Constant angle surfaces in the Lorentzian Heisenberg group

In this paper, we define and, then, we characterize constant angle spacelike and timelike surfaces in the three-dimensional Heisenberg group, equipped with a 1-parameter family of Lorentzian metrics. In particular, we give an explicit local parametrization of these surfaces and we produce some examples.Comment: 13 pages, 8 figure

Explicit Formulas for Non-Geodesic Biharmonic Curves of the Heisenberg Group

We consider the biharmonicity condition for maps between Riemannian manifolds (see [BK]), and study the non-geodesic biharmonic curves in the Heisenberg group H_3. First we prove that all of them are helices, and then we obtain explicitly their parametric equations.Comment: 16 pages, 2 figure

Geodesicity and Isoclinity Properties for the Tangent Bundle of the Heisenberg Manifold with Sasaki Metric

We prove that the horizontal and vertical distributions of the tangent bundle with the Sasaki metric are isocline, the distributions given by the kernels of the horizontal and vertical lifts of the contact form $\omega$ from the Heisenberg manifold $(H_3,g)$ to $(TH_3,g^S)$ are not totally geodesic, and the distributions $F^H=L(E_1^H,E_2^H)$ and $F^V=L(E_1^V,E_2^V)$ are totally geodesic, but they are not isocline. We obtain that the horizontal and natural lifts of the curves from the Heisenberg manifold $(H_3,g)$, are geodesics in the tangent bundle endowed with the Sasaki metric $(TH_3,g^s)$, if and only if the curves considered on the base manifold are geodesics. Then, we get two particular examples of geodesics from $(TH_3,g^s)$, which are not horizontal or natural lifts of geodesics from the base manifold $(H_3,g)$.Comment: 12 page

Immune mechanisms in atopic eczema and the impact of therapy

Lesional skin in atopic eczema (AE) exhibits a T ceil dominated cellular infiltrate suggestive of a type IV hypersensitivity reaction. The T lymphocytes involved appear to be predominantly T helper type 2 cells. Raised IgE levels and positive prick test reactivity to aeroallergens are also commonly seen implicating involvement of allergic immediate type hypersensitivity. The presence of IgE receptors on antigen presenting cells may provide a link between these two mechanisms. In AE, the low affinity IgE receptor, FcγRII or CD23, is found in lesional skin to be largely expressed on Langerhans cells and dermal dendritic cells, that is those cells capable of antigen presentation. This study investigates the relevance of IgE receptors to the pathogenesis of AE in terms of cellular distribution and the regulation of their expression. Relationships between CD23 expression and clinical severity are revealed in the context of local immunological activity in the skin. A cohort of patients with AE were recruited and treated with Chinese herbal therapy (CHT) to test the relationship between immunological parameters and disease severity. Firstly it was established that treatment with CHT in this patient population resulted in an improvement in clinical disease. The distribution of IgE receptors on immunocompetent cells in lesional skin in AE and the emergence of these receptors during differentiation of cells of the monocyte/macrophage series were investigated. The relationship between T cell cytokine release and the level of egression of IgE receptors within the skin was determined. Using a standard clinical scoring system, it was confirmed that CHT improved the clinical status of patients in terms of reducing erythema and surface damage and the area of skin involved. Sequential use of immunoperoxidase and alkaline phosphatase-anti-alkaline-phosphatase immunohistological methods were employed to reveal the distribution of CD23 on mature cells in lesional skin. The results showed that as clinical severity was reduced, the numbers of CD23+ Langerhans cells and the numbers of CD23+ macrophages also decreased. Treatment also lead to a downregulation of the level of CD23 expressed by antigen presenting cells. To determine whether the changing proportions of CD23+ macrophage subsets in lesional skin resulted from dysfunction in monocyte differentiation, peripheral blood monocytes were isolated by adherence and cultured for 7 days. Immunocytochemical staining procedures were used to determine the relative proportions of emerging macrophage subsets and the distribution of CD23. Treatment did not affect the emergence of the RFD1+ inducer macrophage phenotype during the culture period however, there was a significant increase in the proportion of RFD7+ effector macrophages as compared to the situation before treatment. Interestingly, monocytes from patients with AE differentiated faster than those from normal controls but by day 7, the proportions of differentiated macrophages were similar. At day 0, therapy reduced the proportion of RFD1+ monocytes coexpressing CD23 however this difference was lost after 7 days of culture. Notably, throughout the 7-day culture period, larger proportions of monocytes from patients with AE were found to express CD23 compared with normal controls. To investigate aspects of T cell control of CD23 expression, methods of in situ hybridisation were performed on lesional skin before and after clinical improvement to identify the presence of mRNA for Interleukin-2 and Interleukin-4, (Th1 and Th2 type cytokines respectively). Following treatment, there was a decrease in the level of expression of mRNA for IL-4 and no significant change in the level of IL-2 mRNA. This study reveals an aberrant expression of CD23 on antigen presenting cells within lesional skin in AE and that treatment leading to clinical improvement results in a downregulation of CD23 expression. Therapy also leads to a decrease in Th2 activity as demonstrated by reduced IL-4 mRNA levels in the lesions, suggesting that this may also be relevant to the pathogenesis of AE. This research has thus revealed that CD23 expression by antigen presenting cells and local TH2 like T cell activity, is modulated by a course of therapy that improves clinical disease status

案例與例外 : 十三妹作為香港專欄作家 = Hong Kong columnist Shi San Mei : an (exceptional) case study

香港專欄作家十三妹在一九五○年代末突然冒起，以隨筆、漫談吸引了大量讀者。她從來不與報紙編輯或其他專欄作家見面，因而予人神秘之感；但她又在專欄里坦然自述身世和生活，恣意批評政治、社會、文化各方面的現象，樹敵無數。十三妹以寫作為生，卻自言與同行格格不入，本文嘗試利用十三妹專欄裏的豐富材料，勾勒五、六○年代香港職業寫作人的形態，並通過十三妹涉及的紛爭，探討當時文學圏裹的權力關係