多次高温裂解、富集-离子色谱法检测己内酰胺中的痕量氯

建立了多次高温裂解、富集-离子色谱检测己内酰胺(CPL)中痕量氯的分析方法。CPL样品在富氧环境下经3次高温(800℃)裂解后,痕量有机氯转化为氯气或氯化氢气体,经5 mL 10 mmol/L的NaOH溶液吸收、富集,然后转化为氯离子,在阴离子抑制电导检测模式下进行离子色谱分析,检测其中氯离子(Cl-)的含量。在优化的条件下,Cl-在0.05~1.0 mg/L范围内呈良好线性,相关系数为0.999 7,方法检出限为0.37μg/g。对0.8 mg/L的Cl-标准溶液连续进样7次,其保留时间、峰面积、峰高的RSD分别为0.04%、0.24%和0.20%;分别对CPL样品进行处理和检测,得到痕量氯含量的RSD为1.52%(n=4);Cl-标准溶液的转化率为93.3%~104.0%,CPL样品的加标回收率为95.3%~113.1%。该方法操作简单、前处理条件可控、重复性好、检出限低,可满足实际样品中痕量氯的检测。

On the growth of transcendental entire solutions of algebraic differential equations

In this paper, we investigate the growth of transcendental entire solutionsof the following algebraic differential equation a(z)f'~2 +(b_2(z)f^2 +b_1(z)f +b_0(z))f'=d_3(z)f^3+d_2(z)f^2 +d_1(z)f +d_0(z), where a(z), b_i(z) (0<- i <=2) and d_j (z) (0<=j<= 3) are allpolynomials, and this equation relates closely to the following well-known algebraic differentialequation C(z,w)w'~2 + B(z,w)w' + A(z,w) =0, where G(z,w)not ident to 0, B(z,w) and A(z,w) are threepolynomials in z and w. We give relationships between the growth of entire solutions and the degreesof the above three polynomials in detail.

Lame Function and Its Application to Some Nonlinear Evolution Equations

In this paper, based on the Lame function and Jacobi emptic function, the perturbation method is appliedto some nonlinear evolution equations to derive their multi-order solutions.

APPLICATION OF IMPROVED EMD IN VIBRATION SIGNAL FEATURE EXTRACTION OF VEHICLE

In order to truly obtain the feature extraction of vibration signals under the strong background noise, the analysis and improvement of empirical mode decomposition （EMD） is carried on. After that, the improved EMD is applied to the feature extraction of vehicle vibration signals. First, the multi-autocorrelation method is adopted in each input signal,so the noise is reduced effectively. Then, EMD is used to deal with these signals,and the intrinsic mode functions （IMFs） are obtained. Finally, for obtaining the feature information of these signals, the Hilbert transformation and the spectrum analysis are performed in some IMFs. Theoretical analysis and ex- periment verify the effectiveness of the method, which are valuable reference for the same engineering problems.

Heron Triangle and Diophantine Equation

In this paper, we study the quantic Diophantine equation （1） with elementary geometry method, therefore all positive integer solutions of the equation （1） are obtained, and existence of Heron triangle whose median lengths are all positive integer are discussed here.

Multiplicity of positive solutions to weighted nonlinear elliptic system involving critical exponents

This paper deals with the existence and multiplicity of nontrivial solutions to a weighted nonlinear elliptic system with nonlinear homogeneous boundary condition in a bounded domain. By using the Caffarelli-Kohn-Nirenberg inequality and variational method, we prove that the system has at least two nontrivial solutions when the parameter λ belongs to a certain subset of R.

Local solvability of the k-Hessian equations

We give a classification of second-order polynomial solutions for the homogeneous k-Hessian equation σ_k[u] = 0. There are only two classes of polynomial solutions: One is convex polynomial; another one must not be(k + 1)-convex, and in the second case, the k-Hessian equations are uniformly elliptic with respect to that solution. Based on this classification, we obtain the existence of C∞local solution for nonhomogeneous term f without sign assumptions.

Darboux integrability and algebraic limit cycles for a class of polynomial differential systems

This paper deals with the existence of Darboux first integrals for the planar polynomial differential systems x=x-y+P n+1(x,y)+xF2n(x,y),y=x+y+Q n+1(x,y)+yF2n(x,y),where P i(x,y),Q i(x,y)and F i(x,y)are homogeneous polynomials of degree i.Within this class,we identify some new Darboux integrable systems having either a focus or a center at the origin.For such Darboux integrable systems having degrees 5and 9 we give the explicit expressions of their algebraic limit cycles.For the systems having degrees 3,5,7 and 9and restricted to a certain subclass we present necessary and sufficient conditions for being Darboux integrable.

ON FUNCTIONAL DECOMPOSITION OF MULTIVARIATE POLYNOMIALS WITH DIFFERENTIATION AND HOMOGENIZATION

This paper gives a theoretical analysis for the algorithms to compute functional decomposition for multivariate polynomials based on differentiation and homogenization which were proposed by Ye, Dai, and Lam （1999） and were developed by Faugere, Perret （2006, 2008, 2009）. The authors show that a degree proper functional decomposition for a set of randomly decomposable quartic homoge- nous polynomials can be computed using the algorithm with high probability. This solves a conjecture proposed by Ye, Dal, and Lam （1999）. The authors also propose a conjecture which asserts that the decomposition for a set of polynomials can be computed from that of its homogenization and show that the conjecture is valid with high probability for quartic polynomials. Finally, the authors prove that the right decomposition factors for a set of polynomials can be computed from its right decomposition factor space.

THE ZEROS AND ORDER OF MEROMORPHIC SOLUTIONS OF f^(k)+Bf=H(z)

Suppose that B is a rational function having a pole at co of order n ＞ 0 and that H 0 is a meromorphic function satisfying o(H) =β (n+ k)/k. If the differential equation f(k) + Bf =H(z) has a meromorphic solution f, then all meromorphic solutions f satisfy λ(f) = λ(f) = δ(f) = max{β, (n + k)/k},except at most one exceptional meromorphic solution f0.

Integral closure of a quartic extension

Let R be a Noetherian unique factorization domain such that 2 and 3 are units,and let A=R[α]be a quartic extension over R by adding a rootαof an irreducible quartic polynomial p(z)=z4+az2+bz+c over R.We will compute explicitly the integral closure of A in its fraction field,which is based on a proper factorization of the coefficients and the algebraic invariants of p(z).In fact,we get the factorization by resolving the singularities of a plane curve defined by z4+a(x)z2+b(x)z+c(x)=0.The integral closure is expressed as a syzygy module and the syzygy equations are given explicitly.We compute also the ramifications of the integral closure over R.