Possible spectroscopic manifestation of the angular group induced bond alteration (AGIBA) effect in toluene

The most obvious consequence of the concept of aromaticity is the common confidence that in aromatic compounds, bond lengths do not alternate and are between typical to the single and double ones. However, in 1994, performing crystal structure investigations of substituted pyridines and their salts, Krygowski and co‐workers have discovered a very surprising angular group induced bond alteration (AGIBA) effect: It appears that some angular substituents, like methoxy or nitrozo groups, can induce bond alternation in aromatic rings. Crystal studies do not allow one to operate with liquids that are more common in organic chemistry. This paper presents the first possible evidence of spectroscopic manifestations of the AGIBA effect. Raman spectra of the liquid toluene are analyzed. It is found that instead of being single, the line corresponding to the ring breathing vibrations is clearly split by 1.0–1.4 cm^?1, thus indicating the presence of two (cis‐ and trans‐) AGIBA isomers. The energy difference between these isomers estimated in temperature dependent Raman studies is found equal to 6.68 kJ mol^?1. The low‐wavenumber line therefore corresponds to the cis‐AGIBA isomer and the high‐wavenumber line to the trans‐AGIBA isomer stabilized by the AGIBA effect. Copyright © 2007 John Wiley & Sons, Ltd.     

The diameter of randomly perturbed digraphs and some applications

The central observation of this paper is that if εn random arcs are added to any n‐node strongly connected digraph with bounded degree then the resulting graph has diameter 𝒪(lnn) with high probability. We apply this to smoothed analysis of algorithms and property testing. Smoothed Analysis: Recognizing strongly connected digraphs is a basic computational task in graph theory. Even for digraphs with bounded degree, it is NL‐complete. By XORing an arbitrary bounded degree digraph with a sparse random digraph R ∼ 𝔻_n,ε/n we obtain a “smoothed” instance. We show that, with high probability, a log‐space algorithm will correctly determine if a smoothed instance is strongly connected. We also show that if NL ⫅̸ almost‐L then no heuristic can recognize similarly perturbed instances of (s,t)‐connectivity. Property Testing: A digraph is called k‐linked if, for every choice of 2k distinct vertices s₁,…,s_k,t₁,…,t_k, the graph contains k vertex disjoint paths joining s_r to t_r for r = 1,…,k. Recognizing k‐linked digraphs is NP‐complete for k ≥ 2. We describe a polynomial time algorithm for bounded degree digraphs, which accepts k‐linked graphs with high probability, and rejects all graphs that are at least εn arcs away from being k‐linked. © 2007 Wiley Periodicals, Inc. Random Struct. Alg., 2007     

Proximality and Chebyshev sets

This paper is a companion to a lecture given at the Prague Spring School in Analysis in April 2006. It highlights four distinct variational methods of proving that a finite dimensional Chebyshev set is convex and hopes to inspire renewed work on the open question of whether every Chebyshev set in Hilbert space is convex.     

四种多变量校准方法在FTIR多组分分析中的性能比较

本文对四种多变量校准方法－－经典最小二乘法（CLS），偏最小二乘法（PLS），卡尔曼滤波法（KFM）以及人工神经网络法（ANN）－－在多组分浓度分析方面的性能进行了比较。选择五种红外谱图严重混叠的大气有机毒物－－1，3－丁二烯，苯，邻二甲苯，氯苯和丙烯醛－－作为分析对象。分别计算各种方法对该5组分体系的平均预测误差MPE和平均相对误差MRE进行比较。结果表明，偏最小二乘法在处理这类问题中是最稳健的方法。     

Field-of-values analysis of preconditioned iterative methods for nonsymmetric elliptic problems

Summary. The convergence rate of Krylov subspace methods for the solution of nonsymmetric systems of linear equations, such as GMRES or FOM, is studied. Bounds on the convergence rate are presented which are based on the smallest real part of the field of values of the coefficient matrix and of its inverse. Estimates for these quantities are available during the iteration from the underlying Arnoldi process. It is shown how these bounds can be used to study the convergence properties, in particular, the dependence on the mesh-size and on the size of the skew-symmetric part, for preconditioners for finite element discretizations of nonsymmetric elliptic boundary value problems. This is illustrated for the hierarchical basis and multilevel preconditioners which constitute popular preconditioning strategies for such problems. Received May 3, 1996     

A geometric theory forL 2-stability of the inverse problem in a one-dimensional elliptic equation from anH 1-observation

This study provides a stability theory for the nonlinear least-squares formulation of estimating the diffusion coefficient in a two-point boundary-value problem from an error-corrupted observation of the state variable. It is based on analysing the projection of the observation on the nonconvex attainable set.This research was started while G. Chavent visited the Technical University of Graz. Support through the Steiermaerkische Landesregierung is gratefully acknowledged.     

Characteristic of a broadband Ti:LiNbO3 optical modulator with buried electrodes and etched grooves in the buffer layer

Traveling wave Ti:LiNbO₃ Mach-Zehnder optical modulators with buried electrodes and etched grooves in the SiO₂ buffer layer are analyzed by the finite element method. The tradeoff between the bandwidth BW and the half-wave voltage Vπ is discussed. The value of BW/Vπ is used to weight the total performance of the modulator. Taking a thick buffer layer and etching deep grooves in the buffer layer are demonstrated as two effective methods to improve the performance of the modulator. A 3-dB optical bandwidth of 18 GHz with half-wave voltage 5V at a wavelength of 1.55 pm could be obtained even though the electrode is not very thick. When the requirement of half-wave voltage is not very critical, a bandwidth of more than 100 GHz can be obtained.     

关于“信息熵”分析及其应用的研究

本文用Ｓｈａｎｎｏｎ熵函数的观点及最大离散熵原理，探讨了对随机试验项目的优选问题：即压缩某种“不确定性”试验项目的实施与探索．并通过应用实例的计算，获得了满意的聚类效果．这种方法对于信息资料的数据处理及压缩“不确定性“验项目具有普遍意义．     

Determination of tributyltin oxide in coastal marine sediments and mussels by electrothermal atomic absorption spectrometry

We have devised a new method for bis(tributyltin)oxide (TBTO) determination in marine sediments and mussels. This technique involves an n-hexane/methylene chloride mixture extraction and extract purification with a sodium hydroxide wash in order to eliminate interfering compounds. TBTO is then extracted again by nitric acid and converted into an inorganic tin species; the analysis has been effected using Zeeman graphite furnace-atomic absorption spectrophotometry. The method detection limit for the matrices examined is 0.004 μg TBTO g^?1 (wet weight) and is sufficient for the analysis in real samples. The percentage recovery of TBTO from sediments and mussels samples is higher than 85% and 95% respectively. This method has been applied to TBTO level determination in sediments and mussels (Mytilus galloprovincialis) sampled in the harbour area in Taranto, where mussel culture activities are much developed; the TBTO levels obtained in sediments and mussels were in the range 15-47 ng g^?1 (wet weight) and 11-30 ng g^?1 (wet weight) respectively. Such values are comparable with those found in other harbour areas in the Mediterranean Sea.     

Cyclic reduction and FACR methods for piecewise hermite bicubic orthogonal spline collocation

Cyclic reduction and Fourier analysis-cyclic reduction (FACR) methods are presented for the solution of the linear systems which arise when orthogonal spline collocation with piecewise Hermite bicubics is applied to boundary value problems for certain separable partial differential equations on a rectangle. On anN×N uniform partition, the cyclic reduction and Fourier analysis-cyclic reduction methods requireO(N ²log₂ N) andO(N ²log₂log₂ N) arithmetic operations, respectively.