1 Introduction and Main Results
In book [1], Professor C. D. Sogge proved the Theorem 2.2 (page 15) by the method presented by F. John. But I think we can also prove it by another method which is simpler and more dire...1 Introduction and Main Results
In book [1], Professor C. D. Sogge proved the Theorem 2.2 (page 15) by the method presented by F. John. But I think we can also prove it by another method which is simpler and more direct than the original approach.展开更多
In this paper the thickness of a broken zone, a state parameter of roadway surrounding rock, is used as the index to evaluate the stabi1ity of surrounding rock of a deep roadway. The paper gives a theoretic formula fo...In this paper the thickness of a broken zone, a state parameter of roadway surrounding rock, is used as the index to evaluate the stabi1ity of surrounding rock of a deep roadway. The paper gives a theoretic formula for calculating the thickness of the broken zone. The author points out that not only the ultimate strength of rockmass but its residual strength and strain-softening level all have a great influence on the stability of surrounding rock of a deep roadway. The paper’s results show that to reinforce surrounding rock, raise its residual strength and lower its strain-softening level should be taken as a basic requirement for supports of a deep roadway. In addition, the research also indicates that it is impossible for roadway supports to change surrounding rock states of a deep roadway, so it is certain for them to work in a broken state. For this reason, a sufficient yieldable quantity is necessary for roadway supports used in deep mining.展开更多
Demarcating distribution area of goods is often guided by the rule of thumb by business proprietors. However, this method seems to be unsuitable when the demand points increase to a certain large extent. The present w...Demarcating distribution area of goods is often guided by the rule of thumb by business proprietors. However, this method seems to be unsuitable when the demand points increase to a certain large extent. The present work attempted to convert the problem of distribution area demarcation into a localized problem of warehouseing and networking, and tried to establish district-based planning mode based on location based heuristic (LBH). Two methods were used in this study: 1) the manual method to construct the mathematical model and conduct simulation; 2) the automatic method using TransCAD software of geographical information system (GIS) for simulation. By comparing the effects of the two methods, the research provides theoretical support for business proprietors to demarcate the distribution area rationally with the application of GIS system. The results show that GIS has very good graphics construction function to replace complex text, and the automatic demarcating mode with human-machine interaction provides a good business decision-making support.展开更多
It is imperative to evaluate factor of safety against basal heave failure in the design of braced deep excavation in soft clay.Based on previously published field monitoring data and finite element analyses of ground ...It is imperative to evaluate factor of safety against basal heave failure in the design of braced deep excavation in soft clay.Based on previously published field monitoring data and finite element analyses of ground settlements of deep excavation in soft clay,an assumed plastic deformation mechanism proposed here gives upper bound solutions for base stability of braced deep excavations.The proposed kinematic mechanism is optimized by the mobile depth(profile wavelength).The method takes into account the influence of strength anisotropy under plane strain conditions,the embedment of the retaining wall,and the locations of the struts.The current method is validated by comparison with published numerical study of braced excavations in Boston blue clay and two other cases of excavation failure in Taipei.The results show that the upper bound solutions obtained from this presented method is more accurate as compared with the conventional methods for basal heave failure analyses.展开更多
In this paper, the dynamics of mathematical model for infection of thymus gland by HIV-1 is analyzed by applying some perturbation through two different types of delays such as in terms of Hopf bifurcation analysis. F...In this paper, the dynamics of mathematical model for infection of thymus gland by HIV-1 is analyzed by applying some perturbation through two different types of delays such as in terms of Hopf bifurcation analysis. Further, the conditions for the existence of Hopf bifurcation are derived by evaluating the characteristic equation. The direction of Hopf bifurcation and stability of bifurcating periodic solutions are determined by employing the center manifold theorem and normal form method. Finally, some of the numerical simulations are carried out to validate the derived theoretical results and main conclusions are included.展开更多
In this paper, regarding the time delay as a bifurcation parameter, the stability and Hopf bifurcation of the model of competition between two species in a turbidostat with Beddington-DeAngelis functional response and...In this paper, regarding the time delay as a bifurcation parameter, the stability and Hopf bifurcation of the model of competition between two species in a turbidostat with Beddington-DeAngelis functional response and discrete delay are studied. The Hopf bifurcations can be shown when the delay crosses the critical value. Furthermore, based on the normal form and the center manifold theorem, the type, stability and other properties of the bifurcating periodic solutions are determined. Finally, some numerical simulations are given to illustrate the results.展开更多
A SIR model of epidemiological dynamics with stage-structure and a type of nonlinear incidence rate is considered under the assumption that the susceptible individual satisfy the logistic equation. The global attracti...A SIR model of epidemiological dynamics with stage-structure and a type of nonlinear incidence rate is considered under the assumption that the susceptible individual satisfy the logistic equation. The global attractivity of the model is studied using Lyapunov functions and LaSalle＇s invariance principle. By the uniform persistence theories, the permanence of the system and the existence of the positive equilibrium are obtained. Moreover, by the normal form theory and the center manifold presented by Hassard, a stability and Hopf bifurcation analysis of the system around positive equilibrium from a local perspective are performed. Numerical simulation is carried out to illustrate our results.展开更多
文摘1 Introduction and Main Results
In book [1], Professor C. D. Sogge proved the Theorem 2.2 (page 15) by the method presented by F. John. But I think we can also prove it by another method which is simpler and more direct than the original approach.
文摘In this paper the thickness of a broken zone, a state parameter of roadway surrounding rock, is used as the index to evaluate the stabi1ity of surrounding rock of a deep roadway. The paper gives a theoretic formula for calculating the thickness of the broken zone. The author points out that not only the ultimate strength of rockmass but its residual strength and strain-softening level all have a great influence on the stability of surrounding rock of a deep roadway. The paper’s results show that to reinforce surrounding rock, raise its residual strength and lower its strain-softening level should be taken as a basic requirement for supports of a deep roadway. In addition, the research also indicates that it is impossible for roadway supports to change surrounding rock states of a deep roadway, so it is certain for them to work in a broken state. For this reason, a sufficient yieldable quantity is necessary for roadway supports used in deep mining.
基金Funded by Natural Science Foundation of Zhejiang Province of China (No. Y6090417)Social Sciences Foundation of the Ministry of Education of China (No. 09YJA630143)
文摘Demarcating distribution area of goods is often guided by the rule of thumb by business proprietors. However, this method seems to be unsuitable when the demand points increase to a certain large extent. The present work attempted to convert the problem of distribution area demarcation into a localized problem of warehouseing and networking, and tried to establish district-based planning mode based on location based heuristic (LBH). Two methods were used in this study: 1) the manual method to construct the mathematical model and conduct simulation; 2) the automatic method using TransCAD software of geographical information system (GIS) for simulation. By comparing the effects of the two methods, the research provides theoretical support for business proprietors to demarcate the distribution area rationally with the application of GIS system. The results show that GIS has very good graphics construction function to replace complex text, and the automatic demarcating mode with human-machine interaction provides a good business decision-making support.
基金supported by the National Science Foundation for Distinguished Young Scholars of China(Grant No.51325901)the State Key Program of National Natural Science of China(Grant No.51338009)
文摘It is imperative to evaluate factor of safety against basal heave failure in the design of braced deep excavation in soft clay.Based on previously published field monitoring data and finite element analyses of ground settlements of deep excavation in soft clay,an assumed plastic deformation mechanism proposed here gives upper bound solutions for base stability of braced deep excavations.The proposed kinematic mechanism is optimized by the mobile depth(profile wavelength).The method takes into account the influence of strength anisotropy under plane strain conditions,the embedment of the retaining wall,and the locations of the struts.The current method is validated by comparison with published numerical study of braced excavations in Boston blue clay and two other cases of excavation failure in Taipei.The results show that the upper bound solutions obtained from this presented method is more accurate as compared with the conventional methods for basal heave failure analyses.
文摘In this paper, the dynamics of mathematical model for infection of thymus gland by HIV-1 is analyzed by applying some perturbation through two different types of delays such as in terms of Hopf bifurcation analysis. Further, the conditions for the existence of Hopf bifurcation are derived by evaluating the characteristic equation. The direction of Hopf bifurcation and stability of bifurcating periodic solutions are determined by employing the center manifold theorem and normal form method. Finally, some of the numerical simulations are carried out to validate the derived theoretical results and main conclusions are included.
基金Acknowledgments The authors would like to thank the editors and the anonymous referees for their helpful suggestions and comments which led to the improvement of our original manuscript. This work is supported by the National Natural Science Foundation of China （Grant Nos. 11561022, 11261017）, the China Postdoctoral Science Foundation （Grant No. 2014M562008）.
文摘In this paper, regarding the time delay as a bifurcation parameter, the stability and Hopf bifurcation of the model of competition between two species in a turbidostat with Beddington-DeAngelis functional response and discrete delay are studied. The Hopf bifurcations can be shown when the delay crosses the critical value. Furthermore, based on the normal form and the center manifold theorem, the type, stability and other properties of the bifurcating periodic solutions are determined. Finally, some numerical simulations are given to illustrate the results.
文摘A SIR model of epidemiological dynamics with stage-structure and a type of nonlinear incidence rate is considered under the assumption that the susceptible individual satisfy the logistic equation. The global attractivity of the model is studied using Lyapunov functions and LaSalle＇s invariance principle. By the uniform persistence theories, the permanence of the system and the existence of the positive equilibrium are obtained. Moreover, by the normal form theory and the center manifold presented by Hassard, a stability and Hopf bifurcation analysis of the system around positive equilibrium from a local perspective are performed. Numerical simulation is carried out to illustrate our results.
