Dimension characterizations of complexity classes

When it comes to writing an essay in English about Chinese novels,its important to consider both the cultural context and the literary aspects that make these works unique. Here are some key points to include in your essay to ensure a comprehensive and insightful analysis:1.Introduction to Chinese Literature:Begin by providing a brief overview of Chinese literature,its history,and its significance in world literature.Mention how Chinese novels have evolved over time,from classical works like Dream of the Red Chamber to modern novels that have gained international acclaim.2.Themes and Motifs:Discuss the common themes and motifs found in Chinese novels. These can include themes of love,loss,social hierarchy,and the human condition.Motifs might include the use of nature,dreams,and historical events to convey deeper meanings.3.Cultural Context:Its crucial to understand the cultural context in which these novels were written.Explain how Chinese society,history,and philosophy have influenced the stories and characters.For example,the concept of face social reputation and the importance of family and filial piety are often central to the narratives.nguage and Style:Analyze the language and style of Chinese novels.Discuss how the authors use language to create vivid imagery,convey emotions,and develop characters.You might also want to touch on the challenges of translating Chinese literature into English,as the original text often contains cultural nuances and linguistic subtleties that can be lost in translation.5.Character Development:Explore the development of characters in Chinese novels. Discuss how characters are often complex and multidimensional,reflecting the complexities of Chinese society.Consider how the characters journeys and transformations contribute to the overall narrative.6.Narrative Structure:Chinese novels often have a different narrative structure compared to Western literature.Discuss how the structure of Chinese novels can be episodic,with multiple plotlines and a nonlinear progression of events.This can be a point of comparison with Western novels,which often follow a more linear narrative structure.7.Influence on Modern Literature:Consider the influence of Chinese novels on contemporary literature,both in China and internationally.Discuss how modern authors have been inspired by traditional Chinese storytelling and how they have adapted these stories to fit a modern context.8.Conclusion:Summarize the main points of your essay and reflect on the significance of Chinese novels in the broader context of world literature.Discuss the enduring appeal of these works and their relevance to readers today.9.Works Cited:If youve referenced specific novels or authors,be sure to include a list of works cited to give credit to the original sources.Remember,when writing about Chinese novels,its essential to approach the subject with respect for the cultural and historical context.This will allow you to provide a nuanced and thoughtful analysis that does justice to the richness of Chinese literature.。

AM 算术平均数ama 半规管膨隆amacrine cell 无长突细胞amacrine 无长突的amalgamate 合并amalgamation 混合种amaroid 苦味质amasesis 咀嚼不能amathophobia 恐尘埃症amativeness 恋爱嗜好amatory 恋爱的amaurosis fugax 一时性黑蒙amaurosis 黑蒙amaurosis 全盲amaurotic familial idiocy 黑蒙性先天白痴amaurotic idiocy 黑蒙性白痴amaurotic 黑蒙性amaxophobia 乘车恐怖症amazement 惊愕ambidexterity 两手同能ambidextrality 两手同能ambidextrism 两手同利ambidextrous 两手同利ambidextrously 两手同利的ambient conditions 周围情况ambient noise 周围环境噪声ambient pressure 环境压力ambient vision 周围环境视觉ambiequal type 两向型ambiequal 两向的ambiguity cue 模棱线索ambiguity intolerance 难忍的模棱两可ambiguity tolerance 模棱容忍度ambiguity tolerance 易忍的模棱两可ambiguity 模棱两可ambiguous case 两可情况ambiguous figure 两可图形ambiguous perspective 交变透视ambiguous stimulus 模棱刺激ambiguous word 歧义字ambiguous 两可图ambilateral 两侧的ambilerosity 两手不利ambilingual 双语的ambiopia 复视ambisextrous 两性的ambisexual 两性的ambisexuality 两性人ambit 界限ambitendency 矛盾意向ambition 雄心ambitious paranoia 夸大性偏执狂ambivalence of the will 意志矛盾ambivalence 矛盾心态ambivalent depression 矛盾性抑郁症ambivalent personality 矛盾人格ambivalent phase 矛盾期ambivalent word 词义对立词ambivalent 矛盾的ambiversion 两向性格ambivert 两向性格者amblyacousia 听觉迟钝amblyaphia 触觉迟钝amblygeustia 味觉迟钝amblyope 弱视者amblyopia 弱视amblyopiatrics 弱视矫正法amblyscope 立体像融合镜amblyscope 弱视镜amblystomas 蝾螈类ambrosiac 麝香气ambulate 行走ambulatory automatism 觉醒游行症ambulatory psychotherapy 自助式心理治疗ambustion 灼伤amelanotic 不含黑色素的amelioration 褒义化amend 修正amenity 愉快amenorrhoea 闭经ament 白痴ament 精神错乱者amentia 智力缺陷American Educational Research Journal 美国教育研究American Geriatrics Association 美国老年病学协会American Journal of Community Psychology 美国社区心理学杂志American Journal of Mental Retardation 美国智力迟钝杂志American Journal of Psychoanalysis 美国心理分析杂志American Journal of Psychology 美国心理学杂志American Neurological Association 美国神经病学协会American Organizational Psychology Association 美国组织心理学协会American Physiological Association 美国生理学会American Psychiatric Association 美国精神病学会American Psychoanalyst 美国精神分析学家American Psychoanalytic Association 美国精神分析协会American Psychological Association 美国心理学会American Psychologist 美国心理学家美国心理学家American Psychopathological Society 美国精神病理学会American Science Information Institute 美国科学情报学会American Sign Language 美语手语American Society for Genetics 美国遗传学学会amerism 分音节不能Ames demonstration 艾姆斯深度知觉演示Ames demonstration 空间错觉演示Ames illusions 艾姆斯错觉Amesametrometer 屈光不正测量器ametropia 屈光不正amiability 和蔼amicine 生长抑制素amimia 表情缺失amine oxidase inhibitor 胺氧化酶抑制物amine 胺amino acid 氨基酸amino acid autoradiography 氨基酸放射自显术aminoacidopathy 氨基酸缺陷病aminoaciduria 氨基酸尿aminogram 氨基酸谱aminophylline 氨茶碱aminosis 氨基酸过多症ammeter 安培计Ammon samnalgesia 遗忘止痛法amnemomic aphasia 遗忘性失语amnesia amimia 遗忘性表情不能amnesia confabulation 失忆性虚构amnesia optica 视觉缺失amnesia syndrome 遗忘综合症amnesia 健忘症amnesia 失忆症amnesic amimia 遗忘性表情不能amnesic aphasia 遗忘性失语amnesic color blindness 遗忘性色盲amnesic 遗忘的amnestic aphasia 健忘性失语amnestic apraxia 遗忘性失用症amnestic syndrome 失忆综合症amnestic syndrome 遗忘综合症amodal completion 变形的完成amodal perception 变形知觉amoeba 变形虫amoeboid movement 变形运动amok 残暴性狂症among groupsamoral character 非道德品格amoral 非道德的amoralism 非道德论amorality 超道德amorality 非道德amorous 多情的amorpha 无定形病amorphinism 吗啡断瘾状态amorphism 无定形性amorphognosia 形态失认amorphosynthesis 形态综合不能amorphous personality 无定型人格amorphous type 情绪淡漠amort 意气消沉的amotio retinae 视网膜脱落amotio 脱落amotivational syndrome 缺动机综合症amount of change 变动量amount of forgetting 遗忘量amount of information 信息量amount of input information 输入信息量amount of inspection 检验数量amount of reinforcement 强化量amount of sweat 汗量amount of transmitted information 信息传递量amount of variability 变异量amount of work 工作量amount 总数amour propreamour 不正当男女关系amp 安培amphamphoterodiplopia 两眼复视ampheclexis 两性选择amphetamine 安非他明amphibian 两栖类amphiblestritis 视网膜炎amphibolia 不稳定期amphibology 模棱两可amphichroic reaction 两性反应amphichroic 两性的amphichromatic 两性反应的amphicrania 两侧头痛amphicroic 两性的amphigonous inheritance 双亲遗传amphilepsis 双亲遗传amphimixis 两性融合amphineura 双神经网amphoric 空瓮性amphorophony 空瓮性语音amphoteric 两性的amphoterodiplopia 两眼复视amphotony 交感迷走神经过敏ampliate 放大的ampliation 运动因果错觉amplification 放大amplifier stage 放大级amplifier 放大器amplitude distortion 波幅畸变amplitude distribution analysis 振幅分布分析amplitude of accommodation 调节幅度amplitude of convergence 会聚幅度amplitude of cycles 循环幅度amplitude of fluctuation 波动幅度amplitude of variation 幅度变化amplitude of vibration 振幅amplitude of wave 波幅amplitude probability density 振幅概率密度amplitude ratio 振幅比率amplitude velocity 幅速amplitude modulatedamplitude 幅amplitude 幅度ampulla 壶腹ampullitis 壶腹炎amuck 杀人狂症状amulet 护身符amusement motive 游乐性动机amusia 乐歌不能amusia 失音症amyasthenia 肌无力amychophobia 恐抓伤症amyelencephalia 无脑脊髓畸形amyeletrophy 脊髓萎缩amyelia 无脊髓畸形amyelic nerve fiber 无髓神经纤维amyelic 无髓的amyelinic fiber 无髓鞘纤维amyelinic 无髓鞘的amyelonic 无髓的amygdala 扁桃体amygdala 杏仁核amygdaline 扁桃体的amygdaloid body 杏仁体amygdaloid nucleus 杏仁核amylene hydrate 水合戊烯amylenization 戊烯麻醉amylobarbitone 异戊巴比妥amynology 免疫学amyo esthesiaamyocardia 心肌无力amyoesthesia 肌觉缺失amyoplasia 肌发育不全amyostasia 肌震颤amyosthenia 肌无力amyotaxia 肌运动失调amyotaxy 肌共济失调amyotonia 肌弛缓amyotrophia 肌萎缩amyotrophic lateral sclerosis 肌肉萎缩性一侧硬化amyotrophic 肌肉萎缩的amytal interview 阿密妥面谈amytal test 阿密妥测验anabasis 病加重期anabiosis 回生anabolic effect 合成作用anabolic phenomenon 合成代谢现象anabolic 合成代谢anabolism 合成代谢anabolite 合成代谢产物anabology 后加演化anaboly 后加演化anacamptic 折射的anacamptometer 反射计anacatesthesia 彷徨不安感anachoresis 摄菌作用anachoresis 退隐anachronism 时代错乱anaclasimeter 屈光检查仪anaclasis 光折射anaclastic 折射的anaclisis 依附性anaclitic choice 依赖性择配anaclitic depression 依赖性抑郁anaclitic identification 依附性认同anaclitic object choice 依赖对象选择anaclitic object 依附对象anaclitic therapy 依赖治疗法anaclitic 依附的anacmesis 成熟受阻anacousia 全聋anacusia 全聋anadipsia 剧渴anadrenalismus 肾上腺机能缺失anaemia 贫血anaemotrophy 血液滋养不足anaerobic respiration 缺氧呼吸anaerobiosis 厌氧生活anaerosis 呼吸间断anaesthesia 麻木anaesthesia 麻醉anaesthetization by acupuncture 针刺麻醉anaesthetization 麻醉anagenesis 再生anaglyph method 视差图像法anaglyph 视差图像anaglyphoscope 反视镜anaglyphoscope 观立体镜观立体镜anagocytic 抑制细胞再生的anagoge 理想精神anagogic interpretation 潜因释梦anagram 字谜anagram 拚字图anahormone 类激素anakusis 全聋anal character 肛门性格anal erotism 肛原性anal fixation 肛门期滞留作用anal impotence 肛门无能anal masochism 肛门被虐性anal masturbation 肛门手淫anal personality 肛门期性格anal phase 肛门期anal sadism 肛门加虐性anal stage 肛门期anal expulsiveanal expulsiveanal rapeanal retentiveanal retentiveanaleptics 兴奋剂analgesia algera 痛区感觉缺失analgesia 失痛症analgesics 镇痛药analgesimeter 痛觉测量器analog code 模拟编码analog computation 模拟计算analog computer 模拟计算机analog control 模拟控制analog data 模拟数据analog display 模拟显示analog network 模拟网络analog psychology 模拟心理学analog quantity 模拟量analog representation 类比表征analog signal 模拟信号analog simulation 相似模拟analog systems 模拟系统analog 类似analog 模拟analogical change 类推变化analogical extension 类推扩展analogical inference 类比推理analogical method 类推法analogical probation 类推论证analogical reasoning 类比推理analogical 类拟的analogies of experience 经验类比analogies test 类比测验analogism 类比推理analogist 类推者analogous argumentation 类比论证analogous concept 类比概念analogous evolution 平行进化analogous inference 类比推理analogous type 模拟型analogue computer 模拟计算机analogue digital conversion 模拟数字转换analogue display 模拟显示analogue method 模拟法analogue model 模拟模型analogue signal 模拟信号analogue technique 模拟技术analogue transmission 模拟传输analogue type 模拟型analogue 类似物analogue 模拟analogy of attribution 属性类比analogy of proportionality 比例类比analogy test 模拟测验analogy 类比analysand 被分析者analysand 精神分析对象analysator 分析器analysis approach 分析研究analysis by filtering 过滤式分析analysis by synthesis theory 综合分析理论analysis by synthesis 综合分析analysis chart 分析图analysis language 分析型语言analysis of correlation 相关分析analysis of covariance model 协方差分析模型analysis of covariance structures 协方差结构分析analysis of covariance table 协方差分析表analysis of covariance 协方差分析analysis of data 数据分析analysis of human error 人为失误分析analysis of language 语言分析analysis of Latin Square 拉丁方阵分析analysis of learning potential 学习潜能分析analysis of matter 质料分析analysis of motion 运动分析analysis of network 网络分析Analysis of Readiness Skills 已备技能分析analysis of sensation 感觉分析analysis of variance 方差分析analysis of variance model 方差分析模型analysis of variance of factorial design 析因设计方差分析analysis of variance table 方差分析表analysis situs 拓朴学analysis tolerance 耐力分析analysis generalizationanalysis 分析analysor 分析器analyst programmeranalyst 分析者analytic group psychotherapy 分析团体心理治疗法analytic language 分析性语言analytic mechanics 分析力学analytic method 分析法analytic process 分析过程analytic proposition 分析命题analytic psychology 分析心理学analytic psychotherapy 分析心理治疗analytic reliability 分析信度analytic therapy 分析疗法analytic thinking 分析思维analytic syntheticanalytical activity 分析活动analytical argument 分析的论辩analytical chemistry 分析化学analytical conceptualizing style 分析考量型analytical diagnostic test 分析诊断测验analytical geometry 解析几何analytical judgment 分析判断analytical language 分析性语言analytical method of teaching 分析教学法analytical method 分析法analytical model 解析模型analytical probation 分析的论证analytical psychology 分析心理学analytical psychotherapy 分析心理治疗法analytical rating 分析的评定法analytical realism 分析实在论analytical research 分析性研究Analytical Scale for Judging of Handwriting 评判书法分析量表analytical scale 分析量表analytical social sciences 分析的社会科学analytical structure 分析结构analytical system 分析系统analytical test 分析测验analytical theory 分析论分析论analytical thinking 分析思维analytical type 分析型analyticity 分析性analytics 解析学analyze 分析analyzer 分析器anamnesis reaction 回忆反应anamnesis 回忆anamorphism 渐变anamorphosis 渐进anamorphosis 歪象ananabasia 登高不能ananastasia 起立不能anancasm 强迫性重复行为anancastia 强迫性反应性格anancastic 强迫观念与行为的anandia 运动性失语anandria 男性特征缺乏anankastia 强迫性反应性格anapepsia 胃蛋白酶缺乏anaphia 触觉缺失anaphia 失触觉症anaphoria 上隐斜眼anaphrodisia 性欲缺乏anaphrodisiac 制欲的anaphylactic reaction 心理过敏反应anaphylactic shock 过敏性休克anaphylactin 过敏素anaphylactogen 过敏源anaphylactogenesis 过敏反应发生anaphylaxis 过敏性anaphylodiagnosis 过敏性诊断法anapnograph 呼吸速度描记器anaptic 触觉缺失anarchic 反常的anarchism 无政府主义anarchist 无政府主义者anarchy 无政府状态anarithmia 计算不能anarthria 口吃anastral figure 无星图像anastral spindle 无星纺锤体anastral 无星的Anatman 无我anatomia chirurgica 外科解剖学anatomia medica 内科解剖学anatomia pathologica 病理解剖学anatomia topographica 局部解剖学anatomia 解剖学anatomical age 解剖年龄anatomical features 解剖特点anatomical lens 解剖镜anatomical physiology 解剖生理学anatomicomedical 医用解剖学的anatomicopathological 病理解剖学的anatomicophysiological 解剖生理学的anatomicosurgical 外科解剖学的anatomist 解剖学家anatomize 解剖anatomy 解剖学anatomypathology 病理解剖学anatropia 上隐斜眼anatta 无我anaxon 无轴索神经细胞ancestor language 母语ancestor worship 祖先崇拜ancestor 原始现象ancestral features 遗传性状ancestry 祖先anchor point 参照点anchor stimulus 参照刺激anchor test 参照测验anchorage effect 参照效应anchored scaleanchoring approach 参照法anchoring effect 参照效应anchoring group 参照组anchoring of ego 自我安妥anchoring points 参照点anchylosis 关节僵硬ancient civilization 古代文明ancient psychological thought 古代的心理学思想ancient 古代的ancillary estimator 辅助估计量Andersch sandrocentric theory 男性本位说androcentric 以男性为中心的androgamone 雄配素androgen 男性荷尔蒙androgen 雄性激素androgenization 雄激素化作用androglossia 女性男声androgyne 两性体androgyneity 两性畸形androgynism 两性现象androgynoid 女化男性androgynous personality 双性人性androgynus 男化女性androgyny 双性性格andromania 慕男狂androphobia 恐男人症androphobia 男子恐怖症androsterone 雄酮anecdotage 轶事集anecdotal evidence 轶事证据anecdotal method 轶事法anecdotal record 轶事记录anecdote 轶事anecdotist 轶事收集者anechoic chamber 消声室anechoic 无回声的anemic anoxia 贫血性缺氧anemophobia 恐风症anemophobia 通风恐怖症anemotaxis 向风性anemotropism 趋风性anepithymia 食欲不振anerethisia 兴奋缺失anergasia 活动力缺失anergastic reaction 活动力缺乏性反应anergastic 器质性精神病的anergia 无力anergic 无变应性的anergy 无力anerythropsia 红色盲anesthecinesia 感觉与运动能力缺失anesthesia functional 机能性感觉缺失anesthesia 感觉缺失anesthetic resistance memory 抗麻醉性记忆anesthetic 麻醉的anesthetization 麻醉法anesthetized animal 麻醉动物anesthetospasm 麻醉期痉挛anestrus 不动情期anethopathy 病态性悖德anetiological 非病原学的anetoderma 皮肤松垂anfractuosity 纡曲Angelucci sanger 愤怒angiectomy 血管切除术angina 咽痛angioedema 血管性水肿angiography 血管造影法angiology 血管学angiometer 血管运动描记器angioneuralgia 血管神经痛angioneurosis 血管神经病angiospastic anesthesia 血管痉挛性感觉缺失angiosthenia 动脉张力angiotensin 血管紧缩素angiotensinogen 血管紧缩素原angle illusion 角度错觉angle of contact 接触角angle of convergence 辐合角angle of incidence 入射角angle of iris 虹膜角angle of reflection 反射角angle of repose 隐角angle range 角范围angle tolerance 角耐性angle transformation 角变换angle visualAnglomania 英国狂Anglophobia 英国恐怖症angophrasia 言语涩滞angry aggression 愤怒性攻击angry womanangry 愤怒angst 焦虑angstrom 埃Angstrom sanguish 苦恼angular curve 角曲线angular displacement 角曲移置angular gyrus 角回angular mandibula 下颔角angulus anterior 前角angusty 狭窄anheaphia 触觉缺失anhedonia 快感缺乏anhelation 气促anhidrosis 无汗症anhistic 无构造的anhormonia 激素缺乏anhydraemia 缺水血症anhydromyelia 脊髓液缺乏anhydrous alcohol 无水酒精aniconia 无映象anility 老年型痴愚anility 衰老anima 女性意像anima 阴性基质animal aggression 动物攻击行为animal anatomy 动物解剖学animal behavior 动物行为animal biological rhythm 动物生物节律animal breeding 动物育种animal clinical psychology 动物临床心理学animal communication 动物通信animal community 动物群落animal courtship behavior 动物求偶行为animal cult 动物崇拜animal dispersal 动物传播animal distress call 动物危难叫喊animal ecology 动物生态学animal ethology 动物生态学animal ethology 动物习性学animal experiment 动物试验animal genetics 动物遗传学animal geography 动物地理学animal gregarious behavior 动物合群行为animal hemisphere 动物性半球animal host 动物寄主animal house 动物屋animal hypnosis 动物催眠animal inoculation 动物接种animal instinct 动物本能animal instinctive behavior 动物本能行为animal intelligence 动物的智能Animal Learning and Behavior 动物学习与行为animal learning 动物学习animal magnetism 动物磁性说animal mating behavior 动物配偶行为animal migration 动物迁移animal navigation behavior 动物导航行为animal parental behavior 动物的父母行为animal physiology 动物生理学animal population 动物种群animal protection 动物保护animal psychology 动物心理学animal psychophysics 动物心理物理学animal sexual behavior 动物性行为animal society 动物社会animal sociology 动物社会学animal spirit 动物的元气animal unit 动物单位animal vocalization 动物发声animal spiritanimal 动物animalism 动物性animalization 动物化animate 动物名词animation 活跃animatism 物活论animism 泛灵论animistic materialism 物活论唯物主义animosity 仇恨animus 男性意向animus 阳性基质anincretinosis 内分泌缺乏anion 阴离子aniseikonia 网膜异象症aniso accommodationanisochromasia 色素不均anisocoria 瞳孔不均anisogeny 雌雄异型遗传anisomerism 不对称性anisometrope 屈光参差者anisometropia 屈光不等anisophoria 垂直向隐斜视anisopia 两眼视力不等anisotropic distribution 异向异性分布anisotropic 各向异性的anisotropism 各向异性anisotropy of space 空间方向错误anisotropy of visual space 视觉空间方向错误anisotropy of visual space 视野异形anisotropy 方向错误ankle clonus 踝阵挛ankle jerk 足踝反射ankle joint 踝关节ankle reflexankyloglossia 结舌ankylophobia 关节强硬恐怖症ankylosis 关节强硬anlage 基础annals 年鉴annex 附加annihilate 消灭annihilation anxiety 毁灭焦虑anniversary hypothesis 周年假说anniversary reaction 周年反应Anno Domini 公元annotation 注释announce 宣布annoyance of noise 噪声烦扰度annoyance threshold 烦恼阈限annoyance 烦恼annoyer 烦恼物annual data 年度资料annual death rate 年死亡率annual gradient 年度化率annual improvement factor 年增长因素annual rate of growth 年增长率annual returns 年报Annual Review of Psychology 心理学年鉴annual seasons 年季度annual succession 年演替annual 一年生的annuity 年金annul 取消annulospiral ending 环螺形末梢annulus 环anodal depression 阴极性阻抑anodal dosing contraction 阴极通电收缩anodal opening contraction 阴极断电收缩anodmia 失嗅症anodyne 止痛的anodynia 无痛anoesis 无意识anoia 白痴anomalies 异常的因果情况anomalism 反常现象anomalopia 色觉异常anomaloscope 色觉鉴别器anomalotrophy 营养异常anomalous contour 不规则轮廓anomalous differences 异常误差anomalous personality 异常人格anomalous retinal correspondence 视网膜异常对应anomalous structure 异常结构anomalous substitution 反常取代anomalous succession 不规则演替anomalous trichromatism 三色觉异常anomaly of visual perception 视知觉异常anomaly 反常anomia 称名不能anomic aphasia 命名性失语anomic suicide 失范型自杀anomic 反常状态anomie 规范缺失anomie 失范anomy theory 反常状态理论anonym 匿名者anonymous 匿名的anophoria 上隐斜视anopia 上斜视anopsia 废用性弱视anorchus 无睾者anorexia nervosa 神经性厌食症anorexia 厌食症anorgasmy 性快感缺乏anorthography 运动性失写症anorthopia 眼偏视anorthoscope 动景镜anorthoscope 弱视镜anorthosis 直立不能anosmatic 嗅觉缺乏的anosmia 失嗅症anosmia 嗅觉缺失anosmic aphasia 嗅觉性失语anosodiaphoria 疾病漠视anosognosia 疾病失认症anosphrasia 嗅觉丧失anostosis 骨发育不全another world 另一世界anotropia 上显斜视ANOVA 方差分析anovulation 排卵停止anovulia 排卵停止anoxemia 缺氧血症anoxia 缺氧症anoxic 缺氧的ANS 自主神经系统ansa 脊神经Anstie sanswer key 答案answer up 对应迅速answer 回答answering model 回答模式antagonism 颉抗作用antagonist reflex 颉抗反射antagonist 颉抗性antagonistic action 颉抗作用antagonistic behavior 斗争性行为antagonistic color 对抗色antagonistic contradiction 对抗性矛盾antagonistic cooperation 对抗合作antagonistic muscle 颉抗肌antagonistic process 对抗过程antagonistic reflex 颉抗反射antagonistic substance 对抗物质antagonistic symbiosis 对抗共生antagonistic 敌对的antagonistic 颉抗的antagonize 起反作用antalgic reaction 防痛反应antalgic 防痛的antapoplectic 防止中风的antasthenic 恢复体力的ante mortem 死前antecardium 腹上部antecedent circumstance 先行情况antecedent condition 先行条件antecedent ground 先行根据antecedent consequent前件后因antecedent 前因antecedents of interpersonal attraction 人际吸引条件antecessor 先行者antecurvature 前弯antedating reaction 提前反应antedating response 提前反应anteflection 前屈antenatal training 胎教antenatal 胎儿的antenna 触角antennae nerve 触角神经antennal nerve 触觉神经antennal neuromere 触角神经元节antennal organ 触觉器antennal process 触角突antennal receptor 触角感受器antennal segment 触觉节antennal sensilla 触角感器antennal 触觉的antenniferous tubercle 触角突antenniferous 触角的antennulary ganglion 触角神经节antennulary 触角的antenuptial 婚前的antephialtic 抗梦魇的antergic 对抗作用的antergic 拮抗的anterior basal membrane 前基膜anterior blastomere 前裂球anterior centrosome 前中心体anterior chamber 前房anterior coelom 前体腔anterior column 前柱anterior commissure 前连合anterior cornu 前角突anterior gray commissure 前灰质连合anterior horn 前角anterior lobe hormones 脑垂体前叶激素anterior lobe of hypophysis 脑下垂体前叶anterior lobe 前叶anterior nerve root 前神经根anterior neuropore 前神经孔anterior nucleus 前核anterior orbit 前眶anterior palate 前腭anterior pituitary gland 脑垂腺前叶anterior pituitary hormones 脑垂体前叶激素anterior pituitary likeanterior pituitary 脑垂体前叶anterior pyramidal tract 前锥体束anterior radicle cell 前根细胞anterior root 前根anterograde amnesia 顺行性遗忘anterograde amnesia 远事遗忘anterograde degeneration 顺行性变性anterograde 顺行的anteromedian 前中裂anterotic 制欲的antetype 前型antetype 先型anthophilous 喜花的anthophobia 花恐怖症anthracometer 二氧化碳测量器anthropic factor 人为因素anthropic 人为的anthropobiology 人类生物学anthropocentric theory 人类中心说anthropocentrism 人类中心论anthropochorous 人传播的anthropochory 人为传播anthropogenesis 人类起源anthropogenetic sere 人为演替系列anthropogenetic succession 人为演替anthropogenetic 人类起源的anthropogenetic 人为的anthropogenic succession 人为演替anthropogenic 人为的anthropogeny 人类起源anthropogeography 人类地理学anthropography 人类分布学anthropography 人类志anthropoid 类人猿Anthropoidea 类人猿亚目Anthropoids 类人目anthropokinetics 人类活动学anthropological linguistics 人类语言学anthropological materialism 人类学唯物主义anthropological studies 人类学研究anthropological viewpoint 人类学观点anthropologism 人类主义anthropologist 人类学家anthropology 人类学anthropometer 人体测量器anthropometric test 人体测验anthropometrist 人体测量学家anthropometry 人体测量学anthropomorphic dummy 人体模型anthropomorphic system 拟人系统anthropomorphic thinking 拟人化思维anthropomorphism 拟人论anthropomorphology 人类形态学anthroponomy 人类行为学anthroponomy 人体进化论anthropopathy 情感拟人说anthropophagy 嗜食人肉anthropophobia 恐见人症anthroposociology 人类社会学anthroposophy 人性论anthroposophy 人智学anthropotomy 人体解剖学anthysteric 抗癔病的anti symmetric law 反对称律anti symmetry 反对称性anti temptation 抗拒诱惑anti cathexisanti coincidenceanti competitionanti Ganti illiteracyanti instinctanti insulinanti intellectualism反智主义anti interferenceanti intraceptionanti introspectionanti logyanti maniacalanti mentalismanti Oedipusanti pollutionanti predatoranti rationalismanti rationalityanti socialanti temptationanti traitantiadrenergic 抗肾上腺素能的antiamboceptor 抗介体antianaphylactin 抗过敏素antianaphylaxis 抗过敏antiandrogen 抗雄激素antianxiety drug 抗焦虑剂antianxiety 抗焦虑的antiarrhythmic 抗心律失常的antibacterial 抗细菌的antibiosis 抗菌antibiotics 抗菌素antibody like receptor 抗体样受体antic 滑稽动作anticathexis 反感情投注anticathexis 反精神宣泄anticephalalgic 抗头痛的anticholinergic drug 抗胆碱能药anticholinesterase 抗胆碱脂酶anticipation adaptation 前发适应anticipation anxiety 预期焦虑anticipation error 期望误差anticipation judgment 预期判断anticipation method 提示法anticipation method 预期法anticipation invigorationanticipation 预期anticipative anxiety 预期焦虑anticipator 期望者anticipatory aggression 防卫性攻击anticipatory anxiety 预期焦虑anticipatory assimilation 先行同化anticipatory behavior 预期行为anticipatory conditioned response 先期条件反应anticipatory control 先期控制anticipatory dissimilation 先行异化anticipatory error 预期错误anticipatory goal reaction 预期目标反应anticipatory goal response 预期目标反应anticipatory guidance 先期辅导anticipatory image 预期表象anticipatory imagination 预期想象anticipatory insanity 先发性精神病anticipatory method 预期法anticipatory of experience 经验的预测anticipatory reaction 预先反应anticipatory response 预先反应anticipatory schema 预期图式anticipatory socialization 预期社会化anticipatory survey 前景调查anticipatory symbol 预期症候anticipatory timing 预期计时anticlinal 对外倾斜的anticonformity behavior 反从众行为anticonformity 反从众性anticonvulsant 抗惊厥的anticonvulsant 镇痉剂anticonvulsive drug 镇痉挛剂anticonvulsive 镇痉的anticultural group 反文化集团anticultural 反文化的anticyclone 反气旋antidemocratic personality 反民主的人格antidepressant drug 抗抑郁剂antidinic 防眩晕的antidipsetic 止渴的antidiuresis 抑制尿分泌antidiuretic hormone 抗利尿激素antidromic conduction 逆向传导antidromic impulse 逆向冲动antidromic nerve impulse 逆向神经冲动antidromic 逆向的antidumping laws 反倾销法antidumping 反倾销antiepileptic 抗癫痫的antierotica 制性欲剂antiestrogenic 抗雌激素的antievolution 反进化论antievolutionist 反进化论者antigonadotrophic 抗促性腺激素的Antigone complex 安提戈涅情结Antigone complex 纯爱情结antigrowth hormone 抗生长激素antigrowth 抗生长的antihallucinatory 抗幻觉的antihistamines 抗组胺antihormone 抗激素antihypertensive 抗高血压的antihypnotic 抗眠的antihysteric 抗癔病的antijamming 抗干扰antikantism 反康德派antiketogenesis 抗生酮作用antikinesis 抗动态antikinesis 逆向运行antilethargic 抗嗜眠的antilogical 反逻辑antimaniacal drugs 抗躁狂剂antimaniacal 抗躁狂的antimanic agents 抗躁狂药物antimatter 反物质antimere 对称部antimetabolite 抗代谢物antimetropia 远近视antimicrobial 抗菌的antimongolism 反相先天愚型antimongoloid 反相先天愚型样的antinarcotic 抗麻醉的antinauseant 止恶心的antineuralgic 止神经痛的antineuritic 抗神经炎的antineurotoxin 抗神经毒素antinomian 唯信仰论者antinomianism 唯信仰论antinomy of distance 距离的矛盾antinomy of reason 理性的矛盾antinomy of Russell 罗素悖论antinomy 二律背反antinomy 自相矛盾antiparalytic 抗麻醉的antiparasympathomimetic 拟抗副交感的antipathy 反感antiphrases 反语antiphrasis 反语法antipode 对映体antiposia 厌饮antipositivism 反实证主义antipredatory aggression 反掠夺攻击antiproperty 对立的性质antipsychiatry 反精神病学antipsychologism 反心理主义antipsychotic drug 抗精神病药物antipsychotic 抗精神病的antipsychotics 抗精神病药antiquarian 喜爱古物的antiquity 古代风习antiracism 反种族主义antiscience 反科学antisensibilisin 抗致敏素antiskeptical 反怀疑论antisocial aggression 反社会性攻击antisocial behavior 反社会行为antisocial child 反社会儿童antisocial group 反社会群体antisocial personality disorder 反社会性人格障碍antisocial personality 反社会型人格antisocial reaction 反社会反应antisocial socialization 反社会社会化antisocial violence 反社会的暴力行为antisocial 不爱社交的antisocial 反社会的antisociality 反社会性antispasmodic 镇痉的antisymmetric relation 反对称关系antisymmetrical state 反对称态antisympathetic 抗交感神经的antithesis concept 对偶概念antithesis 对立antithetical ideas 对立思想antithing 对立物antithyrotropic hormone 抗促甲状腺激素antitrinitarianism 非三位一体论antitrismus 张口痉挛antitrope 对称体antitropic 相似对称的antiverbalism 反语词主义antivivisection 反活体解剖antiworld 反物质世界Anton sAnton Babinskiantonym test 反义字测验antonym 反义字antonymy 反义现象antorphine 丙烯去甲吗啡antrophose 中枢性光幻觉anxietas 焦虑anxiety attack 焦虑发作anxiety battery 焦虑成套测验anxiety complex 焦虑情结anxiety conservation 焦虑保存anxiety disorder 焦虑性障碍anxiety dream 恶梦anxiety hierarchy 焦虑层序anxiety hysteria 焦虑癔症anxiety melancholia 焦虑忧郁症anxiety neurosis 焦虑神经症anxiety psychosis 焦虑精神病anxiety reaction 焦虑反应anxiety reduction theory 焦虑消灭论anxiety scale 焦虑量表anxiety state 焦虑状态anxiety test 焦虑测验anxiety tolerance 焦虑耐量anxiety 焦虑anxiolytic drugs 抗焦虑药物anxiolytic 抗焦虑的anxiolytics 抗焦虑药anxious expectation 焦躁的期待anxiousness 焦急AP 动作电位APA Monitor 美国心理学会通讯apagoge 反证法apallesthesia 振动觉缺失apandria 远男症apanthropia 远人症aparalytic 无麻痹的aparathyrosis 甲状旁腺机能缺失apareunia 性交不能apastia 拒食apathetic dementia 冷漠性痴呆apathetic type 冷漠型apathia 无情感的apathism 冷淡病apathy syndrome 冷漠综合症apathy 冷漠apathy 情感淡漠APC 自动程序控制ape 类人猿apeidosis 形态渐失apeirophobia 无限恐怖apeman 猿人aperiodic reinforcement 不定期强化aperiodic tracking signals 非周期性追踪信号aperiodic 非周期性aperiodicity 非周期性aperture color 孔隙色apery 仿效apex beat 心尖博动apex cordis 心尖apex linguae 舌尖apexcardiogram 心尖心动图apexcardiography 心尖心动描记法Apgar Scale 阿普加量表Apgar score 阿普加新生儿评分APH 脑垂体前叶激素aphagia 不食症aphagia 吞咽不能aphasia area 失语症关连中枢aphasia zone 失语症关连区aphasia 失语症aphasiac 失语的aphasiac 失语者aphasiologist 失语症学家Aphasiology 失语症学aphasiology 失语症学aphemesthesia 听读不能aphemia 运动性失语症aphephobia 恐接触症。

我最喜欢的作家是jk罗琳英语作文J.K. Rowling is a renowned author celebrated for her captivating storytelling and imaginative prowess. Born onJuly 31, 1965, in Yate, Gloucestershire, England, Rowling's literary journey began with her creation of the magical world of Harry Potter.The Harry Potter series, comprising seven books, follows the life of a young wizard, Harry Potter, and his friends Hermione Granger and Ron Weasley as they navigate the challenges of both the wizarding and Muggle worlds. Theseries begins with "Harry Potter and the Philosopher's Stone" (published as "Harry Potter and the Sorcerer's Stone" in the United States) and concludes with "Harry Potter and the Deathly Hallows." Each book unfolds a new adventure for Harry, revealing layers of mystery, friendship, and courage.Rowling's writing style is characterized by its rich detail, intricate plot development, and profound characterizations. She skillfully interweaves elements of fantasy, adventure, and coming-of-age themes throughout the series. The magical elements, such as spells, magical creatures, and the Hogwarts School of Witchcraft and Wizardry, captivate readers of all ages, transporting them into a world where the ordinary and extraordinary blend seamlessly.Beyond the magical aspects, Rowling explores universal themes such as love, friendship, loyalty, and the battle between good and evil. Her characters are nuanced and evolve over the course of the series, facing personal challenges and moral dilemmas that resonate with readers on a profound level. From the courageous Harry Potter to the complex Severus Snape, Rowling creates a diverse cast that adds depth and dimensionto her narrative.The success of the Harry Potter series extends beyond the books themselves. It has inspired a vast fandom, withmillions of readers worldwide immersing themselves in the wizarding world through books, films, merchandise, and fan communities. The film adaptations, produced by Warner Bros. Pictures, brought Rowling's magical universe to life on the big screen, further cementing its place in popular culture.In addition to her work on Harry Potter, J.K. Rowling has authored other books, including "The Casual Vacancy" and the Cormoran Strike series under the pseudonym Robert Galbraith. Her storytelling prowess continues to captivate readers and critics alike, demonstrating her versatility as an author.Overall, J.K. Rowling's impact on literature is profound and enduring. Through her imaginative storytelling, compelling characters, and universal themes, she has created a literary legacy that resonates across generations. Her ability to transport readers to magical realms whileaddressing fundamental truths about human nature ensures that her work will continue to inspire and enchant readers for years to come.。

Characterization of microstructure,mechanical properties and corrosion resistance of dissimilar welded joint between 2205duplex stainless steel and 16MnRShaogang Wang *,Qihui Ma,Yan LiCollege of Material Science and Technology,Nanjing University of Aeronautics and Astronautics,Nanjing 210016,Chinaa r t i c l e i n f o Article history:Received 23March 2010Accepted 10July 2010Available online 16July 2010Keywords:A.Ferrous metals and alloys D.WeldingF.Microstructurea b s t r a c tThe joint of dissimilar metals between 2205duplex stainless steel and 16MnR low alloy high strength steel are welded by tungsten inert gas arc welding (GTAW)and shielded metal arc welding (SMAW)respectively.The microstructures of welded joints are investigated using scanning electron microscope,optical microscope and transmission electron microscopy respectively.The relationship between mechanical properties,corrosion resistance and microstructure of welded joints is evaluated.Results indicate that there are a decarburized layer and an unmixed zone close to the fusion line.It is also indi-cated that,austenite and acicular ferrite structures distribute uniformly in the weld metal,which is advantageous for better toughness and ductility of joints.Mechanical properties of joints welded by the two kinds of welding technology are satisfied.However,the corrosion resistance of the weldment produced by GTAW is superior to that by SMAW in chloride solution.Based on the present work,it is con-cluded that GTAW is the suitable welding procedure for joining dissimilar metals between 2205duplex stainless steel and 16MnR.Ó2010Elsevier Ltd.All rights reserved.1.IntroductionDuplex stainless steel (DSS)consists of approximately equal amounts of austenite and ferrite,which results in the favorable mechanical properties and corrosion resistance.The higher strength properties allow weight savings,which reduce fabrication costs and enable lighter support structures to be used.The higher corrosion resistance,in particular against stress corrosion cracking,makes them preferably applied in certain environments such as chemical tankers,pressure vessels,pipes to heat exchangers,paper machines and ocean engineering [1–3].With the growing applica-tion of new materials and higher requirements for materials,a great need occurs for component or structure of dissimilar metals.However,the joining of dissimilar metals is generally more chal-lenging than that of similar metals,which is usually due to several factors such as the differences in chemical compositions and ther-mal expansion coefficients,resulting in different residual stresses situation across the different regions of weldments as well as the migration of carbon element from the steel with higher carbon content to the steel with relatively lower carbon content.If the welding process is not well controlled,some weld defects such as dilutions and cracks will generate in the weld metal and leadto great decrease of properties of the welded joint.There are some researches about failure analysis or mechanical performance for dissimilar metals joints.Ul-Hamid et al.[4]have addressed that carbon diffusion in the dissimilar joint between carbon steel pipe and type 304stainless steel elbows resulted in cracking after a rel-atively short period of usage.Lee et al.[5]have also reported creep–fatigue damage of dissimilar weldment of modified 9Cr–1Mo steel (ASME Grade 91)and 316L stainless steel in a liquid me-tal reactor.In order to overcome the technical problems and take full advantage of the properties of different metals,it is necessary to pay more attention to the joining of dissimilar metals,so as to produce high quality welded joints between them.At present,some investigations have been conducted on weld-ing of duplex stainless steel,almost all common fusion welding techniques can be used to weld duplex stainless steel through selecting appropriate filler metals and parameters such as heat in-put [6,7].Explosive welding can be thought as a feasible method to produce composite plates.Kaçar and Acarer [8]have addressed that explosive welding process can be used successfully for clad-ding duplex stainless steel on the vessel steels without losing prop-erties such as corrosion resistance and mechanical properties.However,compared to the welding of similar metals,there is lim-ited information about microstructure/property relationships in dissimilar material welds between duplex stainless steel and low alloy high strength steel.Increasing application of these steels will0261-3069/$-see front matter Ó2010Elsevier Ltd.All rights reserved.doi:10.1016/j.matdes.2010.07.012*Corresponding author.Tel.:+8602552112901;fax:+8602552112626.E-mail address:sgwang@ (S.G.Wang).require a better understanding of the mechanics associated with welding of dissimilar metals.Since GTAW and SMAW are widely employed in engineering application,in the current work,a few at-tempts have been made to produce dissimilar material welded joint between DSS and low alloy high strength steel.At the same time,some results are presented as reference for the practical welding of these types of dissimilar metals.2.Experimental material and procedureThe base metals employed in this presentation are duplex stain-less steel2205and low alloy high strength steel16MnR.The chem-ical compositions of base metals andfiller metals are given in3.Results and discussion3.1.Microstructure of welded jointsThe preparation of microstructure samples of dissimilar metals joint is much difficult.Therefore,special operation procedure should be used.Both of the weld metal(WM)and2205base metal are etched by aqua-regia.However,the bonding region at the side of16MnR is etched by5%nital solution alone,and16MnR base me-tal should be prevented from being etched by aqua-regia.The interfacial microstructure of16MnR–WM is shown in Fig.2.It is a region with about30l m width near the fusion line.The existing of this region can be attributed to the thermal conductivity of theTable1Chemical compositions of base metals andfiller metals(wt.%).Elements C Mn P S Si Cr Ni Mo NBase metal SAF22050.0160.820.0240.0010.3622.48 5.46 3.120.16 16MnR0.15 1.380.0160.0140.32––––Filler metal ER22090.013 1.540.0180.0070.4922.928.61 3.180.17 E22090.0260.900.0250.0020.9022.1010.00 2.840.18 832S.G.Wang et al./Materials and Design32(2011)831–837Moreover,some short rod-like carbides,granular carbides and is-land-like carbides are observed at higher amplification electron microscope,as shown in Fig.4c and d respectively.However,the result shows that no carbides such as M23C6or martensite are ob-served in the unmixed zone.Therefore,it can be concluded that the development of such a morphology is attributed to decomposition of pearlite at16MnR side and formation of Fe3C at the WM side. The decomposition model is shown in Fig.5.The optical micrograph of weld metal is shown in Fig.6.From Fig.6,the morphology of acicular ferrite in austenite matrix has been observed,which is characterized by large amount of austen-ite.However,in terms of ferrite content in the joint,there is not much variation between the two weld metals in welded joints A and B,and the ferrite volume fraction is only17.3%and14.5%(ob-improving joint crack resistance and reducing the inhomogeneous distribution of weld structure during multi-pass welding.Generally,the formation of martensite,M23C6(chromium car-bide),Cr2N and r phase depends on the base materials joined and welding conditions according to Refs.[15,16].Therefore,X-ray diffraction analysis is carried out on the weld metal and the re-sults are shown in Fig.7.There are only a and c phases in both of the weld metals,and no precipitation of M23C6(chromium car-bide),Cr2N or r phase is found in the weld metal,which is advan-tageous to mechanical properties and corrosion resistance of the joint.3.2.Mechanical properties834S.G.Wang et al./Materials and Design32(2011)831–837si-cleavage fracture,as shown in Fig.9d.Microhardness profile across the joint interface is shown inFig.10.The microhardness distributions of two kinds of welded joints are almost the same.Obviously,the hardness value of weld metal is higher than that of the16MnR base metal and the 16MnR HAZ.With the distance increasing away from interface, the microhardness values vary to a certain extent.The highest hardness values of the two joint interface are approximately 224HV and220HV respectively.It is because the carbon element migrates from the16MnR side to weld metal during welding due to the difference of chemical compositions between16MnR and weld metal.Similar result is reported by Kaçar and Acarer[8],studied the explosively welded joint between DSS andCorrosion behaviororder to evaluate the corrosion resistance of weldis sealed with A/B glue,leaving about10mmÂ10mm area,3.5%NaCl solution is used as corrosion solution,the sche-matic diagram is shown in Fig.11.Electrochemical corrosion test results of2205DSS base metal and weld metal are shown in Fig.12and Table4respectively. These samples display more or less similar behaviors in terms of In general,the higher the value is,the better corrosion resistance of the material is.Therefore,in3.5%NaCl solution,corrosion resis-tance order of the samples is:2205DSS BM>joint A>joint B.The pitting corrosion resistance of the DSS BM is much better compared to the two weld metals,as can be seen from the polari-zation plot.The DSS BM sample does not display any corrosion in 3.5%NaCl solution and there is no pit in the sample examined after the potentiodynamic cyclic scanning.And the good pitting resis-tance behaviors of weld metal are attributed to the addition of Cr,Ni,elements[19].The alloying element Cr could improve the stability of passivefilms,and the Ni would decrease the overall dis-solution rates of Fe and Cr[20].Moreover,the heat input of joint A is different from that of joint B,which affects the weld microstruc-ture and results in the difference of formation condition of metal surface passivefilm.Generally,thefiner the grain is,the more eas-ily the compact passivefilm forms.As a result,the corrosive ions cannot readily diffuse through the passivefilm and the metal pre-sents better corrosion resistance,so the joint A has better corrosion resistance compared to joint B.When welded joint is etched in chloride solution,defects gener-ated in the welding process(such as welding spatter or inclusion) possibly make it lose its ability to protect the surface passivefilm. As a result,a chromium-depleted zone appears around weld metal, which makes the surface activated,and the joint presents an ac-tive–passive behavior.The initiation sites for the pits are located at the ferrite–austenite grain boundaries and once formed they rapidly propagate from ferrite to austenite,as described in Ref.[21].It can be seen from Fig.13that ferrite grains are etched,leav-ing lots of grooves at the ferrite–austenite grain boundaries,and the remaining white strips are austenite.This selective localized corrosion is attributed to difference of the electrochemical poten-tial,caused by the ratio of biphase in weld metal.It is concluded that the austenite grains are by far more resistant to the chloride environment than that of the ferrite grains.4.ConclusionsThe investigation of welding between2205DSS and16MnR by GTAW and SMAW respectively reach the following conclusions:Fig.10.Hardness curves of16MnR–WM interface. Fig.12.Polarization curves of DSS BM and weld metals.Attribute to decomposition of pearlite at16MnR side and for-mation of Fe3C at the WM side,a decarburization layer and an un-mixed zone are observed at the interface of16MnR/WM.The microstructure of weld metal consists of austenite and acic-ular ferrite,and both of the two kinds of joints are characterized by a high content of austenite,which is beneficial to mechanical prop-erties and corrosion resistance.Sigma phase or M23C6intermetallic compounds are not observed in current case through analysis of XRD.The impact toughness of the weld metal is similar to that of 16MnR,but it is much higher than that of16MnR HAZ.The weld metal and16MnR HAZ welded by GTAW present a ductile mode of fracture,while the pattern of16MnR HAZ welded by SMAW be-longs to quasi-cleavage fracture.The fracture of the joint welded by GTAW occurs in the zone of 16MnR base metal,while the fracture position of the joint welded by SMAW is in16MnR HAZ.However,the average tensile strength of welded joints is582.4MPa,564.6MPa respectively.Both of them can meet the tensile strength requirements of engineering structure.The joint produced by SMAW has higher susceptibility to pitting corrosion in chloride solution than that of weldment produced by GTAW.Based on the present work,it is summarized that GTAW with filler metal ER2209is the suitable welding procedure for dissimilar metals joining between2205duplex stainless steel and16MnR in the practical application.References[1]Sieurin H,Sandström R.Austenite reformation in the heat-affected zone ofduplex stainless steel2205.Mater Sci Eng A2006;418:250–6.[2]Olsson J,Snis M.Duplex–A new generation of stainless steels for desalinationplants.Desalination2007;205:104–13.[3]Kurt B.The interface morphology of diffusion bonded dissimilar stainless steeland medium carbon steel couples.J Mater Process Technol2007;190:138–41.[4]Ul-Hamid A,Tawancy HM,Abbas NM.Failure of weld joints between carbonsteel pipe and304stainless steel elbows.Eng Fail Anal2005;12:181–91. [5]Lee HY,Lee SH,Kim JB,Lee JH.Creep–fatigue damage for a structure withdissimilar metal welds of modified9Cr–1Mo steel and316L stainless steel.Int J Fatigue2007;29:1868–79.[6]Ureña A,Otero E,Utrilla MV,Munez CJ.Weldability of a2205duplex stainlesssteel using plasma arc welding.J Mater Process Technol2007;182:624–31. [7]Muthupandi V,Bala Srinivasan P,Seshadri SK,Sundaresan S.Effect of weldmetal chemistry and heat input on the structure and properties of duplex stainless steel welds.Mater Sci Eng A2003;358:9–16.[8]Kaçar R,Acarer M.Microstructure–property relationship in explosively weldedduplex stainless steel–steel.Mater Sci Eng A2003;363:290–6.[9]Naffakh H,Shamanian M,Ashrafizadeh F.Dissimilar welding of AISI310austenitic stainless to nickel-based alloy Inconel657.J Mater Process Technol 2009;209:3628–39.[10]Sireesha M,Shankar V,Albert SK,Sundaresan S.Microstructural features ofdissimilar welds between316LN austenitic stainless steel and alloy800.Mater Sci Eng A2000;292:74–82.[11]Srinivasan PB,Muthupandi V,Dietzel W,Sivan V.Microstructure and corrosionbehavior of shielded metal arc-welded dissimilar joints comprising duplex stainless steel and low alloy steel.J Mater Eng Perform2006;15:758–64. [12]Srinivasan PB,Muthupandi V,Dietzel W,Sivan V.An assessment of impactstrength and corrosion behaviour of shielded metal arc welded dissimilar weldments between UNS31803and IS2062steels.Mater Des 2006;27:182–91.[13]You YY,Shiue RK,Shiue RH,Chen C.The study of carbon migration indissimilar welding of the modified9Cr–1Mo steel.J Mater Sci Lett 2001;20:1429–32.[14]Migiakis K,Papadimitriou GD.Effect of nitrogen and nickel on themicrostructure and mechanical properties of plasma welded UNS S32760 super-duplex stainless steels.J Mater Sci2009;44:6372–83.[15]McPherson NA,Chi K,Mclean MS,Baker TN.Structure and properties of carbonsteel to duplex stainless steel submerged arc welds.Mater Sci Technol 2003;19:219–26.[16]Rajeev R,Samajdar I,Raman R,Harendranath CS,Kale GB.Origin of hard andsoft zone formation during cladding of austenitic/duplex stainless steel on plain carbon steel.Mater Sci Technol2001;17:1005–11.[17]Badji R,Bouabdallah M,Bacroix B,Kahloun C,Belkessa B,Maza H.Phasetransformation and mechanical behavior in annealed2205duplex stainless steel welds.Mater Charact2008;59:447–53.[18]Palmer TA,Elmer JW,Babu SS.Observations of ferrite/austenitetransformations in the heat affected zone of2205duplex stainless steel spot welds using time resolved X-ray diffraction.Mater Sci Eng A 2004;374:307–21.[19]Tavares SSM,Pardal JM,Lima LD,Bastos IN,Nascimento AM,de Souza JA.Characterization of microstructure,chemical composition,corrosion resistance and toughness of a multipass weld joint of superduplex stainless steel UNS S32750.Mater Charact2007;58:610–6.[20]Olsson C-OA,Landolt D.Passivefilms on stainless steels-chemistry,structureand growth.Electrochim Acta2003;48:1093–104.[21]Kordatos JD,Fourlaris G,Papadimitriou G.The effect of cooling rate on themechanical and corrosion properties of SAF2205(UNS31803)duplex stainless steel welds.Scripta Mater2001;44:401–8.S.G.Wang et al./Materials and Design32(2011)831–837837。

第38卷第4期2020年11月江苏师范大学学报(自然科学版)Journal of Jiangsu Normal University(Natural Science Edition)Vol38，No4Nov，2020文章编号：2095-4298(2020)04-0048-03Abel范畴上平衡对的若干注记何东林，李煜彥〔陇南师范高等专科学校数信学院，甘肃陇南742500)摘要：设犃是一个Abel范畴,(:r,y)是犃上的一个平衡对.利用同调代数的方法，研究平衡对(狓y)的若干性质和等价刻画，讨论与其相关的2个维数：狓分解维数(狓res.dim(U))和y余分解维数(y cores.dim(U))，其中U为犃中任意对象.证明了对于Abel范畴犃中的任意正合列(《)：0f M fN7T,如果()在函子Hom犃(狓，一)下正合且狓关于扩张封闭，那么以下说法成立：1)若M G狓,则狓res.dim(N)W狓res.dim(L)；2)若N G狓，则狓res.dim(L) W狓res.dim(M)+1;3)若L G狓且狓关于满同态的核封闭，则狓res.dim(M)=j c-res.dim(N).关键词：Abel范畴；平衡对;维数；拉回图中图分类号：O154文献标识码：A doi：103969/j issn2095-4298202004012Some notes of balanced pairs in Abel categoriesHeDonglin，LiYuyan(School of Mathematics&Information Sciences,Longnan Teachers College,Longnan742500, Gansu,China)Abstract:Let A be an Abel category,(狓，y)a balanced pair in犃.Using methods of homology algebras,some prop­erties and equivalent characterizations of balanced pair(狓，y)are investigated in this paper,two dimensions c reso­lution dimension c-res.dim(犝)and y coresolution dimension y-cores.dim(犝)are discussed with U an arbitrary ob­ject of A.It is proved that for any exact sequence()：0f M f N f L f0of A,if()is exact under functors Hom A(c,―)and c is closed under extensions,then the following statements are held:1)if M G c,then c-res.dim(N)^c-res.dim(L)；2)if N G c,then c-res.dim(L)^c-res.dim(AM)+1；3)if L G c and c is closed under kernels of epimorphisms,then c-res.dim(Ad)=c-res.dim(N).Keywords：Abelcategory；balancedpair；dimension；pu l backdiagramHomotopy等价是同调代数理论研究的热点之一，许多学者先后对其进行了研究［1一5］.特别地, Chen［］引入了平衡对的概念，并研究了基于平衡对的Homotopy等价，作为应用，证明了在左Goren-stein环上，Gorenstein投射模的Homotopy范畴与Gorenstein内射模的Homotopy范畴之间存在一个三角等价.Li等［7］引入并讨论了由平衡对(c,y)导出的余挠理论，并证明当y的c分解维数有限时,y 的有界Homotopy范畴包含在c中.基于以上研究背景，本文将讨论平衡对(c,y)的若干性质和等价刻画，并进一步研究与其相关的c分解维数和y余分解维数，以及短正合列中各项的c分解维数与y 余分解维数之间的关系1基本知识和定义文中的A均指Abel范畴，子范畴均指A的关于同构和直和因子封闭的加法全子范畴.P(A)和1(A)分别表示A的所有投射对象和内射对象组成的子范畴.设c是A的一个子范畴，且XGc,M是A中任意对象,称同态aXfM是对象M的右c逼近旧，如果对任意同态p：X'fM(X'Gc),都存在同态7：XfX',使得Y=a.对偶地，可定义M的左c 逼近.如果A中每个对象都存在右c逼近，那么称子范畴c是反变有限的;如果A中每个对象都存在左c逼近,那么称子范畴c是共变有限的.设c是A的一个反变有限子范畴,y是A的一个共变有限子范畴，如果存在复形X2f X j f X l M f0(其中X i G c),且该复形在函子Hom A(c,—)下正合，则称该复形为对象M的一个c分解［7］，记作X°f M.如果存在复形0f M f犢0f 犢1f犢2f…(其中犢G y),且该复形在函子Hom A(—,y)下正合，则称该复形为对象M的一个y余分解［7］，记作M f Y°.记c-res dim(M)=收稿日期：2019-11-10基金项目：甘肃省高等学校创新基金项目(2020A-277),甘肃省高等学校创新能力提升项目(2019B-224) 作者简介：何东林，女，讲师，硕士，主要从事同调代数方面的研究.第4期何东林，等：Abel范畴上平衡对的若干注记49inf{n|存在Hom A(c,—)下正合的复形0f X“f…f X i f X0f M f0(其中&G c)},y-cores.dim(M) =inf{m|存在Hom A(—,y)下正合的复形0—M f 犢0f Y1f…f Y犿f0(其中0G y)},分别称为对象M的狓分解维数和y余分解维数.定义1[]设cy是Abel范畴A的子范畴，称(c,y)是一个平衡对，如果以下条件成立：1)狓在A中是反变有限的狔在A中是共变有限的；2) 对任意MGA,都存在Hom A(—,y)下正合的狓分解---X2f X1f X0f M f0，其中X2G c；3)对任意MG A,都存在Hom A(c,—)下正合的y余分解0fMfY0f Y1f Y2f…，其中0G y.例11)设Abel范畴A具有足够的投射对象和内射对象，则(犘(A),1(A))是一个平衡对.2)设R是一个环犘犘(犚)和P i(犚)分别表示所有纯投射模(即关于纯正合列投射的模)和纯内射模(即关于纯正合列内射的模)组成的左R模范畴的子范畴，则(P p(R)P i(R))是一个平衡对.3)设R是一个n-Gorenstein环，即R是双边Noether环并且双边自内射维数不超过某个非负整数”G p(R)和G i(R)分别表示所有Gorenstein投射模和Gorenstein内射模组成的左R模范畴的子范畴，则(G p(R)G i(R))是一个平衡对.引理1[7]设(c,y)是A上的一个平衡对M 和N是A中任意2个对象，且X°f M和N f Y°分别为M的c分解和N的y余分解，则Ext(M,N)=Ext y(M,N),其中Ext(M,N)=H,(Hom A(X°,N)),Ex t；(M,N)= H,(Hom A(M9Y°)).为了方便，不妨将Abel群Ext(M,N)和Ex t；(M,N)均记为Ex t；(M,N).对任意对象丁GA,如果Ex佇】(犜，犜)=0,则称犜是关自正交的.2主要结果定理1设(c,y)是A上的一个平衡对，则对任意K G c Pl y,都有Exe1(K,K)=0.证由引理1知，对任意对象A G A,X G c和Y G y,有Ex t；(X,A)=0=Ex i(A,Y).从而对任意K G c Q y和任意i>1,都有Ex i(K,K)=0,即ExL(K,K)=0.定理2设(c,y)是A上的一个平衡对，且丁是兴自正交的，则丁的任意直和因子也是兴自正交的.证设犜是犜的任意直和因子，且犜=犜。

第10卷第2期2013年2月Journal of Hubei University of Economics(Humanities and Social Sciences)湖北经济学院学报（人文社会科学版）Feb.2013Vol.10No.2引言上世纪70年代末，曼德尔布罗特（B.Mandelbrot ）发表了分形几何学的专著《分形：形状、机遇和维数》。

之后的几十年间，分形理论迅速应用于其他学科之中，产生了很多的交叉学科，并推动各个学科产生了许多新的研究领域。

分形几何作为数学学科非线性科学的三大前沿之一，其分形分维（Fractaldimension ）理论为各学科提供了全新的思考方式和解决方法[1]。

结合分形几何而建立起来的分形时间、分形空间等新概念，又为建立分形哲学体系和美学体系奠定了理论基础。

分形理论的哲学探索与美学研究，便是从对时间、空间的分形特征这一崭新角度进行再认识并展开研究的[2]。

本文通过在文学研究领域引入分形思想，对比分析和研究了中西方小说中的人物特点、故事发展、情节结构等内容。

笔者试图通过一个全新的视角，对比研究中西方小说创作的特点和共同的美学价值判断。

1．小说中人物及人物关系的分形特征分析小说创作中通常喜欢创作出具有相似背景和不同命运的对比人物形象，通过对相似人物不同命运的描述，来增强小说的感染力和文学色彩。

这种处理方法正好暗合分形几何中对自相似问题的描述和美学判断。

例如《红楼梦》中的贾宝玉和甄宝玉[3]，曹雪芹从两个人物的名字和他们的经历中有意设计成有许多的共同点，然后再描述不同的命运。

这种既相似又有区别的描述过程，让人们联想作者是在通过甄宝玉来描写贾宝玉的另一面，然后通过对两个人物命运的安排来进一步突出和丰富了贾宝玉鲜活的人物形象。

不仅生活环境和家中地位甚至名字年龄身材相貌相同，更奇怪的是两人从童年到少年时的性格情趣也如此相似：都顽皮淘气，“极恶读书，最喜在内帏厮混”，都不想显身扬名、走仕途经济之路，呈现出离经叛道的色彩。

The formation of ones personality is a complex and multifaceted process that involves a variety of factors.Here are some key elements that contribute to the development of an individuals character:1.Genetic Influence:Our genes play a significant role in determining certain traits,such as temperament and predispositions to certain behaviors.However,genetics is just one piece of the puzzle.2.Early Childhood Experiences:The experiences we have during our early years, particularly the interactions with our primary caregivers,can shape our personality. Secure attachment in early childhood can lead to a more confident and secure adult personality.3.Family Environment:The values,beliefs,and behaviors modeled by family members can greatly influence a persons character.A supportive and nurturing family environment can foster positive traits such as empathy and resilience.4.Cultural and Social Factors:The culture in which a person is raised can have a profound impact on their personality.Social norms,expectations,and the collective values of a society can shape an individuals behavior and attitudes.cational Experiences:The educational system and the learning environment can also contribute to personality development.Teachers,peers,and the curriculum can all play a role in shaping a persons interests,values,and social skills.6.Personal Choices and Decisions:As individuals grow older,they begin to make more choices and decisions for themselves.These choices can significantly influence the development of their personality,as they reflect personal values and priorities.7.Life Events and Experiences:Major life events,such as moving to a new place, starting a new job,or experiencing a loss,can have a lasting impact on a persons character.These experiences can lead to personal growth or changes in ones outlook on life.8.Peer Influence:Friends and peers can also have a significant impact on personality development.The company we keep can influence our attitudes,behaviors,and values.9.Media and Technology:The media we consume and the technology we use can also shape our personalities.Exposure to different ideas,perspectives,and cultural content can broaden our horizons or reinforce certain beliefs and attitudes.10.SelfReflection and Personal Growth:Lastly,the ability to reflect on ones experiences and engage in personal growth can lead to the development of a more mature and wellrounded personality.In conclusion,the formation of personality is a dynamic and ongoing process that is influenced by a combination of innate factors,environmental influences,and personal agency.It is through the interplay of these elements that an individuals unique character is shaped.。

第61卷 第6期吉林大学学报(理学版)V o l .61 N o .62023年11月J o u r n a l o f J i l i nU n i v e r s i t y (S c i e n c eE d i t i o n )N o v 2023d o i :10.13413/j .c n k i .jd x b l x b .2023048n -F I 内射复形及其性质原雪娟,张翠萍(西北师范大学数学与统计学院,兰州730070)摘要:将n -F I 内射模推广到复形层面.首先,给出n -F I 内射复形的定义;其次,证明复形C 是n -F I 内射复形当且仅当每个层次是n -F I 内射模,且对任意F P -内射维数不超过n 的复形X ,复形H o m (X ,C )正合;最后,利用复形的覆盖刻画n -F I 内射复形.关键词:n -F I 内射模;F P -内射复形;n -F I 内射复形中图分类号:O 153.3 文献标志码:A 文章编号:1671-5489(2023)06-1319-05n -F I I n j e c t i v eC o m p l e x e s a n d I t sP r o pe r t i e s Y U A N X u e j u a n ,Z H A N GC u i p i n g(C o l l e g e o f M a t h e m a t i c s a n dS t a t i s t i c s ,N o r t h w e s tN o r m a lU n i v e r s i t y ,L a n z h o u 730070,C h i n a )A b s t r a c t :n -F I i n j e c t i v em o d u l e sw e r e g e n e r a l i z e d t o t h e c o m p l e x l e v e l .F i r s t l y,w e g a v e t h e d e f i n i t i o n o f n -F I i n j e c t i v e c o m p l e x e s .S e c o n d l y ,w e p r o v e d t h a t a c o m p l e x C w a s n -F I i n j e c t i v e c o m p l e x i f a n d o n l y i f e a c ht e r m w a s n -F I i n j e c t i v e m o d u l ea n d H o m (X ,C )w a sa c y c l i cf o ra n y c o m pl e x X w i t h F P -i d (X )ɤn .F i n a l l y ,n -F I i n j e c t i v e c o m p l e x e sw e r e c h a r a c t e r i z e db y c o v e r s o f c o m p l e x e s .K e yw o r d s :n -F I i n j e c t i v em o d u l e ;F P -i n j e c t i v e c o m p l e x ;n -F I i n j e c t i v e c o m p l e x 收稿日期:2023-02-14.第一作者简介:原雪娟(1996 ),女,汉族,硕士研究生,从事同调理论的研究,E -m a i l :1452520212@q q .c o m.通信作者简介:张翠萍(1974 ),女,汉族,博士,副教授,从事同调理论的研究,E -m a i l :z h a n g c p@n w n u .e d u .c n .基金项目:国家自然科学基金(批准号:11761060).0 引 言设R 是环,M 是左R -模.如果对任意有限表示左R -模A ,E x t 1R (A ,M )=0,则称M 是F P -内射模.模M 的F P -内射维数定义为F P -i d R (M )=i n f {n |E x t n +1R (A ,M )=0,A 是有限表示左R -模,n 是非负整数}.如果这样的n 不存在,则F P -i d R (M )=ɕ.设C 是左R -模的类,C ɪC .如果对任意的C ᶄɪC ,H o m R (C ᶄ,φ):H o m R (C ᶄ,C )ңH o m R (C ᶄ,M )是满同态,则称φ是M 的C -预覆盖[1];如果对任意的同态g :C ңC ,均有φg =φ,则g 是同构,称C -预覆盖φ:C ңM 为M 的C -覆盖.对偶地,可定义C -预包络和C -包络.如果对任意F P -内射左R -模G ,E x t 1R (G ,M )=0,则称左R -模M 是F I -内射模[2].文献[2]给出了该类模的一些性质和等价刻画;文献[3]对F I -内射模做了推广,引入了n -F I 内射模,并证明了模M是n -F I 内射模当且仅当对任意正合列0ңM ңE ңL ң0,E ңL 是L 的F P n -预覆盖,当且仅当M 是B的F P n -预覆盖f :A ңB 的核,其中A 是内射左R -模,当且仅当对任意正合列0ңA ңB ңC ң0,H o m R (-,M )作用是正合的,其中C ɪF P n (R )(F P n (R )表示F P -内射维数不超过n 的左R -模的类);文献[4]研究了F I -内射复形,给出了F I -内射复形的等价刻画,并证明了复形C 是F I -内射复形当且仅当每个层次都是F I -内射模,且对任意F P -内射复形X ,复形H o m (X ,C )正合.受上述结论的启发,本文将n -F I 内射模推广到复形范畴,引入n -F I 内射复形的概念,并讨论n -F I内射复形与其层次模之间的关系,最后从覆盖的角度刻画n -F I 内射复形.1 预备知识本文用R 表示有单位元的环,模均指酉模,用M o d R (M o d R o p)表示左(右)R -模范畴,ℤ表示整数集.对于R -模序列X = ңX m +1d Xm +ң1X m d XңmX m -1ң ,如果对任意整数m ,满足d X m d X m +1=0,则称X 是R -模的复形.复形X 的第m 次平移记为X [m ].设M 是R -模,则S m (M )表示复形 ң0ңM ң0ң ,其中M 在第m 层次,M =S 0(M ).D m (M )表示复形 ң0ңM i d ңMM ң0ң ,其中M 在第(m -1)和m 层次,췍M =D 0(M ).用C (R )表示所有R -模的复形范畴.设X 和Y 是复形,H o m (X ,Y )表示所有从X 到Y 的复形链映射构成的A b e l 群.对任意整数i ȡ1,E x t i (-,-)表示左正合函子H o m (-,-)的第i 次右导出函子,E x t 1d w (X ,Y )表示由层次可裂的复形短正合列构成的群,它是E x t 1(X ,Y )的子群.H o m (X ,Y )表示如下A b e l 群的复形:ңᵑt ɪℤH o m R (X t ,Y i +t )d ңiᵑt ɪℤH o mR(X t ,Y i -1+t )ң ,H o m (X ,Y )i =ᵑt ɪℤH o m R (X t ,Y i +t ),对任意的f =(f t )t ɪℤɪH o m (X ,Y )i ,均有d i ((f t )t ɪℤ)=(d Y i +t f t -(-1)i f t -1d Xt )t ɪℤ.设H o m (X ,Y )=ℤ(H o m (X ,Y ))是复形,则它的第n 层次H o m (X ,Y )n 是由X 到Y[n ]的态射构成的A b e l 群.它的微分由δn (f ):X ңY [n -1]给出,且对任意整数m ,(δn f )m =(-1)n δXf m ,f ɪHo m (X ,Y )n .函子H o m (X ,Y )的右导出函子记为E x t i (X ,Y ),表示如下的复形: ңE x t i (X ,Y [n +1])ңE x t i (X ,Y [n ])ңE x t i(X ,Y [n -1])ң ,其微分由Y 的微分诱导.设f :X ңY 是复形的链映射,如果对任意整数i ,存在R -模同态S i :X i ңY i +1,使得f i =d Y i +1S i +S i -1d Xi ,则称f 是零伦的,记为f ~0.态射f 的映射锥记为M (f ),M (f )i =Y i 췍X i -1,其中d M (f )i=d Yi f i -10-d Xi æèçöø÷-1.定义1[3] 设R 是环,n 是非负整数.如果对任意F P -内射维数不超过n 的左R -模X ,有E x t 1R (X ,M )=0,则称左R -模M 是n -F I 内射模.定义2[5] 如果对任意有限表示复形A ,有E x t 1(A ,C )=0,则称复形C 是F P -内射复形.复形X 的F P -内射维数定义为F P -i d (X )=i n f {n E x t n +1(A ,X )=0,A 是有限表示复形,n 是非负整数}.如果这样的n 不存在,则规定F P -i d (X )=ɕ.定义3[4] 如果对任意F P -内射复形X ,有E x t 1(X ,C )=0,则称复形C 是F I -内射复形.引理1 设X 是复形,M 是R -模,则:0231 吉林大学学报(理学版) 第61卷1)E x t i ȡ1(X ,췍M [n ])≅E x t i ȡ1R (X n -1,M );2)E x t i ȡ1(췍M [n ],X )≅E x t i ȡ1R (M ,X n ).证明:1)取M 的内射分解0ңM ңI 0ңI 1ң .令K i =K e r (I i ңI i +1),i ȡ0,则有复形的正合列0ң췍M [n ]ң췍I 0[n ]ң췍I 1[n ]ң ,其中췍I i [n ]是内射复形,i =0,1, .由文献[6]中引理3.1可得E x t i ȡ1(X ,췍M [n ])≅E x t 1(X ,췍K i -1[n ])≅E x t 1R (X n -1,K i -1)≅E x t i ȡ1R (X n -1,M ). 对偶地,可证结论2).2 主要结果下面设n 是非负整数.定义4 设C 是复形.如果对任意F P -内射维数不超过n 的复形X ,有E x t 1(X ,C )=0,则称C 是n -F I 内射复形.显然,0-F I 内射复形是F I -内射复形,内射复形是n -F I 内射复形.设m ,n 是非负整数且m >n ,则m -F I 内射复形是n -F I 内射复形.命题1 设I 是任意指标集,(C i )i ɪI 是R -模的一簇复形.则ᵑC i 是n-F I 内射复形当且仅当每个C i 是n-F I 内射复形.证明:设X 是复形且F P -i d (X )ɤn ,因为E x t 1(X ,ᵑCi )≅ᵑEx t 1(X ,C i),所以结论成立.引理2 设X 是复形且F P -i d (X )ɤn ,则对任意整数m ,均有F P -i d R (X m )ɤn .证明:设A 是有限表示R -模,则췍A [m ]是有限表示复形.由引理1中2)可得E x t n +1R (A ,X m )≅E x t n +1(췍A [m ],X )=0,所以F P -i d R (X m )ɤn .引理3 设X 是复形且F P -i d (X )ɤn ,则对任意整数m ,有F P -i d (X [m ])ɤn .证明:设A 是有限表示复形,则有E x t n +1(A ,X [m ])≅E x t n +1(A [-m ],X )=0,所以F P -i d (X [m ])ɤn .引理4 设M 是R -模且F P -i d R (M )ɤn ,则对任意整数m ,有F P -i d (췍M [m ])ɤn .证明:设A 是有限表示复形,则由文献[7]中引理2.2知,对任意整数m ,A m -1都是有限表示模.由引理1中1)可得E x t n +1(A ,췍M [m ])≅E x t n +1R (A m -1,M )=0,所以F P -i d (췍M [m ])ɤn .定理1 设C 是复形,则下列结论等价:1)C 是n -F I 内射复形;2)对任意F P -内射维数不超过n 的复形X ,有E x t 1(X ,C )=0;3)对任意整数m ,C m 是n -F I 内射模,且对任意F P -内射维数不超过n 的复形X ,复形H o m (X ,C )正合.证明:1)⇒2).设X 是复形且F P -i d (X )ɤn ,因为C 是n -F I 内射复形,所以有E x t 1(X ,C )=0,从而对任意整数m ,有E x t 1(X ,C [m ])=0.由m 的任意性可得E x t 1(X ,C )=0.2)⇒1).设X 是复形且F P -i d (X )ɤn ,则对任意整数m ,由引理3知,F P -i d (X [m ])ɤn ,所以有E x t 1(X ,C [m ])≅E x t 1(X [-m ],C )=0,1231 第6期 原雪娟,等:n -F I 内射复形及其性质2231吉林大学学报(理学版)第61卷从而E x t1(X,C)=0,故C是n-F I内射复形.1)⇒3).设M是R-模且F P-i d R(M)ɤn,由引理4知,对任意整数m,F P-i d(췍M[m])ɤn,从而E x t1(췍M[m],C)=0.由引理1中2)可得E x t1R(M,C m)≅E x t1(췍M[m],C)=0,所以C m是n-F I内射模.设X是复形且F P-i d(X)ɤn,由引理3知F P-i d(X[1-m])ɤn.因为C是n-F I内射复形,所以E x t1(X[1-m],C)=0,从而E x t1(X[1],C[m])≅E x t1(X[1-m],C)=0.令f:XңC[m]是复形的链映射,则有复形的可裂正合列0ңC[m]ңM(f)ңX[1]ң0.由文献[8]中推论2.2知f同伦于0.从而由文献[9]中引理2.1知,复形H o m(X,C)正合.3)⇒1).设X是复形且F P-i d(X)ɤn,根据引理2和引理3知,对任意整数m,t,F P-i d R(X[-t]m)ɤn.设0ңCңYңX[-t]ң0(1)是复形的正合列,因为C m是n-F I内射模,所以E x t1R(X[-t]m,C m)=0.于是正合列0ңC mңY mңX[-t]mң0可裂.故正合列(1)同构于复形的正合列0ңCңM(f)ңX[-t]ң0,(2)其中f:X[-t-1]ңC.由引理3知F P-i d(X[-t-1])ɤn,所以H o m(X[-t-1],C)正合.故f同伦于0.由文献[8]中推论2知,正合列(2)可裂,从而正合列(1)可裂,进而E x t1(X,C[t])≅E x t1(X[-t],C)=0.由t的任意性可得E x t1(X,C)=0,因此C是n-F I内射复形.证毕.推论1设M是R-模,则M是n-F I内射模当且仅当췍M是n-F I内射复形.证明:充分性.由定理1可得.必要性.设X是复形且F P-i d(X)ɤn,由引理1和引理2可得E x t1(X,췍M)≅E x t1R(X-1,M)=0.故由定理1知,췍M是n-F I内射复形.证毕.令F P n是所有F P-内射维数不超过n的复形的类,F P n(R)是所有F P-内射维数不超过n的模的类.定理2设C是复形,则下列结论等价:1)C是n-F I内射复形;2)对任意复形正合列0ңCңXңYң0,XңY是Y的F P n-预覆盖,其中XɪF P n;3)存在复形B的F P n-预覆盖f:AңB,使得C≅K e r(f),其中A是内射复形;4)对任意复形正合列0ңAңBңXң0,0ңH o m(X,C)ңH o m(B,C)ңH o m(A,C)ң0正合,其中XɪF P n.证明:1)⇒2).设0ңCңXңYң0是复形的短正合列,其中XɪF P n.令XᶄɪF P n,则由定理1知E x t1(Xᶄ,C)=0,从而有正合列H o m(Xᶄ,X)ңH o m(Xᶄ,Y)ң0.因此XңY是Y的F P n-预覆盖.1)⇒4).由定理1可得.2)⇒3).取复形正合列0ңCңE(C)ңE(C)/Cң0,其中E(C)是内射复形,所以E(C)ɪF P n.由2)知结论成立.3)⇒1).由3)可得复形的正合列0ңC ңAңfB ,其中A 是内射复形.从而有正合列0ңC ңA ңI m (f )ң0.易得A ңI m (f )是F P n -预覆盖.设X ɪF P n ,则有如下正合列:H o m (X ,A )f ң*H o m (X ,I m (f ))ңE x t 1(X ,C )ң0.因为f *是满的,所以E x t 1(X ,C )=0.由定理1知C 是n -F I 内射复形.4)⇒1).设X ɪF P n ,取复形的正合列0ңAңgB ңX ң0,其中B 是投射复形.从而有正合列H o m (B ,C )g ң*H o m (A ,C )ңE x t 1(X ,C )ң0.由4)知g *是满的,于是有E x t 1(X ,C )=0.故由定理1知,C 是n -F I 内射复形.证毕.由推论1和定理2可得以下推论.推论2[3] 设M 是R -模,则下列结论等价:1)M 是n -F I 内射模;2)对任意R -模的正合列0ңM ңE ңK ң0,E ңK 是K 的F P n -预覆盖,其中E ɪF P n (R );3)存在模B 的F P n -预覆盖h :A ңB ,使得M ≅K e r (h ),其中A 是内射模;4)对任意R -模的正合列0ңA ңB ңX ң0,有0ңH o m (X ,M )ңH o m (B ,M )ңH o m (A ,M )ң0正合,其中X ɪF P n (R ).参考文献[1] E N O C H SEE .I n j e c t i v e a n dF l a tC o v e r s ,E n v e l o p e s a n dR e s o l v e n t s [J ].I s r a e l JM a t h ,1981,39(3):189-209.[2] MA O LX ,D I N G N Q.F I -I n j e c t i v e a n dF I -F l a tM o d u l e s [J ].JA l g e b r a ,2007,309(1):367-385.[3] G A OZ H.O n 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