A time-indexed LP-based approach for min-sum job-shop problems

In this paper we propose two time-indexed IP formulations for job-shop scheduling problems with a min-sum objective. The first model has variables associated to job scheduling patterns. The exponential number of variables calls for a column generation scheme which is carried out by a dynamic programming procedure. The second model is of network flow type with side constraints. This model can be strengthened by adding cutting inequalities of clique type. It turns out that the two models are equivalent, since the dual of the second formulation is equivalent to the compact dual of the first model. However, they require significantly different solution approaches and may behave differently in terms of computing time and memory usage. Good upper bounds are found by a heuristic procedure that randomly generates schedules from fractional solutions. These features allow for an effective pruning of the branch-and-bound tree and narrowing the gap between lower and upper bounds. However, the size of both models is critically affected by the time-indexed formulation which may heavily slow down the computation.     

Nonlocal Venttsel' diffusion in fractal‐type domains: Regularity results and numerical approximation

We study a nonlocal Venttsel' problem in a nonconvex bounded domain with a Koch‐type boundary. Regularity results of the strict solution are proved in weighted Sobolev spaces. The numerical approximation of the problem is carried out, and optimal a priori error estimates are obtained.     

NMR study of the spin polarization in dilute Al-Mn alloys

The spatial dependence of the spin density oscillations σ(r) around Mn impurities in Al-Mn dilute alloys has been studied by ²⁷Al four pulse NMR experiments. The concentration dependence of the magnetic broadening $\text{ΔH}{}^{\mathrm{i}}\text{1}\text{2}$ of the ²⁷Al line is found slower than linear. This result, together with the temperature dependence of the magnetic broadening as measured by CW NMR, demonstrates both the preasymptotic depression of σ(r) in Al-Mn and the long range damping of σ(r) associated with the finite mean free path at high T.     

Venttsel’ problems in fractal domains

A nonsteady Venttsel’ problem in a fractal domain Ω or in the corresponding prefractal domain Ω _h is studied. Existence, uniqueness, and regularity results for the strict solution, in both cases, are established as well as convergence results of the solutions of the approximating problems in varying Hilbert spaces.     

Homogenization for conductive thin layers of pre-fractal type

The aim of this work is to obtain convergence results for the solutions of transmission problems across highly conductive layers of pre-fractal type from the point of view of homogenization. We prove the M-convergence of the energy functionals to an energy functional which incorporates a singular term, supported within the layer. From the convergence of the energy functionals we deduce the convergence of the approximating solutions to the limit solution in a suitable sense.