From the Editors
Yang Kuang Ying-Cheng Lai Zhiming Zheng
Mathematical Biosciences & Engineering 2004, 1(1): i-ii doi: 10.3934/mbe.2004.1.1i
It is easy to argue that we are entering a new golden era of science and engineering. The predominant approach of conducting timely and in-depth scienti c research is forever changed from cycles of simple experiment and theory to cycles that combine of experiment, theory, mathematical modeling, and analysis. The landscape of science is now clearly dominated by the peaks of biosciences. Integrative and interdisciplinary research in life sciences and engineering is no longer merely a slogan but aggressively and collectively pursued and practiced by researchers. This shift of paradigms greatly enhances the central importance of mathematical and computational modeling and analysis in scienti c and engineering endeavors. With this exciting backdrop in mind, the American Institute of Mathematical Sciences (AIMS) and Beihang University have decided to launch a joint international journal on mathematical biosciences and engineering. This journal will maximally serve the scienti c communities in both developed and developing countries.

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Necessary and sufficient conditions for semi-uniform ergodic theorems and their applications
Zuohuan Zheng Jing Xia Zhiming Zheng
Discrete & Continuous Dynamical Systems - A 2006, 14(3): 409-417 doi: 10.3934/dcds.2006.14.409
It has been established one-side uniform convergence in both the Birkhoff and sub-additive ergodic theorems under conditions on growth rates with respect to all the invariant measures. In this paper we show these conditions are both necessary and sufficient. These results are applied to study quasiperiodically forced systems. Some meaningful geometric properties of invariant sets of such systems are presented. We also show that any strange compact invariant set of a $\mathcal{C}^1$ quasiperiodically forced system must support an invariant measure with a non-negative normal Lyapunov exponent.
keywords: quasiperiodically forced systems. strange attractors Ergodic theorems

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