LCM and MCM: specification of a control system using dynamic logic and process algebra

LCM 3.0 is a specification language based on dynamic logic and process algebra, and can be used to specify systems of dynamic objects that communicate synchronously. LCM 3.0 was developed for the specification of object-oriented information systems, but contains sufficient facilities for the specification of control to apply it to the specification of control-intensive systems as well. In this paper, the results of such an application are reported. The paper concludes with a discussion of the need for theorem-proving support and of the extensions that would be needed to be able to specify real-time properties

Resolutions and Cohomologies of Toric Sheaves. The affine case

We study equivariant resolutions and local cohomologies of toric sheaves for affine toric varieties, where our focus is on the construction of new examples of decomposable maximal Cohen-Macaulay modules of higher rank. A result of Klyachko states that the category of reflexive toric sheaves is equivalent to the category of vector spaces together with a certain family of filtrations. Within this setting, we develop machinery which facilitates the construction of minimal free resolutions for the smooth case as well as resolutions which are acyclic with respect to local cohomology functors for the general case. We give two main applications. First, over the polynomial ring, we determine in explicit combinatorial terms the Z^n-graded Betti numbers and local cohomology of reflexive modules whose associated filtrations form a hyperplane arrangement. Second, for the non-smooth, simplicial case in dimension d >= 3, we construct new examples of indecomposable maximal Cohen-Macaulay modules of rank d - 1.Comment: 39 pages, requires packages ams*, enumerat

Selenium and tellurium concentrations of Carboniferous British coals

The authors wish to thank Kier Group, the British Coal Utilisation Research Association (BCURA) and Uniper (E.On) for kindly providing coal samples. The authors are grateful to Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq), Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES), and Fundação de Amparo à Pesquisa do Estado do Rio Grande do Sul (FAPERGS) for supporting this study. The authors are grateful for the thorough and constructive comments from two anonymous reviewers, as well as the careful editorial handling of Prof. Ian Somerville. This work was supported by the NERC under Grant number NE/L001764/1.Peer reviewedPublisher PD

The Lax pair for C_2-type Ruijsenaars-Schneider model

We study the C_2 Ruijsenaars-Schneider(RS) model with interaction potential of trigonometric type. The Lax pairs for the model with and without spectral parameter are constructed. Also given are the involutive Hamiltonians for the system. Taking nonrelativistic limit, we obtain the Lax pair of C_2 Calogero-Moser model.Comment: LaTeX2e, 10 pages, some misprints corrected and sections rearrange

The Dn Ruijsenaars-Schneider model

The Lax pair of the Ruijsenaars-Schneider model with interaction potential of trigonometric type based on Dn Lie algebra is presented. We give a general form for the Lax pair and prove partial results for small n. Liouville integrability of the corresponding system follows a series of involutive Hamiltonians generated by the characteristic polynomial of the Lax matrix. The rational case appears as a natural degeneration and the nonrelativistic limit exactly leads to the well-known Calogero-Moser system associated with Dn Lie algebra.Comment: LaTeX2e, 14 pages; more remarks are added in the last sectio