Calculus of functors,operad formality,and rational homology of embedding spaces

Let M be a smooth manifold and V a Euclidean space. Let [`(\textEmb)] \overline{{{\text{Emb}}}} (M,V) be the homotopy fiber of the map Emb(M,V) → Imm(M,V). This paper is about the rational homology of [`(\textEmb)] \overline{{{\text{Emb}}}} (M,V). We study it by applying embedding calculus and orthogonal calculus to the bifunctor (M,V)↦ HQ ∧ [`(\textEmb)] \overline{{{\text{Emb}}}} (M,V)₊. Our main theorem states that if

Cochain model for thickenings and its application to rational LS-category

A thickening of a finite CW-complex X is by definition a compact manifold M of the same simple homotopy type as X. We give a model for the cochain complex of the boundary of that manifold, C ^*(δM), as a module over the cochain algebra C ^*(X). We also show how to construct an algebraic model of the rational homotopy type of δC ^*(M) from a model of X. Using this rational model, we prove a new formula for the rational Lusternik–Schnirelmann category of X. Received: 24 September 1999     

Development and Performance Characteristics of a Capillary Dosage Unit with in Situ Weight Sensor for the Preparation of Known Amounts of Gaseous Voc's in Air

Abstract

This paper describes the design, performance and operation of a home-made capillary dosage unit with in situ weight sensor. This continuous injection technique is developed to produce dynamic gas phase calibration mixtures of VOC's in a diluent gas at occupational hygiene levels. A new advance in the technique allows the calculation of the amounts of pollutants emitted into the carrier gas, directly from the gravimetric measurements.

This is achieved by a built-in weight sensor which is monitored without interfering with the injection process. The survey of the capillary dosage unit(s) is managed by a microcomputer which automatically lists the amounts of pollutants introduced into the diluent gas. The capillary dosage technique thus becomes related directly to a primary standard.

The homogeneity and stability of the test gas generated is shown to be better than 1% relative standard deviation over periods of up to 24 hours. The VOC concentrations in the manifold are known with a total uncertainty of between 2 and 3%SS.     

Round-robin tournaments generated by the Circle Method have maximum carry-over

The Circle Method is widely used in the field of sport scheduling to generate schedules for round-robin tournaments. If in such a tournament, team A played team B in its previous match and is now playing team C, team C is said to receive a carry-over effect from team B. The so-called carry-over effect value is a number that can be associated to each round-robin schedule; it represents a degree of unbalancedness of the schedule with respect to carry-over. Here, we prove that, for an even number of teams, the Circle Method generates a schedule with maximum carry-over effect value, answering an open question.     

Oxidation Monitoring by Fluorescence Spectroscopy Reveals the Age of Fingermarks

No forensic method exists that can reliably estimate the age of fingermarks found at a crime scene. Information on time passed since fingermark deposition is desired as it can be used to distinguish between crime related and unrelated fingermarks and to support or refute statements made by the fingermark donors. We introduce a non‐contact method that can estimate the age of fingermarks. Fingermarks were approached as protein–lipid mixtures and an age‐estimation model was build based on the expected protein and lipid oxidation reactions. Two measures of oxidation are required from the fingermark to estimate its age: 1) the relative amount of fluorescent oxidation products 2) the rate at which these products are formed. Fluorescence spectroscopy was used to obtain these measures. We tested the method on 44 fingermarks and were able to estimate the age of 55 % of the male fingermarks, up to three weeks old with an uncertainty of 1.9 days.     

Time slack-based techniques for robust project scheduling subject to resource uncertainty

The resource-constrained project scheduling problem (RCPSP) has been the subject of a great deal of research during the previous decades. This is not surprising given the high practical relevance of this scheduling problem. Nevertheless, extensions are needed to be able to cope with situations arising in practice such as multiple activity execution modes, activity duration changes and resource breakdowns. In this paper we analytically determine the impact of unexpected resource breakdowns on activity durations. Furthermore, using this information we develop an approach for inserting explicit idle time into the project schedule in order to protect it as well as possible from disruptions caused by resource unavailabilities. This strategy will be compared to a traditional simulation-based procedure and to a heuristic developed for the case of stochastic activity durations.     

Multirate time stepping for accelerating explicit discontinuous Galerkin computations with application to geophysical flows

This paper presents multirate explicit time‐stepping schemes for solving partial differential equations with discontinuous Galerkin elements in the framework of Large‐scale marine flows. It addresses the variability of the local stable time steps by gathering the mesh elements in appropriate groups. The real challenge is to develop methods exhibiting mass conservation and consistency. Two multirate approaches, based on standard explicit Runge–Kutta methods, are analyzed. They are well suited and optimized for the discontinuous Galerkin framework. The significant speedups observed for the hydrodynamic application of the Great Barrier Reef confirm the theoretical expectations. Copyright © 2012 John Wiley & Sons, Ltd.     

Practical evaluation of five partly discontinuous finite element pairs for the non‐conservative shallow water equations

This paper provides a comparison of five finite element pairs for the shallow water equations. We consider continuous, discontinuous and partially discontinuous finite element formulations that are supposed to provide second‐order spatial accuracy. All of them rely on the same weak formulation, using Riemann solver to evaluate interface integrals. We define several asymptotic limit cases of the shallow water equations within their space of parameters. The idea is to develop a comparison of these numerical schemes in several relevant regimes of the subcritical shallow water flow. Finally, a new pair, using non‐conforming linear elements for both velocities and elevation (P?P), is presented, giving optimal rates of convergence in all test cases. P?P₁ and P?P₁ mixed formulations lack convergence for inviscid flows. P?P₂ pair is more expensive but provides accurate results for all benchmarks. P?P provides an efficient option, except for inviscid Coriolis‐dominated flows, where a small lack of convergence is observed. Copyright © 2009 John Wiley & Sons, Ltd.