On the convergence of multipoint Padé-type approximants and quadrature formulas associated with the unit circle

We study the convergence of rational interpolants with prescribed poles on the unit circle to the Herglotz-Riesz transform of a complex measure supported on [–, ]. As a consequence, quadrature formulas arise which integrate exactly certain rational functions. Estimates of the rate of convergence of these quadrature formulas are also included.This research was performed as part of the European project ROLLS under contract CHRX-CT93-0416.     

应用DQE增量迭代法分析斜直井内管柱的非线性屈曲

基于斜直井内管柱屈曲的平衡微分方程,构建DQE (Differential Quadrature Element)增量迭代法,对斜直井内管柱的非线性屈曲进行计算.通过与有限元的计算结果对比,验证方法的正确性.DQE法方法简单、易于实施,计算量少、精度较高,所得到的螺旋屈曲计算结果与实验结果吻合,最大井壁约束力随上端载荷的增加而增大.对于工程中比较长的受压段管柱,其屈曲是一个局部非线性稳定性问题,屈曲首先从下端开始发生,随着上端载荷的增加,逐渐向上扩展;上端边界条件对下端局部屈曲无明显影响.     

Analysis of the coupling constants ga0ηπ0 and ga0η＇ π0 with light-cone QCD sum rules

In this article, we take the point of view that the light scalar meson a0（980） is a conventional qqstate, and calculate the coupling constants ga0ηπ0 and ga0ηπ0 with the light-cone QCD sum rules. The central value of the coupling constant ga0ηπ0 is consistent with that extracted from the radiative decay φ（1020） → a0（980）γ→ηπ0γ. The central value and lower bound of the decay width Γa0→ηπ0 =127＋8448 MeV are compatible with the experimental data of the total decay width Γa0（980） = （50-100） MeV from the Particle Data Group with a very model dependent estimation （the decay width can be much larger）, while the upper bound is too large. We give a possible explanation for the discrepancy between the theoretical calculation and experimental data.     

Schur‐convexity and quadrature formulae

This paper aims to contribute to the exploration of quadrature formulae by proving that the error of a quadrature formula has the Schur‐convexity property. The emphasis is on the quadrature formulae with the maximum degree of precision. The Schur‐convexity of the error has an interesting implication – the monotonicity of the error. Namely, it turns out that the absolute value of the error is always smaller on a smaller interval (of the two which share the same midpoint).     

Generalized Bessel functions: Theory and their applications

This paper presents 2 new classes of the Bessel functions on a compact domain [0,T] as generalized‐tempered Bessel functions of the first‐ and second‐kind which are denoted by GTBFs‐1 and GTBFs‐2. Two special cases corresponding to the GTBFs‐1 and GTBFs‐2 are considered. We first prove that these functions are as the solutions of 2 linear differential operators and then show that these operators are self‐adjoint on suitable domains. Some interesting properties of these sets of functions such as orthogonality, completeness, fractional derivatives and integrals, recursive relations, asymptotic formulas, and so on are proved in detail. Finally, these functions are performed to approximate some functions and also to solve 3 practical differential equations of fractionalorders.     

Do Antarafacial Cycloadditions Occur? Cycloaddition of Heptafulvalene with Tetracyanoethylene

The cycloaddition of heptafulvalene ( 1 ) with tetracyanoethylene (TCNE) was previously described as an example of an antarafacial cycloaddition, a [π¹⁴_a+π²_s] process that afforded only the trans cycloadduct by virtue of the edge-to-face approach of TCNE, facilitated by the S shape of 1 . The reaction has been investigated in depth and found not to be a concerted antarafacial process. At low temperature, the reaction is observed to give a mixture of cis and trans cycloadducts as well as a [4+2] cycloadduct. The mixture of products is converted to the trans cycloadduct by equilibration upon warming to room temperature. Studies with diethyl 2,3-dicyanofumarate and -maleate confirmed the formation of cis cycloadducts. DFT studies at the M06-2X/6-311+G(2d,p) SCRF=acetone level of theory show that the originally proposed edge-to-face approach of TCNE to 1 is highly disfavored, whereas a stepwise mechanism involving the addition of TCNE at C2 to form a zwitterion followed by collapse at either C2′ or C7′ is energetically accessible. The Diels-Alder adduct is also formed in a stepwise reaction by competitive addition of TCNE at C4 of 1 . These studies suggest that edge-to-face interactions are prohibitive in even the most favorable cases.     

Synthesis and Characterization of Li‐containing Boron Carbide r‐Li~1B13C2

Transparent and nearly colorless single crystals of r‐LiB₁₃C₂ were obtained by reaction of boron with Li₂CO₃ in a Cu melt at 1250–1300 °C. The structure analysis [R3 m, a = 5.6535(1), c = 12.5320(2) Å, 421 independent reflections, 22 parameters, R₁ = 0.034, wR₂ = 0.093] revealed a crystal structure that can be described as a filling variant of rhombohedral B₁₃C₂. Li⁺ is located in a void above or below the linear CBC unit. The site occupation is close to 50 % resulting in an electron‐precise composition according to Wade's rules if a positive charge is given to the CBC entity: Li⁺(B₁₂)^2–(CBC)⁺. The displacement parameters of the CBC unit indicate disorder in the [001] direction, that relates to the short Li–C distance and the partial occupation of the Li⁺ site. The composition is confirmed by EELS measurements of single crystals. Band gap calculations give a value of 2.94 eV, which is in agreement to the crystals being colorless. The evaluation of the electron density by application of the QTAIM formalism as proposed by Bader modifies the assignment pictured above according to Wade's rules. In agreement to the electronegativities the carbon atoms carry a negative charge (–2.31/–2.42) and the effective charges are: Li^+0.81(B₁₂)^+2.02(CBC)^–2.83.     

Everything you wanted to know about phase and reference frequency in one- and two-dimensional NMR spectroscopy

The fundamental concept of phase discussed in this tutorial aimed at providing students with an explanation of the delays and processing parameters they may find in nuclear magnetic resonance (NMR) pulse programs. We consider the phase of radio-frequency pulses, receiver, and magnetization and how all these parameters are related to phases and offsets of signals in spectra. The impact of the off-resonance effect on the phase of the magnetization is discussed before presenting an overview of how adjustment of the time reference of the free induction decay avoids first-order correction of the phase of spectra. The main objective of this tutorial is to show how the relative phase of a pulse and the receiver can be used to change the reference frequency along direct and indirect dimensions of NMR experiments. Unusual of phase incrementation with non-90° angles will be illustrated on one- and two-dimensional NMR spectra.     

An in silico expert system for the identification of eye irritants

This report describes development of an in silico, expert rule-based method for the classification of chemicals into irritants or non-irritants to eye, as defined by the Draize test. This method was developed to screen data-poor cosmetic ingredient chemicals for eye irritancy potential, which is based upon exclusion rules of five physicochemical properties – molecular weight (MW), hydrophobicity (log P), number of hydrogen bond donors (HBD), number of hydrogen bond acceptors (HBA) and polarizability (Pol). These rules were developed using the ADMET Predictor software and a dataset of 917 eye irritant chemicals. The dataset was divided into 826 (90%) chemicals used for training set and 91 (10%) chemicals used for external validation set (every 10th chemical sorted by molecular weight). The sensitivity of these rules for the training and validation sets was 72.3% and 71.4%, respectively. These rules were also validated for their specificity using an external validation set of 2011 non-irritant chemicals to the eye. The specificity for this validation set was revealed as 77.3%. This method facilitates rapid screening and prioritization of data poor chemicals that are unlikely to be tested for eye irritancy in the Draize test.