We study the Hausdorff measure of linear Cantor setE, on the unit interval, under the strong seperated condition. We give a necessary and sufficient condition for ?(E)=∣E∣° by using the contracting ratio and th...We study the Hausdorff measure of linear Cantor setE, on the unit interval, under the strong seperated condition. We give a necessary and sufficient condition for ?(E)=∣E∣° by using the contracting ratio and the first gap. This condition is easy to use. Key words linear Cantor set - Hausdorff measure - strong seperated condition CLC number O 174. 12 Foundation item: Supported by the National Natural Science Foundation of China (10171028)Biography: Ma Chao (1975-), male, Ph. D. candidate, research direction: fractal geometry.展开更多
Define a linear Cantor set C to be the attractor of a linear iterated function system fj （x） =rjx ＋ bj（j = 1,2,…,N）, on the line satisfying the sures with respect to C,we study the centered upper and the centere...Define a linear Cantor set C to be the attractor of a linear iterated function system fj （x） =rjx ＋ bj（j = 1,2,…,N）, on the line satisfying the sures with respect to C,we study the centered upper and the centered lower density for Ф（t） = t^s withunnatural choices and with natural choices of s.展开更多
There are many important concepts in linear algebra, such as linear correlation and linear independence, eigenvalues and eigenvectors, and so on. The article provides a graphical explanation of how to distinguish betw...There are many important concepts in linear algebra, such as linear correlation and linear independence, eigenvalues and eigenvectors, and so on. The article provides a graphical explanation of how to distinguish between the concepts of linear correlation and linear independence. The conclusion points out that linear independence means that there are no two (base) vectors with the same direction in a vector graph;otherwise, it is a linear correlation.展开更多
文摘We study the Hausdorff measure of linear Cantor setE, on the unit interval, under the strong seperated condition. We give a necessary and sufficient condition for ?(E)=∣E∣° by using the contracting ratio and the first gap. This condition is easy to use. Key words linear Cantor set - Hausdorff measure - strong seperated condition CLC number O 174. 12 Foundation item: Supported by the National Natural Science Foundation of China (10171028)Biography: Ma Chao (1975-), male, Ph. D. candidate, research direction: fractal geometry.
文摘Define a linear Cantor set C to be the attractor of a linear iterated function system fj （x） =rjx ＋ bj（j = 1,2,…,N）, on the line satisfying the sures with respect to C,we study the centered upper and the centered lower density for Ф（t） = t^s withunnatural choices and with natural choices of s.
文摘There are many important concepts in linear algebra, such as linear correlation and linear independence, eigenvalues and eigenvectors, and so on. The article provides a graphical explanation of how to distinguish between the concepts of linear correlation and linear independence. The conclusion points out that linear independence means that there are no two (base) vectors with the same direction in a vector graph;otherwise, it is a linear correlation.
