Synthesis of Relativistic Wave Equations: The Noninteracting Case

We study internal structure of the Duffin-Kemmer-Petiau equations for spin 0 and spin 1 mesons. We show that in the noninteracting case full covariant solutions of the s=0 and s=1 DKP equations are generalized solutions of the Dirac equation

Structure of prime finitely presented monomial algebras

AbstractThe structure of a finitely presented monomial algebra K[X]/K[I] over a field K is described. Here X is a finitely generated free monoid and I is a prime ideal of X that is finitely generated. As an application, a new structural proof of the recent result of Bell and Pekcagliyan [J. Bell, P. Pekcagliyan, Primitivity of finitely presented monomial algebras, preprint, arXiv: 0712.0815v1] on the primitivity of such algebras is presented, which yields a positive solution to the trichotomy problem, raised by Bell and Smoktunowicz [J. Bell, A. Smoktunowicz, The prime spectrum of algebras of quadratic growth, J. Algebra 319 (2008) 414–431], in the finitely presented case. Our approach is based on a new result on the form of prime Rees factors of semigroups satisfying the ascending chain condition on one-sided annihilators and on its refinement in the case of finitely presented factors of the form X/I

Research on the Cities of Pre-Partition Poland in the Last Decade (Trends, Achievements, Perspectives): Bibliographical Survey

The article contains a synthetic review of the most important subjects and directions of research in the field of the history of cities and townspeople in pre-partition Poland (to the end of the eighteenth century) based on scholarly publications from the last ten years. The author characterises the attitude of contemporary historians of cities towards questionnaires and research methods worked out in the second half of the twentieth century in the area of socio-economic history. He also outlines the prospects for the further development of Polish urban historiography, emphasising the importance of taking inspiration from the achievements of cultural anthropology and the cooperation of historians with representatives of other humanistic disciplines