Reactions of metal carbonyl cluster complexes with multidentate phosphine ligands; reactions with bis(diphenylphosphino)methane

Reactions of Rh₆(CO)₁₆ with bis(diphenylphosphino)methane (dppm) gave Rh₆(CO)₁₄(dppm), Rh₆(CO)₁₂(dppm)₂, or Rh₆(CO)₁₀(dppm)₃, depending upon the reaction conditions. Rh₄(CO)₁₀(dppm) may be obtained from the reaction of Rh₄(CO)₁₂ with dppm, but this derivative rapidly decomposes in solution to give Rh₄(CO)₈(dppm)₂, Rh₆(CO)₁₄(dppm), and Rh₆(CO)₁₂(dppm)₂. Ir₄(CO)₁₀(dppm) and Ir₄(CO)₈(dppm)₂ have also been prepared, and their structures are discussed on the basis of infrared and ³¹P NMR spectroscopic data.     

Second-order Green's function calculations of the ionization potential of a (H2)7 chain embedded in a homogeneous electric field

Summary The vertical ionization potential and the related pole strength of a model alternant chain of 14 hydrogen atoms subject to a homogeneous electric field, parallel to the chain and of increasing intensity are calculated, in the framework of a 6–31G** basis set, at the second-order level of the many-body Green's function theory. Trends observed with orbital relaxation, pair removal and pair relaxation effects are interpreted in terms of deformations of the electron density.     

A constructive approach to examination timetabling based on adaptive decomposition and ordering

In this study, we investigate an adaptive decomposition and ordering strategy that automatically divides examinations into difficult and easy sets for constructing an examination timetable. The examinations in the difficult set are considered to be hard to place and hence are listed before the ones in the easy set in the construction process. Moreover, the examinations within each set are ordered using different strategies based on graph colouring heuristics. Initially, the examinations are placed into the easy set. During the construction process, examinations that cannot be scheduled are identified as the ones causing infeasibility and are moved forward in the difficult set to ensure earlier assignment in subsequent attempts. On the other hand, the examinations that can be scheduled remain in the easy set. Within the easy set, a new subset called the boundary set is introduced to accommodate shuffling strategies to change the given ordering of examinations. The proposed approach, which incorporates different ordering and shuffling strategies, is explored on the Carter benchmark problems. The empirical results show that the performance of our algorithm is broadly comparable to existing constructive approaches.     

An optimal<Emphasis Type="Italic">L</Emphasis><Superscript><Emphasis Type="Italic">p</Emphasis></Superscript>-bound on the Krein spectral shift function

Let ξ_A,B be the Krein spectral shift function for a pair of operatorsA, B, with C =A-B trace class. We establish the bound

Convergent iterative schemes for time parallelization

Parallel methods are usually not applied to the time domain because of the inherit sequentialness of time evolution. But for many evolutionary problems, computer simulation can benefit substantially from time parallelization methods. In this paper, we present several such algorithms that actually exploit the sequential nature of time evolution through a predictor-corrector procedure. This sequentialness ensures convergence of a parallel predictor-corrector scheme within a fixed number of iterations. The performance of these novel algorithms, which are derived from the classical alternating Schwarz method, are illustrated through several numerical examples using the reservoir simulator Athena.

     

A shortest path-based approach to the multileaf collimator sequencing problem

The multileaf collimator sequencing problem is an important component in effective cancer treatment delivery. The problem can be formulated as finding a decomposition of an integer matrix into a weighted sequence of binary matrices whose rows satisfy a consecutive ones property. Minimising the cardinality of the decomposition is an important objective and has been shown to be strongly NP-hard, even for a matrix restricted to a single column or row. We show that in this latter case it can be solved efficiently as a shortest path problem, giving a simple proof that the one-row problem is fixed-parameter tractable in the maximum intensity. We develop new linear and constraint programming models exploiting this result. Our approaches significantly improve the best known for the problem, bringing real-world sized problem instances within reach of exact algorithms.