共查询到20条相似文献,搜索用时 0 毫秒
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János Pach 《Discrete and Computational Geometry》1986,1(1):73-81
It is proved that for any centrally symmetric convex polygonal domainP and for any natural numberr, there exists a constantk=k(P, r) such that anyk-fold covering of the plane with translates ofP can be split intor simple coverings. 相似文献
3.
Martin Costabel 《Annali di Matematica Pura ed Applicata》1983,133(1):305-326
Summary
The operators of the single layer potential, double layer potential, and the Hilbert transform, acting on plane curves with corners, are members of the class of integral operators which we define in this paper. We use expansions in homogeneous kernels of increasing degree to define lower order symbols via local Mellin transforms. In this way we can study the mapping properties in (augmented) Sobolev spaces including Garding inequalities and higher regularity, thus generalizing the results of [3]and [4]from polygons to curved polygons. 相似文献
4.
Chung-Wu Ho 《Geometriae Dedicata》1980,9(4):451-460
Given a star-shaped polygon in the euclidean plane and a vertex v of the polygon, the author characterizes all those points w in the plane such that when the vertex v moves to w along a straight line path, while all other vertices of the polygon are fixed, the polygon remains star-shaped. An example is given to show that this characterization fails for the star-shaped polyhedral spheres in the 3-dimensional euclidean space. 相似文献
5.
Zh. Kaidasov 《Journal of Mathematical Sciences》2007,141(1):1087-1090
Two theorems about properties of infinite polygons on the Lobachevsky plane are proved.
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Translated from Fundamental’naya i Prikladnaya Matematika (Fundamental and Applied Mathematics), Vol. 11, No. 1, Geometry,
2005. 相似文献
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I. O. Arushanyan 《Moscow University Mathematics Bulletin》2014,69(4):174-176
An approximate method of solving an integral equation of the potential theory for a Dirichlet problem for the Laplace operator is proposed in the case when domains are curvilinear polygons with piecewise analytic boundaries. The proposed method is exponentially convergent with respect to the number of quadrature nodes in use. 相似文献
8.
Several aperiodic hyperbolic tiling systems consisting of a single convex tile are constructed.
Research partially supported by GIF grant no. G-454.213.06.95 and SFB 343 Bielefeld.
The work of the first author was supported in part by NSF grant DMS-9424613.
The work of the second author was supported in part by a grant of the Israel Academy of Sciences, and by the Edmund Landau
Center for Research in Mathematical Analysis supported by the Minerva Foundation (Federal Republic of Germany). 相似文献
9.
This paper concerns the topology of configuration spaces of linkages whose underlying graph is a single cycle. Assume that the edge lengths are such that there are no configurations in which all the edges lie along a line. The main results are that, modulo translations and rotations, each component of the space of convex configurations is homeomorphic to a closed Euclidean ball and each component of the space of embedded configurations is homeomorphic to a Euclidean space. This represents an elaboration on the topological information that follows from the convexification theorem of Connelly, Demaine, and Rote. 相似文献
10.
In this paper we consider the problem of partitioning a plane compact convex body into equal-area parts, i.e., an equipartition,
by means of chords. We prove two basic results that hold with some specific exceptions: (a) When chords are pairwise non-crossing,
the dual tree of the partition has to be a path, (b) A convex n-gon admits no equipartition produced by more than n chords having a common interior point. 相似文献
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Summary. An elliptic boundary value problem in the interior or exterior of a polygon is transformed into an equivalent first kind boundary
integral equation. Its Galerkin discretization with degrees of freedom on the boundary with spline wavelets as basis functions is analyzed. A truncation strategy is presented
which allows to reduce the number of nonzero elements in the stiffness matrix from to entries. The condition numbers are bounded independently of the meshwidth. It is proved that the compressed scheme thus obtained
yields in operations approximate solutions with the same asymptotic convergence rates as the full Galerkin scheme in the boundary energy
norm as well as in interior points. Numerical examples show the asymptotic error analysis to be valid already for moderate
values of .
Received March 12, 1994 / Revised version received January 9, 1995 相似文献
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Given a convex compact setK ? ?2 what is the largestn such thatK contains a convex latticen-gon? We answer this question asymptotically. It turns out that the maximaln is related to the largest affine perimeter that a convex set contained inK can have. This, in turn, gives a new characterization ofK 0, the convex set inK having maximal affine perimeter. 相似文献
16.
In this paper, a numerical scheme based on a Gauss-like cubature formula from Sammariva and Vianello (2007) [1] is introduced for approximate solution of integral equations over a polygonal domain with a piecewise straight lines boundary in R2. The proposed technique is a meshless like method with sufficient precision, which does not require any discretization of the polygon domain or any preprocessing such as mesh refinement. The error analysis of the method is provided and some numerical experiments are also presented to evaluate the performance of the proposed algorithm. 相似文献
17.
Indirect and direct boundary integral equations equivalent to the original boundary value problem of differential equation of plane elasticity are established rigorously. The unnecessity or deficiency of some customary boundary integral equations is indicated by examples and numerical comparison. 相似文献
18.
R.E Miles 《Advances in Mathematics》1973,10(2):256-290
The probability distributions (defined in an ergodic sense) of various aggregates of random convex polygons determined by the standard isotropic Poisson line process in the plane are investigated. 相似文献
19.
Pascal Laubin 《Numerische Mathematik》1998,79(1):107-140
We propose collocation methods with smoothest splines to solve the integral equation of the second kind on a plane polygon.
They are based on the bijectivity of the double layer potential between spaces of Sobolev type with arbitrary high regularity
and involving the singular functions generated by the corners. If splines of order are used, we get quasi-optimal estimates in -norm and optimal order convergence for the -norm if . Numerical experiments are presented.
Received November 20, 1996 / Accepted March 10, 1997 相似文献
20.
This paper is developed toI
2(2g).c-geometries, namely, point-line-plane structures where planes are generalized 2g-gons with exactly two lines on every point and any two intersecting lines belong to a unique plane.I
2(2g).c-geometries appear in several contexts, sometimes in connection with sporadic simple groups. Many of them are homomorphic images of truncations of geometries belonging to Coxeter diagrams. TheI
2(2g).c-geometries obtained in this way may be regarded as the standard ones. We characterize them in this paper. For everyI
2(2g).c-geometry , we define a numberw(), which counts the number of times we need to walk around a 2g-gon contained in a plane of , building up a wall of planes around it, before closing the wall. We prove thatw()=1 if and only if is standard and we apply that result to a number of special cases. 相似文献