13,137 research outputs found
Rotation Numbers, Boundary Forces and Gap labelling
We review the Johnson-Moser rotation number and the -theoretical gap
labelling of Bellissard for one-dimensional Schr\"odinger operators. We compare
them with two further gap-labels, one being related to the motion of Dirichlet
eigenvalues, the other being a -theoretical gap label. We argue that the
latter provides a natural generalisation of the Johnson-Moser rotation number
to higher dimensions.Comment: 10 pages, version accepted for publicatio
On stronger conjectures that imply the Erd\"os-Moser conjecture
The Erd\"os-Moser conjecture states that the Diophantine equation , where , has no solution for positive integers
and with . We show that stronger conjectures about
consecutive values of the function , that seem to be more naturally, imply
the Erd\"os-Moser conjecture.Comment: 7 page
Bringing Sexy Back: Unauthorized Film Editing, Copyright, and How Removing Reproductive Acts Violates Reproduction Rights
The Multicolored Asian Ladybird, Harmonia axyridis, is an extremely successful invasive species. Here we suggest that, in addition to many other traits, the dorsal spines of its larvae contribute to their success, as suggested by behavioral observations of agonistic interactions between H. axyridis and European coccinellids. In coccinellids, the role of dorsal spines in these interactions has been poorly studied and they could be a physical protection against intraguild predators. Dorsal spines of second instar H. axyridis larvae were removed with micro-scissors, which resulted in spineless larvae after molting (spineless group). These larvae were then exposed to starved Coccinella septempunctata larvae. Two control categories were also submitted to interactions: H. axyridis larvae with all their spines (control group) and with their spines, but injured by pin stings (injured group). Spine removal at the second instar did not hamper H. axyridis development. The bite rate by C. septempunctata was significantly higher on the spineless H. axyridis and more dorsally located compared to the control and injured groups, while no bite rate difference was observed between the injured and the control group. Our results suggest that in addition to behavioral and chemical defenses, the dorsal spines play a significant protective role against bites. Therefore, spines in ladybirds could be considered as a morphological defense against intraguild predation. In H. axyridis, these defenses might contribute to its success in food resources already exploited by other guild members and thus further facilitate the invasion of new areas.SCOPUS: ar.jinfo:eu-repo/semantics/publishe
Formal Solutions of a Class of Pfaffian Systems in Two Variables
In this paper, we present an algorithm which computes a fundamental matrix of
formal solutions of completely integrable Pfaffian systems with normal
crossings in two variables, based on (Barkatou, 1997). A first step was set in
(Barkatou-LeRoux, 2006) where the problem of rank reduction was tackled via the
approach of (Levelt, 1991). We give instead a Moser-based approach. And, as a
complementary step, we associate to our problem a system of ordinary linear
singular differential equations from which the formal invariants can be
efficiently derived via the package ISOLDE, implemented in the computer algebra
system Maple.Comment: Keywords: Linear systems of partial differential equations, Pfaffian
systems, Formal solutions, Moser-based reduction, Hukuhara- Turritin normal
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