A class of nonlinear and continuous type Leontief model and its corresponding conditional input-output equation are introduced, and two basic problems under the so called positive or negative boundary assumption are p...A class of nonlinear and continuous type Leontief model and its corresponding conditional input-output equation are introduced, and two basic problems under the so called positive or negative boundary assumption are presented. By approaches of nonlinear analysis some solvability results of this equation and continuous perturbation properties of the relative solution sets are obtained, and some economic significance are illustrated by the remark.展开更多
The stability of slopes is always of great concern in the field of rock engineering. The geometry and orientation of pre-existing discontinuities show a larger impact on the behavior of slopes that is often used to de...The stability of slopes is always of great concern in the field of rock engineering. The geometry and orientation of pre-existing discontinuities show a larger impact on the behavior of slopes that is often used to describe the measurement of the steepness, incline, gradient, or grade of a straight line. One of the structurally controlled modes of failure in jointed rock slopes is plane failure. There are numerous analytical methods for the rock slope stability including limit equilibrium, stress analysis and stereographic methods. The limiting equilibrium methods for slopes under various conditions against plane failure have been previously proposed by several investigators. However, these methods do not involve water pressure on sliding surfaces assessments due to water velocity and have not yet been validated by case study results. This paper has tried to explore the effects of forces due to water pressure on discontinuity surfaces in plane failure through applying the improved equations. It has studied the effect of water flow velocity on sliding surfaces in safety factor, as well. New equations for considering water velocity (fluid dynamics) are presented. To check the validity of the suggested equations, safety factor for a case study has been determined. Results show that velocity of water flow had significant effect on the amount of safety factor. Also, the suggested equations have higher validity rate compared to the current equations.展开更多
As a consequence of global warming and rising sea levels, the oceans are becoming a matter of concern for more and more people because these changes will impact the growth of living organisms as well as people＇s livi...As a consequence of global warming and rising sea levels, the oceans are becoming a matter of concern for more and more people because these changes will impact the growth of living organisms as well as people＇s living standards. In particular, it is extremely important that the oceans absorb massive amounts of carbon dioxide. This paper takes a pragmatic approach to analyzing the oceans with respect to the causes of discontinuities in oceanic variables of carbon dioxide sinks. We report on an application of chemical, physical and biological methods to analyze the changes of carbon dioxide in oceans. Based on the relationships among the oceans, land, atmosphere and sediment with respect to carbon dioxide, the foundation of carbon dioxide in shell-building and ocean acidification, the changes in carbon dioxide in the oceans and their impact on climate change, and so on, a vital conclusion can be drawn from this study. Specifically, under the condition that the oceans are not disturbed by external forces, the oceans are a large carbon dioxide sink. The result can also be inferred by the formula： C=A-B and G=E＋F when the marine ecosystem can keep a natural balance and the amount of carbon dioxide emission is limited within the calrying capacity of the oceans.展开更多
As a basic mathematical structure,the system of inequalities over symmetric cones and its solution can provide an effective method for solving the startup problem of interior point method which is used to solve many o...As a basic mathematical structure,the system of inequalities over symmetric cones and its solution can provide an effective method for solving the startup problem of interior point method which is used to solve many optimization problems.In this paper,a non-interior continuation algorithm is proposed for solving the system of inequalities under the order induced by a symmetric cone.It is shown that the proposed algorithm is globally convergent and well-defined.Moreover,it can start from any point and only needs to solve one system of linear equations at most at each iteration.Under suitable assumptions,global linear and local quadratic convergence is established with Euclidean Jordan algebras.Numerical results indicate that the algorithm is efficient.The systems of random linear inequalities were tested over the second-order cones with sizes of 10,100,,1 000 respectively and the problems of each size were generated randomly for 10 times.The average iterative numbers show that the proposed algorithm can generate a solution at one step for solving the given linear class of problems with random initializations.It seems possible that the continuation algorithm can solve larger scale systems of linear inequalities over the secondorder cones quickly.Moreover,a system of nonlinear inequalities was also tested over Cartesian product of two simple second-order cones,and numerical results indicate that the proposed algorithm can deal with the nonlinear cases.展开更多
文摘A class of nonlinear and continuous type Leontief model and its corresponding conditional input-output equation are introduced, and two basic problems under the so called positive or negative boundary assumption are presented. By approaches of nonlinear analysis some solvability results of this equation and continuous perturbation properties of the relative solution sets are obtained, and some economic significance are illustrated by the remark.
文摘The stability of slopes is always of great concern in the field of rock engineering. The geometry and orientation of pre-existing discontinuities show a larger impact on the behavior of slopes that is often used to describe the measurement of the steepness, incline, gradient, or grade of a straight line. One of the structurally controlled modes of failure in jointed rock slopes is plane failure. There are numerous analytical methods for the rock slope stability including limit equilibrium, stress analysis and stereographic methods. The limiting equilibrium methods for slopes under various conditions against plane failure have been previously proposed by several investigators. However, these methods do not involve water pressure on sliding surfaces assessments due to water velocity and have not yet been validated by case study results. This paper has tried to explore the effects of forces due to water pressure on discontinuity surfaces in plane failure through applying the improved equations. It has studied the effect of water flow velocity on sliding surfaces in safety factor, as well. New equations for considering water velocity (fluid dynamics) are presented. To check the validity of the suggested equations, safety factor for a case study has been determined. Results show that velocity of water flow had significant effect on the amount of safety factor. Also, the suggested equations have higher validity rate compared to the current equations.
基金Financial support was provided by the National Natural Science Foundation of China (41106094)the Department of Science and Technology Project (BS2010NY030)
文摘As a consequence of global warming and rising sea levels, the oceans are becoming a matter of concern for more and more people because these changes will impact the growth of living organisms as well as people＇s living standards. In particular, it is extremely important that the oceans absorb massive amounts of carbon dioxide. This paper takes a pragmatic approach to analyzing the oceans with respect to the causes of discontinuities in oceanic variables of carbon dioxide sinks. We report on an application of chemical, physical and biological methods to analyze the changes of carbon dioxide in oceans. Based on the relationships among the oceans, land, atmosphere and sediment with respect to carbon dioxide, the foundation of carbon dioxide in shell-building and ocean acidification, the changes in carbon dioxide in the oceans and their impact on climate change, and so on, a vital conclusion can be drawn from this study. Specifically, under the condition that the oceans are not disturbed by external forces, the oceans are a large carbon dioxide sink. The result can also be inferred by the formula： C=A-B and G=E＋F when the marine ecosystem can keep a natural balance and the amount of carbon dioxide emission is limited within the calrying capacity of the oceans.
基金Supported by National Natural Science Foundation of China (No.10871144)the Seed Foundation of Tianjin University (No.60302023)
文摘As a basic mathematical structure,the system of inequalities over symmetric cones and its solution can provide an effective method for solving the startup problem of interior point method which is used to solve many optimization problems.In this paper,a non-interior continuation algorithm is proposed for solving the system of inequalities under the order induced by a symmetric cone.It is shown that the proposed algorithm is globally convergent and well-defined.Moreover,it can start from any point and only needs to solve one system of linear equations at most at each iteration.Under suitable assumptions,global linear and local quadratic convergence is established with Euclidean Jordan algebras.Numerical results indicate that the algorithm is efficient.The systems of random linear inequalities were tested over the second-order cones with sizes of 10,100,,1 000 respectively and the problems of each size were generated randomly for 10 times.The average iterative numbers show that the proposed algorithm can generate a solution at one step for solving the given linear class of problems with random initializations.It seems possible that the continuation algorithm can solve larger scale systems of linear inequalities over the secondorder cones quickly.Moreover,a system of nonlinear inequalities was also tested over Cartesian product of two simple second-order cones,and numerical results indicate that the proposed algorithm can deal with the nonlinear cases.
