The Dirac equation without spinors

In the first part of the paper we give a tensor version of the Dirac equation. In the second part we formulate and analyse a simple model equation which for weak external fields appears to have properties similar to those of the 2--dimensional Dirac equation.Comment: 20 pages. Submitted for publication in the proceedings of the conference `Functional analysis, partial differential equations and applications', Rostock (Germany) 31 August--4 September 199

A supercritical elliptic problem in a cylindrical shell

We consider the problem $$-\Delta u=|u|^{p-2}u in \Omega, u=0 on \partial\Omega,$$ where $\Omega:=\{(y,z)\in\mathbb{R}^{m+1}\times\mathbb{R}^{N-m-1}: 0<a<|y|<b<\infty\}$, $0\leq m\leq N-1$ and $N\geq2$. Let $2_{N,m}^{\ast}:=2(N-m)/(N-m-2)$ if $m<N-2$ and $2_{N,m}^{\ast}:=\infty$ if $m=N-2$ or $N-1$. We show that $2_{N,m}^{\ast}$ is the true critical exponent for this problem, and that there exist nontrivial solutions if $2<p<2_{N,m}^{\ast}$ but there are no such solutions if $p\geq2_{N,m}^{\ast}$

Solitary waves in the Nonlinear Dirac Equation

In the present work, we consider the existence, stability, and dynamics of solitary waves in the nonlinear Dirac equation. We start by introducing the Soler model of self-interacting spinors, and discuss its localized waveforms in one, two, and three spatial dimensions and the equations they satisfy. We present the associated explicit solutions in one dimension and numerically obtain their analogues in higher dimensions. The stability is subsequently discussed from a theoretical perspective and then complemented with numerical computations. Finally, the dynamics of the solutions is explored and compared to its non-relativistic analogue, which is the nonlinear Schr{\"o}dinger equation. A few special topics are also explored, including the discrete variant of the nonlinear Dirac equation and its solitary wave properties, as well as the PT-symmetric variant of the model

Ethnicity, socioeconomic status, transfusions and risk of hepatitis B and hepatitis C infection

This study identifies the risk factors for hepatitis B virus (HBV) and hepatitis C virus (HCV) and measures the prevalence of hepatitis B surface antigen (HBsAg) and antibody to hepatitis C (anti-HCV) in the general population of Jakarta. A population-based sample of 985 people aged 15 and above was surveyed. Risk factors were identified through questionnaires and home visits. Serum was analysed for HBsAg, antibody to hepatitis B surface antigen (anti-HBs), anti-HCV, aspartate aminotransferase (AST) and alanine aminotransferase (ALT). The seroprevalence was: 4.0% (39/985) for HBsAg, 17.2% (170/985) for anti-HBs, and 3.9% (38/985) for anti-HCV. The risk factors for hepatitis B and hepatitis C infection had little in common. Low socioeconomic status was a strong risk factor for HBsAg (adjusted odds ratio (OR) 18.09; 95% confidence interval (CI) 2.35–139.50). In addition, the Chinese group has 2.97 higher risk of having HBV infection compared with the Malayan ethnic group (adjusted OR 2.97; 95% CI 1.22–7.83). There was moderate positive trend between family size and risk of HBsAg positivity ( P = 0.130). Age over 50 (adjusted OR 14.72; 95% CI 4.35–49.89) and history of transfusion were significant risk factors for hepatitis C (adjusted OR 3.03; 95% CI 1.25–7.33). Hepatitis B and hepatitis C infections have different risk factors in Jakarta, a high risk in population for both diseases. Hepatitis B transmission is associated with low socioeconomic status, Chinese ethnic group and large family size, while hepatitis C is associated with an older age and a history of transfusions.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/72591/1/j.1440-1746.1997.tb00365.x.pd

Influence of climatic variables on crown condition in pine forests of Northern Spain

Producción CientíficaThe aim of this study was to find relationships between crown condition and some climatic parameters to identify which are those having a main influence on crown condition, and how this influence is shown in the tree (crown transparency), and to contribute to the understanding of how these parameters will affect under future climate change scenarios

Illness perceptions and explanatory models of viral hepatitis B & C among immigrants and refugees: a narrative systematic review.

© 2015 Owiti et al.; licensee BioMed Central. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly credited. The Creative Commons Public Domain Dedication waiver (http://creativecommons.org/publicdomain/zero/1.0/) applies to the data made available in this article, unless otherwise stated.BACKGROUND: Hepatitis B and C (HBV, HCV) infections are associated with high morbidity and mortality. Many countries with traditionally low prevalence (such as UK) are now planning interventions (screening, vaccination, and treatment) of high-risk immigrants from countries with high prevalence. This review aimed to synthesise the evidence on immigrants' knowledge of HBV and HCV that might influence the uptake of clinical interventions. The review was also used to inform the design and successful delivery of a randomised controlled trial of targeted screening and treatment. METHODS: Five databases (PubMed, CINHAL, SOCIOFILE, PsycINFO & Web of Science) were systematically searched, supplemented by reference tracking, searches of selected journals, and of relevant websites. We aimed to identify qualitative and quantitative studies that investigated knowledge of HBV and HCV among immigrants from high endemic areas to low endemic areas. Evidence, extracted according to a conceptual framework of Kleinman's explanatory model, was subjected to narrative synthesis. We adapted the PEN-3 model to categorise and analyse themes, and recommend strategies for interventions to influence help-seeking behaviour. RESULTS: We identified 51 publications including quantitative (n = 39), qualitative (n = 11), and mixed methods (n = 1) designs. Most of the quantitative studies included small samples and had heterogeneous methods and outcomes. The studies mainly concentrated on hepatitis B and ethnic groups of South East Asian immigrants residing in USA, Canada, and Australia. Many immigrants lacked adequate knowledge of aetiology, symptoms, transmission risk factors, prevention strategies, and treatment, of hepatitis HBV and HCV. Ethnicity, gender, better education, higher income, and English proficiency influenced variations in levels and forms of knowledge. CONCLUSION: Immigrants are vulnerable to HBV and HCV, and risk life-threatening complications from these infections because of poor knowledge and help-seeking behaviour. Primary studies in this area are extremely diverse and of variable quality precluding meta-analysis. Further research is needed outside North America and Australia

Enhancement of Tumour-Specific Immune Responses In Vivo by ‘MHC Loading-Enhancer’ (MLE)

BACKGROUND:Class II MHC molecules (MHC II) are cell surface receptors displaying short protein fragments for the surveillance by CD4+ T cells. Antigens therefore have to be loaded onto this receptor in order to induce productive immune responses. On the cell surface, most MHC II molecules are either occupied by ligands or their binding cleft has been blocked by the acquisition of a non-receptive state. Direct loading with antigens, as required during peptide vaccinations, is therefore hindered. PRINCIPAL FINDINGS:Here we show, that the in vivo response of CD4+ T cells can be improved, when the antigens are administered together with 'MHC-loading enhancer' (MLE). MLE are small catalytic compounds able to open up the MHC binding site by triggering ligand-release and stabilizing the receptive state. Their enhancing effect on the immune response was demonstrated here with an antigen from the influenza virus and tumour associated antigens (TAA) derived from the NY-ESO-1 protein. The application of these antigens in combination with adamantane ethanol (AdEtOH), an MLE compound active on human HLA-DR molecules, significantly increased the frequency of antigen-specific CD4+ T cells in mice transgenic for the human MHC II molecule. Notably, the effect was evident only with the MLE-susceptible HLA-DR molecule and not with murine MHC II molecules non-susceptible for the catalytic effect of the MLE. CONCLUSION:MLE can specifically increase the potency of a vaccine by facilitating the efficient transfer of the antigen onto the MHC molecule. They may therefore open a new way to improve vaccination efficacy and tumour-immunotherapy