弱(L_1,L_2)-BLD映射的正则性

本文首先将文［１］中的ＢＬＤ映射推广为弱（Ｌ１，Ｌ２）－ＢＬＤ映射，并证明了如下正则性结果：存在两个可积指数 Ｐ１＝Ｐ１（ｎ，Ｌ１，Ｌ２）＜ｎ＜ｑ１＝ｑ１（ｎ，Ｌ１，Ｌ２），使得对任意弱（Ｌ１，Ｌ２）－ＢＬＤ映射ｆ∈（Ω，Ｒｎ），都有ｆ∈（Ω，Ｒｎ），即ｆ为（Ｌ１，Ｌ２）－ＢＬＤ映射．     

On additives, morphological evolution and dielectric breakdown in low density polyethylene

A series of low density polyethylene systems has been studied with respect to structural evolution and short-term dielectric breakdown behaviour. All materials were based upon a single polymer, that is commonly used in high voltage applications, but with different additives. In all three of these systems, multiple melting transitions were observed, as a result of molecular fractionation effects during crystallization. In the virgin polymer, a space-filling banded spherulitic morphology was found to develop at low temperatures (102 °C and below) whereas, at higher temperatures, only a few isolated axialites were observed. Inclusion of the antioxidant resulted in greatly increased nucleation densities, such that, at low temperatures, no evidence of spherulitic organisation remained. At higher temperatures, sheaf-like lamellar aggregates developed, which were much smaller and much more numerous than in the case of the virgin polymer. Further addition of dicumyl peroxide (DCP) resulted in the rapid formation of a crosslinked network at 200 °C. Some crosslinking also occurred at 150 °C, but over a much longer timescale. Where extensive crosslinking occurred prior to crystallization, the resulting gel inhibited structural development, such that only a few small, isolated sheaves were able to form at 102 °C. In view of the principal application area of this material, the breakdown strength of each of the above systems was then measured and the whole data set was analysed statistically. When structural factors were considered alongside the statistics, no clear trends emerged to indicate that either the compositional or morphological variations were reflected in the short-term electrical failure processes.     

Naphthyl azomesogens with lateral chloro groups

A homologous series of azomesogens, 2″-[4-(4′-n-alkoxybenzoyloxy)-2-chlorophenylazo] naphthalenes, with lateral chloro groups was synthesised. All the homologues synthesized exhibit enantiotropic nematic mesophase. The mesomorphic properties of the present series are compared with other structurally related series to evaluate the effect of lateral chloro group and its position on mesomorphism This paper was presented at the 10th National Conference on Liquid Crystals held at Bangalore, India during 9–11 October 2003.     

A classical no-interaction theorem for bosonic strings and its quantum significance

We show that, in dimensions equal or greater than three, classical strings do not join or split. This is part of a no-interaction theorem that is also proved. The quantum theory is considered.     

On the onset of separation in turbulent boundary layer flow over two-dimensional humps of various size

Summary The available laboratory data of turbulent boundary layer flow over two-dimensional obstacles have been examined in order to identify the parameters (such as the aspect ratio or the surface roughness) driving the onset of separation. A comparison with some linearized models suitable for atmospheric applications is also made. It results that i) the model response can be highly sensitive to the detailed shape of the obstacle; ii) the ratio between obstacle length and boundary layer thickness is relevant in determining the pressure perturbation near the surface; iii) the surface shear stress is poorly described in most cases and in particular in the obstacle wake.

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Riassunto I dati di laboratorio disponibili, relativi a strati limite turbolenti su ostacoli bidimensionali, sono stati esaminati al fine di identificare i parametri guida della separazione (quali la pendenza o la rugosità della superficie). Inoltre è stato fatto un confronto con i risultati di alcuni modelli linearizzati adatti per applicazioni atmosferiche. Ne risulta che i) la risposta del modello è molto sensibile alla forma dettagliata dell’ostacolo; ii) il rapporto fra la lunghezza dell’ostacolo e lo spessore dello strato limite turbolento incidente è importante nel determinare la perturbazione della pressione vicino alla superficie; iii) lo ?shear stress? superficiale non è riprodotto con accuratezza nella maggioranza dei casi, in particolare nella scia dell’ostacolo.

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Резюме Анализируются имеющиеся лабораторные данные по турбулентному течению в пограничном слое над двумерными препятствиями, чтобы идентифицировать параметры (такие как аспектное отношение или шероховатость поверхности), определяющие возникновение отрыва. Проводится сравнение с некоторыми линеаризованными моделями, удобными для атмосферных приложений. Получены следующие результаты: 1) модельный отклик может быть очень чувствительным к детальной форме препятствия; 2) отношение между длиной препятствия и толщиной поверхностного слоя является существенным при определении возмущения давления вблизи поверхности; 3) напряжение поверхностного сдвига плохо описывается в большинстве случаев и, в частности, в спутной струе.

     

Development of a quantitative FI-MS technique for the characterization of high- and nonboiling saturated hydrocarbon mixtures

Summary Using a saturated non-boiling hydrocarbon mixture, the influence of two parameters on the results of field ionization mass spectrometry (FI-MS) measurements was studied: (a) the potential difference between the FI emitter and the counterelectrode; (b) the emitter temperature.Variation of the potential difference had only a minor effect on the average molecular mass measured and had no evident effect on the relative ring number distribution in the sample. In contrast, when the emitter temperature was increased, higher average molecular masses were recorded. Moreover, the average molecular masses shifted to higher ring numbers. In order to control the relationship between the described influences during mixture analysis, measuring instructions have been developed that enable the quantitative analysis of unknown saturated samples. However, average molecular mass of the mixture must be known.

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Entwicklung einer quantitativen FI-MS-Methode zur Charakterisierung von gesättigten hoch- und nichtsiedenden Kohlenwasserstoffgemischen

     

On the stability of Riemannian manifold with parallel spinors

Inspired by the recent work [HHM03], we prove two stability results for compact Riemannian manifolds with nonzero parallel spinors. Our first result says that Ricci flat metrics which also admit nonzero parallel spinors are stable (in the direction of changes in conformal structures) as the critical points of the total scalar curvature functional. Our second result, which is a local version of the first one, shows that any metric of positive scalar curvature cannot lie too close to a metric with nonzero parallel spinor. We also prove a rigidity result for special holonomy metrics. In the case of SU(m) holonomy, the rigidity result implies that scalar flat deformations of Calabi-Yau metric must be Calabi-Yau. Finally we explore the connection with a positive mass theorem of [D03], which presents another approach to proving these stability and rigidity results. Dedicated to Jeff Cheeger for his sixtieth birthday