Prehomogeneous vector spaces and ergodic theory II

We apply M. Ratner's theorem on closures of unipotent orbits to the study of three families of prehomogeneous vector spaces. As a result, we prove analogues of the Oppenheim Conjecture for simultaneous approximation by values of certain alternating bilinear forms in an even number of variables and certain alternating trilinear forms in six and seven variables.

     

Research on the reasoning, teaching and learning of probability and uncertainty

In this editorial, we set out the aims in the call to publish papers on informal statistical inference, randomness, modelling and risk. We discuss how the papers published in this issue have responded to those aims. In particular, we note how the nine papers contribute to some of the major debates in mathematics and statistics education, often taking contrasting positions. Such debates range across: (1) whether knowledge is fractured or takes the form of mental models; (2) heuristic or intuitive thinking versus operational thinking as for example in dual process theory; (3) the role of different epistemic resources, such as perceptions, modelling, imagery, in the development of probabilistic reasoning; (4) how design and situation impact upon probabilistic learning.     

Synthesis of isomeric triazolopyrrolopyrimidines

4‐Hydrazino‐7H‐pyrrolo[2,3‐d]pyrimidines ( 4 ) were cyclocondensed with formic acid or triethyl orthoformate to give 7H‐1,2,4‐triazolo[1,5‐c]pyrrolo[3,2‐e]pyrimidines ( 5 ) and 7H‐1,2,4‐triazolo[4,3‐c]pyrrolo‐[3,2‐e]pyrimidines ( 6 ) respectively. The [4,3‐c]‐isomers ( 6 ) were rearranged into thermodynamically more stable [1,5‐c]‐isomers ( 5 ). The identical compounds ( 5 ) were prepared using another route by reacting 3‐amino‐4‐imino‐7H‐pyrrolo[2,3‐d]pyrimidines ( 3 ) with formic acid or triethylorthoformate. Reaction of 2‐amino‐3‐cyanopyrroles ( 1 ) with triethyl orthoformate followed by hydrazinolysis afforded ( 3 ) via the formation of N‐ethoxymethylene‐2‐amino‐3‐cyanopyrroles ( 2 ).     

Growth and characterization of L‐alanine doped KDP crystals

Potassium Dihydrogen Phosphate (KDP) is an excellent inorganic nonlinear optical (NLO) material with different device applications. Most of amino acids possess NLO property; therefore, it is of interest to dope them in KDP crystals. In the present study, amino acid L‐alanine doped KDP crystals were grown by slow aqueous solvent evaporation technique. The doping of L‐alanine was confirmed by the paper chromatography, the CHN analysis and the FT‐IR spectroscopy. The powder XRD was carried out to assess the single phase nature of the samples. The effect of doping on thermal stability of the crystals was studied by TGA and the kinetic and thermodynamic parameters of dehydration were evaluated. As the amount of doping increased the thermal stability of crystals decreased. However, the second harmonic generation (SHG) efficiency and the UV‐Vis spectroscopy studies indicated that as the L‐alanine doping increased the SHG efficiency and optical transmission percentage increased. The dielectric behavior of the samples has been studied. The variation of dielectric constant, dielectric loss (tanδ), a.c.resistivity and a.c.conductivity with frequency of applied field in the range from 100 Hz to 100 kHz was studied. The dielectric constant and dielectric loss decreased with increase the value of frequency of applied field. The dielectric constant and the dielectric loss values of L‐alanine doped KDP crystals were lower than the pure KDP crystals. The results are discussed. (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Discovery of aminoglycoside mimetics by NMR-based screening of Escherichia coli A-site RNA

A method is described for the NMR-based screening for the discovery of aminoglycoside mimetics that bind to Escherichia coli A-site RNA. Although aminoglycosides are clinically useful, they exhibit high nephrotoxicity and ototoxicity, and their overuse has led to the development of resistance to important microbial pathogens. To identify a new series of aminoglycoside mimetics that could potentially overcome the problems associated with toxicities and resistance development observed with the aminoglycosides, we have prepared large quantities of E. coli 16 S A-site RNA and conducted an NMR-based screening of our compound library in search for small-molecule RNA binders against this RNA target. From these studies, several classes of compounds were identified as initial hits with binding affinities in the range of 70 microM to 3 mM. Lead optimization through synthetic modifications of these initial hits led to the discovery of several small-molecule aminoglycoside mimetics that are structurally very different from the known aminoglycosides. Structural models of the A-site RNA/ligand complexes were prepared and compared to the three-dimensional structures of the RNA/aminoglycoside complexes.     

Locating Gases in Porous Materials: Cryogenic Loading of Fuel‐Related Gases Into a Sc‐based Metal–Organic Framework under Extreme Pressures

An alternative approach to loading metal organic frameworks with gas molecules at high (kbar) pressures is reported. The technique, which uses liquefied gases as pressure transmitting media within a diamond anvil cell along with a single‐crystal of a porous metal–organic framework, is demonstrated to have considerable advantages over other gas‐loading methods when investigating host–guest interactions. Specifically, loading the metal–organic framework Sc₂BDC₃ with liquefied CO₂ at 2 kbar reveals the presence of three adsorption sites, one previously unreported, and resolves previous inconsistencies between structural data and adsorption isotherms. A further study with supercritical CH₄ at 3–25 kbar demonstrates hyperfilling of the Sc₂BDC₃ and two high‐pressure displacive and reversible phase transitions are induced as the filled MOF adapts to reduce the volume of the system.