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91.
92.
Self-Affine Sets and Graph-Directed Systems 总被引:1,自引:0,他引:1
Abstract. A self-affine set in R
n
is a compact set T with A(T)= ∪
d∈ D
(T+d) where A is an expanding n× n matrix with integer entries and D
={d
1
, d
2
,···, d
N
} ⊂ Z
n
is an N -digit set. For the case N = | det(A)| the set T has been studied in great detail in the context of self-affine tiles. Our main interest in this paper is to consider the
case N > | det(A)| , but the theorems and proofs apply to all the N . The self-affine sets arise naturally in fractal geometry and, moreover, they are the support of the scaling functions in
wavelet theory. The main difficulty in studying such sets is that the pieces T+d, d∈ D, overlap and it is harder to trace the iteration. For this we construct a new graph-directed system to determine whether
such a set T will have a nonvoid interior, and to use the system to calculate the dimension of T or its boundary (if T
o
≠ ). By using this setup we also show that the Lebesgue measure of such T is a rational number, in contrast to the case where, for a self-affine tile, it is an integer. 相似文献
93.
94.
Anthony To-Ming Lau 《Journal of Functional Analysis》2008,254(10):2513-2533
In this paper, we explore the properties of projections of norm one on general Banach algebras, in particular the relation with conditional expectations for algebras which arise in harmonic analysis. 相似文献
95.
In this paper, we shall establish a fixed point property on Fréchet spaces for left reversible semitopological semigroups generalizing some classical results. 相似文献
96.
97.
There is relatively little information on glasses based on chlorides, bromides and iodides. Because of the recent interest in fluoride it is the objective of this paper to evaluate the potential for preparing new halide glasses and to offer some predictions on the properties of glasses based on chlorides, bromides and iodides. The predictions of glass-forming tendency, viscosity, chemical durability and structures are discussed. 相似文献
98.
Eike Lau 《Inventiones Mathematicae》2008,171(3):617-628
Over p-adic Nagata rings, formal p-divisible groups are classified by nilpotent displays according to T. Zink. We extend this result to arbitrary p-adic rings. The proof uses the Grothendieck–Illusie deformation theory of truncated p-divisible groups. 相似文献
99.
In this paper, we study the multi-machine scheduling problem with earliness and tardiness penalties and sequence dependent
setup times. This problem can be decomposed into two subproblems—sequencing and timetabling. Sequencing focuses on assigning
each job to a fixed machine and determine the job sequence on each machine. We call such assignment a semi-schedule. Timetabling
focuses on finding an executable schedule from the semi-schedule via idle-time insertion. Sequencing is strongly NP-hard in
general. Although timetabling is polynomial-time solvable, it can become a computational bottleneck if the procedure is executed
many times within a larger framework. This paper makes two contributions. We first propose a quantum improvement to the computational
efficiency of the timetabling algorithm. We then apply it within a squeaky wheel optimization framework to solve the sequencing
and overall problem. Finally, we demonstrate the strength of our proposed algorithms by experiments. 相似文献
100.
Mark C. Biesinger Brad P. Payne Leo W. M. Lau Andrea Gerson Roger St. C. Smart 《Surface and interface analysis : SIA》2009,41(4):324-332
Quantitative chemical state X‐ray photoelectron spectroscopic analysis of mixed nickel metal, oxide, hydroxide and oxyhydroxide systems is challenging due to the complexity of the Ni 2p peak shapes resulting from multiplet splitting, shake‐up and plasmon loss structures. Quantification of mixed nickel chemical states and the qualitative determination of low concentrations of Ni(III) species are demonstrated via an approach based on standard spectra from quality reference samples (Ni, NiO, Ni(OH)2, NiOOH), subtraction of these spectra, and data analysis that integrates information from the Ni 2p spectrum and the O 1s spectra. Quantification of a commercial nickel powder and a thin nickel oxide film grown at 1‐Torr O2 and 300 °C for 20 min is demonstrated. The effect of uncertain relative sensitivity factors (e.g. Ni 2.67 ± 0.54) is discussed, as is the depth of measurement for thin film analysis based on calculated inelastic mean free paths. Copyright © 2009 John Wiley & Sons, Ltd. 相似文献