Encapsulating Formal Methods within Domain Specific Languages: A Solution for Verifying Railway Scheme Plans

The development and application of formal methods is a long standing research topic within the field of computer science. One particular challenge that remains is the uptake of formal methods into industrial practices. This paper introduces a methodology for developing domain specific languages for modelling and verification to aid in the uptake of formal methods within industry. It illustrates the successful application of this methodology within the railway domain. The presented methodology addresses issues surrounding faithful modelling, scalability of verification and accessibility to modelling and verification processes for practitioners within the domain.     

Stochastic matrices over cones

The notion of a stochastic operator in an ordered Banach space is specialized to a finite dimensional ordered real vector space. The classical limit theorems are obtained, and an application is made to non-homogeneous Markov chains. Finally, groups of nonnegative matrices are discussed.     

Mass spectral rearrangements of N,N-bis(4′-arylthio-2′-butynyl)anilines and N,N-bis(4′-arylsulfonyl-2′-butynyl)anilines

The title compounds display unusual modes of fragmentation under electron impact. One of the dominant modes is the concerted elimination of the two arylthio and arylsulfonyl moieties followed by further extrusion of the C₆H₄ unit as a cumulene. No elimination of SO₂ is observed from any of the sulfones nor an expulsion of the C₄H₄ fragment. Such behavior contrasts strikingly with that of 1,4-diarylsulfonyl-2-butynes and of the 1,6-diarylsulfonyl-2,4-hexadiynes.     

Borrowing hydrogen: iridium-catalysed reactions for the formation of C-C bonds from alcohols

Alcohols have been employed as substrates for C-C bond-forming reactions which involve initial activation by the temporary removal of hydrogen to form an aldehyde. The intermediate aldehyde is converted into an alkene via a Horner-Wadsworth-Emmons reaction, nitroaldol and aldol reactions. The 'borrowed hydrogen' is then returned to the alkene to form a C-C bond.     

On the critical dynamics of disordered spin systems

The dynamic critical behaviour of spin systems with quenched impurities, and of amorphous spin systems as characterized by the additional presence of random anisotropy directions, is studied by renormalization group methods to second order in=4–d. For the Halperin-Hohenberg-Ma model with purely relaxational dynamics it is concluded that in three dimensions (d=3) the critical slowing down should be enhanced by impurities for systems with Ising type statics, whereas there is no change forXY- and Heisenberg systems. For amorphous systems, however, the critical dynamics should change also in theXY- and Heisenberg cases. Furthermore, it is concluded that additional conserved, but noncritical modes become always statically decoupled from the order parameter for systems with impurities, but not for amorphous systems. Thus, for the impure system, the energy density mode and the asymmetric models of Halperin, Hohenberg and Siggia are ruled out. But the effects of dynamic coupling remain: Especially, the relationz=d/2 for the dynamic exponent of planar and isotropic antiferromagnets is modified for impure or amorphous systems.     

Complexation of the triply-bonded dirhenium(II) complex Re(2)Cl(4)(mu-dppm)(2) (dppm = Ph(2)PCH(2)PPh(2)) by up to three acetylene molecules

The triply bonded dirhenium(II) synthons Re(2)X(4)(mu-dppm)(2) (X = Cl, Br; dppm = Ph(2)PCH(2)PPh(2)) react with acetylene at room temperature in CH(2)Cl(2) and acetone to afford the bis(acetylene) complexes Re(2)X(4)(mu-dppm)(2)(mu:eta(2),eta(2)-HCCH)(eta(2)-HCCH) (X = Cl (3), Br(4)). Compound 3 has been derivatized by reaction with RNC ligands in the presence of TlPF(6) to give unsymmetrical complexes of the type [Re(2)Cl(3)(mu-dppm)(2)(mu:eta(2),eta(2)-HCCH)(eta(2)-HCCH)(CNR)]PF(6) (R = Xyl (5), Mes (6), t-Bu (7)), in which the RCN ligand has displaced the chloride ligand cis to the eta(2)-HCCH ligand. The reaction of 3 with an additional 1 equiv of acetylene in the presence of TlPF(6) gives the symmetrical all-cis isomer of [Re(2)Cl(3)(mu-dppm)(2)(mu:eta(2),eta(2)-HCCH)(eta(2)-HCCH)(2)]PF(6) (8). The two terminal eta(2)-HCCH ligands in 8 are very labile and can be displaced by CO and XylNC to give the complexes [Re(2)Cl(3)(mu-dppm)(2)(mu:eta(2),eta(2)-HCCH)(L)(2)]Y (L = CO when Y = PF(6) (9); L = CO when Y = (PF(6))(0.5)/(H(2)PO(4))(0.5) (10); L = XylNC when Y = PF(6) (11)). These substitution reactions proceed with retention of the all-cis stereochemistry. Single-crystal X-ray structure determinations have been carried out on complexes 3, 5, 8, 10, and 11. In no instance have we found that the acetylene ligands undergo reductive coupling reactions.     

Properties of functions in an auxiliary spline space

Summary This note examines functions in an auxiliary spline space related to geometrically continuous splines. Previous work [3, 4] required results about the existence and number of zeros of certain functions in this space, as well as results on how to combine these functions. This note provides improved versions of these results.