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.     

Five-step phase-shifting algorithms with unknown values of phase shift

The presented work offers new algorithms for phase evaluation in interferometric measurements. Several phase-shifting algorithms with an arbitrary but constant phase-shift between captured intensity frames are proposed. These phase calculation algorithms need to measure five frames of the intensity of the interference field. The algorithms are similarly derived as so called Carré algorithm. The phase evaluation process then does not depend on the linear phase shift errors. Furthermore, the detailed analysis of the algorithms with respect to most important factors, which affect interferometric measurements, is carried out. It is also studied the dependency of the evaluation algorithms on the phase shift values, and the proposed phase calculation algorithms are compared with respect to the resulting phase errors. The influence of most important factors in the measurement and evaluation process was simulated as systematic and random errors using a proposed mathematical model.     

Reagent concentration effects in the REM resin solid phase synthesis of tertiary amines

The use of reagent concentration has resulted in increased rates for all stages of the REM resin synthesis of tertiary amines. These increases in rate translate into faster reaction times, higher yields and lower reagent consumption. Of the methods examined, the most successful was the use of perfluorous solvents, either alone or with a small amount of organic co-solvent.     

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…     

立体定向合成粘虫性信息素

粘虫是一种多食性害虫,分布极广。它的危害对象包括麦类、水稻、玉米等十多种粮食和经济作物。1979年Takahashi等首先确定粘虫雄蛾(Mythimna Separata male)的性信息素,这是由8:1比例混合的(Z)-11-十六碳烯-1-醇乙酸酯3和(Z)-11-十六碳烯-1-醇4组