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21.
Rolf Klein 《Computational Geometry》1992,1(6):325-351
A polygon with two distinguished vertices, s and g, is called a street if the two boundary chains from s to g are mutually weakly visible. For a mobile robot with on-board vision system we describe a strategy for finding a short path from s to g in a street not known in advance, and prove that the length of the path created does not exceed 1 +
π times the length of the shortest path from s to g. Experiments suggest that our strategy is much better than this, as no ratio bigger than 1.8 has yet been observed. This is complemented by a lower bound of 1.41 for the relative detour each strategy can be forced to generate. 相似文献
22.
Ya. B. Vorobets 《Mathematical Notes》1997,62(1):56-63
Periodic trajectories of billiards in rational polygons satisfying the Veech alternative, in particular, in right triangles
with an acute angle of the form π/n with integern are considered. The properties under investigation include: symmetry of periodic trajectories, asymptotics of the number
of trajectories whose length does not exceed a certain value, stability of periodic billiard trajectories under small deformations
of the polygon.
Translated fromMatematicheskie Zametki, Vol. 62, No. 1, pp. 66–75, July, 1997.
Translated by V. N. Dubrovsky 相似文献
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We give explicit formulas for the Bhattacharya function of 𝔪-primary complete monomial ideals in two variables in terms of the vertices of the Newton polyhedra or in terms of the decompositions of the ideals as products of simple ideals. 相似文献
27.
Joseph Zaks 《Geometriae Dedicata》1997,67(2):223-232
Extending earlier results in the plane, we prove that every n-polygon in sufficiently general position in d-dimensional projective space, n d + 2, gives rise to a derived n-polygon, which preserves a few functions; these functions are the cyclial product of (actually affine) ratios of various points, obtained by proper projections on suitable lines. 相似文献
28.
We define the notion of a translation ovoid in the classical generalized quadrangles and hexagons of order q, and we enumerate all known examples; translation spreads are defined dually. A modification of the known ovoids in the generalized hexagon H(q), q=32h+1, yields new ovoids of that hexagon. Dualizing and projecting along reguli, we obtain an alternative construction of the Roman ovoids due to Thas and Payne. Also, we construct a new translation spread in H(q) for any 1 mod 3, q odd, with the property that any projection along reguli yields the classical ovoid in the generalized quadrangle Q(4,q). Finally, we prove that for q odd, the new example is the only non-Hermitian translation spread in H(q) with the property that any projection along reguli yields the classical ovoid in Q(4,q). 相似文献
29.
A model in statistical physics is presented based on assigning non-Abelian phase factors to the turning points of polygons in three dimensions. This model allows for an exact solution and exhibits an unexpectedly rich phase structure. The model as well as the solution are obtained by a generalization of the methods of Kac and Ward and by mapping the problem to a Markov process as was done by Feynman for the two-dimensional Ising model 相似文献
30.
In this paper we study the possible orders of a non-abelian representation group of a slim dense near hexagon. We prove that
if the representation group R of a slim dense near hexagon S is non-abelian, then R is a 2-group of exponent 4 and |R|=2
β
, 1+NPdim(S)≤β≤1+dimV(S), where NPdim(S) is the near polygon embedding dimension of S and dimV(S) is the dimension of the universal representation module V(S) of S. Further, if β=1+NPdim(S), then R is necessarily an extraspecial 2-group. In that case, we determine the type of the extraspecial 2-group in each case. We
also deduce that the universal representation group of S is a central product of an extraspecial 2-group and an abelian 2-group of exponent at most 4.
This work was partially done when B.K. Sahoo was a Research Fellow at the Indian Statistical Institute, Bangalore Center with
NBHM fellowship, DAE Grant 39/3/2000-R&D-II, Govt. of India. 相似文献