On the structure of subsets of an orderable group with some small doubling properties

The aim of this paper is to present a complete description of the structure of subsets S of an orderable group G satisfying |S^2| = 3|S|-2 and is non-abelian

Lattice distortion in hcp rare gas solids

The lattice distortion parameter $\delta \equiv c/a-\sqrt{8/3}$ has been calculated as a function of molar volume for the hcp phases of He, Ar, Kr and Xe. Results from both semi-empirical potentials and density functional theory are presented. Our study shows that $\delta$ is negative for helium in the entire pressure range. For Ar, Kr and Xe, however, $\delta$ changes sign from negative to positive as the pressure increases, growing rapidly in magnitude at higher pressures.Comment: Submitted to Low. Temp. Phys., 14 pages, 5 figure

A Meinardus theorem with multiple singularities

Meinardus proved a general theorem about the asymptotics of the number of weighted partitions, when the Dirichlet generating function for weights has a single pole on the positive real axis. Continuing \cite{GSE}, we derive asymptotics for the numbers of three basic types of decomposable combinatorial structures (or, equivalently, ideal gas models in statistical mechanics) of size $n$, when their Dirichlet generating functions have multiple simple poles on the positive real axis. Examples to which our theorem applies include ones related to vector partitions and quantum field theory. Our asymptotic formula for the number of weighted partitions disproves the belief accepted in the physics literature that the main term in the asymptotics is determined by the rightmost pole.Comment: 26 pages. This version incorporates the following two changes implied by referee's remarks: (i) We made changes in the proof of Proposition 1; (ii) We provided an explanation to the argument for the local limit theorem. The paper is tentatively accepted by "Communications in Mathematical Physics" journa

The Lagrange and Markov spectra from the dynamical point of view

This text grew out of my lecture notes for a 4-hours minicourse delivered on October 17 \& 19, 2016 during the research school "Applications of Ergodic Theory in Number Theory" -- an activity related to the Jean-Molet Chair project of Mariusz Lema\'nczyk and S\'ebastien Ferenczi -- realized at CIRM, Marseille, France. The subject of this text is the same of my minicourse, namely, the structure of the so-called Lagrange and Markov spectra (with an special emphasis on a recent theorem of C. G. Moreira).Comment: 27 pages, 6 figures. Survey articl

Poisson's ratio in cryocrystals under pressure

We present results of lattice dynamics calculations of Poisson's ratio (PR) for solid hydrogen and rare gas solids (He, Ne, Ar, Kr and Xe) under pressure. Using two complementary approaches - the semi-empirical many-body calculations and the first-principle density-functional theory calculations we found three different types of pressure dependencies of PR. While for solid helium PR monotonically decreases with rising pressure, for Ar, Kr, and Xe it monotonically increases with pressure. For solid hydrogen and Ne the pressure dependencies of PR are non-monotonic displaying rather deep minimums. The role of the intermolecular potentials in this diversity of patterns is discussed.Comment: Fizika Nizkikh Temperatur 41, 571 (2015

The comprehensive cohort model in a pilot trial in orthopaedic trauma

Background: The primary aim of this study was to provide an estimate of effect size for the functional outcome of operative versus non-operative treatment for patients with an acute rupture of the Achilles tendon using accelerated rehabilitation for both groups of patients. The secondary aim was to assess the use of a comprehensive cohort research design (i.e. a parallel patient-preference group alongside a randomised group) in improving the accuracy of this estimate within an orthopaedic trauma setting. Methods: Pragmatic randomised controlled trial and comprehensive cohort study within a level 1 trauma centre. Twenty randomised participants (10 operative and 10 non-operative) and 29 preference participants (3 operative and 26 non-operative). The ge range was 22-72 years and 37 of the 52 patients were men. All participants had an acute rupture of their Achilles tendon and no other injuries. All of the patients in the operative group had a simple end-to-end repair of the tendon with no augmentation. Both groups then followed the same eight-week immediate weight-bearing rehabilitation programme using an off-the-shelf orthotic. The disability rating index (DRI; primary outcome), EQ-5D, Achilles Total Rupture Score and complications were assessed ed at two weeks, six weeks, three months, six months and nine months after initial injury. Results: At nine months, there was no significant difference in DRI between patients randomised to operative or non-operative management. There was no difference in DRI between the randomised group and the parallel patient preference group. The use of a comprehensive cohort of patients did not provide useful additional information as to the treatment effect size because the majority of patients chose non-operative management. Conclusions: Recruitment to clinical trials that compare operative and non-operative interventions is notoriously difficult; especially within the trauma setting. Including a parallel patient preference group to create a comprehensive cohort of patients has been suggested as a way of increasing the power of such trials. In our study, the comprehensive cohort model doubled the number of patients involved in the study. However, a strong preference for non-operative treatment meant that the increased number of patients did not significantly increase the ability of the trial to detect a difference between the two interventions

Processing Bi-Pb-Sr-Ca-Cu-O superconductors from amorphous state

The bismuth based high T sub c superconductors can be processed via an amorphous Bi-Pb-Sr-Ca-Cu oxide. The amorphous oxides were prepared by melting the constituent powders in an alumina crucible at 1200 C in air followed by pouring the liquid onto an aluminum plate, and rapidly pressing with a second plate. In the amorphous state, no crystalline phase was identified in the powder x ray diffraction pattern of the quenched materials. After heat treatment at high temperature the amorphous materials crystallized into a glass ceramic containing a large fraction of the Bi2Sr2Ca2Cu3O(x) phase T sub c = 110 K. The processing method, crystallization, and results of dc electrical resistivity and ac magnetic susceptibility measurements are discussed