Fibred spaces and non-linear connections

Summary We give the fibre structure to the two complementary distributions, one being holomonic and the other being in general non-holomonic, by assigning the structure preserving transformations of the coordinates and of the frames. By the conversion from such fibred spaces we derive the spaces of non-linear connections as their image, in which we point out that the usual conditions imposed on C_kji and the covariant differentiation of g_ji in the metric spaces of non-linear connections can be interpreted respectively as the parallel and isometric conditions imposed on the fibre of the corresponding fibred Riemannian spaces. To Enrico Bompiani on his scientific Jubilee.     

Electrical resistivities of the uranium carbides

Electrical resistivities of arc-melted uranium carbides, UC, UC₂, U₂C₃ and UC + UC₂, were measured over the temperature range between 4 and 1900 K. The monocarbide, dicarbide and the mixture of carbides showed metallic character in their resistivity dependence on temperature above 30 K, while below this the resistivities were constant. U₂C₃ showed a knee in the resistivity curve at 54.0 K corresponding to a magnetic transition. Above 1100 K, the resistivity of U₂C₃ did not vary with temperature. The resistivity of the mixture (UC + UC₂ with U₂C₃ precipitates) showed an arrest between 800 and 950 K.     

Some cross-section theorems on the tangent bundle over a finslerian manifold

Summary Let T(M) be the tangent bundle over a Finslerian manifold M of n-dimension endowed with the Cartan connection ∇. One makes T(M) into a 2n dimensional affinely connected manifold by assigning a connection ∇^c to T(M). The cross-section of a vector field V defined in M reveals in T(M) an n-dimensional submanifold and its geometry is developed by means of the affine subspace theory and of the affine collineations in the base Finsler manifold. This work was supported by the National Research Council of Canada, 1970–1971, A-4037. Entrata in Redazione il giorno 8 maggio 1971.     

Gaugeability for Feynman-Kac functionals with applications to symmetric -stable processes

For symmetric -stable processes, an analytic criterion for a measure being gaugeable was obtained by Z.-Q. Chen (2002), M. Takeda (2002) and M. Takeda and T. Uemura (2004). Applying it, we consider the ultracontractivity of Feynman-Kac semigroups and expectations of the number of branches hitting closed sets in branching symmetric -stable processes.