By V. E. Voskresenski
Because the overdue Sixties, equipment of birational geometry were used effectively within the idea of linear algebraic teams, specifically in mathematics difficulties. This book--which could be seen as an important revision of the author's e-book, Algebraic Tori (Nauka, Moscow, 1977)--studies birational houses of linear algebraic teams targeting mathematics functions. the most subject matters are kinds and Galois cohomology, the Picard team and the Brauer crew, birational geometry of algebraic tori, mathematics of algebraic teams, Tamagawa numbers, $R$-equivalence, projective toric forms, invariants of finite transformation teams, and index-formulas. effects and functions are fresh. there's an in depth bibliography with extra reviews which may function a consultant for additional interpreting.
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Extra resources for Algebraic Groups and Their Birational Invariants (Translations of Mathematical Monographs)
240–243, 1993.  R. W. Rollins, P. Parmanada, and P. Sherard, “Controlling chaos in highly dissipative system–a simple recursive algorithm,” Phys. Rev. E, vol. 47, pp. 780–783, 1993.  R. Roy, T. W. Murphy, T. D. Maier, and Z. Gills, “Dynamical control of a chaotic laser–experimental stabilization of globally coupled system,” Phys. Rev. , vol. 68, pp. 1259–1262, 1992. November 25, 2009 9:55 World Scientific Review Volume - 9in x 6in Controlling Chaos in a Chaotic Neural Network RecentProgress-chapter2 43  A.
974–993, 1999.  M. Adachi, and K. Aihara, “Associative dynamics in a chaotic neural network,” Neural Networks, vol. 10, pp. 83–98, 1997.  M. Shiino, T. Fukai, “Self-consistent signal-to-noise analysis of the statistical behavior of analog neural networks and enhancement of the storage capacity,” Phys. Rev. E, vol. 48, pp. 867–897, 1993.  M. Nakagawa, “An artiﬁcial neuron model with a periodic activation function,” J, Phys. Soc. Jpn, vol. 64, pp. 1023–1031, 1995.  Y. Hayashi, “Oscillatory neural network and learning of continuously transformed patterns,” Neural Networks, vol.
The above investigations indicate that the dynamics of the chaotic neuron or chaotic neural networks can be changed from chaotic behavior to a periodic state or a ﬁxed point. However, these works did not refer to the associative memory of the controlled chaotic neural networks or the relation between the stable output of a controlled chaotic neural network and its initial state. From the viewpoint of the application of chaotic neural networks, the associative memory is important with possible information processing, such as memory retrieval and pattern recognition.