This paper deals with extensions of higher-order optimality conditions for scalar optimization to multiobjective optimization.A type of directional derivatives for a multiobjective function is proposed,and with this n...This paper deals with extensions of higher-order optimality conditions for scalar optimization to multiobjective optimization.A type of directional derivatives for a multiobjective function is proposed,and with this notion characterizations of strict local minima of order k for a multiobjective optimization problem with a nonempty set constraint are established,generalizing the corresponding scalar case obtained by Studniarski[3].Also necessary not sufficient and sufficient not necessary optimality conditions for this minima are derived based on our directional derivatives,which are generalizations of some existing scalar results and equivalent to some existing multiobjective ones.Many examples are given to illustrate them there.展开更多
Bifunctional oxide-zeolite-based composites(OXZEO)have emerged as promising materials for the direct conversion of syngas to olefins.However,experimental screening and optimization of reaction parameters remain resour...Bifunctional oxide-zeolite-based composites(OXZEO)have emerged as promising materials for the direct conversion of syngas to olefins.However,experimental screening and optimization of reaction parameters remain resource-intensive.To address this challenge,we implemented a three-stage framework integrating machine learning,Bayesian optimization,and experimental validation,utilizing a carefully curated dataset from the literature.Our ensemble-tree model(R^(2)>0.87)identified Zn-Zr and Cu-Mg binary mixed oxides as the most effective OXZEO systems,with their light olefin space-time yields confirmed by physically mixing with HSAPO-34 through experimental validation.Density functional theory calculations further elucidated the activity trends between Zn-Zr and Cu-Mg mixed oxides.Among 16 catalyst and reaction condition descriptors,the oxide/zeolite ratio,reaction temperature,and pressure emerged as the most significant factors.This interpretable,data-driven framework offers a versatile approach that can be applied to other catalytic processes,providing a powerful tool for experiment design and optimization in catalysis.展开更多
We studied how bioflocculants,produced by white-rot fungi,affect flocculation in slime water.Based on a test in an orthogonal design,flocculation conditions were optimized.The results show that flocculation activity i...We studied how bioflocculants,produced by white-rot fungi,affect flocculation in slime water.Based on a test in an orthogonal design,flocculation conditions were optimized.The results show that flocculation activity is at its highest when the following conditions are met:slime water concentration 27.42 g/L;coagulant aid(CaCl_2) mass concentration 5.0 g/L;two-segment stirrings:the first at a stirring speed of 60 r/min for 180 s and the second 180 r/min for 60 s;a pH of 11 and a flocculant concentration of 15 mL/L.The flocculation activity can be up to 98.71%of bioflocculants at the time.Further experiments indicate that most of the flocculation active material is found outside the mycelium cells.This is the extracellular secretion produced by mycelium cells during the fermentation process.This flocculant has strong thermal stability.Many kinds of cations have a flocculation function to assist bioflocculants.This aid-flocculation effect of the divalent cation Ca^(2+) is obvious in the bioflocculant produced by the white-rot fungus.Therefore,this is of great value when applied to control engineering in the battle against water pollution.展开更多
In this paper, both Fritz John and Karush-Kuhn-Tucker necessary optimality conditions are established for a （weakly） LU-efficient solution in the considered nonsmooth multiobjective programming problem with the mult...In this paper, both Fritz John and Karush-Kuhn-Tucker necessary optimality conditions are established for a （weakly） LU-efficient solution in the considered nonsmooth multiobjective programming problem with the multiple interval-objective function. Further, the sufficient optimality conditions for a （weakly） LU-efficient solution and several duality results in Mond-Weir sense are proved under assumptions that the functions constituting the considered nondifferentiable multiobjective programming problem with the multiple interval- objective function are convex.展开更多
This article is concerned with second-order necessary and sufficient optimality conditions for optimal control problems governed by 3-dimensional Navier-Stokes equations. The periodic state constraint is considered.
Pjridine has been generally synthesized by aldehydes and ammonia in a turbulent fluidized-bed reactor. In this paper, a novel riser reactor was proposed for pyridine synthesis. Experiment result showed that the yield ...Pjridine has been generally synthesized by aldehydes and ammonia in a turbulent fluidized-bed reactor. In this paper, a novel riser reactor was proposed for pyridine synthesis. Experiment result showed that the yield of pyridine and 3-picoline decreased, but the selectivity of pyridine over 3-picoline increased compared to turbulent fluidized-bed reactor. Based on experimental data, a modified kinetic model was used for the determination of optimal operating condition for riser reactor. The optimal operating condition of riser reactor given by this modified model was as follows： The reaction temperature of 755 K, catalyst to feedstock ratio （CTFR） of 87, residence timeof3.8sandinitialacetaldehydesconcentrationof0.0029mol.L-1 （acetaldehydes to formaldehydes ratio by mole （ATFR） of 0.65 and ammonia to aldehydes ratio by mole （ATAR） of 0.9, water contention of 63wt% （formaldehyde solution））.展开更多
New classes of functions namely (V, ρ)_(h,φ)-type I, quasi (V, ρ)_(h,φ)-type I and pseudo (V, ρ)_(h,φ)-type I functions are defined for multiobjective programming problem by using BenTal's generalized algebr...New classes of functions namely (V, ρ)_(h,φ)-type I, quasi (V, ρ)_(h,φ)-type I and pseudo (V, ρ)_(h,φ)-type I functions are defined for multiobjective programming problem by using BenTal's generalized algebraic operation. The examples of (V, ρ)_(h,φ)-type I functions are given. The sufficient optimality conditions are obtained for multi-objective programming problem involving above new generalized convexity.展开更多
The concepts of alpha-order Clarke's derivative, alpha-order Adjacent derivative and alpha-order G.Bouligand derivative of set-valued mappings are introduced, their properties are studied, with which the Fritz Joh...The concepts of alpha-order Clarke's derivative, alpha-order Adjacent derivative and alpha-order G.Bouligand derivative of set-valued mappings are introduced, their properties are studied, with which the Fritz John optimality condition of set-valued vector optimization is established. Finally, under the assumption of pseudoconvexity, the optimality condition is proved to be sufficient.展开更多
The solubilization of elastin by Bacillus licheniformis elastase cannot be analyzed by conventional kinetic methods because the biologically relevant substrate is insoluble and the concentration of enzyme-substrate co...The solubilization of elastin by Bacillus licheniformis elastase cannot be analyzed by conventional kinetic methods because the biologically relevant substrate is insoluble and the concentration of enzyme-substrate complex has no physical meaning. In this paper we report the optimization of elastolysis conditions and analysis of elastolytic kinetics. Our results indicated that the hydrolyzing temperature and time are very important factors affecting elastolysis rate. The optimized conditions using central composite design were as follows： elastolysis temperature 50 ℃, elastase concentration 1 × 10^4 U/ml, elastin 80 mg, elastolytic time 4 h. Investigation of the effects of substrate content, elastase concentration and pH was also revealed that low or high elastin content inhibits the elastolysis process. Increasingelastase improves elastin degradation, but high elastase may change the kinetics characterization. Alkaline environment can decrease elastin degradation rate and pH may affect elastolysis by changing elastase reaction pH. To further elucidate the elastolysis process, the logistic model was used to elastolysis kinetics study showing clearly that the logistic model can reasonably explain the elastolysis process, especially under lower elastase concentration. However, there is still need for more investigations with the aid of other methods, such as biochemical and molecular methods.展开更多
Quadratic 0-1 problems with linear inequality constraints are briefly considered in this paper.Global optimality conditions for these problems,including a necessary condition and some sufficient conditions,are present...Quadratic 0-1 problems with linear inequality constraints are briefly considered in this paper.Global optimality conditions for these problems,including a necessary condition and some sufficient conditions,are presented.The necessary condition is expressed without dual variables.The relations between the global optimal solutions of nonconvex quadratic 0-1 problems and the associated relaxed convex problems are also studied.展开更多
This paper studies a class of multiobjective generalized fractional programming problems, where the numerators of objective functions are the sum of differentiable function and convex function, while the denominators ...This paper studies a class of multiobjective generalized fractional programming problems, where the numerators of objective functions are the sum of differentiable function and convex function, while the denominators are the difference of differentiable function and convex function. Under the assumption of Calmness Constraint Qualification the Kuhn-Tucker type necessary conditions for efficient solution are given, and the Kuhn-Tucker type sufficient conditions for efficient solution are presented under the assumptions of （F, α, ρ, d）-V-convexity. Subsequently, the optimality conditions for two kinds of duality models are formulated and duality theorems are proved.展开更多
An optimized nonlinear grey Bernoulli model was proposed by using a particle swarm optimization algorithm to solve the parameter optimization problem. In addition, each item in the first-order accumulated generating s...An optimized nonlinear grey Bernoulli model was proposed by using a particle swarm optimization algorithm to solve the parameter optimization problem. In addition, each item in the first-order accumulated generating sequence was set in turn as an initial condition to determine which alternative would yield the highest forecasting accuracy. To test the forecasting performance, the optimized models with different initial conditions were then used to simulate dissolved oxygen concentrations in the Guantlng reservoir inlet and outlet （China）. The empirical results show that the optimized model can remarkably improve forecasting accuracy, and the particle swarm optimization technique is a good tool to solve parameter optimization problems. What＇s more, the optimized model with an initial condition that performs well in in-sample simulation may not do as well as in out-of-sample forecasting.展开更多
In this paper, we introduce generalized essentially pseudoconvex function and generalized essentially quasiconvex function, and give sufficient optimality conditions of the nonsmooth generalized convex multi-objective...In this paper, we introduce generalized essentially pseudoconvex function and generalized essentially quasiconvex function, and give sufficient optimality conditions of the nonsmooth generalized convex multi-objective programming and its saddle point theorem about cone efficient solution. We set up Mond-Weir type duality and Craven type duality for nonsmooth multiobjective programming with generalized essentially convex functions, and prove them.展开更多
According to the design principle of the central composite experimental,the method of response surface analysis with three factors and three levels was adopted based on one factor test.A second-order quadratic equatio...According to the design principle of the central composite experimental,the method of response surface analysis with three factors and three levels was adopted based on one factor test.A second-order quadratic equation for photocatalysis of Procion Red MX-5B was built.Response surface and contour were graphed with the decoloration rate of Procion Red MX-5B as the response value.Based on the analysis of the response surface plots and their corresponding contour plots,effects of pH value,irradiation time and catalyst loading were explored.By using this new method,the optimum decoloration condition was obtained as follows:pH value,1.3;irradiation time,49.9 min;catalyst loading,0.57 g/L.In the optimization,R-Squared and Adj R-Squared correlation coefficients for quadratic model were evaluated quite satisfactorily as 0.9310 and 0.8620,respectively.Under the optimum conditions established,the performance of 99.47% for color removal was experimentally reached.It was found that all factors considered have an important effect on the decolorization efficiency of Procion Red MX-5B.By the ANOVA analysis and model confirmation the optimal solution obtained using RSM was experimentally validated and credible with preferable instructional ability for experiments.展开更多
In the present study, a response surface methodology was used to optimize the electroleaching of Mn from low-grade pyrolusite. Ferrous sulfate heptahydrate was used in this reaction as a reducing agent in sulfuric aci...In the present study, a response surface methodology was used to optimize the electroleaching of Mn from low-grade pyrolusite. Ferrous sulfate heptahydrate was used in this reaction as a reducing agent in sulfuric acid solutions. The effect of six process variables, including the mass ratio of ferrous sulfate heptahydrate to pyrolusite, mass ratio of sulfuric acid to pyrolusite, liquid-to-solid ratio, current density, leaching temperature, and leaching time, as well as their binary interactions, were modeled. The results revealed that the order of these factors with respect to their effects on the leaching efficiency were mass ratio of ferrous sulfate heptahydrate to pyrolusite 〉 leaching time 〉 mass ratio of sulfuric acid to pyrolusite 〉 liquid-to-solid ratio 〉 leaching temperature 〉 current density. The optimum conditions were as follows： 1.10：1 mass ratio of ferrous sulfate heptahydrate to pyrolusite, 0.9：1 mass ratio of sulfuric acid to pyrolusite, liquid-to-solid ratio of 0.7：1, current density of 947 A/m^2, leaching time of 180 min, and leaching temperature of 73°C. Under these conditions, the predicted leaching efficiency for Mn was 94.1%; the obtained experimental result was 95.7%, which confirmed the validity of the model.展开更多
In this paper, necessary optimality conditions for a class of Semi-infinite Variational Problems are established which are further generalized to a class of Multi-objective Semi-Infinite Variational Problems. These co...In this paper, necessary optimality conditions for a class of Semi-infinite Variational Problems are established which are further generalized to a class of Multi-objective Semi-Infinite Variational Problems. These conditions are responsible for the development of duality theory which is an extremely important feature for any class of problems, but the literature available so far lacks these necessary optimality conditions for the stated problem. A lemma is also proved to find the topological dual of as it is required to prove the desired result.展开更多
There are two approaches of defining the solutions of a set-valued optimization problem： vector criterion and set criterion. This note is devoted to higher-order optimality conditions using both criteria of solutions...There are two approaches of defining the solutions of a set-valued optimization problem： vector criterion and set criterion. This note is devoted to higher-order optimality conditions using both criteria of solutions for a constrained set-valued optimization problem in terms of higher-order radial derivatives. In the case of vector criterion, some optimality conditions are derived for isolated （weak） minimizers. With set criterion, necessary and sufficient optimality conditions are established for minimal solutions relative to lower set-order relation.展开更多
Sparse optimization has witnessed advancements in recent decades,and the step function finds extensive applications across various machine learning and signal processing domains.This paper integrates zero norm and the...Sparse optimization has witnessed advancements in recent decades,and the step function finds extensive applications across various machine learning and signal processing domains.This paper integrates zero norm and the step function to formulate a doublesparsity constrained optimization problem,wherein a linear equality constraint is also taken into consideration.By defining aτ-Lagrangian stationary point and a KKT point,we establish the first-order and second-order necessary and sufficient optimality conditions for the problem.Furthermore,we thoroughly elucidate their relationships to local and global optimal solutions.Finally,special cases and examples are presented to illustrate the obtained theorems.展开更多
Numerical simulation of turbulent mixing process of polydisperse quartz particle(particle size distribution in the range of 0.1-0.4 mm)flow with Ar and Ar-H2 plasma generated by radio frequency inductively coupled pla...Numerical simulation of turbulent mixing process of polydisperse quartz particle(particle size distribution in the range of 0.1-0.4 mm)flow with Ar and Ar-H2 plasma generated by radio frequency inductively coupled plasma(RF-ICP)torch has been made.An approximate two-stage approach has been proposed to calculate the spatial-temporal distributions of temperature and resulting thermal stress in quartz particles during dynamic heating in polydisperse plasma flow.The influence of working gas compositions,particle size distributions,injection angle and flow rate of carrier gas on the thermal destruction conditions of quartz particles has been determined under different particle feed rates.It is found that all the solid quartz particles(0.1-0.4 mm)could be thermal destructed without overheating in RF-ICP torch system,when the hydrogen volume fraction in working gases is more than 1.5%-2%and particle feed rate is in a certain range.The values of the maximum and minimum feed rates have been determined under different hydrogen volume fractions.An optimal particle injection angle and flow rate of carrier gas is found around 50°-60°and 160-220 slpm,under which the value of maximum equivalent thermal stress in quartz particles is highest.展开更多
In this paper, we establish a second-order sufficient condition for constrained optimization problems of a class of so called t-stable functions in terms of the first-order and the second-order Dini type directional d...In this paper, we establish a second-order sufficient condition for constrained optimization problems of a class of so called t-stable functions in terms of the first-order and the second-order Dini type directional derivatives. The result extends the corresponding result of [D. Bednarik and K. Pastor, Math. Program. Ser. A, 113（2008）, 283-298] to constrained optimization problems.展开更多
文摘This paper deals with extensions of higher-order optimality conditions for scalar optimization to multiobjective optimization.A type of directional derivatives for a multiobjective function is proposed,and with this notion characterizations of strict local minima of order k for a multiobjective optimization problem with a nonempty set constraint are established,generalizing the corresponding scalar case obtained by Studniarski[3].Also necessary not sufficient and sufficient not necessary optimality conditions for this minima are derived based on our directional derivatives,which are generalizations of some existing scalar results and equivalent to some existing multiobjective ones.Many examples are given to illustrate them there.
基金funded by the KRICT Project (KK2512-10) of the Korea Research Institute of Chemical Technology and the Ministry of Trade, Industry and Energy (MOTIE)the Korea Institute for Advancement of Technology (KIAT) through the Virtual Engineering Platform Program (P0022334)+1 种基金supported by the Carbon Neutral Industrial Strategic Technology Development Program (RS-202300261088) funded by the Ministry of Trade, Industry & Energy (MOTIE, Korea)Further support was provided by research fund of Chungnam National University。
文摘Bifunctional oxide-zeolite-based composites(OXZEO)have emerged as promising materials for the direct conversion of syngas to olefins.However,experimental screening and optimization of reaction parameters remain resource-intensive.To address this challenge,we implemented a three-stage framework integrating machine learning,Bayesian optimization,and experimental validation,utilizing a carefully curated dataset from the literature.Our ensemble-tree model(R^(2)>0.87)identified Zn-Zr and Cu-Mg binary mixed oxides as the most effective OXZEO systems,with their light olefin space-time yields confirmed by physically mixing with HSAPO-34 through experimental validation.Density functional theory calculations further elucidated the activity trends between Zn-Zr and Cu-Mg mixed oxides.Among 16 catalyst and reaction condition descriptors,the oxide/zeolite ratio,reaction temperature,and pressure emerged as the most significant factors.This interpretable,data-driven framework offers a versatile approach that can be applied to other catalytic processes,providing a powerful tool for experiment design and optimization in catalysis.
基金the Shenhuo Mining Group Co.Ltd.,China for its financial support.At the same time,we also thank the National Natural Science Foundation of China(No.40373044)the Natural Science Foundation of Jiangsu Province (No.05KJD610209) for their supportthe Jiangsu Key Laboratory of Resources and Environmental Information Engineering for its technical support.
文摘We studied how bioflocculants,produced by white-rot fungi,affect flocculation in slime water.Based on a test in an orthogonal design,flocculation conditions were optimized.The results show that flocculation activity is at its highest when the following conditions are met:slime water concentration 27.42 g/L;coagulant aid(CaCl_2) mass concentration 5.0 g/L;two-segment stirrings:the first at a stirring speed of 60 r/min for 180 s and the second 180 r/min for 60 s;a pH of 11 and a flocculant concentration of 15 mL/L.The flocculation activity can be up to 98.71%of bioflocculants at the time.Further experiments indicate that most of the flocculation active material is found outside the mycelium cells.This is the extracellular secretion produced by mycelium cells during the fermentation process.This flocculant has strong thermal stability.Many kinds of cations have a flocculation function to assist bioflocculants.This aid-flocculation effect of the divalent cation Ca^(2+) is obvious in the bioflocculant produced by the white-rot fungus.Therefore,this is of great value when applied to control engineering in the battle against water pollution.
文摘In this paper, both Fritz John and Karush-Kuhn-Tucker necessary optimality conditions are established for a （weakly） LU-efficient solution in the considered nonsmooth multiobjective programming problem with the multiple interval-objective function. Further, the sufficient optimality conditions for a （weakly） LU-efficient solution and several duality results in Mond-Weir sense are proved under assumptions that the functions constituting the considered nondifferentiable multiobjective programming problem with the multiple interval- objective function are convex.
基金This work was supported by National Natural Science Foundation of China (10401041)Natural Science Foundation of Hubei Province (2004ABA009)
文摘This article is concerned with second-order necessary and sufficient optimality conditions for optimal control problems governed by 3-dimensional Navier-Stokes equations. The periodic state constraint is considered.
基金Supported by the National Basic Research Program of China(973 Program,2012CB215000)
文摘Pjridine has been generally synthesized by aldehydes and ammonia in a turbulent fluidized-bed reactor. In this paper, a novel riser reactor was proposed for pyridine synthesis. Experiment result showed that the yield of pyridine and 3-picoline decreased, but the selectivity of pyridine over 3-picoline increased compared to turbulent fluidized-bed reactor. Based on experimental data, a modified kinetic model was used for the determination of optimal operating condition for riser reactor. The optimal operating condition of riser reactor given by this modified model was as follows： The reaction temperature of 755 K, catalyst to feedstock ratio （CTFR） of 87, residence timeof3.8sandinitialacetaldehydesconcentrationof0.0029mol.L-1 （acetaldehydes to formaldehydes ratio by mole （ATFR） of 0.65 and ammonia to aldehydes ratio by mole （ATAR） of 0.9, water contention of 63wt% （formaldehyde solution））.
基金Supported by the NSF of Shaanxi Provincial Educational Department(06JK152)
文摘New classes of functions namely (V, ρ)_(h,φ)-type I, quasi (V, ρ)_(h,φ)-type I and pseudo (V, ρ)_(h,φ)-type I functions are defined for multiobjective programming problem by using BenTal's generalized algebraic operation. The examples of (V, ρ)_(h,φ)-type I functions are given. The sufficient optimality conditions are obtained for multi-objective programming problem involving above new generalized convexity.
基金the National Natural Science Foundation(69972036) and the Natural Science Foundation of Shanxi province(995L02)
文摘The concepts of alpha-order Clarke's derivative, alpha-order Adjacent derivative and alpha-order G.Bouligand derivative of set-valued mappings are introduced, their properties are studied, with which the Fritz John optimality condition of set-valued vector optimization is established. Finally, under the assumption of pseudoconvexity, the optimality condition is proved to be sufficient.
基金Project (No. Y304203) supported by the Natural Science Foundationof Zhejiang Province, China
文摘The solubilization of elastin by Bacillus licheniformis elastase cannot be analyzed by conventional kinetic methods because the biologically relevant substrate is insoluble and the concentration of enzyme-substrate complex has no physical meaning. In this paper we report the optimization of elastolysis conditions and analysis of elastolytic kinetics. Our results indicated that the hydrolyzing temperature and time are very important factors affecting elastolysis rate. The optimized conditions using central composite design were as follows： elastolysis temperature 50 ℃, elastase concentration 1 × 10^4 U/ml, elastin 80 mg, elastolytic time 4 h. Investigation of the effects of substrate content, elastase concentration and pH was also revealed that low or high elastin content inhibits the elastolysis process. Increasingelastase improves elastin degradation, but high elastase may change the kinetics characterization. Alkaline environment can decrease elastin degradation rate and pH may affect elastolysis by changing elastase reaction pH. To further elucidate the elastolysis process, the logistic model was used to elastolysis kinetics study showing clearly that the logistic model can reasonably explain the elastolysis process, especially under lower elastase concentration. However, there is still need for more investigations with the aid of other methods, such as biochemical and molecular methods.
文摘Quadratic 0-1 problems with linear inequality constraints are briefly considered in this paper.Global optimality conditions for these problems,including a necessary condition and some sufficient conditions,are presented.The necessary condition is expressed without dual variables.The relations between the global optimal solutions of nonconvex quadratic 0-1 problems and the associated relaxed convex problems are also studied.
基金Supported by Chongqing Key Lab. of Operations Research and System Engineering
文摘This paper studies a class of multiobjective generalized fractional programming problems, where the numerators of objective functions are the sum of differentiable function and convex function, while the denominators are the difference of differentiable function and convex function. Under the assumption of Calmness Constraint Qualification the Kuhn-Tucker type necessary conditions for efficient solution are given, and the Kuhn-Tucker type sufficient conditions for efficient solution are presented under the assumptions of （F, α, ρ, d）-V-convexity. Subsequently, the optimality conditions for two kinds of duality models are formulated and duality theorems are proved.
基金supported by the National Natural Science Foundation of China (Nos. 51178018 and 71031001)
文摘An optimized nonlinear grey Bernoulli model was proposed by using a particle swarm optimization algorithm to solve the parameter optimization problem. In addition, each item in the first-order accumulated generating sequence was set in turn as an initial condition to determine which alternative would yield the highest forecasting accuracy. To test the forecasting performance, the optimized models with different initial conditions were then used to simulate dissolved oxygen concentrations in the Guantlng reservoir inlet and outlet （China）. The empirical results show that the optimized model can remarkably improve forecasting accuracy, and the particle swarm optimization technique is a good tool to solve parameter optimization problems. What＇s more, the optimized model with an initial condition that performs well in in-sample simulation may not do as well as in out-of-sample forecasting.
文摘In this paper, we introduce generalized essentially pseudoconvex function and generalized essentially quasiconvex function, and give sufficient optimality conditions of the nonsmooth generalized convex multi-objective programming and its saddle point theorem about cone efficient solution. We set up Mond-Weir type duality and Craven type duality for nonsmooth multiobjective programming with generalized essentially convex functions, and prove them.
基金Sponsored by the National Natural Science Foundation of China (Grant No. 51078100)the National Creative Research Groups granted by NSFC(Grant No. 50821002)+1 种基金Excellent Youth Foundation of Heilongjiang Scientific Committee(Grant No. JC2010-03)State Key Laboratory of Urban Water Resource and Environment(Grant No. 2010DX11)
文摘According to the design principle of the central composite experimental,the method of response surface analysis with three factors and three levels was adopted based on one factor test.A second-order quadratic equation for photocatalysis of Procion Red MX-5B was built.Response surface and contour were graphed with the decoloration rate of Procion Red MX-5B as the response value.Based on the analysis of the response surface plots and their corresponding contour plots,effects of pH value,irradiation time and catalyst loading were explored.By using this new method,the optimum decoloration condition was obtained as follows:pH value,1.3;irradiation time,49.9 min;catalyst loading,0.57 g/L.In the optimization,R-Squared and Adj R-Squared correlation coefficients for quadratic model were evaluated quite satisfactorily as 0.9310 and 0.8620,respectively.Under the optimum conditions established,the performance of 99.47% for color removal was experimentally reached.It was found that all factors considered have an important effect on the decolorization efficiency of Procion Red MX-5B.By the ANOVA analysis and model confirmation the optimal solution obtained using RSM was experimentally validated and credible with preferable instructional ability for experiments.
基金financially supported by the "121" Scientific and Technological Supporting Demonstration Project of Chongqing, China (No. cstc2014zktjccx B0043)the Scientific Research and Technology Development Program of Guangxi, China (No. 2014BA10016)
文摘In the present study, a response surface methodology was used to optimize the electroleaching of Mn from low-grade pyrolusite. Ferrous sulfate heptahydrate was used in this reaction as a reducing agent in sulfuric acid solutions. The effect of six process variables, including the mass ratio of ferrous sulfate heptahydrate to pyrolusite, mass ratio of sulfuric acid to pyrolusite, liquid-to-solid ratio, current density, leaching temperature, and leaching time, as well as their binary interactions, were modeled. The results revealed that the order of these factors with respect to their effects on the leaching efficiency were mass ratio of ferrous sulfate heptahydrate to pyrolusite 〉 leaching time 〉 mass ratio of sulfuric acid to pyrolusite 〉 liquid-to-solid ratio 〉 leaching temperature 〉 current density. The optimum conditions were as follows： 1.10：1 mass ratio of ferrous sulfate heptahydrate to pyrolusite, 0.9：1 mass ratio of sulfuric acid to pyrolusite, liquid-to-solid ratio of 0.7：1, current density of 947 A/m^2, leaching time of 180 min, and leaching temperature of 73°C. Under these conditions, the predicted leaching efficiency for Mn was 94.1%; the obtained experimental result was 95.7%, which confirmed the validity of the model.
文摘In this paper, necessary optimality conditions for a class of Semi-infinite Variational Problems are established which are further generalized to a class of Multi-objective Semi-Infinite Variational Problems. These conditions are responsible for the development of duality theory which is an extremely important feature for any class of problems, but the literature available so far lacks these necessary optimality conditions for the stated problem. A lemma is also proved to find the topological dual of as it is required to prove the desired result.
基金Supported by the National Natural Science Foundation of China(11361001)Natural Science Foundation of Ningxia(NZ14101)
文摘There are two approaches of defining the solutions of a set-valued optimization problem： vector criterion and set criterion. This note is devoted to higher-order optimality conditions using both criteria of solutions for a constrained set-valued optimization problem in terms of higher-order radial derivatives. In the case of vector criterion, some optimality conditions are derived for isolated （weak） minimizers. With set criterion, necessary and sufficient optimality conditions are established for minimal solutions relative to lower set-order relation.
基金Supported by the National Key R&D Program of China(No.2023YFA1011100)NSFC(No.12131004)。
文摘Sparse optimization has witnessed advancements in recent decades,and the step function finds extensive applications across various machine learning and signal processing domains.This paper integrates zero norm and the step function to formulate a doublesparsity constrained optimization problem,wherein a linear equality constraint is also taken into consideration.By defining aτ-Lagrangian stationary point and a KKT point,we establish the first-order and second-order necessary and sufficient optimality conditions for the problem.Furthermore,we thoroughly elucidate their relationships to local and global optimal solutions.Finally,special cases and examples are presented to illustrate the obtained theorems.
文摘Numerical simulation of turbulent mixing process of polydisperse quartz particle(particle size distribution in the range of 0.1-0.4 mm)flow with Ar and Ar-H2 plasma generated by radio frequency inductively coupled plasma(RF-ICP)torch has been made.An approximate two-stage approach has been proposed to calculate the spatial-temporal distributions of temperature and resulting thermal stress in quartz particles during dynamic heating in polydisperse plasma flow.The influence of working gas compositions,particle size distributions,injection angle and flow rate of carrier gas on the thermal destruction conditions of quartz particles has been determined under different particle feed rates.It is found that all the solid quartz particles(0.1-0.4 mm)could be thermal destructed without overheating in RF-ICP torch system,when the hydrogen volume fraction in working gases is more than 1.5%-2%and particle feed rate is in a certain range.The values of the maximum and minimum feed rates have been determined under different hydrogen volume fractions.An optimal particle injection angle and flow rate of carrier gas is found around 50°-60°and 160-220 slpm,under which the value of maximum equivalent thermal stress in quartz particles is highest.
基金The Graduate Students Innovate Scientific Research Program (YJSCX2008-158HLJ) of Heilongjiang Provincesupported by the Distinguished Young Scholar Foundation (JC200707) of Heilongjiang Province of China
文摘In this paper, we establish a second-order sufficient condition for constrained optimization problems of a class of so called t-stable functions in terms of the first-order and the second-order Dini type directional derivatives. The result extends the corresponding result of [D. Bednarik and K. Pastor, Math. Program. Ser. A, 113（2008）, 283-298] to constrained optimization problems.
