c-di-GMP displays a monovalent metal ion-dependent polymorphism

Cyclic diguanosine monophosphate (c-di-GMP) is known to be an important signaling molecule that regulates the formation of bacterial biofilms. We demonstrate here by UV, CD, and NMR that it displays a surprising polymorphism that varies with the monovalent counterion and is consistent with the formation of a G-quartet structure in K+ and a stacked structure in Li+ or Na+. The ability of this rigid molecule to adopt different alignments may be important to its biological role.     

<Emphasis Type="Italic">L</Emphasis><Superscript><Emphasis Type="Italic">p</Emphasis></Superscript> estimates for the biest I. The Walsh case

We prove L^p estimates (Theorem 1.8) for the Walsh model of the biest, a trilinear multiplier with singular symbol. The corresponding estimates for the Fourier model will be obtained in the sequel [11] biest of this paper.     

L p bounds for a maximal dyadic sum operator

The authors prove L ^p bounds in the range 1<p< for a maximal dyadic sum operator on R ⁿ . This maximal operator provides a discrete multidimensional model of Carlesons operator. Its boundedness is obtained by a simple twist of the proof of Carlesons theorem given by Lacey and Thiele [7] adapted in higher dimensions [9]. In dimension one, the L ^p boundedness of this maximal dyadic sum implies in particular an alternative proof of Hunts extension [4] of Carlesons theorem on almost everywhere convergence of Fourier integrals. Mathematics Subject Classification (2000):Primary 42A20, Secondary 42A24Grafakos is supported by the NSF. Tao is a Clay Prize Fellow and is supported by a grant from the Packard Foundation.     

A sum-product estimate in finite fields,and applications

Let A be a subset of a finite field for some prime q. If for some > 0, then we prove the estimate for some = () > 0. This is a finite field analogue of a result of [ErS]. We then use this estimate to prove a Szemerédi-Trotter type theorem in finite fields, and obtain a new estimate for the Erdös distance problem in finite fields, as well as the three-dimensional Kakeya problem in finite fields.     

From here to Bologna

The Bologna process promises to create a unified education system in 45 countries by 2010. Is this an achievable goal? Terry Mitchell looks at the ins and outs of Bologna.     

A 1:1 adduct between di­methyl­tin dibromide and N‐methyl­pyrrolidinone (NMP)

The title compound, di­bromo­di­methyl(N‐methyl­pyrrolidin‐2‐one‐O)­tin(IV), [SnBr₂(CH₃)₂(C₅H₉NO)], exhibits pentacoordination of the Sn atom, with long and short Sn—Br bonds [2.6737 (4) and 2.5256 (4) Å, respectively]. The distorted trigonal–bipyramidal coordination polyhedron has two methyl groups and one Br atom in the equatorial plane, the second Br atom and the N‐methyl­pyrrolidinone (NMP) ligand occupying the apical positions.     

Analysis of an Optimal Control Problem Related to the Anaerobic Digestion Process

Our aim in this work is to synthesize optimal feeding strategies that maximize, over a time period, the biogas production in a continuously filled bioreactor controlled by its dilution rate. Such an anaerobic process is described by a four-dimensional dynamical system. Instead of modeling the optimization of the biogas production as a Lagrange-type optimal control problem, we propose a slightly different optimal control approach in this paper: We study the minimal time control problem to reach a target point, which is chosen in such a way that it maximizes the biogas production at steady state. Thanks to the Pontryagin maximum principle and the geometric control theory, we provide an optimal feedback control for the minimal time control problem, when the initial conditions are taken within the invariant and attractive manifold of the system. The optimal synthesis exhibits turnpike and anti-turnpike singular arcs and a cut locus.