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.

Research progress on semi-continuous casting of magnesium alloys under external field

High-performance magnesium alloys are moving towards a trend of being produced on a large scale and in an integrated manner.The foundational key to their successful production is the high-quality cast ingots.Magnesium alloys produced through the conventional semi-continuous casting process inevitably contain casting defects,which makes it challenging to manufacture high-quality ingots.The integration of external field assisted controlled solidification technology,which combines physical fields such as electromagnetic and ultrasonic fields with traditional semi-continuous casting processes,enables the production of high-quality magnesium alloy ingots characterized by a homogeneous microstructure and absence of cracks.This article mainly summarizes the technical principles of those external field assisted casting process.The focus is on elaborating the refinement mechanism of different types of electromagnetic fields,ultrasonic fields,and combined physical fields during the solidification of magnesium alloys.Finally,the development prospects of producing highquality magnesium alloy ingots through semi-continuous casting under the external field were discussed.

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.

Direct-chill semi-continuous casting process of three-layer composite ingot of 4045/3004/4045 aluminum alloys

Three-layer composite ingot of 4045/3004/4045 aluminum alloys was prepared by direct-chill semi-continuous casting process,the temperature field distribution near the composite interface,macro-morphology,microstructure and composition distribution of the composite interface were investigated.The results show that semi-solid layer with a certain thickness forms near the interface due to the effect of cooling plate,which ensures successful implementation of casting the composite ingot.Two different aluminum alloys are well bonded metallurgically.The mechanical properties of composite interface were measured,the tensile and shearing strengths of composite interface are 105 and 88 MPa,respectively,which proves that the composite interface is a kind of metallurgical bonding.

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.

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.

Effect of high-intensity ultrasonic field on process of semi-continuous casting for AZ80 magnesium alloy billets

Under the high-intensity ultrasonic field,AZ80 magnesium alloy was semi-continuously cast.The effects of ultrasonic intensity on the as-cast microstructures and mechanical properties were investigated.The results show that the microstructures of the alloy cast under high-intensity ultrasonic field are fine and uniform,and the grains are equiaxed,rose-shaped or globular with an average size of 257μm.High-intensity field significantly decreases the grain size,changes the morphologies of theβ-Mg17Al12 phases and reduces their area fraction.It is also shown that a proper increase in ultrasonic intensity is helpful to obtain fine,uniform and equiaxed as-cast microstructures.The optimum ultrasonic parameters are that frequency is 20 kHz and ultrasonic intensity is 1 368 W.The mechanical tests show that the mechanical properties of the as-cast AZ80 magnesium alloy billets cast under ultrasonic field are greatly improved,and with increasing the ultrasonic intensity,the mechanical properties of the entire alloy billets are much higher and more uniform than those of the alloy without ultrasonic field.

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 ~C for 4 h. 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℃, 4 h ＋ 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 inter-granular fracture, in which the inter-granular mode is dominant in the alloy peak-aged at 200℃.

Effects of Ce on microstructure of semi-continuously cast Mg-1.5Zn-0.2Zr magnesium alloy ingots

Mg-1.5Zn-0.2Zr-xCe (x=0, 0.1, 0.3, 0.5, mass fraction, %) alloys were prepared by conventional semi-continuous casting. The effect of rare earth Ce on the microstructure of Mg-1.5Zn-0.2Zr-xCe alloys was studied and the distribution of Ce was analyzed by optical microscopy (OM), X-ray diffractometry (XRD) and scanning electron microscopy (SEM). The results indicate that Ce element exists in the form of Mg12Ce phase and has an obvious refining effect on the microstructure of test alloys. As the Ce content increases, the grain size reduces, the grain boundaries turn thinner, and the distribution of Mg12Ce precipitates becomes more and more dispersed. The Mg-1.5Zn-0.2Zr alloy with 0.3%Ce has the best refinement effect. From center to periphery of the ingot, the amount of granular precipitates in the grain reduces. In longitudinal section of the ingot, some relative long columnar grains appear.

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.

Microstructure and mechanical properties of AZ31 alloy ingot fabricated by semi-continuous casting

The AZ31 alloy ingot with diameter of 110 mm and length of 3500 mm was fabricated successfully. The compositions and microstructure morphologies of the ingot at different locations were performed, which indicated that the chemical composition distributed homogeneously through the whole alloy ingot and the average grain size increased from the surface to the center. The results of the EDS and element face-scanning illustrated that the eutectic compounds mainly consisted of fl-Mg17Al12 and a small amount of fl-Mgl7（AlZn）12. Furthermore, slight improvements of the strength and ductility were observed from the center to the surface along the axial direction of the alloy ingot, while both the strength and elongation to failure of the samples along the radial direction are higher than that along the axial direction. The fine grain strengthening was the main contributors to the strength of the as-casted AZ31 alloy.

Biogas by two-stage microbial anaerobic and semi-continuous digestion of Chinese cabbage waste

Anaerobic digestion of Chinese cabbage waste was investigated through a pilot-scale two-stage digester at a mesophilic temperature of 37 ℃. In the acidification digester, the main product was acetic acid, with the maxi- mum concentration of 4289 mg·L^-1 on the fourth day, accounting for 50.32% of total volatile fatty acids. The oxidation reduction potential （ORP） and NH^＋-N level decreased gradually with hydraulic retention time （HRT） of acidification. In the second digestion phase, the maximum methanogenic bacterial concentration reached 9.6 × 10^10ml^-1 at the organic loading rate （OLR） of 3.5-4 kg VS·m^-3, with corresponding HRT of 12-16 days. Accordingly, the optimal biogas production was 0.62 m^3· （kg VS）^-1, with methane content of 65%-68%;. ORP and NH4^＋-N levels in the methanizer remained between -500 and -560 mV and 2000-4500mg· L^-1, respec- tively. Methanococcus and Methanosarcina served as the main methanogens in the anaerobic digester.

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.