1. The real variable 2. Scalars and vectors 3. Tensors 4. Matrices 5. Multiple integrals 6. Potential theory 7. Operational methods 8. Physical applications of the operational method 9. Numerical methods 10. Calculus of variations 11. Functions of a complex variable 12. Contour integration and Bromwich's integral 13. Contour integration 14. Fourier's theorem 15. The factorial and related functions 16. Solution of linear differential equations of the second order 17. Asymptotic expansions 18. The equations of potential, waves and heat conduction 19. Waves in one dimension and waves with spherical symmetry 20. Conduction of heat in one and three dimensions 21. Bessel functions 22. Applications of Bessel functions 23. The confluent hypergeometric function 24. Legendre functions and associated functions 25. Elliptic functions Notes Appendix on notation Index.

Methods of Mathematical Physics. By Harold Jeffreys and Bertha Swirles Jeffreys. Pp. viii, 679. 63s. 1946. (Cambridge University Press)

Linear Algebra and Projective Geometry Buildings and Grassmannians Classical Grassmannians Polar and Half-Spin Grassmannians.

Grassmannians of Classical Buildings

The Grassmann space of fc-subspaces of a polar space is defined and its geometry is examined. In particular, its cliques, subspaces and automorphisms are characterized. An analogue of Chow's theorem for the Grassmann space of fc-subspaces of a polar spaces is proved.

Geometry of polar Grassmann spaces

Automorphisms of non-trivial spine spaces are either, type-preserving, or type-exchanging, that is, they map stars onto stars or exchange them with tops. In the first case they are given by semi-linear bijections, in the latter, by sesqui-linear forms.

Automorphisms of spine spaces

Geometric version of Wigner's theorem for Hilbert Grassmannians

Two geometries can be considered in the structure of linear complements: an affine spine space and an affine space. An affine spine space arises from a space of pencils. In terms of this geometry an affine partial line space may be defined. It is extensible to the affine space. Automorphisms of the affine spine space are automorphisms of appropriate affine space.

Geometry of the structure of linear complements

Orthogonality of subspaces in metric-projective geometry

Metric affine geometry on the universe of lines

We prove that a projective Grassmannian can be recovered from the complement of one of its Grassmann substructures. Even more, the underlying projective space with the interval of its distinguished subspaces can be recovered.

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Mariusz Żynel

Papers

Geometry of polar Grassmann spaces

Geometry of the structure of linear complements

Orthogonality of subspaces in metric-projective geometry

Metric affine geometry on the universe of lines

Complements of Grassmann substructures in projective Grassmannians