On F-connections

ON f-CONNECTIONS OF POSITIVE DEFINITE MATRICES

In this paper, by using Mond-Pečarić method we provide some inequalities for connections of positive definite matrices. Next, we discuss specifications of the obtained results for some special cases. In doing so, we use α-arithmetic, α-geometric and α-harmonic operator means.

Shen's Processes on Finslerian Connections

Simulation of Planar I/F Networks with Delayed Connections

This paper studies the synchronization characteristics of a locally connected, planar network of (leaky) integrate-andfire ( I/F ) neurons after Hopfield & Hertz [7]. Simulations were conducted using both the Java programming language and the MatLab protyping language in order to detect implementation errors. Further, two different algorithms were used in the simulations. The first method was a...

On (T,f )-connections of matrices and generalized inverses of linear operators

In this note, generalized connections σT,f are investigated, where AσT,fB = TAfT − A (B) for positive semidefinite matrix A and hermitian matrix B, and operator monotone function f : J → R on an interval J ⊂ R. Here the symbol T A denotes a reflexive generalized inverse of a positive bounded linear operator TA. The problem of estimating a given generalized connection by other ones is studied. T...

The works of Charles Ehresmann on connections: from Cartan connections to connections on fibre bundles

Around 1923, Élie Cartan introduced affine connections on manifolds and defined the main related concepts: torsion, curvature, holonomy groups. He discussed applications of these concepts in Classical and Relativistic Mechanics; in particular he explained how parallel transport with respect to a connection can be related to the principle of inertia in Galilean Mechanics and, more generally, can...