Geometry and Nature Vol. 203.

Intro -- Contents -- List of Participants -- Preface -- W. K. Clifford as a geometer -- Part I. Clifford Algebras -- Clifford and the 'square root' ideas -- Dirac's algebra and Brauer-Wall groups -- 1. Dirac's algebra -- 2. Mod-2 graded algebras -- 3. Duality in Brauer-Wall group -- 4. Anti-centre -- 5. Structure theorem for BW(k) -- 6. The quaternion model for H5 -- Linear endomorphisms of Clifford algebras -- Part II. Riemannian Surfaces -- Uniformizations of Riemann surfaces: Poincaré theta series, Riemann's theta function and theta constants -- Adapted metrics and Mobius transformations defined over Clifford algebras -- Part III. Information Geometry -- Information geometry -- 1. Introduction -- 2. Riemannian Manifold with Dual Affine Connections -- 3. Dually flat manifolds -- 4. Some Unsolved Mathematical Questions -- 5. Manifold of Probability Distributions -- 6. Applications of Information Geometry -- 7. Conclusions -- References -- An example of dynamical behaviour of the relative entropy -- Information geometry and learning in formal neural networks -- Statistical dynamics and information geometry -- Part IV. Noncommutative Geometry -- On finite differential calculi -- Some aspects of noncommutative differential geometry -- Connections of bimodules in non-commutative geometry -- Riemannian and non-commutative geometry in physics -- Spectral model and fuzzy mass relations -- Part V. Cosmology and General Relativity -- Not so simple universe -- Extended tensorial curvature analysis for embeddings and foliations -- Spaces admitting a foliation by isotropic hypersurfaces -- An alternative to inflation -- Part VI. Symplectic Geometry and Self-Similar Structures -- A class of homogeneous symplectic manifolds -- rth order conditionally convergent series of fractal domains -- Part VII: Field Theory -- Chern-Simons vortices.

The generalized local instability criterion from the geodesic deviation equation.

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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.