In the paper, we study the stability of Hilbert space generalized frames under perturbations. We get some results that are in spirit close to classical results for discrete frames, due to OLE Christensen.
Terrain texture analysis is an important method of digital terrain analysis in quantitative geomorphological research and in the exploration of the spatial heterogeneity and autocorrelation of terrain features. Howeve...Terrain texture analysis is an important method of digital terrain analysis in quantitative geomorphological research and in the exploration of the spatial heterogeneity and autocorrelation of terrain features. However, a major issue often neglected in previous studies is the calculation unit of the terrain texture, that is, the stability analysis unit. As the test size increases, the derived terrain textures become increasingly similar so that their differences can be ignored. The test size of terrain texture is defined as the stability analysis unit. This study randomly selected 48 areas within the Loess Plateau in northern Shaanxi in China as the study sites and used the gray level co-occurrence matrix to calculate the terrain texture. The stability analysis unit of the terrain texture was then extracted, and its spatial distribution pattern in the Loess Plateau was studiedusing spatial interpolation method. Four terrain texture metrics, i.e., homogeneity, energy, correlation, and contrast, were extracted on the basis of the stability analysis unit, and the spatial variation patterns of these parameters were studied. Results showed that the spatial distribution pattern and the terrain texture metrics reflected a trend of high–low–high from north to south, which correlated with the spatial distribution of the landforms at the Loess Plateau. In addition, the terrain texture measures was significantly correlated with the terrain factors of gully density and slope, and this relationship showed that terrain texture measures based on the stability analysis unit could reflect the basic characteristics of terrain morphology. The stability analysis unit provided a reasonable analytical scale for terrain texture analysis and could be used as a measure of the regional topography to accurately describe basic terrain characteristics.展开更多
In fact, the failure of any slope takes place progressively, but the progressive failure mechanism has not been emphasized sufficently in the present stability analysis of slopes. This paper provides an example of the...In fact, the failure of any slope takes place progressively, but the progressive failure mechanism has not been emphasized sufficently in the present stability analysis of slopes. This paper provides an example of the progressive slope failure which took place at Pingzhuang west surface coal mine and was numbered the 26th slide. The three-dimensional reliability model for progressive slope failure is used to study the failure process of the 26th slide. The outcomes indicate that the progressive failure is indeed the failure mechanism of the slide.展开更多
This paper presents a design of boundary controllers implemented at the top end for global stabilization of a marine riser in a three dimensional space under environmental loadings. Based on the energy approach, nonli...This paper presents a design of boundary controllers implemented at the top end for global stabilization of a marine riser in a three dimensional space under environmental loadings. Based on the energy approach, nonlinear partial differential equations of motion, including bending-bending and longitudinal-bending couplings for the risers are derived. The couplings cause mutual effects between the three independent directions in the riser＇s motions, and make it difficult to minimize its vibrations. The Lyapunov direct method is employed to design the boundary controller. It is shown that the proposed boundary controllers can effectively reduce the riser＇s vibration. Stability analysis of the closed-loop system is performed using the Lyapunov direct method. Numerical simulations illustrate the results.展开更多
The changes of stress and strain around the shaft under the non-axial symmetrical loads during the excavation are analyzed with the finite element semi-analytical method based on the separated variable method. The cha...The changes of stress and strain around the shaft under the non-axial symmetrical loads during the excavation are analyzed with the finite element semi-analytical method based on the separated variable method. The change laws of deformation and stress of surrounding rocks are obtaied. Moreover, an optimum method of the design and construction of the shaft lining is de veloped. which presents a new train of thought of the design and costruction of the shaft and has important theoretical value and extensive application prospects.展开更多
Applying the similarity transformation, we construct the exact vortex solutions for topological charge S≥1 and the approximate fundamental soliton solutions for S = 0 of the two-dimensional cubic-quintic nonlinear Sc...Applying the similarity transformation, we construct the exact vortex solutions for topological charge S≥1 and the approximate fundamental soliton solutions for S = 0 of the two-dimensional cubic-quintic nonlinear Schrodinger equation with spatially modulated nonlinearities and harmonic potential. The linear stability analysis and numerical simulation are used to exam the stability of these solutions. In different profiles of cubic-quintic nonlinearities, some stable solutions for S 〉 0 and the lowest radial quantum number n = 1 are found. However, the solutions for n ≥ 2 are all unstable.展开更多
Nowadays, biological resource in prey-predator ecosystem is commercially harvested and sold with aim of achieving economic interest. Furthermore, harvest effort is usually influ- enced by variation of economic interes...Nowadays, biological resource in prey-predator ecosystem is commercially harvested and sold with aim of achieving economic interest. Furthermore, harvest effort is usually influ- enced by variation of economic interest of harvesting and spatial heterogeneous environ- ment. In this paper, a delayed differential-algebraic bio-economic model is proposed, which is utilized to investigate interaction and coexistence mechanism of biological pop- ulation in the harvested ecosystem due to the variation of economic interest of harvesting as well as the change of population spatial diffusion and gestation delay. Local stability analysis of the proposed model without gestation delay and diffusion reveals that there is a phenomenon of singularity induced bifurcation due to the variation of economic interest of harvesting, and state feedback controllers are designed to stabilize the pro- posed model at the interior equilibrium. Furthermore, local stability of the proposed model with gestation delay and diffusion is studied, which reveals that the interior equi- librium loses its stability at some critical values of gestation delay and corresponding cycle occurs. It is also shown that population spatial diffusion and harvesting have a stabilizing effect on population dynamics. Finally, numerical simulations are carried out to show consistency with theoretical analysis obtained in this paper.展开更多
文摘In the paper, we study the stability of Hilbert space generalized frames under perturbations. We get some results that are in spirit close to classical results for discrete frames, due to OLE Christensen.
基金supported by the National Natural Science Foundation of China (Grant Nos. 41471316, 41571383, 41671389)the Priority Academic Program Development of Jiangsu Higher Education Institutions-PAPD (Grant No. 164320H101)the Key Project of Natural Science Research of Anhui Provincial Department of Education (Grant No. KJ2015A171)
文摘Terrain texture analysis is an important method of digital terrain analysis in quantitative geomorphological research and in the exploration of the spatial heterogeneity and autocorrelation of terrain features. However, a major issue often neglected in previous studies is the calculation unit of the terrain texture, that is, the stability analysis unit. As the test size increases, the derived terrain textures become increasingly similar so that their differences can be ignored. The test size of terrain texture is defined as the stability analysis unit. This study randomly selected 48 areas within the Loess Plateau in northern Shaanxi in China as the study sites and used the gray level co-occurrence matrix to calculate the terrain texture. The stability analysis unit of the terrain texture was then extracted, and its spatial distribution pattern in the Loess Plateau was studiedusing spatial interpolation method. Four terrain texture metrics, i.e., homogeneity, energy, correlation, and contrast, were extracted on the basis of the stability analysis unit, and the spatial variation patterns of these parameters were studied. Results showed that the spatial distribution pattern and the terrain texture metrics reflected a trend of high–low–high from north to south, which correlated with the spatial distribution of the landforms at the Loess Plateau. In addition, the terrain texture measures was significantly correlated with the terrain factors of gully density and slope, and this relationship showed that terrain texture measures based on the stability analysis unit could reflect the basic characteristics of terrain morphology. The stability analysis unit provided a reasonable analytical scale for terrain texture analysis and could be used as a measure of the regional topography to accurately describe basic terrain characteristics.
文摘In fact, the failure of any slope takes place progressively, but the progressive failure mechanism has not been emphasized sufficently in the present stability analysis of slopes. This paper provides an example of the progressive slope failure which took place at Pingzhuang west surface coal mine and was numbered the 26th slide. The three-dimensional reliability model for progressive slope failure is used to study the failure process of the 26th slide. The outcomes indicate that the progressive failure is indeed the failure mechanism of the slide.
文摘This paper presents a design of boundary controllers implemented at the top end for global stabilization of a marine riser in a three dimensional space under environmental loadings. Based on the energy approach, nonlinear partial differential equations of motion, including bending-bending and longitudinal-bending couplings for the risers are derived. The couplings cause mutual effects between the three independent directions in the riser＇s motions, and make it difficult to minimize its vibrations. The Lyapunov direct method is employed to design the boundary controller. It is shown that the proposed boundary controllers can effectively reduce the riser＇s vibration. Stability analysis of the closed-loop system is performed using the Lyapunov direct method. Numerical simulations illustrate the results.
文摘The changes of stress and strain around the shaft under the non-axial symmetrical loads during the excavation are analyzed with the finite element semi-analytical method based on the separated variable method. The change laws of deformation and stress of surrounding rocks are obtaied. Moreover, an optimum method of the design and construction of the shaft lining is de veloped. which presents a new train of thought of the design and costruction of the shaft and has important theoretical value and extensive application prospects.
基金Supported by the National Natural Science Foundation of China under Grant No. 11175158the Natural Science Foundation ofZhejiang Province of China under Grant No. LY12A04001
文摘Applying the similarity transformation, we construct the exact vortex solutions for topological charge S≥1 and the approximate fundamental soliton solutions for S = 0 of the two-dimensional cubic-quintic nonlinear Schrodinger equation with spatially modulated nonlinearities and harmonic potential. The linear stability analysis and numerical simulation are used to exam the stability of these solutions. In different profiles of cubic-quintic nonlinearities, some stable solutions for S 〉 0 and the lowest radial quantum number n = 1 are found. However, the solutions for n ≥ 2 are all unstable.
文摘Nowadays, biological resource in prey-predator ecosystem is commercially harvested and sold with aim of achieving economic interest. Furthermore, harvest effort is usually influ- enced by variation of economic interest of harvesting and spatial heterogeneous environ- ment. In this paper, a delayed differential-algebraic bio-economic model is proposed, which is utilized to investigate interaction and coexistence mechanism of biological pop- ulation in the harvested ecosystem due to the variation of economic interest of harvesting as well as the change of population spatial diffusion and gestation delay. Local stability analysis of the proposed model without gestation delay and diffusion reveals that there is a phenomenon of singularity induced bifurcation due to the variation of economic interest of harvesting, and state feedback controllers are designed to stabilize the pro- posed model at the interior equilibrium. Furthermore, local stability of the proposed model with gestation delay and diffusion is studied, which reveals that the interior equi- librium loses its stability at some critical values of gestation delay and corresponding cycle occurs. It is also shown that population spatial diffusion and harvesting have a stabilizing effect on population dynamics. Finally, numerical simulations are carried out to show consistency with theoretical analysis obtained in this paper.
