The successive iteration (started by Lagrange and Gauss) produces a new mean from two given ones. Several examples of matrix means are given that require the proof of the matrix monotonicity of the corresponding representing function. The paper contains extensions of the logarithmic mean and it is obtained that the Stolarsky mean can be used also for matrices. 2000 Mathematics Subject Classific...

In this paper we retrieve slow oscillation of a real sequence fromCesàro summability of its generator sequence under some one-sided condition. References[1] F. Dik, Tauberian theorems for convergence and subsequential convergence with moderatelyoscillatory behavior, Math. Morav. 5: 19–56 (2001).[2] M. Dik, Tauberian theorems for sequences with moderately oscillatory control modu...

In this paper we introduce a sharpening of the Parikh mapping and investigate its basic properties. The new mapping is based on square matrices of a certain form. The classical Parikh vector appears in such a matrix as the second diagonal. However, the matrix product gives more information about a word than the Parikh vector. We characterize the matrix products and establish also an interesting...

In classical sociology, there is a sharp separation between the superstructure reflecting cultural ideals and the concrete Structural Base (SB). The authors hypothesize a Doxical Superstructure (DS) in its own space at a higher level, containing concepts such as completeness, necessity and possibility associated with abstract concepts like beliefs, ethics, knowledge, relations and science. The ...

In this paper we construct explicit solutions and calculate the corresponding τ -function to the system of Schlesinger equations describing isomonodromy deformations of 2 × 2 matrix linear ordinary differential equation whose coefficients are rational functions with poles of the first order; in particular, in the case when the coefficients have four poles of the first order and the correspondin...

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...