域上2×2矩阵代数保立方幂等的映射

设F为元素个数大于3的域,M2(F)为F上的2×2矩阵代数,T2(F)≡{T| T3=T,T∈M2(F)}.所有满足φ:M2(F)→M2(F),A+λB∈T2(F)＝>φ(A)+λφ(B)∈T2(F),∨A,B∈T2(F),λ∈F的单映射构成的集合用Φ表示.利用保立方幂等映射和原象之间的关系刻画了集合Φ中元素的形式.     

M2（R）上保持积AB-BAT的映射

设M2(R)是二阶实矩阵代数,A,B∈M2(R),定义新积[A B]T=AB-BAT,其中AT表示矩阵A的转置.φ是M2(R)→M2(R)上的非线性齐次双射且满足([A B]T)=[φ(A)φ(B)]T,则存在正交矩阵Q∈M2(R),对任意矩阵A∈M2(R),都有φ(A)=QAQT.     

一阶常微分方程的一个新的可积类型

证明了若F,Q∈C,而f,h∈C′,且f≠0（其中C表示连续函数的集合,C′表示可导函数的集合）,则一阶常微分方程dydx-f′f(y h)=QF(y hf)-h′可积。并由此结果引出了非线性微分方程一系列新的实用的可积类型,推广了古典的和近代的可积性结果,扩大了微分方程封闭求积的范围。     

关于中心化子的一类映射

X表示实数域或复数域F上的Banach空间,设M是X上的一个标准算子代数,I是M的单位元.证明了若可加映射φ:M→B(X)满足(V)A∈M,(E)非零实数m和n,有(m+n)φ(A2)-mAφ(A)-nφ(A)A∈FI.则(E)λ∈F,使得φ(A)=λA.     

F(S_n)中公式集Γ的全体结论之集D(Γ)的结构

探讨原子公式集为有限集Sn时,二值命题逻辑F(Sn)中公式集Γ的所有结论之集D(Γ)的结构.利用F(Sn)中公式在可证等价意义下的一般表示, 通过建立一个特殊映射,将F(Sn)中公式之间的合取∧、析取∨及否定┐的运算转化为在可证等价意义下某集合的子集之间的求交∩,求并∪,求补′的运算.进而得到(1) 对于A∈F(Sn),Γ( F(Sn),给出了A∈D(Γ)是否成立的充要条件;(2) 对于Γ( F(Sn),给出了Γ是否相容的充要条件;(3) 对于Γ( F(Sn),在可证等价意义下,给出了D(Γ)中所含F(Sn)中公式的个数;(4) 对于Γ1,Γ2 F(Sn),给出了D(Γ1)与D(Γ2)之间的关系;(5) 对于A∈F(Sn),Γ( F(Sn),在可证等价意义下,给出了D(Γ)中与A距离最近的公式.     

The cardinality of μM,D orthogonal exponentials of self-affine measures with two-elements digit set

对于由M=pIN(|p|＞1,p∈Z),D={0,l1 e1+l2 e2+…+lN eN}(∈)ZN (l21+22+…+l2N≠0,lj∈Z,j=1,2,…,N)决定的自仿测度μM,D,支撑在吸引子T(M,D)上.证明当p为奇数时,L2(μM,D)空间中的正交指数函数系最多有2个元素,而且2是最好的估计;当p为偶数时,L2(μM,D)空间中存在含有无限个元素的正交指数函数系.     

平面几何图形相似性的代数刻画

证明了映射T:R2→R2是自相似映射,即TX=k·XU+T0 ((V)X∈R2),其中U为实的2阶正交矩阵, k>0为实数,当且仅当存在常数k>0使得d(TX,TY)=k·d(X,Y) ((V)X,Y∈R2);证明了平面上所有自相似映射之集关于复合运算成为一个群,且平面上的所有自相似压缩映射之集是一个半群;平面上的任一自相似映射T将平面上的任一条直线映射为直线且平面上任一区域D在T下的像T(D)也是一个平面区域. 作为应用,研究了平面图形的相似性.     

三角代数上的广义高阶Jordan导子

设F=(fi)i∈N是环(R)上的一族可加映射,如果a,b ∈(R)且存在一个高阶导子D=(di)i∈N,有fn(ab)=∑fi(a)dj(b),则称F是一个广义高阶导子;如果存在一个高阶Jordan导子D=(dj)i∈N,有fn(a2)=∑i+j=n fi(a)dj(a),则称F是一个广义高阶Jordan导子.证明了...     

关于亚纯函数正规族与分担值

研究亚纯函数单向分担3个公共值的亚纯函数的正规性.利用在函数极点处构造函数结合Hurwitz定理得到了一个更一般的正规定则.设F是区域D上的亚纯函数族,a≠0,b≠0,c为相互判别的有限复数,M1,M3是2个正数,若f∈F,满足(ⅰ)f′=a→|f-c|≥M1,(ⅱ)f=b→f′=b,(ⅲ)f=c→|f′|≤M3,则F在D上正规.     

集合学习漫谈

正中国是由五十六个民族组成的大家庭;15计管班全体同学;小于10的所有质数;到线段AB两端距离相等的所有点组成的图形。常言道:"物以类聚,人以群分"。其实,用数学的观点来看,这就是一种最朴素、最生活化的集合的概念。上面的四句话分别表示中国民族的集合、15计管班全体同学的集合、小于10的质数集合和AB的垂直平分线(点的集会)。集合是数学中最基本的概念之一,集合论也成为现代数学中重要的基础理论。集合是高职数学教材第     

Textural Properties of Cold-set Gels Induced from Heat-denatured Whey Protein Isolates

A 9% whey protein (WP) isolate solution at pH 7.0 was heat-denatured at 80°C for 30 min. Size-exclusion HPLC showed that native WP formed soluble aggregates after heat-treatment. Additions of CaCl2 (10–40 mM), NaCl (50–400 mM) or glucono-delta-lactone (GDL, 0.4–2.0%, w/v) or hydrolysis by a protease from Bacillus licheniformis caused gelation of the denatured solution at 45°C. Textural parameters, hardness, adhesiveness, and cohesiveness of the gels so formed changed markedly with concentration of added salts or pH by added GDL. Maximum gel hardness occurred at 200 mM NaCl or pH 4.7. Increasing CaCl2 concentration continuously increased gel hardness. Generally, GDL-induced gels were harder than salt-induced gels, and much harder than the protease-induced gel.     

Occurrence of bisphenol-F-diglycidyl ether (BFDGE) in fish canned in oil

The levels of bisphenol-F-diglycidyl ether (BFDGE) were quantified as part of a European survey on the migration of residues of epoxy resins into oil from canned fish. The contents of BFDGE in cans, lids and fish collected from all 15 Member States of the European Union and Switzerland were analysed in 382 samples. Cans and lids were separately extracted with acetonitrile. The extraction from fish was carried out with hexane followed by re-extraction with acetonitrile. The analysis was performed by reverse phase HPL C with fluorescence detection. BFDGE could be detected in 12% of the fish, 24% of the cans and 18% of the lids. Only 3% of the fish contained BFDGE in concentrations considerably above 1mg/kg. In addition to the presented data, a comparison was made with the levels of BADGE (bisphenol-A-diglycidyl ether)analysed in the same products in the context of a previous study.     

Contribution of European research to risk analysis

The European Commission's, Quality of Life Research Programme, Key Action 1—Health, Food & Nutrition is mission-oriented and aims, amongst other things, at providing a healthy, safe and high-quality food supply leading to reinforced consumer confidence in the safety of European food. Its objectives also include the enhancing of the competitiveness of the European food supply. Key Action 1 is currently supporting a number of different types of European collaborative projects in the area of risk analysis. The objectives of these projects range from the development and validation of prevention strategies including the reduction of consumers risks; development and validation of new modelling approaches; harmonization of risk assessment principles, methodologies, and terminology; standardization of methods and systems used for the safety evaluation of transgenic food; providing of tools for the evaluation of human viral contamination of shellfish and quality control; new methodologies for assessing the potential of unintended effects of genetically modified (genetically modified) foods; development of a risk assessment model for Cryptosporidium parvum related to the food and water industries; to the development of a communication platform for genetically modified organism, producers, retailers, regulatory authorities and consumer groups to improve safety assessment procedures, risk management strategies and risk communication; development and validation of new methods for safety testing of transgenic food; evaluation of the safety and efficacy of iron supplementation in pregnant women; evaluation of the potential cancer-preventing activity of pro- and pre-biotic ('synbiotic') combinations in human volunteers. An overview of these projects is presented here.     

低温带皮菜籽粕微粉的不同粒级部分的功能特性

为研究低温带皮菜籽粕微粉的不同粒级部分的功能特性,以经低温脱脂的带皮菜籽粕为原料,经微粉碎后筛分成212~425μm、150~212μm和106~150μm的3个不同粒级的微粉样品,检测这些样品的吸水性、吸油性、乳化性和乳化稳定性、蛋白质体外消化率。结果表明:1 3个不同粒级的微粉样品之间的粗纤维含量存在显著差异,表明三者的结构组成成分有一定差异。23个微粉样品的乳化活性和乳化稳定性随粒度级别的减小而显著增加(P0.01)。33个微粉样品的蛋白质体外消化率随粒度级别的减小而显著增加(P0.01)。4不同粒级带皮菜籽粕微粉样品的吸水性与吸油性受其结构组成物质不同和粒度的双重影响,与粒度的相关性不明显。     

Microbiology of food taints

Fresh and processed foods are often spoilt by the presence of undesirable flavours and odours caused by microbial action. The aim of this paper is to review the current knowledge of microbiologically induced taints that occur in a wide range of foodstuffs, including meats, poultry, fish, crustaceans, milk, dairy products, fruits, vegetables, cereals and cereal products. Examples have been chosen where the compounds responsible for the taint have been identified and sufficient data obtained to demonstrate the involvement of microorganisms. However, in some cases the full identity of the causative organism may not have been elucidated. The types of microorganisms covered by this review include bacteria, fungi, yeasts, actinomycetes and cyanobacteria. Although cyanobacteria do not in general infect foods, their presence in aqueous systems and water supplies can lead to off-flavours in aquatic organisms and processed foodstuffs. Several examples of each of these processes are discussed. Wherever possible, the likely biosynthetic pathway used by the microorganism to produce the offending compound in a foodstuff is indicated.     

Analysis for organic residues from aids to polymerization used to make plastics intended for food contact

Polymers intended for food contact use have been analysed for organic residues which could be attributed to a range of substances employed as polymerization aids (e.g. initiators and catalysts). A wide range of polymers was extracted with solvents and the extracts analysed by gas chromatography-mass spectrometry (GC-MS). The overwhelming majority of substances identified were not derived from aids to polymerization but were oligomers, additives and adventitious contaminants. However, a small number of substances were identified as initiator residues. These included tetramethylsuccinonitrile (TMSN) which was observed in two polymers and it derived from recombination of two azobisisobutyronitrile (AIBN) initiator radicals. Methyl benzoate, benzoic acid, biphenyl and phenyl benzoate were detected in one poly(methyl methacrylate) sample and in two polyvinylchlorides and they are thought to be derived from benzoyl peroxide initiator. TMSN was subsequently targeted for analysis of poly-(methyl methacrylate) plastics using proton nuclear magnetic resonance spectrometry (¹     

Tests of potential functional barriers for laminated multilayer food packages. Part II: Medium molecular weight permeants

Experiments were performed to characterize the kinetics of the permeation of different medium molecular weight model permeants: bisphenol A, warfarin and anthracene, from liquid paraffin, through a surrogate potential functional barrier (25 microns-thick orientated polypropylene--OPP) into the food simulants olive oil and 3% (w/v) acetic acid. The characterization of permeation kinetics generally observed the permeation models previously reported to explain the experimental permeation results obtained for a low molecular weight group of model permeants. In general, the model permeants exhibited behaviour consistent with their relative molecular weights with respect to (a) the time taken to attain steady-state permeation into the food simulant in which they were more soluble, (b) their subsequent steady-state permeation rates, and (c) their partition between liquid paraffin and the OPP membrane.     

The development of reference materials for paralytic shellfish poisoning toxins in lyophilized mussel. I: Interlaboratory studies of methods of analysis

This paper describes the first part of a project undertaken to develop mussel reference materials for Paralytic Shellfish Poisoning (PSP) toxins. Two interlaboratory studies were undertaken to investigate the performance of the analytical methodology for several PSP toxins, in particular saxitoxin (STX) and decarbamoyl-saxitoxin (dc-STX) in lyophilized mussels, and to set criteria for the acceptance of results to be applied during the second part of the project: the certification exercise. In the first study, 18 laboratories were asked to measure STX and dc-STX in rehydrated lyophilized mussel material and to identify as many other PSP toxins as possible with a method of their choice. In the second interlaboratory study, 15 laboratories were additionally asked to determine quantitatively STX and dc-STX in rehydrated lyophilized mussel and in a saxitoxin-enriched mussel material. The first study revealed that three out of four postcolumn derivatization methods and one pre-column derivatization method sufficed in principle to determine STX and dc-STX. Most participants (13 of 18) obtained acceptable calibration curves and recoveries. Saxitoxin was hardly detected in the rehydrated lyophilized mussels and results obtained for dc-STX yielded a CV of 58% at a mass fraction of 1.86 mg/kg. Most participants (14 out of 18) identified gonyautoxin-5 (GTX-5) in a hydrolysed extract provided. The first study led to provisional criteria for linearity, recovery and separation. The second study revealed that 6 out of 15 laboratories were able to meet these criteria. Results obtained for dc-STX yielded a CV of 19% at a mass fraction of 3.49mg/kg. Results obtained for STX in the saxitoxin-enriched material yielded a CV of 19% at a mass fraction of 0.34mg/kg. Saxitoxin could not be detected in the PSP-positive material. Hydrolysis was useful to confirm the identity of GTX5 and provided indicative information about C1 and C2 toxins in the PSP-positive material. The methods used in the second interlaboratory study showed sufficiently consistent analysis results to undertake a certification exercise to assign certified values for STX and dc-STX in lyophilized mussel.     

The Ministry of Environmental Protection Issued "Feasible Technology Guidelines for Pollution Prevention and Control in Wood Pulping Process of the Paper Industry (Trial)" and Two Other Guiding Technical Documents

On December 27t＂, 2013, the Ministry of Environmenta Protection announced that, in order to implement ＂The Environmental Protection Law of the People＇ s Republic of China＂, improve the working system in environmenta protection technologies, and promote technologica advancement in pollution prevention, the Ministry of Environmental Protection sponsored the formulation of three guiding technical documents including ＂Feasible Technology Guidelines for Pollution Prevention and Contro n Wood Pulping Process of the Paper Industry （Trial）＂     

1~(st) Intelli-Tissue~ EcoEc Tissue Machine Supplied by PMP Group Successfully Put into Operation in China

正On April 29th,2014,Intelli-Tissue EcoEc tissue machine supplied by PMP Group successfully put into operation at Hebei Xuesong Paper Co.,Ltd.,this is the first such kind of paper machine of PMP Group in China.