Multi-Item Scheduling by Benders' Decomposition

Scheduling the production of several items requires the determination of production quantities in different periods in the presence of resource constraints. Several approximate and heuristic algorithms have been proposed to solve this problem. However, no method for finding an optimal solution has as yet been developed. It is shown that the problem may be solved advantageously using Benders' decomposition. The subproblem in Benders' decomposition is shown to be a transportation problem, and some strategies for solving the master problem are indicated. The paper concludes with a sample problem demonstrating the application of the method.     

Laser writing techniques for photomask fabrication using a femtosecond laser

Photomasks are the backbone of microfabrication industries. Currently they are fabricated by a lithographic process, which is very expensive and time consuming since it is a multi-step process. These issues can be addressed by fabricating photomasks by direct femtosecond laser writing, which is a single-step process and comparatively cheaper and faster than lithography. In this paper we discuss our investigations on the effect of two types of laser writing techniques, namely front- and rear-side laser writing, with regard to the feature size and the edge quality of a feature. It is proved conclusively that for the patterning of masks, front-side laser writing is a better technique than rear-side laser writing with regard to smaller feature size and better edge quality. Moreover the energy required for front-side laser writing is considerably lower than that for rear-side laser writing. Received: 22 May 2001 / Accepted: 14 September 2001 / Published online: 17 October 2001     

Distances between oriented curves in geometric modeling

We consider the choice of a functional to measure the distance between two parametric curves. We identify properties of such a distance functional that are important for geometric design. Several popular definitions of distance are examined, and new functionals are presented which satisfy the desired properties. This revised version was published online in August 2006 with corrections to the Cover Date.     

Multiple recurrence and infinite measure preserving odometers

A family of infinite measure preserving odometers is presented which exhibit examples ofp-recurrent but notp+1-recurrent ergodic transformations for everyp>1.     

Optimization of in-vacuo template-stripped Pt surfaces via UHV STM

A recently demonstrated [1] in-vacuo template-stripping process is applied to the study of platinum films stripped from ultra-flat silicon-oxide surfaces. Template-stripped (TS) Pt surfaces, prepared with a range of post-deposition annealing times prior to being stripped from the templating surface in an ultra-high vacuum (UHV) environment, are examined by UHV scanning tunneling microscopy (STM). These studies reveal that without post-deposition annealing, TS Pt surfaces are largely made up of poorly-ordered, granular nanostructures undesirable for many applications. The post-deposition annealing treatments explored in the study result in the emergence and continuous growth of large smooth crystallites. Issues with crystallite orientation relative to the TS surface and artefacts arising as a result of the epoxy used in the template-stripping process are presented and discussed in relation to optimizing the template-stripping procedure for specific applications such as self-assembled monolayer (SAM) formation for molecular electronics. PACS 68.37.Ef; 68.47.De; 68.55.Jk; 81.05.Bx; 81.15.Ef     

Advancing Mathematical Activity: A Practice-Oriented View of Advanced Mathematical Thinking

The purpose of this article is to contribute to the dialogue about the notion of advanced mathematical thinking by offering an alternative characterization for this idea, namely advancing mathematical activity. We use the term advancing (versus advanced) because we emphasize the progression and evolution of students' reasoning in relation to their previous activity. We also use the term activity, rather than thinking. This shift in language reflects our characterization of progression in mathematical thinking as acts of participation in a variety of different socially or culturally situated mathematical practices. For these practices, we emphasize the changing nature of students' mathematical activity and frame the process of progression in terms of multiple layers of horizontal and vertical mathematizing.     

Visions: The coming revolutions in particle physics

We study the branching ratio, CP-violating asymmetry, forward-backward asymmetry and the CP-violating asymmetry in the forward-backward asymmetry for the exclusive decay B → Kτ⁺τ⁻ in the two Higgs doublet model with tree level flavor changing neutral currents (model III). We analyse the dependencies of these quantities on the neutral Higgs boson contributions and the CP parameter sinθ in the model III. We observe that to determine the neutral Higgs boson effects, the measurements of the forward-backward asymmetry and the CP-violating asymmetry in the forward-backward asymmetry for the decay B → Kτ⁺τ⁻ are promising.