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141.
《随机分析与应用》2013,31(4):731-753
For a sequence of independent random elements {V n ,n≥1} in a real separable Banach space X, necessary and, separately, sufficient conditions are provided for the strong law of large numbers ∑ i=1 n (V i ?c i )/b n →0 almost certainly to hold where {c n ,n≥1} and {b n >0,n≥1} are suitable sequences of centering elements in X and norming constants, respectively. The necessity result extends a real line result of Martikainen[14] to a Banach space setting. The sufficiency result assumes that X is of Rademacher type p (1≤p≤2) and is new even when X is the real line. It is general enough to include as special cases a strong law of Adler, Rosalsky, and Taylor[2] for sums of independent and identically distributed random elements and a strong law of Heyde[9] for sums of independent (real-valued) random variables. Illustrative examples are provided showing that the results are sharp and an example is presented satisfying the hypotheses of the sufficiency result but not those of Heyde's[9] theorem. 相似文献
142.
143.
Pranabendu Ganguly Juran Chandra Biswas Samir Kumar Lahiri 《Fiber and Integrated Optics》2013,32(6):511-520
Integrated optic directional couplers consisting of curved waveguides are simulated analytically by solving the Riccati equation. The coupling coefficient between the curved waveguides with a parabolically varying gap and the condition of total power transfer between the waveguides are derived. In order to compute the overall coupling coefficient and hence the power distribution along the waveguides for Ti:LiNbO 3 curved waveguide directional couplers, the coupling coefficient for straight waveguide couplers is computed for different gaps using the effective-index-based matrix method (EIMM). Finally, the power distribution in the curved waveguides along the length is computed. The method is mostly analytical except the effective-index method and is computationally simple. 相似文献
144.
Victor M. Kruglov 《随机分析与应用》2013,31(4):674-683
Kolmogorov's weak law of large numbers for i.i.d. random variables is generalized to a larger class distributions and to a wide class of normalizing sequences. The result is extended to maximal sums of negatively associated identically distributed random variables. 相似文献
145.
B. Wierzbowska K. Piotrowski J. Koralewska A. Matynia N. Hutnik K. Wawrzyniecki 《Crystal Research and Technology》2008,43(4):381-389
The experimental results concerning continuous mass crystallization process in L(+)‐ascorbic acid – water system are presented and discussed. Influence of L(+)‐ascorbic acid concentration in a feeding solution and mean residence time of suspension in laboratory DT MSMPR crystallizer on product crystal size distribution as well as nucleation and growth kinetics were determined. Kinetic parameter values were evaluated on the basis of size–independent growth (SIG) kinetic model (McCabe's ΔL law). It was observed, that within the examined range of crystallizer productivity (120–1600 kg LAA crystals m–3h–1) crystal product population of mean size Lm from 0.2 to 0.3 mm and CV from 66.6 to 49% is withdrawn. Linear growth rate values present decreasing trend (from ca. 7 · 10–8 to ca. 6 · 10–8 m s–1) with the productivity increase (assuming constant mean residence time of suspension τ = 900 s). Occurrence of secondary nucleation within the circulated and mixed suspension, resulting from crystal attrition and breakage, was observed. The parameter values in design equation connecting linear growth rate and suspension density with nucleation rate were determined. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
146.
147.
148.
Due to the applications in network coding, subspace codes and designs have received many attentions. Suppose that and is an ‐dimensional space over the finite field . A ‐spread is a ‐set of ‐dimensional subspaces of such that each nonzero vector is contained in exactly one element of it. A partial ‐parallelism in is a set of pairwise disjoint ‐spreads. As the number of ‐dimensional subspaces in is , there are at most spreads in a partial ‐parallelism. By studying the independence numbers of Cayley graphs associated to a special type of partial ‐parallelisms in , we obtain new lower bounds for partial ‐parallelisms. In particular, we show that there exist at least pairwise disjoint ‐spreads in . 相似文献
149.
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
150.
The point code of a Steiner triple system uniquely determines the system when the number of vectors whose weight equals the replication number agrees with the number of points. The existence of a Steiner triple system with this minimum point code property is established for all v 1,3 (mod 6) with v 15. 相似文献