Sequences,claws and cyclability of graphs

A subset S of vertices of a graph G is called cyclable in G if there is in G some cycle containing all the vertices of S. We give two results on the cyclability of a vertex subset in graphs, one of which is related to “hamiltonian-nice-sequence” conditions and the other of which is related to “claw-free” conditions. They imply many known results on hamiltonian graph theory. Moreover, the analogous results related to the hamilton-connectivity or to the existence of dominating cycle are also given. © 1996 John Wiley & Sons, Inc.     

The Soave,Twu and Boston–Mathias alpha functions in cubic equations of state. Part II. Modeling of thermodynamic properties of pure compounds

Cubic equations of state (EoS) are commonly used for industrial applications, due to their simplicity in predicting pure compound and mixture thermodynamic properties in vapor and liquid phases. The accuracy of their predictions mainly depends on the choice of the attractive term a(T) and numerous models were developed in literature for this purpose. Among them, the Soave and the Twu models have acquired a wide popularity, as well as the Boston–Mathias model commonly used for supercritical applications. However, most of the works concerned with the comparison of literature attractive terms only focuses on the representation of pure component saturation properties. In particular, the analysis of the respective influence of the EoS and the first and second derivatives of the alpha function on the modeling of enthalpies and heat capacities with respect to temperature and pressure, especially in the supercritical range, was never reported in literature. This is precisely the purpose of the present study.     

Scaling Invariants and Symmetry Reduction of Dynamical Systems

Scalings form a class of group actions that have theoretical and practical importance. A scaling is accurately described by a matrix of integers. Tools from linear algebra over the integers are exploited to compute their invariants, rational sections (a.k.a. global cross-sections), and offer an algorithmic scheme for the symmetry reduction of dynamical systems. A special case of the symmetry reduction algorithm applies to reduce the number of parameters in physical, chemical or biological models.     

Neighborhood unions and extremal spanning trees

We generalize a known sufficient condition for the traceability of a graph to a condition for the existence of a spanning tree with a bounded number of leaves. Both of the conditions involve neighborhood unions. Further, we present two results on spanning spiders (trees with a single branching vertex). We pose a number of open questions concerning extremal spanning trees.     

One-pot synthesis of 1-hydroxymethylene-1,1-bisphosphonate partial esters

A selective one-pot procedure of synthesis of 1-hydroxymethylene-1,1-bisphosphonic partial trimethylesters and P,P-, P,P′-diesters was described.