Lower Bound for the Maximal Number of Facets of a 0/1 Polytope

Let $f_{n-1}(P)$ denote the number of facets of a polytope $P$ in ${\Bbb R}^n$. We show that there exist 0/1 polytopes $P$ with $$f_{n-1}(P)\geq\left (\frac{cn}{\log^2 n}\right )^{n/2},$$ where $c>0$ is an absolute constant. This improves earlier work of Barany and Por on a question of Fukuda and Ziegler.     

A statistical model for evaluation and prediction of the noise exposure in a construction equipment area

A statistical model for evaluating and predicting the equivalent noise level and the noise exposure at a working area was made. The method is based on the statistical theory of regression analysis. The results are expressed as a functional expansion and the stochastic models that give the solution to the problem are confidence zones and prediction zones of noise, which are valid in every similar case.     

From fluid relaxations to practical algorithms for job shop scheduling: the makespan objective

We design an algorithm, called the fluid synchronization algorithm (FSA), for the job shop scheduling problem with the objective of minimizing the makespan. We round an optimal solution to a fluid relaxation, in which we replace discrete jobs with the flow of a continuous fluid, and use ideas from fair queueing in the area of communication networks in order to ensure that the discrete schedule is close to the one implied by the fluid relaxation. FSA produces a schedule with makespan at most C _max+(I+2)P _max J _max, where C _max is the lower bound provided by the fluid relaxation, I is the number of distinct job types, J _max is the maximum number of stages of any job-type, and P _max is the maximum processing time over all tasks. We report computational results based on all benchmark instances chosen from the OR library when N jobs from each job-type are present. The results suggest that FSA has a relative error of about 10% for N=10, 1% for N=100, 0.01% for N=1000. In comparison to eight different dispatch rules that have similar running times as FSA, FSA clearly dominates them. In comparison to the shifting bottleneck heuristic whose running time and memory requirements are several orders of magnitude larger than FSA, the shifting bottleneck heuristic produces better schedules for small N (up to 10), but fails to provide a solution for larger values of N. Received: September 1999 / Accepted: September 2001?Published online March 14, 2002     

Artificial compressibility, characteristics-based schemes for variable-density, incompressible, multispecies flows: Part II. Multigrid implementation and numerical tests

The paper presents an investigation of the accuracy and efficiency of artificial compressibility, characteristics-based (CB) schemes for variable-density incompressible flows. The CB schemes have been implemented in conjunction with a multigrid method for accelerating numerical convergence and a fourth-order, explicit Runge–Kutta method for the integration of the governing equations in time. The implementation of the CB schemes is obtained in conjunction with first-, second- and third-order interpolation formulas for calculating the variables at the cell faces of the computational volume. The accuracy and efficiency of the schemes are examined against analytical and experimental results for diffusion broadening in two- and three-dimensional microfluidic channels, a problem that has motivated the development of the present methods. Moreover, unsteady, inviscid simulations have been performed for variable-density mixing layer. The computations revealed that accuracy and efficiency depend on the CB scheme design. The best multigrid convergence rates were exhibited by the conservative CB scheme, which is obtained by the fully conservative formulation of the variable-density, incompressible equations.     

Examen de la loi d'arrhenius de la diffusion dans les solides

Validity of the Arrhenius law has been investigated by measuring the influence of temperature on the transport processes in very pure single crystals of sodium iodide. For the first time, due to the high experimental accuracy and the precision of the temperature control, diffusion coefficients could be measured in a solid in steps of a few degrees up to a few tenths of a degree of the temperature of fusion. We have studied: (a) ionic conductivity, (b) self-diffusion of the cation Na⁺ and (c) self-diffusion of the anion I^?. The three transport processes follow the same temperature dependence: (a) strict verification of the Arrhenius law over several orders of magnitude up to about thirty degrees below the melting point and (b) in the last thirty degrees a positive departure from the simple exponential law is observed which increases rapidly to reach 50% at fusion. The different possible reasons of this departure are discussed. The phenomenon seems to be connected with the lattice dynamics before melting.     

On images of Borel measures under Borel mappings

Let and be metric spaces. We show that the tight images of a (fixed) tight Borel probability measure on , under all Borel mappings , form a closed set in the space of tight Borel probability measures on with the weak-topology. In contrast, the set of images of under all continuous mappings from to may not be closed. We also characterize completely the set of tight images of under Borel mappings. For example, if is non-atomic, then all tight Borel probability measures on can be obtained as images of , and as a matter of fact, one can always choose the corresponding Borel mapping to be of Baire class 2.

     

Topology on Asymptotic Algebras of Generalized Functions and Applications

 Starting from a locally convex metrisable topological space and from any asymptotic scale, we construct a generalized extension of this space. To those extensions, we associate Hausdorff topologies. We introduce the notion of a temperate map, with respect to a given asymptotic scale, between two locally convex metrisable semi-normed spaces. We show that such mappings extend in a canonical way to mappings between the respective generalized extensions. We give an application to nonlinear Dirichlet boundary value problems with singular data in the framework of generalized extensions.     

H2/air autoignition: The nature and interaction of the developing explosive modes

Appropriate algorithmic tools are employed for the analysis of the explosive modes developing during the autoignition of homogeneous mixtures. The ability of these tools to provide significant physical understanding is demonstrated in the case of the homogeneous ignition of a stoichiometric H₂/air mixture, modelled by two different chemical kinetics mechanisms. It is shown that the ignition process evolves in two stages. The first stage is characterised by the development of two explosive timescales (one fast and one slow), that lead the system away from equilibrium. As the end of the first stage is approached, the two explosive timescales converge, they merge and then they disappear. In the second stage only dissipative timescales develop, which drive the system all the way to equilibrium. It is shown that throughout the first stage the fast explosive timescale is generated by chain reactions. The slow explosive timescale is initially generated by an initiation reaction that produces the radicals required for the start-up of the fast mode, while later on it is generated by reactions that are responsible for the heat released. These findings are validated with sensitivity analysis results for the ignition delay time and are employed in order to clarify the discrepancies in the solution provided by the two different chemical kinetics mechanisms considered.     

One‐Pot Transformation of Simple Furans into 4‐Hydroxy‐2‐cyclopentenones in Water

A highly efficient one‐pot transformation of readily accessible furans into 4‐hydroxy‐2‐cyclopentenones in H₂O, using singlet oxygen as oxidant, has been developed.