We obtain an equation among invariants obtained from the Alexander module of an amphicheiral link. For special cases, it deduces necessary conditions on the Alexander polynomial. By using the present results and some ...We obtain an equation among invariants obtained from the Alexander module of an amphicheiral link. For special cases, it deduces necessary conditions on the Alexander polynomial. By using the present results and some known results, we show that the Alexander polynomial of an algebraically split component- preservingly （±）-amphicheiral link with even components is zero, and we determine prime amphieheiral links with at least 2 components and up to 9 crossings.展开更多
We propose a novel texture clustering method. A classical type of(approximate) shift invariant discrete wavelet transform(DWT),dual tree DWT,is used to decompose texture images. Multiple signatures are generated from ...We propose a novel texture clustering method. A classical type of(approximate) shift invariant discrete wavelet transform(DWT),dual tree DWT,is used to decompose texture images. Multiple signatures are generated from the obtained high-frequency bands. A locality preserving approach is applied subsequently to project data from high-dimensional space to low-dimensional space. Shift invariant DWT can represent image texture information efficiently in combination with a histogram signature,and the local geometrical structure of the dataset is preserved well during clustering. Experimental results show that the proposed method remarkably outperforms traditional ones.展开更多
基金supported by National Natural Science Foundation of China (Grant No. 10801021/a010402)
文摘We obtain an equation among invariants obtained from the Alexander module of an amphicheiral link. For special cases, it deduces necessary conditions on the Alexander polynomial. By using the present results and some known results, we show that the Alexander polynomial of an algebraically split component- preservingly （±）-amphicheiral link with even components is zero, and we determine prime amphieheiral links with at least 2 components and up to 9 crossings.
基金supported by the Hi-Tech Research and Development Program (863) of China (Nos. 2007AA01Z311 and 2007AA04Z1A5)the National Basic Research Program (973) of China (No. 2009CB32 0804)+1 种基金the National Research Foundation for the Doctoral Program of Higher Education of China (No. 20060335114)the Science and Technology Program of Zhejiang Province, China (No. 2007C21006)
文摘We propose a novel texture clustering method. A classical type of(approximate) shift invariant discrete wavelet transform(DWT),dual tree DWT,is used to decompose texture images. Multiple signatures are generated from the obtained high-frequency bands. A locality preserving approach is applied subsequently to project data from high-dimensional space to low-dimensional space. Shift invariant DWT can represent image texture information efficiently in combination with a histogram signature,and the local geometrical structure of the dataset is preserved well during clustering. Experimental results show that the proposed method remarkably outperforms traditional ones.
