7,872 research outputs found
Singularities of flat extensions from generic surfaces with boundaries
We solve the problem on flat extensions of a generic surface with boundary in
Euclidean 3-space, relating it to the singularity theory of the envelope
generated by the boundary. We give related results on Legendre surfaces with
boundaries via projective duality and observe the duality on boundary
singularities. Moreover we give formulae related to remote singularities of the
boundary-envelope.Comment: Several typos are corrected (2010. Jan.
Global classification of curves on the symplectic plane
We consider the global symplectic classification problem of plane curves.
First we give the exact classification result under symplectomorphisms, for the
case of generic plane curves, namely immersions with transverse
self-intersections. Then the set of symplectic classes form the symplectic
moduli space which we completely describe by its global topological term. For
the general plane curves with singularities, the difference between
symplectomorphism and diffeomorphism classifications is clearly described by
local symplectic moduli spaces of singularities and a global topological term.
We introduce the symplectic moduli space of a global plane curve and the local
symplectic moduli space of a plane curve singularity as quotients of mapping
spaces, and we endow them with differentiable structures in a natural way.Comment: 25 pages 3 figure
THE EFFECTS OF THE TRANSPORTATION COSTS IN R&D TECHNOLOGY SECTOR ON THE ENDOGENOUS GRWOTH
The paper centers on investigating theoretically how the transportation costs of R&D technology, none of the transportation costs in final goods and intermediate inputs, affect the long-run endogenous economic growth. The basic ideas adopted in this paper are different from well-known models in the sense that the prices of R&D technology are influenced by the transportation cost in R&D technology sector and the accumulated profit of the intermediate inputs over time is equal to the price of R&D technology, and thus the transportation costs indirectly influence the endogenous growth. That is, the larger are only the transportation costs of R&D technology, the higher is the price of R&D technology and the slower is endogenous economic growth.Transportation Costs, R&D Technology, Endogenous Growth
Monge-Amp\`ere Systems with Lagrangian Pairs
The classes of Monge-Amp\`ere systems, decomposable and bi-decomposable
Monge-Amp\`ere systems, including equations for improper affine spheres and
hypersurfaces of constant Gauss-Kronecker curvature are introduced. They are
studied by the clear geometric setting of Lagrangian contact structures, based
on the existence of Lagrangian pairs in contact structures. We show that the
Lagrangian pair is uniquely determined by such a bi-decomposable system up to
the order, if the number of independent variables . We remark that, in
the case of three variables, each bi-decomposable system is generated by a
non-degenerate three-form in the sense of Hitchin. It is shown that several
classes of homogeneous Monge-Amp\`ere systems with Lagrangian pairs arise
naturally in various geometries. Moreover we establish the upper bounds on the
symmetry dimensions of decomposable and bi-decomposable Monge-Amp\`ere systems
respectively in terms of the geometric structure and we show that these
estimates are sharp (Proposition 4.2 and Theorem 5.3)
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