Seeking Transparency: Rock Crystals across the Medieval Mediterranean, edited by Cynthia Hahn and Avinoam Shalem. Mann Verlag 2020. 334pp., 36 pl., index. Hardback €49. ISBN-13: 9783786128434.

This paper presents a new set of bivariate discrete orthogonal moments which are based on bivariate Hahn polynomials with non-separable basis. The polynomials are scaled to ensure numerical stability. Their computational aspects are discussed in detail. The principle of parameter selection is established by analyzing several plots of polynomials with different kinds of parameters. Appropriate p...

was established by Hahn [1; p. 217] in 1927, and independently by Banach [2; p. 212] in 1929, who also generalized Theorem 0 for real spaces, to the situation in which the functional q :E^>R is an arbitrary subadditive, positive homogeneous functional [2; p. 226]. Theorem 0 was not established for complex spaces until 1938, when it was deduced from the real theorem by Bohnenblust and Sobczyk [3...

For the Hahn and Krawtchouk polynomials orthogonal on the set {0, . . . , N} new identities for the sum of squares are derived which generalize the trigonometric identity for the Chebyshev polynomials of the first and second kind. These results are applied in order to obtain conditions (on the degree of the polynomials) such that the polynomials are bounded (on the interval [0, N ]) by their va...

† : The views expressed here are those of the authors and do not necessarily represent the views of the Federal Reserve Bank of Philadelphia or the Federal Reserve System.

We construct some generalized difference Hahn sequence spaces by mean of sequence of modulus functions. The topological properties and some inclusion relations of spaces h p ((F, u, Δ(r)) are investigated. Also we compute the dual of these spaces, and some matrix transformations are characterized.

Let K denote a field, and let V denote a vector space over K with finite positive dimension. We consider a pair of linear transformations A : V → V and A : V → V that satisfy the following two conditions: (i) There exists a basis for V with respect to which the matrix representing A is irreducible tridiagonal and the matrix representing A is diagonal. (ii) There exists a basis for V with respec...

Let K denote a field, and let V denote a vector space over K with finite positive dimension. We consider a pair of linear transformations A : V → V and A : V → V that satisfy the following two conditions: (i) There exists a basis for V with respect to which the matrix representing A is irreducible tridiagonal and the matrix representing A is diagonal. (ii) There exists a basis for V with respec...

An application of a fuzzy classification technique for automated grading and sorting of clouds imagery has been presented. The specific requirements in the processing for classification are pointed out considering the relevant textural and spectral featu:es. The methodology for generating the fuzzy logic classifier is also presented and some preliminary observa-• lions are reported. 1 Introduct...