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
Advanced traveler information systems （ATIS） can not only improve drivers＇ accessibility to the more accurate route travel time information, but also can improve drivers＇ adaptability to the stochastic network cap...Advanced traveler information systems （ATIS） can not only improve drivers＇ accessibility to the more accurate route travel time information, but also can improve drivers＇ adaptability to the stochastic network capacity degradations. In this paper, a mixed stochastic user equilibrium model was proposed to describe the interactive route choice behaviors between ATIS equipped and unequipped drivers on a degradable transport network. In the proposed model the information accessibility of equipped drivers was reflected by lower degree of uncertainty in their stochastic equilibrium flow distributions, and their behavioral adaptability was captured by multiple equilibrium behaviors over the stochastic network state set. The mixed equilibrium model was formulated as a fixed point problem defined in the mixed route flows, and its solution was achieved by executing an iterative algorithm. Numerical experiments were provided to verify the properties of the mixed network equilibrium model and the efficiency of the iterative algorithm.展开更多
The lg c-pH diagram of the CaCl2-Ca（OH）2-H2O system and its two subsystems at 298.15 K are constructed according to the theory of thermodynamic equilibrium. The interaction characteristics between the solubility of ...The lg c-pH diagram of the CaCl2-Ca（OH）2-H2O system and its two subsystems at 298.15 K are constructed according to the theory of thermodynamic equilibrium. The interaction characteristics between the solubility of CaCl2 and Ca（OH）e can be found out from the diagrams. CaCl26H2O （s）, Ca（OH）2（s） and solution coexist when the pH value of solution is about 10.8. CaC12 with the minimum solubility of 1 682.4 g/L is in equilibrium with solution when the pH value is lower than 9.4, and Ca（OH）2 with the minimum solubility of 2.749 g/L is in equilibrium with solution at the pH value over 12.1, which provides a theoretical basis for the treatment and reuse of calcium chloride mother liquor for collocating lime cream which is the precipitant in the process of synthesizing magnesium hydroxide.展开更多
We consider a single server constant retrial queue,in which a state-dependent service policy is used to control the service rate.Customer arrival follows Poisson process,while service time and retrial time are exponen...We consider a single server constant retrial queue,in which a state-dependent service policy is used to control the service rate.Customer arrival follows Poisson process,while service time and retrial time are exponential distributions.Whenever the server is available,it admits the retrial customers into service based on a first-come first-served rule.The service rate adjusts in real-time based on the retrial queue length.An iterative algorithm is proposed to numerically solve the personal optimal problem in the fully observable scenario.Furthermore,we investigate the impact of parameters on the social optimal threshold.The effectiveness of the results is illustrated by two examples.展开更多
Reaction of the non-substituted/substituted unsymmetric pinene-derived complex[Pt(N^C^N')Cl]with the aryl isocyanide 2,6-dimethylphenyl isocyanide(CNXyl)afforded a mixture of two isomeric species:the ionic complex...Reaction of the non-substituted/substituted unsymmetric pinene-derived complex[Pt(N^C^N')Cl]with the aryl isocyanide 2,6-dimethylphenyl isocyanide(CNXyl)afforded a mixture of two isomeric species:the ionic complex[Pt(κ^(3)-N^C^N')(CNXyl)]Cl([A]Cl)and the molecular complex[Pt(κ^(2)-N^C^N')(CNXyl)Cl](B).Isomer B was almost the dominating product.The structures of the isomer B derivatives bearing-CF_(3)and-Cl substituents on the pyridine ring of the pinene moiety(5B and 7B,respectively)have been confirmed by single-crystal X-ray diffraction,revealing a slightly distorted square planar geometry with trans-N_(N^C^N'),CNR configuration(The terminal N atom of theκ^(2)-N^C^N'ligand is trans to the isocyanide ligand CNXyl.).Isomer B is thermodynamically more stable,as confirmed by theoretical calculations.CCDC:2416415,5B;2416414,7B.展开更多
This study proposes an alternative calculation mode for stresses on the slip surface(SS).The calculation of the normal stress(NS)on the SS involves examining its composition and expanding its unknown using the Taylor ...This study proposes an alternative calculation mode for stresses on the slip surface(SS).The calculation of the normal stress(NS)on the SS involves examining its composition and expanding its unknown using the Taylor series.This expansion enables the reasonable construction of a function describing the NS on the SS.Additionally,by directly incorporating the nonlinear Generalized Hoke-Brown(GHB)strength criterion and utilizing the slope factor of safety(FOS)definition,a function of the shear stress on the SS is derived.This function considers the mutual feedback mechanism between the NS and strength parameters of the SS.The stress constraints conditions are then introduced at both ends of the SS based on the spatial stress relation of one point.Determining the slope FOS and stress solution for the SS involves considering the mechanical equilibrium conditions and the stress constraint conditions satisfied by the sliding body.The proposed approach successfully simulates the tension-shear stress zone near the slope top and provides an intuitive description of the concentration effect of compression-shear stress of the SS near the slope toe.Furthermore,compared to other methods,the present method demonstrates superior processing capabilities for the embedded nonlinear GHB strength criterion.展开更多
Reinforcement of slopes using soil nailing can effectively improve slope stability, and it has been widely used in upgrading cut slopes. Based on the assumptions of stresses on the slip surface, a new method for analy...Reinforcement of slopes using soil nailing can effectively improve slope stability, and it has been widely used in upgrading cut slopes. Based on the assumptions of stresses on the slip surface, a new method for analyzing the stability of a slope reinforced with soil nails was established in the limit equilibrium theory framework, by considering that slope sliding occurs owing to shear failure of the slip surface, which subjects to Mohr–Coulomb(M–C) strength criterion. Meanwhile, in order to easily analyze the stability of a soil nailed slope in actual engineering and facilitate optimum design of parameters for soil nailing, factor of safety(FOS) contour curve charts were drawn on the basis of the established linear proportional relationship between the spacing of soil nails and slope height, and the length of soil nails and slope height. Then, by analyzing and verifying the results obtained from classic examples, some conclusions can be got as follows: 1) The results obtained from the current method are close to those obtained from the traditional limit equilibrium methods, and the current method can provide a strict solution for the slope FOS as it satisfies all the static equilibrium conditions of a sliding body, thus confirming the feasibility of the current method; 2) The slope FOS contour curve charts can be used not only to reliably analyze the stability of a soil nailed slope, but also to design optimally the parameters of soil nailing for the slope with a certain safety requirement.展开更多
Hoek–Brown(HB)strength criterion can reflect rock’s inherent failure nature,so it is more suitable for analyzing the stability of rock slopes.However,the traditional limit equilibrium methods are at present only sui...Hoek–Brown(HB)strength criterion can reflect rock’s inherent failure nature,so it is more suitable for analyzing the stability of rock slopes.However,the traditional limit equilibrium methods are at present only suitable for analyzing the rock slope stability using the linear equivalent Mohr–Coulomb(EMC)strength parameters instead of the nonlinear HB strength criterion.Therefore,a new method derived to analyze directly the rock slope stability using the nonlinear HB strength criterion for arbitrary curve slip surface was described in the limit equilibrium framework.The current method was established based on certain assumptions concerning the stresses on the slip surface through amending the initial normal stressσ0 obtained without considering the effect of inter-slice forces,and it can satisfy all static equilibrium conditions of the sliding body,so the current method can obtain the reasonable and strict factor of safety(FOS)solutions.Compared with the results of other methods in some examples,the feasibility of the current method was verified.Meanwhile,the parametric analysis shows that the slope angleβhas an important influence on the difference of the results obtained using the nonlinear HB strength criterion and its linear EMC strength parameters.Forβ≤45°,both of the results are similar,showing the traditional limit equilibrium methods using the linear EMC strength parameters and the current method are all suitable to analyze rock slope stability,but forβ>60°,the differences of both the results are obvious,showing the actual slope stability state can not be reflected in the traditional limit equilibrium methods,and then the current method should be used.展开更多
Based on the reliability budget and percentile travel time(PTT) concept, a new travel time index named combined mean travel time(CMTT) under stochastic traffic network was proposed. CMTT here was defined as the convex...Based on the reliability budget and percentile travel time(PTT) concept, a new travel time index named combined mean travel time(CMTT) under stochastic traffic network was proposed. CMTT here was defined as the convex combination of the conditional expectations of PTT-below and PTT-excess travel times. The former was designed as a risk-optimistic travel time index, and the latter was a risk-pessimistic one. Hence, CMTT was able to describe various routing risk-attitudes. The central idea of CMTT was comprehensively illustrated and the difference among the existing travel time indices was analyzed. The Wardropian combined mean traffic equilibrium(CMTE) model was formulated as a variational inequality and solved via an alternating direction algorithm nesting extra-gradient projection process. Some mathematical properties of CMTT and CMTE model were rigorously proved. Finally, a numerical example was performed to characterize the CMTE network. It is founded that that risk-pessimism is of more benefit to a modest(or low) congestion and risk network, however, it changes to be risk-optimism for a high congestion and risk network.展开更多
Excess lithium in alumina is significantly bad for aluminum reduction.In this study,the concentration variation of lithium ion in sodium aluminate solution with addition of synthetic lithium aluminate was investigated...Excess lithium in alumina is significantly bad for aluminum reduction.In this study,the concentration variation of lithium ion in sodium aluminate solution with addition of synthetic lithium aluminate was investigated.Elevating temperature,increasing caustic soda concentration,reducing alumina concentration or raising molar ratioαk improved equilibrium concentration of lithium ion in sodium aluminate solution.Agitation speed had a minimal effect on lithium ion concentration.Over 0.65 g/L lithium ion equilibrium concentration was observed in digestion process,whereas 35 mg/L lithium ion concentration remained in solution after precipitation time of 9 h.Moreover,equilibrium concentration decreased sharply from digestion of boehmite or diaspore to seed precipitation,about 95%lithium was precipitated into red mud(bauxite residue)and aluminum hydroxide.This study provides a valuable perspective in removal or extraction of lithium from sodium aluminate solution in alumina refineries.展开更多
A non-cooperative game is proposed to perform the sub-carrier assignment and power allocation for the multi-cell orthogonal frequency division multiple access（OFDMA） system.The objective is to raise the spectral eff...A non-cooperative game is proposed to perform the sub-carrier assignment and power allocation for the multi-cell orthogonal frequency division multiple access（OFDMA） system.The objective is to raise the spectral efficiency of the system and prolong the life time of user nodes.This paper defines a game player as a cell formed by the unique base station and the served users.The utility function considered here measures the user＇s achieved utility per power.Each individual cell＇s goal is to maximize the total utility of its users.To search the Nash equilibrium（NE） of the game,an iterative and distributed algorithm is presented.Since the NE is inefficient,the pricing of user＇s transmission power is introduced to improve the NE in the Pareto sense.Simulation results show the proposed game outperforms the water-filling algorithm in terms of fairness and energy efficiency.Moreover,through employing a liner pricing function,the energy efficiency could be further improved.展开更多
Two calculation modes for the effect of external load on slope stability, i.e., mode I in which the external load is thought to act on slope surface, and mode II in which the external load is thought to act on slip su...Two calculation modes for the effect of external load on slope stability, i.e., mode I in which the external load is thought to act on slope surface, and mode II in which the external load is thought to act on slip surface along the force action line, were considered. Meanwhile, four basic distribution patterns of external load were used, of which complex external loads could be composed. In analysis process, several limit equilibrium methods, such as Swedish method, simplified Bishop method, simplified Janbu method, Spencer method, Morgenstern-Price(M-P) method, Sarma method, and unbalanced thrust method, were also adopted to contrast their differences in slope stability under the external load. According to parametric analysis, some conclusions can be obtained as follows:(1) The external load, with the large magnitude, small inclination angle, and acting position close to the slope toe,has more positive effect on slope stability;(2) The results calculated using modes I and II of external load are similar, indicating that the calculation mode of external load has little influence on slope stability;(3) If different patterns of external loads are equivalent to each other, their slope stability under these external loads are the same, and if not, the external load leads to the better slope stability,as action position of the resultant force for external load is closer to the lower sliding point of slip surface.展开更多
The assumption widely used in the user equilibrium model for stochastic network was that the probability distributions of the travel time were known explicitly by travelers. However, this distribution may be unavailab...The assumption widely used in the user equilibrium model for stochastic network was that the probability distributions of the travel time were known explicitly by travelers. However, this distribution may be unavailable in reality. By relaxing the restrictive assumption, a robust user equilibrium model based on cumulative prospect theory under distribution-free travel time was presented. In the absence of the cumulative distribution function of the travel time, the exact cumulative prospect value(CPV) for each route cannot be obtained. However, the upper and lower bounds on the CPV can be calculated by probability inequalities.Travelers were assumed to choose the routes with the best worst-case CPVs. The proposed model was formulated as a variational inequality problem and solved via a heuristic solution algorithm. A numerical example was also provided to illustrate the application of the proposed model and the efficiency of the solution algorithm.展开更多
The fuzzy non-cooperative game with fuzzy payoff function is studied. Based on fuzzy set theory with game theory, the fuzzy Nash equilibrium of fuzzy non-cooperative games is proposed. Most of researchers rank fuzzy n...The fuzzy non-cooperative game with fuzzy payoff function is studied. Based on fuzzy set theory with game theory, the fuzzy Nash equilibrium of fuzzy non-cooperative games is proposed. Most of researchers rank fuzzy number by its center of gravity or by the real number with its maximal membership. By reducing fuzzy number into a real number, we lose much fuzzy information that should be kept during the operations between fuzzy numbers. The fuzzy quantities or alternatives are ordered directly by Yuan＇s binary fuzzy ordering relation. In doing so, the existence of fuzzy Nash equilibrium for fuzzy non-cooperative games is shown based on the utility function and the crisp Nash theorem. Finally, an illustrative example in traffic flow patterns of equilibrium is given in order to show the detailed calculation process of fuzzy Nash equilibrium.展开更多
The solvability of the coupled Riccati differential equations appearing in the differential game approach to the formation control problem is vital to the finite horizon Nash equilibrium solution.These equations(if so...The solvability of the coupled Riccati differential equations appearing in the differential game approach to the formation control problem is vital to the finite horizon Nash equilibrium solution.These equations(if solvable)can be solved numerically by using the terminal value and the backward iteration.To investigate the solvability and solution of these equations the formation control problem as the differential game is replaced by a discrete-time dynamic game.The main contributions of this paper are as follows.First,the existence of Nash equilibrium controls for the discretetime formation control problem is shown.Second,a backward iteration approximate solution to the coupled Riccati differential equations in the continuous-time differential game is developed.An illustrative example is given to justify the models and solution.展开更多
The violation of monotonicity on reliability measures(RMs)usually makes the mathematical programming algorithms less efficient in solving the reliability-based user equilibrium(RUE)problem.The swapping algorithms prov...The violation of monotonicity on reliability measures(RMs)usually makes the mathematical programming algorithms less efficient in solving the reliability-based user equilibrium(RUE)problem.The swapping algorithms provide a simple and convenient alternative to search traffic equilibrium since they are derivative-free and require weaker monotonicity.However,the existing swapping algorithms are usually based on linear swapping processes which cannot naturally avoid overswapping,and the step-size parameter update methods do not take the swapping feature into account.In this paper,we suggest a self-regulating pairwise swapping algorithm(SRPSA)to search RUE.SRPSA comprises an RM-based pairwise swapping process(RMPSP),a parameter self-diminishing operator and a termination criterion.SRPSA does not need to check the feasibility of either solutions or step-size parameter.It is suggested from the numerical analyses that SRPSA is effective and can swap to the quasi-RUE very fast.Therefore,SRPSA offers a good approach to generate initial points for those superior local search algorithms.展开更多
From the view of information flow, a super-network equilibrium optimization model is proposed to compute the solution of the operation architecture which is made up of a perceptive level, a command level and a firepow...From the view of information flow, a super-network equilibrium optimization model is proposed to compute the solution of the operation architecture which is made up of a perceptive level, a command level and a firepower level. Firstly, the optimized conditions of the perceptive level, command level and firepower level are analyzed respectively based on the demand of information relation,and then the information supply-and-demand equilibrium model of the operation architecture super-network is established. Secondly,a variational inequality transformation(VIT) model for equilibrium optimization of the operation architecture is given. Thirdly, the contraction projection algorithm for solving the operation architecture super-network equilibrium optimization model with fuzzy demands is designed. Finally, numerical examples are given to prove the validity and rationality of the proposed method, and the influence of fuzzy demands on the super-network equilibrium solution of operation architecture is discussed.展开更多
Traditional rigid body limit equilibrium method （RBLEM） was adopted for the stability evaluation and analysis of rock slope under earthquake scenario. It is not able to provide the real stress distribution of the st...Traditional rigid body limit equilibrium method （RBLEM） was adopted for the stability evaluation and analysis of rock slope under earthquake scenario. It is not able to provide the real stress distribution of the structure, while the strength reduction method relies on the arbitrary decision on the failure criteria. The dynamic limit equilibrium solution was proposed for the stability analysis of sliding block based on 3-D multi-grid method, by incorporating implicit stepping integration FEM. There are two independent meshes created in the analysis： One original 3-D FEM mesh is for the simulation of target structure and provides the stress time-history, while the other surface grid is for the simulation of sliding surface and could be selected and designed freely. As long as the stress time-history of the geotechnical structure under earthquake scenario is obtained based on 3-D nonlinear dynamic FEM analysis, the time-history of the force on sliding surface could be derived by projecting the stress time-history from 3-D FEM mesh to surface grid. After that, the safety factor time-history of the sliding block will be determined through applying limit equilibrium method. With those information in place, the structure＇s aseismatic stability ean be further studied. The above theory and method were also applied to the aseismatic stability analysis of Dagangshan arch dam＇s right bank high slope and compared with the the result generated by Quasi-static method. The comparative analysis reveals that the method not only raises the FEM＇s capability in accurate simulation of complicated geologic structure, but also increases the flexibility and comprehensiveness of limit equilibrium method. This method is reliable and recommended for further application in other real geotechnical engineering.展开更多
In the limit equilibrium framework, two- and three-dimensional slope stabilities can be solved according to the overall force and moment equilibrium conditions of a sliding body. In this work, based on Mohr-Coulomb(M-...In the limit equilibrium framework, two- and three-dimensional slope stabilities can be solved according to the overall force and moment equilibrium conditions of a sliding body. In this work, based on Mohr-Coulomb(M-C) strength criterion and the initial normal stress without considering the inter-slice(or inter-column) forces, the normal and shear stresses on the slip surface are assumed using some dimensionless variables, and these variables have the same numbers with the force and moment equilibrium equations of a sliding body to establish easily the linear equation groups for solving them. After these variables are determined, the normal stresses, shear stresses, and slope safety factor are also obtained using the stresses assumptions and M-C strength criterion. In the case of a three-dimensional slope stability analysis, three calculation methods, namely, a non-strict method, quasi-strict method, and strict method, can be obtained by satisfying different force and moment equilibrium conditions. Results of the comparison in the classic two- and three-dimensional slope examples show that the slope safety factors calculated using the current method and the other limit equilibrium methods are approximately equal to each other, indicating the feasibility of the current method; further, the following conclusions are obtained: 1) The current method better amends the initial normal and shear stresses acting on the slip surface, and has the identical results with using simplified Bishop method, Spencer method, and Morgenstern-Price(M-P) method; however, the stress curve of the current method is smoother than that obtained using the three abovementioned methods. 2) The current method is suitable for analyzing the two- and three-dimensional slope stability. 3) In the three-dimensional asymmetric sliding body, the non-strict method yields safer solutions, and the results of the quasi-strict method are relatively reasonable and close to those of the strict method, indicating that the quasi-strict method can be used to obtain a reliable slope safety factor.展开更多
Unbalanced agricultural production decision becomes the great block that influences the effective distribution of social resources, national grain security, social stability and economic development. This paper took t...Unbalanced agricultural production decision becomes the great block that influences the effective distribution of social resources, national grain security, social stability and economic development. This paper took the game theory as an analyzed tool to describe the interactional processes among the peasants, and set up the game theory model of independent decision and joint decision by peasants. It was shown that the government＇s positive guide and the market environment macroscopically controlled by the government could effectively increased the peasants＇ income展开更多
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Projects(51378119,51578150)supported by the National Natural Science Foundation of China
文摘Advanced traveler information systems （ATIS） can not only improve drivers＇ accessibility to the more accurate route travel time information, but also can improve drivers＇ adaptability to the stochastic network capacity degradations. In this paper, a mixed stochastic user equilibrium model was proposed to describe the interactive route choice behaviors between ATIS equipped and unequipped drivers on a degradable transport network. In the proposed model the information accessibility of equipped drivers was reflected by lower degree of uncertainty in their stochastic equilibrium flow distributions, and their behavioral adaptability was captured by multiple equilibrium behaviors over the stochastic network state set. The mixed equilibrium model was formulated as a fixed point problem defined in the mixed route flows, and its solution was achieved by executing an iterative algorithm. Numerical experiments were provided to verify the properties of the mixed network equilibrium model and the efficiency of the iterative algorithm.
基金Project(2008BAB35B04) supported by National High Technology Research and Development Program of ChinaProject(2010QZZD003) supported by Advanced Research Program of Central South University,China
文摘The lg c-pH diagram of the CaCl2-Ca（OH）2-H2O system and its two subsystems at 298.15 K are constructed according to the theory of thermodynamic equilibrium. The interaction characteristics between the solubility of CaCl2 and Ca（OH）e can be found out from the diagrams. CaCl26H2O （s）, Ca（OH）2（s） and solution coexist when the pH value of solution is about 10.8. CaC12 with the minimum solubility of 1 682.4 g/L is in equilibrium with solution when the pH value is lower than 9.4, and Ca（OH）2 with the minimum solubility of 2.749 g/L is in equilibrium with solution at the pH value over 12.1, which provides a theoretical basis for the treatment and reuse of calcium chloride mother liquor for collocating lime cream which is the precipitant in the process of synthesizing magnesium hydroxide.
基金supported by the National Natural Science Foundation of China(Grant No.11971486)。
文摘We consider a single server constant retrial queue,in which a state-dependent service policy is used to control the service rate.Customer arrival follows Poisson process,while service time and retrial time are exponential distributions.Whenever the server is available,it admits the retrial customers into service based on a first-come first-served rule.The service rate adjusts in real-time based on the retrial queue length.An iterative algorithm is proposed to numerically solve the personal optimal problem in the fully observable scenario.Furthermore,we investigate the impact of parameters on the social optimal threshold.The effectiveness of the results is illustrated by two examples.
文摘Reaction of the non-substituted/substituted unsymmetric pinene-derived complex[Pt(N^C^N')Cl]with the aryl isocyanide 2,6-dimethylphenyl isocyanide(CNXyl)afforded a mixture of two isomeric species:the ionic complex[Pt(κ^(3)-N^C^N')(CNXyl)]Cl([A]Cl)and the molecular complex[Pt(κ^(2)-N^C^N')(CNXyl)Cl](B).Isomer B was almost the dominating product.The structures of the isomer B derivatives bearing-CF_(3)and-Cl substituents on the pyridine ring of the pinene moiety(5B and 7B,respectively)have been confirmed by single-crystal X-ray diffraction,revealing a slightly distorted square planar geometry with trans-N_(N^C^N'),CNR configuration(The terminal N atom of theκ^(2)-N^C^N'ligand is trans to the isocyanide ligand CNXyl.).Isomer B is thermodynamically more stable,as confirmed by theoretical calculations.CCDC:2416415,5B;2416414,7B.
基金Project(52278380)supported by the National Natural Science Foundation of ChinaProject(2023JJ30670)supported by the National Science Foundation of and Technology Major Project of Hunan Province,China。
文摘This study proposes an alternative calculation mode for stresses on the slip surface(SS).The calculation of the normal stress(NS)on the SS involves examining its composition and expanding its unknown using the Taylor series.This expansion enables the reasonable construction of a function describing the NS on the SS.Additionally,by directly incorporating the nonlinear Generalized Hoke-Brown(GHB)strength criterion and utilizing the slope factor of safety(FOS)definition,a function of the shear stress on the SS is derived.This function considers the mutual feedback mechanism between the NS and strength parameters of the SS.The stress constraints conditions are then introduced at both ends of the SS based on the spatial stress relation of one point.Determining the slope FOS and stress solution for the SS involves considering the mechanical equilibrium conditions and the stress constraint conditions satisfied by the sliding body.The proposed approach successfully simulates the tension-shear stress zone near the slope top and provides an intuitive description of the concentration effect of compression-shear stress of the SS near the slope toe.Furthermore,compared to other methods,the present method demonstrates superior processing capabilities for the embedded nonlinear GHB strength criterion.
基金Project(2015M580702)supported by the Postdoctoral Science Foundation of ChinaProject(51608541)supported by the National Natural Science Foundation of ChinaProject(2014122066)supported by the Guizhou Provincial Department of Transportation Foundation,China
文摘Reinforcement of slopes using soil nailing can effectively improve slope stability, and it has been widely used in upgrading cut slopes. Based on the assumptions of stresses on the slip surface, a new method for analyzing the stability of a slope reinforced with soil nails was established in the limit equilibrium theory framework, by considering that slope sliding occurs owing to shear failure of the slip surface, which subjects to Mohr–Coulomb(M–C) strength criterion. Meanwhile, in order to easily analyze the stability of a soil nailed slope in actual engineering and facilitate optimum design of parameters for soil nailing, factor of safety(FOS) contour curve charts were drawn on the basis of the established linear proportional relationship between the spacing of soil nails and slope height, and the length of soil nails and slope height. Then, by analyzing and verifying the results obtained from classic examples, some conclusions can be got as follows: 1) The results obtained from the current method are close to those obtained from the traditional limit equilibrium methods, and the current method can provide a strict solution for the slope FOS as it satisfies all the static equilibrium conditions of a sliding body, thus confirming the feasibility of the current method; 2) The slope FOS contour curve charts can be used not only to reliably analyze the stability of a soil nailed slope, but also to design optimally the parameters of soil nailing for the slope with a certain safety requirement.
基金Project(2015M580702)supported by China Postdoctoral Science FoundationProject(51608541)supported by the National Natural Science Foundation of ChinaProject(2014122066)supported by the Guizhou Provincial Department of Transportation Foundation,China
文摘Hoek–Brown(HB)strength criterion can reflect rock’s inherent failure nature,so it is more suitable for analyzing the stability of rock slopes.However,the traditional limit equilibrium methods are at present only suitable for analyzing the rock slope stability using the linear equivalent Mohr–Coulomb(EMC)strength parameters instead of the nonlinear HB strength criterion.Therefore,a new method derived to analyze directly the rock slope stability using the nonlinear HB strength criterion for arbitrary curve slip surface was described in the limit equilibrium framework.The current method was established based on certain assumptions concerning the stresses on the slip surface through amending the initial normal stressσ0 obtained without considering the effect of inter-slice forces,and it can satisfy all static equilibrium conditions of the sliding body,so the current method can obtain the reasonable and strict factor of safety(FOS)solutions.Compared with the results of other methods in some examples,the feasibility of the current method was verified.Meanwhile,the parametric analysis shows that the slope angleβhas an important influence on the difference of the results obtained using the nonlinear HB strength criterion and its linear EMC strength parameters.Forβ≤45°,both of the results are similar,showing the traditional limit equilibrium methods using the linear EMC strength parameters and the current method are all suitable to analyze rock slope stability,but forβ>60°,the differences of both the results are obvious,showing the actual slope stability state can not be reflected in the traditional limit equilibrium methods,and then the current method should be used.
基金Project(2012CB725403-5)supported by National Basic Research Program of ChinaProject(71131001-2)supported by National Natural Science Foundation of China+1 种基金Projects(2012JBZ005)supported by Fundamental Research Funds for the Central Universities,ChinaProject(201170)supported by the Foundation for National Excellent Doctoral Dissertation of China
文摘Based on the reliability budget and percentile travel time(PTT) concept, a new travel time index named combined mean travel time(CMTT) under stochastic traffic network was proposed. CMTT here was defined as the convex combination of the conditional expectations of PTT-below and PTT-excess travel times. The former was designed as a risk-optimistic travel time index, and the latter was a risk-pessimistic one. Hence, CMTT was able to describe various routing risk-attitudes. The central idea of CMTT was comprehensively illustrated and the difference among the existing travel time indices was analyzed. The Wardropian combined mean traffic equilibrium(CMTE) model was formulated as a variational inequality and solved via an alternating direction algorithm nesting extra-gradient projection process. Some mathematical properties of CMTT and CMTE model were rigorously proved. Finally, a numerical example was performed to characterize the CMTE network. It is founded that that risk-pessimism is of more benefit to a modest(or low) congestion and risk network, however, it changes to be risk-optimism for a high congestion and risk network.
基金Project(2015BAB04B01)supported by the National Key Technology R&D Program of ChinaProject(FA2017029)supported by Science and Technology Program of Chongzuo,ChinaProject(CSUZC201811)supported by the Open-End Fund for the Valuable and Precision Instruments of Central South University,China
文摘Excess lithium in alumina is significantly bad for aluminum reduction.In this study,the concentration variation of lithium ion in sodium aluminate solution with addition of synthetic lithium aluminate was investigated.Elevating temperature,increasing caustic soda concentration,reducing alumina concentration or raising molar ratioαk improved equilibrium concentration of lithium ion in sodium aluminate solution.Agitation speed had a minimal effect on lithium ion concentration.Over 0.65 g/L lithium ion equilibrium concentration was observed in digestion process,whereas 35 mg/L lithium ion concentration remained in solution after precipitation time of 9 h.Moreover,equilibrium concentration decreased sharply from digestion of boehmite or diaspore to seed precipitation,about 95%lithium was precipitated into red mud(bauxite residue)and aluminum hydroxide.This study provides a valuable perspective in removal or extraction of lithium from sodium aluminate solution in alumina refineries.
基金supported by the National Natural Science Foundation of China(60972059)the Fundamental Research Funds for the Central Universities of China(2010QNA27)+2 种基金China Postdoctoral Science Foundation(20100481185)the Ph.D.Programs Foundation of Ministry of Education of China(20090095120013)the Talent Introduction Program and Young Teacher Sailing Program of China University of Mining and Technology
文摘A non-cooperative game is proposed to perform the sub-carrier assignment and power allocation for the multi-cell orthogonal frequency division multiple access（OFDMA） system.The objective is to raise the spectral efficiency of the system and prolong the life time of user nodes.This paper defines a game player as a cell formed by the unique base station and the served users.The utility function considered here measures the user＇s achieved utility per power.Each individual cell＇s goal is to maximize the total utility of its users.To search the Nash equilibrium（NE） of the game,an iterative and distributed algorithm is presented.Since the NE is inefficient,the pricing of user＇s transmission power is introduced to improve the NE in the Pareto sense.Simulation results show the proposed game outperforms the water-filling algorithm in terms of fairness and energy efficiency.Moreover,through employing a liner pricing function,the energy efficiency could be further improved.
基金Project(2015M580702)supported by the China Postdoctoral Science FoundationProject(51608541)supported by the National Natural Science Foundation of ChinaProject(2014122006)supported by the Guizhou Provincial Department of Transportation Foundation,China
文摘Two calculation modes for the effect of external load on slope stability, i.e., mode I in which the external load is thought to act on slope surface, and mode II in which the external load is thought to act on slip surface along the force action line, were considered. Meanwhile, four basic distribution patterns of external load were used, of which complex external loads could be composed. In analysis process, several limit equilibrium methods, such as Swedish method, simplified Bishop method, simplified Janbu method, Spencer method, Morgenstern-Price(M-P) method, Sarma method, and unbalanced thrust method, were also adopted to contrast their differences in slope stability under the external load. According to parametric analysis, some conclusions can be obtained as follows:(1) The external load, with the large magnitude, small inclination angle, and acting position close to the slope toe,has more positive effect on slope stability;(2) The results calculated using modes I and II of external load are similar, indicating that the calculation mode of external load has little influence on slope stability;(3) If different patterns of external loads are equivalent to each other, their slope stability under these external loads are the same, and if not, the external load leads to the better slope stability,as action position of the resultant force for external load is closer to the lower sliding point of slip surface.
基金Project(2012CB725400)supported by the National Basic Research Program of ChinaProjects(71271023,71322102,7121001)supported by the National Natural Science Foundation of China
文摘The assumption widely used in the user equilibrium model for stochastic network was that the probability distributions of the travel time were known explicitly by travelers. However, this distribution may be unavailable in reality. By relaxing the restrictive assumption, a robust user equilibrium model based on cumulative prospect theory under distribution-free travel time was presented. In the absence of the cumulative distribution function of the travel time, the exact cumulative prospect value(CPV) for each route cannot be obtained. However, the upper and lower bounds on the CPV can be calculated by probability inequalities.Travelers were assumed to choose the routes with the best worst-case CPVs. The proposed model was formulated as a variational inequality problem and solved via a heuristic solution algorithm. A numerical example was also provided to illustrate the application of the proposed model and the efficiency of the solution algorithm.
基金supported by the National Natural Science Foundation of China (70771010)
文摘The fuzzy non-cooperative game with fuzzy payoff function is studied. Based on fuzzy set theory with game theory, the fuzzy Nash equilibrium of fuzzy non-cooperative games is proposed. Most of researchers rank fuzzy number by its center of gravity or by the real number with its maximal membership. By reducing fuzzy number into a real number, we lose much fuzzy information that should be kept during the operations between fuzzy numbers. The fuzzy quantities or alternatives are ordered directly by Yuan＇s binary fuzzy ordering relation. In doing so, the existence of fuzzy Nash equilibrium for fuzzy non-cooperative games is shown based on the utility function and the crisp Nash theorem. Finally, an illustrative example in traffic flow patterns of equilibrium is given in order to show the detailed calculation process of fuzzy Nash equilibrium.
文摘The solvability of the coupled Riccati differential equations appearing in the differential game approach to the formation control problem is vital to the finite horizon Nash equilibrium solution.These equations(if solvable)can be solved numerically by using the terminal value and the backward iteration.To investigate the solvability and solution of these equations the formation control problem as the differential game is replaced by a discrete-time dynamic game.The main contributions of this paper are as follows.First,the existence of Nash equilibrium controls for the discretetime formation control problem is shown.Second,a backward iteration approximate solution to the coupled Riccati differential equations in the continuous-time differential game is developed.An illustrative example is given to justify the models and solution.
基金Projects(71601015,71501013,71471014)supported by the National Natural Science Foundation of ChinaProject(2015JBM060)supported by the Fundamental Research Funds for the Central Universities,China
文摘The violation of monotonicity on reliability measures(RMs)usually makes the mathematical programming algorithms less efficient in solving the reliability-based user equilibrium(RUE)problem.The swapping algorithms provide a simple and convenient alternative to search traffic equilibrium since they are derivative-free and require weaker monotonicity.However,the existing swapping algorithms are usually based on linear swapping processes which cannot naturally avoid overswapping,and the step-size parameter update methods do not take the swapping feature into account.In this paper,we suggest a self-regulating pairwise swapping algorithm(SRPSA)to search RUE.SRPSA comprises an RM-based pairwise swapping process(RMPSP),a parameter self-diminishing operator and a termination criterion.SRPSA does not need to check the feasibility of either solutions or step-size parameter.It is suggested from the numerical analyses that SRPSA is effective and can swap to the quasi-RUE very fast.Therefore,SRPSA offers a good approach to generate initial points for those superior local search algorithms.
基金supported by the National Natural Science Foundation of China (71771216,71701209)Shaanxi Natural Science Foundation (2019 JQ-250)。
文摘From the view of information flow, a super-network equilibrium optimization model is proposed to compute the solution of the operation architecture which is made up of a perceptive level, a command level and a firepower level. Firstly, the optimized conditions of the perceptive level, command level and firepower level are analyzed respectively based on the demand of information relation,and then the information supply-and-demand equilibrium model of the operation architecture super-network is established. Secondly,a variational inequality transformation(VIT) model for equilibrium optimization of the operation architecture is given. Thirdly, the contraction projection algorithm for solving the operation architecture super-network equilibrium optimization model with fuzzy demands is designed. Finally, numerical examples are given to prove the validity and rationality of the proposed method, and the influence of fuzzy demands on the super-network equilibrium solution of operation architecture is discussed.
基金Project(2013-KY-2) supported by the State Key Laboratory of Hydroscience and Engineering of Hydroscience, ChinaProject(50925931)supported by the National Funds for Distinguished Young Scientists, China
文摘Traditional rigid body limit equilibrium method （RBLEM） was adopted for the stability evaluation and analysis of rock slope under earthquake scenario. It is not able to provide the real stress distribution of the structure, while the strength reduction method relies on the arbitrary decision on the failure criteria. The dynamic limit equilibrium solution was proposed for the stability analysis of sliding block based on 3-D multi-grid method, by incorporating implicit stepping integration FEM. There are two independent meshes created in the analysis： One original 3-D FEM mesh is for the simulation of target structure and provides the stress time-history, while the other surface grid is for the simulation of sliding surface and could be selected and designed freely. As long as the stress time-history of the geotechnical structure under earthquake scenario is obtained based on 3-D nonlinear dynamic FEM analysis, the time-history of the force on sliding surface could be derived by projecting the stress time-history from 3-D FEM mesh to surface grid. After that, the safety factor time-history of the sliding block will be determined through applying limit equilibrium method. With those information in place, the structure＇s aseismatic stability ean be further studied. The above theory and method were also applied to the aseismatic stability analysis of Dagangshan arch dam＇s right bank high slope and compared with the the result generated by Quasi-static method. The comparative analysis reveals that the method not only raises the FEM＇s capability in accurate simulation of complicated geologic structure, but also increases the flexibility and comprehensiveness of limit equilibrium method. This method is reliable and recommended for further application in other real geotechnical engineering.
基金Project(51608541)supported by the National Natural Science Foundation of ChinaProject(2015M580702)supported by the Postdoctoral Science Foundation of ChinaProject(201508)supported by the Postdoctoral Science Foundation of Central South University,China
文摘In the limit equilibrium framework, two- and three-dimensional slope stabilities can be solved according to the overall force and moment equilibrium conditions of a sliding body. In this work, based on Mohr-Coulomb(M-C) strength criterion and the initial normal stress without considering the inter-slice(or inter-column) forces, the normal and shear stresses on the slip surface are assumed using some dimensionless variables, and these variables have the same numbers with the force and moment equilibrium equations of a sliding body to establish easily the linear equation groups for solving them. After these variables are determined, the normal stresses, shear stresses, and slope safety factor are also obtained using the stresses assumptions and M-C strength criterion. In the case of a three-dimensional slope stability analysis, three calculation methods, namely, a non-strict method, quasi-strict method, and strict method, can be obtained by satisfying different force and moment equilibrium conditions. Results of the comparison in the classic two- and three-dimensional slope examples show that the slope safety factors calculated using the current method and the other limit equilibrium methods are approximately equal to each other, indicating the feasibility of the current method; further, the following conclusions are obtained: 1) The current method better amends the initial normal and shear stresses acting on the slip surface, and has the identical results with using simplified Bishop method, Spencer method, and Morgenstern-Price(M-P) method; however, the stress curve of the current method is smoother than that obtained using the three abovementioned methods. 2) The current method is suitable for analyzing the two- and three-dimensional slope stability. 3) In the three-dimensional asymmetric sliding body, the non-strict method yields safer solutions, and the results of the quasi-strict method are relatively reasonable and close to those of the strict method, indicating that the quasi-strict method can be used to obtain a reliable slope safety factor.
文摘Unbalanced agricultural production decision becomes the great block that influences the effective distribution of social resources, national grain security, social stability and economic development. This paper took the game theory as an analyzed tool to describe the interactional processes among the peasants, and set up the game theory model of independent decision and joint decision by peasants. It was shown that the government＇s positive guide and the market environment macroscopically controlled by the government could effectively increased the peasants＇ income
