Ensembles sur lesquels les polynômes sont déterminés par leur image

Let be a non-empty subset of the complex plane , and , two complex polynomials. If and having the same image on implies , we say that is a generalized unicity set (for polynomials). We construct in this paper a subset of such that and are generalized unicity sets, and we give an example of a generalized unicity set which is open, connected and unbounded.

RÉSUMÉ. Soit un sous-ensemble non vide du plan complexe , et , deux fonctions polynômes à coefficients complexes. Si l'égalité entraîne , on dira que est un ensemble d'unicité généralisée (pour les polynômes). On construit dans cet article un sous-ensemble de tel que et sont d'unicité généralisée, et on donne aussi l'exemple d'un ensemble d'unicité généralisée qui est ouvert, connexe et non borné.

     

An improved approximation ratio for the minimum latency problem

Given a tour visitingn points in a metric space, thelatency of one of these pointsp is the distance traveled in the tour before reachingp. Theminimum latency problem (MLP) asks for a tour passing throughn given points for which the total latency of then points is minimum; in effect, we are seeking the tour with minimum average arrival time. This problem has been studied in the operations research literature, where it has also been termed the delivery-man problem and the traveling repairman problem. The approximability of the MLP was first considered by Sahni and Gonzalez in 1976; however, unlike the classical traveling salesman problem (TSP), it is not easy to give any constant-factor approximation algorithm for the MLP. Recently, Blum et al. (A. Blum, P. Chalasani, D. Coppersimith, W. Pulleyblank, P. Raghavan, M. Sudan, Proceedings of the 26th ACM Symposium on the Theory of Computing, 1994, pp. 163–171) gave the first such algorithm, obtaining an approximation ratio of 144. In this work, we develop an algorithm which improves this ratio to 21.55; moreover, combining our algorithm with a recent result of Garg (N. Garg, Proceedings of the 37th IEEE Symposium on Foundations of Computer Science, 1996, pp. 302–309) provides an approximation ratio of 10.78. The development of our algorithm involves a number of techniques that seem to be of interest from the perspective of the TSP and its variants more generally. © 1998 The Mathematical Programming Society, Inc. Published by Elsevier Science B.V.Supported by NSF contract 9302476-CCR and an NEC research grant.Author supported by an ONR Graduate Fellowship.     

Einen Universalapparat

Ohne Zusammenfassung     

Ein neuer Gasentwicklungsapparat

Ohne Zusammenfassung     

Synthesis optimization of organic xerogels produced from convective air-drying of resorcinol-formaldehyde gels

Resorcinol-formaldehyde gels were produced at 50, 70 and 90 °C and with three different R/C ratios (500, 1000 and 2000). The effect of these variables combined with that of aging time was studied in order to optimize the synthesis conditions. The convective air-drying process was used, and the drying duration was studied with regard to the synthesis conditions. The aging time has no effect on the pore texture after 24 h at 90 °C or 48 h at 70 °C, whatever the R/C value. The synthesis-aging step can be shortened by increasing the temperature. Nevertheless, the pore size tends then to decrease, especially when R/C is high, but this can be counterbalanced by increasing R/C. Moreover, bubbles often appear in the gel at high synthesis temperature, which limits the temperature to about 70 °C in the case of monolithic parts. At 70 °C and with an air velocity of 2 m/s, the elimination of 90% of the solvent requires 1 h drying when the pore size reaches 400-600 nm, 2.5 h for 50 nm wide pores and 3 h when the pore size decreases to 15-20 nm. The drying duration does not exceed 8 h in all cases and could be shortened by increasing the temperature at the end of the process.     

Gas-phase stereoselective binding to Mn/salen catalysts

Gas-phase equilibrium measurements have been used to determine the stereoselectivity of binding the enantiomers of 1-phenylethanol to manganese/salen asymmetric epoxidation catalysts. There is significant selectivity in the gas-phase binding, and the results are compared to data from condensed-phase epoxidations. The study demonstrates the utility of a novel internal standard approach that allows for rapid, accurate measures of the stereoselectivity of gas-phase ligand binding. Moreover, the data suggest that gas-phase binding stereoselectivity could be a potential predictor of condensed-phase enantioselectivity.     

Convergence of an adaptive semi-Lagrangian scheme for the Vlasov-Poisson system

An adaptive semi-Lagrangian scheme for solving the Cauchy problem associated to the periodic 1+1-dimensional Vlasov-Poisson system in the two- dimensional phase space is proposed and analyzed. A key feature of our method is the accurate evolution of the adaptive mesh from one time step to the next one, based on a rigorous analysis of the local regularity and how it gets transported by the numerical flow. The accuracy of the scheme is monitored by a prescribed tolerance parameter ε which represents the local interpolation error at each time step, in the L ^∞ metric. The numerical solutions are proved to converge in L ^∞ towards the exact ones as ε and Δt tend to zero provided the initial data is Lipschitz and has a finite total curvature, or in other words, that it belongs to . The rate of convergence is , which should be compared to the results of Besse who recently established in (SIAM J Numer Anal 42(1):350–382, 2004) similar rates for a uniform semi-Lagrangian scheme, but requiring that the initial data are in . Several numerical tests illustrate the effectiveness of our approach for generating the optimal adaptive discretizations.     

Filling of a given boundary by p-gons and related problems

We consider here (p,s)-polycycles (3ps) i.e. plane graphs, such that all interior faces are p-gons, all interior vertices are s-valent and any vertex of the boundary (i.e. the exterior face) has valency within [2,s]. The boundary sequence of a (p,s)-polycycle P is the sequence b(P) enumerating, up to a cyclic shift or reversal, the consecutive valencies of vertices of the boundary. We show that the values p=3,4 are the only ones, such that the boundary sequence defines its (p,3)-filling (i.e. a (p,3)-polycycle with given boundary) uniquely.Also we give new results in the enumeration of maps M_n(p,q) (i.e. plane 3-valent maps with only p- and q-gonal faces, such that the q-gons are organized in an n-ring) and two of their generalizations.Both problems are similar (3-valent filling by p-gons of a boundary or of a ring of q-gons) and the same programs were used for both computations.     

Asymptotic results for bifurcations in pure bending of rubber blocks

The bifurcation of an incompressible neo-Hookean thick blockwith a ratio of thickness to length , subject to pure bending,is considered. The two incremental equilibrium equations correspondingto a nonlinear pre-buckling state of strain are reduced to afourth-order linear eigenproblem that displays a multiple turningpoint. It is found that for 0 < < , the block experiencesan Euler-type buckling instability which in the limit degeneratesinto a surface instability. Singular perturbation methods enableus to capture this transition, while direct numerical simulationscorroborate the analytical results.     

Design of phenotypic screens for bioactive chemicals and identification of their targets by genetic and proteomic approaches

Cell-based screening using phenotypic assays is a useful means of identifying bioactive chemicals for use as tools to elucidate complex cellular processes. However, the chemicals must display sufficient selectivity and their targets have to be identified. We describe how cell-based screening assays can be designed to maximize the likelihood of discovering selective compounds through the choice of positive readouts, low chemical concentrations and long incubation periods. Examining the potency, efficacy and activity range of chemicals can further help set apart those likely to act more specifically. Identifying the cellular targets of active chemicals can be especially demanding. Secondary screens and the cautious use of the candidate approach can help narrow down their mechanisms of action, but biased approaches may lead to the identification of secondary or even irrelevant targets. We discuss strategies for unbiased target identification by sampling potential targets at the genome-wide and proteome-wide levels.