765 research outputs found
Homotopy Groups of the Space of Curves on a Surface
We explicitly calculate the fundamental group of the space of
all immersed closed curves on a surface . It is shown that , n>1 for . It is also proved that , and , n>2, for
equal to or .Comment: 8 pages, 1 figure This paper will appear in Math. Scand. probably in
Vol. 86, no. 1, 200
Arnold-type Invariants of Curves on Surfaces
Recently V. Arnold introduced Strangeness and invariants of generic
immersions of an oriented circle to . Here these invariants are
generalized to the case of generic immersions of an oriented circle to an
arbitrary surface . We explicitly describe all the invariants satisfying
axioms, which naturally generalize the axioms used by V. Arnold.Comment: 25 pages, 11 figure
Arnold-type invariants of wave fronts on surfaces
AbstractRecently, Arnold's St and JΒ± invariants of generic planar curves have been generalized to the case of generic planar wave fronts. We generalize these invariants to the case of wave fronts on an arbitrary surface F. All invariants satisfying the axioms which naturally generalize the axioms used by Arnold are explicitly described. We also give an explicit formula for the finest order one J+-type invariant of fronts on an orientable surface Fβ S2. We obtain necessary and sufficient conditions for an invariant of nongeneric fronts with one nongeneric singular point to be the Vassiliev-type derivative of an invariant of generic fronts. As a byproduct, we calculate all homotopy groups of the space of Legendrian immersions of S1 into the spherical cotangent bundle of a surface
The universal order one invariant of framed knots in most S^1-bundles over orientable surfaces
It is well-known that self-linking is the only Z valued Vassiliev invariant
of framed knots in S^3. However for most 3-manifolds, in particular for the
total spaces of S^1-bundles over an orientable surface F not S^2, the space of
Z-valued order one invariants is infinite dimensional. We give an explicit
formula for the order one invariant I of framed knots in orientable total
spaces of S^1-bundles over an orientable not necessarily compact surface F not
S^2. We show that if F is not S^2 or S^1 X S^1, then I is the universal order
one invariant, i.e. it distinguishes every two framed knots that can be
distinguished by order one invariants with values in an Abelian group.Comment: Published by Algebraic and Geometric Topology at
http://www.maths.warwick.ac.uk/agt/AGTVol3/agt-3-3.abs.htm
Mapped Null Hypersurfaces and Legendrian Maps
For an -dimensional space-time define a mapped null
hypersurface to be a smooth map (that is not necessarily
an immersion) such that there exists a smooth field of null lines along
that are both tangent and -orthogonal to We study relations between
mapped null hypersurfaces and Legendrian maps to the spherical cotangent bundle
of an immersed spacelike hypersurface We show
that a Legendrian map \wt \lambda: L^{m-1}\to (ST^*M)^{2m-1} defines a mapped
null hypersurface in On the other hand, the intersection of a mapped null
hypersurface with an immersed spacelike hypersurface
defines a Legendrian map to the spherical cotangent
bundle This map is a Legendrian immersion if came from a
Legendrian immersion to for some immersed spacelike hypersurface
Comment: 13 pages, 1 figur
New heuristics for the minimum fundamental cut basis problem
Given an undirected connected network and a weight function finding a basis of the cut space with minimum sum of the cut weights is termed Minimum Cut Basis Problem. This problem can be solved, e.g., by the algorithm of Gomory and Hu [GH61]. If, however, fundamentality is required, i.e., the basis is induced by a spanning tree T in G, the problem becomes NP-hard. Theoretical and numerical results on that topic can be found in Bunke et al. [BHMM07] and in Bunke [Bun06]. In the following we present heuristics with complexity O(m log n) and O(mn), where n and m are the numbers of vertices and edges respectively, which obtain upper bounds on the aforementioned problem and in several cases outperform the heuristics of Schwahn [Sch05]
Extracellular Production and Degradation of Superoxide in the Coral Stylophora pistillata and Cultured Symbiodinium
Reactive oxygen species (ROS) are thought to play a major role in cell death pathways and bleaching in scleractinian corals. Direct measurements of ROS in corals are conspicuously in short supply, partly due to inherent problems with ROS quantification in cellular systems.In this study we characterized the dynamics of the reactive oxygen species superoxide anion radical (O(2)(-)) in the external milieu of the coral Stylophora pistillata. Using a sensitive, rapid and selective chemiluminescence-based technique, we measured extracellular superoxide production and detoxification activity of symbiont (non-bleached) and aposymbiont (bleached) corals, and of cultured Symbiodinium (from clades A and C). Bleached and non-bleached Stylophora fragments were found to produce superoxide at comparable rates of 10(-11)-10(-9) mol O(2)(-) mg protein(-1) min(-1) in the dark. In the light, a two-fold enhancement in O(2)(-) production rates was observed in non-bleached corals, but not in bleached corals. Cultured Symbiodinium produced superoxide in the dark at a rate of . Light was found to markedly enhance O(2)(-) production. The NADPH Oxidase inhibitor Diphenyleneiodonium chloride (DPI) strongly inhibited O(2)(-) production by corals (and more moderately by algae), possibly suggesting an involvement of NADPH Oxidase in the process. An extracellular O(2)(-) detoxifying activity was found for bleached and non-bleached Stylophora but not for Symbiodinium. The O(2)(-) detoxifying activity was partially characterized and found to resemble that of the enzyme superoxide dismutase (SOD).The findings of substantial extracellular O(2)(-) production as well as extracellular O(2)(-) detoxifying activity may shed light on the chemical interactions between the symbiont and its host and between the coral and its environment. Superoxide production by Symbiodinium possibly implies that algal bearing corals are more susceptible to an internal build-up of O(2)(-), which may in turn be linked to oxidative stress mediated bleaching
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