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1.
An exact formula for the various measure dimensions of attractors associated with contracting similitudes is given. An example is constructed showing that for more general affine maps the various measure dimensions are not always equal.Communicated by Michael F. Barnsley. 相似文献
2.
The Morita-Baylis-Hillman (MBH)-type reaction of α,β unsaturated δ-lactone with various aldehydes has been achieved without the direct use of a Lewis base. The new MBH process can be conveniently carried out by the slow addition of the diethylaluminum iodide into the solution of lactone and aldehyde in dichloromethane at 0°C. Modest to good yields were obtained (50-65%) for eight examples. 相似文献
3.
A simple model, consisting of ‘two-body’ reactant and product trajectories joined by an instantaneous switch, is proposed for the alkali atom-alkyl iodide rebound reactions. The electronic potential surfaces governing these trajectories are justified in terms of the electron jump model. Encouraging overall agreement is found with extensive molecular beam data for the K, Cs + CH3I reactions. 相似文献
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Clyde D Hardin 《Journal of multivariate analysis》1982,12(3):385-401
The so-called spectral representation theorem for stable processes linearly imbeds each symmetric stable process of index p into Lp (0 < p ≤ 2). We use the theory of Lp isometries for 0 < p < 2 to study the uniqueness of this representation for the non-Gaussian stable processes. We also determine the form of this representation for stationary processes and for substable processes. Complex stable processes are defined, and a complex version of the spectral representation theorem is proved. As a corollary to the complex theory we exhibit an imbedding of complex Lq into real or complex Lp for 0 < p < q ≤ 2. 相似文献
8.
Douglas P. Hardin Thomas A. Hogan 《Proceedings of the American Mathematical Society》2000,128(7):1941-1950
Local refinable finitely generated shift-invariant spaces play a significant role in many areas of approximation theory and geometric design. In this paper we present a new approach to the construction of such spaces. We begin with a refinable function which is supported on . We are interested in spaces generated by a function built from the shifts of .
9.
W. L. Hardin 《Analytical and bioanalytical chemistry》1898,37(3):205-208
10.
For N-point best-packing configurations ω N on a compact metric space (A,ρ), we obtain estimates for the mesh-separation ratio γ(ω N ,A), which is the quotient of the covering radius of ω N relative to A and the minimum pairwise distance between points in ω N . For best-packing configurations ω N that arise as limits of minimal Riesz s-energy configurations as s→∞, we prove that γ(ω N ,A)≦1 and this bound can be attained even for the sphere. In the particular case when N=5 on S 2 with ρ the Euclidean metric, we prove our main result that among the infinitely many 5-point best-packing configurations there is a unique configuration, namely a square-base pyramid $\omega_{5}^{*}$ , that is the limit (as s→∞) of 5-point s-energy minimizing configurations. Moreover, $\gamma(\omega_{5}^{*},S^{2})=1$ . 相似文献