Preparation of 2,9-dioxabicyclo[3.3.1]nonanes. A model for tirandamycin

An efficient synthesis of a 2,9-dioxabicyclo[3.3.1]nonane system, similar to that of tirandamycin, is accomplished from 2,3-dimethylfuran.     

Fragment–molecule adduct ion formation in positive methane chemical ionization mass spectrometry1

Fragment–molecule (F⁺M) adduct ions of a variety of heterocyclic systems have been observed in positive methane chemical ionization spectra at relatively low sample concentrations, i.e. in the microgram range. The relative abundance of these adduct ions increases with sample concentration. Possible mechanisms of formation of F⁺M are discussed. Formation of such ions should be recognized as an artifact, otherwise such F⁺M adduct ions in chemical and electron ionization may be mistaken for impurities present in a sample.     

Crown ether complexes of potassium and thallium(I) 2- and 4-nitrophenoxides

18-Crown-6 and dicyclohexano-18-crown-6 complexes of potassium 2- and 4-nitrophenoxide, and 18-crown-6 complexes of thallium(I) 2- and 4-nitrophenoxide have been synthesized. Solvent effects on the visible spectra of the nitrophenoxide anions are independent of the nature of the cation and the nature of the complexing agent. The 18-crown-6 complex of thallium(I) 2-nitrophenoxide is a 1:2 complex. All the other complexes are 1:1. X-ray crystallographic examination of the potassium dicyclohexano-18-crown-6 complexes showed the potassium ion is octacoordinated in the 2-nitrophenoxide and heptacoordinated in the 4-nitrophenoxide.     

Triarylphosphine-stabilized platinum nanoparticles in three-dimensional nanostructured films as active electrocatalysts

Ligand-stabilized platinum nanoparticles (Pt NPs) can be used to build well-defined three-dimensional (3-D) nanostructured electrodes for better control of the catalyst architecture in proton exchange membrane fuel cells (PEMFCs). Platinum NPs of 1.7 +/- 0.5 nm diameter stabilized by the water-soluble phosphine ligand, tris(4-phosphonatophenyl)phosphine (TPPTP, P(4-C6H4PO3H2)3), were prepared by ethylene glycol reduction of chloroplatinic acid and subsequent treatment of the isolated nanoparticles with TPPTP. The isolated TPPTP-stabilized Pt NPs were characterized by multinuclear magnetic resonance spectroscopy (31P and 195Pt NMR), high-resolution transmission electron microscopy (HRTEM), X-ray photoelectron spectroscopy (XPS), and extended X-ray absorption fine structure (EXAFS). The negatively charged TPPTP-Pt NPs were electrostatically deposited onto a glassy carbon electrode (GCE) modified with protonated 4-aminophenyl functional groups (APh). Multilayers were assembled via electrostatic layer-by-layer deposition with cationic poly(allylamine HCl) (PAH). These multilayer films are active for the key hydrogen fuel cell reactions, hydrogen oxidation (anode) and oxygen reduction (cathode). Using a rotating disk electrode configuration, fully mass-transport limited kinetics for hydrogen oxidation was obtained after 3 layers of TPPTP-Pt NPs with a total Pt loading of 4.2 microg/cm2. Complete reduction of oxygen by four electrons was achieved with 4 layers of TPPTP-Pt NPs and a total Pt loading of 5.6 microg/cm2. A maximum current density for oxygen reduction was reached with these films after 5 layers resulting in a mass-specific activity, i(m), of 0.11 A/mg(Pt) at 0.9 V. These films feature a high electrocatalytic activity and can be used to create systematic changes in the catalyst chemistry and architecture to provide insight for building better electrocatalysts.     

Robust optimization of contaminant sensor placement for community water systems

We present a series of related robust optimization models for placing sensors in municipal water networks to detect contaminants that are maliciously or accidentally injected. We formulate sensor placement problems as mixed-integer programs, for which the objective coefficients are not known with certainty. We consider a restricted absolute robustness criteria that is motivated by natural restrictions on the uncertain data, and we define three robust optimization models that differ in how the coefficients in the objective vary. Under one set of assumptions there exists a sensor placement that is optimal for all admissible realizations of the coefficients. Under other assumptions, we can apply sorting to solve each worst-case realization efficiently, or we can apply duality to integrate the worst-case outcome and have one integer program. The most difficult case is where the objective parameters are bilinear, and we prove its complexity is NP-hard even under simplifying assumptions. We consider a relaxation that provides an approximation, giving an overall guarantee of near-optimality when used with branch-and-bound search. We present preliminary computational experiments that illustrate the computational complexity of solving these robust formulations on sensor placement applications.     

Raman and surface‐enhanced Raman spectroscopic studies of the 15‐mer DNA thrombin‐binding aptamer

Aptamers are single‐stranded oligonucleotides that selectively bind to their target molecules owing to their ability to form secondary structures and shapes. The 15‐mer (5′‐GGTTGGTGTGGTTGG‐3′) DNA thrombin‐binding aptamer (TBA) binds to thrombin following the formation of a quadruplex structure via the Hoogsten‐type G–G interactions. In the present study, Raman and SERS spectra of TBA and thiolated TBA (used to facilitate covalent bonding to metal nanoparticle) in different conditions are investigated. The spectra of the two analogs exhibit vibrations, such as the C8N7 H2 deformation band at ∼1480 cm⁻¹ of the guanine tetrad, that are characteristic of the quadruplex structure in the presence of K⁺ ions or at low temperature. Interestingly, SERS spectra of the two analogs differ markedly from their respective normal Raman spectra, possibly due to changes in the conformation of the aptamer upon binding, as well as to the specific interaction of individual vibrational modes with the metal surface. In addition, the SERS spectra of the thiolated aptamer show significant changes with different concentrations, which may be due to different orientation of the molecule with respect to the metal surface. This study provides useful information for the development of label‐free aptamer‐based SERS sensors and assays. Copyright © 2009 John Wiley & Sons, Ltd.     

The Emergence of Mathematical Modeling Competencies: An Investigation of Prospective Secondary Mathematics Teachers

A study with prospective teachers without prior mathematical modeling experience sheds light on how their newly developed conceptual understanding of modeling manifested itself in their work on the final task of a modeling module within a pedagogy course in secondary mathematics curriculum and assessment. The main purpose of the module was to provide opportunity for the prospective teachers to experience the Common Core Mathematical Practice Model with Mathematics and begin to develop competency in modeling. Their work and reflections displayed a range of proficiency in several competencies associated with the modeling process. Examples of their work illustrating these ranges are provided. The prospective teachers expressed both struggle and rewards during the process, and reflected on challenges for teaching modeling. The results suggest that infusing modules in existing courses can be an effective way to elevate prospective teachers from unfamiliarity with modeling to noticeable levels of proficiency in various modeling sub-competencies.     

A curve of nilpotent Lie algebras which are not Einstein nilradicals

The only known examples of non-compact Einstein homogeneous spaces are standard solvmanifolds (special solvable Lie groups endowed with a left invariant metric), and according to a long standing conjecture, they might be all. The classification of Einstein solvmanifolds is equivalent to the one of Einstein nilradicals, i.e. nilpotent Lie algebras which are nilradicals of the Lie algebras of Einstein solvmanifolds. Up to now, very few examples of \mathbb N{\mathbb N}-graded nilpotent Lie algebras that cannot be Einstein nilradicals have been found. In particular, in each dimension, there are only finitely many known. We exhibit in the present paper two curves of pairwise non-isomorphic nine-dimensional two-step nilpotent Lie algebras which are not Einstein nilradicals.