三维荧光二阶校正法用于尿液样中氢化可的松的定量测定

本文提出了三维荧光光谱结合二阶校正算法实现人体尿液样中氢化可的松定量测定的新方法。氢化可的松本身的荧光较弱,但与浓硫酸反应后可以生成强荧光的化合物。利用这一特性,采用浓硫酸为氧化剂,设定在激发波长为300-370nm、发射波长为400-580nm范围内测定尿液样中氢化可的松的三维荧光光谱,构建三维响应数据阵,然后运用基于三线性分解的二阶校正算法进行解析。当组分数N取3时,采用基于平行因子分析（PARAFAC）算法的Z-阶校正法的平均回收率为98.6±4.1％,预测残差平方根（RMSEP）为0.0114;采用基于满秩平行因子分析（FRA-PARAFAc）算法的二阶校正法的平均回收率和RMSEP分别为99.3±2.4％和0.0066。两种算法可以得到相近且满意的结果。     

Use of pseudo-sample extraction and the projection technique to estimate the chemical rank of three-way data arrays

Determining the rank of a trilinear data array is a first step in subsequent trilinear component decomposition. Different from estimating the rank of bilinear data, it is more difficult to decide the significant number of component to fit the trilinear decompositions exactly. General methods of rank estimation utilize the information contained in the singular values but ignore information from eigenvectors. In this paper, a rank estimating method specifically for trilinear data arrays is proposed. It uses the idea of direct trilinear decomposition (DTLD) to compress the cube matrix into two pseudo sample matrices which are then decomposed by singular value decomposition. Two eigenvectors combined with the projection technique are used to estimate the rank of trilinear data arrays. Simulated trilinear data arrays with homoscedastic and heteroscedastic noise, different noise levels, high collinearity, and real three-way data arrays have been used to illustrate the feasibility of the proposed method. Compared with other factor-determining methods, for example use of the factor indication function (IND), residual percentage variance (RPV), and the two-mode subspace comparison approach (TMSC), the results showed that the new method can give more reliable answers under the different conditions applied.      

Analytical solution and meaning of feasible regions in two-component three-way arrays

Although many efforts have been directed to the development of approximation methods for determining the extent of feasible regions in two- and three-way data sets; analytical determination (i.e. using only finite-step direct calculation(s) instead of the less exact numerical ones) of feasible regions in three-way arrays has remained unexplored. In this contribution, an analytical solution of trilinear decomposition is introduced which can be considered as a new direct method for the resolution of three-way two-component systems. The proposed analytical calculation method is applied to the full rank three-way data array and arrays with rank overlap (a type of rank deficiency) loadings in a mode. Close inspections of the analytically calculated feasible regions of rank deficient cases help us to make clearer the information gathered from multi-way problems frequently emerged in physics, chemistry, biology, agricultural, environmental and clinical sciences, etc. These examinations can also help to answer, e.g., the following practical question: “Is two-component three-way data with proportional loading in a mode actually a three-way data array?” By the aid of the additional information resulted from the investigated feasible regions of two-component three-way data arrays with proportional profile in a mode, reasons for the inadequacy of the seemingly trilinear data treatment methods published in the literature (e.g., U-PLS/RBL-LD that was used for extraction of quantitative and qualitative information reported by Olivieri et al. (Anal. Chem. 82 (2010) 4510–4519)) could be completely understood.     

WELL-POSEDNESS FOR THE CAUCHY PROBLEM TO THE HIROTA EQUATION IN SOBOLEV SPACES OF NEGATIVE INDICES

The local well-posedness of the Cauchy problem for the Hirota equation is established for low regularity data in Sobolev spaces Hs(s≥-1/4). Moreover, the global well-posedness for L2 data follows from the local well-posedness and the conserved quantity. For data in Hs(s > 0), the global well-posedness is also proved. The main idea is to use the generalized trilinear estimates, associated with the Fourier restriction norm method.     

Singular lines of trilinear forms

We prove that an alternating e-form on a vector space over a quasi-algebraically closed field always has a singular (e-1)-dimensional subspace, provided that the dimension of the space is strictly greater than e. Here an (e-1)-dimensional subspace is called singular if pairing it with the e-form yields zero. By the theorem of Chevalley and Warning our result applies in particular to finite base fields. Our proof is most interesting in the case where e=3 and the space has odd dimension n; then it involves a beautiful equivariant map from alternating trilinear forms to polynomials of degree . We also give a sharp upper bound on the dimension of subspaces all of whose two-dimensional subspaces are singular for a non-degenerate trilinear form. In certain binomial dimensions the trilinear forms attaining this upper bound turn out to form a single orbit under the general linear group, and we classify their singular lines.     

Well-posedness for the Cauchy problem of coupled Hirota equations with low regularity data

The local well-posedness of the Cauchy problem for the coupled Hirota equations is established in Sobolev spaces Hs×Hs by the Fourier restriction norm method.     

基于自加权交替三线性分解的荧光检测油类污染物

设计水中油类污染物检测仪,采用脉冲氙灯作为光源,选择阶跃型多模纯石英光纤对激发光和发射光进行传输。采用非对称Czemy-Turner光路的高精度光栅单色器。应用该装置测定柴油、汽油和煤油的荧光光谱,0#柴油、97#汽油和煤油的最佳激发波长/发射波长分别为：290/330,270/300和280/330 nm。检出限：柴油(0.025 mg·L-1)、汽油(0.042 mg·L-1)和煤油(0.054 mg·L-1)。相对误差：柴油(2.55%),汽油(2.06%)和煤油(1.71%),实验表明所设计的检测仪具有较高的测量精度。配置不同浓度的柴油、汽油和煤油的混合溶液,测量其三维荧光光谱,采用自加权交替三线性分解算法对光谱数据进行分解,预测浓度及回收率均表明自加权交替三线性分解算法对混合油类物质有较高的分辨能力。     

Determination of Protolytic Constants by Trilinear Fluorescence Spectroscopy

Protolytic equilibria often have profound effects on chemical activity, since protolytic species usually behave quite differently. It is therefore important to characterize the protolytic properties of important chemicals. Here we present a new approach to study protolytic equilibria of fluorescent species that is extremely accurate and relies on minimum assumptions. We show that by measuring 2-dimensional excitation/emission scans of samples at different pH. the 3-dimensional experimental data set, I(lambda(ex), lambda(em), C(pH)), can be unambiguously decomposed into the spectral responses of the protolytic species present as well as their concentration. The approach is demonstrated on the protolytic equilibrium of fluorescein. Although the fluorescein monoanion cannot be obtained in pure form, the spectra and concentrations of both fluorescein species, as well as the protolytic constant, are determined with excellent accuracy. The proposed method is general and can be applied not only for studies of protolytic equilibria, but on any chemical equilibria and chemical reactions involving fluorescent species.     

On the Two-Dimensional Navier—Stokes Equations with the Free Boundary Condition

In this article we consider the two-dimensional Navier—Stokes equations with free boundary condition (open surface), and derive a number of different results: a new orthogonal property for the nonlinear term, improved a priori estimates on the solution, an upper bound on the dimension of the attractor which agrees with the conventional theory of turbulence; finally, for elongated rectangular domains, an improved Lieb—Thirring (collective Sobolev) inequality leads to an upper bound on the dimension of the attractor which might be optimal. Accepted 11 July 1996