2008 NOV 3 - (VerticalNews.com) -- 'We show a regularity criterion to the harmonic heat flow from 2-dimensional Riemannian manifold M into a sphere. It is shown that a weak solution of the harmonic heat flow from 2-dimensional manifold into a sphere is regular under the criterion (T)integral(0) parallel to del u(tau)parallel to(B) (M) (2)(Or) d tau where B M O-r is the space of bounded mean oscillations on M. A sharp version of the Sobolev inequality of the Brezis-Gallouet type is introduced on M. A monotonicity formula by the mean oscillation is established and applied for proving such a regularity criterion for weak solutions as above. ...read more

  2008 NOV 3 - (VerticalNews.com) -- According to a study from Netherlands, "The epicardium is embryologically formed by outgrowth of proepicardial cells over the naked heart tube. Epicardium-derived cells (EPDCs) migrate into the myocardium, contributing to myocardial architecture, valve development, and the coronary vasculature."

  "Defective EPDC formation causes valve malformations, myocardial thinning, and coronary defects. In the atrioventricular (AV) valves and the fibrous heart skeleton isolating atrial from ventricular myocardium, EPDCs colocalize with periostin, a matrix molecule involved in remodeling. We investigated whether proepicardial outgrowth inhibition affected periostin expression and how this related to development of the AV valves and fibrous heart skeleton. Periostin expression by epicardium and EPDCs was confirmed in vitro in primary cultures of human and quail EPDCs. Disturbing EPDC formation in quail embryos reduced periostin expression in the endocardial cushions and AV junction. Disturbed fibrous tissue development resulted in AV myocardial connections reflected by preexcitation electrocardiographic patterns. We conclude that EPDCs are local producers of periostin. Disturbance of EPDC formation results in decreased cardiac periostin levels and hampers the development of fibrous tissue in AV junction and the developing AV valves," wrote H. Lievenema and colleagues, Leiden University ...read more

  2008 NOV 3 - (VerticalNews.com) -- "We consider the dynamics of an inextensible elastic closed wire in the plane under uniform high pressure. In 1967, Tadjbakhsh and Odeh (J. Math. Anal. Appl. 18:59-74, 1967) posed a variational problem to determine the shape of a buckled elastic ring under uniform pressure," scientists writing in the journal Calculus of Variations and Partial Differential Equations report.

  "In order to comprehend a dynamics of the wire, we consider the following two mathematical questions: (i) can we construct a gradient flow for the Tadjbakhsh-Odeh functional under the inextensibility condition?; (ii) what is a behavior of the wire governed by the gradient flow near every critical point of the Tadjbakhsh-Odeh variational problem? For (i), first we derive a system of equations which governs the gradient flow, and then, give an affirmative answer to (i) by solving the system involving fourth order parabolic equations. For (ii), we first prove a stability and instability of each critical point by considering the second variation formula of the Tadjbakhsh-Odeh functional. Moreover, we give a lower bound of its Morse index," wrote S. Okabe and colleagues, Tohoku University ...read more