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The necessity of creating a classification has been substantiated for scalar property isolines dia grams of ternary systems having different numbers of singular points per element of the concentration sim plex. The total number of possible diagrams has been determined, and the topologically feasible diagram structures containing two singular points per open element of the concentration simplex have been synthe sized.

| The properties of integral operators (with a kernel depending on scalar product) acting on Banach spaces of measures and functions on the sphere S n¡ 1 are studied. A theorem of unique solvability of a¯rst-kind equation for measure is proved. Asymptotic formulae for eigenvalues of the kernel are derived. The results are used in proving theorems on the unique reconstructibility of a closed convex hypersurface from its curvature integrals and on its smoothness. Existence of a centrally symmetric closed convex hypersurface with a given curvature integral of projection is also demonstrated.State Technical University. E-Mail: stepaw49@rol.ru Brought to you by | Tokyo Daigaku Authenticated Download Date | 5/25/15 4:40 PM Brought to you by | Tokyo Daigaku Authenticated Download Date | 5/25/15 4:40 PM

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