Information Computing and Applications: Second International by Yan Yan, Xinghua Ma, Dongmei Li, Liping Du, Yankun Li

By Yan Yan, Xinghua Ma, Dongmei Li, Liping Du, Yankun Li (auth.), Chunfeng Liu, Jincai Chang, Aimin Yang (eds.)

The two-volume set, CCIS 243 and CCIS 244, constitutes the refereed lawsuits of the second one foreign convention on info Computing and functions, ICICA 2010, held in Qinhuangdao, China, in October 2011. The 191 papers offered in either volumes have been rigorously reviewed and chosen from various submissions. they're prepared in topical sections on computational statistics, social networking and computing, evolutionary computing and functions, info schooling and alertness, net and internet computing, clinical and engineering computing, method simulation computing, bio-inspired and DNA computing, web and internet computing, multimedia networking and computing, parallel and dispensed computing.

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Extra resources for Information Computing and Applications: Second International Conference, ICICA 2011, Qinhuangdao, China, October 28-31, 2011. Proceedings, Part II

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On Sufficient and Necessary Condition of a Strong Law of Large Numbers for Negatively Associated Random Variables. Chinese Journal of Applied Probability and Statistics 24(4) (2008) 3. : Complete Convergence for Randomly Weighted Sums of Negatively Associated Random Variables. Journal of Jiangxi Normal University(natural sciences edition) 33(6) (2009) 4. : Strong Convergence for Weighted Sums of Negatively Associated Arrays. Chinese Annals of Mathematics, Series B 31(2) (2010) 5. : On the strong law of large numbers.

A right twisted weak smash product A*H is defined on the vector space A ⊗ H . Define a multiplication[6] (a ⊗ h)(b ⊗ g ) = a (h1 → b ← S (h3 )) ⊗ h2 g on tensor space A ⊗ H , for all a, b ∈ A, h, l ∈ H . 1. Let A be an H-module algebra and A*H the right twisted smash product algebta ,then ∀a, b ∈ A,g, h ∈ H, the following conditions hold[7] 1)(1* h)(1* g) = 1* hg ˆ *1) ˆ = ab *1ˆ 2)(a *1)(b ˆ 3)(a *1)(1* h) = a * h ˆ = h → a ← S(h ) * h 4)(1* h)(a *1) 1 3 2 Proof: By the definition of multiplication of A*H , the 4th condition is clearly true .

1) f is GA - convex ( GA - concave) function on I . (2) f (e x ) is convex (concave) function on ln I . (3) xf ′( x) is increasing(decreasing) on I . Lemma 4[16]. Let I ⊂ R+ is a interval, and f : x → R+ is a positive real-valued function, then the following propositions are equivalent. (1) f is HA - convex ( HA - concave) function on I . (2) f (1 x) is convex (concave) function on 1 I . (3) x 2 f ′( x) is increasing (decreasing) on I . Lemma 5. Let I ⊂ R+ is a interval, and f : x → R+ is a positive real-valued function, then the following propositions are equivalent.

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