Smarandache Ceil函数的均值

Smarandache函数的相关性质是初等数论和解析数论研究的一个重要问题.本文利用初等方法给出了Smarandache Ceil函数Sk(n)与n的k次补数函数ak(n)之间的关系式(Sk(n))k=ak(n)·n,再利用解析方法给出了Sk(n)一个渐近公式∑n≤xSk(n)=ζ(2k-1)/2x2∏p(1-1/p2+p-1/p2k-1+p2k-2)+O(x3/2+ε).     

一个数论函数与最小素因子函数的混合均值

设n∈N ,Smarandache函数V(1)=1;当n>1时,令n=p11αp22α…prrα是n的标准分解式,V(n)=min1≤i≤r{iα.pi}.利用初等方法研究了一个包含Smarandache函数与最小素因子函数的混合均值,并给出了一个有趣的渐近公式.     

关于Smarandache素数可加补数列

研究著名的Smarandache素数可加补函数SPAC（n）的均值1/n∑a=1^n SPAC（a）的敛散性,利用初等及解析方法,给出了均值1/n∑a=1^n SPAC（a）一个较强的下界估计,证明均值1/n∑a=1^n SPAC（a）是发散的,从而解决了由数论专家Kenichiro Kashihara提出的一个关于函数SPAC（n）的猜想．     

关于Smarandache函数的一个方程

n∈N+,著名的伪Smarandache函数Z(n)定义为满足∑mk=1k能被n整除的最小正整数m,即Z(n)=min{m:n|(m(m+1))/2}.Smarandache互反函数Sc(n)定义为满足y|n!且1≤y≤m的最大正整数m,即Sc(n)=max{m:y|n!,1≤y≤m;m+1 n!}.借助同余方程,利用初等方法,分析数论函数性质,研究了包含伪Smarandache函数Z(n),Smarandache互反函数Sc(n)的方程Sc(n)+Z(n)=2n的解的问题,并给出一些有趣的结果.     

关于欧拉函数φ(n)的一个混合均值

对任意的正整数n,φ(n)和Zw(n)分别表示关于n的Euler函数和伪Smarandache无平方因子函数.利用初等和解析的方法,研究Euler函数和伪Smarandache无平方因子函数的混合均值问题,并给出一个渐近公式.     

2个Smarandache LCM函数的混合均值估计

研究了Smarandache LCM函数SL(n)与r角形数函数ur(n)和vr(n)的混合均值问题.利用初等方法和解析方法,给出了2个有趣的渐近公式,发展了F.Smarandache教授在《Only Problems,Not Solution》中涉及的相关研究工作.     

广义Sierpinski垫上正交指数函数的个数

联系到一个扩张整矩阵和一个数字集M=〔p p1 0 0 p p2 0 0 p〕,D={〔0 0 0〕,〔1 0 0〕,〔0 1 0〕,〔0 0 1〕}的自仿测度μM,D是支撑在迭代函数系{Φd(x)=M-1(x+d)}d∈D关于广义三维Sierpinski垫的吸引子T(M,D)上,且被该吸引子所惟一确定,其中p是奇数,p1,p2∈Z.利用M,D零集的性质,证明了在L2(μM,D)空间中最多存在4个相互正交的指数函数且4是最好估计.     

一个包含Smarandache函数的方程

应罗马尼亚数论专家F．Smarandache教授的要求,寻求一个包含Smarandache函数的方程的整数解．利用初等方法,获得了这个方程的所有正整数解,发展了F．Smarandache教授在《Only Problems,Not Solution））中涉及的相关研究工作．     

岭估计均方误差的下界

讨论岭估计的一些理论问题，给出了若干岭估计均方误差的下界函数。     

压力函数的调和分解及其估计

研究了压力函数的调和分解及其估计.应用Simader关于Laplace方程弱解的Lp估计的结果和R.Müller给定的B ipotential算子的变分估计,将压力函数分解成了一个可测函数p0和奇异部分ph~,并证明了ph~是调和的.进一步,为p0,ph~提供了最理想的先验估计.     

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.     

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.     

Analysis of benzo[a]pyrene in spiked fatty foods by second derivative synchronous spectrofluorimetry after microwave-assisted treatment of samples

A simple, rapid and inexpensive method has been developed for the determination of benzo[a     

The development of reference materials for paralytic shellfish poisoning toxins in lyophilized mussel. II: Certification study

This paper describes the second part of a project undertaken to develop certified mussel reference materials for paralytic shellfish poisoning toxins. In the first part two interlaboratory studies were undertaken to investigate the performance of the analytical methodology for several PSP toxins, in particular saxitoxin and decarbamoyl-saxitoxin in lyophilized mussels, and to set criteria for the acceptance of results to be applied during the certification exercise. Fifteen laboratories participated in this certification study and were asked to measure saxitoxin and decarbamoyl-saxitoxin in rehydrated lyophilized mussel material and in a saxitoxin-enriched mussel material. The participants were allowed to use a method of their choice but with an extraction procedure to be strictly followed. The study included extra experiments to verify the detection limits for both saxitoxin and decarbamoyl-saxitoxin. Most participants (13 of 15) were able to meet all the criteria set for the certification study. Results for saxitoxin.2HCl yielded a certified mass fraction of <0.07 mg/kg in the rehydrated lyophilized mussels. Results obtained for decarbamoyl-saxitoxin.2HCl yielded a certified mass fraction of 1.59+/-0.20 mg/kg. The results for saxitoxin.2HCl in enriched blank mussel yielded a certified mass fraction of 0.48 +/- 0.06 mg/kg. These certified reference materials for paralytic shellfish poisoning toxins in lyophilized mussel material are the first available for laboratories to test their method for accuracy and performance.     

Announcing a new international peer-reviewed journal:Food Science and Human Wellness now accepting manuscript submission in English

<正>We are pleased to announce the launch of a new international peer-reviewed journal-Food Science and Human Wellness,ISSN 2213-4530,which is an open access journal,produced and hosted by Elsevier B.V.on behalf of Beijing Academy of Food Sciences.Food Science and Human Wellness is an international peer-reviewed English journal that provides a forum for the dissemination of the     

Chinese CTP Market

According to Printing and Printing Equipment Industries Association of China（PEIAC）＇s statistics to the plate manufucturer in China, in 2013, the actual offset plate production has reached 346 million square meters in China. Among them, the CTP production volume was 245 million square meters, up by 11% than that of last year; the total sales of the CTP plate was 239 million square meters, up by 13%.     

Preparatory Work of Print China 2015 is Going Smoothly

正Held at Guangdong Modern International Exhibition Center,Print China 2015 will cover 7exhibition halls,besides the original Hall No.3,4,5,6,7,the newly built F zone of Hall 3 will be used too.The total area will be140,000 square meters.Hall 3:Offset and large printing equipment,package printing equipment,post press