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71.
In this paper we investigate the nearly small twist mappings with intersection property. With a certain non-degenerate condition, we proved that the most of invariant tori of the original small twist mappings will survive afer small perturtations. The persisted invariant tori are close to the unperturbed ones when the perturbation are small. The orbits reduced by those mappings are quasi-periodic in the invariant tori with the frequences closing to the original ones. 相似文献
72.
Summary The purpose of this paper is to establish extremal values for inner and
outer radii of the unit ball of a Minkowski space for the Holmes--Thompson and
Busemann measures. Furthermore, we confirm a conjecture of C. A. Rogers and G. C. Shephard on ellipsoids. 相似文献
73.
Roy Joshua 《K-Theory》2002,27(3):197-244
This is the second part of our work on the intersection theory of algebraic stacks. The main results here are the following. We provide an intersection pairing for all smooth Artin stacks (locally of finite type over a field) which we show reduces to the known intersection pairing on the Chow groups of smooth Deligne–Mumford stacks of finite type over a field as well as on the Chow groups of quotient stacks associated to actions of linear algebraic groups on smooth quasi-projective schemes modulo torsion. The former involves also showing the existence of Adams operations on the rational étale K-theory of all smooth Deligne–Mumford stacks of finite type over a field. In addition, we show that our definition of the higher Chow groups is intrinsic to the stack for all smooth stacks and also stacks of finite type over the given field. Next we establish the existence of Chern classes and Chern character for Artin stacks with values in our Chow groups and extend these to higher Chern classes and a higher Chern character for perfect complexes on an algebraic stack, taking values in cohomology theories of algebraic stacks that are defined with respect to complexes of sheaves on a big smooth site. As a by-product of our techniques we also provide an extension of higher intersection theory to all schemes locally of finite type over a field. As the higher cycle complex, by itself, is a bit difficult to handle, the stronger results like contravariance for arbitrary maps between smooth stacks and the intersection pairing for smooth stacks are established by comparison with motivic cohomology. 相似文献
74.
Yi-Jen Chiang 《Computational Geometry》1998,9(4):211-236
We present an extensive experimental study comparing the performance of four algorithms for the following orthogonal segment intersection problem: given a set of horizontal and vertical line segments in the plane, report all intersecting horizontal-vertical pairs. The problem has important applications in VLSI layout and graphics, which are large-scale in nature. The algorithms under evaluation are our implementations of distribution sweep and three variations of plane sweep. Distribution sweep is specifically designed for the situations in which the problem is too large to be solved in internal memory, and theoretically has optimal I/O cost. Plane sweep is a well-known and powerful technique in computational geometry, and is optimal for this particular problem in terms of internal computation. The three variations of plane sweep differ by the sorting methods (external versus internal sorting) used in the preprocessing phase and the dynamic data structures (B-tree versus 2-3-4-tree) used in the sweeping phase. We generate the test data by three programs that use a random number generator while producing some interesting properties that are predicted by our theoretical analysis. The sizes of the test data range from 250 thousand segments to 2.5 million segments. The experiments provide detailed quantitative evaluation of the performance of the four algorithms, and the observed behavior of the algorithms is consistent with their theoretical properties. This is, to the best of our knowledge, the first experimental algorithmic study comparing the practical performance between external-memory algorithms and conventional algorithms with large-scale test data. 相似文献
75.
本文主要建立了凸体几何中Busemann-Petty问题的一个对偶均质积分形式,并将Funk截面定理推广到了对偶均质积分形式. 相似文献
76.
We study the perturbation property of best approximation to a set defined by an abstract nonlinear constraint system. We show that, at a normal point, the perturbation property of best approximation is equivalent to an equality expressed in terms of normal cones. This equality is related to the strong conical hull intersection property. Our results generalize many known results in the literature on perturbation property of best approximation established for a set defined by a finite system of linear/nonlinear inequalities. The connection to minimization problem is considered.The authors thank the referees for valuable suggestions.K.F. Ng - This author was partially supported by Grant A0324638 from the National Natural Science Foundation of China and Grants (2001) 01GY051-66 and SZD0406 from Sichuan Province.
Y.R. He -This author was supported by a Direct Grant (CUHK) and an Earmarked Grant from the Research Grant Council of Hong Kong. 相似文献
77.
Hans Raj Tiwary 《Discrete and Computational Geometry》2008,40(3):469-479
For polytopes P
1,P
2⊂ℝ
d
, we consider the intersection P
1∩P
2, the convex hull of the union CH(P
1∪P
2), and the Minkowski sum P
1+P
2. For the Minkowski sum, we prove that enumerating the facets of P
1+P
2 is NP-hard if P
1 and P
2 are specified by facets, or if P
1 is specified by vertices and P
2 is a polyhedral cone specified by facets. For the intersection, we prove that computing the facets or the vertices of the
intersection of two polytopes is NP-hard if one of them is given by vertices and the other by facets. Also, computing the
vertices of the intersection of two polytopes given by vertices is shown to be NP-hard. Analogous results for computing the
convex hull of the union of two polytopes follow from polar duality. All of the hardness results are established by showing
that the appropriate decision version, for each of these problems, is NP-complete. 相似文献
78.
We show several estimates on the probability distribution of some data at points in real complete intersection varieties: norms of real affine solutions, condition number of real solution of real systems of multi-variate polynomial equations and convergence radius of Newton's operator for under-determined system of multi-variate polynomial equations. 相似文献
79.
In this paper, we show that the strong conical hull intersection property (CHIP) completely characterizes the best approximation to any x in a Hilbert space X from the set
K:=C∩{xX:-g(x)S},