Couplings and Strong Approximations to Time-Dependent Empirical Processes Based on I.I.D. Fractional Brownian Motions

We define a time-dependent empirical process based on n i.i.d. fractional Brownian motions and establish Gaussian couplings and strong approximations to it by Gaussian processes. They lead to functional laws of the iterated logarithm for this process.     

Equivalent linearization for systems subjected to non-stationary random excitation

The method of eauivalent linearization is applied to the general problem of the response of non-linear discrete systems to non-stationary random excitation. Conditions for minimum equation difference are determined which do not depend explicitly on lime but only on the instantaneous statistics of the response process. Using the equivalent linear parameters, a deterministic non-linear ordinary differential equation for the covariance matrix is derived. An example is given of a damped Duffing oscillator subjected to modulated white noise.     

An efficient synthesis of highly functionalized chiral lactams

A new method was developed to synthesize highly functionalized lactams via a one pot reductive amination/lactam formation reaction. This methodology is amenable for parallel synthesis and was used to prepare a large number of lactam analogs in a library format with good ee (de) retention.     

Shear-induced disruption of dense nanoemulsion gels

The structural evolution and rheology of dense nanoemulsion gels, which have been formed by creating strong attractions between slippery nanodroplets, are explored as a function of steady shear rate using rheological small-angle neutron scattering (rheo-SANS). For applied stresses above the yield stress of the gel, the network yields, fracturing into aggregates that break and reform as they tumble and interact in the shear flow. The average aggregate size decreases with increasing shear rate; meanwhile, droplet rearrangements within the clusters, allowed by the slippery nature of the attractive interaction, increase the local density within the aggregates. At the highest shear rates, all clusters disaggregate completely into individual droplets.     

Synthesis of a library of oligothiophenes and their utilization as fluorescent ligands for spectral assignment of protein aggregates

Molecular probes for selective identification of protein aggregates are important to advance our understanding of the molecular pathogenesis underlying protein aggregation diseases. Here we report the chemical design of a library of anionic luminescent conjugated oligothiophenes (LCOs), which can be utilized as ligands for detection of protein aggregates. Certain molecular requirements were shown to be necessary for detecting (i) early non-thioflavinophilic protein assemblies of Aβ1-42 and insulin preceding the formation of amyloid fibrils and (ii) for obtaining distinct spectral signatures of the two main pathological hallmarks observed in human Alzheimer's diease brain tissue (Aβ plaques and neurofibrillary tangles). Our findings suggest that a superior anionic LCO-based ligand should have a backbone consisting of five to seven thiophene units and carboxyl groups extending the conjugated thiophene backbone. Such LCOs will be highly useful for studying the underlying molecular events of protein aggregation diseases and could also be utilized for the development of novel diagnostic tools for these diseases.     

Synthesis of 6-substituted-4-hydroxy-2-pyridinones via intramolecular ketene trapping of functionalized enamine-dioxinones

The synthesis of various 6-substituted-4-hydroxy-2-pyridinones is reported. The functionalized keto-dioxinones were constructed via a diethylzinc mediated crossed Claisen condensation reaction and subsequent enamine formation, thermolysis, and cyclization-aromatization providing the pyridinone unit.     

A sulfone-based strategy for the preparation of 2,4-disubstituted furan derivatives

2,4-Disubstituted furans are prepared by treating 2,3-dibromo-1-phenylsulfonyl-1-propene (DBP, 2) with 1,3-diketones under basic conditions. The furan-forming step involves a deacetylation, and the selectivity of this process depends upon the steric demand of the R group. The substituent in position 4 is elaborated by reaction of sulfonyl carbanions with alkyl halides, acyl halides, and aldehydes. Oxidative or reductive desulfonylation produces the 2,4-disubstituted furans in 60-92% yield. This strategy has been used to prepare rabdoketone A (12) and the naturally occurring nematotoxic furoic acid 13.     

Linking [Fe(III)3] triangles with "double-headed"phenolic oximes

The use of "double-headed" phenolic oximes produces a trigonal antiprismatic [Fe(III)(3)](2) cluster with an "internal cavity" filled with an additional Fe(3+) ion. Magnetic measurements reveal that the competition between different exchange interactions leads to a low-spin ground multiplet weakly separated in energy from a complex pattern of low-lying excited levels.     

Probing interactions in exploratory teaching: a case study

This study investigates an exploratory teaching style used in an undergraduate geometry course to help students identify an ellipse. We attempt to probe beneath the surface of exploration to understand how the actions of teachers can contribute to developing students’ competence in justifying an ellipse. We analyse the complex interactions between student, content, and teacher, and discuss explicit pedagogical strategies that help students develop a higher level of geometric reasoning. The findings indicate that students engaged in guided explorations by the teacher and in group discussions with peers were able to identify an ellipse and justify their reasoning.