An everywhere convergent series representation of the distribution of Hotelling's generalized T0

A new series representation of the exact distribution of Hotelling's generalized T₀² statistic is obtained. Unlike earlier work, the series representation given here is everywhere convergent. Explicit formulae are given for both the null and the non-central distributions. Earlier results by [1], 215013;225), which are convergent on the interval [0, 1), are also derived quite simply from our formulae. The paper therefore provides a solution to the long standing problem of the exact distribution of the T₀² statistic in the general case.     

Complexity of local search for the p-median problem

We study the complexity of finding local minima for the p-median problem. The relationship between Swap local optima, 0–1 local saddle points, and classical Karush–Kuhn–Tucker conditions is presented. It is shown that the local search problems with some neighborhoods are tight PLS-complete. Moreover, the standard local descent algorithm takes exponential number of iterations in the worst case regardless of the tie-breaking and pivoting rules used. To illustrate this property, we present a family of instances where some local minima may be hard to find. Computational results with different pivoting rules for random and Euclidean test instances are discussed. These empirical results show that the standard local descent algorithm is polynomial in average for some pivoting rules.     

Massively parallel LES of azimuthal thermo-acoustic instabilities in annular gas turbines

Increasingly stringent regulations and the need to tackle rising fuel prices have placed great emphasis on the design of aeronautical gas turbines, which are unfortunately more and more prone to combustion instabilities. In the particular field of annular combustion chambers, these instabilities often take the form of azimuthal modes. To predict these modes, one must compute the full combustion chamber, which remained out of reach until very recently and the development of massively parallel computers. In this article, full annular Large Eddy Simulations (LES) of two helicopter combustors, which differ only on the swirlers' design, are performed. In both computations, LES captures self-established rotating azimuthal modes. However, the two cases exhibit different thermo-acoustic responses and the resulting limit-cycles are different. With the first design, a self-excited strong instability develops, leading to pulsating flames and local flashback. In the second case, the flames are much less affected by the azimuthal mode and remain stable, allowing an acceptable operation. Hence, this study highlights the potential of LES for discriminating injection system designs. To cite this article: P. Wolf et al., C. R. Mecanique 337 (2009).     

Exploiting equalities in polynomial programming

We propose a novel approach for solving polynomial programs over compact domains with equality constraints. By means of a generic transformation, we show that existing solution schemes for the, typically simpler, problem without equalities can be used to address the problem with equalities.     

Modeling the effect of external electric field and current on the stochastic dynamics of ATPase nano-biomolecular motors

The rotary motion of the F₀ part of the F₀F₁-ATPase motor that synthesizes the ATP molecules used by the intracellular stepping motors, such as kinesins, is modeled within a stochastically fluctuating medium via the application of the Langevin dynamics wherein the random intramembrane fluctuations are represented by a white noise. We have investigated the influence of an applied electric field and an applied electric current on this rotary motion, and the subsequent production rate of the ATP molecules. It is seen that the application of a field, or a current, changes both the elastic behavior of the cell membrane and the transmembrane potential. These changes in turn transform the dynamics of the F₀ part of the motor. We have found that at low fields, the role of transmembrane potential becomes significant in the production rate of the ATP molecules, whereas at high fields the changes induced in the surface tension of the membrane also contribute to the production rate of the ATP.     

Economical tight examples for the biased Erd?s-Selfridge theorem

A positional game is essentially a generalization of tic-tac-toe 0;played on a hypergraph (V,F). A pivotal result in the study of positional games is the Erd?s-Selfridge 0;theorem, which gives simple criteria for the existence of a Breaker's winning strategy on a hypergraph F. It has been shown that the Erd?s-Selfridge 0;theorem can be tight and that numerous extremal systems exist for that theorem. We focus on a generalization of the Erd?s-Selfridge 0;theorem proven by Beck for biased (p:q) 0;games, which we call the (p:q)-Erd?s-Selfridge 0;theorem. We show that for pn-uniform hypergraphs there is a unique extremal system for the (p:q)-Erd?s-Selfridge 0;theorem (q?2) when Maker 0;must win in exactly n turns (i.e., as quickly as possible).     

A New Supramolecular Assembly Formed by Melamine and Sulfuric Acid

Polymeric melaminium sulfate [(LH₂)₂(SO₄)₂]_n has been synthesized by reaction of melamine L with sulfuric acid in aqueous solution. The compound was characterized by elemental analysis, ¹H NMR, ESI MS and a single crystal X‐ray diffraction analysis. The architecture of the assembly formed is based on hydrogen bonded dimers of diprotonated melaminium cations (LH₂)²⁺ which are linked by a hydrogen bonded network with sulfate ions forming 2D sheets. A 3D polymeric structure results from the presence of mutual hydrogen bonds between sulfate ions and melaminium cations in different sheets. Significant π‐π stacking is also present between the aromatic cations in this supramolecular arrangement.     

Self‐assembly of π‐conjugated bis(terpyridine) ligands with zinc(II) ions: New metallosupramolecular materials for optoelectronic applications

A series of main‐chain metallopolymers ( P1–P10 ) was prepared by the self‐assembly of rigid‐linear π‐conjugated bis(terpyridine) monomers ( 1–10 ) with Zn^II ions and was fully characterized. The polymerization was additionally confirmed by UV/vis titration experiments. A strong increase in viscosities (around 1.6 times) relative to those of the monomer solutions was found. The thermal stability of P1–P10 compared with that of 1–10 was enhanced as a result of the metallopolymerization. The electro‐optical properties of the materials were investigated in detail. Tuning of the electrochemical and photophysical properties was enabled; thus, bright purple to green photoluminescent (PL) emission (PL quantum yields of 0.12–0.81) for P1–P10 was observed in solution with the emission color strongly depending on the nature of the π‐conjugated bis(terpyridine) system. Thin homogeneous films of P6 were prepared by solution processing, that is, spin‐coating and inkjet‐printing, and exhibited intense yellow PL emission in the solid state. © 2009 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 47: 4083–4098, 2009