38 research outputs found
Singularities of bi-Hamiltonian systems
We study the relationship between singularities of bi-Hamiltonian systems and
algebraic properties of compatible Poisson brackets. As the main tool, we
introduce the notion of linearization of a Poisson pencil. From the algebraic
viewpoint, a linearized Poisson pencil can be understood as a Lie algebra with
a fixed 2-cocycle. In terms of such linearizations, we give a criterion for
non-degeneracy of singular points of bi-Hamiltonian systems and describe their
types
Renal pericytes: regulators of medullary blood flow
Regulation of medullary blood flow (MBF) is essential in maintaining normal kidney function. Blood flow to the medulla is supplied by the descending vasa recta (DVR), which arise from the efferent arterioles of juxtamedullary glomeruli. DVR are composed of a continuous endothelium, intercalated with smooth muscle-like cells called pericytes. Pericytes have been shown to alter the diameter of isolated and in situ DVR in response to vasoactive stimuli that are transmitted via a network of autocrine and paracrine signalling pathways. Vasoactive stimuli can be released by neighbouring tubular epithelial, endothelial, red blood cells and neuronal cells in response to changes in NaCl transport and oxygen tension. The experimentally described sensitivity of pericytes to these stimuli strongly suggests their leading role in the phenomenon of MBF autoregulation. Because the debate on autoregulation of MBF fervently continues, we discuss the evidence favouring a physiological role for pericytes in the regulation of MBF and describe their potential role in tubulo-vascular cross-talk in this region of the kidney. Our review also considers current methods used to explore pericyte activity and function in the renal medulla
Foliations of Isonergy Surfaces and Singularities of Curves
It is well known that changes in the Liouville foliations of the isoenergy
surfaces of an integrable system imply that the bifurcation set has
singularities at the corresponding energy level. We formulate certain
genericity assumptions for two degrees of freedom integrable systems and we
prove the opposite statement: the essential critical points of the bifurcation
set appear only if the Liouville foliations of the isoenergy surfaces change at
the corresponding energy levels. Along the proof, we give full classification
of the structure of the isoenergy surfaces near the critical set under our
genericity assumptions and we give their complete list using Fomenko graphs.
This may be viewed as a step towards completing the Smale program for relating
the energy surfaces foliation structure to singularities of the momentum
mappings for non-degenerate integrable two degrees of freedom systems.Comment: 30 pages, 19 figure
A sociocultural analysis of the development of pre-service and beginning teachers’ pedagogical identities as users of technology
This paper reports on a study that investigated the pedagogical practices and beliefs of pre-service and beginning teachers in integrating technology into the teaching of secondary school mathematics. A case study documents how one teachers modes of working with technology changed over time and across different school contexts, and identifies relationships between a range of personal and contextual factors that influenced the development of his identity as a teacher. This analysis views teachers learning as increasing participation in sociocultural practices, and uses Valsiners concepts of the Zone of Proximal Development, Zone of Free Movement, and Zone of Promoted Action to offer a dynamic way of theorising teacher learning as identity formation
Sociocultural considerations in aging men's health: implications and recommendations for the clinician
http://dx.doi.org/10.1016/j.jomh.2009.07.00
Symplectic invariants near hyperbolic-hyperbolic points
International audienceWe construct symplectic invariants for Hamiltonian integrable systems of 2 degrees of freedom possessing a fixed point of hyperbolic-hyperbolic type. These invariants consist in some signs which determine the topology of the critical Lagrangian fibre, together with several Taylor series which can be computed from the dynamics of the system.We show how these series are related to the singular asymptotics of the action integrals at the critical value of the energy-momentum map. This gives general conditions under which the non-degeneracy conditions arising in the KAM theorem (Kolmogorov condition, twist condition) are satisfied. Using this approach, we obtain new asymptotic formulae for the action integrals of the C. Neumann system. As a corollary, we show that the Arnold twist condition holds for generic frequencies of this syste