THE REGULARITY OF THE FREE BOUNDARY FOR STRIKE RESET OPTION

A strike reset option is an option that allows its holder to reset the strike price to the prevailing underlying asset price at a moment chosen by the holder. The pricing model of the option can be formulated as a parabolic variational inequality and the optimal reset strategy is the free boundary. The smoothness of the free boundary in some cases was showed in our article published in JDE. We would prove its smoothness in the other case in this paper by a generalized comparison principle for the variational inequality.     

响应面法对3,5-二硝基水杨酸比色法测定水果中还原糖含量条件的优化

采用3,5-二硝基水杨酸(DNS)比色法测定水果中还原糖的含量,在单因素试验的基础上,采用三因素三水平的响应面分析法(RSM)优化DNS法测定苹果还原糖的最佳条件,同时建立数学模型并验证其可靠性。回归方程失拟项不显著(P=0.133 7),预测值与实际值吻合(R~2=0.957 4);影响DNS法测定还原糖含量的因素主次顺序为:DNS用量﹥反应温度﹥显色时间;DNS法测定还原糖含量的最佳条件为:DNS用量4.0 m L,显色时间5.0 min,反应温度87.0℃,测得还原糖实际浓度为94.66 mg/L,与理论预测值基本相符。按照优化的最佳条件,以苹果、桃、葡萄、哈密瓜、脐橙、菠萝6种代表性水果为对象验证该方法的精密度、重复性和准确度,其标准偏差为0.1%~0.5%,相对标准偏差为2.0%~4.8%,加标回收率为90.6%~104.2%。该方法简便、快速,准确度高,重现性好,适合于苹果及其他水果中还原糖的测定。     

Optimization of Maceration Conditions for Improving the Extraction of Phenolic Compounds and Antioxidant Effects of Momordica Charantia L. Leaves Through Response Surface Methodology (RSM) and Artificial Neural Networks (ANNs)

The main goals of this research were the chemical and biological characterization of the bitter melon (Momordica charantia) isolate obtained by traditional (maceration) extraction, as well as optimization of this process using response surface methodology (RSM) and artificial neural networks (ANNs). Experiments were performed using Box–Behnken experimental design on three levels and three variables: extraction temperature (20?°C, 40?°C, and 60?°C), solvent concentration (30%, 50%, and 70%) and extraction time (30, 60, and 90?min). The measurements consisted of 15 randomized runs with 3 replicates in a central point. The antioxidant activity of obtained extracts was determined by the 1,1-diphenyl-2-picrylhydrazyl (DPPH), cupric ion reducing antioxidant capacity (CUPRAC) and ferric reducing antioxidant power (FRAP) assays while chemical characterization was done in terms of the total phenolic content (TPC). The methodology shows positive influence of solvent concentration on all four observed outputs, while temperature showed a negative impact. RSM showed that the optimal extraction conditions were 20?°C, 70% methanol, and an extraction time of 52.2?min. Under these conditions, the TPCs were 20.66 milligrams of gallic acid equivalents (mg GAE/g extract), DPPH 30.22 milligrams of trolox equivalents (mg TE/g extract), CUPRAC 67.78 milligrams of trolox equivalents (mg TE/g extract), and FRAP 45.48 milligrams of trolox equivalents (mg TE/g extract). The neural network coupled with genetic algorithms (ANN-GA) was also used to optimize the conditions for each of the outputs separately. It is anticipated that results reported herein will establish baseline data and also demonstrate that that the present model can be applied in the food and pharmaceutical industries.     

表面响应曲面法优化微生物中聚β-羟基丁酸酯提取条件的研究

利用表面响应曲面法(RSM)优化次氯酸钠/氯仿混合溶液提取微生物体内聚β-羟基丁酸酯(PHB)的过程,选取了次氯酸钠的百分含量、反应时间、反应温度以及混合液中次氯酸钠与氯仿不同比例为因子,以PHB/MLSS为响应因子。实验结果表明提取的最佳条件是NaClO为13%、反应温度为45℃、反应时间为2.8h,NaClO∶CHCl3(V/V)为1.3。利用最佳操作条件,提取出来的产量可以提高25%。     

完全广义混合强非线性变分包含的解的灵敏性分析

引入并研究了Hilbert空间中一类新的完全广义混合强非线性变分包含．利用改进的隐预解算子技巧分析了此变分包含的解的灵敏性，所得结果改进并推广了以往相应结果．     

STUDY OF THE EQUIVALENT THEOREM OF GENERALIZED VARIATIONAL PRINCIPLES IN ELASTICITY

The relations of all generalized variational principles in elasticity are studied by employing the invariance theorem of field theory. The infinitesimal scale transformation in field theory was employed to investigate the equivalent theorem. Among the results found particularly interesting are those related to that all generalized variational principles in elasticity are equal to each other. Also studied result is that only two variables are independent in the functional and the stress-strain relation is the variational constraint condition for all generalized variational principles in elasticity. This work has proven again the conclusion of Prof. Chien Wei-zang.     

Convergence of the solution for a domain decomposed,heterogeneously modeled flow past a concave profile problem

The free streamline problem investigated is that of fluid flow past a symmetric truncated concave‐shaped profile between walls. An open wake or cavity is formed behind the profile. Conformal mapping techniques are used to solve this problem. The problem formulated in the hodograph plane is decomposed into two nonoverlapping domains. Heterogeneous modeling is then used to describe the problems, i.e., a different governing differential equation in each domain. In one of these domains, a Baiocchi‐type transformation is used to obtain a fixed domain formulation for the part of the transformed problem containing an unknown boundary. In the other domain, the Baiocchi‐type transformation is extended across the boundary between the two domains, thus yielding a different problem formulation. This also assures that the dependent variables and their normal derivatives are continuous along this common boundary. The numerical solution scheme, a successive over‐relaxation approach, is applied over the whole problem domain with the use of a projection‐operation over only the fixed domain formulated part. Numerical results are obtained for the case of a truncated circular profile. These results are found to be in good agreement with another published result. The existence and uniqueness of the solution to the problem as a variational inequality is shown, and the convergence of the numerical solution using a domain decomposition method scheme is demonstrated by assuming some convergence property on the common interface of the two subdomains. © 2000 John Wiley & Sons, Inc. Numeer Methods Partial Differential Eq 16: 459–479, 2000     

The regularity of the free boundary for strike reset option

A strike reset option is an option that allows its holder to reset the strike price to the prevailing underlying asset price at a moment chosen by the holder. The pricing model of the option can be formulated as a parabolic variational inequality and the optimal reset strategy is the free boundary. The smoothness of the free boundary in some cases was showed in our article published in JDE. We would prove its smoothness in the other case in this paper by a generalized comparison principle for the variational inequality.     

Synthesis of nanocomposites of iron oxide/gold (Fe3O4/Au) loaded on activated carbon and their application in water treatment by using sonochemistry: Optimization study

This paper focuses on the finding best operational conditions using response surface methodology (RSM) for Rhodamine123 (R123) and Disulfine blue (DSB) dyes removal by ultrasound assisted adsorption onto Au-Fe₃O₄ nanoparticles loaded on activated carbon (Au-Fe₃O₄ NPs-AC). The influences of variables such as initial R123 (X₁) and DSB concentration (X₂), pH (X₃), adsorbent mass (X₄) and sonication time (X₅) on their removal were investigated by small central composite design (CCD) under response surface methodology. The significant variables and the possible interactions among variables were investigated and estimated accordingly. The best conditions were set as: 4 min, 4.0, 0.025 g, 13.5 and 26.5 mg L⁻¹ for sonication time, pH, adsorbent weight, initial R123 and DSB concentration, respectively. At above conditions, the adsorption equilibrium and kinetic follow the Langmuir isotherm and pseudo-second-order kinetic model, respectively. The maximum monolayer capacity (Q_max) of 71.46 and 76.38 mg g⁻¹ for R123 and DSB show sufficiency of model for well presentation of experimental data.