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We prove that a finite solvable group G has at least (49p+1)/60 conjugacy classes whenever p is a prime such that p2 divides the order of G. We also construct an infinite family of finite solvable groups, where this bound is attained. 相似文献
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Marianne Gerny Burkhard Alpers 《International Journal of Computers for Mathematical Learning》2004,9(1):25-57
In this article we describe a mathematical microworld for investigating car motion on a racing course and its use with a group of grade 12 students. The microworld is concerned with the mathematical construction of courses and functions which describe car motion. It is implemented in the computer algebra system, Maple®, which provides the means to represent courses and functions symbolically and graphically. We describe the learning opportunities offered by the microworld in relation to the research literature on functions. Various facets and layers of the function concept are addressed in the microworld, and we suggest how work in the microworld might help in overcoming some well-known misconceptions.This revised version was published online in September 2005 with corrections to the Cover Date. 相似文献
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Mária Meiarová Katarína Hubinská tefan Toma Burkhard Koch Albrecht Berkessel 《Monatshefte für Chemie / Chemical Monthly》2007,138(11):1181-1186
Summary.
N-Toluensulfonyl-l-prolin amide was tested as catalyst in the enantioselective Michael addition of carbonyl compounds to (E)-β-nitrostyrene in nine ionic liquids under different reaction conditions. The reaction rates and enantioselectivities were
strongly dependent on the ionic liquids. Change of enantioselectivity was observed too and it is attributed to both the cation
and the anion of ionic liquid. The best yields (up to 98%) and enantioselectivity (70% ee) of product were obtained in a basic ionic liquid [bmim]BF4 at room temperature. 相似文献
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Confined thin film melt polymerization (CTFMP) of naphthalene chloride/hydroquinone (NCMQ, 1/1, molar)mixtures at polymerization temperatures (T_p) below ca. 300℃ resulted in relatively thick, elongated crystals. Polymerizationof NC/HQ above 300℃ between glass yielded well-formed lamellar crystals ca. 100 A thick. Phase Ⅰ and Ⅱ [001] EDpatterns were obtained for all T_p, the relative amount of phase Ⅰ increasing with T_p. Polymerization of naphthalenedicarboxylic acid/hydroquinione diacetate 1/1 mixtures at high T_p also yielded lamellar crystals that "curled up" off of thesubstrate. When the high temperature CTFMP polymerization was conducted between mica, aggregates of lamellae on-edgedeveloped but epitaxial growth did not occur. Epitaxial growth of lamellae between mica could be obtained, however, byconfined thin film solution polymerization, with both of the latter samples yielding apparently related ED patterns from adifferent unit cell than phase Ⅰ or Ⅱ. Fiber patterns, obtained from sheared samples, indicated considerably greater crystaldisorder than in the nascent crystals. Refinement of the phase Ⅰ unit cell parameters, based on the [001] and [01 1] EDpatterns, with modeling based on Cerius~2, suggests a monoclinic phase Ⅰ unit cell with a = 7.76, b = 5.71, c = 14.99 A, α = γ= 90°, β= 99.7°, ρ = 1.47 g/cm~3, space group P12_1/al. 相似文献
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Zein films plasticized with oleic acid were formed by solution casting, by the stretching of moldable resins, and by blown film extrusion. The effects of the forming process on film structure were investigated by X-ray diffraction. Wide-angle X-ray scattering (WAXS) patterns showed d-spacings at 4.5 and 10 A, which were attributed to the zein alpha-helix backbone and inter-helix packing, respectively. The 4.5 A d-spacing remained stable under processing while the 10 A d-spacing varied with processing treatment. Small-angle X-ray scattering (SAXS) detected a long-range periodicity for the formed films but not for unprocessed zein, which suggests that the forming process-promoted film structure development is possibly aided by oleic acid. The SAXS d-spacing varied among the samples (130-238 A) according to zein origin and film-forming method. X-ray scattering data suggest that the zein molecular structure resists processing but the zein supramolecular arrangements in the formed films are dependent on processing methods. Structural model for a zein molecular aggregate (based on Matsushima et al.10). Rectangular prisms of individual zein molecules are hexagonally aligned parallel to each other. 相似文献
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Thomas M. Klapötke Burkhard Krumm Dieter Naumann 《Journal of fluorine chemistry》2004,125(6):997-1005
The perfluoroaryl tellurolates C6F5TeLi (1) and 4-CF3C6F4TeLi (2) were prepared. These intermediates were identified by NMR spectroscopy and may form, depending on the reaction conditions, either the corresponding ditellanes C6F5TeTeC6F5 (3) and CF3C6F4TeTeC6F4CF3 (4) by subsequent oxidation, or in the case of 1, a telluranthrene (C6F4Te)2 (5) by reaction with itself. The halogenation products of 5, ( C6F4Te)2F4 (6), (C6F4Te)2Cl4 (7), (C6F4Te)2Br4 (8), as well as the azidation product (C6F4Te)2(N3)4 (9) were synthesized. Furthermore, in pursuit of our recent work on tellurium azides, the syntheses and properties of R2Te(N3)2 (R=CF3 (10), C6F2H3 (11)) and RTe(N3)3 (R=CF3 (12) and C6F5 (13)) are reported. The crystal structures of CF3C6F4TeTeC6F4CF3 (4), (C6F4Te)2Br4 (8), and (C6F2H3)2Te(N3)2 (11) were determined. 相似文献