An analysis method based on the fuzzy Lyapunov functions is presented to analyze the stability of the continuous affine fuzzy systems. First, a method is introduced to deal with the consequent part of the fuzzy local ...An analysis method based on the fuzzy Lyapunov functions is presented to analyze the stability of the continuous affine fuzzy systems. First, a method is introduced to deal with the consequent part of the fuzzy local model. Thus, the stability analysis method of the homogeneous fuzzy system can be used for reference. Stability conditions are derived in terms of linear matrix inequalities based on the fuzzy Lyapunov functions and the modified common Lyapunov functions, respectively. The results demonstrate that the stability result based on the fuzzy Lyapunov functions is less conservative than that based on the modified common Lyapunov functions via numerical examples. Compared with the method which does not expand the consequent part, the proposed method is simpler but its feasible region is reduced. Finally, in order to expand the application of the fuzzy Lyapunov functions, the piecewise fuzzy Lyapunov function is proposed, which can be used to analyze the stability for triangular or trapezoidal membership functions and obtain the stability conditions. A numerical example validates the effectiveness of the proposed approach.展开更多
This investigation is an analysis of the influence of landform instability on the distribution of land-use dynamics in a hydrographical basin, located in the Mexican Volcanic Belt mountain range (central Mexico), curr...This investigation is an analysis of the influence of landform instability on the distribution of land-use dynamics in a hydrographical basin, located in the Mexican Volcanic Belt mountain range (central Mexico), currently affected by substantial changes in land use and deforestation. A landform map was produced, in addition to seven attribute maps - altimetry, drainage density, slope, relief energy, potential erosion, geology and tectonics - which were considered as factors for determining landform instability through Multi-criteria Evaluation Analysis. Likewise, the direction and rhythm of land-use dynamics were analyzed in four dates - between 1976 and 2000 - and cross tabulations were made between them, in order to analyze the trends and processes of land-use dynamics. Afterwards, the databases obtained were cross tabulated with the landform variables to derive areas, percentages and correlation indices. In the study area, high-instability landforms are associated with most ancient volcanic and sedimentary landforms, where high altitude, drainage density, slope and potential to develop gravitational and fluvial processes are the major factors favouring a land-use pattern, dominated by the conservation of extensive forest land, abandonment of human land use and regeneration of disturbed areas. In contrast, low-instability landforms correspond to alluvial plains and lava hills covered by pyroclasts, where low potential erosion to develop fluvial processes, added to water and soil availability and accessibility, have favoured a land-use pattern dominated by the expansion of agroforestry plantations and human settlements, showing a marked trend towards either intensification or permanence of the current land use and with little abandonment and regeneration.展开更多
Let （Ω＊ （M）, d） be the de Rham cochain complex for a smooth compact closed manifolds M of dimension n. For an odd-degree closed form H, there is a twisted de Rham cochain complex （Ω＊ （M）, d ＋ H∧） and its...Let （Ω＊ （M）, d） be the de Rham cochain complex for a smooth compact closed manifolds M of dimension n. For an odd-degree closed form H, there is a twisted de Rham cochain complex （Ω＊ （M）, d ＋ H∧） and its associated twisted de Rham cohomology H＊ （M, H）. The authors show that there exists a spectral sequence {Ep/r.q, dr } derived from the filtration Fp（Ω＊ （M）） = （¤i〉p Ωi（M） of Ω＊ （M）, which converges to the twisted de Rham cohomology H＊（M, H）. It is also shown that the differentials in the spectral sequence can be given in terms of cup products and specific elements of Massey products as well, which generalizes a result of Atiyah and Segal. Some results about the indeterminacy of differentials are also given in this paper.展开更多
基金Specialized Research Fund for the Doctoral Program of Higher Education ( No. 20090092110051)the Key Project of Chinese Ministry of Education ( No. 108060)the National Natural Science Foundation of China ( No. 51076027, 51036002, 51106024)
文摘An analysis method based on the fuzzy Lyapunov functions is presented to analyze the stability of the continuous affine fuzzy systems. First, a method is introduced to deal with the consequent part of the fuzzy local model. Thus, the stability analysis method of the homogeneous fuzzy system can be used for reference. Stability conditions are derived in terms of linear matrix inequalities based on the fuzzy Lyapunov functions and the modified common Lyapunov functions, respectively. The results demonstrate that the stability result based on the fuzzy Lyapunov functions is less conservative than that based on the modified common Lyapunov functions via numerical examples. Compared with the method which does not expand the consequent part, the proposed method is simpler but its feasible region is reduced. Finally, in order to expand the application of the fuzzy Lyapunov functions, the piecewise fuzzy Lyapunov function is proposed, which can be used to analyze the stability for triangular or trapezoidal membership functions and obtain the stability conditions. A numerical example validates the effectiveness of the proposed approach.
基金the National Autonomous University of Mexico, under project DGAPA-PAPIIT number IN-300911-3
文摘This investigation is an analysis of the influence of landform instability on the distribution of land-use dynamics in a hydrographical basin, located in the Mexican Volcanic Belt mountain range (central Mexico), currently affected by substantial changes in land use and deforestation. A landform map was produced, in addition to seven attribute maps - altimetry, drainage density, slope, relief energy, potential erosion, geology and tectonics - which were considered as factors for determining landform instability through Multi-criteria Evaluation Analysis. Likewise, the direction and rhythm of land-use dynamics were analyzed in four dates - between 1976 and 2000 - and cross tabulations were made between them, in order to analyze the trends and processes of land-use dynamics. Afterwards, the databases obtained were cross tabulated with the landform variables to derive areas, percentages and correlation indices. In the study area, high-instability landforms are associated with most ancient volcanic and sedimentary landforms, where high altitude, drainage density, slope and potential to develop gravitational and fluvial processes are the major factors favouring a land-use pattern, dominated by the conservation of extensive forest land, abandonment of human land use and regeneration of disturbed areas. In contrast, low-instability landforms correspond to alluvial plains and lava hills covered by pyroclasts, where low potential erosion to develop fluvial processes, added to water and soil availability and accessibility, have favoured a land-use pattern dominated by the expansion of agroforestry plantations and human settlements, showing a marked trend towards either intensification or permanence of the current land use and with little abandonment and regeneration.
基金supported by the National Natural Science Foundation of China(No.11171161)the Scientific Research Foundation for the Returned Overseas Chinese Scholars of the State Education Ministry(No.2012940)
文摘Let （Ω＊ （M）, d） be the de Rham cochain complex for a smooth compact closed manifolds M of dimension n. For an odd-degree closed form H, there is a twisted de Rham cochain complex （Ω＊ （M）, d ＋ H∧） and its associated twisted de Rham cohomology H＊ （M, H）. The authors show that there exists a spectral sequence {Ep/r.q, dr } derived from the filtration Fp（Ω＊ （M）） = （¤i〉p Ωi（M） of Ω＊ （M）, which converges to the twisted de Rham cohomology H＊（M, H）. It is also shown that the differentials in the spectral sequence can be given in terms of cup products and specific elements of Massey products as well, which generalizes a result of Atiyah and Segal. Some results about the indeterminacy of differentials are also given in this paper.
