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复指数系的完备性 被引量:1
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作者 邓冠铁 《数学年刊(A辑)》 CSCD 北大核心 2005年第4期537-542,共6页
对直线上的非负凸函数α,设Cα是由直线R上所有满足当t趋向无穷大时,f(t)exp(-α(t))趋向零的复连续函数f全体,在一致范数下,Cα是Banach空间.文中得到了复指数系在Cα中完备的充要条件.
关键词 完备性 BANACH空间 指数系
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随机指数系的完备性和极小性
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作者 柯思宇 高志强 邓冠铁 《数学年刊(A辑)》 CSCD 北大核心 2010年第4期385-394,共10页
得到了随机指数系在加权Banach空间C_α中完备和极小的充要条件,其中C_α是实直线R上的复连续函数在权α的一致范数下组成的Banach空间.这些结果可以看作是Malliavin经典结果的概率推广.
关键词 随机指数系 完备性 极小性
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加权Banach空间中随机指数系完备的若干结论
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作者 王越 杨向东 《应用数学》 CSCD 北大核心 2017年第4期946-952,共7页
在允许随机序列上密度无限且减弱权函数是凸函数的条件下,采用新的方法得到C_α中随机指数函数系完备性的充分必要条件,其中C_α是定义在R上的复连续函数构成的加权Banach空间,且要求函数在一致范数下当t→∞时以f(t)exp(-α(t))趋于零.
关键词 完备性 加权Banach空间 随机指数系 上密度无限
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复指数系的不完备性和最小性 被引量:1
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作者 邓冠铁 《中国科学(A辑)》 CSCD 北大核心 2007年第7期769-778,共10页
本文得到复指数系E(Λ,M)在C_α中不完备的一个充分必要条件,其中C_α是所有在实轴R上连续,且当t趋向无穷时,f(t)exp(-α(t))趋向零的复函数f组成的集合.在一致范数‖f‖_α=sup{|f(t)e^(-α(t))|:t∈R}下,C_α是一个Banach空间.证明... 本文得到复指数系E(Λ,M)在C_α中不完备的一个充分必要条件,其中C_α是所有在实轴R上连续,且当t趋向无穷时,f(t)exp(-α(t))趋向零的复函数f组成的集合.在一致范数‖f‖_α=sup{|f(t)e^(-α(t))|:t∈R}下,C_α是一个Banach空间.证明了在不完备的情形下,复指数系E(Λ,M)是最小的并且复指数系E(Λ,M)中线性组合的闭包中的任意函数可以延拓成由Taylor-Dirichlet级数表示的整函数. 展开更多
关键词 不完备性 最小性 指数系
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空间Sierpinski垫上的五元素正交指数系 被引量:2
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作者 张佳妮 李建林 王琦 《数学学报(中文版)》 CSCD 北大核心 2018年第4期625-630,共6页
设p1,p2,p3∈Z/{0,±1},e1,e2,e3是R3上标准的单位正交基,由扩张矩阵M=diag[p1,p2,p3]和数字集D={0,e1,e2,e3}确定的自仿测度μM,D是支撑在空间Sierpinski垫T(M,D)上,其对应的Hilbert空间L2(μM,D)上正交指数系的有限性与无限... 设p1,p2,p3∈Z/{0,±1},e1,e2,e3是R3上标准的单位正交基,由扩张矩阵M=diag[p1,p2,p3]和数字集D={0,e1,e2,e3}确定的自仿测度μM,D是支撑在空间Sierpinski垫T(M,D)上,其对应的Hilbert空间L2(μM,D)上正交指数系的有限性与无限性问题已经解决.在有限的情形下,空间L2(μM,D)上正交指数系基数的最佳上界为“4”的猜测还未完全解决.本文构造出了此空间上一列五元素正交指数函数系,说明上述最佳上界为“4”的猜测是错误的. 展开更多
关键词 自仿测度 正交指数系 非谱性 数字集
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空间自仿测度下无限正交指数系存在的条件 被引量:2
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作者 李敏 李建林 《数学进展》 CSCD 北大核心 2016年第3期332-342,共11页
自仿测度μ_M,D的谱与非谱问题是自仿测度谱理论研究的主要内容之一,而μ_M,D-正交指数系的有限性或无限性问题在研究自仿测度是否为谱测度中起着重要的作用.本文主要探讨空间自仿测度下无限正交指数系存在的条件.通过利用函数m_D(x)零... 自仿测度μ_M,D的谱与非谱问题是自仿测度谱理论研究的主要内容之一,而μ_M,D-正交指数系的有限性或无限性问题在研究自仿测度是否为谱测度中起着重要的作用.本文主要探讨空间自仿测度下无限正交指数系存在的条件.通过利用函数m_D(x)零点集Z(m_D)中的非零中间点(即坐标为0或1/2的点)的性质,得到存在无限μ_(M,D)-正交指数系的许多条件,为进一步研究自仿测度μ_(M,D)的谱性质奠定基础. 展开更多
关键词 自仿测度 正交指数系 数字集
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有限μM,D-正交指数函数系的一个充分条件
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作者 李娜 李建林 《数学年刊(A辑)》 CSCD 北大核心 2019年第4期457-466,共10页
设μM,D是由仿射迭代函数系{φd(x)=M^-1-(x+d)}d∈D唯一确定的自仿测度,它的谱与非谱性质与Hilbert空间L^2(μM,D)中正交指数函数系的有限性和无限性有着直接的关系.本文将利用矩阵的初等变换给出μM,D正交指数函数系有限性的一个充分... 设μM,D是由仿射迭代函数系{φd(x)=M^-1-(x+d)}d∈D唯一确定的自仿测度,它的谱与非谱性质与Hilbert空间L^2(μM,D)中正交指数函数系的有限性和无限性有着直接的关系.本文将利用矩阵的初等变换给出μM,D正交指数函数系有限性的一个充分条件.由于这个条件只与矩阵M的行列式有关,因此,它在μM,D的非谱性的判断方面便于直接验证. 展开更多
关键词 自仿测度 正交指数函数 非谱性 行列式
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加权Banach空间中指数函数系完备的稳定性(英文)
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作者 杨向东 王越 《数学杂志》 2018年第1期103-112,共10页
本文研究了加权Banach空间中指数函数系完备的稳定性问题.利用解析函数扰动的方法,获得了加权Banach空间中指数函数系完备的稳定性若干结果,推广了现有有限区间Banach空间上的经典结果.
关键词 稳定性 指数函数 完备性 BANACH空间
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复指数函数系在E^p[σ]中的完备性
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作者 柯思宇 邓冠铁 《北京师范大学学报(自然科学版)》 CAS CSCD 北大核心 2009年第3期232-237,共6页
通过推广的Carleman公式,给出了复指数函数系在半带形上某些解析函数组成的Banach空间中不完备的充要条件.
关键词 指数函数 完备性 BANACH空间
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一类直和数字集下正交指数函数系的基数
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作者 张新苗 《西安文理学院学报(自然科学版)》 2019年第2期1-4,共4页
设M∈M2(■)为整数扩张矩阵,即M的所有特征值的模都大于1,D_1为有限数字集且D_1={(0 0),(-1 0),(11)},P=[0 p_1 p_2 0],其中p_1=±3,p_2=±1,当det(M)≠3■时,由整数扩张矩阵M和数字集D=D_1PD_1所确定的L^2(μ_(M,D))空间上... 设M∈M2(■)为整数扩张矩阵,即M的所有特征值的模都大于1,D_1为有限数字集且D_1={(0 0),(-1 0),(11)},P=[0 p_1 p_2 0],其中p_1=±3,p_2=±1,当det(M)≠3■时,由整数扩张矩阵M和数字集D=D_1PD_1所确定的L^2(μ_(M,D))空间上正交指数函数系的基数为9,即μ_(M,D)为非谱测度. 展开更多
关键词 正交指数函数 非谱测度 数字集
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Satellite remote sensing reveals overwhelming recovery of forest from disturbances in Asia
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作者 Yiying Zhu Hesong Wang Anzhi Zhang 《Atmospheric and Oceanic Science Letters》 2025年第1期46-51,共6页
Forest ecosystems play key roles in mitigating human-induced climate change through enhanced carbon uptake;however,frequently occurring climate extremes and human activities have considerably threatened the stability ... Forest ecosystems play key roles in mitigating human-induced climate change through enhanced carbon uptake;however,frequently occurring climate extremes and human activities have considerably threatened the stability of forests.At the same time,detailed accounts of disturbances and forest responses are not yet well quantified in Asia.This study employed the Breaks For Additive Seasonal and Trend method-an abrupt-change detection method-to analyze the Enhanced Vegetation Index time series in East Asia,South Asia,and Southeast Asia.This approach allowed us to detect forest disturbance and quantify the resilience after disturbance.Results showed that 20%of forests experienced disturbance with an increasing trend from 2000 to 2022,and Southeast Asian countries were more severely affected by disturbances.Specifically,95%of forests had robust resilience and could recover from disturbance within a few decades.The resilience of forests suffering from greater magnitude of disturbance tended to be stronger than forests with lower disturbance magnitude.In summary,this study investigated the resilience of forests across the low and middle latitudes of Asia over the past two decades.The authors found that most forests exhibited good resilience after disturbance and about two-thirds had recovered to a better state in 2022.The findings of this study underscore the complex relationship between disturbance and resilience,contributing to comprehension of forest resilience through satellite remote sensing. 展开更多
关键词 Forest ecosystem Enhanced vegetation index Breaks for additive seasonal and trend method DISTURBANCE RESILIENCE
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基于有性测定选育杉木三优无性系
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作者 齐明 朱培林 《江西林业科技》 2012年第3期17-21,共5页
为了选育三优(生长快,材质优,抗贫瘠)杉木无性系,开展31个杉木无性系养分胁迫双因素的容器育苗随机区组试验,8株小区。调查苗高、地径和存活率,每个小区抽取生长中等偏上的植株3株,测定地上生物量、地下生物量、总生物量、根冠比和全株... 为了选育三优(生长快,材质优,抗贫瘠)杉木无性系,开展31个杉木无性系养分胁迫双因素的容器育苗随机区组试验,8株小区。调查苗高、地径和存活率,每个小区抽取生长中等偏上的植株3株,测定地上生物量、地下生物量、总生物量、根冠比和全株P含量,并将P含量的高低作为耐贫瘠的一个重要指标。统计分析表明:(1)在无性系间除了存活率和根冠比未达到显著差异外,其它研究性状在无性系间均存在显著差异,因此具有无性系选择的基础。(2)所有研究性状在不同的养分胁迫处理间有极明显的差异,说明杉木的扦插圃地和造林地的选择十分重要。(3)无性系与养分胁迫处理间的互作表现复杂。(4)各研究性状具有一定的变异和中度以上的重复力。基于方差分析结果,采用主成分选择指数,按一定的选择强度,整个试验共评选出13个优良无性系,其中耐磷和钾(喜氮肥)的无性系7个:A4,A7,A9,A11,A13,A18,A26;耐磷(喜氮钾肥)的无性系7个:A9,A13,A16,A18,A28,A29,A30;不耐贫瘠(喜氮磷钾肥)的无性系8个:A9,A11,A13,A18,A20,A24,A26,A28;从整个试验平均值的的信息评选出优良无性系8个:A9,A11,A13,A18,A24,A26,A28和A25。各种条件下表现均优的无性系有:A9,A13,A18,A26,A28,它们表现突出,同时也很稳定。这些无性系可直接在生产上推广应用。 展开更多
关键词 杉木 无性 选择 主成分选择指数
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具有2个数字集的自仿测度μM,D正交指数函数的个数
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作者 王晓珍 《纺织高校基础科学学报》 CAS 2012年第2期132-134,共3页
对于由M=pIN(|p|>1,p∈Z),D={0,l1e1+l2e2+…+lNeN}ZN(l21+22+…+l2N≠0,lj∈Z,j=1,2,…,N)决定的自仿测度μM,D,支撑在吸引子T(M,D)上.证明当p为奇数时,L2(μM,D)空间中的正交指数函数系最多有2个元素,而且2是最好的估计;当p为偶... 对于由M=pIN(|p|>1,p∈Z),D={0,l1e1+l2e2+…+lNeN}ZN(l21+22+…+l2N≠0,lj∈Z,j=1,2,…,N)决定的自仿测度μM,D,支撑在吸引子T(M,D)上.证明当p为奇数时,L2(μM,D)空间中的正交指数函数系最多有2个元素,而且2是最好的估计;当p为偶数时,L2(μM,D)空间中存在含有无限个元素的正交指数函数系. 展开更多
关键词 自仿测度 迭代函数 FOURIER变换 正交指数函数
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n次对称群中n元置换的一些性质
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作者 唐善刚 李伟 孙海 《佳木斯大学学报(自然科学版)》 CAS 2009年第5期757-759,共3页
在n次对称群中引入了刻画n元置换性质的指数概念与同型置换的概念,然后基于对指数概念与同型置换概念的研究得到了n元置换的一些性质描述.
关键词 n次对称群 指数 指数系 同型置换 轮换
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WEIGHTED ALGORITHM FOR FINGERPRINTING RELATIONAL DATABASES 被引量:1
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作者 崔新春 秦小麟 +1 位作者 管致锦 束瑜 《Transactions of Nanjing University of Aeronautics and Astronautics》 EI 2008年第2期148-154,共7页
The necessity and the feasibility of introducing attribute weight into digital fingerprinting system are given. The weighted algorithm for fingerprinting relational databases of traitor tracing is proposed. Higher wei... The necessity and the feasibility of introducing attribute weight into digital fingerprinting system are given. The weighted algorithm for fingerprinting relational databases of traitor tracing is proposed. Higher weights are assigned to more significant attributes, so important attributes are more frequently fingerprinted than other ones. Finally, the robustness of the proposed algorithm, such as performance against collusion attacks, is analyzed. Experimental results prove the superiority of the algorithm. 展开更多
关键词 digital fingerprinting relational database systems copyright protection attribute weight traitor tracing
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RITSD Analysis of the Agronomic Traits of Somaclonal in Rice 被引量:6
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作者 谢戎 杨正林 +3 位作者 刘成元 李永洪 桑贤春 何光华 《Agricultural Science & Technology》 CAS 2010年第1期36-41,共6页
[Objective]The aim was to study the sensitive response characteristics of the main agronomic traits of somaclonal and the variation of sensitive response of the lines of somaclonal to sowing date. [Method]The RITSD ch... [Objective]The aim was to study the sensitive response characteristics of the main agronomic traits of somaclonal and the variation of sensitive response of the lines of somaclonal to sowing date. [Method]The RITSD changing of agronomic traits was studied by using 24 rice somaclonal and its donor parent under two sowing dates. [Result]The average values of RITSD were higher (over one) for the traits of pant height (PH),density of spikelets (DS),filled spikelets per panicle (FSP),spikelets per panicle (SP) and grain weight per plant (GWP),but lower for days of sowing to heading (DSH),effective panicles (EP),panicle length (PL),seed setting rate (SS) and 1 000-grain weight (1 000-GW). These showed that PH,DS,FSP,SP and GWP were easily affected by sowing date and tended to higher with the later sowing; the RITSD of somaclonal changed with the agronomic traits. The frequency of RITSD' variation of DSH and PH was higher than that of PL. The RITSD' value of EP,PL,DS,FSP,SP and SS became higher,and higher or lower for DSH and GWP in different somaclonal; compared with the donor,20 of 24 was significantly different,and the frequency of RITSD variation was over 83. 3%,however,RITSD of the most lines (75%) changed only for 1-2 characters; cluster analysis showed that the RITSD of agronomic traits belonged to different combinations of somaclonal in rice. [Conclusion]the study had provided a theoretical basis for the screening and using of the somaclonal. 展开更多
关键词 Rice (Oryza sativa L.) Somaclonal Respondence Index of Trait to Sowing Date (RITSD) Agronomic traits VARIATION
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Happiness Index-oriented Tourism Area Management 被引量:1
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作者 余子萍 《Journal of Landscape Research》 2010年第3期55-57,共3页
The establishment of happiness index evaluation system for tourism resorts is an effective approach to enhance the scientific development of resorts and the well-being of people. Through analyzing happiness indexes of... The establishment of happiness index evaluation system for tourism resorts is an effective approach to enhance the scientific development of resorts and the well-being of people. Through analyzing happiness indexes of population in tourism resorts, this study aims to provide references for the scientific development of resorts. 展开更多
关键词 RESORTS Happiness index Evaluation system HUMAN-CENTERED
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The Application of Pearson Correlational Analysis Method in Air Quality Analysis of Beijing-Tianjin-Hebei Region 被引量:15
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作者 杨宁 冀德刚 李双金 《Agricultural Science & Technology》 CAS 2015年第3期590-592,共3页
Based on the analysis of monitoring data on six pollution indexes of SO2, NO2, CO, O3, PM10 and PM2.5 from 53 monitoring points in 7 cities, including Beijing, Tianjin, Shijiazhuang, etc., from April 8 of 2014 to July... Based on the analysis of monitoring data on six pollution indexes of SO2, NO2, CO, O3, PM10 and PM2.5 from 53 monitoring points in 7 cities, including Beijing, Tianjin, Shijiazhuang, etc., from April 8 of 2014 to July 23 of 2014, this article adopted Pearson correlation coefficient method to determine the relevance among each pollutant of these cities with the help of SPSS. The results showed that such three leading indexes as SO2, PM10 and PM2.5 had strong correlation in Beijing, Tianjin and main cities of Hebei. Finally, some suggestions and preventive measures for the cooperative governance of air pollution in Beijing-Tianjin-Hebei Region were put forward, hoping this can help them. 展开更多
关键词 Pearson Correlation coefficient Linear interpolation Monitoring indicators Air quality
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Dynamic Variation and Simulation of Extinction Coefficient of Corn Population
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作者 祁红彦 周广胜 +1 位作者 李荣平 刘志 《Agricultural Science & Technology》 CAS 2011年第11期1724-1728,共5页
[Objective] The aim was to study the dynamic variation of extinction coefficient of corn population, so as to improve the accuracy of assessment on net primary productivity (NPP) or yield. [Method] Based on the data... [Objective] The aim was to study the dynamic variation of extinction coefficient of corn population, so as to improve the accuracy of assessment on net primary productivity (NPP) or yield. [Method] Based on the data of photosynthetic active radiation and leaf area index during corn growing season (from May to September) in 2006, observed in Jinzhou observation station of corn farmland ecosystem, China Meteorological Administration, the dynamic variation of extinction coefficient of corn population was analyzed. [Result] There was a great daily variation in the extinction coefficient of corn population during growing season, and the maximum value appeared from 7:00 to 9:00 and from 15:00 to 17:00, while the minimum could be found around 12:00, but the amplitude of variation decreased in tasseling stage. On a large time scale (5 d), there was a parabolic relationship between extinction coefficient (K) and leaf area index (LAI), with determination coefficient R2 of 0.960 7. The simulation equation of extinction coefficient, based on the sun elevation angle or leaf area index, had poor accuracy at various time during growing season, so a new dynamic model of extinction coefficient was established, namely K=λ(0.784 8-0.001 6θ)(0.154 8LAI2-0.558 6LAI+0.654). [Conclusion] The effect of sun elevation angle and leaf area index on extinction coefficient during corn growing season was considered in the new dynamic model of extinction coefficient, and its simulated result was superior to that of single-factor model. 展开更多
关键词 Corn population Sun elevation angle Leaf area index Extinction coefficient
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燕山地区大红峪组火山岩古风化作用新认识 被引量:1
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作者 林晓辉 秦正永 《火山地质与矿产》 2001年第4期284-291,共8页
大红峪组火山岩 ,在成岩后受古风化作用影响引起化学成分的变化 ,特别是深风化带岩石后期K2 O沉积的影响 ,造成从未风化到深风化岩石在TAS图解、碱度系数、岩系指数及岩石类型等方面相应地发生变化。在TAS图解上 ,岩石向碱性增加、SiO2... 大红峪组火山岩 ,在成岩后受古风化作用影响引起化学成分的变化 ,特别是深风化带岩石后期K2 O沉积的影响 ,造成从未风化到深风化岩石在TAS图解、碱度系数、岩系指数及岩石类型等方面相应地发生变化。在TAS图解上 ,岩石向碱性增加、SiO2 减少方向变化。碱度系数变大 ,岩系指数的变化使火山岩反映为从钙碱性到超碱性。岩石类型也出现不确定性。深风化带岩石根据岩石化学成分计算标准矿物时 ,出现白榴石、霞石等碱性矿物 ,而实际矿物未见这一现象 ,也是后期K2 O沉积影响的结果。排除古风化的影响 ,作者认为大红峪组火山岩应为钾质的粗面岩和粗面玄武岩 ,属钙碱系列。粗面玄武岩为铝过饱和型 ,粗面岩为正常型。不存在明显的岩浆分离结晶作用 ,其原始岩浆应以基性为主。由于上述的原因 ,影响了对岩浆来源、构造环境的判断。推断其构造环境 ,是在总的海进条件下 ,出现多次的海退 ,伴有多次火山喷发活动 ,水动能比较大 ,气候干旱 ,封闭、半封闭的海盆中富含钾的环境。 展开更多
关键词 古风化作用 火山岩 TAS图解 碱度 指数 燕山地区 大红峪组
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