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991.
本文指出了“关于自相似集的一个维数定理”一文中的一些问题。并给出反例说明该文的结论是不正确的。 相似文献
992.
Darin R. Stephenson James J. Zhang 《Proceedings of the American Mathematical Society》1997,125(6):1593-1605
We show that every graded locally finite right noetherian algebra has sub-exponential growth. As a consequence, every noetherian algebra with exponential growth has no finite dimensional filtration which leads to a right (or left) noetherian associated graded algebra. We also prove that every connected graded right noetherian algebra with finite global dimension has finite GK-dimension. Using this, we can classify all connected graded noetherian algebras of global dimension two.
993.
994.
对求解三维抛物型偏微分方程,利用待定参数法构造出一族新的高精度的三层显式差分格式,其精度为O(Δt3+Δx4+Δy4+Δz4),并论证了其稳定性,通过数值实例可见其精度较文[1]提高2位有效数字. 相似文献
995.
Alec Norton 《Proceedings of the American Mathematical Society》1999,127(10):3111-3118
If is the (unique) minimal set for a diffeomorphism of the circle without periodic orbits, , then the upper box dimension of is at least . The method of proof is to introduce the exponent into the proof of Denjoy's theorem.
996.
Zhou Shengfan 《Proceedings of the American Mathematical Society》1999,127(12):3623-3631
An estimate on the Hausdorff dimension of the global attractor for damped nonlinear wave equations, in two cases of nonlinear damping and linear damping, with Dirichlet boundary condition is obtained. The gained Hausdorff dimension is bounded and is independent of the concrete form of nonlinear damping term. In the case of linear damping, the gained Hausdorff dimension remains small for large damping, which conforms to the physical intuition.
997.
998.
999.
非退化扩散过程的相交性与极函数 总被引：5，自引：1，他引：4
该文证明了在适当的条件下,任何两个独立的一维扩散过程相交的概率为1,相交的时间集的Hausdorff维数为;讨论了扩散过程的极函数,在适当的条件下,得到了类似于Brown运动一样的结果． 相似文献
1000.
Robert S. Strichartz 《Transactions of the American Mathematical Society》1999,351(5):1705-1752
For a compact Hausdorff space that is pathwise connected, we can define the connectivity dimension to be the infimum of all such that all points in can be connected by a path of Hausdorff dimension at most . We show how to compute the connectivity dimension for a class of self-similar sets in that we call point connected, meaning roughly that is generated by an iterated function system acting on a polytope such that the images of intersect at single vertices. This class includes the polygaskets, which are obtained from a regular -gon in the plane by contracting equally to all vertices, provided is not divisible by 4. (The Sierpinski gasket corresponds to .) We also provide a separate computation for the octogasket (), which is not point connected. We also show, in these examples, that , where the infimum is taken over all paths connecting and , and denotes Hausdorff measure, is equivalent to the original metric on . Given a compact subset of the plane of Hausdorff dimension and connectivity dimension , we can define the isoperimetric profile function to be the supremum of , where is a region in the plane bounded by a Jordan curve (or union of Jordan curves) entirely contained in , with . The analog of the standard isperimetric estimate is . We are particularly interested in finding the best constant and identifying the extremal domains where we have equality. We solve this problem for polygaskets with . In addition, for we find an entirely different estimate for as , since the boundary of has infinite measure. We find that the isoperimetric profile function is discontinuous, and that the extremal domains have relatively simple polygonal boundaries. We discuss briefly the properties of minimal paths for the Sierpinski gasket, and the isodiametric problem in the intrinsic metric.