Directional Threading and Sliding of a Dissymmetrical Foldamer Helix on Dissymmetrical Axles

We have investigated the self‐assembly of a dissymmetrical aromatic oligoamide helix on linear amido‐carbamate rods. A dissymmetric sequence bearing two differentiated ends is able to wrap around dissymmetric dumbbell guest molecules. Structural and thermodynamic investigations allowed us to decipher the mode of binding of the helix that can bind specifically to the amide and carbamate groups of the rod. In parallel kinetic studies of threading and sliding of the helix along linear axles were also monitored by ¹H NMR. Results show that threading of a dissymmetrical host can be kinetically biased by the nature of the guest terminus allowing a preferential sense of sliding of the helix. The study presented below further demonstrates the valuable potential of foldaxanes to combine designed molecular recognition patterns with fine control of self‐assembly kinetics to conceive complex supramolecular events.     

Sur L'equation Diophantienne (xn-1)/(x-1)=yq, III

In this paper we study the diophantine equation of the title,which was first introduced by Nagell and Ljunggren during thefirst half of the twentieth century. We describe a method whichallows us, on the one hand when n is fixed, to obtain an upperbound for q, and on the other hand when n and q are fixed, toobtain upper bounds for x and y which are far sharper than thosederived from the theory of linear forms in logarithms. We alsoshow how these bounds can be used even when they seem too largefor a straightforward enumeration of the remaining possiblevalues of x. By combining all these techniques, we are ableto solve the equation in many cases, including the case whenn has a prime divisor less than 13, or the case when n has aprime divisor which is less than or equal to 23 and distinctfrom q. 2000 Mathematical Subject Classification: primary 11D41;secondary 11J86, 11Y50.     

Non-minimal scalar-flat Kähler surfaces and parabolic stability

A new construction is presented of scalar-flat Kähler metrics on non-minimal ruled surfaces. The method is based on the resolution of singularities of orbifold ruled surfaces which are closely related to rank-2 parabolically stable holomorphic bundles. This rather general construction is shown also to give new examples of low genus: in particular, it is shown that \(\mathbb{CP}^2\) blown up at 10 suitably chosen points, admits a scalar-flat Kähler metric; this answers a question raised by Claude LeBrun in 1986 in connection with the classification of compact self-dual 4-manifolds.     

Hydrodynamic Structure of the Augmented Born-Infeld Equations

The Born-Infeld system is a nonlinear version of Maxwells equations. We first show that, by using the energy density and the Poynting vector as additional unknown variables, the BI system can be augmented as a 10×10 system of hyperbolic conservation laws. The resulting augmented system has some similarity with magnetohydrodynamics (MHD) equations and enjoys remarkable properties (existence of a convex entropy, Galilean invariance, full linear degeneracy). In addition, the propagation speeds and the characteristic fields can be computed in a very easy way, in contrast with the original BI equations. Then, we investigate several limit regimes of the augmented BI equations, by using a relative-entropy method going back to Dafermos, and recover the Maxwell equations for low fields, some pressureless MHD equations for high fields, and pressureless gas equations for very high fields.     

Chemoselective signalling of selected phospho-anions using lanthanide luminescence

Selectivity in the binding of phosphorylated tyrosine residues to aqua-lanthanide complexes is signalled by changes in spectral form by luminescence emission and 1H NMR spectroscopy.     

Molecular logic: a half-subtractor based on tetraphenylporphyrin

Spectroscopic changes from a solution of the amphophile 5,10,15,20-tetraphenylporphyrin in N,N-dimethylformamide using inputs of acid (HClaq) and base (KOBut) are interpreted as XOR and INHIBIT logic operations. The combination of these two operations gives rise to a device that acts as a molecular half-subtractor.     

Retracts of Products of Chordal Graphs

In this article, we characterize the graphs G that are the retracts of Cartesian products of chordal graphs. We show that they are exactly the weakly modular graphs that do not contain K_{2, 3}, the 4‐wheel minus one spoke , and the k‐wheels (for as induced subgraphs. We also show that these graphs G are exactly the cage‐amalgamation graphs as introduced by Bre?ar and Tepeh Horvat (Cage‐amalgamation graphs, a common generalization of chordal and median graphs, Eur J Combin 30 (2009), 1071–1081); this solves the open question raised by these authors. Finally, we prove that replacing all products of cliques of G by products of Euclidean simplices, we obtain a polyhedral cell complex which, endowed with an intrinsic Euclidean metric, is a CAT(0) space. This generalizes similar results about median graphs as retracts of hypercubes (products of edges) and median graphs as 1‐skeletons of CAT(0) cubical complexes. © 2012 Wiley Periodicals, Inc. J. Graph Theory 73: 161–180, 2013