2‐(2‐Oxoimidazolidinyl)ethyl 2‐methyl­prop‐2‐enoate

In the crystal structure of the title compound, C₉H₁₄N₂O₃, the molecules are linked by N—H?O=C bonds into chains parallel to [001]. Large crystals are readily obtained, presumably because of the hydrogen bonds and an energetically stable conformation of the mol­ecule.     

Introducing a Hydrogen‐Bond Donor into a Weakly Nucleophilic Brønsted Base: Alkali Metal Hexamethyldisilazides (MHMDS,M=Li,Na, K,Rb and Cs) with Ammonia

Alkali metal 1,1,1,3,3,3‐hexamethyldisilazide (MHMDSs) are one of the most utilised weakly nucleophilic Brønsted bases in synthetic chemistry and especially in natural product synthesis. Like lithium organics, they aggregate depending on the employed donor solvents. Thus, they show different reactivity and selectivity as a function of their aggregation and solvation state. To date, monomeric LiHMDS with monodentate donor bases was only characterised in solution. Since the first preparation of LiHMDS in 1959 by Wannagat and Niederprüm, all efforts to crystallise monomeric LiHMDS in the absence of chelating ligands failed. Herein, we present ammonia adducts of LiHMDS, NaHMDS, KHMDS, RbHMDS and CsHMDS with unprecedented aggregation motifs: 1) The hitherto missing monomeric key compound in the LiHMDS aggregation architectures. Monomeric crystal structures of trisolvated LiHMDS ( 1 ) and NaHMDS ( 2 ), showing unique intermolecular hydrogen bonds, 2) the unprecedented tetrasolvated KHMDS ( 3 ) and RbHMDS ( 4 ) dimers and 3) the disolvated CsHMDS ( 5 ) dimer with very close intermolecular Si?CH₃???Cs s‐block “agostic” interactions have been prepared and characterised by single‐crystal X‐ray structure analysis.     

Set-based corral control in stochastic dynamical systems: making almost invariant sets more invariant

We consider the problem of stochastic prediction and control in a time-dependent stochastic environment, such as the ocean, where escape from an almost invariant region occurs due to random fluctuations. We determine high-probability control-actuation sets by computing regions of uncertainty, almost invariant sets, and Lagrangian coherent structures. The combination of geometric and probabilistic methods allows us to design regions of control, which provide an increase in loitering time while minimizing the amount of control actuation. We show how the loitering time in almost invariant sets scales exponentially with respect to the control actuation, causing an exponential increase in loitering times with only small changes in actuation force. The result is that the control actuation makes almost invariant sets more invariant.     

Observation of two-neutrino double-beta decay in 136Xe with the EXO-200 detector

We report the observation of two-neutrino double-beta decay in (136)Xe with T(1/2) = 2.11 ± 0.04(stat) ± 0.21(syst) × 10(21) yr. This second-order process, predicted by the standard model, has been observed for several nuclei but not for (136)Xe. The observed decay rate provides new input to matrix element calculations and to the search for the more interesting neutrinoless double-beta decay, the most sensitive probe for the existence of Majorana particles and the measurement of the neutrino mass scale.     

Preparation of water-soluble magnetic nanocrystals using aryl diazonium salt chemistry

A novel and facile methodology for the in situ surface functionalization of Fe(3)O(4) nanoparticles is proposed, based on the use of aryl diazonium salts chemistry. The grafting reaction involves the formation of diazoates in a basic medium. These species are unstable and dediazonize along a homolytic pathway to give aryl radicals which further react with the Fe(3)O(4) NPs during their formation and stop their growth. Advantages of the present approach rely not only on the simplicity, rapidity, and efficiency of the procedure but also on the formation of strong Fe(3)O(4)-aryl surface bonds, highly suitable for further applications.     

Integrability,computation and applications

The study of integrable systems and the notion of integrability has been re-energized with the discovery that infinite-dimensional systems such as the Korteweg-de Vries equation are integrable. In this paper, the following novel aspects of integrability are described: (i) solutions of Darboux, Brioschi, Halphen-type systems and their relationships to monodromy problems and automorphic functions, (ii) computational chaos in integrable systems, (iii) we explain why we believe that homoclinic structures and homoclinic chaos associated with nonlinear integrable wave problems, will be observed in appropriate laboratory experiments.     

Free channel fourier transform in the long-rangen-body problem

Research supported by NSF grant DMS-8807816.