Linearized and rational approximation method for solving non‐linear Burgers' equation

A new numerical method called linearized and rational approximation method is presented to solve non‐linear evolution equations. The utility of the method is demonstrated for the case of differentiation of functions involving steep gradients. The solution of Burgers' equation is presented to illustrate the effectiveness of the technique for the solution of non‐linear evolution equations exhibiting nearly discontinuous solutions. Copyright © 2004 John Wiley & Sons, Ltd.     

Ahlfors-régularité des quasi-minima de Mumford–Shah

Let be an open set. We consider on Ω the competitors (U,K) for the reduced Mumford–Shah functional, that is to say the Mumford–Shah functional in which the -norm of U term is removed, where K is a closed subset of Ω and U is a function on ΩK with gradient in  . The main result of this paper is the following: there exists a constant c for which, whenever (U,K) is a quasi-minimizer for the reduced Mumford–Shah functional and B(x,r) is a ball centered on K and contained in Ω with bounded radius, the -measure of is bounded above by cr^N−1 and bounded below by c⁻¹r^N−1.     

Influence of moisture on the viscoelastic relaxations in long aliphatic chain contained semiaromatic polyamide, (PA9‐T) fiber

The effect of moisture on the mechanical relaxation processes of semiaromatic semicrystalline polyamides synthesized by a long‐chain aliphatic diamine and terephthalic acid was investigated by dynamic viscoelastic analysis (DVA) and differential scanning calorimetry (DSC). Moreover, the implication of moisture with the amorphous and crystalline domains was also examined by temperature‐dependent wide‐angle X‐ray diffraction and Fourier transform infrared spectra. The characteristics of the relaxations such as α, β, γ, and the pronounced peak shoulder appeared at 25–100 °C in DVA tan δ curves were found to be strongly susceptible to the presence of moisture. With moisture evaporation, the peak shoulder of 25–100 °C and the β‐relaxation disappeared. The former is anticipated to originate from to the side group motion of hydrogen‐bonded water, whereas the later one is from the motions of the amide–water complex units. With the disappearance of the β‐relaxation, the γ‐relaxation appeared simultaneously in much lower temperatures and ultimately coupled with the δ‐relaxation. The γ‐relaxation is attributed to be associated with the molecular motion of the amide group and δ‐relaxation with for the motion of the methylene units. The existence of two types of water was identified in the polymer, namely, tightly bound and loosely bound. The tightly bound water is believed to be directly connected by hydrogen bonding with the strong polar groups and the loosely bound water weakly links with those connected water making hydrogen bridges. The moisture acts as a plasticizer in the polymer matrix, which causes quite a large depression in its glass transition temperature (T_g). WAXD and FTIR studies corroborated the existence of water solely in amorphous regions, i.e., no rapport of water with the crystalline parts. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 2878–2891, 2003     

A general converse theorem for mean‐value theorems in linear elasticity

We prove a rather general mean‐value formula in the theory of elasticity, which expresses the value of the displacement at the centre of a sphere in terms of certain combinations of integral averages over the sphere itself of the traction and the displacement. We also establish the corresponding converse to this mean‐value formula under minimal smoothness assumptions on the displacement. Copyright © 2006 John Wiley & Sons, Ltd.     

Quadratic transformations of the sixth Painlevé equation with application to algebraic solutions

In 1991, one of the authors showed the existence of quadratic transformations between the Painlevé VI equations with local monodromy differences (1/2, a, b, ±1/2) and (a, a, b, b). In the present paper we give concise forms of these transformations. They are related to the quadratic transformations obtained by Manin and Ramani–Grammaticos–Tamizhmani via Okamoto transformations. To avoid cumbersome expressions with differentiation, we use contiguous relations instead of the Okamoto transformations. The 1991 transformation is particularly important as it can be realized as a quadratic‐pull back transformation of isomonodromic Fuchsian equations. The new formulas are illustrated by derivation of explicit expressions for several complicated algebraic Painlevé VI functions. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

One-pot synthesis of an ionic half-sandwich complex of neodymium. Application to isoprene polymerisation catalysis

The reaction of one equivalent of Nd(BH₄)₃(THF)₃ with an half equivalent of dialkylmagnesium in the presence of a stoichiometric amount of pentamethylcyclopentadiene cleanly affords a new kind of half-sandwich of neodymium that is stable toward comproportionation. This strategy can be advantageously applied to generate in situ catalysts allowing the controlled polymerisation of isoprene.     

First Total Synthesis of 12-Hydroxy-13-methylpodocarpa-9, 11, 13-trien-3-one

12-Hydroxy-13-methylpodocarpa-9, 11, 13-trien-3-one 9 was isolated from the twigs ofCroton salutaris1. Many diterpenes exhibit significant bioactivities, such as antibac-terial and antitumour and 9 has a rare structure. In order to study the relationshipb…     

GC-MS与GC-FTIR联合测定C9烃馏分组成

混合碳九组成复杂,估计为环状烯烃、芳烃、多环烃、烷烃等,目前该产品主要用于生产石油树脂。随着我国乙烯生产能力的不断扩大,其产量也在不断增加,为充分利用碳九资源,研究开拓其新的应用领域非常必要。而此研究的首要条件在于对其组成进行较为全面、准确地分析。传统的分析方法不能对其组成提供详尽的数据资料,直接影响了对碳九进行综合利用研究。GC-MS兼有GC的高效分离能力与MS很好的定性功能,且灵敏度较高,是分析有机混合物十分有效的手段。本文将GC-MS应用于碳九组成的定性分析中。但由于碳九组分中含有较多的同分异构体如三甲苯与二甲苯等,同分异构体的质谱图几乎相同,GC-MS对其不易鉴别,而红外(FTIR)对有机物同分异构体尤其苯系物的异构体具有非常好的鉴别能力。因此本文将GC-MS与GC-FTIR联合使用,对碳九组成进行定性分析,样品定量采用色谱氢火焰检测器峰面积归一化法得到的各组分峰面积相对百分含量,较好地解决了碳九组分的定性定量问题,为开发碳九新的应用领域提供依据。     

新试剂3,5—二溴—4—偶氮8—羟基喹啉苯基荧光酮光度法测定微量铝

在溴化十六烷基三甲胺（ＣＴＭＡＢ）存在下，ＰＨ６，０的ＨＡｃ－ＮａＡｃ缓冲介质中，铝与新试剂３，５－二溴－４－偶氮８－羟基喹啉苯基荧光酮形成红色三元胶束配合物，最大吸收波长位于５６４ｎｍ，表观摩尔吸光系数ε为１．３５×１０＾５．ｍｏｌ＾－１．ｃｍ＾－１，铝浓度在０～５μｇ／２５ｍＬ范围内符合比耳定律，拟定的方法用于铝铁黄铜中微量铝的测定，结果满意。