Asymptotic Lower Bound for the Relative Disparities of Truncated-Path-Integral Partition Functions

Any truncated-path-integral partition function of a nonrelativistic quantum system in thermodynamic equilibrium—one obtained by means of the Feynman path-integral-procedure using a finite number of such integrals—is known to have a value not less than that of the exact one corresponding to it. A rigorous asymptotic lower bound obtained for the relative disparity in their values—the difference in their values divided by that of the exact partition function— confirms asymptotic positive-definiteness of the original upper bound. Values determined directly for a linear harmonic oscillator agree asymptotically with values of they bound.     

Preparation and Electrophilic Substitution of 1-Trimethylsilylpentadienyllithium

Pentadienyllithium (16) was regioselectively and efficiently transformed to 1-trimethylsilyl-2,4-pentadiene (17) by reaction with chlorotrimethylsilane (Scheme 5). Deprotonation of 17 and subsequent electrophilic attack furnished the regioisomeric products 12 and/or 13 in good yields (Schemes 5 and 6). The utility of the reaction 18 → 12 for the convergent assembly of the 1-silyl-1,3-butadiene unit with an olefinic dienophile is further illustrated by the smooth intramolecular Diels-Alder reaction 19 → 20 .     

Promoting effect of ionic liquids on ligand substitution reactions

Ionic liquid solvents N-hexylpyridinium bistrifylimide ([C₆pyr][Tf₂N]] and 1-butyl-3-methylimidazolium hexafluorophosphate ([C₄mim][PF₆]) promoted the displacement of anionic ligands by pyridine derivatives in trans-(Ph₃P)₂Rh(CO)NO₃ to a much greater extent than did dichloromethane. Thus, addition of a slight excess of 2-fluoropyridine to trans-(Ph₃P)₂Rh(CO)NO₃ in [C₄mim][PF₆] gave a 29:71 product mixture of trans-(Ph₃P)₂Rh(CO)NO₃:[trans-(Ph₃P)₂Rh(CO)(2-fluoropyridine)][NO₃], while the ratio was 91:9 in dichloromethane.     

REMARKABLE INHIBITION OF OXYGEN QUENCHING OF PHOSPHORESCENCE BY COMPLEXATION WITH CYCLODEXTRINS

The phosphorescence of the 4-bromo-l-naphthoyl group is readily quenched by molecular oxygen in homogeneous solvents. However, when this lumophore is complexed with γ-cyclodextrin in aqueous solution at room temperature, its phosphorescence is observed even under 1 atm of oxygen! Phosphorescence decay data indicated that two types of probe/cyclodcxtrin complexes are formed with lifetimes of 600 u,s and 3.5 ms. Oxygen completely quenches the fast decay, but only partially quenches the slow decay.     

Oxidative C-C bond-forming reaction of electron-rich alkylbenzyl ether with trimethylvinyloxysilane

Treatment of an electron-rich benzyl ether with DDQ at ambient temperature followed by addition of a silyl enol ether undergoes a C-C bond-forming reaction to afford 3-alkoxy-3-phenyl-propionyl compound. This is a general reaction and works well with a variety of silyl enol ethers to give carbonyl products in yields ranging from 10 to 85%.     

Improved methods for 1H-3H heteronuclear shift correlation

A better understanding of the structure of complex 3H-labeled molecules can be obtained by complete assignment of their 1H and 3H solution-state NMR spectra. The assignment process is aided by the detection of heteronuclear chemical shift correlations between 1H and 3H nuclei. Heteronuclear correlation (HETCOR) experiments previously applied to this task exhibit several drawbacks caused by the nature of both the pulse sequences and 1H-3H spin systems. The range of J-couplings involved in 1H-3H coupling networks make it challenging to perform correlation experiments using methods that rely on coherences created during free precession periods and interrupted by transfer pulses. Two alternative HETCOR experiments are demonstrated for 1H-3H systems in the present work and are shown to have advantages over earlier methods. The first experiment is known as hetero-TOCSY and correlates heteronuclear chemical shifts using J-cross polarization. This experiment achieves both homonuclear and heteronuclear mixing and connects the chemical shifts of all 1H and 3H nuclei in a coupling network. A second HETCOR experiment uses the heteronuclear Overhauser effect to obtain through-space correlations between nearby nuclei. The 1H-3H HETCOR experiments are phase sensitive and typically contain more correlations than other methods, which is beneficial for assignment purposes, while being sensitive enough to be applicable to routine analytical samples. The experiments were used to analyze 3H incorporation in sub-milligram quantities of 3H-labeled pharmaceutical derivatives with complex labeling schemes.     

Development and validation of a high-throughput double solid phase extraction-liquid chromatography-tandem mass spectrometry method for the determination of tetrodotoxin in human urine and plasma

A sensitive analytical method for the determination of tetrodotoxin (TTX) in urine and plasma matrices was developed using double solid phase extraction (C18 and hydrophilic interaction liquid chromatography) and subsequent analysis by HPLC coupled with tandem mass spectrometry. The double SPE sample cleanup efficiently reduced matrix and ion suppression effects. Together with the use of ion pair reagent in the mobile phase, isocratic elution became possible which enabled a shorter analysis time of 5.5 min per sample. The assay results were linear up to 500 ng mL⁻¹ for urine and 20 ng mL⁻¹ for plasma. The limit of detection and limit of quantification were 0.13 ng mL⁻¹ and 2.5 ng mL⁻¹, respectively, for both biological matrices. Recoveries were in the range of 75-81%. To eliminate the effect of dehydration and variations in urinary output, urinary creatinine-adjustment was made. TTX was quantified in eight urine samples and seven plasma samples from eight patients suspected of having TTX poisoning. TTX was detected in all urine samples, with concentrations ranging from 17.6 to 460.5 ng mL⁻¹, but was not detected in any of the plasma samples. The creatinine-adjusted TTX concentration in urine (ranging from 7.4 to 41.1 ng μmol⁻¹ creatinine) correlated well with the degree of poisoning as observed from clinical symptoms.     

What becomes of global color

The recent demise of certain global unbroken symmetry generators in the presence of a grand unified magnetic monopole leads us to consider more carefully the notion of charges associated with gauge symmetries. It turns out that global transformations associated with the generators of the gauge group, and their charges, make sense only for extended systems which are sufficiently localized. GUT monopoles fail this criterion. Detailed consideration of the monopole-antimonopole system helps remove apparent paradoxes related to the chromodyon excitations of a single monopole and agrees with the previous result that some, but not all, of the states naively expected do exist. The remaining states ns needed to fill out color multiplets are spread throughout space; they are recovered as long-lived excitations when an antimonopole is brought in from infinity.     

Aluminoxane–epoxi–siloxane hybrids waveguides

Boehmite–GPTS (GPTS-glycidoxypropyltrimethoxysilane) hybrids (BGS) have been prepared by the sol–gel methodology. Spectroscopic properties and structural features have been evaluated from the initial sols to xerogels as a function of composition. Eu³⁺-containing BGS samples were also prepared, and the Eu^{3+ 5}D₀ state emission quantum efficiency was observed to depend on the boehmite–siloxane interactions. Boehmite–siloxane heterocondensation was inferred from vibrational spectroscopy and ¹³C, ²⁹Si, and ²⁷Al nuclear magnetic resonance results. Unreacted epoxi groups could be identified in the final material being an important characteristic for the future applications. Good optical quality and mechanical properties lead to the preparation of thin films deposited on glass substrates by dip and spin-coating. Refractive index could be tuned by the relative boehmite and GPTS content. Waveguide properties have also been studied by m-lines spectroscopy and guided modes together with attenuation measurements suggest potential application of the prepared films in integrated optics.     

Evaluation of laser level populations of erbium-doped glasses

A simulation of erbium-doped glass systems, which provides population density for the excited states involved in the 1.5 μm and also for 2.7 μm emissions when pumped around 980 nm, is presented. To describe the diode pump laser processes, a theoretical model based in a coupled system of differential rate equations was developed. The approach used and the obtained spectroscopic parameters are discussed. The materials under study are two oxide glasses, lead fluoroborate (PbO-PbF₂-B₂O₃), and heavy metal oxide (Bi₂O₃-PbO-Ga₂O₃) and a fluoride glass (ZrF₄-BaF₂-LaF₃-AlF₃-NaF), all of them doped with Er³⁺.