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 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.

AN OPTIMAL CONTROL PROBLEM FOR A LOTKA-VOLTERRA COMPETITION MODEL WITH CHEMO-REPULSION

In this paper we study a bilinear optimal control problem for a diffusive Lotka-Volterra competition model with chemo-repulsion in a bounded domain of ℝ^(ℕ),N=2,3.This model describes the competition of two species in which one of them avoid encounters with rivals through a chemo-repulsion mechanism.We prove the existence and uniqueness of weak-strong solutions,and then we analyze the existence of a global optimal solution for a related bilinear optimal control problem,where the control is acting on the chemical signal.Posteriorly,we derive first-order optimality conditions for local optimal solutions using the Lagrange multipliers theory.Finally,we propose a discrete approximation scheme of the optimality system based on the gradient method,which is validated with some computational experiments.

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.

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.

A Variant Constrained Genetic Algorithm for Solving Conditional Nonlinear Optimal Perturbations

A variant constrained genetic algorithm （VCGA） for effective tracking of conditional nonlinear optimal perturbations （CNOPs） is presented. Compared with traditional constraint handling methods, the treatment of the constraint condition in VCGA is relatively easy to implement. Moreover, it does not require adjustments to indefinite pararneters. Using a hybrid crossover operator and the newly developed multi-ply mutation operator, VCGA improves the performance of GAs. To demonstrate the capability of VCGA to catch CNOPS in non-smooth cases, a partial differential equation, which has ＂on off＂ switches in its forcing term, is employed as the nonlinear model. To search global CNOPs of the nonlinear model, numerical experiments using VCGA, the traditional gradient descent algorithm based on the adjoint method （ADJ）, and a GA using tournament selection operation and the niching technique （GA-DEB） were performed. The results with various initial reference states showed that, in smooth cases, all three optimization methods are able to catch global CNOPs. Nevertheless, in non-smooth situations, a large proportion of CNOPs captured by the ADJ are local. Compared with ADJ, the performance of GA-DEB shows considerable improvement, but it is far below VCGA. Further, the impacts of population sizes on both VCGA and GA-DEB were investigated. The results were used to estimate the computation time of ~CGA and GA-DEB in obtaining CNOPs. The computational costs for VCGA, GA-DEB and ADJ to catch CNOPs of the nonlinear model are also compared.

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.

SECOND-ORDER OPTIMALITY CONDITIONS FOR OPTIMAL CONTROL PROBLEMS GOVERNED BY 3-DIMENSIONAL NEVIER-STOKES EQUATIONS

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.

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.

Algorithm Studies on How to Obtain a Conditional Nonlinear Optimal Perturbation (CNOP)

The conditional nonlinear optimal perturbation （CNOP）, which is a nonlinear generalization of the linear singular vector （LSV）, is applied in important problems of atmospheric and oceanic sciences, including ENSO predictability, targeted observations, and ensemble forecast. In this study, we investigate the computational cost of obtaining the CNOP by several methods. Differences and similarities, in terms of the computational error and cost in obtaining the CNOP, are compared among the sequential quadratic programming （SQP） algorithm, the limited memory Broyden-Fletcher-Goldfarb-Shanno （L-BFGS） algorithm, and the spectral projected gradients （SPG2） algorithm. A theoretical grassland ecosystem model and the classical Lorenz model are used as examples. Numerical results demonstrate that the computational error is acceptable with all three algorithms. The computational cost to obtain the CNOP is reduced by using the SQP algorithm. The experimental results also reveal that the L-BFGS algorithm is the most effective algorithm among the three optimization algorithms for obtaining the CNOP. The numerical results suggest a new approach and algorithm for obtaining the CNOP for a large-scale optimization problem.

Sufficient Optimality Conditions for Multiobjective Programming Involving (V, ρ)h,ψ-type Ⅰ Functions

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.

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.

Applications of Conditional Nonlinear Optimal Perturbation to the Study of the Stability and Sensitivity of the Jovian Atmosphere

A two-layer quasi-geostrophic model is used to study the stability and sensitivity of motions on smallscale vortices in Jupiter＇s atmosphere. Conditional nonlinear optimal perturbations （CNOPs） and linear singular vectors （LSVs） are both obtained numerically and compared in this paper. The results show that CNOPs can capture the nonlinear characteristics of motions in small-scale vortices in Jupiter＇s atmosphere and show great difference from LSVs under the condition that the initial constraint condition is large or the optimization time is not very short or both. Besides, in some basic states, local CNOPs are found. The pattern of LSV is more similar to local CNOP than global CNOP in some cases. The elementary application of the method of CNOP to the Jovian atmosphere helps us to explore the stability of variousscale motions of Jupiter＇s atmosphere and to compare the stability of motions in Jupiter＇s atmosphere and Earth＇s atmosphere further.

Global optimality conditions for quadratic 0-1 programming with inequality constraints

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.

Optimality conditions and duality for a class of nondifferentiable multiobjective generalized fractional programming problems

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.

Idealized Experiments for Optimizing Model Parameters Using a 4D-Variational Method in an Intermediate Coupled Model of ENSO

Large biases exist in real-time ENSO prediction, which can be attributed to uncertainties in initial conditions and model parameters. Previously, a 4D variational （4D-Vat） data assimilation system was developed for an intermediate coupled model （ICM） and used to improve ENSO modeling through optimized initial conditions. In this paper, this system is further applied to optimize model parameters. In the ICM used, one important process for ENSO is related to the anomalous temperature of subsurface water entrained into the mixed layer （Te）, which is empirically and explicitly related to sea level （SL） variation. The strength of the thermocline effect on SST （referred to simply as ＂the thermocline effect＂） is represented by an introduced parameter, （l＇Te. A numerical procedure is developed to optimize this model parameter through the 4D-Var assimilation of SST data in a twin experiment context with an idealized setting. Experiments having their initial condition optimized only, and having their initial condition plus this additional model parameter optimized, are compared. It is shown that ENSO evolution can be more effectively recovered by including the additional optimization of this parameter in ENSO modeling. The demonstrated feasibility of optimizing model parameters and initial conditions together through the 4D-Var method provides a modeling platform for ENSO studies. Further applications of the 4D-Vat data assimilation system implemented in the ICM are also discussed.

Optimality Conditions and Duality for Nonsmooth Multiobjective Programms with Generalized Essential Convexity

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.

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.