Second-order calibration of excitation-emission matrix fluorescence spectra for determination of glutathione in human plasma

A rapid non-separative spectroflourimetric method based on the second-order calibration of the excitation-emission data matrix was proposed for the determination of glutathione (GSH) in human plasma. In the phosphate buffer solution of pH 8.0 GSH reacts with ortho-phthaldehyde (OPA) to yield a fluorescent adduct with maximum fluorescence intensity at about 420 nm. To handle the interfering effects of the OPA adducts with aminothiols other than GSH in plasma as well as intrinsic fluorescence of human plasma, parallel factor (PARAFAC) analysis as an efficient three-way calibration method was employed. In addition, to model the indirect interfering effect of the plasma matrix, PARAFAC was coupled with standard addition method. The two-component PARAFAC modeling of the excitation-emission matrix fluorescence spectra accurately resolved the excitation and emission spectra of GSH, plasma (or plasma constituents). The concentration-related PARAFAC score of GSH represented a linear correlation with the concentration of added GSH, similar to that is obtained in simple standard addition method. Using this standard addition curve, the GSH level in plasma was found to be 6.10 ± 1.37 μmol L⁻¹. The accuracy of the method was investigated by analysis of the plasma samples spiked with 1.0 μmol L⁻¹ of GSH and a recovery of 97.5% was obtained.     

A semi-discretization method based on quartic splines for solving one-space-dimensional hyperbolic equations

In this paper, based on C³ quartic splines, a semi-discretization method containing two schemes is constructed to solve one-space-dimensional linear hyperbolic equations. It is shown that both schemes are unconditionally stable and their approximation orders are of O(k⁵+h⁴) and of O(k⁷+h⁴) with k and h being step sizes in time and space, respectively, which are much higher than those of other published schemes. A numerical example is presented and the results are compared with other published numerical results.     

A computational comparison of reformulations of the perspective relaxation: SOCP vs. cutting planes

The Perspective Reformulation generates tight approximations to MINLP problems with semicontinuous variables. It can be implemented either as a Second-Order Cone Program, or as a Semi-Infinite Linear Program. We compare the two reformulations on two MIQPs in the context of exact or approximate Branch-and-Cut algorithms.     

Reduction and Reconstruction Aspects of Second-Order Dynamical Systems with Symmetry

We examine the reduction process of a system of second-order ordinary differential equations which is invariant under a Lie group action. With the aid of connection theory, we explain why the associated vector field decomposes in three parts and we show how the integral curves of the original system can be reconstructed from the reduced dynamics. An illustrative example confirms the results.      

含有咪唑生色团系列树型有机分子二阶非线性光学性质的密度泛函理论研究

应用密度泛函理论(DFT)B3LYP/6-31G*方法计算研究了系列树型含有咪唑生色团的有机分子的结构和非线性光学性质.计算结果表明:该系列分子具有A- -D- -A(A:受体,D:给体)结构,分子基态的偶极矩、极化率、二阶NLO系数( )随共轭链的增长及吸电子基的增强而增大;同时,前线轨道能级差值越小此类分子的二阶极化率总有效值( )越大.计算的吸收光谱显示此系列树型分子在低能区域247.79nm-419.87nm都有一个最强吸收,并且均是最高占据轨道与最低空轨道之间的跃迁.     

Spin-1/2 Ising model on a AFM/FM two-layer Bethe lattice in a staggered magnetic field

A bilayer spin-1/2 Ising model consisting of two superposed Bethe lattices with antiferromagnetic/ferromagnetic interactions is studied by the use of exact recursion relations in a pairwise approach in the presence of an external staggered magnetic field. Besides the ground state phase diagrams calculated in different possible planes of the model parameters space, the thermal variations of the order-parameters and the free energy are investigated to obtain the temperature-dependent phase diagrams of the model for different values of the coordination numbers q. Our calculations reveal that depending on the strength of the model parameters, the model exhibits a variety of interesting phase transitions and therefore phase diagrams.     

Modulation instability in metamaterials with fourth-order linear dispersion,second-order nonlinear dispersion,and three kinds of saturable nonlinearites

The linearized nonlinear propagation equation and its coefficients, gain spectrum of modulation instability (MI) in metamaterials (MMs) with fourth-order linear dispersion, second-order nonlinear dispersion, and three kinds of saturable nonlinearites, are analytically deduced by utilizing the linear stability analysis and Drude electromagnetic model. Then variations of gain spectra of MI with the normalized angular frequencies and the optical power densities are calculated in real units. In the negative refractive region, two kinds of gain spectra are discovered. The first (second) one is close to (far from) the zero perturbation frequencies and it corresponds to the lower (higher) normalized angular frequencies. Moreover, the second one has higher cutoff frequency, which is obviously beneficial to generation of high-repetition-rate pulse trains. While in the positive refractive region, only the first kind of gain spectra is found. With increase of the optical power densities, the peak gains and the spectral widths of MI increase before decrease, but they vary the most rapidly (slowly) for the exponential (conventional) saturable nonlinearities. The MI characteristics and their corresponding applications can be adjusted by several methods.     

A novel unsplit perfectly matched layer for the second-order acoustic wave equation

When solving acoustic field equations by using numerical approximation technique, absorbing boundary conditions (ABCs) are widely used to truncate the simulation to a finite space. The perfectly matched layer (PML) technique has exhibited excellent absorbing efficiency as an ABC for the acoustic wave equation formulated as a first-order system. However, as the PML was originally designed for the first-order equation system, it cannot be applied to the second-order equation system directly. In this article, we aim to extend the unsplit PML to the second-order equation system. We developed an efficient unsplit implementation of PML for the second-order acoustic wave equation based on an auxiliary-differential-equation (ADE) scheme. The proposed method can benefit to the use of PML in simulations based on second-order equations. Compared with the existing PMLs, it has simpler implementation and requires less extra storage. Numerical results from finite-difference time-domain models are provided to illustrate the validity of the approach.     

Local second-order approximations and applications in optimization

A new general abstract scheme for local second-order approximations and second-order generalized directional derivatives is presented. Applications to optimization are provided.     

Multi-way partial least-squares and residual bi-linearization for the direct determination of monohydroxy-polycyclic aromatic hydrocarbons on octadecyl membranes via room-temperature fluorescence excitation emission matrices

Multi-way partial least-squares (N-PLS) is combined to the residual bi-linearization procedure (RBL) for the direct analysis of metabolites of polycyclic aromatic hydrocarbons in urine samples. Metabolite analysis is carried out via a two-step experimental procedure based on solid-phase extraction and room temperature fluorescence spectroscopy. Excitation-emission matrices are recorded from octadecyl (C18) membranes that serve as solid substrates for sample extraction and spectroscopic measurements. Excellent metabolite recoveries were obtained in all cases, which varied from 96.2 ± 1.35% (9-hydroxyphenanthrene) to 99.7 ± 0.49% (3-hydroxybenzo[a]pyrene). Background correction of extraction membranes is carried out with a new alternating least-squares (ALS) procedure adapted to second order data. The performance of N-PLS/RBL is compared to the well-established multivariate curve resolution-alternating least-squares (MCR-ALS) algorithm. Both algorithms provided similar analytical figures of merit, including their ability to handle unknown interference in urine samples. With only 10 mL of sample, the limits of detection varied between 0.06–0.08 ng mL⁻¹ (1-hydroxypyrene) and 0.016–0.018 ng mL⁻¹ (2-hydroxyfluorene). When compared to previously reported univariate calibration data, the limits of detection via N-PLS/RBL and MCR-ALS are approximately one order of magnitude higher. This was somehow expected due to the effect of unexpected components in multivariate figures of merit, i.e. a more realistic approach to the analysis of metabolites in human urine samples.