Partial cooperation formulation is a more viable option than optimistic＇s and pessimistic＇s to solve an ill-posed bilevel programming problem.Aboussoror＇s partial cooperation model uses a constant as a cooperation ...Partial cooperation formulation is a more viable option than optimistic＇s and pessimistic＇s to solve an ill-posed bilevel programming problem.Aboussoror＇s partial cooperation model uses a constant as a cooperation index to describe the degree of follower＇s cooperation.The constant only indicates the leader＇s expectation coefficient for the follower＇s action,not the follower＇s own willingness.To solve this situation,a new model is proposed by using the follower＇s satisfactory degree as the cooperation degree.Then,because this new cooperation degree is a function which is dependent on the leader＇s choice and decided by the follower＇s satisfactory degree,this paper proves such proposed model not only leads an optimal value between the optimistic value and pessimistic＇s,but also leads a more satisfactory solution than Aboussoror＇s.Finally,a numerical experiment is given to demonstrate the feasibility of this new model.展开更多
In this paper,a new model for inverse network flow problems,robust partial inverse problem is presented. For a given partial solution,the robust partial inverse problem is to modify the coefficients optimally such tha...In this paper,a new model for inverse network flow problems,robust partial inverse problem is presented. For a given partial solution,the robust partial inverse problem is to modify the coefficients optimally such that all full solutions containing the partial solution become optimal under new coefficients. It has been shown that the robust partial inverse spanning tree problem can be formulated as a combinatorial linear program,while the robust partial inverse minimum cut problem and the robust partial inverse assignment problem can be solved by combinatorial strongly polynomial algorithms.展开更多
In the studies of nonlinear partial differential equations, the influence, from the singularities of coefficients to the singularities of solution, is a field that has not been dealt with. In this paper, we discuss a ...In the studies of nonlinear partial differential equations, the influence, from the singularities of coefficients to the singularities of solution, is a field that has not been dealt with. In this paper, we discuss a simple case of semilinear equations under the frame of the space of conormal distributions. We prove the result that the solution has the same singularities on the hypersurface in which the coefficients have the conormal singularities.展开更多
In this paper, by using the optimal stopping theory, the semilinear Black-Scholes partial differential equation （PDE） was invesigated in a fixed domain for valuing two assets of American （call-max/put-min） options...In this paper, by using the optimal stopping theory, the semilinear Black-Scholes partial differential equation （PDE） was invesigated in a fixed domain for valuing two assets of American （call-max/put-min） options. From the viscosity solution of a PDE, a unique viscosity solution was obtained for the semilinear Black-Scholes PDE.展开更多
The enthalpies of mixing for the PbCl_2-NaCl-BaCl_2 ternary molten salt mixtures have been measured along four iso-αPbCl_2 Iines by using a SETARAM calorimeter at 873 K.The results show that the molar enthalpy of mix...The enthalpies of mixing for the PbCl_2-NaCl-BaCl_2 ternary molten salt mixtures have been measured along four iso-αPbCl_2 Iines by using a SETARAM calorimeter at 873 K.The results show that the molar enthalpy of mixing between iso-αPbCl_2 liquid binary subsystems PbCl_2-NaCl and PbCl_2-BaCl_2 is near zero.approximately fitting the partial ideal solution model.展开更多
We establish an extension result of existence and partial regularity for the nonzero Neumann initial-boundary value problem of the Landau-Lifshitz equation with nonpositive anisotropy constants in three or four dimens...We establish an extension result of existence and partial regularity for the nonzero Neumann initial-boundary value problem of the Landau-Lifshitz equation with nonpositive anisotropy constants in three or four dimension space. The partial regularity is proved up to the boundary and this result is an important supplement to those for the Dirichlet problem or the homogeneous Neumann problem.展开更多
Regarding the rapid compensation of the influence of the Earth＇ s disturbing gravity field upon trajectory calculation,the key point lies in how to derive the analytical solutions to the partial derivatives of the st...Regarding the rapid compensation of the influence of the Earth＇ s disturbing gravity field upon trajectory calculation,the key point lies in how to derive the analytical solutions to the partial derivatives of the state of burnout point with respect to the launch data.In view of this,this paper mainly expounds on two issues：one is based on the approximate analytical solution to the motion equation for the vacuum flight section of a long-range rocket,deriving the analytical solutions to the partial derivatives of the state of burnout point with respect to the changing rate of the finalstage pitch program;the other is based on the initial positioning and orientation error propagation mechanism,proposing the analytical calculation formula for the partial derivatives of the state of burnout point with respect to the launch azimuth.The calculation results of correction data are simulated and verified under different circumstances.The simulation results are as follows：（1） the accuracy of approximation between the analytical solutions and the results attained via the difference method is higher than 90%,and the ratio of calculation time between them is lower than 0.2%,thus demonstrating the accuracy of calculation of data corrections and advantages in calculation speed;（2） after the analytical solutions are compensated,the longitudinal landing deviation of the rocket is less than 20 m and the lateral landing deviation of the rocket is less than 10 m,demonstrating that the corrected data can meet the requirements for the hit accuracy of a long-range rocket.展开更多
Based upon the research to the economic equilibrium problems,we present a kind of new mathematical programming problem——interaction programming problem (abbreviated by IPP). The IPP is composed of two or multiple pa...Based upon the research to the economic equilibrium problems,we present a kind of new mathematical programming problem——interaction programming problem (abbreviated by IPP). The IPP is composed of two or multiple parametric programming problems which is interrelated with each other. The IPP reflects the equality and mutual benefit relationship between two (or among multiple) economic planners in an economic system. In essence, the IPP is similar to the generalized Nash equilibria (GNE) game which has been given several names in the literature: social equilibria games, pseudo-Nash equilibria games, and equilibrium programming problems. In this paper, we establish the mathematical model and some basic concepts to the IPP. We investigate the structure and the properties of the IPP.We also give a necessary and sufficient conditions for the existence of the equilibrium points to a kind of linear IPP.展开更多
[AlO4Al12(OH)24(H2O)12]7+ (Al13) formation in electrolysis process is studied. The results detected by27Al NMR spectroscopy show that high content of Al13 polymer is formed in the partially hydrolyzed aluminum solutio...[AlO4Al12(OH)24(H2O)12]7+ (Al13) formation in electrolysis process is studied. The results detected by27Al NMR spectroscopy show that high content of Al13 polymer is formed in the partially hydrolyzed aluminum solution prepared by controlled electrolysis process. In the produced electrolyte of total Al concentration ([AlT]) 2.0 mol · L?1 with a basicity (B = OH/Al molar ratios) of 2.0, the content of Al13 polymer is over 60% of total Al. Dynamic light scattering shows that the size distribution of the final electrolyte solutions ([AlT] = 2.0 mol · L?1) is trimodal with B = 2.0 and bimodal with B = 2.5. The aggregates of Al13 complexes increase the particle size of partially hydrolyzed aluminum solution.展开更多
基金supported by the National Natural Science Foundation of China(1140145071171150+4 种基金71471143)the Hubei Provincial Department of Education(B2015348D20141101)the Hubei Province Key Laboratory of Systems Science in Metallurgical Process(Y201518Z201401)
文摘Partial cooperation formulation is a more viable option than optimistic＇s and pessimistic＇s to solve an ill-posed bilevel programming problem.Aboussoror＇s partial cooperation model uses a constant as a cooperation index to describe the degree of follower＇s cooperation.The constant only indicates the leader＇s expectation coefficient for the follower＇s action,not the follower＇s own willingness.To solve this situation,a new model is proposed by using the follower＇s satisfactory degree as the cooperation degree.Then,because this new cooperation degree is a function which is dependent on the leader＇s choice and decided by the follower＇s satisfactory degree,this paper proves such proposed model not only leads an optimal value between the optimistic value and pessimistic＇s,but also leads a more satisfactory solution than Aboussoror＇s.Finally,a numerical experiment is given to demonstrate the feasibility of this new model.
基金Supported by National Natural Science Foundation of China(79790 1 30 ) and National863Hi- TechProject(863- 30 6- ZT0 4 - 0 4 -
文摘In this paper,a new model for inverse network flow problems,robust partial inverse problem is presented. For a given partial solution,the robust partial inverse problem is to modify the coefficients optimally such that all full solutions containing the partial solution become optimal under new coefficients. It has been shown that the robust partial inverse spanning tree problem can be formulated as a combinatorial linear program,while the robust partial inverse minimum cut problem and the robust partial inverse assignment problem can be solved by combinatorial strongly polynomial algorithms.
文摘In the studies of nonlinear partial differential equations, the influence, from the singularities of coefficients to the singularities of solution, is a field that has not been dealt with. In this paper, we discuss a simple case of semilinear equations under the frame of the space of conormal distributions. We prove the result that the solution has the same singularities on the hypersurface in which the coefficients have the conormal singularities.
基金Project supported by the National Natural Science Foundation of China (Grant No.10271072)
文摘In this paper, by using the optimal stopping theory, the semilinear Black-Scholes partial differential equation （PDE） was invesigated in a fixed domain for valuing two assets of American （call-max/put-min） options. From the viscosity solution of a PDE, a unique viscosity solution was obtained for the semilinear Black-Scholes PDE.
文摘The enthalpies of mixing for the PbCl_2-NaCl-BaCl_2 ternary molten salt mixtures have been measured along four iso-αPbCl_2 Iines by using a SETARAM calorimeter at 873 K.The results show that the molar enthalpy of mixing between iso-αPbCl_2 liquid binary subsystems PbCl_2-NaCl and PbCl_2-BaCl_2 is near zero.approximately fitting the partial ideal solution model.
基金Supported by the Science Foundation of Zhejiang Sci-Tech University(No.0905828-Y)
文摘We establish an extension result of existence and partial regularity for the nonzero Neumann initial-boundary value problem of the Landau-Lifshitz equation with nonpositive anisotropy constants in three or four dimension space. The partial regularity is proved up to the boundary and this result is an important supplement to those for the Dirichlet problem or the homogeneous Neumann problem.
文摘Regarding the rapid compensation of the influence of the Earth＇ s disturbing gravity field upon trajectory calculation,the key point lies in how to derive the analytical solutions to the partial derivatives of the state of burnout point with respect to the launch data.In view of this,this paper mainly expounds on two issues：one is based on the approximate analytical solution to the motion equation for the vacuum flight section of a long-range rocket,deriving the analytical solutions to the partial derivatives of the state of burnout point with respect to the changing rate of the finalstage pitch program;the other is based on the initial positioning and orientation error propagation mechanism,proposing the analytical calculation formula for the partial derivatives of the state of burnout point with respect to the launch azimuth.The calculation results of correction data are simulated and verified under different circumstances.The simulation results are as follows：（1） the accuracy of approximation between the analytical solutions and the results attained via the difference method is higher than 90%,and the ratio of calculation time between them is lower than 0.2%,thus demonstrating the accuracy of calculation of data corrections and advantages in calculation speed;（2） after the analytical solutions are compensated,the longitudinal landing deviation of the rocket is less than 20 m and the lateral landing deviation of the rocket is less than 10 m,demonstrating that the corrected data can meet the requirements for the hit accuracy of a long-range rocket.
文摘Based upon the research to the economic equilibrium problems,we present a kind of new mathematical programming problem——interaction programming problem (abbreviated by IPP). The IPP is composed of two or multiple parametric programming problems which is interrelated with each other. The IPP reflects the equality and mutual benefit relationship between two (or among multiple) economic planners in an economic system. In essence, the IPP is similar to the generalized Nash equilibria (GNE) game which has been given several names in the literature: social equilibria games, pseudo-Nash equilibria games, and equilibrium programming problems. In this paper, we establish the mathematical model and some basic concepts to the IPP. We investigate the structure and the properties of the IPP.We also give a necessary and sufficient conditions for the existence of the equilibrium points to a kind of linear IPP.
基金This work was supported by the National Natural Science Foundation of China (Grant No. 50108016).
文摘[AlO4Al12(OH)24(H2O)12]7+ (Al13) formation in electrolysis process is studied. The results detected by27Al NMR spectroscopy show that high content of Al13 polymer is formed in the partially hydrolyzed aluminum solution prepared by controlled electrolysis process. In the produced electrolyte of total Al concentration ([AlT]) 2.0 mol · L?1 with a basicity (B = OH/Al molar ratios) of 2.0, the content of Al13 polymer is over 60% of total Al. Dynamic light scattering shows that the size distribution of the final electrolyte solutions ([AlT] = 2.0 mol · L?1) is trimodal with B = 2.0 and bimodal with B = 2.5. The aggregates of Al13 complexes increase the particle size of partially hydrolyzed aluminum solution.
