in his paper mentioned in the title, which appears in the same issue of this journal, mehdi radjabalipour derives the cyclic decomposition of an algebraic linear transformation. a more general structure theory for linear transformations appears in irving kaplansky's lovely 1954 book on infinite abelian groups. we present a translation of kaplansky's results for abelian groups into the...

The identification of fJ(1710) as the lightest scalar glueball is supported at present by two different sets of calculations. For the valence approximation to the infinite volume continuum limit of the lightest scalar glueball mass, a calculation on GF11 [1], using 25000 to 30000 gauge configurations, gives 1740 ± 71 MeV. An independent calculation by the UKQCD-Wuppertal [2] collaboration, usin...

The isosinglet scalar mesons f0(1710), f0(1500), f0(1370) and their mixing are studied. We employ two recent lattice results as the starting point; one is the isovector scalar meson a0(1450) which displays an unusual property of being nearly independent of quark mass for quark masses smaller than that of the strange, and the other is the scalar glueball mass at 1710 MeV in the quenched approxim...

‎In this paper‎, ‎we characterize the class of orthogonality preserving operators on an infinite-dimensional Hilbert space $H$ as scalar multiples of unitary operators between $H$ and some closed subspaces of $H$‎. ‎We show that any circle (centered at the origin) is the spectrum of an orthogonality preserving operator‎. ‎Also‎, ‎we prove that every compact normal operator is a strongly orthogo...

 module over a ring is a general mathematical concept for many examples of mathematicalobjects that can be added to each other and multiplied by scalar numbers.In this paper, we consider a module over a ring as a universe and by using the notion of reference points, we provide local approximations for  subsets of the universe.

A saddle point variational (SPV ) method was applied to the Dirac equation as an example of a fully relativistic equation with both negative and positive energy solutions. The effect of the negative energy states was mitigated by maximizing the energy with respect to a relevant parameter while at the same time minimizing it with respect to another parameter in the wave function. The Cornell pot...