Determination of the required HLB values of some essential oils

UPLC-MS/MS法测定鲫鱼中呋喃唑酮代谢物的不确定度评估黎英权，朱伟霞（广东宏科检测技术有限公司，广东惠州 516100）摘 要：依照GB/T 21311—2007应用超高效液相色谱串联质谱法测定鲫鱼中呋喃唑酮代谢物（Furazolidone，AOZ）的残留量，并评定测定过程的不确定度，以提高测定结果的准确性。

通过分析得出，鲫鱼中AOZ的含量为9.605 μg·kg-1，扩展不确定度为0.630 μg·kg-1（k=2）。

在影响鲫鱼中AOZ残留量测定结果的不确定度分量中，标准溶液配制、标准曲线的拟合以及样品重复性测量占比较大，可通过减少这3个不确定度的分量来提高结果的准确性。

关键词：超高效液相色谱串联质谱法；呋喃唑酮；鲫鱼；不确定度Evaluation of Uncertainty in Determination of AOZ Residuesin Crucian Carp by LC-MS/MSLI Yingquan, ZHU Weixia(Guangdong Hongke Testing Technology Co., Ltd., Huizhou 516100, China) Abstract: According to GB/T 21311—2007, ultra-high performance liquid chromatography and mass spectrometry (UPLC-MS/MS) was used to determine the residual amount of furazolidone (AOZ) in crucian carp and assess its uncertainty, so as to improve the accuracy of the determination of AOZ in aquatic products by UPLC-MS/MS. According to the analysis, the content of AOZ in crucian carp is 9.605 μg·kg-1, and its extended uncertainty is 0.630 μg·kg-1 (k=2). Among the uncertainty components that affect the results of AOZ residue in crucian carp, the preparation of standard solution, the fitting of standard curve and the repeatability measurement of sample account for the most. The accuracy of the results can be improved by reducing the components of these three uncertainties.Keywords: ultra-high performance liquid chromatography and mass spectrometry; furazolidone; crucian carp; uncertainty呋喃唑酮（Furazolidone，AOZ）能抑制大多数的病毒和真菌生长，且价格便宜，所以水产养殖户们通常用其治疗一些由病菌引发的疾病[1-3]。

Density of states near the Anderson transition in a space of dimensionality d؍4؊⑀I.M.SuslovP.L.Kapitsa Institute of Physical Problems,Russian Academy of Sciences,117334Moscow,Russia͑Submitted5November1996͒Zh.E´ksp.Teor.Fiz.111,1896–1914͑May1997͒Asymptotically accurate results have been obtained for the average Green’s function and thedensity of states in a Gaussian random potential for dimensionality of space dϭ4Ϫ⑀over theentire energy region,including the vicinity of the mobility threshold.For Nϳ1͑N is theorder of the perturbation theory͒only parquet terms corresponding to higher terms in1/⑀are takeninto account.For large N all powers of1/⑀are taken into account with their coefficientscalculated in the main asymptotic limit in N.This calculation is performed by combining thecondition of renormalization theory with the Lipatov asymptotic limit.©1997American Institute of Physics.͓S1063-7761͑97͒02605-X͔1.INTRODUCTIONAccording to generally accepted thinking,1,2the single-electron density of states does not have a singularity at theAnderson transition,in contrast to the conductivity and thelocalization radius of the wave functions.3–6Nevertheless,itscalculation is of fundamental significance since all knownmethods break down in the vicinity of the transition.In ad-dition,the density of states and the conductivity,definedrespectively by the average Green’s function͗G(x,xЈ)͘andthe correlator͗G R G A͘,are not completely independent.Astudy in the parquet approximation shows7that the math-ematical difficulties in both cases are of the same nature andare connected with the‘‘ghost’’pole problem.On the otherhand,to satisfy the Ward identity linking the eigenenergypart with the irreducible vertex in the Bethe–Salpeterequation8would require exact agreement of the diagramstaken into account in the calculation of the conductivity anddensity of states;this circumstance is not dealt with in any ofthe presently existing theories7with the exception of thetheory recently proposed in Ref.9.For weak disorder the mobility threshold lies in the vi-cinity of the starting boundary of the spectrum,at which therandom potential can be taken to be Gaussian by virtue of thepossibility of averaging over scales that are small in com-parison with the wavelength of the electron,but large incomparison with the distance between scatterers͑the so-called Gaussian segment of the spectrum10͒.Calculation ofthe average Green’s function for the Schro¨dinger equationwith Gaussian random potential reduces to the problem of asecond-order phase transition with an n-component order pa-rameter␸ϭ(␸1,␸2,...,␸n)in the limit n→0.11,12In thiscase the coefficients in the Ginzburg–Landau HamiltonianH͕␸͖ϭ͵d d x ͩ12cٌ͉␸͉2ϩ12␬02͉␸͉2ϩ14u͉␸͉4ͪ͑1͒are linked with the parameters of the disordered system by the relationsc0ϭ1/2m,␬02ϭϪE,uϭϪa0d W2/2,͑2͒where d is the dimensionality of the space,m and E are the mass and energy of the particle,a0is the lattice constant,and W is the amplitude of the random potential͑in what follows we take c0ϭ1͒.The‘‘incorrect’’sign of the coefficient of ͉␸͉4leads to the inapplicability of the usual mean-fieldtheory and the necessity of afluctuational treatment11,13over the entire parameter space;the functional integrals for uϽ0are understood in the sense of an analytic continuation from positive u,which for a retarding Green’s function is carried out through the lower half-plane.12The present paper completes the program of constructing a(4Ϫ⑀)-expansion initiated in Refs.14–16.The dimension-ality of the space dϭ4is singled out for the Hamiltonian͑1͒from considerations of renormalizability:for dϾ4the theory is not renormalizable and the discreteness of the lattice is of fundamental significance,ensuring the existence of a cutoff parameter⌳ϳa0Ϫ1at high momenta14;for dϭ4a logarith-mic situation holds sway,admitting the existence of both non-renormalizable15and renormalizable models16;for dϽ4the theory is renormalizable with the help of one sub-traction,and passage to the continuum limit a0→0, a0d W2→const is possible.The use of simplifications arising at high dimensionalities to construct a(4Ϫ⑀)-dimensional theory requires the successive consideration of all four types of theories;this was done in Refs.14–16and in the present work.The results of this work have already been published in a brief exposition in Ref.17.2.STRUCTURE OF THE APPROXIMATIONThe calculation of the average Green’s function ͗G(p,␬)͑͘p is the momentum and␬is the renormalized value of␬0͒reduces in the standard way to a calculation of the eigenenergy⌺(p,␬),for which the structure of the perturbation-theory series in four-dimensional space at pϭ0has the form15⌺͑0,␬͒Ϫ⌺͑0,0͒ϭ␬2͚Nϭ1ϱu N͚Kϭ0NA N Kͩln⌳␬ͪK.͑3͒Reference16established the structure of the approximation which allows one to obtain asymptotically accurate results ͑in the limit of weak disorder͒for a renormalizable class of models,this being the zeroth approximation for the (4Ϫ⑀)-dimensional theory.For Nϳ1it is sufficient to takeaccount of the coefficients A N N corresponding to the ‘‘leading logarithms;’’for large N this approximation is insufficient in light of the higher rate of growth with respect to N of the coefficients of the lower-order logarithms:therefore it is gen-erally speaking necessary to take account of all the coeffi-cients A N K ,but it suffices to calculate them in the leading asymptotic limit in N .The latter is possible by combining the condition of renormalizability of the theory with the Li-patov asymptotic limit.18The sum of the high-order terms of the perturbation-theory series gives a nontrivial contribution associated with the divergence of the series and is important only for nega-tive u ;this latter result explains why in the usual theory of phase transitions it is possible to restrict the calculation to the leading logarithmic approximation.19,20For d ϭ4Ϫ⑀the expansion analogous to ͑3͒has the form␬2ϩ⌺͑0,␬͒Ϫ⌺͑0,0͒ϵ␬2Y ͑␬͒ϭ␬2͚N ϭ0ϱ͑u ⌳Ϫ⑀͒N ͚K ϭ0NA N K ͑⑀͒ϫͫ͑⌳/␬͒⑀Ϫ1⑀ͬK,͑4͒where the coefficients A N K (⑀)are finite in the limit ⑀→0andA 00(⑀)ϵ1.Expansion ͑4͒follows from the fact that the quan-tity Y in N th-order perturbation theory is a homogeneous polynomial of degree N built up from ⌳Ϫ⑀and ␬Ϫ⑀:indeed,in the transition from the N th-order diagram to the (N ϩ1)-th–order diagram the dimensionality in the momen-tum decreases by ⑀͑Ref.21͒,which gives the factor ⌳Ϫ⑀or ␬Ϫ⑀depending on whether high or low momenta determine the corresponding contribution.Separating out the factor ⑀ϪK ensures the correct limit in expansion ͑3͒as ⑀→0.The standard procedure for carrying out the ⑀-expansion 11,13consists in expanding the coefficients A N K (⑀)in powers of ⑀A N K ͑⑀͒ϭ͚L ϭ0ϱA N K ,L ⑀L͑5͒and preserving in each order of the perturbation theory someof the higher orders in 1/⑀;the first ⑀-approximation corre-sponds to taking account of only the coefficients A N N ,0,which coincide with the coefficients of the leading logarithms in expansion ͑3͒.As is the case for d ϭ4,such an approxima-tion is insufficient for u Ͻ0due to the higher rate of growth with N of the coefficients of the lower terms in 1/⑀:limitingthe expansion to the coefficients A N N ,0is possible only for N ϳ1,whereas for larger N it is necessary to take into ac-count all the coefficients A N K ,L,calculating them in the lead-ing asymptotic limit in N .According to Eq.͑4͒the quantity Y is a function of g 0ϵu ⌳Ϫ⑀and ⌳/␬;it satisfies the Callan–Symanzik equa-tionͩץץln ⌳ϩW ͑g 0,⑀͒ץץg 0ϩV ͑g 0,⑀͒ͪY ϭ0,͑6͒which expresses the condition of renormalizability of the theory,and Eq.͑15͒of Ref.16,which was obtained in an analogous way.The functions W (g 0,⑀)and V (g 0,⑀)can be expanded in the following series:W ͑g 0,⑀͒ϭ͚M ϭ1ϱW M ͑⑀͒g 0M ϭ͚M ϭ1ϱ͚M Јϭ0ϱW M ,M Јg 0M ⑀M Ј,͑7͒V ͑g 0,⑀͒ϭ͚M ϭ1ϱV M ͑⑀͒g 0M ϭ͚M ϭ1ϱ͚M Јϭ0ϱV M ,M Јg 0M ⑀M Ј,whose first coefficients were calculated in Ref.21:W 1͑⑀͒ϭϪ⑀,W 2,0ϭK 4͑n ϩ8͒,͑8͒W 3,0ϭϪ3K 42͑3n ϩ14͒,V 1,0ϭϪK 4͑n ϩ2͒͑according to Ref.16the function V (g 0,⑀)coincides withthe function ␩2(g 0,⑀)introduced in Ref.21͒;the quantity K 4is defined in Eqs.͑14͒.Substituting expansions ͑4͒and ͑7͒into Eq.͑6͒leads to a system of equations for the coef-ficients A N K (⑀):͑K ϩ1͒A N K ϩ1͑⑀͒ϭ͑N ϪK ͒⑀A N K ͑⑀͒Ϫ͚M ϭ1N ϪK͓͑N ϪM ͒W M ϩ1͑⑀͒ϩV M ͑⑀͔͒A N ϪM K͑⑀͒,͑9͒or for the coefficients A N K ,L:͑K ϩ1͒A N K ϩ1,L ϭ͑N ϪK ͒A NK ,L Ϫ1͑1Ϫ␦L ,0͒Ϫ͚M ϭ1N ϪK͚M Јϭ0L͓͑N ϪM ͒W M ϩ1,M ЈϩV M ,M Ј͔A N ϪMK ,L ϪM Ј.͑10͒Wilson’s method 11,13is based on the fact that in then th ⑀-approximation one needs to know the coefficients A NN ϪK ,L for K ϩL рn Ϫ1,for which Eqs.͑10͒yield the closed system of difference equationsϪNx N ϭ͓W 2,0͑N Ϫ1͒ϩV 1,0͔x N Ϫ1,Ϫ͑N Ϫ1͒y N ϭ͓W 2,0͑N Ϫ1͒ϩV 1,0͔y N Ϫ1ϩ͓W 3,0͑N Ϫ2͒ϩV 2,0͔x N Ϫ2,ϪNz N ϭ͓W 2,0͑N Ϫ1͒ϩV 1,0͔z N Ϫ1ϩ͓W 2,1͑N Ϫ1͒ϩV 1,1͔x N Ϫ1Ϫy N ,͑11͒͑where x N ϵA N N ,0,y N ϵA N N Ϫ1,0,z N ϵA N N ,1,...͒,which issolvable by the method of variation of parameters;22assign-ing the initial conditions and determining the quantities W 2,0,V 1,0,...requires the calculation of some lower or-ders of the perturbation theory.In particular,for the coeffi-cients A N N ,0we easily obtainA N N ,0ϭ͑ϪW 2,0͒N⌫͑N Ϫ␤0͒⌫͑N ϩ1͒⌫͑Ϫ␤0͒,␤0ϭϪV 1,0W 2,0ϭn ϩ2n ϩ8.͑12͒To investigate the higher orders in ⑀,the Wilson method turns out to be ineffective,and it is more convenient to start with ͑9͒.Information about the coefficients A N K (⑀)forN ӷ1can be obtained by the Lipatov method,18according to which the later coefficients of the expansion in u of the func-tional integrals with the Hamiltonian ͑1͒are determined by the saddle-point configurations—instantons—and have fac-torial growth in N .For factorial series there exists a simple algebra that enables one to manipulate them as simply as finite expressions,15which in turn enables one to find the expansion coefficients of arbitrary M -point Green’s func-tions,proceed from them to the eigenenergy and the vertex parts,etc.According to Sec.6,the N th coefficient of the expansion of ⌺(p ,␬)in powers of u has the form͓⌺͑p ,␬͔͒N ϭc 2⌫͑N ϩb ͒ϫa N͵ϱd ln R 2R Ϫ2͗␾c 3͘Rp ͗␾c 3͘ϪRpϫexp ͩϪN f ͑␬R ͒ϩN ⑀ln R ϩ2K d I 4͑␬R ͒1Ϫ͑⌳R ͒Ϫ⑀⑀ͪ,͑13͒wherea ϭϪ3K 4,b ϭd ϩ22,c 2ϭc ͑3K 4͒7/2,f ͑x ͒ϭϪ⑀2͑C ϩ2ϩln ␲͒Ϫ3x 2ͩC ϩ12ϩln x 2ͪ,͗␾c 3͘p ϭ8&␲2pK 1͑p ͒,I 4͑x ͒ϭI ˜4exp ͑f ͑x ͒͒,I ˜4ϭ163S 4,S d ϭ2␲d /2/⌫͑d /2͒,K d ϭS d ͑2␲͒Ϫd ,͑14͒C is Euler’s constant,K 1(x )is the modified Bessel function,and the constant c is defined below in Sec.VI.Re-expanding series ͑4͒␬2ϩ⌺͑0,␬͒Ϫ⌺͑0,0͒ϭ␬2͚N ϭ0ϱ͑u ␬Ϫ⑀͒N ͚K ϭ0NB N K ͑⑀͒ϫͫ1Ϫ͑⌳/␬͒Ϫ⑀⑀ͬK,͑15͒in such a way that the coefficients B N K (⑀)are related to thecoefficients A N K(⑀)byA N K ͑⑀͒ϭ͚K Јϭ0KC N ϪK ЈN ϪK B N K Ј͑⑀͒⑀K ϪK Ј,͑16͒setting p ϭ0in Eq.͑13͒,making the substitution R →R /␬,and transforming the exponentialexp ͭ2K d I 4͑R ͒1Ϫ͑⌳R /␬͒Ϫ⑀⑀ͮϭexp ͭ2K d I 4͑R ͒1ϪR Ϫ⑀⑀ͮϫ͚K ϭ0ϱ͕2K d I 4͑R ͒R Ϫ⑀͖K K !ͫ1Ϫ͑⌳/␬͒Ϫ⑀⑀ͬK,͑17͒we obtain for the coefficients B N K (⑀)at large NB N K ͑⑀͒ϭc ˜2⌫͑N ϩb ͒aN 1K !͵ϱd ln R 2R Ϫ2ϫ͑2K d I 4͑R ͒R Ϫ⑀͒Kϫexp ͩϪN f ͑R ͒ϩN ⑀ln R ϩ2K d I 4͑R ͒1ϪR Ϫ⑀⑀ͪ,͑18͒where c ˜2ϭc 2͗␾c 3͘02.By analogy with the case d ϭ4͑Ref.16͒,the Lipatov method reproduces the coefficients B N K (⑀)well only for K ӶN ,which is connected with their rapid falloff with K and the limited accuracy (ϳ1/N )of the lead-ing asymptotic behavior.Substituting ͑18͒into Eq.͑16͒,we obtain the following result for the coefficients A N K (⑀)with N ӷ1:A N K ͑⑀͒ϭc ˜2⌫͑N ϩb ͒a N C NK ͵ϱd ln R 2R Ϫ2ϫͩ⑀ϩ2K d I ˜4Ne f ͑R ͒Ϫ⑀ln R ͪKϫexp ͩϪN f ͑R ͒ϩN ⑀ln R ϩ2K d I 4͑R ͒1ϪR Ϫ⑀⑀ͪ,͑19͒which follows from Eq.͑18͒under the condition that the sum in Eq.͑16͒is determined by values of K ЈӶN .Retaining only the term with M ϭ1in the sum ͑9͒,it is easy to con-vince oneself that the equation so obtained is satisfied by the result ͑19͒for K ӶN in the case N ⑀Շ1and for all K for N ⑀ӷ1.The latter has to do with the fact that for N ⑀ӷ1,the sum in Eq.͑16͒is determined by values of K ЈϳK /⑀N ӶN for all K in the region of applicability of formula ͑18͒.The indicated reduction of Eq.͑9͒is possible at large N by virtue of the factorial growth of A N K (⑀)under the assumption that W N (⑀)and V N (⑀)grow more slowly than A N 0(⑀).This latter result can be assumed to be a consequence of the validity of formula ͑19͒for K ϭ0,1,2͑see Ref.16for a more detailed exposition ͒.The system of equations ͑9͒determines the coefficients A N K(⑀)with K Ͼ0for prescribed A N 0(⑀).Since Eq.͑19͒is valid for the latter for all N ӷ1,it can be used as a boundary condition on system of equations ͑9͒,which enables one to determine all the A N K (⑀)with large N .Thus,retaining only the leading order in 1/⑀for N ϳ1,defined by the coefficients ͑12͒,it is not hard to find the sum of series ͑4͒.3.STUDY OF THE COEFFICIENTS A N K(⑀)We will limit the sum ͑9͒to terms with M ϭ1and M ϭ2:KA N K ͑⑀͒ϭ͑N ϪK ϩ1͒⑀A N K͑⑀͒ϪW 2͑⑀͓͒N Ϫ1Ϫ␤͑⑀͔͒ϫA N Ϫ1K Ϫ1͑⑀͒ϪW 3͑⑀͒NA N Ϫ2K Ϫ1͑⑀͒,͑20͒Here␤͑⑀͒ϭϪV 1͑⑀͒W 2͑⑀͒——→⑀→0␤0.͑21͒We set A NN ϩ1(⑀)ϭ0by definition in order to account for theabsence of the last term in Eq.͑20͒with K ϭN .The last term in Eq.͑20͒is of order ϳ1/N in comparison with the previous term and is taken to lowest order in 1/N ;the need to take it into account has to do with the fact that to calculate A N K (⑀)with K ϳN from the assigned values of A N 0(⑀)requires ϳN iterations,and for an accuracy of each iteration of ϳ1/N the errors build up.In what follows we will drop the argument ⑀in the intermediate formulas.Making the substitutionA N K ϭ͑ϪW 2͒K⌫͑N Ϫ␤͒⌫͑K ϩ1͒⌫͑N ϪK Ϫ␤͒A N ϪK 0X N ,N ϪK͑22͒in Eq.͑20͒and introducing the notationh M ϭϪ⑀W 2A M ϩ10A M0M ϩ1M Ϫ␤,f M ϭW 3W 2A M Ϫ10A M 0͑M Ϫ1Ϫ␤͒,͑23͒we obtainX N ,M ϭh M X N ,M ϩ1ϩX N Ϫ1,M ϩf MN XN Ϫ2,M Ϫ1͑24͒with boundary conditionX N ,N ϭ1.͑25͒Rewriting Eq.͑24͒in the formX N ,M ϭ͑l ˆM ϩ␦ˆM ͒X N ,M ϩ1,͑26͒wherel ˆM ϵh M ϩe Ϫipˆ,␦ˆMϵf M Ne Ϫ2ip ˆ,͑27͒e Ϫipˆis the shift operator by Ϫ1,which operates on both arguments,and invoking the boundary condition ͑25͒,it is easy to obtainX N ,M ϭ͑l ˆM ϩ␦ˆM ͒͑l ˆM ϩ1ϩ␦ˆM ϩ1͒...͑l ˆN Ϫ1ϩ␦ˆN Ϫ1͒X N ,Nϭl ˆM l ˆM ϩ1...l ˆN Ϫ11ϩ͚p 1ϭMN Ϫ1l ˆM ...l ˆp 1Ϫ1␦ˆp 1l ˆp 1ϩ1...l ˆN Ϫ11ϩ͚p 1ϭM N Ϫ2͚p 2ϭp 1ϩ1N Ϫ1l ˆM ...l ˆp 1Ϫ1␦ˆp 1l ˆp 1ϩ1...l ˆp 2Ϫ1ϫ␦ˆp 2l ˆp 2ϩ1...l ˆN Ϫ11ϩ....͑28͒We do not indicate the argument N of the operator ␦ˆ,which is shown on the left side of the equation.The main contribu-tion to the sum comes from terms with a small number ofoperators ␦ˆ,which are not difficult to calculate.The result l ˆM l ˆM ϩ1...l ˆM ЈϪ1ϭ͚L ϭ0M ЈϪMC M ЈϪM Lh M h M ϩ1...h M ЈϪL Ϫ1e ϪiLp ˆ,͑29͒which determines the zeroth-order term in ␦ˆ,follows by in-duction.For products with one ␦ˆoperator we have l ˆM ...l ˆp 1Ϫ1␦ˆp 1l ˆp 1ϩ1...l ˆM ЈϪ1ϭ͚L 1ϭ0p 1ϪM ͚L 2ϭ0M ЈϪp 1Ϫ1C p 1ϪM L 1C M ЈϪp1Ϫ1L2h M ...h p 1ϪL 1Ϫ1ϫf p 1ϪL 1N ϪL 1h p 1ϪL 1Ϫ1...h M ЈϪL 1ϪL 2Ϫ3e Ϫi ͑L 1ϩL 2ϩ2͒p ˆ.͑30͒Noting that by virtue of ͑23͒f p 1ϪL 1h p 1ϪL 1Ϫ1ϭͩϪ⑀W 3W 22ͪ͑p 1ϪL 1͒,͑31͒we reduce the result ͑30͒to the formͩϪ⑀W 3W 22͚ͪLh M ...h M ЈϪL Ϫ3e Ϫi ͑L ϩ2͒pˆϫ͚L1C p 1ϪM L1C M ЈϪp 1Ϫ1L ϪL 1p 1ϪL 1N ϪL 1.͑32͒The sum over L 1has a saddle-point at L c ϭL (p 1ϪM )/(M ЈϪM Ϫ1);replacing L 1by L c in the last fraction in ͑32͒and making use of the addition theorem for binomial coefficients ͑Ref.22,p.745͒we obtainͩϪ⑀W 3W 22͚ͪLC M ЈϪM Ϫ1Lh M ...h M ЈϪL Ϫ3e Ϫi ͑L ϩ2͒pˆϫp 1Ϫ͑p 1ϪM ͒␶N Ϫ͑p 1ϪM ͒␶ͯ␶ϭL /͑M ЈϪM Ϫ1͒.͑33͒Result ͑33͒has the same structure as ͑29͒,and by induction it is not hard to find products with a moderate number s of ␦ˆoperators;from Eq.͑28͒we obtain X N ,M ϭ͚s ϭ0ϱͩϪ⑀W 3W 22ͪs ͚L ϭ0min ͕N ϪM Ϫs ,N Ϫ2s ͖ϫC N ϪM Ϫs L h M ...h N ϪL Ϫ2s Ϫ1ϫ͚p 1ϭMN Ϫsp 1Ϫ͑p 1ϪM ͒␶N Ϫ͑p 1ϪM ͒␶͚p 2ϭp 1ϩ1N Ϫs ϩ1ϫp 2Ϫ2Ϫ͑p 2ϪM Ϫ1͒␶N Ϫ2Ϫ͑p 2ϪM Ϫ1͒␶͚p s ϭp s Ϫ1ϩ1N Ϫ1ϫp s Ϫ2s ϩ2Ϫ͑p s ϪM Ϫs ϩ1͒␶N Ϫ2s ϩ2Ϫ͑p s ϪM Ϫs ϩ1␶ͯ␶ϭL /͑N ϪM Ϫs ͒.͑34͒Calculating the sum over p 1,p 2,...,p s in the two over-lapping regions of parameter space,we obtain the following results for it (␶Јϵ1Ϫ␶):1s !ͭM ϩ␶Ј͑N ϪM ͒͑1Ϫ␶Ј͒2lnN␶ЈN ϩ͑1Ϫ␶Ј͒M Ϫ␶Ј͑N ϪM ͒1Ϫ␶Јͮs,max ͕␶ЈN ,M ͖ӷs ,͑35͒1s !⌫͑M ϩ␶ЈN ϩ1͒⌫͑M ϩ␶ЈN Ϫs ϩ1͒ͭlnN ␶ЈN ϩM ϪsϪ␶ЈN␶ЈN ϩMͮs,␶ЈN ϳM ϳs .͑36͒In the first case it is possible to neglect quantities ϳs in thefractions within the summation range,and transform from sums to integrals;in the second case it is possible to calcu-late the sums systematically by separating out the two high-est powers of the large logarithms.Formula ͑36͒is valid literally for s ӷ1,whereas for s ϳ1the difference between the expression in braces and ln N exceeds the accuracy of the calculation.The producth M h M ϩ1...h N ϪL Ϫ2s Ϫ1ϭͩϪ⑀W 2ͪN ϪL Ϫ2s ϪMA N ϪL Ϫ2s0A M0ϫ⌫͑M Ϫ␤͒⌫͑M ϩ1͒⌫͑N ϪL Ϫ2s ϩ1͒⌫͑N ϪL Ϫ2s Ϫ␤͒͑37͒entering into expression ͑34͒depends on the coefficients A N 0,which are assumed to be known.By analogy with the case d ϭ4͑Ref.16͒,in the (N ,K )plane it is possible to distinguish two regions in Fig.1:region I,in which the sum in ͑34͒is determined by indices N ϪL Ϫ2s ӷ1,such that the Lipatov asymptotic limit is valid for the coefficients A N 0,and region II ͑M Ӷln N ,N ⑀Ӷ1͒,‘‘controlled’’by the trivial co-efficient A 00ϭ1.Between regions I and II lies the region of non-universality—region III ͑M ϳln N ,N ⑀Շ1͒,in which in-formation about the coefficients A N 0with N ϳ1is important.Region III does not make a substantial contribution to the sum ͑4͒.The conditions N ϪL Ϫ2s ӷ1,max ͕␶ЈN ,M ͖ӷ1,and N ϪM ϪL ӷs are satisfied in region I for N ⑀տ1.This en-ables one to use ͑19͒for A N 0and ͑35͒for the sum over p i ,and neglect the magnitude of s in the slowly varying func-tions within the summation range in ͑34͒and to sum over s .After substituting the result back into ͑22͒,we obtainA N N ϪM ϭ⑀N ϪM M !c ˜2⌫͑N Ϫ␤͒a N ͚L ϭ0N ϪM͑N ϪL ͒!L !͑N ϪL ϪM ͒!ϫͩϪW 2a ⑀ͪLJ ͑N ϪL ͒͑N ϪL ͒b ϩ␤e S ͑L ͒,͑38͒whereJ ͑N ͒ϭ͵ϱd ln R 2R Ϫ2exp ͩϪN f ͑R ͒ϩN ⑀ln Rϩ2K d I 4͑R ͒1ϪR Ϫ⑀⑀ͪ,͑39͒S ͑L ͒ϭW 3⑀a 2L ͩN ϪL ϪMN ϪLͪ2ϫͫ1ϩ͑N ϪL ͒͑N ϪM ͒L ͑N ϪM ϪL ͒ln N ϪL Nͬ.͑40͒For N ϪM ӶN or N ⑀ӷ1,the sum over L in ͑38͒isdetermined by values L ӶN ,and ͑38͒goes over to ͑19͒.For M ϳ1,͑38͒becomesA NN ϪM ͑⑀͒ϭ1M !⑀N ϪMc ˜2⌫͑NϪ␤͒a N ͱt /2␲exp ͫf ϱ͑Nt ln N Ϫ1͒ϩ1tͬϫ͵ϱdx exp ͫϪt 2ͩN Ϫ1tϪxͪ2ͬϫx M ϩb ϩ␤Ϫf ϱNt J ͑x ͒,͑41͒wheret ϭϪ⑀a W 2——→⑀→03⑀n ϩ8,f ϱϭW 3aW 2——→⑀→03n ϩ14n ϩ8.͑42͒The assumptions made in the derivation of ͑41͒are fulfilled in the region Nt Ͼ1or 1ϪNt Ӷ⑀1/2.For N ⑀Ӷ1,the sum over L in ͑34͒is determined by the neighborhood of the upper limit of the sum,so that ␶ЈӶ1;for M ӷln N and M ϳln N ,Eqs.͑35͒and ͑36͒apply,respec-tively.For M Ӷln N ,terms with s уM ,L ϭN Ϫ2s dominate,and by virtue of the equality A 00ϭ1we have the following result for region II:A NN ϪM ͑⑀͒ϭ͑ϪW 2͒N ⌫͑N Ϫ␤͒⌫͑N ϩ1͒⌫͑Ϫ␤͚͒L ϭ0ϱ⑀L1M !L!FIG.1.Regions I and II,which give nonperturbative and quasiparquet con-tributions to the sum ͑4͒;the parameter t ϳ⑀is defined by formula ͑42͒.Thenonperturbative contribution is estimated in effect for N ϭ␬⑀/au ;the in-equality ␬⑀/au Ͼ1/t corresponds to a positive value of ⌬͑see Eq.͑45͒͒.ϫͩϪW 3W 22ͪM ϩL͑N ln N ͒M ϩL ,͑43͒which can be obtained from the system of equations ͑11͒byseparating out the leading asymptotic behavior in N for A NN ϪK ,L.For N ⑀ln N Ӷ1,terms with s рM dominate,and for arbitrary M we have the resultX N ,M ϭ⌫͑M Ϫ␤͒A M0͚s ϭ0M A M Ϫs0⌫͑M Ϫs Ϫ␤͒1s !ϫͩW 3W 2ln NM Ϫs ϩ1ͪse t ͑N ϪM ͒M ,͑44͒whose region of applicability expands without limit as⑀→0,and this result transforms to Eqs.͑42͒and ͑43͒of Ref.16for d ϭ4.4.ENERGY RENORMALIZATION AND DECAYAs in the case d ϭ4͑Ref.16͒,there are two important contributions to the sum ͑4͒—a nonperturbative and a quasi-parquet contribution,arising respectively from regions I and II ͑Fig.1͒.We restrict the discussion to the continuum limit ⌳→ϱ,in which only the coefficients A N N (⑀)remain in the sum ͑4͒.The quasiparquet contribution is calculated on the basis of formula ͑43͒,and has the form͓Y ͑␬͔͒quasiparq ϭͫ⌬ϩW 3͑⑀͒W 2͑⑀͒u ␬Ϫ⑀ln ⌬ͬ␤͑⑀͒,⌬ϵ1ϩW 2͑⑀͒u␬Ϫ⑀⑀,͑45͒where the coefficients W 2(⑀),W 3(⑀),and ␤͑⑀͒can be taken to zeroth order in ⑀.Within the limits of accuracy of the calculations,the argument ⌬of the logarithm can be re-placed by its minimum value ⌬˜ϳ⑀ln ⑀͑defined by Eqs.͑51͒and ͑52͒below ͒,since for ⌬ӷ⌬˜the logarithmic term is un-important.Therefore ͑45͒can be rewritten in the form͓Y ͑␬͔͒quasiparq ϭ͓1ϩW 2,0u ˜␬Ϫ⑀/⑀͔␤0,u ˜ϵu ͫ1ϩW 3,0W 2,02⑀ln ⌬˜ͬ,͑46͒which differs from the parquet form 23only by the substitu-tion of u ˜for u .To calculate the nonperturbative contribution,we setA N N ͑⑀͒ϭc ˜2⌫͑N ϩb ͒⑀N a N F ͑N ͒͑47͒and sum ͑4͒from some large N 0to infinity according to Eq.͑46͒in Ref.16:͓⌺͑0,␬͔͒nonpert ϵi ⌫0͑␬2͒ϭi ␲c ˜2␬2͑␬⑀/au ͒b eϪ␬⑀/auF ͑␬⑀/au ͒.͑48͒The nonperturbative contribution is associated with the di-vergence of the series,and formally arises from the region ofarbitrarily large N .However,it must be calculated on the basis of ͑41͒,not ͑19͒,since the correction factor distinguish-ing ͑41͒from ͑19͒is evaluated in effect for N ϭ␬⑀/au andturns out to be substantial.I did not recognize this circum-stance in Ref.17;therefore,Eqs.͑22͒and ͑23͒in Ref.17differ from Eqs.͑52͒,͑53͒,and ͑55͒below.Approximating the series ͑4͒by the sum of contributions ͑46͒and ͑48͒,we obtain␬02Ϫ␬c 2ϭ␬2͓1ϩ8K 4u ˜␬Ϫ⑀/⑀͔1/4ϩi ⌫0͑␬2͒,␬2ϭϪE Ϫi ⌫,͑49͒where ␬c 2ϭ⌺(0,0)and we have allowed for the fact that ␬02ϭ␬2ϩ⌺(0,␬).Equation ͑49͒is solved like Eq.͑93͒in Ref.15.Setting␬2ϭ͉␬͉2eϪi ␸,x ϭ2⑀͉ͫͩ␬͉2⌫cͪ⑀/2Ϫ1ͬ,⌫c ϭͩ8K 4͉u ˜͉⑀ͪ2/⑀͑50͒and separating the real and imaginary parts of ͑49͒,we ob-tain a connection between the decay ⌫and the renormalized energy E with the unrenormalized energy E B ϭϪ␬02in para-metric form:⌫ϭ⌫c ͩ1ϩ⑀x2ͪ2/⑀sin ␸,E ϭϪ⌫c ͩ1ϩ⑀x2ͪ2/⑀cos ␸,ϪE B ϩE c ϭ⌫c ͩ1ϩ⑀x2ͪ2/⑀ͩ⑀x /21ϩ⑀x /2ͪ1/4ͫcos ͩ␸ϩ␸4xͪϪtan␸͑1ϩ2⑀x ͒3sin ͩ␸ϩ␸4xͪͬ,͑51͒where E c is defined by Eq.͑108͒in Ref.15,and x (␸)is asingle-valued function in the interval 0Ͻ␸Ͻ␲,analogous to the function shown in Fig.2of Ref.15,and implicitly defined by the equationsin ͩ␸ϩ␸4x ͪϭe Ϫ4x /3x 1/4I ͑x ͒cos␸͑1ϩ2⑀x ͒3,͑52͒whereI ͑x ͒ϭc ˜2ͩ34ͪ1/4ͩ␲t 2ͪ1/2ϫexp ͭϪf ϱϩf ϱͩ1ϩ⑀x 2ͪln ͫ⌬˜ͩ1ϩ⑀x 2ͪͲtͬͮϫ͵0ϱdz exp ͫϪt 2ͩ⑀x 2tϪz ͪ2ͬz b ϩ␤Ϫf ϱ͑1ϩ⑀x /2͒J ͑z ͒.͑53͒Equations ͑51͒and ͑52͒simplify substantially in two over-lapping regions.For x ӷln(1/⑀),i.e.,at high ͉E ͉,where theright-hand side of Eq.͑52͒is small and the quantity ␸is near 0or ␲,we obtain the asymptotic behavior of ⌫(E ),⌫͑E ͒ϭͭ18␲⑀E ͓͑E /⌫c ͒⑀/2Ϫ1͔Ϫ1,E ӷ⌫,⌫0͑E ͓͒1Ϫ͉͑E ͉/⌫c ͒Ϫ⑀/2͔Ϫ1/4,ϪE ӷ⌫,͑54͒which produce the illusion of a ghost pole 7(⌫0(E )ϵ⌫0(͉␬͉2)).For large positive E the result of the kinetic equation is reproduced;for large negative E the de-cay becomes purely nonperturbative.At low energies,x Շ⑀Ϫ1/2,we havesin ͩ␸ϩ␸4x ͪϭI ͑0͒e Ϫ4x /3x 1/4cos ␸3,I ͑0͒ϳ⑀Ϫ7/12ͩln 1⑀ͪ17/12,͑55͒which describes the neighborhood of the ghost pole and has the same functional form as the four-dimensional equation ͑see Eq.͑51͒in Ref.16for x Ӷx 0and Eq.͑100͒in Ref.15͒.The minimum values of ⌬and x are reached simultaneously,and to logarithmic accuracy they are⌬min ϵ⌬˜Ϸ78⑀ln 1⑀,x min Ϸ716ln 1⑀,͑56͒so that the detour about the pole must be taken at a distance of the order of ⑀ln(1/⑀).5.DENSITY OF STATESTo calculate the density of states requires a knowledge of the eigenenergy ⌺(p ,␬)for finite momenta 15;like p ϭ0,this quantity consists of a nonperturbative and a quasiparquet contribution.The quasiparquet contribution is given by the parquet equations ͑Ref.15,Sec.7͒with the substitutionu →uˆ;the proof of this is completely analogous to the situ-ation d ϭ4͑Ref.16,Sec.5͒.The nonperturbative contribu-tion turns out to be important only in the region of large negative E ,where it is directly determined by the Lipatov asymptotic behavior,and can be calculated on the basis of formula ͑13͒͑for N ϭ␬⑀/au ӷ1/⑀the correction factor dis-tinguishing results of the type ͑41͒and ͑19͒is equal to unity ͓͒⌺͑p ,␬͔͒nonpert ϭi ␲c 2␬2ͩ␬⑀auͪbeϪ␬⑀/auϫ͵ϱd ln R 2R Ϫ2͗␾c 3͘pR /␬͗␾c 3͘ϪpR /␬ϫexp ͭϪ␬⑀au͓f ͑R ͒Ϫ⑀ln R ͔ϩ2K d I 4͑R ͒⑀ͮ.͑57͒For p ϭ0the integral is governed by the neighborhood of the saddle point R 0,which is a root of the equation⑀ϭ6R 02͑Ϫln R 0ϩln 2ϪC Ϫ1͒,͑58͒so that R 0Ϸͱ⑀/3ln(1/⑀).For p Շ␬R 0Ϫ1,Eq.͑57͒does notdepend on p ;for p տ␬R 0Ϫ1it falls off rapidly with increasing p .By virtue of the logarithmic accuracy of the following calculations ͑Ref.15,Sec.8͒the result͓⌺͑p ,␬͔͒nonpert Ϸ͓⌺͑0,␬͔͒nonpert ␪͑␬R 0Ϫ1Ϫp ͒.͑59͒suffices.Taking the above into account,the final expression for ⌺(p ,␬)has the form⌺͑p ,␬͒Ϫ⌺͑0,␬͒ϭ␬2ͭ1Ϫ32ͫt ͑x ͒t ͑x ϱ͒ͬϪ1/4ϩ12ͫt ͑x ͒t ͑x ϱ͒ͬϪ3/4ͮϪi ⌫0͑␬2͒␪͑p Ϫ␬R 0Ϫ1͒͑60͒͑cf.Eq.͑116͒in Ref.15͒,wheret ͑x ͒ϭ1ϩ8K 4u ˜x /⑀,x ϭp Ϫ⑀,x ϱϭ␬Ϫ⑀.͑61͒Substituting ͑60͒into Eqs.͑117͒and ͑118͒of Ref.15for d ϭ4Ϫ⑀,we obtain␯ϭ⌫c4␲͉u ˜͉ͩ1ϩ⑀x 2ͪ2/⑀ͭͩ1ϩ2⑀xͪϪ1/4ͩ1ϪR 0⑀2ϩ⑀xͪϫsin ͩ␸ϩ␸4x ͪϪͩ1ϩ2⑀xͪϪ3/4sin ͩ␸ϩ3␸4xͪͮ,͑62͒which together with ͑51͒and ͑52͒,determines the density of states ␯(E )in parametric form.Let us now turn our attention to the presence of scaling:for the energy measured in units of ⌫c and the density ofstates in units of ⌫c /͉u ˜͉,all dependences are determined by universal functions that are independent of the degree of dis-order.For ͉E ͉ӷ⌫,we have the asymptotic behavior␯͑E ͒ϭΆ12K 4E ͑d Ϫ2͒/2ͫ1ϪͩE ⌫cͪϪ⑀/2ͬϪ1/4,E ӷ⌫,⌫0͑E ͒4␲͉u ˜͉ͭ1ϪR 0⑀2͉ͩE ͉⌫c ͪϪ⑀/2Ϫͫ1Ϫ͉ͩE ͉⌫c ͪϪ⑀/2ͬ1/2ͮ,ϪE ӷ⌫,͑63͒indicating a ghost pole.For large positive E ,the function ␯(E )transforms into the density of states of an ideal system,and at large negative energies E we obtain the following result for the fluctuation tail:␯͑E ͒ϭK 4␲⌫0͑E ͉͒E ͉Ϫ⑀/2ln 1R 0ϭc ˜2K 4ͩ2␲3ln 1R 0ͪ1/2R 0Ϫ3͉E ͉͑d Ϫ2͒/2ͫI ˜4͉E ͉⑀/24͉u ͉ͬ͑d ϩ1͒/2ϫexp ͩ2K d I 4͑R 0͒⑀ϪI 4͑R 0͉͒E ͉⑀/24͉u ͉R 0⑀ͪ,͑64͒whose energy dependence coincides with that obtained in Refs.25–27,and corresponds to the well-known Lifshits law 28;the discrepancy at ⑀→0is eliminated for finite cutoff parameter ⌳.Oddly enough,for ⑀x Ӷ1Eqs.͑51͒–͑53͒and ͑62͒have the same functional form as those for d ϭ4͑Ref.16͒,i.e.,the behavior of all physical quantities in the vicinity of the mobility threshold turns out to be effectively four-dimensional.As in Refs.15and 16,the phase transition point is shifted into the complex plane,which ensures regu-larity of the density of states at all energies.R 0⑀differs substantially from unity only when ␬⑀/u Ӷ1/⑀,the terms in braces in ͑63͒cancelling almost exactly.Letting R 0→1in ͑60͒is tantamount to completely neglecting ͓⌺(p ,␬)͔nonpert ,since the domain of integration in Eq.͑118͒of Ref.15is p տ␬.Thus,͓⌺(p ,␬)͔nonpert is。

固相萃取-气相色谱法测定水环境中邻苯二甲酸酯沈斐;苏晓燕;李睿;朱培瑜;许燕娟;陈静【摘要】采用固相萃取法对水样进行提取富集，气相色谱法测定水中6种邻苯二甲酸酯类有机污染物，并对方法进行了探索、优化和验证。

对水体pH在固相萃取过程中对邻苯二甲酸酯萃取回收率的影响进行了研究，解决了邻苯二甲酸2-乙基己基酯和邻苯二甲酸二正辛酯回收率不高的问题。

在空白水加标实验中，邻苯二甲酸酯的回收率能达到93.2％～116.3％。

除此之外，还对工业废水和地表水进行了加标回收实验，获得了较高的回收率及测定精度。

%The development, optimisation and validation of a method for the determination of trace levels of phthalate esters in aqueous media is described. Extraction is by solid phase extraction followed by GC analysis. By adjusting the pH to the sample before the SPE, the recovery may be improved when di-(2-ethylhexyl) phthalate ( DEHP) and di-n-octylphthalate ( DnOP) determination is required. The accuracy determined as recovery was93.2%-116.3% for both compounds in distilled water. In addition, recoveries and method precision of phthalates were measured in wastewater and surface water.【期刊名称】《中国环境监测》【年(卷),期】2014(000)001【总页数】4页(P150-153)【关键词】邻苯二甲酸酯;固相萃取;pH;气相色谱【作者】沈斐;苏晓燕;李睿;朱培瑜;许燕娟;陈静【作者单位】无锡市环境监测中心站，江苏无锡214000;无锡市环境监测中心站，江苏无锡 214000;无锡市环境监测中心站，江苏无锡 214000;无锡市环境监测中心站，江苏无锡 214000;无锡市环境监测中心站，江苏无锡 214000;无锡市环境监测中心站，江苏无锡 214000【正文语种】中文【中图分类】X830.2邻苯二甲酸酯是环境中常见的有机污染物，特别是作为塑料增塑剂，由于未聚合到塑料基质中，随着使用时间的推移，逐渐转移到环境中，造成对大气、水体和土壤等的污染。

文章编号:1003 —7969 (2003) 01 —0058 —03 中图分类号: T Q64519 + 6 文献标识码:A 流态溶血磷脂性能及H LB 值的测定汪勇1 ,欧仕益1 ,李爱军1 ,王兴国2(11 暨南大学食品科学与工程系,510632 广州市;21 江南大学食品学院,214036 江苏省无锡市惠河路170 号)摘要:测定了流态大豆溶血磷脂的理化指标。

研究了在不同p H 值下流态溶血磷脂的乳化性能,证明溶血磷脂有很好的抗酸能力。

测定了溶血磷脂的HL B值,并推导了溶血磷脂酸值和HL B值的关系。

关键词:溶血磷脂;磷脂;乳化性能;H LB值溶血磷脂(Lysophospholipids) 是由各种磷脂失去一个脂肪酸基团所形成的磷脂的统称。

虽然失去α 或β位脂肪酸的磷脂都称作溶血磷脂,由于β位的酰基易于转移到α位,故其化学结构通式见图1 。

从化学结构可以看出溶血磷脂的亲水性能要比磷脂强,因为它增加了亲水性的羟基。

由此溶血磷脂更加适合用做OΠW 型乳化剂,有文献报道其乳化体系具有抗酸、抗盐以及抗高温等优点[ 1 ] 。

O 式,有利于产业化时自动控制产品的性能。

1 材料与方法111 实验试剂与材料流态大豆浓缩磷脂( HLB = 4) ,美国中央大豆公司;流态大豆溶血磷脂,自制[ 6 ] ; 大豆色拉油,东海粮油(工业) 有限公司。

112 实验仪器均质机,L04 - 2 型离心机, PHS - 29A 型酸度计。

CH2 O C RHO CH OCH2 O P O XOH X:胆碱、乙醇胺、丝氨酸、肌醇等R :脂肪酸基团113 实验方法11311 磷脂理化指标的测定酸值:滴定法,按照A. O. C. S Official Method Ja2b - 87 。

乙醚不溶物:重量法,按照A. O. C. S Official Method Ja3 - 87 。

磷脂图1 溶血磷脂结构通式溶血磷脂一般由磷脂经磷脂酶A2 水解制得,通常反应的底物是浓缩磷脂[ 2 - 5 ] ,得到的溶血磷脂在常温下流动性很好,我们称之为流态溶血磷脂。