Upper semi-continuity of attractors for multivalued semi-flow under random perturbation

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.

Existence and Upper Semi-Continuity of Random Attractors for Nonclassical Diffusion Equation with Multiplicative Noise on Rn

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 H1(Rn). 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.

Fuzzy Semi-continuity of fuzzy number-valued function

In this paper we discuss the conecept and property of fuzzy semi continuous function.

Semi-Continuity of Complex Fuzzy Functions

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.

Sub-Differential Characterizations of Non-Smooth Lower Semi-Continuous Pseudo-Convex Functions on Real Banach Spaces

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.

Equilibria of the Abstract Economy under Almost Lower Semi-continuous Assumption

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.

Preparation of 2024/3003 gradient materials by semi-continuous casting using double-stream-pouring technique

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.

Study on Semi-Continuous Technology System for Soft Material Stripping in Large Surface Mines

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.

Effects of casting process on microstructures and flow stress behavior of Mg-9Gd-3Y-1.5Zn-0.8Zr semi-continuous casting billets

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.

Effects of heat treatment on microstructure and mechanical properties of Mg-8Gd-3Y-0.5Zr(wt.%)alloy fabricated by semi-continuous casting

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 ℃.

Immobilization of trophic anaerobic acetogen for semi-continuous syngas fermentation

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.

Inhomogeneity of microstructure and mechanical properties of a 500 mm diameter heavy section semi-continuous cast AZ61 magnesium alloy ingot

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.

Effect of Middle-frequency Electromagnetic Field on the Semi-continuous Casting for ZK60 Billets

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.

Effect of Cooling Intensity and Position on Solidification in Semi-Continuous Casting of Copper

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.

Regularization Methods to Approximate Solutions of Variational Inequalities

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 (y0, 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.

The Hyperspace of the Regions Below of Continuous Maps from the Converging Sequence

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.

CONTINUITY OF GENERALIZED INVERSES OF LINEAR OPERATORS IN BANACH SPACES AND ITS APPLICATIONS

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.

AN EXTREMUM THEORY OF THE RESIDUAL FUNCTIONAL IN SOBOLEV SPACES W^(m,p)t(Ω)

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.

SET VALUE MAPPING AND ITS APPLICATION

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.

COMMON FIXED POINT OF GENERALIZED WEAKLY CONTRACTIVE MAPS IN PARTIAL METRIC SPACES

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.