Hopf fibrations are characterized by being fiberwise homogeneous

Heinz Hopf's famous fibrations of the 2n+1-sphere by great circles, the 4n+3-sphere by great 3-spheres, and the 15-sphere by great 7-spheres have a number of interesting properties. Besides providing the first examples of homotopically nontrivial maps from one sphere to another sphere of lower dimension, they all share two striking features: (1) Their fibers are parallel, in the sense that any two fibers are a constant distance apart, and (2) The fibrations are highly symmetric. For example, there is a fiber-preserving isometry of each total space which takes any given fiber to any other one. Hopf fibrations have been characterized up to isometry by the first property above, initially among all fibrations of spheres by great subspheres, and later in the stronger sense among all fibrations of spheres by smooth subspheres. In this paper, we show that the Hopf fibrations are also characterized by their "fiberwise homogeneity" expressed above in (2), and in the strong sense among all fibrations of spheres by smooth subspheres. In the special case of the 3-sphere fibered by great circles, we prove something stronger. We prove that a fibration of a connected open set by great circles which is locally fiberwise homogeneous is part of a Hopf fibration.Comment: 14 pages, 1 figure. Added reference

On the Composition of Gauge Structures

A formulation for a non-trivial composition of two classical gauge structures is given: Two parent gauge structures of a common base space are synthesized so as to obtain a daughter structure which is fundamental by itself. The model is based on a pair of related connections that take their values in the product space of the corresponding Lie algebras. The curvature, the covariant exterior derivatives and the associated structural identities, all get contributions from both gauge groups. The various induced structures are classified into those whose composition is given just by trivial means, and those which possess an irreducible nature. The pure irreducible piece, in particular, generates a complete super-space of ghosts with an attendant set of super-BRST variation laws, both of which are purely of a geometrical origin.Comment: Few elaborations are added to section 4 and section 5. To be published in Journal of Physics A: Mathematical and General. 21 page

On the quasihydrostatic flows of radiatively cooling self-gravitating gas clouds

Two model problems are considered, illustrating the dynamics of quasihydrostatic flows of radiatively cooling, optically thin self-gravitating gas clouds. In the first problem, spherically symmetric flows in an unmagnetized plasma are considered. For a power-law dependence of the radiative loss function on the temperature, a one-parameter family of self-similar solutions is found. The authors concentrate on a constant-mass cloud, one of the cases, when the self-similarity indices are uniquely selected. In this case, the self-similar flow problem can be formally reduced to the classical Lane-Emden equation and therefore solved analytically. The cloud is shown to undergo radiative condensation, if the gas specific heat ratio {gamma} > 4/3. The condensation proceeds either gradually, or in the form of (quasihydrostatic) collapse. For {gamma} < 4/3, the cloud is shown to expand. The second problem addresses a magnetized plasma slab that undergoes quasihydrostatic radiative cooling and condensation. The problem is solved analytically, employing the Lagrangian mass coordinate

Clinical practice: Protein-losing enteropathy in children

Protein-losing enteropathy (PLE) is a rare complication of a variety of intestinal disorders characterized by an excessive loss of proteins into the gastrointestinal tract due to impaired integrity of the mucosa. The clinical presentation of patients with PLE is highly variable, depending upon the underlying cause, but mainly consists of edema due to hypoproteinemia. While considering PLE, other causes of hypoproteinemia such as malnutrition, impaired synthesis, or protein loss through other organs like the kidney, liver, or skin, have to be excluded. The disorders causing PLE can be divided into those due to protein loss from intestinal lymphatics, like primary intestinal lymphangiectasia or congenital heart disease and those with protein loss due to an inflamed or abnormal mucosal surface. The diagnosis is confirmed by increased fecal concentrations of alpha-1-antitrypsin. After PLE is diagnosed, the underlying cause should be identified by stool cultures, serologic evaluation, cardiac screening, or radiographic imaging. Treatment of PLE consists of nutrition state maintenance by using a high protein diet with supplement of fat-soluble vitamins. In patients with lymphangiectasia, a low fat with medium chain triglycerides (MCT) diet should be prescribed. Besides dietary adjustments, appropriate treatment for the underlying etiology is necessary and supportive care to avoid complications of edema. PLE is a rare complication of various diseases, mostly gastrointestinal or cardiac conditions that result into loss of proteins in the gastrointestinal tract. Prognosis depends upon the severity and treatment options of the underlying disease

The burden of respiratory syncytial virus (RSV) associated acute lower respiratory infections in children with Down syndrome:A systematic review and meta-analysis

Background Acute lower respiratory tract infections (ALRIs) caused by respiratory syncytial virus (RSV) are a leading cause of hospitalization in infants. Numerous risk factors have been identified in the aetiology of severe RSV-associated ALRI necessitating hospitalisation, including prematurity and congenital heart disease. Down syndrome (DS), a common genetic disorder associated with congenital and dysmorphic features, has recently been identified as an independent risk factor for RSV-associated ALRI requiring hospitalisation; however, the disease burden of RSV-associated ALRI in this population has not yet been established. Similarly, the impact of DS as an independent risk factor has not yet been quantified. We aimed therefore to estimate the incidence of admissions in children with DS, and by comparing this with unaffected children, to quantify the risk of DS independent of other risk factors. Methods A systematic review of the existing literature published between 1995 and March 1, 2017 was performed to quantify the incidence of hospitalisation due to RSV-associated ALRI in children with DS. Meta-analyses were performed on extracted data using STATA statistical software, and hospitalisation rates for children with and without DS under the age of 2 were calculated. Findings 5 articles were ultimately deemed eligible for analyses. Analyses were limited to children under the age of 2 years. We calculated the hospitalisation rate for children with DS in this age group to be 117.6 per 1000 child-years (95% CI 67.4-205.2), vs a rate of 15.2 per 1000 child-years (95% CI 8.3-27.6) in unaffected children. This indicates DS contributes to a 6.8 (95% CI 5.5-8.4) fold increase in the relative risk of hospitalisation for RSV-associated ALRI. Interpretation Though limited by a small number of articles, this review found sufficient evidence to conclude DS was a significant independent risk factor for the development of severe RSV-associated ALRI requiring hospitalisation. Further studies are needed to define the impact of DS in conjunction with other comorbidities on the risk of severe RSV infection. Determining benefits of immunoprophylaxis or future vaccines against RSV in this at-risk population is warranted