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1)  Inche breadth and overlap
生态位宽度和重叠值
2)  Niche breadth and overlap
生态位宽度和重叠
3)  Niche overlap
生态位重叠值
4)  Niche overlap
生态位重叠度
1.
The result showed that the largest nutritional niche overlap occurred between I.
结果表明,环链棒束孢与粉棒束孢的营养生态位重叠度最大,与球孢白僵菌时间生态重叠度最大。
5)  niche overlap
生态位重叠
1.
But there has been no clear correlation;Artemisia annua and Aneurolepidium chinense,Artemisia mongolia and Poa annua niche overlap between high on their .
(2)黄花蒿(Artemisia annua)与羊草(Aneurolepidium chinese),蒙古蒿(Artemisia mongolia)与早熟禾(Poa annua)之间的生态位重叠最高,说明它们对空间资源的利用效率比较高,能充分的利用资源。
2.
24 communities have been carried out and the niche breadths,niche overlaps,multi-interspecies association,and pair-interspecies association of 13 populations are obtained on the investigation.
选择了其扩散区域内的24个样地进行群落学调查,测定了群落中13个种群的生态位宽度、生态位重叠、多物种间总体关联性及成对物种间联结性,结果表明:①水盾草入侵沉水植物群落13个种群中,水盾草的生态位宽度最大,金鱼藻(Ceratophyllum demersum)、黑藻(Hydrilla verticillata)和苦草(Vallisneria natans)次之。
3.
In this paper,plant niche breadth and niche overlap were analyzed on oasis-desert ecotone in Fukang of Xinjiang,with 7 measurements.
对于生态位宽度和生态位重叠已有多种计测公式 ,这些公式的生态学合理性和应用上的可操作性 ,一直是生态学家关注的问题[1,7,9] 。
6)  niche overlaps
生态位重叠
1.
The niche breadth,niche overlaps and niche similarity of 10 main trees species in the Mt.
以Levins和Shannon-Wiener生态位宽度和Pianka重叠指数对甘肃小陇山锐齿栎林的10个主要种群生态位宽度和生态位重叠及生态相似性进行了研究,分析了生态位宽度和生态位重叠的关系,揭示了各种群在群落中的功能地位及其生态适应性。
2.
The niche breadth,and niche overlaps of 10 main trees species in the Mountain Xiaolong in Gansu were measured using the formula proposed by Levins,Shannon-Wiener and Pianka.
以Levins和Shannon-Wiener生态位宽度及Pianka重叠指数为依据,将土壤有机质、土壤pH值、土壤全N分别作为反映各主要种群生长环境的资源轴,对小陇山锐齿栎林的10个主要种群生态位宽度和生态位重叠进行了研究。
3.
The niche characteristics of 17 dominant species of plant communities in Tianlong Mountains were analyzed, including the 40 quadrats were divided into 6 types of commnities by TWINSPAN,and the niche breadths and niche overlaps of main dominant species in the communities in Tianlong Mountains were measured by using Levins,Shannon-Wiener and Petraits s methods.
对天龙山植被的17个优势种群生态位进行了研究,首先用TWINSPAN与传统群落的分析方法,把40个样方分为6个群落类型,用Levins和Shannon-wiener生态位宽度和Petraitis生态位特定重叠指数测定群落中优势种群生态位宽度和生态位重叠,并分析其生态学意义。
补充资料:力学量的可能值和期待值
      在量子力学中,力学量F用作用于波函数上的算符弲表示。在数学上,对于一个算符,满足
  
  
  的函数 ui(r)称为弲的本征函数,式中Fi是与r无关的数,称为本征值。如果ui(r)描写微观粒子的状态,则它必须满足单值、连续和有限的标准条件。在这种限制之下,上式中的本征值可以取一系列分立值,或取一定范围内的连续数值。
  
  在测量力学量F时,观察到的只能是它的本征值。若一个力学量的本征值具有分立谱,我们说这个力学量是量子化的。
  
  量子力学中假定力学量的全部本征函数组成一个完全系;这意思是说:描写体系的任一状态的波函数ψ都可以用力学量的本征函数ui展开:
  
  
  在ψ和ui都是归一化的情况下,上式中的展开系数сi具有如下的物理意义:在ψ态中测量力学量时,得到结果为Fi的几率是|сi|2
  
  因此,若微观粒子的定态波函数是某力学量算符的本征函数ui(r),则在这一状态中,力学量F取确定值Fi
  
  在ψ态中对力学量进行多次测量,把所得结果加以平均,就得出力学量在ψ态中的期待值,以〈F〉表示:
  
  
  上式称为力学量的期待值公式。如果ψ不是归一化的,那么期待值公式应写为
  
  
  

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