Understanding the relationship between landscape pattems and ecological processes has been a central yet challenging research theme in landscape ecology. Over the past decades, many landscape metrics have been propose...Understanding the relationship between landscape pattems and ecological processes has been a central yet challenging research theme in landscape ecology. Over the past decades, many landscape metrics have been proposed but few directly incorporated ecological processes. In this paper, we developed a landscape index, namely, location-weighted landscape index （LWLI） to highlight the role of landscape type in ecological processes, such as nutrient losses and soil erosion. Within the framework of the Lorenz curve theory, we develop this index by integrating land- scape pattern and point-based measurements at a watershed scale. The index can be used to characterize the contribution of landscape pattern to ecological processes （e.g. nutrient losses） with respect to a specific monitoring point in a watershed. Through a case study on nutrient losses in an agricultural area in northeastern China, we found that nutrient losses tended to be higher for a watershed with a higher LWLI value, and vice versa. It implied that LWLI can be used to evaluate the potential risk of nutrient losses or soil erosion by comparing their values across watersheds. In addition, this index can be extended to characterize ecological processes, such as the effect of landscape pattern on wildlife inhabitation and urban heat island effect. Finally, we discuss several problems that should be paid attention to when applying this index to a heterogeneous landscape site.展开更多
Within framework of zero curvature representation theory, a family of integrable rational semi-discrete systems is derived from a matrix spectral problem. The Hamiltonian forms of obtained semi-discrete systems are co...Within framework of zero curvature representation theory, a family of integrable rational semi-discrete systems is derived from a matrix spectral problem. The Hamiltonian forms of obtained semi-discrete systems are constructed by means of the discrete trace identity. The Liouville integrability for the obtained family is demonstrated. In the end, a reduced family of obtained semi-discrete systems and its Hamiltonian form are worked out.展开更多
For multi-cell curve box girder, the finite strip governing equation was derived on the basis of Novozhilov theory and orthogonal property of harmonious function series. Dynamic Bayesian error function of mechanical p...For multi-cell curve box girder, the finite strip governing equation was derived on the basis of Novozhilov theory and orthogonal property of harmonious function series. Dynamic Bayesian error function of mechanical parameters of multi-cell curve box girder was achieved with Bayesian statistical theory. The corresponding formulas of dynamic Bayesian expectation and variance were obtained. After the one-dimensional optimization search method for the automatic determination of step length of the mechanical parameter was put forward, the optimization identification calculative formulas were also obtained by adopting conjugate gradient method. Then the steps of dynamic Bayesian identification of mechanical parameters of multi-cell curve box girder were stated in detail. Through analysis of a classic example, the dynamic Bayesian identification processes of mechanical parameters are steadily convergent to the true values, which proves that dynamic Bayesian theory and conjugate gradient theory are suitable for the identification calculation and the compiled procedure is correct. It is of significance that the foreknown information of mechanical parameters should be set with reliable practical engineering experiences instead of arbitrary selection.展开更多
The roots of hyperbolic polynomials satisfy the linear inequalities that were previously established for the eigenvalues of Hermitian matrices,after a conjecture by A.Horn.Among them are the so-called Weyl and Lidski...The roots of hyperbolic polynomials satisfy the linear inequalities that were previously established for the eigenvalues of Hermitian matrices,after a conjecture by A.Horn.Among them are the so-called Weyl and Lidskiǐ inequalities.An elementary proof of the latter for hyperbolic polynomials is given.This proof follows an idea from H.Weinberger and is free from representation theory and Schubert calculus arguments,as well as from hyperbolic partial differential equations theory.展开更多
基金Under the auspices of Chinese Academy of Sciences (No. KZCX2-YW-421)National Natural Science Foundation of China (No. 40621061, 30570319)
文摘Understanding the relationship between landscape pattems and ecological processes has been a central yet challenging research theme in landscape ecology. Over the past decades, many landscape metrics have been proposed but few directly incorporated ecological processes. In this paper, we developed a landscape index, namely, location-weighted landscape index （LWLI） to highlight the role of landscape type in ecological processes, such as nutrient losses and soil erosion. Within the framework of the Lorenz curve theory, we develop this index by integrating land- scape pattern and point-based measurements at a watershed scale. The index can be used to characterize the contribution of landscape pattern to ecological processes （e.g. nutrient losses） with respect to a specific monitoring point in a watershed. Through a case study on nutrient losses in an agricultural area in northeastern China, we found that nutrient losses tended to be higher for a watershed with a higher LWLI value, and vice versa. It implied that LWLI can be used to evaluate the potential risk of nutrient losses or soil erosion by comparing their values across watersheds. In addition, this index can be extended to characterize ecological processes, such as the effect of landscape pattern on wildlife inhabitation and urban heat island effect. Finally, we discuss several problems that should be paid attention to when applying this index to a heterogeneous landscape site.
基金Supported by the Science and Technology Plan Projects of the Educational Department of Shandong Province of China under Grant No. J08LI08
文摘Within framework of zero curvature representation theory, a family of integrable rational semi-discrete systems is derived from a matrix spectral problem. The Hamiltonian forms of obtained semi-discrete systems are constructed by means of the discrete trace identity. The Liouville integrability for the obtained family is demonstrated. In the end, a reduced family of obtained semi-discrete systems and its Hamiltonian form are worked out.
基金supported by the National Natural Science Foundation of China (Grant Nos. 10772078 and 11072108)the Transportation Science Foundation of Jiangsu Province (Grant No. 09Y012)
文摘For multi-cell curve box girder, the finite strip governing equation was derived on the basis of Novozhilov theory and orthogonal property of harmonious function series. Dynamic Bayesian error function of mechanical parameters of multi-cell curve box girder was achieved with Bayesian statistical theory. The corresponding formulas of dynamic Bayesian expectation and variance were obtained. After the one-dimensional optimization search method for the automatic determination of step length of the mechanical parameter was put forward, the optimization identification calculative formulas were also obtained by adopting conjugate gradient method. Then the steps of dynamic Bayesian identification of mechanical parameters of multi-cell curve box girder were stated in detail. Through analysis of a classic example, the dynamic Bayesian identification processes of mechanical parameters are steadily convergent to the true values, which proves that dynamic Bayesian theory and conjugate gradient theory are suitable for the identification calculation and the compiled procedure is correct. It is of significance that the foreknown information of mechanical parameters should be set with reliable practical engineering experiences instead of arbitrary selection.
文摘The roots of hyperbolic polynomials satisfy the linear inequalities that were previously established for the eigenvalues of Hermitian matrices,after a conjecture by A.Horn.Among them are the so-called Weyl and Lidskiǐ inequalities.An elementary proof of the latter for hyperbolic polynomials is given.This proof follows an idea from H.Weinberger and is free from representation theory and Schubert calculus arguments,as well as from hyperbolic partial differential equations theory.
