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Computational Tools in Weighted Persistent Homology

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Chinese Annals of Mathematics,Series B 2021年第2期42卷 237-258页

作者： shiquan ren Chengyuan WU Jie WU Yau Mathematical Sciences Center Tsinghua UniversityBeijing 100084China Department of Mathematics National University of SingaporeSingapore 119076Singapore Institute of High Performance Computing A*STARSingapore 138632Singapore School of Mathematical Sciences Hebei Normal UniversityShijiazhuang 050024China Center for Topology and Geometry based Technology Hebei Normal University050024China.

In this paper, the authors study further properties and applications of weighted homology and persistent homology. The Mayer-Vietoris sequence and generalized Bockstein spectral sequence for weighted homology are introduced. For applications, the authors show an algorithm to construct a filtration of weighted simplicial complexes from a weighted network. They also prove a theorem to calculate the mod p^(2) weighted persistent homology provided with some information on the mod p weighted persistent homology.

关键词： Algebraic topology Persistent homology Weighted persistent homology Bockstein spectral sequence

A Künneth Formula for Finite Sets

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Chinese Annals of Mathematics,Series B 2021年第6期42卷 801-812页

作者： Chong WANG shiquan ren Jian LIU School of Mathematics Renmin University of ChinaBeijing 100872China Department of Mathematics and Statistics Cangzhou Normal UniversityCangzhou 061000HebeiChina School of Mathematics and Statistics Henan UniversityKaifeng 475001HenanChina School of Mathematical Sciences Hebei Normal UniversityShijiazhuang 050024China

In this paper,the authors define the homology of sets,which comes from and contains the ideas of path homology and embedded ***,A Kunneth formula for sets associated to the homology of sets is given.

关键词： Künneth formula Finite set Principal ideal domain Cartesian product Free R-module

LOCAL INFLUENCE IN DISCRIMINANT ANALYSIS

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Systems Science and Mathematical Sciences 1995年第1期8卷 27-36页

作者： WANG Xueren ren shiquan SHI Lei (Department of Statistics, Yunnan University, Kunming 650091, China) 云南大学统计系云南昆明

ＬＯＣＡＬＩＮＦＬＵＥＮＣＥＩＮＤＩＳＣＲＩＭＩＮＡＮＴＡＮＡＬＹＳＩＳＷＡＮＧＸｕｅｒｅｎ；ＲＥＮＳｈｉｑｕａｎ；ＳＨＩＬｅｉ（ＤｅｐａｒｔｍｅｎｔｏｆＳｔａｔｉｓｔｉｃｓ，ＹｕｎｎａｎＵｎｉｖｅｒｓｉｔｙ，Ｋｕｎ... 详细信息

ＬＯＣＡＬＩＮＦＬＵＥＮＣＥＩＮＤＩＳＣＲＩＭＩＮＡＮＴＡＮＡＬＹＳＩＳＷＡＮＧＸｕｅｒｅｎ；ＲＥＮＳｈｉｑｕａｎ；ＳＨＩＬｅｉ（ＤｅｐａｒｔｍｅｎｔｏｆＳｔａｔｉｓｔｉｃｓ，ＹｕｎｎａｎＵｎｉｖｅｒｓｉｔｙ，Ｋｕｎｍｉｎｇ６５００９１，Ｃｈｉｎａ）...

关键词： Discriminant analysis generalized cook statistic perturbation scheme local influence.

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Δ-集分次子集的霍奇理论和离散莫尔斯定理

南开大学学报（自然科学版） 2021年第5期54卷 7-13页

作者：王冲任世全沧州师范学院数学与统计学院河北沧州061000 中国人民大学数学学院北京100872 清华大学丘成桐数学科学中心北京100084

超图的嵌入同调和有向图的道路同调可以被Δ-集分次子集的嵌入同调统一.受此启发给出了Δ-集分次子集的霍奇理论和代数离散莫尔斯定理.

关键词： Δ-集嵌入同调霍奇同构定理霍奇分解定理离散莫尔斯定理

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顶点加权有向图的持续同调

数学进展 2020年第6期49卷 737-755页

作者：王冲任世全林勇中国人民大学数学学院北京100872 沧州师范学院数学与统计学院沧州河北061000 清华大学丘成桐数学科学中心北京100084

本文回顾了文献[*** ***.,2016,11(2):209-230]中引入的同调,讨论了权重对持续权重道路同调的影响,证明了顶点加权有向图连接的库尼斯公式的持续形式.

关键词：有向图权重道路同调持续权重道路同调库尼斯公式

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多反应变量重复测量的混合效应模型及其应用

生物数学学报 1999年第2期14卷 229-234页

作者：任仕泉陈峰杨树勤吴先萍四川大学管理科学系成都610065 南通医学院医学统计学教研室南通226001 华西医科大学卫生统计学教研室成都610041 四川省卫生防疫站成都610031

本文给出了多反应变量重复测量的协方差矩阵结构，探讨了用迭代广义最小二乘法来求解其带协变量和不带协变量的混合效应模型中固定效应和随机效应系数，并对１９９１年四川省高血压调查资料进行实例分析，得到其结论符合实际情况．

关键词：多反应变量重复测量混合效应模型

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有向图的基本群和覆盖

数学进展 2023年第2期52卷 235-249页

作者：王冲任世全刘秀贵沧州师范学院数学与统计系河北沧州061000 河南大学数学与统计学院河南开封475004 南开大学数学科学学院天津300071

本文基于范畴理论,主要研究了有向图和其对应的无向图(简称为图)在不同同伦等价意义下基本群之间的关系,证明了覆盖映射所诱导的覆盖图和底图的基本群之间的同态是单同态.设G是连通有向图,G是G的万有覆盖,覆盖映射为p.我们证明了G的覆... 详细信息

本文基于范畴理论,主要研究了有向图和其对应的无向图(简称为图)在不同同伦等价意义下基本群之间的关系,证明了覆盖映射所诱导的覆盖图和底图的基本群之间的同态是单同态.设G是连通有向图,G是G的万有覆盖,覆盖映射为p.我们证明了G的覆盖转化群D(G,p)同构于G在C-同伦意义下的基本群.

关键词： C-同伦基本群覆盖有向图同伦提升性质

Tuning the cross-linked structure of basic poly(ionic liquid)to develop an efficient catalyst for the conversion of vinyl carbonate to dimethyl carbonate

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Chinese Journal of Chemical Engineering 2024年第8期72卷 106-116页

作者： Zhaoyang Qi shiquan Zhong Huiyun Su Changshen Ye Limei ren Ting Qiu Jie Chen College of Chemical Engineering Fuzhou UniversityFuzhou 350108China Department of Chemical Engineering Shijiazhuang UniversityShijiazhuang 050035China Qingyuan Innovation Laboratory Quanzhou 362801China Fuzhou University International Joint Laboratory of Thermochemical Conversion of Biomass Fuzhou UniversityFuzhou 350108China

Dimethyl carbonate(DMC)is a crucial chemical raw material widely used in organic synthesis,lithiumion battery electrolytes,and various other *** current primary industrial process employs a conventional sodium methoxide basic catalyst to produce DMC through the transesterification reaction between vinyl carbonate and ***,the utilization of this catalyst presents several challenges during the process,including equipment corrosion,the generation of solid waste,susceptibility to deactivation,and complexities in separation and *** address these limitations,a series of alkaline poly(ionic liquid)s,i.e.[DVBPIL][PHO],[DVCPIL][PHO],and[TBVPIL][PHO],with different crosslinking degrees and structures,were synthesized through the construction of cross-linked polymeric monomers and *** poly(ionic liquid)s exhibit cross-linked structures and controllable cationic and anionic *** was conducted to investigate the effect of the cross-linking degree and structure on the catalytic performance of transesterification in synthesizing *** was discovered that the appropriate cross-linking degree and structure of the[DVCPIL][PHO]catalyst resulted in a DMC yield of up to 80.6%.Furthermore,this catalyst material exhibited good stability,maintaining its catalytic activity after repeated use five times without significant *** results of this study demonstrate the potential for using alkaline poly(ionic liquid)s as a highly efficient and sustainable alternative to traditional catalysts for the transesterification synthesis of DMC.

关键词： Poly(ionic liquid) Cross-linking degree Dimethyl carbonate production Transesterification reaction Mechanism

Male heterogametic sex determination in Rana dybowskii based on sex-linked molecular markers

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Integrative Zoology 2022年第1期17卷 105-114页

作者： Yuan XU Zhiheng DU Jiayu LIU Hang SU Fangyong NING shiquan CUI Lijuan WANG Jianming LIU Chuanshuai ren Shengwei DI Xiujuan BAI College of Animal Science and Technology Northeast Agricultural UniversityHarbinChina College of Life Sciences Northeast Agricultural UniversityHarbinChina College of Agricultural Eastern Liaoning UniversityDandongChina Yili Animal Science Research Institute YiningChina Animal Husbandry Administration of Huadian HuadianChina Branch of Animal Husbandry and Veterinary of Heilongjiang Academy of Agricultural Sciences QiqiharChina

Identifying the mechanism for sex determination in amphibians is *** little is known about sex determination mechanisms of Rana dybowskii,a species of importance to evolutionary and conservation *** screened for sex-linked molecular markers in *** in China using target region amplification polymorphism with 2 fixed primers against the sequences of *** found 2 male-linked molecular markers in ***,which were 222 bp and 261 bp *** detection rates of 222 bp marker in males form Xinglong,Huadian,and Dandong were 93.79%,69.64%,and 13.64%,respectively,while the rate in females from Huadian was 27.50%.Besides,the detection rates of 261 bp marker in the above 3 regions were only observed in males at the rate of 93.79%,87.50%,and 32.73%,*** inheritance patterns of sex-linked molecular markers showed that the 2 sex-linked molecular markers were *** to the XY-male parent,progeny from XX-pseudo-male parent possessed lower sex reversal ratio at the same rearing temperature,and the proportion of female froglets from an XX-pseudo-male parent was more than 95%at low rearing temperature(15°C).Our findings suggest that *** displays male heterogamety,and the 2 sex-linked molecular markers may have a guiding significance for the protection and utilization of ***.

关键词： male-linked molecular markers Rana dybowskii sexual reversal TRAP markers