涉及重级的亚纯函数族的正规定则

针对徐焱的定理给出了其逆命题成立的条件,进一步改进了Hayman猜想.并得到了新的正规定则:k∈N,设F是D内亚纯函数族,(V)f∈F在D内的零点之级≥k+2,极点之级≥2,h(z)≠0是D上的亚纯函数,若f(k)(z)≠h(z),z∈D,则F在D内正规.     

关于亚纯函数及其k阶导数的惟一性

研究亚纯函数与其k阶导数分担一个IM公共值和一个CM公共值在一定条件下的惟一性问题,考虑吴桂荣有关亚纯函数及其k阶导数具有1CM公共值在一定条件下的惟一性问题,利用构造辅助函数结合Nevanlinna第二基本定理的方法证明了:设f与g为非常数亚纯函数,1为f(k)与g(k)的CM公共值,k∈N,∞为f与g的IM公共值,如果(k+1)-Nr,1f+(k+1)-Nr,1g+2(k+1)N-(r,f)+(1/2)N-D(r,f)(λ+o(1))T(r)(r∈I),其中λ1/2,T(r)=max{T(r,f),T(r,g)},-ND表示相应于f与g所有极点的重级均不相同的f极点的精简密指量,则f(z)≡g(z)或者f(k)(z).g(k)(z)≡1.     

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.     

亚纯函数的正规族与分担集

应用Zalcman-Pang引理,研究了涉及分担集的亚纯函数正规族,所得定理推广了林国斌与陈俊凡的结果．设F为区域D内的一族亚纯函数,h为有穷正数,k为正整数,S={b1,b2},其中b1,b2是2个互异有穷复数,若Vf∈F,f-bi（i=1,2）的零点重级至少为k,且满足（1）f和L（f）分担集合S,（2）当L（f）（z）∈S时,f^（k＋1）（z）≠0且L′（f）（z）｜≤h,则F在区域D内正规．     

两种修正的Meyer-Knig—Zeller算子对有界变差函数的点态逼近度

0 引言M_n(f,x)=sum from k=0 to ∞ f(k/n+k)M_(nk)(x),0≤x≤1.(0.1)其中 M_(nk)(x)=((n+k-1)/k)x~k(1-x)~n陈文忠和郭顺生研究了 M_n(f,x)对[0,1]上的有界变差函数的点态逼近度,证得定理1 设 f∈B∨[0,1],x∈(0,1)。则当 n 充分大时,有     

具有二个公共值的亚纯函数的惟一性

研究两个亚纯函数共享一个IM公共值和一个CM公共值在一定条件下的惟一性问题.考虑了M.Ozawa和仪洪勋有关两个亚纯函数具有2CM公共值的惟一性问题,利用构造辅助函数结合Nevanlinna第二基本定理的方法证明了:设f(z)与g(z)为非常数亚纯函数,1为其CM公共值,∞为其IM公共值,如果N2(r,1/f) N2(r,1/g) -ND(r,f) 2-N(r,f)<(λ o(1))T(r)(r∈I),其中λ<1,T(r)=max{T(r,f),T(r,g)},-ND(r,f)表示相应于f与g所有极点的重级均不相同的f极点的精简密指量,N2(r,1/f)=-N(r,1/f) -N(2(r,1/f),则f(z)≡g(z)或f(z).g(z)≡1.     

分担多项式的全纯函数的正规族

运用Zalcman引理,证明了设F为区域D内的一个全纯函数族,k∈N+(≥2),P(z)是一个多项式,且(e)(P(z))相似文献   

亚纯函数与整函数的复合函数的Julia方向

证明了开平面上有限正级超越亚纯函数f(z)与超越整函数g(z)的复合函数φ(z)=f{g(z)}，至少存在一条Julia方向．     

integral from x to 0 sin(t)dt在x=0的右导数

设 f(x)在区间[0,a]上可积,在[0,a]上连续,且有无限多个零点 x_i(i=1,2,3,…):a≥x_1>x_2>…>x_m>x_(n+1)>…>0,■(x_n-x_(n+1))/x_n=0;■■f(t)dt 则 F■(0)=0.     

具有有限时滞的差分系统的稳定性

考虑具有有限时滞的差分系统 :x(n +1) =f (n,xn) ,n∈ Z,(1)其中 f :Z× Cd → Rk ,f(n,0 )≡ 0 ,n∈ Z,Cd 是所有函数φ:Z[- l,0 ]→ Rk,Z[- l,0 ] ={ - l,… ,- 1,0 }构成的集合 ,xn 定义为 xn(m) =x(n +m) ,m∈ Z[- l,0 ] .对向前差分算子得到了系统 (1)的零解的一致渐进稳定性 .     

Reliable identification of grapevine rootstock varieties using RAPD PCR on woody samples

Since grapevine ( Vitis spp .) rootstock material is being traded increasingly as disbudded woody material a lack of distinctive morphological features on such material necessitates an alternative and reliable means of identification. Methods described here were developed for rapid and efficient extraction of DNA from woody samples rich in phenolic compounds and polysaccharides, and for subsequent identification of varieties by RAPD PCR. Using these methods, and with the application of only one selected RAPD primer, we were able to differentiate sixteen rootstock varieties, including the seven varieties most commonly used in Germany. Problems commonly encountered with reproducibility of RAPD patterns were avoided by choosing primers with a dinucleotide sequence and a high G/C content that allowed a rather high annealing temperature of 45°C. Methods described here should also be useful for other horticultural crops, especially those with woody tissues rich in phenolic compounds and polysaccharides.     

An internet compendium of analytical methods and spectroscopic information for monomers and additives used in food packaging plastics

An internet website (http://cpf.jrc.it/smt/) has been produced as a means of dissemination of methods of analysis and supporting spectroscopic information on monomers and additives used for food contact materials (principally packaging). The site which is aimed primarily at assisting food control laboratories in the European Union contains analytical information on monomers, starting substances and additives used in the manufacture of plastics materials. A searchable index is provided giving PM and CAS numbers for each of 255 substances. For each substance a data sheet gives regulatory information, chemical structures, physico-chemical information and background information on the use of the substance in particular plastics, and the food packaging applications. For monomers and starting substances (155 compounds) the infra-red and mass spectra are provided, and for additives (100 compounds); additionally proton NMR are available for about 50% of the entries. Where analytical methods have been developed for determining these substances as residual amounts in plastics or as trace amounts in food simulants these methods are also on the website. All information is provided in portable document file (PDF) format which means that high quality copies can be readily printed, using freely available Adobe Acrobat Reader software. The website will in future be maintained and up-dated by the European Commission's Joint Research Centre (JRC) as new substances are authorized for use by the European Commission (DG-ENTR formerly DGIII). Where analytical laboratories (food control or other) require reference substances these can be obtained free-ofcharge from a reference collection housed at the JRC and maintained in conjunction with this website compendium.     

Chlorohydrins of bisphenol A diglycidyl ether (BADGE) and of bisphenol F diglycidyl ether (BFDGE) in canned foods and ready-to-drink coffees from the Japanese market

BADGE.2HCl and BFDGE.2HCl were determined in 28 samples of ready-to-drink canned coffee and 18 samples of canned vegetables (10 corn, 5 tomatoes and 3 others), all from the Japanese market. HPLC was used as the principal analytical method and GCMS for confirmation of relevant LC fractions. BADGE.2HCl was found to be present in one canned coffee and five samples of corn, BFDGE.2HCl in four samples of canned tomatoes and in one canned corn. No sample was found which exceeded the 1mg/kg limit of the EU for the BADGE chlorohydrins. However the highest concentration was found for the sum of BFDGE.2HCl and BFDGE.HCl.H₂O at a level of 1.5mg/kg. A Beilstein test confirmed that all cans containing foods contaminated with BADGE.2HCl or BFDGE.2HCl had at lest one part coated with a PVC organosol.     

European priorities for research to support legislation in the area of food contact materials and articles

A strong science base is required to underpin the planning and decision-making process involved in determining future European community legislation on materials and articles in contact with food. Significant progress has been made in the past 5 years in European funded work in this area, with many developments contributing to a much better understanding of the migration process, and better and simpler approaches to food control. In this paper this progress is reviewed against previously identified work-areas (identified in 1994) and conclusions are reached about future requirements for R&D to support legislation on food contact materials and articles over the next 5 or so years.     

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.     

Aroma characterization of various apricot varieties using headspace–solid phase microextraction combined with gas chromatography–mass spectrometry and gas chromatography–olfactometry

The characterization of the aromatic profile of several apricot cultivars with molecular tracers in order to obtain objective data concerning the aromatic quality of this fruit was undertaken using headspace–solid phase microextraction (HS–SPME). Six apricot cultivars were selected according to their organoleptic characteristics: Iranien, Orangered, Goldrich, Hargrand, Rouge du Roussillon and A4025. The aromatic intensity of these varieties measured by HS–SPME–Olfactometry were defined and classified according to the presence and the intensity of grassy, fruity and apricot like notes. In the six varieties, 23 common volatile compounds were identified by HS–SPME–GC–MS. Finally, 10 compounds, ethyl acetate, hexyl acetate, limonene, β-cyclocitral, γ-decalactone, 6-methyl-5-hepten-2-one, linalool, β-ionone, menthone and (E)-hexen-2-al were recognized by HS–SPME–GC–O as responsible of the aromatic notes involved in apricot aroma and considered as molecular tracers of apricot aromatic quality which could be utilized to discriminate apricot varieties.     

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

The advent of the functional barrier concept in food packaging has brought with it a requirement for fast tests of permeation through potential barrier materials. In such tests it would be convenient for both foodstuffs and materials below the functional barrier (sub-barrier materials) to be represented by standard simulants. By means of inverse gas chromatography, liquid paraffin spiked with appropriate permeants was considered as a potential simulant of sub-barrier materials based on polypropylene (PP) or similar polyolefins. Experiments were performed to characterize the kinetics of the permeation of low molecular weight model permeants (octene, toluene and isopropanol) from liquid paraffin, through a surrogate potential functional barrier (25 μm-thick oriented PP) into the food simulants olive oil and 3% (w/v) acetic acid. These permeation results were interpreted in terms of three permeation kinetic models regarding the solubility of a particular model permeant in the post-barrier medium (i.e. the food simulant). The results obtained justify the development and evaluation of liquid sub-barrier simulants that would allow flexible yet rigorous testing of new laminated multilayer packaging materials.     

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.