Ill-posedness of degenerate dispersive equations

In this article we provide numerical and analytical evidence that some degenerate dispersive partial differential equations are ill-posed. Specifically we study the K(2,2) equation $u_t = (u^2)_{xxx} + (u^2)_{x}$ and the "degenerate Airy" equation $u_t = 2 u u_{xxx}$. For K(2,2) our results are computational in nature: we conduct a series of numerical simulations which demonstrate that data which is very small in $H^2$ can be of unit size at a fixed time which is independent of the data's size. For the degenerate Airy equation, our results are fully rigorous: we prove the existence of a compactly supported self-similar solution which, when combined with certain scaling invariances, implies ill-posedness (also in $H^2$)

On Unitarity Based Relations Between Various Lepton Family Violating Processes

Simple "unitarity inspired" relations between two- and three-body lepton flavor violating decays are noted and discussed. In the absence of cancellations, the existing strong bounds on $\mu \to 3e$ and $\mu\to e\gamma\gamma$ severly constrain two-body lepton flavor violating decays.Comment: 5 pages, 3 figure

Brick-pits of Leicestershire

Leicester City once had thriving extractive industries within its limits, but these have changed over the years as workings have developed more within the surrounding county. The extractive industries were the quarrying of clay for brick-making, gypsum for plaster, sand and sandstone for building, as well as limestone quarries worked for lime, building stone and the manufacture of mortar. Few traces of these are visible today. The brick industry is therefore only one of many that worked the ground in the city and county. Surveys of Leicester’s industries for the British Association meetings of 1907, 1933 and 1968 (which were held in Leicester) make little mention of brick making, but there are records of much earlier production (McWhirr, 1997)

Atlas of Avoidable Hospitalisations in Australia: ambulatory care-sensitive conditions

Avoidable hospitalisations represent a range of conditions for which hospitalisation should be able to be avoided because the disease or condition has been prevented from occurring, or because individuals have had access to timely and effective primary care. This report addresses the level and extent of regional variation in Australia in a sub-set of avoidable hospitalisations, namely those arising from ambulatory care-sensitive (ACS) conditions. ACS conditions are certain conditions for which hospitalisation is considered potentially avoidable through preventive care and early disease management, usually delivered in a primary care setting, for example by a general medical practitioner, or at a community health centre

Rare Kaon Decays

The current status of rare kaon decay experiments is reviewed. New limits in the search for Lepton Flavor Violation are discussed, as are new measurements of the CKM matrix.Comment: 8 pages, 3 figures, LaTeX, presented at the 3rd International Conference on B Phyiscs and CP Violation, Taipei December 3-7, 199

Development of a DNA-Liposome Complex for Gene Delivery Applications

The association structures formed by cationic liposomes and DNA(Deoxyribonucleic acid)-liposome have been effectively utilized as gene carriers in transfection assays. In this research study, cationic liposomes were prepared using a modified lipid film hydration method consisting of a lyophilization step for gene delivery applications. The obtained results demonstrated that the mean particle size had no significant change while the polydispersity (PDI) increased after lyophilization. The mean particle size slightly reduced after lyophilization (520 ± 12 nm to 464 ± 25 nm) while the PDI increased after lyophilization (0.094 ± 0.017 to 0.220 ± 0.004). In addition. The mean particle size of vesicles increases when DNA is incorporated to the liposomes (673 ± 27 nm). According to the Scanning Electron Microscopy(SEM) and transmission electron microscopy (TEM) images, the spherical shape of liposomes confirmed their successful preservation and reconstitution from the powder. It was found that liposomal formulation has enhanced transfection considerably compared to the naked DNA as negative control. Finally, liposomal formulation in this research had a better function than Lipofectamine® 2000 as a commercialized product because the cellular activity (cellular protein) was higher in the prepared lipoplex than Lipofectamine® 2000

Monte Carlo simulations of ordering in ferromagnetic-antiferromagnetic bilayers

Monte Carlo simulations have been used to study phase transitions on coupled anisotropic ferro/antiferromagnetic (FM/AFM) films of classical Heisenberg spins. We consider films of different thicknesses, with fully compensated exchange across the FM/AFM interface. We find indications of a phase transition on each film, occuring at different temperatures. It appears that both transition temperatures depend on the film thickness.Comment: Revtex, 4 pages, 4 figure

The integrability of Lie-invariant geometric objects generated by ideals in the Grassmann algebra

We investigate closed ideals in the Grassmann algebra serving as bases of Lie-invariant geometric objects studied before by E. Cartan. Especially, the E. Cartan theory is enlarged for Lax integrable nonlinear dynamical systems to be treated in the frame work of the Wahlquist Estabrook prolongation structures on jet-manifolds and Cartan-Ehresmann connection theory on fibered spaces. General structure of integrable one-forms augmenting the two-forms associated with a closed ideal in the Grassmann algebra is studied in great detail. An effective Maurer-Cartan one-forms construction is suggested that is very useful for applications. As an example of application the developed Lie-invariant geometric object theory for the Burgers nonlinear dynamical system is considered having given rise to finding an explicit form of the associated Lax type representation

Paediatric Behçet's disease: a UK tertiary centre experience

There are currently limited data regarding paediatric Behçet's disease (BD), particularly in the UK. We describe the clinical spectrum, treatment and outcome of BD, and explore the relative sensitivities of the criteria for the diagnosis of BD in a UK paediatric cohort. Single retrospective case note review of children with a clinical diagnosis of BD presenting between 1987 and 2012. Demographics, clinical features, treatment and outcomes were recorded. The sensitivities of the International Study Group (ISG) and International Criteria for BD (ICBD) criteria were explored. BD disease activity was calculated using the Behçet's Disease Activity Index (BDAI). Forty-six patients (22 male) were identified. Median age of onset was 4.87 (0.04-15.71) years; median time to diagnosis was 3.74 (0.25-13.48) years. Clinical features were recurrent oral ulceration (97.8 %), recurrent genital ulceration (73.9 %), gastrointestinal (58.7 %), musculoskeletal (47.83 %), cutaneous (23.9 %) involvement and uveitis (2 %). Recurrent genital ulceration was more common in female patients (P = 0.044). Thirty-seven patients (80.4 %) fulfilled the ICBD criteria; only 12 patients (26.1 %) fulfilled the ISG criteria. BDAI score at diagnosis was 7/20 (0-10/20) and significantly decreased to 5/20 (0-9/20) (P < 0.0001) at latest follow-up. The commonest systemic treatment was colchicine (76.1 %); anti-TNFα treatment was reserved for severe cases (15.5 %). Paediatric BD in the UK may present very early in life, sometimes with a family history, and with a low incidence of ocular involvement. Diagnostic delay is common. The majority of our patients required systemic therapy; anti-TNFα was reserved for severe cases and has largely superseded the use of thalidomide