The Effect of Blood Contained in the Samples on the Metabolomic Profile of Mouse Brain Tissue: A Study by NMR Spectroscopy

(1) Recently, metabolic profiling of the tissue in the native state or extracts of its metabolites has become increasingly important in the field of metabolomics. An important factor, in this case, is the presence of blood in a tissue sample, which can potentially lead to a change in the concentration of tissue metabolites and, as a result, distortion of experimental data and their interpretation. (2) In this paper, the metabolomic profiling based on NMR spectroscopy was performed to determine the effect of blood contained in the studied samples of brain tissue on their metabolomic profile. We used 13 male laboratory CD-1^® IGS mice for this study. The animals were divided into two groups. The first group of animals (n = 7) was subjected to the perfusion procedure, and the second group of animals (n = 6) was not perfused. The brain tissues of the animals were homogenized, and the metabolite fraction was extracted with a water/methanol/chloroform solution. Samples were studied by high-frequency ¹H-NMR spectroscopy with subsequent statistical data analysis. The group comparison was performed with the use of the Student’s test. We identified 36 metabolites in the brain tissue with the use of NMR spectroscopy. (3) For the major set of studied metabolites, no significant differences were found in the brain tissue metabolite concentrations in the native state and after the blood removal procedure. (4) Thus, it was shown that the presence of blood does not have a significant effect on the metabolomic profile of the brain in animals without pathologies.     

Finite element simulations of fully non‐linear interaction between vertical cylinders and steep waves. Part 2: numerical results and validation

In Ma, Wu, Eatock Taylor [Finite element simulation of fully non‐linear interaction between vertical cylinders and steep waves. Part 1: methodology and numerical procedure. International Journal for Numerical Methods in Fluids 2001], designated Part 1 hereafter, we have developed the methodology and solution procedure for simulating the three‐dimensional interaction between fixed bodies and steep waves based on a finite element method (FEM). This paper provides extensive numerical results and validation. The effectiveness of the radiation condition is investigated by comparing the results from short and long tanks; the accuracy of the computed data is confirmed through comparison with analytical solutions. The adopted mathematical model is also validated by comparing the obtained numerical results with experimental data. Various test cases, including non‐linear bichromatic and irregular waves and the interactions between waves and one or two cylinders, are analysed. Copyright © 2001 John Wiley & Sons, Ltd.     

圆屏(球)和圆环菲涅耳衍射的解析表达式

在标量衍射理论的基础上，给出了圆屏（球）和圆环菲涅耳衍射的振幅及光强解极表达式。计算了光强分布曲线，并将计算实例和有关资料中的实验与计算结果进行了比较。同时指出所谓无衍射光束实际上是一种菲涅耳衍射现象。     

Metabolomic analysis for the protective effects of mangiferin on sepsis‐induced lung injury in mice

This study aimed to investigate the efficacy of mangiferin, including its known antioxidant and anti‐inflammatory effects on sepsis‐induced lung injury induced by a classical cecal ligation and puncture (CLP) models in mouse using a metabolomics approach. A total of 24 mice were randomly divided into four groups: the sham group was given saline before sham operation. The CLP group received the CLP operation only. HMF and LMF groups were given mangiferin treatment of high dose and low dose of mangiferin, respectively, before the CLP operation. One week after treatment, the mice were sacrificed and their lungs were collected for metabolomics analysis. We developed ultra‐performance liquid chromatography coupled with quadrupole‐time‐of‐flight mass spectrometry to perform lung metabolic profiling analysis. With the methods of principal component analysis and partial least squares discriminant analysis, 58 potential metabolites associated with amino acid metabolism, purine metabolism, lipid metabolism and energy regulation were observed to be increased or reduced in HMF and LMF groups compared with the CLP group. Conclusively, our results suggest that mangiferin plays a protective role in the moderation of sepsis‐induced lung injury through reducing oxidative stress, regulating lipid metabolism and energy biosynthesis.     

On a factorization of the Schrödinger and Klein–Gordon operators

A general scheme for factorizing second‐order time‐dependent operators of mathematical physics is given, which allows a reduction of corresponding second‐order equations to biquaternionic equations of first order. Examples of application of the proposed scheme are presented for both constant and variable coefficients. Copyright © 2008 John Wiley & Sons, Ltd.     

Strong convergence of an iterative method for non‐expansive mappings

Let E be a real reflexive Banach space having a weakly continuous duality mapping J_φ with a gauge function φ, and let K be a nonempty closed convex subset of E. Suppose that T is a non‐expansive mapping from K into itself such that F (T) ≠ ??. For an arbitrary initial value x₀ ∈ K and fixed anchor u ∈ K, define iteratively a sequence {x_n } as follows: x_{n +1} = α_n u + β_n x_n + γ_n Tx_n , n ≥ 0, where {α_n }, {β_n }, {γ_n } ? (0, 1) satisfies α_n +β_n + γ_n = 1, (C 1) lim_{n →∞} α_n = 0, (C 2) ∑^∞_{n =1} α_n = ∞ and (B) 0 < lim inf_{n →∞} β_n ≤ lim sup_{n →∞} β_n < 1. We prove that {x_n } converges strongly to Pu as n → ∞, where P is the unique sunny non‐expansive retraction of K onto F (T). We also prove that the same conclusions still hold in a uniformly convex Banach space with a uniformly Gâteaux differentiable norm or in a uniformly smooth Banach space. Our results extend and improve the corresponding ones by C. E. Chidume and C. O. Chidume [Iterative approximation of fixed points of non‐expansive mappings, J. Math. Anal. Appl. 318 , 288–295 (2006)], and develop and complement Theorem 1 of T. H. Kim and H. K. Xu [Strong convergence of modified Mann iterations, Nonlinear Anal. 61 , 51–60 (2005)]. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

射线成像检测中射线源焦点的影响及修正

本文分析了在工业无损检测中射线源焦点对成像质量的影响，讨论了射线源焦点对成像影响的数学模型，以此为基础，设计了相应的焦点修正算法，并给出了处理结果     

Pedestrian flows and non‐classical shocks

We present a model for the flow of pedestrians that describes features typical of this flow, such as the fall due to panic in the outflow of people through a door. The mathematical techniques essentially depend on the use of non‐classical shocks in scalar conservation laws. Copyright © 2005 John Wiley & Sons, Ltd.