Stability of translating solutions to mean curvature flow

We prove stability of rotationally symmetric translating solutions to mean curvature flow. For initial data that converge spatially at infinity to such a soliton, we obtain convergence for large times to that soliton without imposing any decay rates. The authors are members of SFB 647/B3 “Raum – Zeit – Materie: Singularity Structure, Long-time Behaviour and Dynamics of Solutions of Non-linear Evolution Equations”.     

Problems, Models and Complexity. Part II: Application to the DLSP

In Part I of this study, we suggest to identify an operations research (OR) problem with the equivalence class of models describing the problem and enhance the standard computer-science theory of computational complexity to be applicable to this situation of an often model-based OR context. The Discrete Lot-sizing and Scheduling Problem (DLSP) is analysed here in detail to demonstrate the difficulties which can arise if these aspects are neglected and to illustrate the new theoretical concept. In addition, a new minimal model is introduced for the DLSP which makes this problem eventually amenable to a rigorous analysis of its computational complexity.     

Dielectronic Recombination of Very Heavy Lithiumlike Ions

Hyperfine Interactions - An overview of measurements of dielectronic recombination (DR) with the heaviest lithiumlike ions is presented. The experiments have been carried out at the heavy ion...     

All solid-state sum-frequency generation of 1.12-W continuous-wave laser at 588 nm

A new resonator design for doubly resonant continuous-wave (CW) intracavity sum-frequency mixing (SFM) is reported. 1.12 W of coherent radiation at 588 nm is generated by mixing 1062-nm Nd:GdVO4laser and 1319-nm Nd:YAG laser. The optical-to-optical conversion efficiency is up to 3.7%.     

Idempotency of Extensions via the Bicompletion

Let Top ₀ be the category of topological T ₀-spaces, QU ₀ the category of quasi-uniform T ₀-spaces, T : QU ₀ → Top ₀ the usual forgetful functor and K : QU ₀ → QU ₀ the bicompletion reflector with unit k : 1 → K. Any T-section F : Top ₀ → QU ₀ is called K-true if KF = FTKF, and upper (lower) K-true if KF is finer (coarser) than FTKF. The literature considers important T-sections F that enjoy all three, or just one, or none of these properties. It is known that T(K,k)F is well-pointed if and only if F is upper K-true. We prove the surprising fact that T(K,k)F is the reflection to Fix(TkF) whenever it is idempotent. We also prove a new characterization of upper K-trueness. We construct examples to set apart some natural cases. In particular we present an upper K-true F for which T(K,k)F is not idempotent, and a K-true F for which the coarsest associated T-preserving coreflector in QU ₀ is not stable under K. We dedicate this paper to the memory of Sérgio de Ornelas Salbany (1941–2005).     

Improved modeling and solution methods for the multi-resource routing problem

This paper presents modeling and solution method improvements for the Multi-Resource Routing Problem (MRRP) with flexible tasks. The MRRP with flexible tasks is used to model routing and scheduling problems for intermodal drayage operations in which two resources (tractors and trailers) perform tasks to transport loaded and empty equipment. Tasks may be either well defined, in which both the origin and the destination of a movement are given, or flexible, in which the origin or the destination is chosen by the model. This paper proposes methods to effectively manage the number of options considered for flexible tasks (either feasible origins for a known destination or feasible destinations for a known origin). This modeling change generates sufficient options to allow for low-cost solutions while maintaining reasonable computational effort. We also propose a new solution method that uses randomized route generation. Computational results from test cases show that these changes improve the quality of solutions by at least 5% in the test cases as compared to methods from previous studies.