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Categorical resolutions of a class of derived categories 被引量:4
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作者 Pu Zhang 《Science China Mathematics》 SCIE CSCD 2018年第2期391-402,共12页
We clarify the relation between the subcategory D_(hf)~b(A) of homological finite objects in D^b(A)and the subcategory K^b(P) of perfect complexes in D^b(A), by giving two classes of abelian categories A with enough p... We clarify the relation between the subcategory D_(hf)~b(A) of homological finite objects in D^b(A)and the subcategory K^b(P) of perfect complexes in D^b(A), by giving two classes of abelian categories A with enough projective objects such that D_(hf)~b(A) = K^b(P), and finding an example such that D_(hf)~b(A)≠K^b(P). We realize the bounded derived category D^b(A) as a Verdier quotient of the relative derived category D_C^b(A), where C is an arbitrary resolving contravariantly finite subcategory of A. Using this relative derived categories, we get categorical resolutions of a class of bounded derived categories of module categories of infinite global dimension.We prove that if an Artin algebra A of infinite global dimension has a module T with inj.dimT <∞ such that ~⊥T is finite, then D^b(modA) admits a categorical resolution; and that for a CM(Cohen-Macaulay)-finite Gorenstein algebra, such a categorical resolution is weakly crepant. 展开更多
关键词 homologically finite object perfect complex smooth triangulated category (weakly crepant)categorical resolution (relative) derived category CM-finite Gorenstein algebra
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A hyperspectral image endmember extraction algorithm based on generalized morphology
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作者 王东辉 杨秀坤 赵岩 《Optoelectronics Letters》 EI 2014年第5期387-390,共4页
Generalized morphological operator can generate less statistical bias in the output than classical morphological operator. Comprehensive utilization of spectral and spatial information of pixels, an endmember extracti... Generalized morphological operator can generate less statistical bias in the output than classical morphological operator. Comprehensive utilization of spectral and spatial information of pixels, an endmember extraction algorithm based on generalized morphology is proposed. For the limitations of morphological operator in the pixel arrangement rule and replacement criteria, the reference pixel is introduced. In order to avoid the cross substitution phenomenon at the boundary of different object categories in the image, an endmember is extracted by calculating the generalized opening-closing(GOC) operator which uses the modified energy function as a distance measure. The algorithm is verified by using simulated data and real data. Experimental results show that the proposed algorithm can extract endmember automatically without prior knowledge and achieve relatively high extraction accuracy. 展开更多
关键词 EXTRACTION Morphology PIXELS Spectroscopy Comprehensive utilizations Endmember extraction algorithms Extraction accuracy Generalized morphological operators Hyper spectral images Morphological operator object categories Spatial informations
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