In this paper,we give a survey on the Hill-type formula and its applications.Moreover,we generalize the Hill-type formula for linear Hamiltonian systems and Sturm-Liouville systems with any self-adjoint boundary condi...In this paper,we give a survey on the Hill-type formula and its applications.Moreover,we generalize the Hill-type formula for linear Hamiltonian systems and Sturm-Liouville systems with any self-adjoint boundary conditions,which include the standard Neumann,Dirichlet and periodic boundary conditions.The Hill-type formula connects the infinite determinant of the Hessian of the action functional with the determinant of matrices which depend on the monodromy matrix and boundary conditions.Further,based on the Hill-type formula,we derive the Krein-type trace formula.As applications,we give nontrivial estimations for the eigenvalue problem and the relative Morse index.展开更多
以中国西南喀斯特峰丛洼地为研究区域用标准木法和收获法对人工林、次生林、原生林3个不同类型森林的6个代表性群落的生物量、营养元素生物循环量及循环特征进行了研究。结果表明:(1)不同类型森林群落乔木各器官的养分含量大小顺序为:叶...以中国西南喀斯特峰丛洼地为研究区域用标准木法和收获法对人工林、次生林、原生林3个不同类型森林的6个代表性群落的生物量、营养元素生物循环量及循环特征进行了研究。结果表明:(1)不同类型森林群落乔木各器官的养分含量大小顺序为:叶>枝>根>干,林下植被层和凋落物层的养分含量比较高,其含量普遍高于乔木层各组分,仅次于乔木叶片;各组分中营养元素以K、Ca最高,P、Mg最低;(2)3种类型森林间乔木层的养分积累量总规律表现为原生林(4540.30 kg/hm^2)>次生林(2107.09 kg/hm^2)>人工林(719.51 kg/hm^2),分别占林分养分积累量的88.30%、79.57%和62.60%;(3)3种类型森林生态系统养分总贮量相差不大,均主要集中在土壤层在各层分配格局有所差异;营养元素的年吸收量和年归还量均为次生林>原生林>人工林,年吸收量分别为:418.80、271.17和148.79 kg hm^(-2)a^(-1);年归还量分别为:182.98、111.43和43.37 kg hm_(-2)a^(-1);(4)不同类型森林养分利用系数总规律为人工林(0.35)>次生林(0.20)>原生林(0.10);循环系数则相反,为原生林(0.48)>次生林(0.46)>人工林(0.30);而周转时间为原生林(37.32)>人工林(18.63)>次生林(13.93)。喀斯特峰丛洼地土层薄,养分贮存能力差,森林养分循环能力相对较弱,沿着强、中、弱干扰递减梯度,3种类型森林养分利用效率和循环能力呈增长趋势。展开更多
基金The first author is partially supported by NSFC(Nos.12071255 and 11790271)National Key R&D Program of China(2020YFA0713300)+1 种基金The second authors is partially supported by NSFC(No.11801583)The third author is Partially supported by NSFC(Nos.11471189,and 11871308).
文摘In this paper,we give a survey on the Hill-type formula and its applications.Moreover,we generalize the Hill-type formula for linear Hamiltonian systems and Sturm-Liouville systems with any self-adjoint boundary conditions,which include the standard Neumann,Dirichlet and periodic boundary conditions.The Hill-type formula connects the infinite determinant of the Hessian of the action functional with the determinant of matrices which depend on the monodromy matrix and boundary conditions.Further,based on the Hill-type formula,we derive the Krein-type trace formula.As applications,we give nontrivial estimations for the eigenvalue problem and the relative Morse index.
文摘以中国西南喀斯特峰丛洼地为研究区域用标准木法和收获法对人工林、次生林、原生林3个不同类型森林的6个代表性群落的生物量、营养元素生物循环量及循环特征进行了研究。结果表明:(1)不同类型森林群落乔木各器官的养分含量大小顺序为:叶>枝>根>干,林下植被层和凋落物层的养分含量比较高,其含量普遍高于乔木层各组分,仅次于乔木叶片;各组分中营养元素以K、Ca最高,P、Mg最低;(2)3种类型森林间乔木层的养分积累量总规律表现为原生林(4540.30 kg/hm^2)>次生林(2107.09 kg/hm^2)>人工林(719.51 kg/hm^2),分别占林分养分积累量的88.30%、79.57%和62.60%;(3)3种类型森林生态系统养分总贮量相差不大,均主要集中在土壤层在各层分配格局有所差异;营养元素的年吸收量和年归还量均为次生林>原生林>人工林,年吸收量分别为:418.80、271.17和148.79 kg hm^(-2)a^(-1);年归还量分别为:182.98、111.43和43.37 kg hm_(-2)a^(-1);(4)不同类型森林养分利用系数总规律为人工林(0.35)>次生林(0.20)>原生林(0.10);循环系数则相反,为原生林(0.48)>次生林(0.46)>人工林(0.30);而周转时间为原生林(37.32)>人工林(18.63)>次生林(13.93)。喀斯特峰丛洼地土层薄,养分贮存能力差,森林养分循环能力相对较弱,沿着强、中、弱干扰递减梯度,3种类型森林养分利用效率和循环能力呈增长趋势。
