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ON THE MODULI SPACE OF POLYGONS IN THE EUCLIDEAN PLANE
MODULI SPACE POLYGONS EUCLIDEAN PLANE
2015/10/14
ON THE MODULI SPACE OF POLYGONS IN THE EUCLIDEAN PLANE.
Computing the obstacle number of a plane graph
obstacle number of a plane graph Computational Geometry
2011/10/9
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...
On the polygonal diameter of the interior, resp. exterior, of a simple closed polygon in the plane
Jordan-Brouwer theorem Jordan exterior (interior) Jordan’s curve theorem
2011/2/21
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...
Symplectic birational transformations of the plane
Symplectic birational transformations plane
2011/1/18
We study the group of symplectic birational transformations of the plane.
On equicontinuity of homeomorphisms with finite distortion in the plane
homeomorphisms finite distortion
2011/2/24
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...
Optimal anisotropic three-phase conducting composites: Plane problem
multimaterial composites optimal microstructures bounds for effective properties
2010/12/7
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...
Uniformization of Sierpiński carpets in the plane
Uniformization of Sierpiński carpets plane
2010/12/9
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...
A "hybrid plane" with spin-orbit interaction and magnetic field
"hybrid plane" with spin-orbit interaction magnetic field
2010/12/13
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...
Evolution of plane curves with a curvature adjusted tangential velocity
curvature driven flow of plane curves curvature adjusted tangential velocity
2010/12/6
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...
On triangles determined by subsets of the Euclidean plane, the associated bilinear operators and applications to discrete geometry
triangles determined Euclidean plane associated bilinear operators discrete geometry
2010/12/6
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...
Visually Dynamic Presentation of Proofs in Plane Geometry Part 1. Basic Features and the Manual Input Method
Geometry theorem proving Visually dynamic presentation of proof Dynamic geometry Unordered geometry Gelernter Java Geometry Expert Morley’s theorem Feuerbach’s theorem Pythagorean theorem Pedal triangle
2013/9/9
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...
Visually Dynamic Presentation of Proofs in Plane Geometry
Geometry theorem proving Proof with hierarchical structures Visually dynamic presentation of proof Dynamic geometry Full-angle Deductive database Fixpoint Unordered geometry Hilbert geometry Tarski geometry
2013/9/9
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...