we
study a generalization of the symmetric monoidal trace which applies to
noncommutative situations; its context is a bicategory equipped with an extra
structure called a "shadow." In particular, we prove its functoriality and
2-functoriality, which are essential to its applications in fixed-point theory.
Throughout we make use of an appropriate "cylindrical" type of string diagram,
which we justify formally in an appendix.Comment: 46 pages; v2: reorganized and shortened, added proof for cylindrical
string diagrams; v3: final version, to appear in JHR
Rapid Mixing for Lattice Colorings with Fewer Colors
We provide an optimally mixing Markov chain for 6-colorings of the square
lattice on rectangular regions with free, fixed, or toroidal boundary
conditions. This implies that the uniform distribution on the set of such
colorings has strong spatial mixing, so that the 6-state Potts antiferromagnet
has a finite correlation length and a unique Gibbs measure at zero temperature.
Four and five are now the only remaining values of q for which it is not known
whether there exists a rapidly mixing Markov chain for q-colorings of the
square lattice.Comment: Appeared in Proc. LATIN 2004, to appear in JSTA
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