An attractive candidate for the geometric mean of m positive definite matrices A1, . . . , Am is their Riemannian barycentre G. One of its important properties, monotonicity in the m arguments, has been established recently by J. Lawson and Y. Lim. We give a much simpler proof of this result, and prove some other inequalities. One of these says that, for every unitarily invariant norm, |||G||| ...

The issue of Cα-degree reduction of triangular Bézier surfaces is exposed. It is anticipated that both triangular Bézier surfaces are Cα-continuous at the vertices. The Euclidean norm as well as the L2−norm is used. The final solutions are given in terms of the matrix of degree raising, the Gram matrix, and the Bézier points. Moreover, it is shown that the solutions using both norms are equival...

Let A be a bipartite graph between two sets D and T. Then A defines by Hamming distance, metrics on both T and D. The question is studied which pairs of metric spaces can arise this way. If both spaces are trivial the matrix A comes from a Hadamard matrix or is a BIBD. The second question studied is in what ways A can be used to transfer (classification) information from one of the two sets to ...

In this paper we describe an elementary method for calculating the matrix exponential on an arbitrary time scale. An example is also given to illustrate the result. 2000 Mathematics subject classification: primary 34A30.

We study the combinatorial and structural properties of the circle map sequences. We introduce an embedding procedure which gives a map Φ : Ω → W := {R,L} from the hull(closure of the set of translates) to the sequence of embedding operations through which we study the structure of Ω. We also study the set of admissible words and classify them in terms of their appearance. Mathematics Subject C...

We survey the recent mathematical results about aging in certain simple disordered models. We start by the Bouchaud trap model. We then survey the results obtained for simple models of spin-glass dynamics, like the REM (the Random Energy Model, which is well approximated by the Bouchaud model on the complete graph), then the spherical Sherrington-Kirkpatrick model. We will insist on the differe...

In this paper, the matrix extension of the multivariable Humbert polynomials is introduced. Various families of linear, multilinear and multilateral generating matrix functions of these matrix polynomials are presented. Miscellaneous applications are also discussed. 2000 Mathematics Subject Classification: 33C25; 15A60

We generalise a method of Xiao Gang to construct ’prototypes’ of fibred surfaces with maximal irregularity without being a product. This enables us, in the case of fibre genus g = 3 to describe the possible singular fibres and to calculate the invariants of these surfaces. We also prove structure theorems on the moduli space for fibred surfaces with fibre genus g = 2 and g = 3. Mathematics Subj...

Date: September 2, 2008. 2000 Mathematics Subject Classification. 42C40, 43A65,43A70.