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The Extension Dimension of Subcategories and Recollements of Abelian Categories

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Acta Mathematica Sinica,English Series 2024年第4期40卷 1042-1058页

作者： Xin MA Ye Yang PENG zhao yong huang College of Science Henan University of EngineeringZhengzhou 451191P.R.China Department of Mathematics Nanjing UniversityNanjing 210093P.R.China

We investigate the behavior of the extension dimension of subcategories of abelian categories under ***Λ',Λ,Λ"be art in algebras such that(modΛ',mod A,modΛ")is a recollement,and let D'and D"be subcategories of modΛand modΛ"*** any n,m≥0,under some conditions,we get dimΩ^(k)(D)≤dimΩ^(n)(D')+dimΩ^(m)(D")+1,where k=max{m,n}and D is the subcategory of modΛglued by D'and D";moreover,we give a sufficient condition such that the converse inequality holds *** applications,some results for Igusa-Todorov subcategories and syzygy finite sub categories are obtained.

关键词： Recollements extension dimension Igusa–Todorov subcategories syzygy finite subcategories

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k-Gorenstein Modules

Acta Mathematica Sinica,English Series 2007年第8期23卷 1463-1474页

作者： zhao yong huang Department of Mathematics Nanjing University Nanjing 210093 P. R. China

Let A and F be artin algebras and ∧UГa paper, we first introduce the notion of k-Gorenstein faithfully balanced selforthogonal bimodule. In this modules with respect to ∧UГ and then characterize it in terms of the U-resolution dimension of some special injective modules and the property of the functors Ext^i （Ext^i （-, U）, U） preserving monomorphisms, which develops a classical result of Auslander. As an application, we study the properties of dual modules relative to Gorenstein bimodules. In addition, we give some properties of ∧UГwith finite left or right injective dimension.

关键词： κ-Gorenstein modules grade of modules injective dimension

Relative Syzygies and Grade of Modules

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Acta Mathematica Sinica,English Series 2013年第3期29卷 489-504页

作者： Zeng Feng LIU zhao yong huang Department of Mathematics Nanjing University

Recently, Takahashi established a new approximation theory for finitely generated modules over commutative Noetherian rings, which unifies the spherical approximation theorem due to Auslan- der and Bridger and the Cohen-Macaulay approximation theorem due to Auslander and Buchweitz. In this paper we generalize these results to much more general case over non-commutative rings. As an application, we establish a relation between the injective dimension of a generalized tilting module w and the finitistic dimension with respect to w.

关键词： n-l-Syzygy modules n-w-torsionfree modules approximation presentations grade

Relative Left Derived Functors of Tensor Product Functors

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Acta Mathematica Sinica,English Series 2016年第7期32卷 753-764页

作者： Jun Fu WANG zhao yong huang School of Mathematical Sciences and Chemical Engineering Changzhou Institute of Technology Department of Mathematics Nanjing University

We introduce and study the relative lett derive functor Torn（￡,￡1） category, which unifies several related left derived functors. Then we give some criteria for computing the -resolution dimensions of modules in terms of the properties of Torn（￡,￡1） . We also construct a complete and hereditary cotorsion pair relative to balanced pairs. Some known results are obtained as corollaries.

关键词： Tensor product functors relative left derived functors balanced pairs cotorsion pairs,(co)resolution dimension

On F-Almost Split Sequences

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Acta Mathematica Sinica,English Series 2010年第6期26卷 1149-1164页

作者： Xiao Jin ZHANG zhao yong huang College of Mathematics & Physics Nanjing University of Information Science & Technology Nanjing 210044 P. R. China Department of Mathematics Nanjing University Nanjing 210093 P. R. China

Let A be an Artinian algebra and F an additive subbifunctor of Ext,（-, -） having enough projectives and injectives. We prove that the dualizing subvarieties of mod A closed under F-extensions have F-almost split sequences. Let T be an F-cotilting module in mod A and S a cotilting module over F = End（T）. Then Horn（-, T） induces a duality between F-almost split sequences in ⊥FT and almost sl31it sequences in ⊥S, where addrS = Hom∧（f（F）, T）. Let A be an F-Gorenstein algebra, T a strong F-cotilting module and 0→A→B→C→0 and F-almost split sequence in ⊥*** the injective dimension of S as a Г-module is equal to d, then C≌（ΩCM^-dΩ^dDTrA^＊）^＊,where（-）^＊=Hom（g,T）.In addition, if the F-injective dimension of A is equal to d, then A≌ΩMF^-dDΩFop^-d TrC≌ΩCMF^-d ≌F^d DTrC.

关键词： F-almost split sequences almost split sequences F-Gorenstein algebras

Resolving Subcategories of Triangulated Categories and Relative Homological Dimension

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Acta Mathematica Sinica,English Series 2017年第11期33卷 1513-1535页

作者： Xin MA Ti Wei zhao zhao yong huang Department of Mathematics Nanjing UniversityNanjing 210093P.R.China

We introduce and study （pre）resolving subcategories of a triangulated category and the homological dimension relative to these subcategories. We apply the obtained properties to relative Gorenstein categories.

关键词： (Pre)resolving subcategories triangulated categories relative homological dimension,Gorenstein categories

Thymidylate synthase and thymidine phosphorylase gene expression as predictive parameters for the efficacy of 5-fluorouraci-based adjuvant chemotherapy for gastric cancer

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World Journal of Gastroenterology 2007年第37期13卷 5030-5034页

作者： Dong Hua zhao-Hui huang yong Mao Jian-Zhong Deng Oncology Institute of Wuxi the Fourth Affiliated Hospital ofSuzhou University Wuxi 214062 Jiangsu Province China

AIM： To investigate the prognostic role of thymidylate synthase （TS） and thymidine phosphorylase （TP） mRNA levels in T3 or T4 gastric cancer treated with 5-fluorouraci-based adjuvant chemotherapy. METHODS： Fifty-one patients with T3 or T4 gastric cancer received systemic 5-fluorouraci-based adjuvant chemotherapy, and intratumoral expression of TS and TP in 51 gastric cancer tissue samples was tested by realtime quantitative PCR.RESULTS： The median disease-free survival （DFS） time was 10.2 mo in the patients. There were no significant differences in DFS between the groups with high and low levels of TP. However, the group with low level of TS had a longer DFS （14.4 mo vs 8.3 mo, P = 0.017）. The median overall survival （OS） time was 18.5 mo, and there were significant differences in OS between the groups with high and low levels of TS or TP （for TS, 17.0 mo vs 21.3 mo, P = 0.010; for TP, 16.6 mo vs 22.5 too, P = 0.009）. Moreover, the coupled low expression of these two genes was strongly associated with a longer survival time of patients as compared with that of a single gene.CONCLUSION： Expression of TS and TP mRNA is a useful predictive parameter for the survival of postoperative gastric cancer patients after 5-fluorouracilbased adjuvant chemotherapy.

关键词： 5-fluorouracil Gastric cancer Thymidine phosphorylase Thymidylate synthase

Whole Lung Lavage Treatment of Chinese Patients with Autoimmune Pulmonary Alveolar Proteinosis： A Retrospective Long-term Follow-up Study

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Chinese Medical Journal 2015年第20期128卷 2714-2719页

作者： Yu-Yue zhao Hui huang yong-Zhe Liu Xin-Yu Song Shan Li Zuo-Jun Xu Department of Respiratory Medicine Peking Union Medical College Hospital Chinese Academy of Medical Sciences and Peking Union Medical College Beijing 100730 China

Background： Pulmonary alveolar proteinosis （PAP） is a rare lung disease, the most common type of which is autoimmune PAP. The gold standard therapy for PAP is whole lung lavage （WLL）. Few studies have reported the optimal technique with which to evaluate the response to WLL. In this study, we aimed to identify parameters with which to assess the need for repeat WLL during a long-term 8-year follow-up. Methods： We conducted a retrospective analysis of 120 patients with autoimmune PAP with 80 of whom underwent WLL. Physiologic, serologic, and radiologic features of the patients were analyzed during an 8-year follow-up after the first WLL treatment. Results： Of the 40 patients without any intervention, 39 patients either achieved remission or remained stable and only one died of pulmonary infection. Of the 56 patients who underwent WLL for 1 time, 55 remained free from a second WLL and 1 patient died of cancer. Twenty-four required additional treatments after their first WLL. The baseline PaO2, （P = 0.000）, PA-aO2 （P = 0.000）, shunt fraction rate （P = 0.001）, percent of predicted normal diffusing capacity of the lung for carbon monoxide （DLCO%Pred）（P = 0.016）, 6-rain walk test （P = 0.013）, carcinoembryonic antigen （CEA）（P = 0.007）, and neuron-specific enolase （NSE）（P = 0.003） showed significant differences among the three groups. The need for a second WLL was significantly associated with PaO2 （P = 0.000）, CEA （P= 0.050）, the 6-minute walk test （P= 0.026）, and DLCO%Pred （P = 0.041 ）. The DLCO%Pred on admission with a cut-off value of42.1% （P = 0.001） may help to distinguish whether patients with PAP require a second WLL. Conclusions： WLL is the optimal treatment method for PAP and provides remarkable improvements for affected patients. The DLCO%Pred on admission with a cut-offvalue of 42.1% may distinguish whether patients with PAP require a second WLL.

关键词： Diffusing Capacity of the Lung fbr Carbon Monoxide Prognosis Pulmonary Alveolar Proteinosis Treatment:Whole Lung Lavage

1.55-μm supercontinuum based on dispersion-flattened photonic crystal fiber

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Optoelectronics Letters 2007年第5期3卷 346-348页

作者： ZHANG Xia XU yong-zhao huang yong-qing REN Xiao-min Key Laboratory of Optical Communication and Lightwave Technologies Ministry of Education Beijing University of postsand Telecommunications Beijing 100876 China

A dispersion-flattened photonic crystal fiber with normal dispersion is designed for generating flat wideband supercontanuum, and the supercontinuum generation in this fiber is numerically analyzed. The results show that by appropriately designing the photonic crystal fiber, it can achieve flattened dispersion in the normal dispersion region. It is found that a fiber characterized by a flattened dispersion with a small normal dispersion is suitable for a flat wideband supercontinuum generation. In the process of spectral broadening, self-phase modulation effect plays a dominant role. By filtering the supercontinuum, pulses with different central wavelength over a wide spectral range can be obtained. The pulse width is determined by the bandwidth of the filter.

关键词：光学纤维光子晶体色散频率