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141.
PARK Kyewon Koh 《中国科学 数学(英文版)》2011,(3):531-538
We introduce the notion of entropy generating sequence for infinite words and define its dimension when it exists. We construct an entropy generating sequence for each symbolic example constructed by Cassaigne such that the dimension of the sequence is the same as its topological entropy dimension. Hence the complexity can be measured via the dimension of an entropy generating sequence. Moreover, we construct a weakly mixing example with subexponential growth rate. 相似文献
142.
143.
ZHAO YuXin YI ShiHe TIAN LiFeng HE Lin & CHENG ZhongYu College of Aerospace Material Engineering National University of Defense Technology Changsha China 《中国科学G辑(英文版)》2008,51(8):1134-1143
Flow visualization of supersonic mixing layer has been studied based on the high spatiotemporal resolution Nano-based Planar Laser Scattering(NPLS) method in SML-1 wind tunnel. The corresponding images distinctly reproduced the flow structure of laminar,transitional and turbulent region,with which the fractal measurement can be implemented. Two methods of measuring fractal dimension were introduced and compared. The fractal dimension of the transitional region and the fully developing turbulence region of supersonic mixing layer were measured based on the box-counting method. In the transitional region,the fractal dimension will increase with turbulent intensity. In the fully developing turbulent region,the fractal dimension will not vary apparently for different flow structures,which em-bodies the self-similarity of supersonic turbulence. 相似文献
144.
145.
We reinterpret the state space dimension equations for geometric Goppa codes. An easy consequence is that if deg
then the state complexity of
is equal to the Wolf bound. For deg
, we use Clifford's theorem to give a simple lower bound on the state complexity of
. We then derive two further lower bounds on the state space dimensions of
in terms of the gonality sequence of
. (The gonality sequence is known for many of the function fields of interest for defining geometric Goppa codes.) One of the gonality bounds uses previous results on the generalised weight hierarchy of
and one follows in a straightforward way from first principles; often they are equal. For Hermitian codes both gonality bounds are equal to the DLP lower bound on state space dimensions. We conclude by using these results to calculate the DLP lower bound on state complexity for Hermitian codes. 相似文献
146.
Masanori Hino 《Potential Analysis》2002,16(3):249-264
For conservative symmetric diffusions on a general state space (X,m), the short time asymptotic behavior of tlog
X
1
A
T
t
1
B
dm is investigated, where T
t
is the associated semigroup and A and B are measurable subsets of X. It is proved that the superior limit is dominated by the inferior limit up to some absolute constant. When 2 of the associated Dirichlet form is lower bounded, it is shown that the limit exists for any A and B, and is described by the intrinsic metric between them. Applications to infinite-dimensional spaces and fractals are given. 相似文献
147.
Gabriel Nagy 《Proceedings of the American Mathematical Society》2002,130(4):1065-1071
We prove that the value of the quasi-trace on an idempotent element in an AW*-factor of type is the same as the dimension of its left (or right) support.
148.
Thierry Levasseur 《Proceedings of the American Mathematical Society》2002,130(12):3519-3523
Let be a complex semisimple Lie algebra and be its enveloping algebra. We deduce from the work of R. Bezrukavnikov, A. Braverman and L. Positselskii that the Krull-Gabriel-Rentschler dimension of is equal to the dimension of a Borel subalgebra of .
149.
150.
Multi-Fractal Formalism for Quasi-Self-Similar Functions 总被引:1,自引:0,他引:1
The study of multi-fractal functions has proved important in several domains of physics. Some physical phenomena such as fully developed turbulence or diffusion limited aggregates seem to exhibit some sort of self-similarity. The validity of the multi-fractal formalism has been proved to be valid for self-similar functions. But, multi-fractals encountered in physics or image processing are not exactly self-similar. For this reason, we extend the validity of the multi-fractal formalism for a class of some non-self-similar functions. Our functions are written as the superposition of similar structures at different scales, reminiscent of some possible modelization of turbulence or cascade models. Their expressions look also like wavelet decompositions. For the computation of their spectrum of singularities, it is unknown how to construct Gibbs measures. However, it suffices to use measures constructed according the Frostman's method. Besides, we compute the box dimension of the graphs. 相似文献