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ON THE MODULI SPACE OF POLYGONS IN THE EUCLIDEAN PLANE.
Abstract: An obstacle representation of a plane graph G is V(G) together with a set of opaque polygonal obstacles such that G is the visibility graph on V(G) determined by the obstacles. We investigat...
We give a tight upper bound on the polygonal diameter of the interior, resp. exterior, of a simple n-gon, n ≥ 3, in the plane as a function of n, and describe an n-gon (n ≥ 3) for which both upper bou...
We study the group of symplectic birational transformations of the plane.
It is stated equicontinuity and normality of families F of the so–called homeomorphisms with finite distortion on conditions that Kf (z) has finite mean oscillation, singularities of logarithmic typ...
The paper establishes tight lower bound for effective conductivity tensor K∗ of two-imensional three-phase conducting anisotropic composites and defines optimal microstructures. It is assumed t...
Let Si, i ∈ I, be a countable collection of Jordan curves in the extended complex plane bC that bound pairwise disjoint closed Jordan regions. If the Jordan curves are uniform quasicircles and are uni...
We discuss spectral and resonance properties of a Hamiltonian describing motion of an electron moving on a \hybrid surface" consisting on a hal ine attached by its endpoints to a plane under in uence ...
Let G be a plane graph and T an even subset of its vertices. It has been conjectured that if all T-cuts of G have the same parity and the size of every T-cut is at least k, then G contains k edge-disj...
We study evolution of closed embedded plane curves with the normal veloc-ity depending on the curvature, the orientation and position of a curve. We propose a new method of tangential redistribution o...
We prove that if the Hausdorff dimension of the set E  R2 is greater than 74 , then the three-dimensional Lebesgue measure of the set of triangles determined by E is positive. We establish this fact...
With dynamic mediums such as computer displays, we propose a new kind of visually dynamic presentation of proofs in plane geometry. In asingle diagram for the proof, when the proof text goes on step b...
We present the method for automated generation of visually dynamic presentations of plane geometry proofs based on the full-angle method. The proof generated by the full-angle method is organized hier...
<正> In a recent paper the present author has established somerepresentations for a plane curve C in the neighbourhood of a singularpoint O characterized by the property that the tangent t(?) of C at O...

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