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排序方式: 共有599条查询结果,搜索用时 31 毫秒
81.
Let{W1(t), t∈R+} and {W2(t), t∈R+} be two independent Brownian motions with W1(0) = W2(0) = 0. {H (t) = W1(|W2(t)|), t ∈R+} is called a generalized iterated Brownian motion. In this paper, the Hausdorff dimension and packing dimension of the level sets {t ∈[0, T ], H(t) = x} are established for any 0 < T ≤ 1. 相似文献
82.
ABSTRACTWe consider a certain family of CIFSs of the generalized complex continued fractions with a complex parameter space. We show that for each CIFS of the family, the Hausdorff measure of the limit set of the CIFS with respect to the Hausdorff dimension is zero and the packing measure of the limit set of the CIFS with respect to the Hausdorff dimension is positive (main result). This is a new phenomenon of infinite CIFSs which cannot hold in finite CIFSs. We prove the main result by showing some estimates for the unique conformal measure of each CIFS of the family and by using some geometric observations. 相似文献
83.
This study explored two undergraduate precalculus students’ understandings of the idea of logarithm as they completed conceptually oriented exploratory lessons on exponential and logarithmic functions. The students participated in consecutive, individual teaching experiments that focused on Sparky – an animated mystical saguaro that doubled in height every week. The exponential lesson focused on developing students’ conceptions of growth factors and tupling (e.g., doubling) periods as a foundational understanding for conceptualizing logarithms and logarithmic properties meaningfully. This paper characterizes conceptions that are productive for students to acquire in introductory lessons on exponential and logarithmic growth, and discusses two understandings that were revealed to be foundational for students’ development of productive meanings for exponents, logarithms and logarithmic properties. 相似文献
84.
Given a braided vector space
, we show that iterated integrals of operator-valued functions satisfying a certain exchange relation give rise to representations of the quantum shuffle algebra built on
. Using the quantum shuffle construction of the 'upper triangular part'
of a quantum shuffle, this provides a simple proof of the result of Bouwknegt, MacCarthy and Pilch saying that integrals of vertex operators acting on certain Fock modules give rise to representations of
. 相似文献
85.
Let
be a real separable Banach space and {X, X
n, m; (n, m) N
2} B-valued i.i.d. random variables. Set
. In this paper, the compact law of the iterated logarithm, CLIL(D), for B-valued random variables with two-dimensional indices ranging over a subset D of N
2 is studied. There is a gap between the moment conditions for CLIL(N
1) and those for CLIL(N
2). The main result of this paper fills this gap by presenting necessary and sufficient conditions for the sequence
to be almost surely conditionally compact in B, where, for 0, 1 r 2, N
r
(, ) = {(n, m) N
2; n
m n
exp{(log n)
r–1 (n)}} and (·) is any positive, continuous, nondecreasing function such that (t)/(log log t) is eventually decreasing as t , for some > 0. 相似文献
86.
We prove limsup results for nonnegative functionals of convex sets determined by normalized Brownian paths in Banach spaces. This continues the interesting investigation of D. Khoshnevisan into this area, and relates to some classical unsolved isoperimetric problems for the convex hull of curves in d. Section 4 contains the solution of a problem similar to these classical problems. 相似文献
87.
Radu Miculescu Alexandru Mihail 《Proceedings of the American Mathematical Society》2008,136(2):587-592
It is known that Lipscomb's space can be imbedded in Hilbert's space . Let be the imbedded version of endowed with the -induced topology. We show how to construct as the attractor of an iterated function system containing an infinite number of affine transformations of . In this way we answer an open question of J.C. Perry.
88.
Li Xin Zhang 《数学学报(英文版)》2008,24(4):631-646
Let X, X1, X2,... be i.i.d, random variables with mean zero and positive, finite variance σ^2, and set Sn = X1 +... + Xn, n≥1. The author proves that, if EX^2I{|X|≥t} = 0((log log t)^-1) as t→∞, then for any a〉-1 and b〉 -1,lim ε↑1/√1+a(1/√1+a-ε)b+1 ∑n=1^∞(logn)^a(loglogn)^b/nP{max κ≤n|Sκ|≤√σ^2π^2n/8loglogn(ε+an)}=4/π(1/2(1+a)^3/2)^b+1 Г(b+1),whenever an = o(1/log log n). The author obtains the sufficient and necessary conditions for this kind of results to hold. 相似文献
89.
Let {ξ
j
; j ∈ ℤ+
d
be a centered stationary Gaussian random field, where ℤ+
d
is the d-dimensional lattice of all points in d-dimensional Euclidean space ℝd, having nonnegative integer coordinates. For each j = (j
1
, ..., jd) in ℤ+
d
, we denote |j| = j
1
... j
d
and for m, n ∈ ℤ+
d
, define S(m, n] = Σ
m<j≤n
ζ
j
, σ2(|n−m|) = ES
2
(m, n], S
n
= S(0, n] and S
0
= 0. Assume that σ(|n|) can be extended to a continuous function σ(t) of t > 0, which is nondecreasing and regularly varying with exponent α at b ≥ 0 for some 0 < α < 1. Under some additional conditions, we study limsup results for increments of partial sum processes and prove as well the law of the iterated logarithm for such partial sum processes.
Research supported by NSERC Canada grants at Carleton University, Ottawa 相似文献
90.