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991.
For a given planar point set P, consider a partition of P into disjoint convex polygons. In this paper, we estimate the maximum number of convex quadrilaterals in all partitions. 相似文献
992.
We investigate maximal functions involving averages over geodesics in three-dimensional Riemannian manifolds. We first show that one can easily extend the Euclidean results of Bourgain and Wolff if one assumes constant curvature. These results need not hold if this assumption is dropped. Nonetheless, we formulate a generic geometric condition which allows favorable estimates. Curiously, this condition ensures that one is in some sense as far as possible from the constant curvature case. Assuming this, one can prove dimensional estimates for Nikodym-type sets which are essentially optimal. Optimal estimates for the related maximal functions are still open though.
993.
Charles Frohman Razvan Gelca 《Transactions of the American Mathematical Society》2000,352(10):4877-4888
We prove that the Kauffman bracket skein algebra of the cylinder over a torus is a canonical subalgebra of the noncommutative torus. The proof is based on Chebyshev polynomials. As an application, we describe the structure of the Kauffman bracket skein module of a solid torus as a module over the algebra of the cylinder over a torus, and recover a result of Hoste and Przytycki about the skein module of a lens space. We establish simple formulas for Jones-Wenzl idempotents in the skein algebra of a cylinder over a torus, and give a straightforward computation of the -th colored Kauffman bracket of a torus knot, evaluated in the plane or in an annulus.
994.
L. A. Masal’tsev 《Mathematical Notes》2000,67(2):176-182
A representation of the Joachimsthal surfaces (having a family of curvature lines that lie in totally geodesic 2-spheres)
in the sphereS
3 is obtained. It is proved that, if a surface of constant mean curvature inS
3 has one family of curvature lines lying in totally geodesic 2-spheres, then it is a surface of rotation.
Translated fromMatematicheskie Zametki, Vol. 67, No. 2, pp. 221–229, February, 2000. 相似文献
995.
Let (M,F) and (M,F) be two (compact or not) foliated manifolds, C
F
(M, M) the space of smooth maps which send leaves into leaves. In this paper we prove that C
F
(M, M) admits a structure of an infinite-dimensional manifold modeled on LF-spaces, provided that F is a Riemannian foliation or, more generally, when it admits an adapted local addition. 相似文献
996.
997.
Cheng CHEN Fei LIU Xiang ZHANG~ Department of Mathematics Shanghai Jiaotong University Shanghai China 《中国科学A辑(英文版)》2007,(12)
In this paper we characterize the Liouvillian integrable orthogonal separable Hamiltonian systems on T~2 for a given metric,and prove that the Hamiltonian flow on any compact level hypersurface has zero topological entropy.Furthermore,by examples we show that the integrable Hamiltonian systems on T~2 can have complicated dynamical phenomena.For instance they can have several families of invariant tori,each family is bounded by the homoclinic-loop-like cylinders and heteroclinic-loop-like cylinders.As we know,it is the first concrete example to present the families of invariant tori at the same time appearing in such a complicated way. 相似文献
998.
We geometrically study the Legendre duality relation that plays an important role in statistical physics with the standard
or generalized entropies. For this purpose, we introduce dualistic structure defined by information geometry, and discuss
concepts arising in generalized thermostatistics, such as relative entropies, escort distributions and modified expectations.
Further, a possible generalization of these concepts in a certain direction is also considered.
Finally, as an application of such a geometric viewpoint, we briefly demonstrate several new results on the behavior of the
solution to a nonlinear diffusion equation called the porous medium equation. 相似文献
999.
William D. Simmons 《代数通讯》2017,45(7):3137-3149
Differential algebraic geometry seeks to extend the results of its algebraic counterpart to objects defined by differential equations. Many notions, such as that of a projective algebraic variety, have close differential analogues but their behavior can vary in interesting ways. Workers in both differential algebra and model theory have investigated the property of completeness of differential varieties. After reviewing their results, we extend that work by proving several versions of a “differential valuative criterion" and using them to give new examples of complete differential varieties. We conclude by analyzing the first examples of incomplete, finite-rank projective differential varieties, demonstrating a clear difference from projective algebraic varieties. 相似文献
1000.
在自动化高速公路环境下,提出一种改进的宏观离散交通流模型密度控制方法.利用反馈线性化方法,将宏观离散交通流模型转换为一般容易处理的线性系统模型,简化了密度控制器的设计.利用线性系统中具有输入变换的跟踪反馈控制方法,对线性化后的系统模型设计控制律.通过控制该线性系统的状态变量,间接稳定离散交通流模型中的交通流密度,达到对道路交通流拥堵的控制.同时给出设计方法和步骤,仿真实例说明了方法的实用性. 相似文献