Analytic inversion for a general case of certain classes of matrices

The explicit inverse and determinant of a class of matrices are presented. The class under consideration is defined by 4n ? 2 parameters, analytic expressions of which form the elements of the upper Hessenberg type inverse. These analytic expressions enable recursion formulae to be obtained, which reduce the arithmetic operations to O(n ²). The Hadamard product of two specific structures' matrices provides the class presented, special cases of which are already known classes of test matrices.     

Trout‐Skin Gelatin‐Based Edible Films Containing Phenolic Antioxidants: Effect on Physical Properties and Oxidative Stability of Cod‐Liver Oil Model Food

Abstract: Trout‐skin (Oncorhynchus mykiss) gelatin‐based films containing antioxidants (epigallocatechin gallate (EGCG), 50 and 250 ppm w/w) and green tea powder (1% and 20% w/w of gelatin) were tested for tensile strength, elastic modulus, and elongation, and oxygen and water vapor transmission rates, in vitro antioxidant activity using the DPPH (2,2‐diphenyl‐1‐picrylhydrazyl) assay and effect on stabilizing cod‐liver oil held under mild thermal abuse conditions. Cod‐liver oil overlaid with films was stored at 40 °C for 20 d and analyzed for peroxide value (PV) and thiobarbituric acid reactive substances (TBARS). Antioxidant activity was retained in films containing green tea powder, but was reduced (P < 0.05) in EGCG films (20 d, 23 °C). Water vapor transmission rate of the films incorporated with antioxidants did not change significantly (P > 0.05), but the oxygen transmission rate for films with 50 ppm EGCG and 20% green tea powder was significant (P < 0.05). Other physical properties varied with antioxidant incorporation. The TBARS and PV of control oil increased from 0.05 ± 0.01 to 4.71 ± 0.30 g MDA/kg oil and from 3.6 ± 0.2 to 178.3 ± 24.5 millieq peroxides/kg oil, respectively, after 20 d. For cod‐liver oil covered with control or antioxidant‐containing films, TBARS remained below 0.37 g MDA/kg oil and PV below 7 millieq peroxides/kg oil. Incorporation of antioxidants to the films did not reduce oil oxidation (P > 0.05) at the levels tested and this was confirmed by activation energy calculations. The rate of oil oxidation was more dependent upon the inherent oxygen barrier property of the films than the presence of antioxidants. Practical Application: This research has the potential to enhance the utilization of fish skins, a valuable food processing by‐product, as edible films with natural antioxidants to extend the shelf life of foods. The film physical properties and barrier to oxygen and water are investigated.     

Effects of Green Tea Extract and α‐Tocopherol on the Lipid Oxidation Rate of Omega‐3 Oils,Incorporated into Table Spreads,Prepared using Multiple Emulsion Technology

Abstract: This study examined the effectiveness of fat and water soluble antioxidants on the oxidative stability of omega (ω)‐3 rich table spreads, produced using novel multiple emulsion technology. Table spreads were produced by dispersing an oil‐in‐water (O/W) emulsion (500 g/kg 85 camelina/15 fish oil blend) in a hardstock/rapeseed oil blend, using sodium caseinate and polyglycerol polyricinoleate as emulsifiers. The O/W and oil‐in‐water‐in‐oil (O/W/O) emulsions contained either a water soluble antioxidant (green tea extract [GTE]), an oil soluble antioxidant (α‐Tocopherol), or both. Spreads containing α‐Tocopherol had the highest lipid hydroperoxide values, whereas spreads containing GTE had the lowest (P < 0.05), during storage at 5 °C, while p‐Anisidine values did not differ significantly. Particle size was generally unaffected by antioxidant type (P < 0.05). Double emulsion (O/W/O) structures were clearly seen in confocal images of the spreads. By the end of storage, none of the spreads had significantly different G′ values. Firmness (Newtons) of all spreads generally increased during storage (P < 0.05). Practical Application: Lipid oxidation is a major problem in omega‐3 rich oils, and can cause off‐odors and off‐flavors. Double emulsion technology was used to produce omega‐3 enriched spreads (O/W/O emulsions), wherein the omega‐3 oil was incorporated into the inner oil phase, to protect it from lipid oxidation. Antioxidants were added to further protect the spreads by reducing lipid oxidation. Spreads produced had good oxidative stability and possessed functional (omega‐3 addition) properties.     

Lipolysis,lipid peroxidation and texture of Serrano ham processed under different ripening temperature conditions

Lipolysis, lipid peroxidation, texture and rancid taste were investigated in Serrano hams processed under low, medium and high ripening temperature conditions (RTC) for 15 months. Medium RTC hams showed the highest contents of saturated and monounsaturated free fatty acids (FFAs) from month 5 to 15 and of polyunsaturated FFAs from month 7 to 12. The primary peroxidation index decreased during ripening in all hams, with higher levels for low RTC hams from month 5 onwards. Contrarily, the secondary peroxidation index increased during ripening in all hams, with higher levels for medium RTC hams from month 7 onwards. Texture parameters varied significantly among ham muscles. Shear force increased during ripening in all hams, with higher values for medium RTC hams, whereas cutting force was not influenced by RTC or ripening time. Rancid taste scarcely developed during ripening and was not affected by RTC.     

Glycolipids improve lutein bioavailability and accumulation in eyes in mice

Intestinal carotenoid absorption is greatly affected by dietary factors. In this study, it was hypothesized that lipids with varying functional groups may influence differentially lutein bioavailability. Hence, the influence of glyco‐, phospho‐, neutral, crude (mixture of lipids) lipids, or mixed micelles (control) on the percent lutein micellarization in vitro and its postprandial plasma, liver, and eye response in mice were investigated. Results show that the percent micellarization of lutein with crude lipids and glycolipids were higher (91.4 and 45.7%) than control, while no significant difference was found between phospho‐ and neutral lipids. The mean plasma response of lutein was higher for crude‐ (6 times), glyco‐ (3 times), phospho‐ (2.7 times), and neutral (2 times) lipid than control (12.4 ± 1.18 nmol/mL 8 h^?1) group. Lutein levels (pmol/g) in liver were higher in crude (7.4 ± 1) and phospho‐ (3.6 ± 0.8) lipid groups while in eyes it was higher in glyco‐ (54.0) and neutral (21.2) lipid groups than control. The influential effect of glyco‐ and phospholipids may be due to smaller micellar size (glyco‐upto 3.43 µm, phospho‐ upto 5.78 µm) than the neutral lipids (upto 66 µm). Ingestion of lutein with glycolipid or phospholipids may improve lutein bioavailability. Practical applications: The findings of the present study will be useful in nutritional and biomedical applications for feeding lutein with specific lipid combinations to achieve enhanced lutein absorption. Specifically, feeding diet/emulsion with lutein and glyco‐ and phospholipid combination may reduce the risk of macular degeneration, owing to the influential effect of these lipids on intestinal absorption of lutein.     

基于多特定决策类的不完备决策系统正域约简

现有的属性约简方法大部分关注决策系统中的所有决策类，而在实际决策过程中决策者往往仅关注决策系统中的一种或几种决策类。针对上述问题，提出基于多特定决策类的不完备决策系统正域约简的理论框架。首先，给出不完备决策系统单特定决策类正域约简的概念；第二，将单特定决策类正域约简推广到多特定决策类，构造了相应的差别矩阵及区分函数；第三，分析并证明了相关定理，提出基于差别矩阵的不完备决策系统多特定决策类正域约简算法（PRMDM）；最后，选取4组UCI数据集进行实验。在数据集Teaching-assistant-evaluation、House、Connectionist-bench和Cardiotocography上，基于差别矩阵的不完备决策系正域约简算法（PRDM）的平均约简长度分别为4.00、13.00、9.00和20.00，PRMDM算法（多特定决策类中决策类数目为2）的平均约简长度分别为3.00、8.00、8.00和18.00。实验结果验证了PRMDM算法的有效性。