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  • 41A15  (1)
  • 65D10  (1)
  • 68.20  (1)
  • Springer  (2)
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  • 1
    ISSN: 1432-0630
    Keywords: 36.40 ; 61.1.P ; 68.20
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Abstract Fullerene powder mixtures with different C60/C70 ratios have been analyzed by a variety of techniques, and results have been compared. The fullerence mixtures have been characterized as solutions in n-hexane by high-pressure liquid chromatography (HPLC) and UV-VIS spectroscopy. Thin films of fullerenes on Au(111) have been prepared from the mixtures by sublimation. The sublimation process has been studied by simultaneous thermogravimetric and differential thermal analyses. Thin fullerene films on Au(111) have been investigated by scanning tunneling microscopy (STM). The STM images show primarily two types of ballshaped molecules arranged in a lattice with hexagonal symmetry (fcc(111) face, nearest neighbour distance: 1 nm). The two species differ in diameter. STM images of films made of mixtures of different C60/C70 ratios show that C70 molecules display a larger apparent diameter (0.8 nm) and corrugation than C60 molecules (0.7 nm). The C60/C70 ratios obtained by counting the corresponding molecular species in the STM images of the thin films are compared to the C60/C70 ratios determined by HPLC on hexane solutions of the mixtures. The observed differences might be explained by different rates of sublimation for the two species. The STM images reveal film defects (vacancies and boundaries) and dynamic processes (displacement of C70 molecules and vacancies). In films prepared to have a C60 coverage of less than one monolayer, stable structural units of the C60(111) surface consisting of three or seven C60 molecules are revealed by STM. Occasionally, substructure within individual fullerene molecules is observed.
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  • 2
    Electronic Resource
    Electronic Resource
    Springer
    Numerische Mathematik 48 (1986), S. 323-336 
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65L05 ; 65L07 ; 65D07 ; 65D10 ; 41A15 ; CR: G.1.7 ; G.1.2
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary In this paper non-linear splines (depending onn+1 parameters) are used to patch up the solution of an initial value problem in intervals of stepsizeh. The elements of the solution are fixed byq smoothness conditions andd conditions derived from the differential equation in an appropriate setup. The feasibility of the method can be connected to that of the polynomial spline method by a perturbation type argument. Thus the question of convergence forh→0 is closely connected to the linear (polynomial) case. A new elementary prove is given for divergence of the polynomial splines ifq is larger thand+1, as was done by Mülthei [4] with other techniques. A byproduct is an extention of the famous result for polynomial interpolation by Runge on equidistant grids that interpolation of a given function by splines of too high smoothness can cause divergence forh→0.
    Type of Medium: Electronic Resource
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