Counting the number of solutions in combustion and reactive flow problems

Summary Computational methods and comparison theory enable, when combined, an enhanced capability for counting the number of solutions in combustion equations. Very good lower bounds for the last turning point reveal a stable high temperature explosion branch for very small positive exothermicity.     

Chemistry and insulin-mimetic properties of bis(acetylacetonate)oxovanadium(IV) and derivatives

The syntheses and the solid state structural and spectroscopic solution characterizations of VO(Me-acac)2 and VO(Et-acac)2 (where Me-acac is 3-methyl-2,4-pentanedionato and Et-acac is 3-ethyl-2,4-pentanedionato) have been conducted since both VO(acac)2 and VO(Et-acac)2 have long-term in vivo insulin-mimetic effects in streptozotocin-induced diabetic Wistar rats. X-ray structural characterizations of VO(Me-acac)2 and VO(Et-acac)2 show that both contain five-coordinate vanadium similar to the parent VO(acac)2. The unit cells for VO(Et-acac)2 and VO(Me-acac)2 are both triclinic, P1, with a = 9.29970(10) A, b = 13.6117(2) A, c = 13.6642(2) A, alpha = 94.1770(10) degrees, beta = 106.4770(10) degrees, gamma = 106.6350(10) degrees for VO(Et-acac)2 and a = 7.72969(4) A, b = 8.1856(5) A, c = 11.9029(6) A, alpha = 79.927(2) degrees, beta = 73.988(2)degrees, gamma = 65.1790(10)degrees for VO(Me-acac)2. The total concentration of EPR-observable vanadium(IV) species for VO(acac)2 and derivatives in water solution at 20 degreesC was determined by double integration of the EPR spectra and apportioned between individual species on the basis of computer simulations of the spectra. Three species were observed, and the concentrations were found to be time, pH, temperature, and salt dependent. The three complexes are assigned as the trans-VO(acac)2.H2O adduct, cis-VO(acac)2.H2O adduct, and a hydrolysis product containing one vanadium atom and one R-acac- group. The reaction rate for conversion of species was slower for VO(acac)2 than for VO(malto)2, VO(Et-acac)2, and VO(Me-acac)2; however, in aqueous solution the rates for all of these species are slow compared to those of other vanadium species. The concentration of vanadium(V) species was determined by 51V NMR. The visible spectra were time dependent, consistent with the changes in species concentrations that were observed in the EPR and NMR spectra. EPR and visible spectroscopic studies of solutions prepared as for administration to diabetic rats documented both a salt effect on speciation and formation of a new halogen-containing complex. Compound efficacy with respect to long-term lowering of plasma glucose levels in diabetic rats traces the concentration of the hydrolysis product in the administration solution.     

A maximization problem and its application to canonical correlation

Let Σ be an n × n positive definite matrix with eigenvalues λ₁ ≥ λ₂ ≥ … ≥ λ_n > 0 and let M = {x, y | x?Rⁿ, y?Rⁿ, x ≠ 0, y ≠ 0, x′y = 0}. Then for x, y in M, we have that $\text{x′Σy}\text{(x′Σxy′Σy)}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{≤}\text{(λ}{}_1\text{? λ}{}_{\mathrm{n}}\text{)}\text{(λ}{}_1\text{+ λ}{}_{\mathrm{n}}\text{)}$ and the inequality is sharp. If

$\text{∑=}\text{∑}{}_{11}\text{∑}{}_{12}\text{∑}{}_{21}\text{∑}{}_{22}$

is a partitioning of Σ, let θ₁ be the largest canonical correlation coefficient. The above result yields $\text{θ}{}_1\text{≤}\text{(λ}{}_1\text{? λ}{}_{\mathrm{n}}\text{)}\text{(λ}{}_1\text{+ λ}{}_{\mathrm{n}}\text{)}$.     

The smoke ion source: a device for the generation of cluster ions via inert gas condensation

We report the development of an ion source for generating intense, continuous beams of both positive and negative cluster ions. This device is the result of the marriage of the inert gas condensation method with techniques for injecting electrons directly into expanding jets. In the preliminary studies described here, we have observed cluster ion size distributions ranging fromn=1?400 for Pb _n ⁺ and Pb _n ^? , and fromn=12?5700 for Li _n ^? .     

Tellurium-mediated cycloaromatization of acyclic enediynes under mild conditions

The cycloaromatization of acyclic enediynes typically requires very high temperatures (>160 degrees C) and dilute conditions to proceed in a synthetically useful yield. These conditions hinder reaction throughput, inhibiting the use of this reaction for the large-scale production of materials. The reaction of sodium telluride with acyclic arenediynes yields the corresponding tellurepine, which under gentle heating extrudes Te degrees to yield the cycloaromatization product. We have developed conditions that form sodium telluride from inexpensive tellurium metal in situ, and that also perform the desilylation of silylated arenediynes in the same process. Under our conditions, we are able to perform desilylation and cycloaromatization at temperatures as low as 40 degrees C and on a scale as large as 5 g in standard laboratory glassware.     

Three-dimensional concentration field measurements in a mixing layer using magnetic resonance imaging

Magnetic resonance imaging (MRI) was used to measure the three-dimensional, time-averaged concentration distribution in a turbulent two-stream mixing layer. Test fluids and MRI scanning parameters were chosen to give good signal linearity, and a calibration/normalization procedure was developed to reduce the concentration measurement uncertainty. Plain deionized water mixing with a solution of 0.8% gadopentetate dimeglumine in deionized water were selected as test fluids. The concentration of the marked water was measured on an array of 220,000 0.69 mm³ voxels covering the entire flow apparatus. Planar laser-induced fluorescence experiments were performed on the flow centerplane to provide validation data. The uncertainty of a single voxel measurement was estimated to be less than 12% with the largest source of uncertainty being turbulent dephasing. Averaging two runs in which the marked water was switched between the two streams reduced the uncertainty to only 4%. The complete magnetic resonance concentration (MRC) procedure including the adjustment of scanning parameters, a background run, two reference/calibration runs, and multiple concentration measurement runs can be completed in 2–3 h. This work establishes MRC as a viable technique for studying the mixing in complex turbulent liquid flows.     

Electron spin relaxation times and rapid scan EPR imaging of pH‐sensitive amino‐substituted trityl radicals

Carboxy‐substituted trityl (triarylmethyl) radicals are valuable in vivo probes because of their stability, narrow lines, and sensitivity of their spectroscopic properties to oxygen. Amino‐substituted trityl radicals have the potential to monitor pH in vivo, and the suitability for this application depends on spectral properties. Electron spin relaxation times T₁ and T₂ were measured at X‐band for the protonated and deprotonated forms of two amino‐substituted triarylmethyl radicals. Comparison with relaxation times for carboxy‐substituted triarylmethyl radicals shows that T₁ exhibits little dependence on protonation or the nature of the substituent, which makes it useful for measuring O₂ concentration, independent of pH. Insensitivity of T₁ to changes in substituents is consistent with the assignment of the dominant contribution to spin lattice relaxation as a local mode that involves primarily atoms in the carbon and sulfur core. Values of T₂ vary substantially with pH and the nature of the aryl group substituent, reflecting a range of dynamic processes. The narrow spectral widths for the amino‐substituted triarylmethyl radicals facilitate spectral‐spatial rapid scan electron paramagnetic resonance imaging, which was demonstrated with a phantom. The dependence of hyperfine splittings patterns on pH is revealed in spectral slices through the image. Copyright © 2014 John Wiley & Sons, Ltd.     

Gold and gold-iron oxide magnetic glyconanoparticles: synthesis, characterization and magnetic properties

The preparation, characterization and the magnetic properties of gold and gold-iron oxide glyconanoparticles (GNPs) are described. Glyconanoparticles were prepared in a single step procedure in the presence of aqueous solution of thiol functionalized neoglycoconjugates and either gold salts or both gold and iron salts. Neoglycoconjugates of lactose and maltose disaccharides with different linkers were used. Iron-free gold or gold-iron oxide GNPs with controlled gold-iron ratios were obtained. The average core-size diameters are in the range of 1.5-2.5 nm. The GNPs are fully characterized by (1)H NMR spectrometry, transmission electron microscopy (TEM), and UV-vis and X-ray absorption (XAS) spectroscopies. Inductive plasma-atomic emission spectrometry (ICP) and elemental analysis gave the average number of neoglycoconjugates per cluster. The magnetic properties were measured in a SQUID magnetometer. The most remarkable results was the observation of a permanent magnetism up to room temperature in the iron-free gold GNPs, that was not present in the corresponding gold-iron oxide GNPs.     

The application of (Z)-3-aryl-3-haloenoic acids to the synthesis of (Z)-5-benzylidene-4-arylpyrrol-2(5H)-ones

Studies directed at the synthesis of (Z)-5-benzylidene-4-arylpyrrol-2(5H)-ones from (Z)-3-aryl-3-haloenoic acids are described. The successful strategy relies on the preparation of (Z)-3-aryl-3-haloenoic acids from acetophenones through the corresponding (Z)-3-aryl-3-haloenals and the conversion of the (Z)-3-aryl-3-haloenoic acids to (Z)-5-benzylidene-4-aryl-5H-furan-2-ones. The furanones were subsequently treated with primary amines and dehydrated to the corresponding (Z)-5-benzylidene-4-arylpyrrol-2(5H)-ones.