Optimization of elastolysis conditions and elastolytic kinetic analysis with elastase from Bacillus licheniformis ZJUEL31410

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.

Optimization of Extraction Conditions of Pomegranate Peel Polyphenols and Its Protective Effect on Acute Alcoholic Liver Injury in Mice

[Objectives]This study was conducted to explore the optimization of ultrasonic-assisted organic solvent extraction of pomegranate peel polyphenols(PPPs),and to study the protective effect of PPPs on acute alcoholic liver injury in mice.[Methods]The optimal extraction conditions of PPPs were determined by single factor and orthogonal experiments,and an acute alcoholic liver injury model in mice was established.Bifendate was used as the positive control group to investigate the protective effect of low,medium and high doses of PPPs on acute alcoholic liver injury.[Results]The optimum extraction process parameters were followed as 60%ethanol concentration,solid-liquid ratio of 1:40(w/v),extraction temperature of 50℃,and extraction time of 1.5 h,and the yield was 1.42%.The results of animal experiments showed that PPPs could effectively reduce the degree of alcoholic liver injury in mice,reduce the levels of serum alanine aminotransferase(ALT)and aspartate aminotransferase(AST),and reduce the inflammation and necrosis of liver tissue in mice.Meanwhile,the total polyphenols from pomegranate peel also significantly reduced the expression levels of malondialdehyde(MDA),tumor necrosis factor(TNF-α)and interleukin-6(IL-6)in mice,and increased the levels of superoxide dismutase(SOD)and reduced glutathione(GSH)in liver tissue of mice,indicating its antioxidant and anti-inflammatory effects,further illustrating its protective effect on alcoholic liver injury.[Conclusions]PPPs could reduce the expression levels of TNF-α,IL-6 and MDA in mice,and increase the expression levels of SOD and GSH to achieve the protective effect on acute alcoholic liver injury in mice.This study will provide new ideas for the development of new anti-alcoholic liver injury drug resources.

Optimization of Conditions for the Extraction of Melanin from Walnut Husk

[Objective] This study was conducted optimize the conditions for the ex- traction of melanin from walnut husk. [Method] Melanin was isolated from walnut husk through alkali extraction and acid precipitation, and the factors that may influ- ence the extraction efficiency： temperature, duration, NaOH concentration and solid- liquid ratio were set at different levels. [Result] The optimal conditions for the ex- traction of melanin from walhut husk were temperature of 80 ℃, extraction duration of 120 min, NaOH concentration of 70 mol/L, and solid-liquid ratio of 1：20. [Conclu- sion] The optimal conditions for the extraction of melanin from walnut husk deter- mined in the present study will provide references for the development and utiliza- tion of natural melanin.

OPTIMALITY CONDITIONS AND DUALITY RESULTS FOR NONSMOOTH VECTOR OPTIMIZATION PROBLEMS WITH THE MULTIPLE INTERVAL-VALUED OBJECTIVE FUNCTION

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.

KUHN-TUCKER CONDITION AND WOLFE DUALITY OF PREINVEX SET-VALUED OPTIMIZATION

The optimality Kuhn-Tucker condition and the wolfe duality for the preinvex set-valued optimization are investigated. Firstly, the concepts of alpha-order G-invex set and the alpha-order S-preinvex set-valued function were introduced, from which the properties of the corresponding contingent cone and the alpha-order contingent derivative were studied. Finally, the optimality Kuhn-Tucker condition and the Wolfe duality theorem for the alpha-order S-preinvex set-valued optimization were presented with the help of the alpha-order contingent derivative.

THE OPTIMALITY CONDITIONS OF NONCONVEXSET-VALUED VECTOR OPTIMIZATION

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.

Optimization of reaction conditions for the electroleaching of manganese from low-grade pyrolusite

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.

Optimization of the operating conditions in a TiO_2/Fe_3O_4-SiO_2 photocatalytic reactor for the treatment of industrial wastewater containing Procion Red MX-5B

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.

Optimality conditions in set optimization employing higher-order radial derivatives

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.

On Second-order Sufficient Conditions in Constrained Nonsmooth Optimization

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.

Enhanced exergy cost optimization of operating conditions in FCCU main fractionator

Exergy indicates the maximal energy that can do work effectively. Different from optimization of product quality or calculation of generic energy conservation in most previous studies, the application of exergy analysis and exergy cost optimization in petrochemical industry is of great economic and environmental significance. Based on the main fractionator in Jiujiang Petrochemical Complex No. 2 FCCU, an enhanced exergy cost optimization under different operating conditions by adjusting set points of temperature and valves opening degree for flow control is studied in this paper in order to reduce exergy cost and improve the quality of energy. A steadystate optimization algorithm to enhance exergy availability and an objective function comprehensively considering exergy loss are proposed. On the basis of ensuring the quality of petroleum products, the economic benefits can be improved by optimizing the controllable variables due to the fact that exergy cost is decreased.

Higher-order Optimality Conditions for Henig Effcient Solution in Set-valued Optimization under Cone-convexlike Maps

This paper deals with higher-order optimality conditions for Henig effcient solutions of set-valued optimization problems.By virtue of the higher-order tangent sets, necessary and suffcient conditions are obtained for Henig effcient solutions of set-valued optimization problems whose constraint condition is determined by a fixed set.

Optimization of Extraction Conditions for Total Flavonoids from Fructus Aurantii Immaturus and Its Anti-UVB Radiation Activity

[Objectives]Optimum extraction conditions of total flavonoids from Fructus Aurantii Immaturus(TFFAI)and its resistance activity to ultraviolet radiation were investigated in present research.[Methods]The optimal extraction conditions of TFFAI were determined by single factor and orthogonal experiments,and the survival rate of TFFAI on HaCaT cells irradiated with UVB rays was investigated.It s antioxidant capacity was determined by ABTS.[Results]The results showed that the highest yield of TFFAI was obtained with 70%ethanol at a solid-to-liquid ratio of 1:50(w/v)and 40℃for 1.5 h by single-factor and orthogonal experiments.Total flavonoids(0.25-1.00 mg/ml)could significantly improve the survival rate of HaCaT cell line.Meanwhile,the maximum absorption peak of TFFAI was found at 283 nm,and in-vitro antioxidant experiment identified that TFFAI had a good clearance rate to ABTS.It suggestes that TFFAI could protect the cells from UVB damage by absorption of UVB rays and anti-oxidation.[Conclusions]TFFAI played a protective role on UVB irradiated cells through UVB ultraviolet absorption and antioxidant pathways.

Optimization of Selecting Air Conditioning Cold/Heat Sources with Grey Relation Analysis

Selection of air conditioning（AC） cold/heat sources generally concerns about certain aspects and cannot reveal the whole profile of the problems. Grey relation analysis （GRA） is a data processing method to categorize the correlation extent of compared sequences and a certain reference sequence in a system with uncertain information. It is applied to evaluating and selecting AC cold/heat sources from four main aspects, which are technology, economy, reliability, and operation and management. Case study shows that the result for selecting AC cold/heat sources with the GRA method can be more reasonable and convincible. Thus it offers a new approach for designers in heating, ventilating and air conditioning field to compare and evaluate different AC cold/heat sou rces.

A Modified Lagrange Method for Solving Convex Quadratic Optimization Problems

In this paper, a modified version of the Classical Lagrange Multiplier method is developed for convex quadratic optimization problems. The method, which is evolved from the first order derivative test for optimality of the Lagrangian function with respect to the primary variables of the problem, decomposes the solution process into two independent ones, in which the primary variables are solved for independently, and then the secondary variables, which are the Lagrange multipliers, are solved for, afterward. This is an innovation that leads to solving independently two simpler systems of equations involving the primary variables only, on one hand, and the secondary ones on the other. Solutions obtained for small sized problems (as preliminary test of the method) demonstrate that the new method is generally effective in producing the required solutions.

Optimum conditions to treat high-concentration microparticle slime water with bioflocculants

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.

Multi-objective optimization of p-xylene oxidation process using an improved self-adaptive differential evolution algorithm

The rise in the use of global polyester fiber contributed to strong demand of the Terephthalic acid （TPA）. The liquid-phase catalytic oxidation of p-xylene （PX） to TPA is regarded as a critical and efficient chemical process in industry [ 1 ]. PX oxidation reaction involves many complex side reactions, among which acetic acid combustion and PX combustion are the most important. As the target product of this oxidation process, the quality and yield of TPA are of great concern. However, the improvement of the qualified product yield can bring about the high energy consumption, which means that the economic objectives of this process cannot be achieved simulta- neously because the two objectives are in conflict with each other. In this paper, an improved self-adaptive multi-objective differential evolution algorithm was proposed to handle the multi-objective optimization prob- lems. The immune concept is introduced to the self-adaptive multi-objective differential evolution algorithm （SADE） to strengthen the local search ability and optimization accuracy. The proposed algorithm is successfully tested on several benchmark test problems, and the performance measures such as convergence and divergence metrics are calculated. Subsequently, the multi-objective optimization of an industrial PX oxidation process is carried out using the proposed immune self-adaptive multi-objective differential evolution algorithm （ISADE）. Optimization results indicate that application oflSADE can greatly improve the yield of TPA with low combustion loss without degenerating TA quality.

GLOBAL CONVERGENCE OF A CLASS OF OPTIMALLY CONDITIONED SSVM METHODS

This paper explores the convergence of a class of optimally conditioned self scaling variable metric (OCSSVM) methods for unconstrained optimization. We show that this class of methods with Wolfe line search are globally convergent for general convex functions.

Application of the Conditional Nonlinear Optimal Perturbation Method to the Predictability Study of the Kuroshio Large Meander

A reduced-gravity barotropic shallow-water model was used to simulate the Kuroshio path variations. The results show that the model was able to capture the essential features of these path variations. We used one simulation of the model as the reference state and investigated the effects of errors in model parameters on the prediction of the transition to the Kuroshio large meander （KLM） state using the conditional nonlinear optimal parameter perturbation （CNOP-P） method. Because of their relatively large uncertainties, three model parameters were considered： the interracial friction coefficient, the wind-stress amplitude, and the lateral friction coefficient. We determined the CNOP-Ps optimized for each of these three parameters independently, and we optimized all three parameters simultaneously using the Spectral Projected Gradient 2 （SPG2） algorithm. Similarly, the impacts caused by errors in initial conditions were examined using the conditional nonlinear optimal initial perturbation （CNOP-I） method. Both the CNOP-I and CNOP-Ps can result in significant prediction errors of the KLM over a lead time of 240 days. But the prediction error caused by CNOP-I is greater than that caused by CNOP-P. The results of this study indicate not only that initial condition errors have greater effects on the prediction of the KLM than errors in model parameters but also that the latter cannot be ignored. Hence, to enhance the forecast skill of the KLM in this model, the initial conditions should first be improved, the model parameters should use the best possible estimates.

CONE-DIRECTED CONTINGENT DERIVATIVES AND GENERALIZED PREINVEX SET-VALUED OPTIMIZATION

By using cone-directed contingent derivatives, the unified necessary and sufficient optimality conditions are given for weakly and strongly minimal elements respectively in generalized preinvex set-valued optimization.