Reducibility and nonreducibility between equivalence relations

We show that, for , the relation of -equivalence between infinite sequences of real numbers is Borel reducible to the relation of -equivalence (i.e., the Borel cardinality of the quotient is no larger than that of ), but not vice versa. The Borel reduction is constructed using variants of the triadic Koch snowflake curve; the nonreducibility in the other direction is proved by taking a putative Borel reduction, refining it to a reduction map that is not only continuous but `modular,' and using this nicer map to derive a contradiction.

     

A comparison of T2*-weighted magnitude and phase imaging for measuring the arterial input function in the rat aorta following intravenous injection of gadolinium contrast agent

The arterial input function (AIF) is important for quantitative MR imaging perfusion experiments employing Gd contrast agents. This study compared the accuracy of T(2)*-weighted magnitude and phase imaging for noninvasive measurement of the AIF in the rat aorta. Twenty-eight in vivo experiments were performed involving simultaneous arterial blood sampling and MR imaging following Gd injection. In vitro experiments were also performed to confirm the in vivo results. At 1.89 T and TE=3 ms, the relationship between changes in 1/T(2)* in blood (estimated from MR signal magnitude) and Gd concentration ([Gd]) was measured to be approximately 19 s(-1) mM(-1), while that between phase and [Gd] was approximately 0.19 rad mM(-1). Both of these values are consistent with previously published results. The in vivo phase data had approximately half as much scatter with respect to [Gd] than the in vivo magnitude data (r(2)=.34 vs. r(2)=.17, respectively). This is likely due to the fact that the estimated change in 1/T(2)* is more sensitive than the phase to a variety of factors such as partial volume effects and T(1) weighting. Therefore, this study indicates that phase imaging may be a preferred method for measuring the AIF in the rat aorta compared to T(2)*-weighted magnitude imaging.     

Synthesis and characterization of seven-coordinate tripodal imidazole complexes of iron(II) and manganese(II)

The iron(II) and manganese(II) complexes of the N(7) Schiff-base condensate of tris(3-aminopropyl)amine with 1-methyl-2-imidazolecarbaldehyde and the manganese(II) complex of the N(7) Schiff-base condensate of tris(3-aminopropyl)amine with 4-imidazolecarbaldehyde are high-spin mono capped octahedral seven-coordinate complexes with a short, approximately 2.44 è, metal to apical nitrogen bond.     

Sporolides A and B: structurally unprecedented halogenated macrolides from the marine actinomycete Salinispora tropica

[structure: see text] Analysis of the fermentation broth of a strain of the marine actinomycete Salinispora tropica has led to the isolation of two unprecedented macrolides, sporolides A (1) and B (2). The structures and absolute stereochemistries of both metabolites were elucidated using a combination of NMR spectroscopy and X-ray crystallography.     

Application of glycodiversification: expedient synthesis and antibacterial evaluation of a library of kanamycin B analogues

[reaction: see text] The expedient synthesis of a library of kanamycin B analogues is reported. The revealed SAR will guide future designs in developing kanamycin-type aminoglycoside antibiotics against drug-resistant bacteria.     

Synthesis of readily cleavable immobilized 1,10-phenanthroline resins

1,10-Phenanthroline is derivatized and ultimately immobilized on two different polystyrene/divinylbenzene solid supports using convenient methodology. All syntheses are amenable to semiautomatic processing and are scalable for high-throughput screening. A domino copper-catalyzed coupling-cyclization reaction is used to illustrate applicability in catalytic studies.     

Dynamics of chelation-supercritical fluid extraction from wood fibers

The dynamics of supercritical fluid extraction (SFE) of the metal content of wood fibers chelated with lithium bis(trifluoroethyl) dithiocarbamate (FDDC) by supercritical (SF) CO2 was investigated experimentally by monitoring the spectra of the eluted metal complex as a function of time. The characteristic shape of the dynamic SFE curve was determined mainly by the flow conditions in the extraction vessel, the mass transfer resistance in the SF phase, and the solubility. High extraction yields of metal content were obtained in two-stage extraction including static (batch) and dynamic (semi-batch) stages. Increasing the length of the static stage increased the rate of dynamic elution of metal complex until it approached the dynamics of fluid displacement for a continuous stirred tank reactor (CSTR). In such cases, increasing the flow rate had no effect on the dynamic extraction curve when it was plotted using dimensionless time. Efficient chelation-SFE from wood fibers was obtained at a pressure of 20.3 MPa and with a static time of 30 min.     

All frame-spun knots are slice

Frame-spun knots are constructed by spinning a knot of lower dimension about a framed submanifold of . We show that all frame-spun knots are slice (null-cobordant).

     

Experimental implementation of an adiabatic quantum optimization algorithm

We report the realization of a nuclear magnetic resonance computer with three quantum bits that simulates an adiabatic quantum optimization algorithm. Adiabatic quantum algorithms offer new insight into how quantum resources can be used to solve hard problems. This experiment uses a particularly well-suited three quantum bit molecule and was made possible by introducing a technique that encodes general instances of the given optimization problem into an easily applicable Hamiltonian. Our results indicate an optimal run time of the adiabatic algorithm that agrees well with the prediction of a simple decoherence model.     

To fold or to assemble?

We introduce a new class of foldable oligomers consisting of alternating rigid and flexible regions. The rigid segments overlap to give pi-stacked folded conformers whose formation is driven mostly by pi-pi molecular orbital overlaps. As the oligomer concentration increases, the folded molecular structures further self-assemble into larger nanostructures. The dynamic processes of folding and self-organization are monitored with absorption, fluorescence, and NMR spectroscopies. Our results show that folding dominates at low concentrations (< approximately 1 mM) and precedes self-assembly, which occurs over the initial concentration range of approximately 1-100 mM.