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.

**Read or Download Algebraic Groups and Their Birational Invariants (Translations of Mathematical Monographs) PDF**

**Similar linear books**

**Multicollinearity in linear economic models**

It used to be R. Frisch, who in his guides 'Correlation and Scatter research in Statistical Variables' (1929) and 'Statistical Confluence research via entire Regression platforms' (1934) first mentioned the issues that come up if one applies regression research to variables between which a number of autonomous linear family members exist.

**Quaternionic and Clifford Calculus for Physicists and Engineers**

Quarternionic calculus covers a department of arithmetic which makes use of computational ideas to assist resolve difficulties from a large choice of actual platforms that are mathematically modelled in three, four or extra dimensions. Examples of the applying components contain thermodynamics, hydrodynamics, geophysics and structural mechanics.

**Category Theory for Computing Science**

Fine condition. infrequent publication! !

- Linear Algebra, Second Edition: Algorithms, Applications, and Techniques
- Generalized Linear Models: A Bayesian Perspective
- Leitprogramm Mathematik für Physiker 2
- Matrix analysis & applied linear algebra
- Extensions of Rings and Modules
- On the Existence and the Regularity of Solutions of Linear Pseudo-Differential Equations

**Extra resources for Algebraic Groups and Their Birational Invariants (Translations of Mathematical Monographs) **

**Example text**

240–243, 1993. [26] 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. [27] 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 [28] A.

974–993, 1999. [13] M. Adachi, and K. Aihara, “Associative dynamics in a chaotic neural network,” Neural Networks, vol. 10, pp. 83–98, 1997. [14] 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. [15] M. Nakagawa, “An artiﬁcial neuron model with a periodic activation function,” J, Phys. Soc. Jpn, vol. 64, pp. 1023–1031, 1995. [16] 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.