The coordinated development of urban and rural territorial systems has long been a scientific issue of concern in geography and socioeconomic development in China.Based on Territorial Function Theory,this paper establ...The coordinated development of urban and rural territorial systems has long been a scientific issue of concern in geography and socioeconomic development in China.Based on Territorial Function Theory,this paper establishes a theoretical framework to support the coordinated development of urban and rural territorial systems,analyzes the trend of functional evolution,discusses the impact of efficient allocation and orderly element flow on system equivalence development,and puts forward approaches and policy suggestions for equilibrium development in the future.The main conclusions are as follows:(1)The evolution of urban and rural territorial functions has experienced four stages:rural to rural,rural to urban transition,rural to urban,and urban to urban.In this process,territorial functions have been developed to be hierarchical and advanced.(2)Functional evolution enables urban and rural comparative advantages to be transformed from value difference to value equivalence.Increasing the flow intensity and reconstructing the flow space have become the necessary conditions for the coordination of development.(3)Land is the most important resource in China,and land system reform is the key to achieving equivalence development of urban and rural territorial systems,thereby determining the future equilibrium development of the two systems.展开更多
By using an existence theorems of maximal elements for a family of set-valued mappings in G-convex spaces due to the author, some new nonempty intersection theorems for a family of set-valued mappings were established...By using an existence theorems of maximal elements for a family of set-valued mappings in G-convex spaces due to the author, some new nonempty intersection theorems for a family of set-valued mappings were established in noncompact product G-convex spaces. As applications, some equilibrium existence theorems for a system of generalized vector equilibrium problems were proved in noncompact product G-convex spaces. These theorems unify, improve and generalize some important known results in literature.展开更多
The Fusion-Driven Subcritical System(FDS)is a subcritical nuclear energy systemdrived by fusion neutron source.In this paper,an advanced plasma configuration for FDS systemhas been proposed,which aims at high beta,hig...The Fusion-Driven Subcritical System(FDS)is a subcritical nuclear energy systemdrived by fusion neutron source.In this paper,an advanced plasma configuration for FDS systemhas been proposed,which aims at high beta,high bootstrap current and good confinement.Afixed-boundary equilibrium code has been used to obtain ideal equilibrium configuration.In order展开更多
Taking AuCu-sublattice system as an example, we present two discoveries and a method. First, the alloy gene sequences are the central characteristic atom sequences in the basic coordination cluster sequences. Second, ...Taking AuCu-sublattice system as an example, we present two discoveries and a method. First, the alloy gene sequences are the central characteristic atom sequences in the basic coordination cluster sequences. Second, the transmission mode of the information about structures and properties of the alloy genes is described by the alloy gene Gibbs energy partition function. The most valuable method in the system sciences is “the whole obtained from a few parts”. We have established the alloy gene database and holographic alloy positioning system of the Au-Cu system, as well as alloy gene Gibbs energy partition function and equilibrium holographic network phase diagrams of the AuCu-type sublattice system. It means that a standard way for researchers to share predictive algorithms and computational methods may be produced during designing advanced alloys.展开更多
Stability for the manifolds of equilibrium states of a generalized Birkhoff system is studied. A theorem for the stability of the manifolds of equilibrium states of the general autonomous system is used to the general...Stability for the manifolds of equilibrium states of a generalized Birkhoff system is studied. A theorem for the stability of the manifolds of equilibrium states of the general autonomous system is used to the generalized BirkhoiYian system and two propositions on the stability of the manifolds of equilibrium states of the system are obtained. An example is given to illustrate the application of the results.展开更多
By applying a maximal element theorem on product FC-space due to author, some new equilibrium existence theorems for generalized games with fuzzy constraint correspondences are proved in FC-spaces. By using these equi...By applying a maximal element theorem on product FC-space due to author, some new equilibrium existence theorems for generalized games with fuzzy constraint correspondences are proved in FC-spaces. By using these equilibrium existence theorems, some new existence theorems of solutions for the system of generalized vector quasi-equilibrium problems are established in noncompact product FC-spaces. These results improve and generalize some recent results in literature to product FC-spaces without any convexity structure.展开更多
In this study, the constant volume, visual method is used to measure the critical point of CO2+toluene, CO2+cyclohexane, CO2+n-butyraldehyde, CO2+i-butyraldehyde, CO2+methanol and CO2+alcohol binary systems. The relat...In this study, the constant volume, visual method is used to measure the critical point of CO2+toluene, CO2+cyclohexane, CO2+n-butyraldehyde, CO2+i-butyraldehyde, CO2+methanol and CO2+alcohol binary systems. The relationship between critical point and the concentration of the entrainer for different substances has been discussed, and the comparison of the phase behavior of single component system and that of binary systems have been carried out.展开更多
This paper reports a new simple four-dimensional（4 D） hyperjerk chaotic system. The proposed system has only one stable equilibrium point. Hence, its strange attractor belongs to the category of hidden attractors. T...This paper reports a new simple four-dimensional（4 D） hyperjerk chaotic system. The proposed system has only one stable equilibrium point. Hence, its strange attractor belongs to the category of hidden attractors. The proposed system exhibits various dynamical behaviors including chaotic, periodic, stable nature, and coexistence of various attractors. Numerous theoretical and numerical methods are used for the analyses of this system. The chaotic behavior of the new system is validated using circuit implementation. Further, the synchronization of the proposed systems is shown by designing an adaptive integrator backstepping controller. Numerical simulation validates the synchronization strategy.展开更多
This paper studies the regional stability for positive switched linear systems with multi-equilibrium points （PSLS-MEP）. First, a sufficient condition is presented for the regional stability of PSLS-MEP via a common...This paper studies the regional stability for positive switched linear systems with multi-equilibrium points （PSLS-MEP）. First, a sufficient condition is presented for the regional stability of PSLS-MEP via a common linear Lyapunov function. Second, by establishing multiple Lyapunov functions, a dwell time based condition is proposed for the regional stability analysis. Third, a suprasphere which contains all equilibrium points is constructed as a stability region of the considered PSLS-MEP, which is less conservative than existing results. Finally, the study of an illustrative example shows that the obtained results are effective in the regional stability analysis of PSLS-MEP.展开更多
Solid-liquid equilibrium of quaternary system Cd2＋//Cl–, SO42–, NO3–-H2O at 298 K was studied by means of an isothermal solution saturation method. Experimental results indicate that there are three univariant cur...Solid-liquid equilibrium of quaternary system Cd2＋//Cl–, SO42–, NO3–-H2O at 298 K was studied by means of an isothermal solution saturation method. Experimental results indicate that there are three univariant curves BE, AE and CE, one invariant point E and three crystallization fields in the quaternary system. The quaternary system belongs to a simple type, and there are no double salts or solid solution existing. The crystallization zones of equilibrium solid phases are CdCl2·5/2H2O（AEB field）, 3CdSO4·8H2O（AEC field） and Cd（NO3）2·4H2O（BEC field）, respectively. The composition of the invariant point is CdCl2, Cd（NO3）2, CdSO4 and H2O and the contents of which are 17.02%, 45.50%, 4.52% and 32.96%, respectively. The physico-chemical properties of solution in the quaternary system show regular changes along with the increased cadmium concentration. The results indicate that Cd（NO3）2 possessed the highest solubility among those three salts, which means a strong transfer of Cd ion and a high pollution risk of soil environment. And the solubility of CdSO4 would be restrained as the salts existing together.展开更多
In this paper, equilibrium stability of generalized Birkhoff's autonomous system is discussed. First, equilibrium equations of generalized Birkhoff's autonomous system are set up, and the n the linear approx...In this paper, equilibrium stability of generalized Birkhoff's autonomous system is discussed. First, equilibrium equations of generalized Birkhoff's autonomous system are set up, and the n the linear approximate method and direct method of stability in equilibrium st ate are studied. Some results on equilibrium of generalized Birkhoff's autonomou s system are obtained on the basis of Lyapunov's thorem. Last, the applica tion of the results is illustrated with an example.展开更多
By the degree theory on positive cone together with the technique of a priori estimate, the nontrivial equilibrium solutions of a strong nonlinearity and weak coupling reaction diffusion system and the structure of t...By the degree theory on positive cone together with the technique of a priori estimate, the nontrivial equilibrium solutions of a strong nonlinearity and weak coupling reaction diffusion system and the structure of the equilibrium solutions are discussed.展开更多
Having criticized the current architecture of Advanced Traveler Information Systems （ATISs）, this work discusses a new base of requirements to develop a new paradigm for traffic information systems. It mainly integr...Having criticized the current architecture of Advanced Traveler Information Systems （ATISs）, this work discusses a new base of requirements to develop a new paradigm for traffic information systems. It mainly integrates three dimensions within a traffic system： drivers＇ pattern of behavior and preferences, urban traffic desires, and capabilities of traffic information service providers. Based on the above, functional segments from several related backgrounds are brought together to structure a new architecture, called Interactive Traveler Information System （ITIS）. The main interactive feature of this new architecture is a two-way communication track between drivers and the traffic information system provider-in fact, a decision on choosing a road at a particular time for an individual will be made based on the utility of both sides. This new configuration consists of driver-side smartphone application, centric traffic prediction, and decision-maker units, which will shape a new approach of decision-making processes. These all work together to satisfy the designated goal of ITIS, which is preserving the Wardrop equilibrium condition in the traffic network level. Finally, we concentrate on a comparison study, which shows a differentiation between performance of the proposed ITIS and the current ATIS model in a real situation. This has been done with simulations of analogical scenarios. The most noticeable advantage of the proposed architecture is not being limited to a saturation limit, and the positive effect of increasing system penetration in the performance of the newly introduced information system. In conclusion, new research subjects are suggested to be carried out.展开更多
By using an existence theorems of maximal elements for a family of set-valued mappings in G-convex spaces due to the author, some new nonempty intersection theorems for a family of set-valued mappings were established...By using an existence theorems of maximal elements for a family of set-valued mappings in G-convex spaces due to the author, some new nonempty intersection theorems for a family of set-valued mappings were established in noncompact product G-convex spaces. As applications, some equilibrium existence theorems for a system of generalized vector equilibrium problems were proved in noncompact product G-convex spaces. These theorems unify, improve and generalize some important known results in literature.展开更多
By using Fort theorem the generic stability result for the system of generalized vector equilibrium problems is established. Further, by proving the existence and connectivity of minimal essential set the existence re...By using Fort theorem the generic stability result for the system of generalized vector equilibrium problems is established. Further, by proving the existence and connectivity of minimal essential set the existence result of essential components in the solution set is derived.展开更多
A new three-dimensional （3D） continuous autonomous system with one parameter and three quadratic terms is presented firstly in this paper. Countless embedded trumpet-shaped chaotic attractors in two opposite directi...A new three-dimensional （3D） continuous autonomous system with one parameter and three quadratic terms is presented firstly in this paper. Countless embedded trumpet-shaped chaotic attractors in two opposite directions are generated from the system as time goes on. The basic dynamical behaviors of the strange chaotic system are investigated. Another more complex 3D system with the same capability of generating countless embedded trumpet-shaped chaotic attractors is also put forward.展开更多
Based on the extraction equilibrium and mass balances in countercurrent extraction systems, a novel method was studied for dealing with the extraction equilibrium and the mass distribution in a multi-component(gamma-c...Based on the extraction equilibrium and mass balances in countercurrent extraction systems, a novel method was studied for dealing with the extraction equilibrium and the mass distribution in a multi-component(gamma-component) system. The relationships of mass distribution (x(i), y(i), i = 1, ..., lambda) between two phases were expressed by 2 lambda dimensional simultaneous equations. These simultaneous equations can be converted to a one-dimension nonlinear equation, then it was solved by Newton-Raphson algorithm within a few number of iteration. Compared with the regular calculation method for the 2 lambda dimensional simultaneous equations, Newton-Raphson algorithm can decrease the number of iteration, increase the convergence of the equations and accelerate the speed of simulation. It was verified in many multi-component systems with satisfactory results. As an example, a five-component system is demonstrated in this paper.展开更多
Alloys of Mg-Zn-La system in Mg rich corner were prepared, and the phase relationship was investigated at different temperatures such as 200, 300 and 350 ℃ by scanning electron microscopy(SEM), X-ray diffraction(XRD)...Alloys of Mg-Zn-La system in Mg rich corner were prepared, and the phase relationship was investigated at different temperatures such as 200, 300 and 350 ℃ by scanning electron microscopy(SEM), X-ray diffraction(XRD) and electron probe microanalysis with energy dispersive X-ray spectroscopy (EPMA). Two types of phase equilibrium were identified at the different temperatures. One is two-phase equilibrium contained the Mg solid solution and T-phase. The other is three-phase equilibrium which contained the Mg solid solution, MgZn phase and T-phase. T-phase was stable as the temperature changed. The La content in T-phase is constant which is about 8±0.3% (atom fraction); but the Mg content and Zn content of that is changed, and the Zn content in T-phase was from 16.1% to 44%. The solubility of La in MgZn phase was increased from 1.2% to 1.6% as the temperature increasing from 200 to 350 ℃.展开更多
1 INTRODUCTIONVapor-liquid equilibrium(VLE)relations are required for practical use,such as in the designand operation of disitillation equipment.In the conventional experimental methods of vapor-liquid equilibria,som...1 INTRODUCTIONVapor-liquid equilibrium(VLE)relations are required for practical use,such as in the designand operation of disitillation equipment.In the conventional experimental methods of vapor-liquid equilibria,some analytical instruments are applied.They are time-consuming and dif-ficult for multicomponent system because the proper method for the composition analysis isnot easy to be set up.展开更多
A geometrical theorem for the static equilibrium of a common-point-force system has been proven by means of virtual-work principle: The equilibrium point of a common-point force system has a minimal weighted distance ...A geometrical theorem for the static equilibrium of a common-point-force system has been proven by means of virtual-work principle: The equilibrium point of a common-point force system has a minimal weighted distance summation to every fixed point arbitrarily given on each force line with a weighing factor proportional to corresponding force value. Especially the mechanical simulating technique for its inverse problem has been realized by means of pulley block. The conclusions for the inverse problem derived from mechanic method are in accordance with that given by the pure mathematical method, and the self-consistence of the theorem and its inverse problem has been demonstrated. Some application examples in engineering, economy and mathematics have been discussed, especially the possible application in the research of molecular structure, has also been predicted.展开更多
基金National Natural Science Foundation of ChinaNo.41630644。
文摘The coordinated development of urban and rural territorial systems has long been a scientific issue of concern in geography and socioeconomic development in China.Based on Territorial Function Theory,this paper establishes a theoretical framework to support the coordinated development of urban and rural territorial systems,analyzes the trend of functional evolution,discusses the impact of efficient allocation and orderly element flow on system equivalence development,and puts forward approaches and policy suggestions for equilibrium development in the future.The main conclusions are as follows:(1)The evolution of urban and rural territorial functions has experienced four stages:rural to rural,rural to urban transition,rural to urban,and urban to urban.In this process,territorial functions have been developed to be hierarchical and advanced.(2)Functional evolution enables urban and rural comparative advantages to be transformed from value difference to value equivalence.Increasing the flow intensity and reconstructing the flow space have become the necessary conditions for the coordination of development.(3)Land is the most important resource in China,and land system reform is the key to achieving equivalence development of urban and rural territorial systems,thereby determining the future equilibrium development of the two systems.
文摘By using an existence theorems of maximal elements for a family of set-valued mappings in G-convex spaces due to the author, some new nonempty intersection theorems for a family of set-valued mappings were established in noncompact product G-convex spaces. As applications, some equilibrium existence theorems for a system of generalized vector equilibrium problems were proved in noncompact product G-convex spaces. These theorems unify, improve and generalize some important known results in literature.
基金National Sciences Foundation of China(No.10175068)
文摘The Fusion-Driven Subcritical System(FDS)is a subcritical nuclear energy systemdrived by fusion neutron source.In this paper,an advanced plasma configuration for FDS systemhas been proposed,which aims at high beta,high bootstrap current and good confinement.Afixed-boundary equilibrium code has been used to obtain ideal equilibrium configuration.In order
文摘Taking AuCu-sublattice system as an example, we present two discoveries and a method. First, the alloy gene sequences are the central characteristic atom sequences in the basic coordination cluster sequences. Second, the transmission mode of the information about structures and properties of the alloy genes is described by the alloy gene Gibbs energy partition function. The most valuable method in the system sciences is “the whole obtained from a few parts”. We have established the alloy gene database and holographic alloy positioning system of the Au-Cu system, as well as alloy gene Gibbs energy partition function and equilibrium holographic network phase diagrams of the AuCu-type sublattice system. It means that a standard way for researchers to share predictive algorithms and computational methods may be produced during designing advanced alloys.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.10772025,10932002 and 10972127)the Natural Science Foundation of Henan Province,China(Grant No.102300410144)the Beijing Municipal Key Disciplines Fund for General Mechanics and Foundation of Mechanics,China
文摘Stability for the manifolds of equilibrium states of a generalized Birkhoff system is studied. A theorem for the stability of the manifolds of equilibrium states of the general autonomous system is used to the generalized BirkhoiYian system and two propositions on the stability of the manifolds of equilibrium states of the system are obtained. An example is given to illustrate the application of the results.
基金This project was supported by the NSF of Sichuan Education of China(2003A081)and SZD0406
文摘By applying a maximal element theorem on product FC-space due to author, some new equilibrium existence theorems for generalized games with fuzzy constraint correspondences are proved in FC-spaces. By using these equilibrium existence theorems, some new existence theorems of solutions for the system of generalized vector quasi-equilibrium problems are established in noncompact product FC-spaces. These results improve and generalize some recent results in literature to product FC-spaces without any convexity structure.
基金This work was supported by the National Natural Science Foundation of Chinathe Research Fund for the Doctoral Program of Higher Education(20076004,2000001005).
文摘In this study, the constant volume, visual method is used to measure the critical point of CO2+toluene, CO2+cyclohexane, CO2+n-butyraldehyde, CO2+i-butyraldehyde, CO2+methanol and CO2+alcohol binary systems. The relationship between critical point and the concentration of the entrainer for different substances has been discussed, and the comparison of the phase behavior of single component system and that of binary systems have been carried out.
文摘This paper reports a new simple four-dimensional（4 D） hyperjerk chaotic system. The proposed system has only one stable equilibrium point. Hence, its strange attractor belongs to the category of hidden attractors. The proposed system exhibits various dynamical behaviors including chaotic, periodic, stable nature, and coexistence of various attractors. Numerous theoretical and numerical methods are used for the analyses of this system. The chaotic behavior of the new system is validated using circuit implementation. Further, the synchronization of the proposed systems is shown by designing an adaptive integrator backstepping controller. Numerical simulation validates the synchronization strategy.
基金supported by National Natural Science Foundation of China(No.61374065)the Research Fund for the Taishan Scholar Project of Shandong Province
文摘This paper studies the regional stability for positive switched linear systems with multi-equilibrium points （PSLS-MEP）. First, a sufficient condition is presented for the regional stability of PSLS-MEP via a common linear Lyapunov function. Second, by establishing multiple Lyapunov functions, a dwell time based condition is proposed for the regional stability analysis. Third, a suprasphere which contains all equilibrium points is constructed as a stability region of the considered PSLS-MEP, which is less conservative than existing results. Finally, the study of an illustrative example shows that the obtained results are effective in the regional stability analysis of PSLS-MEP.
基金Supported by the National Natural Science Foundation of China(No.40803031)
文摘Solid-liquid equilibrium of quaternary system Cd2＋//Cl–, SO42–, NO3–-H2O at 298 K was studied by means of an isothermal solution saturation method. Experimental results indicate that there are three univariant curves BE, AE and CE, one invariant point E and three crystallization fields in the quaternary system. The quaternary system belongs to a simple type, and there are no double salts or solid solution existing. The crystallization zones of equilibrium solid phases are CdCl2·5/2H2O（AEB field）, 3CdSO4·8H2O（AEC field） and Cd（NO3）2·4H2O（BEC field）, respectively. The composition of the invariant point is CdCl2, Cd（NO3）2, CdSO4 and H2O and the contents of which are 17.02%, 45.50%, 4.52% and 32.96%, respectively. The physico-chemical properties of solution in the quaternary system show regular changes along with the increased cadmium concentration. The results indicate that Cd（NO3）2 possessed the highest solubility among those three salts, which means a strong transfer of Cd ion and a high pollution risk of soil environment. And the solubility of CdSO4 would be restrained as the salts existing together.
文摘In this paper, equilibrium stability of generalized Birkhoff's autonomous system is discussed. First, equilibrium equations of generalized Birkhoff's autonomous system are set up, and the n the linear approximate method and direct method of stability in equilibrium st ate are studied. Some results on equilibrium of generalized Birkhoff's autonomou s system are obtained on the basis of Lyapunov's thorem. Last, the applica tion of the results is illustrated with an example.
文摘By the degree theory on positive cone together with the technique of a priori estimate, the nontrivial equilibrium solutions of a strong nonlinearity and weak coupling reaction diffusion system and the structure of the equilibrium solutions are discussed.
文摘Having criticized the current architecture of Advanced Traveler Information Systems （ATISs）, this work discusses a new base of requirements to develop a new paradigm for traffic information systems. It mainly integrates three dimensions within a traffic system： drivers＇ pattern of behavior and preferences, urban traffic desires, and capabilities of traffic information service providers. Based on the above, functional segments from several related backgrounds are brought together to structure a new architecture, called Interactive Traveler Information System （ITIS）. The main interactive feature of this new architecture is a two-way communication track between drivers and the traffic information system provider-in fact, a decision on choosing a road at a particular time for an individual will be made based on the utility of both sides. This new configuration consists of driver-side smartphone application, centric traffic prediction, and decision-maker units, which will shape a new approach of decision-making processes. These all work together to satisfy the designated goal of ITIS, which is preserving the Wardrop equilibrium condition in the traffic network level. Finally, we concentrate on a comparison study, which shows a differentiation between performance of the proposed ITIS and the current ATIS model in a real situation. This has been done with simulations of analogical scenarios. The most noticeable advantage of the proposed architecture is not being limited to a saturation limit, and the positive effect of increasing system penetration in the performance of the newly introduced information system. In conclusion, new research subjects are suggested to be carried out.
文摘By using an existence theorems of maximal elements for a family of set-valued mappings in G-convex spaces due to the author, some new nonempty intersection theorems for a family of set-valued mappings were established in noncompact product G-convex spaces. As applications, some equilibrium existence theorems for a system of generalized vector equilibrium problems were proved in noncompact product G-convex spaces. These theorems unify, improve and generalize some important known results in literature.
基金Supported by NSF of Chongqing and Science Foundations of Chongqing Jia1otong University
文摘By using Fort theorem the generic stability result for the system of generalized vector equilibrium problems is established. Further, by proving the existence and connectivity of minimal essential set the existence result of essential components in the solution set is derived.
基金supported by the Science Research Foundation of Liaoning Provincial Education Department,China(Grant No.L2013229)
文摘A new three-dimensional （3D） continuous autonomous system with one parameter and three quadratic terms is presented firstly in this paper. Countless embedded trumpet-shaped chaotic attractors in two opposite directions are generated from the system as time goes on. The basic dynamical behaviors of the strange chaotic system are investigated. Another more complex 3D system with the same capability of generating countless embedded trumpet-shaped chaotic attractors is also put forward.
文摘Based on the extraction equilibrium and mass balances in countercurrent extraction systems, a novel method was studied for dealing with the extraction equilibrium and the mass distribution in a multi-component(gamma-component) system. The relationships of mass distribution (x(i), y(i), i = 1, ..., lambda) between two phases were expressed by 2 lambda dimensional simultaneous equations. These simultaneous equations can be converted to a one-dimension nonlinear equation, then it was solved by Newton-Raphson algorithm within a few number of iteration. Compared with the regular calculation method for the 2 lambda dimensional simultaneous equations, Newton-Raphson algorithm can decrease the number of iteration, increase the convergence of the equations and accelerate the speed of simulation. It was verified in many multi-component systems with satisfactory results. As an example, a five-component system is demonstrated in this paper.
基金the National Natural Science Foundation of China (50471025)Natural Science Foundation of Lia-oning Province (20052028)National Key Technology R &D Program(2006BAE04B09-7)
文摘Alloys of Mg-Zn-La system in Mg rich corner were prepared, and the phase relationship was investigated at different temperatures such as 200, 300 and 350 ℃ by scanning electron microscopy(SEM), X-ray diffraction(XRD) and electron probe microanalysis with energy dispersive X-ray spectroscopy (EPMA). Two types of phase equilibrium were identified at the different temperatures. One is two-phase equilibrium contained the Mg solid solution and T-phase. The other is three-phase equilibrium which contained the Mg solid solution, MgZn phase and T-phase. T-phase was stable as the temperature changed. The La content in T-phase is constant which is about 8±0.3% (atom fraction); but the Mg content and Zn content of that is changed, and the Zn content in T-phase was from 16.1% to 44%. The solubility of La in MgZn phase was increased from 1.2% to 1.6% as the temperature increasing from 200 to 350 ℃.
基金Supported by the National Natural Science Foundation of China
文摘1 INTRODUCTIONVapor-liquid equilibrium(VLE)relations are required for practical use,such as in the designand operation of disitillation equipment.In the conventional experimental methods of vapor-liquid equilibria,some analytical instruments are applied.They are time-consuming and dif-ficult for multicomponent system because the proper method for the composition analysis isnot easy to be set up.
文摘A geometrical theorem for the static equilibrium of a common-point-force system has been proven by means of virtual-work principle: The equilibrium point of a common-point force system has a minimal weighted distance summation to every fixed point arbitrarily given on each force line with a weighing factor proportional to corresponding force value. Especially the mechanical simulating technique for its inverse problem has been realized by means of pulley block. The conclusions for the inverse problem derived from mechanic method are in accordance with that given by the pure mathematical method, and the self-consistence of the theorem and its inverse problem has been demonstrated. Some application examples in engineering, economy and mathematics have been discussed, especially the possible application in the research of molecular structure, has also been predicted.
