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1.
For a ? R\alpha \in \mathbf{R}, the class of a-\alpha -order spherical harmonic functions in an open set W í\Omega \subseteq Sn-1\mathbf{S}^{n-1}, Ha(W)H^{\alpha }(\Omega ) is defined as the C2-C^{2}-solutions of Dau=0\Delta _{\alpha }u=0; where Da=Ds+a(n+a-2)\Delta _{\alpha }=\Delta _{s}+\alpha (n+\alpha -2) is the spherical Laplace--Beltrami operator of order a\alpha and Ds\Delta _{s} is the radially independent part of the Laplace operator. We obtain a Green's integral formula for the functions in Ha(W)H^{\alpha }(\Omega ) with kernel expressed as a Gegenbauer function. As generalizations, higher order spherical iterated Dirac operators are defined in a polynomial form. Integral representations of the null solutions to these operators and an intertwining formula relating these operators on the sphere and their analogues in Euclidean space are presented. 相似文献
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Mary E. Neubert DAVID G. ABDALLAH Jr Sandra S. Keast Julie M. Kim Soonnam Lee Ryan M. Stayshich Margaret E. Walsh Rolfe G. Petschek Shin-Tson Wu 《Liquid crystals》2003,30(6):711-731
New diphenyldiacetylenes of the type with A, B = H and/or F; m = 0, 1; n = 1-4; and X = C n H 2n + 1 , F, CF 3 or CN were synthesized and their mesomorphic properties determined by hot stage polarizing microscopy and DSC. When m = 0, all of these compounds showed only a nematic phase except when X = CF 3 when both nematic and smectic A phases were seen. Both clearing and melting temperatures were higher than those reported for substitution with the corresponding alkyl chains but the much larger increase in clearing temperatures produced considerably wider nematic phases. Eutectic mixtures of a few of these olefins yielded nematic materials also having much wider temperature ranges and higher clearing temperatures than the eutectic mixtures of the alkyl compounds, while retaining their high birefringence and low viscosities. Such materials are of interest for beam-steering devices.
Four of the diacetylenes with m = 1 ( A, B = H) were also prepared ( X = C 6 H 13 , F, n = 2, 3). When X was C 6 H 13 ( n = 2), the nematic range was smaller in the 2- than in the 1-olefin but wider than in the alkyl series. When X = F, either no nematic phase or a monotropic one was observed, whereas the 1-olefins gave a much wider nematic phase. Both transition temperatures were lower than those for the corresponding 1-olefin and alkyl analogues. The compound with X = C 6 H 13 and n = 2 had a melting temperature below room temperature. 相似文献
Four of the diacetylenes with m = 1 ( A, B = H) were also prepared ( X = C 6 H 13 , F, n = 2, 3). When X was C 6 H 13 ( n = 2), the nematic range was smaller in the 2- than in the 1-olefin but wider than in the alkyl series. When X = F, either no nematic phase or a monotropic one was observed, whereas the 1-olefins gave a much wider nematic phase. Both transition temperatures were lower than those for the corresponding 1-olefin and alkyl analogues. The compound with X = C 6 H 13 and n = 2 had a melting temperature below room temperature. 相似文献
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Let G be a d‐regular graph G on n vertices. Suppose that the adjacency matrix of G is such that the eigenvalue λ which is second largest in absolute value satisfies λ = o(d). Let Gp with p = α/d be obtained from G by including each edge of G independently with probability p. We show that if α < 1, then whp the maximum component size of Gp is O(log n) and if α > 1, then Gp contains a unique giant component of size Ω(n), with all other components of size O(log n). © 2003 Wiley Periodicals, Inc. Random Struct. Alg., 2004 相似文献
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O. Moze M. Hofmann J. M. Cadogan K. H. J. Buschow D. H. Ryan 《The European Physical Journal B - Condensed Matter and Complex Systems》2003,36(4):511-518
The magnetic structure and ordering temperatures of three intermetallic compounds which crystallize in the tetragonal ThCr2Si2 structure, TbCr2Si2, HoCr2Si2 and ErCr2Si2, have been determined by neutron diffraction, differential scanning calorimetry and magnetization measurements. The Cr-sublattice orders anti-ferromagnetically with Néel temperatures of 758 K for TbCr2Si2, 718 K for HoCr2Si2 and 692 K for ErCr2Si2. Chromium atoms located at 4d crystallographic sites are aligned anti-parallel along the c-axis, with GZCr magnetic modes. In contrast with metallic bcc Cr, the refined room temperature value of the ordered Cr moment is anomalously large for all three compounds. No long range magnetic order of the R sublattice in TbCr2Si2 and HoCr2Si2 is observed, whilst the Er sublattice in ErCr2Si2 orders independently of the Cr sublattice below 2.4 K with moments ferromagnetically aligned in the basal plane.Received: 4 November 2003, Published online: 30 January 2004PACS:
75.25. + z Spin arrangements in magnetically ordered materials (including neutron and spin-polarized electron studies, synchrotron-source X-ray scattering, etc.) - 75.30.Cr Saturation moments and magnetic susceptibilities - 75.50.Ee Antiferromagnetics 相似文献
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Richard A. Cairncross Jeffrey G. Becker Shri Ramaswamy Ryan O'Connor 《Applied biochemistry and biotechnology》1996,131(1-3):774-785
Management of moisture penetration and hydrolytic degradation of polylactide (PLA) is extremely important during the manufacturing,
shipping, storage, and end-use of PLA products. Moisture transport, crystallization, and degradation, in PLA have been measured
through a variety of experimental techniques including size-exclusion chromatography, differential scanning calorimetry, and
X-ray diffraction. Quartz crystal microbalance and dynamic vapor sorption experiments have also been used to measure moisture
sorption isotherms in PLA films with varying crystallinity. A surprising result is that, within the accuracy of the experiments,
crystalline and amorphous PLA films exhibit identical sorption isotherms. 相似文献
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