For each real number x∈(0,1),let[a_(1)(x),a_(2)(x),…,a_n(x),…]denote its continued fraction expansion.We study the convergence exponent defined byτ(x)=inf{s≥0:∞∑n=1(a_(n)(x)a_(n+1)(x))^(-s)<∞},which reflect...For each real number x∈(0,1),let[a_(1)(x),a_(2)(x),…,a_n(x),…]denote its continued fraction expansion.We study the convergence exponent defined byτ(x)=inf{s≥0:∞∑n=1(a_(n)(x)a_(n+1)(x))^(-s)<∞},which reflects the growth rate of the product of two consecutive partial quotients.As a main result,the Hausdorff dimensions of the level sets ofτ(x)are determined.展开更多
M（J, {ms ＊ ns}, {Cs}） be the collection of Cartesian products of two homogenous Moran sets with the same ratios {cs} Where J = [0, 1] × [0, 1]. Then the maximal and minimal values of the Hausdorff dimensions f...M（J, {ms ＊ ns}, {Cs}） be the collection of Cartesian products of two homogenous Moran sets with the same ratios {cs} Where J = [0, 1] × [0, 1]. Then the maximal and minimal values of the Hausdorff dimensions for the elements in M are obtained without any restriction on {msns} or {cs}.展开更多
针对现有相同产品特征识别方法受限于词典覆盖率或语料规模的不足,提出一种基于多维相似度和情感词扩充的识别方法。通过双向长短时记忆条件随机场(bi-directional long short-term memory and conditional random field, Bi-LSTM-CRF)...针对现有相同产品特征识别方法受限于词典覆盖率或语料规模的不足,提出一种基于多维相似度和情感词扩充的识别方法。通过双向长短时记忆条件随机场(bi-directional long short-term memory and conditional random field, Bi-LSTM-CRF)模型抽取产品特征的扩充情感词,综合特征词的语素相似度、同义词林相似度和TF-IDF(term frequency-inverse document frequency)余弦相似度,采用K-medoids聚类算法,识别相同的产品特征。试验结果表明,在手机和笔记本数据集上,该方法的最大调整兰德指数分别达到0.579和0.595 9,而最小熵值分别达到0.782 6和0.745 7,均优于结合语素的调整Jaccard相似度、Word2Vec相似度和基于二分K-means的Word2Vec相似度三种基线试验方法。展开更多
In Artin algebra representation theory there is an important result which states that when the order of G is invertible in A then gl.dim（AG）=gl.dim（A）. With the development of Hopf algebra theory, this result is g...In Artin algebra representation theory there is an important result which states that when the order of G is invertible in A then gl.dim（AG）=gl.dim（A）. With the development of Hopf algebra theory, this result is generalized to smash product algebra. As known, weak Hopfalgebra is an important generalization of Hopf algebra. In this paper we give the more general result, that is the relation of homological dimension between an algebra A and weak smash product algebra A#H, where H is a finite dimensional weak Hopf algebra over a field k and A is an H-module algebra.展开更多
In this paper, we consider the Riesz product dμ =^∞∏j=1（1＋ajRexbjλj（x））dx in local fields, and we obtain the upper and lower bound of its Hausdorff dimension.
Let H be a finite dimensional cocommutative Hopf algebra and A an H-module algebra. In this paper, we characterize the projectivity (injectivity) of M as a left A#σH-module when it is projective (injective) as a left...Let H be a finite dimensional cocommutative Hopf algebra and A an H-module algebra. In this paper, we characterize the projectivity (injectivity) of M as a left A#σH-module when it is projective (injective) as a left A-module. The sufficient and necessary condition for A#σH, the crossed product, to have finite global homological dimension is given, in terms of the global homological dimension of A and the surjectivity of trace maps, provided that H is cocommutative and A is commutative.展开更多
基金supported by the Scientific Research Fund of Hunan Provincial Education Department(21B0070)the Natural Science Foundation of Jiangsu Province(BK20231452)+1 种基金the Fundamental Research Funds for the Central Universities(30922010809)the National Natural Science Foundation of China(11801591,11971195,12071171,12171107,12201207,12371072)。
文摘For each real number x∈(0,1),let[a_(1)(x),a_(2)(x),…,a_n(x),…]denote its continued fraction expansion.We study the convergence exponent defined byτ(x)=inf{s≥0:∞∑n=1(a_(n)(x)a_(n+1)(x))^(-s)<∞},which reflects the growth rate of the product of two consecutive partial quotients.As a main result,the Hausdorff dimensions of the level sets ofτ(x)are determined.
基金Supported by the National Natural Science Foundation of China (No.10771082 and 10871180)
文摘M（J, {ms ＊ ns}, {Cs}） be the collection of Cartesian products of two homogenous Moran sets with the same ratios {cs} Where J = [0, 1] × [0, 1]. Then the maximal and minimal values of the Hausdorff dimensions for the elements in M are obtained without any restriction on {msns} or {cs}.
文摘针对现有相同产品特征识别方法受限于词典覆盖率或语料规模的不足,提出一种基于多维相似度和情感词扩充的识别方法。通过双向长短时记忆条件随机场(bi-directional long short-term memory and conditional random field, Bi-LSTM-CRF)模型抽取产品特征的扩充情感词,综合特征词的语素相似度、同义词林相似度和TF-IDF(term frequency-inverse document frequency)余弦相似度,采用K-medoids聚类算法,识别相同的产品特征。试验结果表明,在手机和笔记本数据集上,该方法的最大调整兰德指数分别达到0.579和0.595 9,而最小熵值分别达到0.782 6和0.745 7,均优于结合语素的调整Jaccard相似度、Word2Vec相似度和基于二分K-means的Word2Vec相似度三种基线试验方法。
基金Project supported by the Cultivation Fund of the Key Scientific and Technical Innovation Project, Ministry of Education of China (No. 704004), the Program for New Century Excellent Talents in Univer-sity (No. 04-0522), and the Natural Science Foundation of Zhejiang Province (No. 102028), China
文摘In Artin algebra representation theory there is an important result which states that when the order of G is invertible in A then gl.dim（AG）=gl.dim（A）. With the development of Hopf algebra theory, this result is generalized to smash product algebra. As known, weak Hopfalgebra is an important generalization of Hopf algebra. In this paper we give the more general result, that is the relation of homological dimension between an algebra A and weak smash product algebra A#H, where H is a finite dimensional weak Hopf algebra over a field k and A is an H-module algebra.
文摘In this paper, we consider the Riesz product dμ =^∞∏j=1（1＋ajRexbjλj（x））dx in local fields, and we obtain the upper and lower bound of its Hausdorff dimension.
基金Foundationitem:The NSF(10271081)of Chinathe NSF(1042004)of Beijing City
文摘Let H be a finite dimensional cocommutative Hopf algebra and A an H-module algebra. In this paper, we characterize the projectivity (injectivity) of M as a left A#σH-module when it is projective (injective) as a left A-module. The sufficient and necessary condition for A#σH, the crossed product, to have finite global homological dimension is given, in terms of the global homological dimension of A and the surjectivity of trace maps, provided that H is cocommutative and A is commutative.
