In this paper the upper semi-continuity of global attractors for multivalued semi-flows under random perturbation was studied. First, the existence of random attractors for multivalued random semi-flows was considered...In this paper the upper semi-continuity of global attractors for multivalued semi-flows under random perturbation was studied. First, the existence of random attractors for multivalued random semi-flows was considered, then it was proved that the global attractors for multivalue semi-flows are the upper semi-continuity under random perturbation. This result can be used in the numerical approximation of multivalued semi-flows and non-autonomous perturbation of multivalued semi-flows.展开更多
This paper is concerned with the existence and upper semi-continuity of random attractors for the nonclassical diffusion equation with arbitrary polynomial growth nonlinearity and multiplicative noise in H<sup>1...This paper is concerned with the existence and upper semi-continuity of random attractors for the nonclassical diffusion equation with arbitrary polynomial growth nonlinearity and multiplicative noise in H<sup>1</sup>(R<sup>n</sup>). First, we study the existence and uniqueness of solutions by a noise arising in a continuous random dynamical system and the asymptotic compactness is established by using uniform tail estimate technique, and then the existence of random attractors for the nonclassical diffusion equation with arbitrary polynomial growth nonlinearity. As a motivation of our results, we prove an existence and upper semi-continuity of random attractors with respect to the nonlinearity that enters the system together with the noise.展开更多
This paper introduces the concept of semi-continuity of complex fuzzy functions, and discusses some of their elementary properties, such as the sum of two complex fuzzy functions of type I upper (lower) semi-continui...This paper introduces the concept of semi-continuity of complex fuzzy functions, and discusses some of their elementary properties, such as the sum of two complex fuzzy functions of type I upper (lower) semi-continuity is type I upper (lower) semi-continuous, and the opposite of complex fuzzy functions of type I upper (lower) semi-continuity is type I lower (upper) semi-continuous. Based on some assumptions on two complex fuzzy functions of type I upper (lower) semi-continuity, it is shown that their product is type I upper (lower) semi-continuous. The paper also investigates the convergence of complex fuzzy functions. In particular, sign theorem, boundedness theorem, and Cauchy's criterion for convergence are kept. In this paper the metrics introduced by Zhang Guangquan was used. This paper gives a contribution to the study of complex fuzzy functions, and extends the corresponding work of Zhang Guangquan.展开更多
In this paper, we characterize lower semi-continuous pseudo-convex functions f : X → R ∪ {+ ∞} on convex subset of real Banach spaces K ⊂ X with respect to the pseudo-monotonicity of its Clarke-Rockafellar Su...In this paper, we characterize lower semi-continuous pseudo-convex functions f : X → R ∪ {+ ∞} on convex subset of real Banach spaces K ⊂ X with respect to the pseudo-monotonicity of its Clarke-Rockafellar Sub-differential. We extend the results on the characterizations of non-smooth convex functions f : X → R ∪ {+ ∞} on convex subset of real Banach spaces K ⊂ X with respect to the monotonicity of its sub-differentials to the lower semi-continuous pseudo-convex functions on real Banach spaces.展开更多
The purpose of this paper is to make a further study on the abstract economy. Here, for the constraint correspondences we assume that they are almost lower semi-continuous (n-lower semi-continuous), which is weaken th...The purpose of this paper is to make a further study on the abstract economy. Here, for the constraint correspondences we assume that they are almost lower semi-continuous (n-lower semi-continuous), which is weaken than that they are lower semi-continuous. Several equilibria existence theorems are proved.展开更多
The 2024/3003 aluminum gradient alloys are prepared by semi continuous casting. The influences of throttle bore diameter of embedded nozzle and temperature of internal melt on composition distribution, macrostructure,...The 2024/3003 aluminum gradient alloys are prepared by semi continuous casting. The influences of throttle bore diameter of embedded nozzle and temperature of internal melt on composition distribution, macrostructure, hardness are analyzed, and the stability of gradient distribution of composition, macrostructure and hardness along the axial direction of the ingot is also studied. The results show that diffe rent composition profiles can be achieved by adjusting the processing parameters; the volume fraction of inner alloy in the ingot can be increased by enlarging the throttle bore diameter and elevating the temperature of inner melt; quasi steady solidification can be realized within 20 s during cast processing, and consistent quality ingot is obtained by controlling the casting speed and liquid height of inner melt.展开更多
Continuous and semi-continuous mining technology has become the main trend of modern surface mines in the world. According to the deposit characteristics of coal basin in China and Chinese situation,this paper discuss...Continuous and semi-continuous mining technology has become the main trend of modern surface mines in the world. According to the deposit characteristics of coal basin in China and Chinese situation,this paper discussed the new semi-continuous technology── shovel - transfer wagon-belt conveyor and its application prospect in large surface coal mines in China.展开更多
Mg-9Gd-3Y-1.5Zn-0.8Zr alloys own high strength,good heat and corrosion resistance.However,it is difficult for the fabrication of large-scale billets,due to the poor deformation ability and strong hot-crack tendency.Th...Mg-9Gd-3Y-1.5Zn-0.8Zr alloys own high strength,good heat and corrosion resistance.However,it is difficult for the fabrication of large-scale billets,due to the poor deformation ability and strong hot-crack tendency.This work investigated the casting process on the microstructures and flow stress behaviors of the semi-continuous casting billets for the fabrication of large-scale Mg-9Gd-3Y-1.5Zn-0.8Zr billets.The casting process(electromagnetic intensity and casting speed)shows outstanding effects on the microstructures and flow stress behavior of the billets.The billets with the specific casting process(I=68 A,V=65 mm/min)exhibit uniform microstructures and good deformation uniformity.展开更多
The microstucture,mechanical properties and fracture behaviors of semi-continuous cast Mg-8Gd-3Y-0.5Zr(wt.%,GW83K) alloy after different heat treatments were investigated.Almost all the eutectic compounds were dissolv...The microstucture,mechanical properties and fracture behaviors of semi-continuous cast Mg-8Gd-3Y-0.5Zr(wt.%,GW83K) alloy after different heat treatments were investigated.Almost all the eutectic compounds were dissolved into the matrix and there was no evident grain growth after optimum solution treatment at 500 ℃for 4h.Further ageing at low temperatures led to significant precipitation hardening,which strengthened the alloy.Peak-aged at 200 ℃,the alloy had the highest ultimate tensile strength(UTS) and lowest elongation at 395 MPa and 2.8%,respectively.When aged at 225 ℃ for 15 h,the alloy exhibited prominent mechanical performance with UTS and elongation of 363 MPa and 5.8%,respectively.With regard to microstructure and tensile properties,the processes of 500 ℃,4h+225℃,15 h are selected as the optimal heat treatment conditions.The alloy under different conditions shows different fracture behaviors:in the as-cast alloy,a quasi-cleavage pattern is observed;after solution treatment,the alloy exhibits a trans-granular quasi-cleavage fracture;after being peak-aged at 200 ℃ and 225 ℃,the fracture mode is a mixed mode of trans-granular and intergranular fracture,in which the inter-granular mode is dominant in the alloy peak-aged at 200 ℃.展开更多
The massive consumption of fossil energy force s people to find new source s of energy.Syngas fermentation has become a hot research field as its high potential in renewable energy production and sustainable developme...The massive consumption of fossil energy force s people to find new source s of energy.Syngas fermentation has become a hot research field as its high potential in renewable energy production and sustainable development.In this study,trophic anaerobic acetogen Morella thermoacetica was successfully immobilized by calcium alginate embedding method.The ability of the immobilized cells on production of acetic acid through syngas fermentation was compared in both airlift and bubble column bioreactors.The bubble column bioreactor was selected as the better type of bioreactor.The production of acetic acid reached 32.3 g·L^(-1) in bubble column bioreactor with a space-time yield of 2.13 g·L^(-1)·d^(-1).The immobilized acetogen could be efficiently reused without significant lag period,even if exposed to air for a short time.A semi-continuous syngas fermentation was performed using immobilized cells,with an average space-time acetic acid yield of 3.20 g·L^(-1)·d^(-1).After 30 days of fermentation,no significant decrea se of the acetic acid production rate was observed.展开更多
For the large magnesium alloy ingot, there is a considerable difference in cooling rate of different parts in the ingot, which leads to non-uniform distribution of the secondary phases, solute segregation and tensile ...For the large magnesium alloy ingot, there is a considerable difference in cooling rate of different parts in the ingot, which leads to non-uniform distribution of the secondary phases, solute segregation and tensile properties. In the present research, an heavy AZ61 alloy ingot with a diameter of 500 mm was made by semi-continuous casting. The microstructure and mechanical properties at different positions along the radial direction of the large ingot were investigated by using an optical microscope(OM), a scanning electron microscope(SEM), an energy dispersive spectroscope(EDS), and a micro-hardness tester. The results indicate that the microstructure of the AZ61 ingot is non-uniform in different locations. It changes from equiaxed to columnar grains from the center to the edge; the average grain size gradually reduces from 1,005 μm to 763 μm, the secondary dendrite arm spacing reduces from 78 μm to 50 μm, and the Mg17(Al,Zn)12 phase is also refined. The micro-hardness value increases from 55.4 HV at the center to 72.5 HV at the edge of the ingot due to the microstructure differences, and the distribution of micro-hardness at the edge of the ingot is more uniform than that in the center. The tensile properties at room temperature show little difference from the center to the edge of the ingot except that the elongation at the edge is only 3.5%, much lower than that at other areas. The fracture mechanism is ductile fracture at the center and cleavage fracture at the edge of the ingot, and at the 1/2 radius of the ingot, a mixture of ductile and cleavage fracture is present.展开更多
The semi-continuous casting of ZK60 magnesium alloy under different middle frequency electromagnetic field conditions was examined.Effects of middle frequency electromagnetic field on microstructure,precipitations and...The semi-continuous casting of ZK60 magnesium alloy under different middle frequency electromagnetic field conditions was examined.Effects of middle frequency electromagnetic field on microstructure,precipitations and tensile properties are investigated.The results show that the microstructures of ZK60 magnesium alloy are refined and distribution uniformity of precipitations is observed after applying the middle frequency electromagnetic field.And the tensile properties of the billets produced by middle frequency electromagnetic field are increased.展开更多
Cooling heat flux effect in both primary and secondary cooling zone has been studied in semi-continuous casting of copper billet. Sufficient cooling is essential to reduce casting defects and to get high productivity,...Cooling heat flux effect in both primary and secondary cooling zone has been studied in semi-continuous casting of copper billet. Sufficient cooling is essential to reduce casting defects and to get high productivity, however low rate of solidification is aimed in order to get coarser grain size and softer metal for less losses in extrusion. A three-dimensional numerical model has been developed including solidification behavior of copper through mushy zone. At steady state and constant casting speed, solid shell thickness is monitored during the reduction of cooling rate at mould region to avoid breaking out. Heat flux intensity at mould plays important role not only in the formation of solid shell thickness. But, pool length and mushy zone thickness can be significantly increased by decreasing primary cooling intensity. Increase intensity of secondary cooling zone for two particular cases of primary cooling is tested. First case is tested at mould inlet water temperature of 38°C, and second case at water temperature of 63°C. Results showed that the combination of increasing secondary cooling intensity and reduction of primary cooling intensity can increase pool length and mushy zone thickness. Also, it is shown that, secondary cooling intensity can be magnified by up to 1.5 times for cooling water temperature of 63°C to get pool length close to that of water temperature of 38°C.展开更多
In this paper, we study the regularization methods to approximate the solutions of the variational inequalities with monotone hemi-continuous operator having perturbed operators arbitrary. Detail, we shall study regul...In this paper, we study the regularization methods to approximate the solutions of the variational inequalities with monotone hemi-continuous operator having perturbed operators arbitrary. Detail, we shall study regularization methods to approximate solutions of following variational inequalities: and with operator A being monotone hemi-continuous form real Banach reflexive X into its dual space X*, but instead of knowing the exact data (y<sub>0</sub>, A), we only know its approximate data satisfying certain specified conditions and D is a nonempty convex closed subset of X;the real function f defined on X is assumed to be lower semi-continuous, convex and is not identical to infinity. At the same time, we will evaluate the convergence rate of the approximate solution. The regularization methods here are different from the previous ones.展开更多
Let S = {1,1/2,1/2^2,…,1/∞ = 0} and I = [0, 1] be the unit interval. We use ↓USC(S) and ↓C(S) to denote the families of the regions below of all upper semi-continuous maps and of the regions below of all conti...Let S = {1,1/2,1/2^2,…,1/∞ = 0} and I = [0, 1] be the unit interval. We use ↓USC(S) and ↓C(S) to denote the families of the regions below of all upper semi-continuous maps and of the regions below of all continuous maps from S to I and ↓C0(S) = {↓f∈↓C(S) : f(0) = 0}. ↓USC(S) endowed with the Vietoris topology is a topological space. A pair of topological spaces (X, Y) means that X is a topological space and Y is its subspace. Two pairs of topological spaces (X, Y) and (A, B) are called pair-homeomorphic (≈) if there exists a homeomorphism h : X→A from X onto A such that h(Y) = B. It is proved that, (↓USC(S),↓C0(S)) ≈(Q, s) and (↓USC(S),↓C(S)/ ↓C0(S))≈(Q, c0), where Q = [-1,1]^ω is the Hilbert cube and s = (-1,1)^ω,c0= {(xn)∈Q : limn→∞= 0}. But we do not know what (↓USC(S),↓C(S))is.展开更多
The perturbation problem of generalized inverse is studied. And some new stability characteristics of generalized inverses were presented. It was also proved that the stability characteristics of generalized inverses ...The perturbation problem of generalized inverse is studied. And some new stability characteristics of generalized inverses were presented. It was also proved that the stability characteristics of generalized inverses were independent of the choice of the generalized inverse. Based on this result, two sufficient and necessary conditions for the lower semi-continuity of generalized inverses as the set-valued mappings are given.展开更多
In the present paper the concept and properties of the residual functional in Sobolev space are investigated. The weak compactness, force condition, lower semi-continuity and convex of the residual functional are prov...In the present paper the concept and properties of the residual functional in Sobolev space are investigated. The weak compactness, force condition, lower semi-continuity and convex of the residual functional are proved. In Sobolev space, the minimum principle of the residual functional is proposed. The minimum existence theoreomfor J(u) =0 is given by the modern critical point theory. And the equivalence theorem or five equivalence forms for the residual functional equation are also proved.展开更多
The dynamics of set value mapping is considered. For the upper semi-continuous set value maps, the existence of attractors under some conditions and the upper semi-continuity of attractors under the perturbation are p...The dynamics of set value mapping is considered. For the upper semi-continuous set value maps, the existence of attractors under some conditions and the upper semi-continuity of attractors under the perturbation are proved. Its application in numerical simulation of differential equation is also considered. The upper semi-continuity of attractors in set value maps under the perturbation is used to show the reasonable of subdivision algorithm and interval arithmetic in numerical simulation of differential equation.展开更多
In this paper, using the context of complete partial metric spaces, some common fixed point results of maps that satisfy the generalized (ψ, Ф)-weak contractive conditions are obtained. Our results generalize, ext...In this paper, using the context of complete partial metric spaces, some common fixed point results of maps that satisfy the generalized (ψ, Ф)-weak contractive conditions are obtained. Our results generalize, extend, unify, enrich and complement many existing results in the literature. Example are given showing the validaty of our results.展开更多
基金Project supported by National Natural Science Foundation of China (Grant No. 10571130)
文摘In this paper the upper semi-continuity of global attractors for multivalued semi-flows under random perturbation was studied. First, the existence of random attractors for multivalued random semi-flows was considered, then it was proved that the global attractors for multivalue semi-flows are the upper semi-continuity under random perturbation. This result can be used in the numerical approximation of multivalued semi-flows and non-autonomous perturbation of multivalued semi-flows.
文摘This paper is concerned with the existence and upper semi-continuity of random attractors for the nonclassical diffusion equation with arbitrary polynomial growth nonlinearity and multiplicative noise in H<sup>1</sup>(R<sup>n</sup>). First, we study the existence and uniqueness of solutions by a noise arising in a continuous random dynamical system and the asymptotic compactness is established by using uniform tail estimate technique, and then the existence of random attractors for the nonclassical diffusion equation with arbitrary polynomial growth nonlinearity. As a motivation of our results, we prove an existence and upper semi-continuity of random attractors with respect to the nonlinearity that enters the system together with the noise.
基金Supported by the National Natural Science Foundationof China ( No. 10 2 710 35 ) and the MultidiscilineScientific Research Fund of Harbin Institute ofTechnology ( HIT.MD. 2 0 0 0 . 2 1)
文摘This paper introduces the concept of semi-continuity of complex fuzzy functions, and discusses some of their elementary properties, such as the sum of two complex fuzzy functions of type I upper (lower) semi-continuity is type I upper (lower) semi-continuous, and the opposite of complex fuzzy functions of type I upper (lower) semi-continuity is type I lower (upper) semi-continuous. Based on some assumptions on two complex fuzzy functions of type I upper (lower) semi-continuity, it is shown that their product is type I upper (lower) semi-continuous. The paper also investigates the convergence of complex fuzzy functions. In particular, sign theorem, boundedness theorem, and Cauchy's criterion for convergence are kept. In this paper the metrics introduced by Zhang Guangquan was used. This paper gives a contribution to the study of complex fuzzy functions, and extends the corresponding work of Zhang Guangquan.
文摘In this paper, we characterize lower semi-continuous pseudo-convex functions f : X → R ∪ {+ ∞} on convex subset of real Banach spaces K ⊂ X with respect to the pseudo-monotonicity of its Clarke-Rockafellar Sub-differential. We extend the results on the characterizations of non-smooth convex functions f : X → R ∪ {+ ∞} on convex subset of real Banach spaces K ⊂ X with respect to the monotonicity of its sub-differentials to the lower semi-continuous pseudo-convex functions on real Banach spaces.
文摘The purpose of this paper is to make a further study on the abstract economy. Here, for the constraint correspondences we assume that they are almost lower semi-continuous (n-lower semi-continuous), which is weaken than that they are lower semi-continuous. Several equilibria existence theorems are proved.
文摘The 2024/3003 aluminum gradient alloys are prepared by semi continuous casting. The influences of throttle bore diameter of embedded nozzle and temperature of internal melt on composition distribution, macrostructure, hardness are analyzed, and the stability of gradient distribution of composition, macrostructure and hardness along the axial direction of the ingot is also studied. The results show that diffe rent composition profiles can be achieved by adjusting the processing parameters; the volume fraction of inner alloy in the ingot can be increased by enlarging the throttle bore diameter and elevating the temperature of inner melt; quasi steady solidification can be realized within 20 s during cast processing, and consistent quality ingot is obtained by controlling the casting speed and liquid height of inner melt.
文摘Continuous and semi-continuous mining technology has become the main trend of modern surface mines in the world. According to the deposit characteristics of coal basin in China and Chinese situation,this paper discussed the new semi-continuous technology── shovel - transfer wagon-belt conveyor and its application prospect in large surface coal mines in China.
基金This research was financially supported by National Basic Research Program of China(Grant No.2013CB632203)the Liaoning Provincial Natural Science Foundation of China(Grant No.201202072)+1 种基金National Key Technology R&D Program of China(2012BAF09B01)the Fundamental Research Foundation of Central Universities(Grant Nos.N120509002 and N120309003).
文摘Mg-9Gd-3Y-1.5Zn-0.8Zr alloys own high strength,good heat and corrosion resistance.However,it is difficult for the fabrication of large-scale billets,due to the poor deformation ability and strong hot-crack tendency.This work investigated the casting process on the microstructures and flow stress behaviors of the semi-continuous casting billets for the fabrication of large-scale Mg-9Gd-3Y-1.5Zn-0.8Zr billets.The casting process(electromagnetic intensity and casting speed)shows outstanding effects on the microstructures and flow stress behavior of the billets.The billets with the specific casting process(I=68 A,V=65 mm/min)exhibit uniform microstructures and good deformation uniformity.
基金financially supported by the National Natural Science Foundation of China(51074106)the National Key Technology R&D Program of China(2011BAE22B01-5)
文摘The microstucture,mechanical properties and fracture behaviors of semi-continuous cast Mg-8Gd-3Y-0.5Zr(wt.%,GW83K) alloy after different heat treatments were investigated.Almost all the eutectic compounds were dissolved into the matrix and there was no evident grain growth after optimum solution treatment at 500 ℃for 4h.Further ageing at low temperatures led to significant precipitation hardening,which strengthened the alloy.Peak-aged at 200 ℃,the alloy had the highest ultimate tensile strength(UTS) and lowest elongation at 395 MPa and 2.8%,respectively.When aged at 225 ℃ for 15 h,the alloy exhibited prominent mechanical performance with UTS and elongation of 363 MPa and 5.8%,respectively.With regard to microstructure and tensile properties,the processes of 500 ℃,4h+225℃,15 h are selected as the optimal heat treatment conditions.The alloy under different conditions shows different fracture behaviors:in the as-cast alloy,a quasi-cleavage pattern is observed;after solution treatment,the alloy exhibits a trans-granular quasi-cleavage fracture;after being peak-aged at 200 ℃ and 225 ℃,the fracture mode is a mixed mode of trans-granular and intergranular fracture,in which the inter-granular mode is dominant in the alloy peak-aged at 200 ℃.
基金supported by the National Key Research and Development Program of China (2019YFA0905000)the National Natural Science Foundation of China (21536004, 21922804, 21776085, and 21871085)the Fundamental Research Funds for the Central Universities (22221818014)。
文摘The massive consumption of fossil energy force s people to find new source s of energy.Syngas fermentation has become a hot research field as its high potential in renewable energy production and sustainable development.In this study,trophic anaerobic acetogen Morella thermoacetica was successfully immobilized by calcium alginate embedding method.The ability of the immobilized cells on production of acetic acid through syngas fermentation was compared in both airlift and bubble column bioreactors.The bubble column bioreactor was selected as the better type of bioreactor.The production of acetic acid reached 32.3 g·L^(-1) in bubble column bioreactor with a space-time yield of 2.13 g·L^(-1)·d^(-1).The immobilized acetogen could be efficiently reused without significant lag period,even if exposed to air for a short time.A semi-continuous syngas fermentation was performed using immobilized cells,with an average space-time acetic acid yield of 3.20 g·L^(-1)·d^(-1).After 30 days of fermentation,no significant decrea se of the acetic acid production rate was observed.
基金financially supported by the National Key Technology R&D Program(No.2012BAF09B04)International Technical Cooperation Project(No.2011DFR50950)of the Ministry of Science and Technology of Chinathe Chongqing Science and Technology Commission(No.CSTC2013JCYJC60001)
文摘For the large magnesium alloy ingot, there is a considerable difference in cooling rate of different parts in the ingot, which leads to non-uniform distribution of the secondary phases, solute segregation and tensile properties. In the present research, an heavy AZ61 alloy ingot with a diameter of 500 mm was made by semi-continuous casting. The microstructure and mechanical properties at different positions along the radial direction of the large ingot were investigated by using an optical microscope(OM), a scanning electron microscope(SEM), an energy dispersive spectroscope(EDS), and a micro-hardness tester. The results indicate that the microstructure of the AZ61 ingot is non-uniform in different locations. It changes from equiaxed to columnar grains from the center to the edge; the average grain size gradually reduces from 1,005 μm to 763 μm, the secondary dendrite arm spacing reduces from 78 μm to 50 μm, and the Mg17(Al,Zn)12 phase is also refined. The micro-hardness value increases from 55.4 HV at the center to 72.5 HV at the edge of the ingot due to the microstructure differences, and the distribution of micro-hardness at the edge of the ingot is more uniform than that in the center. The tensile properties at room temperature show little difference from the center to the edge of the ingot except that the elongation at the edge is only 3.5%, much lower than that at other areas. The fracture mechanism is ductile fracture at the center and cleavage fracture at the edge of the ingot, and at the 1/2 radius of the ingot, a mixture of ductile and cleavage fracture is present.
基金Funded by the National Natural Science Foundation of China (NSFC)(No.50475157)the Key Fund of NSFC (No.50234022)the Key Project of Ministry of Education of China (No.105052)
文摘The semi-continuous casting of ZK60 magnesium alloy under different middle frequency electromagnetic field conditions was examined.Effects of middle frequency electromagnetic field on microstructure,precipitations and tensile properties are investigated.The results show that the microstructures of ZK60 magnesium alloy are refined and distribution uniformity of precipitations is observed after applying the middle frequency electromagnetic field.And the tensile properties of the billets produced by middle frequency electromagnetic field are increased.
文摘Cooling heat flux effect in both primary and secondary cooling zone has been studied in semi-continuous casting of copper billet. Sufficient cooling is essential to reduce casting defects and to get high productivity, however low rate of solidification is aimed in order to get coarser grain size and softer metal for less losses in extrusion. A three-dimensional numerical model has been developed including solidification behavior of copper through mushy zone. At steady state and constant casting speed, solid shell thickness is monitored during the reduction of cooling rate at mould region to avoid breaking out. Heat flux intensity at mould plays important role not only in the formation of solid shell thickness. But, pool length and mushy zone thickness can be significantly increased by decreasing primary cooling intensity. Increase intensity of secondary cooling zone for two particular cases of primary cooling is tested. First case is tested at mould inlet water temperature of 38°C, and second case at water temperature of 63°C. Results showed that the combination of increasing secondary cooling intensity and reduction of primary cooling intensity can increase pool length and mushy zone thickness. Also, it is shown that, secondary cooling intensity can be magnified by up to 1.5 times for cooling water temperature of 63°C to get pool length close to that of water temperature of 38°C.
文摘In this paper, we study the regularization methods to approximate the solutions of the variational inequalities with monotone hemi-continuous operator having perturbed operators arbitrary. Detail, we shall study regularization methods to approximate solutions of following variational inequalities: and with operator A being monotone hemi-continuous form real Banach reflexive X into its dual space X*, but instead of knowing the exact data (y<sub>0</sub>, A), we only know its approximate data satisfying certain specified conditions and D is a nonempty convex closed subset of X;the real function f defined on X is assumed to be lower semi-continuous, convex and is not identical to infinity. At the same time, we will evaluate the convergence rate of the approximate solution. The regularization methods here are different from the previous ones.
基金The NNSF (10471084) of China and by Guangdong Provincial Natural Science Foundation(04010985).
文摘Let S = {1,1/2,1/2^2,…,1/∞ = 0} and I = [0, 1] be the unit interval. We use ↓USC(S) and ↓C(S) to denote the families of the regions below of all upper semi-continuous maps and of the regions below of all continuous maps from S to I and ↓C0(S) = {↓f∈↓C(S) : f(0) = 0}. ↓USC(S) endowed with the Vietoris topology is a topological space. A pair of topological spaces (X, Y) means that X is a topological space and Y is its subspace. Two pairs of topological spaces (X, Y) and (A, B) are called pair-homeomorphic (≈) if there exists a homeomorphism h : X→A from X onto A such that h(Y) = B. It is proved that, (↓USC(S),↓C0(S)) ≈(Q, s) and (↓USC(S),↓C(S)/ ↓C0(S))≈(Q, c0), where Q = [-1,1]^ω is the Hilbert cube and s = (-1,1)^ω,c0= {(xn)∈Q : limn→∞= 0}. But we do not know what (↓USC(S),↓C(S))is.
基金Project supported by the National Natural Science Foundation of China (Nos. 10571150 and 10271053)
文摘The perturbation problem of generalized inverse is studied. And some new stability characteristics of generalized inverses were presented. It was also proved that the stability characteristics of generalized inverses were independent of the choice of the generalized inverse. Based on this result, two sufficient and necessary conditions for the lower semi-continuity of generalized inverses as the set-valued mappings are given.
文摘In the present paper the concept and properties of the residual functional in Sobolev space are investigated. The weak compactness, force condition, lower semi-continuity and convex of the residual functional are proved. In Sobolev space, the minimum principle of the residual functional is proposed. The minimum existence theoreomfor J(u) =0 is given by the modern critical point theory. And the equivalence theorem or five equivalence forms for the residual functional equation are also proved.
基金Project supported by the National Natural Science Foundation of China (No.10571130)
文摘The dynamics of set value mapping is considered. For the upper semi-continuous set value maps, the existence of attractors under some conditions and the upper semi-continuity of attractors under the perturbation are proved. Its application in numerical simulation of differential equation is also considered. The upper semi-continuity of attractors in set value maps under the perturbation is used to show the reasonable of subdivision algorithm and interval arithmetic in numerical simulation of differential equation.
文摘In this paper, using the context of complete partial metric spaces, some common fixed point results of maps that satisfy the generalized (ψ, Ф)-weak contractive conditions are obtained. Our results generalize, extend, unify, enrich and complement many existing results in the literature. Example are given showing the validaty of our results.