Read e-book online The Shabby Chic Home PDF

By Rachel Ashwell

ISBN-10: 0060987685

ISBN-13: 9780060987688

Shabby stylish fashion designer Rachel Ashwell indicates readers tips to flip any apartment or condo right into a cozy, practical, attractive, and fashionable domestic, during this bestselling consultant to getting the main out of flea-market unearths and classic treasures.

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30) We now define n V (t) = V1 (t) + V2 (t) + V1i (t), i=1 where V1i (t) = βi (M1 )βi t t−τi [c1 bi (s + τi ) + c2 gi (s + τi )]| ln x1 (s) − ln x2 (s)| ds. (31) Feedback Control for Permanence and Global Asymptotic Stability 259 It then follows from (22) and (30)–(31) that for t ≥ T + τ D + V (t) ≤ −A1 (t)| ln x1 (t) − ln x2 (t)| − A2 (t)|u 1 (t) − u 2 (t)|, (32) where A1 (t) and A2 (t) are defined in (22). By assumption (H4 ), there exist positive constants α 1 , α 2 and T ∗ ≥ T + τ such that if t ≥ T ∗ Ai (t) ≥ αi > 0, i = 1, 2.

Recently, this same statement was shown to hold for nonlinear equations as well [17]. In Ref. [16], the authors treated the ITEM as a normalized gradient flow and proved its energy diminishing property. The ITEM, in its original form, is quite slow. In addition, it does not always converge to a stationary solution even if the initial function is quite close to the solution. In an effort to improve the convergence rate of the ITEM, the authors of Ref. [15] demonstrated that if the Sobolev gradients are used in the minimization of the energy functional, the convergence of the ITEM can be greatly accelerated (an equivalent possibility was mentioned in passing in Ref.

2sin(2π t) and τ = 1. and has a unique globally asymptotically stable positive periodic solution, that is, Numerical simulation of the above results can be seen in Figure 2. Thus, we give an interesting open problem. CONJECTURE 1. The feedback control has no influence on the globally asymptotically stable of system (3). Acknowledgments This work was partially supported by the Natural Science Foundation of China under the contact 10531030 and partially by NCET. References 1. K. GOPALSAMY and P. WEN, Feedback regulation of logistic growth, Int.

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