Two-dimensional crystallization of hard sphere particles at a liquid–liquid interface

A method for studying crystallization of hard sphere like particles in two dimensions is presented. The method involves trapping the particles at the interface between two immiscible liquids. Particles at the interface undergo 2D Brownian motion, and at sufficiently high densities crystallization is observed. The pseudo hard sphere nature of the particle interactions under these conditions is maintained, as demonstrated by the area density at which crystallization occurs. In contrast to established techniques for studying crystallization in pseudo 2D hard spheres, the particles trapped at the interface undergo no vertical motion, so the system is in principle closer to a true 2D system. The method is therefore amenable to the study of the effects of polydispersity on crystallization behaviour. The advantages and disadvantages of the method are discussed.     

A robust approach to the chance-constrained knapsack problem

In this paper, the chance-constrained knapsack problem (CKP) is addressed. Relying on robust optimization, a tractable combinatorial algorithm is proposed to solve approximately CKP. For two specific classes of uncertain knapsack problems, it is proved to solve CKP at optimality.     

On universal formal power series

The point source of this work is Seleznev's theorem which asserts the existence of a power series which satisfies universal approximation properties in C^∗. The paper deals with a strengthened version of this result. We establish a double approximation theorem on formal power series using a weighted backward shift operator. Moreover we give strong conditions that guarantee the existence of common universal series of an uncountable family of weighted backward shift with respect to the simultaneous approximation. Finally we obtain results on admissible growth of universal formal power series. We especially prove that you cannot control the defect of analyticity of such a series even if there exist universal series in the well-known intersection of formal Gevrey classes.     

Improving the lateral resolution in confocal fluorescence microscopy using laterally interfering excitation beams

The confocal fluorescence microscope is the instrument of choice for biologists. However, compared to other instruments, its resolution is still limited. We propose a simple technique, based on laterally interfering beams, to improve the resolution. One technique consists in using a halve phase plate to modify the illumination, combined with a laterally offset detection. A 90 nm lateral resolution is obtained for properly prepared specimens using readily available dyes. Another approach is to use several excitation beams, slightly shifted and properly dephased, to decrease the lateral extension of the PSF. With this approach, a lateral resolution of 75 nm is predicted with the advantage of a regular confocal detection. Finally, we show how using these techniques in combination with a two-color two-photon excitation could permit to further improve the resolution to 60 nm.     

A new method to study complex materials in solid state chemistry: application to chalcogenide materials

We show that a combined application of Mössbauer spectroscopy and other experimental tools such as X‐ray photoelectron spectroscopy, X‐ray absorption spectroscopy and nuclear magnetic resonance provides a coherent picture of the local electronic structure in chalcogenide materials. In order to develop this idea we propose an analysis of the Sn, Sb and Te local electronic structures for three different systems of materials. The first example concerns the In–Sn–S system. We show that Li insertion in In₁₆Sn₄S₃₂ leads to changes of the Sn oxidation states from Sn(IV) to Sn(II). The second example concerns materials of the Tl–Sb–S system. We show that variations of the ¹²¹Sb Mössbauer isomer shift and surface of the first peak of the X‐ray absorption spectra at the Sb L_III edge can be linearly correlated because of the main influence of the Sb 5s electrons. This is explained by changes in the local environment of the Sb atoms. The last example concerns the crystalline phases of the Tl–Sn–Te system. The formal oxidation numbers of the Te atoms are determined from ¹²⁵Te Mössbauer spectroscopy and X‐ray photoelectron spectroscopy. They are related to the different types of bonds involving the Te atoms in the Tl–Sn–Te compounds.     

Classification des algèbres de Lie graduées simples de croissance ≦1

Sans résumé     

NP-hardness results for the aggregation of linear orders into median orders

Given a collection Π of individual preferences defined on a same finite set of candidates, we consider the problem of aggregating them into a collective preference minimizing the number of disagreements with respect to Π and verifying some structural properties. We study the complexity of this problem when the individual preferences belong to any set containing linear orders and when the collective preference must verify different properties, for instance transitivity. We show that the considered aggregation problems are NP-hard for different types of collective preferences (including linear orders, acyclic relations, complete preorders, interval orders, semiorders, quasi-orders or weak orders), if the number of individual preferences is sufficiently large.