According to Kippenhahn’s classification, numerical ranges W (A) of unitarily irreducible 3 × 3 matrices A come in three possible shapes, an elliptical disk being one of them. The known criterion for the ellipticity of W (A) consists of several equations, involving the eigenvalues of A. It is shown herein that the set of 3× 3 matrices satisfying these conditions is nowhere dense, i.e., one of t...

A range of elliptical undulators (EU) has recently been constructed at ELETTRA, whose main parameters are listed in Table 1 below. They are all based on the APPLE-II scheme [1], but two different terminations have been used due to specific installation requirements. Also, one of them (EU12.5) features a quasi-periodic field to suit special beamline needs. The minimum magnetic gap corresponds to...

In this study, efficient methods for optimal sensor placement (OSP) based on a new geometrical viewpoint for damage detection in structures is presented. The purpose is to minimize the effects of noise on the damage detection process. In the geometrical viewpoint, a sensor location is equivalent to projecting the elliptical noise on to a face of response space which is corresponding to the sens...

By making use of basic hypergeometric functions, a class of complex harmonic meromorphic functions with positive coefficients is introduced. We obtain some properties such as coefficient inequality, growth theorems, and extreme points.

We present several generating functions for sequences involving the central binomial coefficients and the harmonic numbers. In particular, we obtain the generating functions for the sequences ( 2n n ) Hn, ( 2n n ) 1 nHn, ( 2n n ) 1 n+1Hn , and ( 2n n ) n m. The technique is based on a special Euler-type series transformation formula.

Inspired by the recent work of Chu and Fu, we derive some new identities with harmonic numbers from Dixon’s hypergeometric summation formula by applying the derivation operator to the summation of binomial coefficients.

In the present paper we characterize the Besov spaces Bs pq(Γ, μ) on nested fractals in terms of the coefficients of functions with respect to the piecewise harmonic basis.

In this work some distortion theorems and relations between the coefficients of normalized univalent harmonic mappings from the unit disc onto domains on the direction of imaginary axis are obtained.

We evaluate binomial series with harmonic number coefficients, providing recursion relations, integral representations, and several examples. The results are of interest to analytic number theory, the analysis of algorithms, and calculations of theoretical physics, as well as other applications.