Competence-driven project portfolio selection,scheduling and staff assignment

This paper presents a new model for project portfolio selection, paying specific attention to competence development. The model seeks to maximize a weighted average of economic gains from projects and strategic gains from the increment of desirable competencies. As a sub-problem, scheduling and staff assignment for a candidate set of selected projects must also be optimized. We provide a nonlinear mixed-integer program formulation for the overall problem, and then propose heuristic solution techniques composed of (1) a greedy heuristic for the scheduling and staff assignment part, and (2) two (alternative) metaheuristics for the project selection part. The paper outlines experimental results on a real-world application provided by the E-Commerce Competence Center Austria and, for a slightly simplified instance, presents comparisons with the exact solution computed by CPLEX.     

Convergence of the Magnus Series

The Magnus series is an infinite series which arises in the study of linear ordinary differential equations. If the series converges, then the matrix exponential of the sum equals the fundamental solution of the differential equation. The question considered in this paper is: When does the series converge? The main result establishes a sufficient condition for convergence, which improves on several earlier results.     

A pseudo active kinematic constraint for a biological living soft tissue: An effect of the collagen network

Recent studies in mammalian hearts show that left ventricular wall thickening is an important mechanism for systolic ejection, and that during contraction the cardiac muscle develops significant stresses in the muscular cross-fiber direction. We suggested that the collagen network surrounding the muscular fibers could account for these mechanical behaviors. To test this hypothesis we develop a model for large deformation response of active, incompressible, nonlinear elastic and transversely isotropic living soft tissue (such as cardiac or arteries tissues) in which we include a coupling effect between the connective tissue and the muscular fibers. Then, a three-dimensional finite element formulation including this internal pseudo-active kinematic constraint is derived. Analytical and finite element solutions are in a very good agreement. The numerical results show this wall thickening effect with an order of magnitude compatible with the experimental observations.     

State-specific reactions and autoionization dynamics of Ar produced by synchrotron radiation

The long-lived excited states of doubly charged rare gases can markedly affect their reactivity. In this paper we demonstrate the presence of strong state-specific effects in the charge exchange of Ar²⁺ (³P, ¹D and ¹S) with several neutral targets (He, Ne, Kr, Xe, D₂, and CH₄). State sensitive measurements have been performed by producing the different Ar²⁺ electronic states via tunable synchrotron radiation (Elettra-Trieste, Italy and SuperACO-Orsay, France). From the product ion yield data of charge transfer, state-selected total cross-sections have been deduced. Using the state-specific reactivity of Ar²⁺ towards different neutral targets, it has been possible to extract the photon-energy-dependent production branching of the three doubly charged states and to investigate the autoionization dynamics of neutral or singly charged Ar in the vicinity of the double ionization threshold.     

On the Distribution in Residue Classes of Integers with a Fixed Sum of Digits

We give an asymptotic formula for the distribution of those integers n in a residue class, such that n has a fixed sum of base-g digits, with some uniformity over the choice of the modulus and g. We then use this formula to solve the problem of I. Niven of giving an asymptotic formula for the distribution of those integers n divisible by the sum of their base-g digits. Our results also allow us to give a stronger form of a result of M. Olivier dealing with the distribution of integers with a given gcd with their sum of base-g digits.For our friend Jean-Louis Nicolas on his sixtieth birthdayResearch partially supported by the Hungarian National Foundation for Scientific Research, Grant No. T029759, and “Balaton” French-Hungarian exchange program F-18/00.2000 Mathematics Subject Classification: Primary—11A63