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This ebook constitutes the refereed court cases of the sixth overseas convention on clever Computing, ICIC 2010, held in Changsha, China, in August 2010. The eighty five revised complete papers awarded have been rigorously reviewed and chosen from a a number of submissions. The papers are geared up in topical sections on neural networks, evolutionary studying & genetic algorithms, fuzzy thought and types, fuzzy structures and delicate computing, particle swarm optimization and area of interest know-how, supervised & semi-supervised studying, unsupervised & reinforcement studying, combinatorial & numerical optimization, structures biology and computational biology, neural computing and optimization, nature encouraged computing and optimization, wisdom discovery and information mining, synthetic lifestyles and synthetic immune structures, clever computing in picture processing, specific consultation on new hand established biometric equipment, distinctive consultation on fresh advances in photograph segmentation, specified consultation on theories and functions in complicated clever computing, precise consultation on seek dependent software program engineering, designated consultation on bio-inspired computing and purposes, precise consultation on increase in dimensionality relief equipment and its purposes, exact consultation on protein and gene bioinformatics: tools and purposes
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Extra info for Advanced intelligent computing theories and applications : 6th International Conference on Intelligent Computing, ICIC 2010, Changsha, China, August 18-21, 2010. Proceedings
N 22 X. Xu and J. Zhang Proof. Firstly, from (4), it can be concluded that − ξ i [γ i + θ i m / π 2 − 0 . , n . 5 j =1 ∑ n j =1 [| aij | + | cij | κ ij ( μ )] L j ξ j . Obviously Fi (0) < 0 . e. , n . , n . (14) ∫ (15) By Lemma 1, we have ∫ Ω zi (t , x) ∑ ∂ m k =1 ∂x [ Dik k ≤ −θ i ∂zi (t , x ) ]dx ∂xk ∫ ∇z Ω T i (t , x )∇zi (t , x ) dx ≤ −(θ i m / π 2 ) Ω zi2 (t , x)dx , substituting (15) into (14), and from AssumptionsA1-A2, we have D +Vi (t ) ≤ λe λt || zi (t , x) || 2L2 −(θ i m / π 2 )e λt ∑ n j =1 ∫ Ω zi2 (t , x) dx + e λt ∫ L j [| zi (t , x ) | .
By studying the general expression in theorem 2 we can deduce several important corollaries as follows: Corollary 1. If rank ( FP ) = rank ( F ) , then s QA (∞) = s BQ ( ∞ ) = FQ FP+ s P (0) Proof. Let rank ( FP ) = rank ( F ) = r decompose F as follows: ⎡ C1 ⎤ ⎡C ⎤ P× r r× N L×r , D ∈C , C1 ∈ C , F = ⎢ 1 ⎥ ⋅ D = C0 ⋅ D , where C 0 = ⎢ ⎥ ∈ C C C ⎣ 2⎦ ⎣ 2⎦ C 2 ∈ C Q× r FP = C1 D ，F Q = C2 D , rank ( FP ) = rank ( F ) = r = rank (C1 D) ≤ rank (C1 ) , namely rank (C1 ) ≥ r (4) and r = rank(C1D) ≥ rank(C1 ) + rank(D) − r = rank(C1 ) , namely rank(C1 ) ≤ r Combining (4) and (5), we obtain rank (C1 ) = r .
Proof. For all A ∈ AI , C ∈ C I , due to P is a M-matrix, from the property of M-matrix , we know that there exists ξ i > 0 ( i = 1,2, ... 5 ∑ n j =1 ξ j ( a 0ji + c 0ji )L j ≥ δ > 0 . Consider the map (3) endowed with the norm || ⋅ ||= ( ∑ || ⋅ || 2 1/ 2 ) L2 (4) . It is well known that if Eq. (3) is homeomorphism on R n , then (1) has a unique equilibrium point. First of all, we demonstrate the injective part. 20 X. Xu and J. , n : ∑ di (ui ) − di (vi ) = ∂ m k =1 ∂x k [ Dik ∂ (ui − vi ) ]+ ∂xk ∑ n j =1 ( aij + cij )[ g j (u j ) − g j (v j )] .