On the Dynamics of Homeomorphisms on the Unit Ball of Rn

Positivity - Consider a compact convex subset X of R n (n ≥ 2) with non-empty interior and let H(X) be the set of all homeomorphisms from X onto X endowed with the supremum metric. We are...     

On Extension and Continuity of p–Additive Functions

In this paper we prove some properties of p–additive functions as well as p–additive set–valued functions.     

近红外光谱的河蟹新鲜度快速检测研究

河蟹的新鲜度是大多数消费者在购买时所考虑的最重要的因素,挥发性盐基氮(TVB-N)是当前国际通用的评价肉类新鲜度的指标,但其检测工序繁琐、耗费时间长,无法满足当前市场对河蟹新鲜度评价的迫切需求。因此,建立一种快速检测河蟹新鲜度的方法是当前急需解决的一大难题。将购于水产市场的河蟹,采用聚乙烯充氧袋快速运至实验室,样本数共126只。在洁净的工作台上处理后,将螃蟹分为42个实验样品,每个样品3只鲜活螃蟹;42个实验样品放在低温4℃的恒温生化培养箱中贮藏,每天从培养箱中按时取出6个螃蟹样品进行光谱数据采集及新鲜度指标TVB-N的测定,历时7 d。采用近红外光谱(NIRS)对贮藏在不同时间下的河蟹新鲜度进行评价,使用挥发性盐基氮(TVB-N)作为评价河蟹新鲜度的指标,首先通过比较经五折交叉验证(5-fold CrossValidation)算法、 kennard-stone(KS)算法、光谱-理化值共生距离(SPXY)算法三种样本划分方法处理后所建模型的预测效果确定最优样本划分方法,最终采用五折交叉验证(5-fold CrossValidation)算法对样本进行划分。其中的32个样品被划分为训练集进行模型构建,其余的10个样品被划分为测试集用于模型检验。然后在经过五折交叉验证法对样本进行划分的基础上,分别采用小波变换(WT)、 Savitzky-Golay平滑、一阶导数法(Db1)、二阶导数法(Db2)这4种单一算法以及小波变换(WT)与Savitzky-Golay平滑相结合的算法进行预处理,通过比较预处理后所建模型的预测效果,确定了小波变换(WT)预处理为最优光谱预处理方法,从而消除了光谱中的无用信息并提高了信噪比。再次,在WT预处理的基础上,分别采用主成分分析(PCA)法和连续投影(SPA)算法提取光谱特征波段,通过建模比较确定主成分分析(PCA)法为最优波长选择方法,以所选的16个特征波长作为模型的输入,不仅提高了模型的运行速度还可以提高模型的稳定性。最后,在经过PCA特征提取后,分别采用偏最小二乘回归(PLSR)算法和多元线性回归(MLR)算法构建TVB-N定量预测模型,通过比较两种模型的预测效果,确定了偏最小二乘回归(PLSR)模型为最优建模方法,最终确定的最优模型为基于WT-PCA-PLSR建立的模型,模型预测决定系数R^2为0.89,预测均方根误差RMSEP为3.00。综上所述,所建立的预测模型具有较高的精度,可以实现对河蟹新鲜度的快速检测,具有较好的市场应用前景。     

EXPONENTIAL CONVERGENCE OF SAMPLE AVERAGE APPROXIMATION METHODS FOR A CLASS OF STOCHASTIC MATHEMATICAL PROGRAMS WITH COMPLEMENTARITY CONSTRAINTS

In this paper,we propose a Sample Average Approximation(SAA)method for a class ofStochastic Mathematical Programs with Complementarity Constraints(SMPCC)recentlyconsidered by Birbil,Gürkan and Liste[3].We study the statistical properties of obtainedSAA estimators.In particular we show that under moderate conditions a sequence of weakstationary points of SAA programs converge to a weak stationary point of the true problemwith probability approaching one at exponential rate as the sample size tends to infinity.To implement the SAA method more efficiently,we incorporate the method with sometechniques such as Scholtes' regularization method and the well known smoothing NCPmethod.Some preliminary numerical results are reported.     

ON THE CONVERGENCE OF AN APPROXIMATE PROXIMAL METHOD FOR DC FUNCTIONS

In this paper we prove the convergence of the approximate proximal method for DC functions proposed by Sun et al [6]. Our analysis also permits to treat the exact method. We then propose an interesting result in the case where the second component of the DC function is differentiable and provide some computational experiences which proved the efficiency of our method.     

用“三点弯曲法”原理测定钢丝绳张力

通过对根据“三点弯曲法”原理设计的夹持式钢索张力测定传感器的研究，建立钢丝绳张力计算模式，用导出的钢丝绳张力计算公式计算，其结果与试验结果吻合较好。     

一种基于免疫识别的主因子数判断方法

根据免疫算法的基本思想,提出了一种基于免疫识别(IR)的主因子数判断方法.对模拟数据和HPLC-DAD数据的处理结果表明,IR比嵌入误差(IE)、因子指示函数(IND)和交叉验证(CV)更能有效地克服噪音的影响.当实际数据中的非线性和不等性方差噪音使其它方法失效时,IR仍能得到正确的主因子数.     

主成分-人工神经网络在近红外光谱定量分析中的应用

近红外光谱的主成分由非线性迭代偏最小二乘法（ＮＩＰＡＬＳ）求出。主成分作标准化处理后,作为Ｂ－Ｐ神经网络的输入结点进行非线性迭代。该法的优点是,充分利用了全光谱的数据,得到消除噪声后的最佳主成分,能建立非线性模型,Ｂ－Ｐ神经网络迭代时间显著缩短。用该法对大麦中的淀粉含量进行了定量分析研究。结果为：校准和预测的相关系数分别为０．９８１和０．９５３,校准和预测的相对标准偏差分别为１．７０％和２．４８％。     

Determination of antioxidant capacities of vegetable oils by ferric-ion spectrophotometric methods

Two ferric-ion-based total antioxidant capacity methods: 1,10-phenanthroline (Phen) and ferric reducing antioxidant power (FRAP) were used for determination of antioxidant capacities (AC) of the acetonic and methanolic extracts of vegetable oils. The obtained mean Phen and FRAP values for acetonic extracts of olive oils, rapeseed, rice and four sunflower oils (39.3–336.5 and 39.5–339.6 μmol Fe/100 g) were higher than for methanolic extracts (22.8–307.3 and 23.5–300.1 μmol Fe/100 g). However, antioxidant capacities of methanolic extracts of corn oil, blended oils and two sunflower oils with garden green flowers (56.5–312.9 and 53.9–306.5 μmol Fe/100 g for Phen and FRAP methods, respectively) were higher than for acetonic extracts of these oils (54.2–249.2 and 52.9–244.7 μmol Fe/100 g for Phen and FRAP methods, respectively). There is a linear and significant correlation between these two analytical methods (r = 0.9989 and 0.9986 for acetonic and methanolic extracts). Also, total phenolic compounds (TPC) in the studied oils correlated with their antioxidant capacities determined by Phen and FRAP methods (r = 0.9012, 0.7818 and 0.8947, 0.7830 for acetonic and methanolic extracts, respectively). The comparable precision (R.S.D. = 0.8–4.6%, 0.9–4.9% and 0.7–4.0%, 0.6–4.0% for acetonic and methanolic extracts, respectively) and sensitivity ( = 1.27 × 10⁴, 1.11 × 10⁴ and 2.62 × 10⁴ dm³ mol⁻¹ cm⁻¹) for the proposed Phen and the modified FRAP methods, demonstrate the benefit of the Phen method in the routine analysis of antioxidant capacities of vegetable oils.     

基于非负分解方法的质谱成像数据特征提取

质谱成像技术能够在同一个实验里无需标记手段而获得样品表面的分子信息及其分布信息,是当前质谱分析的热点.其分析所得数据量大且复杂,使其特征难以提取.多元统计分析方法,特别是主成分分析法已应用于质谱成像数据的压缩和特征提取.然而由于主成分分析常产生负的数据结果,其意义难以解释且不易分解为单一的特征.本研究开发出一种基于非负分解的质谱成像数据提取方法,能够提取单一的分子特征及其在样品上的分布特征,并将多个单一的特征分布通过红、绿、蓝三色叠加显示,获得轮廓直观的综合特征分布.应用本方法对小鼠脑组织切片质谱成像数据进行分析,可直观分解出灰质区域、白质区域和背景区域,相对主成分分析方法更直观且易于解释.应用本方法对在同一个样品靶上的人膀胱癌变组织和其相邻非癌变组织切片质谱成像数据进行分析,癌变与非癌变组织间差异清晰直观.本研究设计的质谱成像软件可由http://www.msimaging.net获取.