Decay of solutions of ordinary differential equations

We investigate the rate of decay of eigenfunctions of Schrödinger equations using a perturbation method which consists of making a perturbation B of the operator L of the form B[y]=L[y]−(g⁻¹Lg)[y], where g is an appropriately chosen function. In our theory we allow B to be either relatively compact or satisfy a certain boundedness condition. We give some examples which apply the results of our main theorems coupled with recent work on the relative boundedness and compactness of differential operators.     

Characterization of partially transesterified poly(beta-hydroxyalkanoate)s by matrix-assisted laser desorption/ionization time-of-flight mass spectrometry

Matrix-assisted laser desorption/ionization time-of-flight mass spectrometry (MALDI-TOFMS) was used for the characterization of a partially transesterified poly(beta-hydroxyalkanoate) (PHA), a polymer produced by the bacterial strain Alcaligenes eutrophus with saponified vegetable oils as the sole carbon sources. The transesterification was carried out separately under acidic and basic conditions to obtain PHA oligomers weighing <10 kDa. The intact oligomers were detected in their cationized forms, [M + Na]+ and [M + K]+, by MALDI-TOFMS. A composition analysis, using the MALDI-TOF spectra, indicated that the oligomers obtained via acid catalysis contained a methyl 3-hydroxybutyrate end group, and those obtained by base catalysis had a methyl crotonate (olefinic) end group. In addition to hydroxybutyrate (HB), the oligomers were found to contain a small percentage of hydroxyvalerate, which was independently confirmed by gas chromatography/mass spectrometry. In comparison, analysis of a commercial PHA polymer, transesterified under identical conditions, showed only the presence of HB, i.e., a pure poly(HB) homopolymer.     

Synthesis and characterization of new 1,1′-diester,diketone, and dinitrile derivatives of 2,2′-biimidazole

Substituted 1,1′-diester, diketone and dinitrile derivatives are prepared from 2,2′-biimidazole. The reactions involved include: Michael addition with halogenated olefins; nucleophilic substitution with ketones, nitriles, and esters; and condensation with amines.     

Luminescence spectroscopy of matrix-isolated z 6P state atomic manganese

The relaxation of electronically excited atomic manganese isolated in solid rare gas matrices is observed from recorded emission spectra, to be strongly site specific. z 6P state excitation of Mn atoms isolated in the red absorption site in Ar and Kr produces narrow a 4D and a 6D state emissions while blue-site excitation produces z 6P state fluorescence and broadened a 4D and a 6D emissions. MnXe exhibits only a single thermally stable site whose emission at 620 nm is similar to the broad a 6D bands produced with blue-site excitation in Ar and Kr. Thus in Ar(Kr), excitation of the red site at 393 (400) nm produces narrow line emissions at 427.5 (427.8) and 590 (585.7) nm. From their spectral positions, linewidths, and long decay times, these emission bands are assigned to the a 4D72 and a 6D92 states, respectively. Excitation of the blue site at 380 (385.5) nm produces broad emission at 413 (416) nm which, because of its nanosecond radiative lifetime, is assigned to resonance z 6P --> a 6S fluorescence. Emission bands at 438 (440) and 625 (626.8) nm, also produced with blue-site excitation, are broader than their red-site equivalents at 427.5 and 590 nm (427.8 and 585.7 nm in Kr) but from their millisecond and microsecond decay times are assigned to the a 4D and a 6D states. The line features observed in high resolution scans of the red-site emission at 427.5 and 427.8 nm in MnAr and MnKr, respectively, have been analyzed with the W(p) optical line shape function and identified as resolved phonon structure originating from very weak (S=0.4) electron-phonon coupling. The presence of considerable hot-phonon emission (even in 12 K spectra) and the existence of crystal field splittings of 35 and 45 cm(-1) on the excited a 4D72 level in Ar and Kr matrices have been identified in W(p) line shape fits. The measured matrix lifetimes for the narrow red-site a 6D state emissions (0.29 and 0.65 ms) in Ar and Kr are much shorter than the calculated (3 s) gas phase value. With the lifetime of the metastable a 6D92 state shortened by four orders of magnitude in the solid rare gases, it is clear that the probability of the "forbidden" a 6D --> a 6S atomic transition is greatly enhanced in the solid state. A novel feature identified in the present work is the large width and shifted 4D and 6D emissions produced for Mn atoms isolated in the blue sites of Ar and Kr. In contrast, these states produce narrow, unshifted (gas-phase-like) 4D and 6D state emissions from the red site.     

Immobilizing a Fluorescent Dye Offers Potential to Investigate the Glass/Resin Interface

Silane coupling agents are commonly applied to glass fibers to promote fiber/resin adhesion and enhance durability in composite parts. In this study, a coupling agent multilayer on glass was doped with trace levels of the dimethylaminonitrostilbene (DMANS) fluorophore. The fluorophore was immobilized on the glass surface by tethering the molecule to a triethoxy silane coupling agent, creating the DMANS/silane coupling agent molecule (DMSCA). DMSCA was then diluted with commonly used coupling agents and grafted to a glass microscope coverslip to create a model composite interface. A 53-nm blue shift in fluorescence from the immobilized DMSCA can be followed during cure of an epoxy resin overlayer, giving this technique potential to monitor the properties of the fiber/resin interface during composite processing. Contact angle measurements on these coupling agent layers were similar in the presence or absence of the DMSCA molecule, suggesting that trace levels of the fluorescent probe did not affect the structure of the layer. The immobilized DMSCA molecule behaved similarly to the DMANS precursor in solution. Both showed longer wavelength fluorescence in more polar environments. Copyright 2000 Academic Press.     

(Z)-3-p-tolylsulfinylacrylonitrile as a chiral dienophile: diels-alder reactions with furan and acyclic dienes

The behavior of (Z)-3-p-tolylsulfinylacrylonitrile (1) as a chiral dienophile has been evaluated from its reactions with furan and acyclic dienes. Electrostatic interactions of the cyano group with the sulfinyl one restrict the conformational mobility around the C-S bond, thus controlling the pi-facial selectivity, which is almost complete in all cases, the approach of the diene from the less-hindered face of the dienophile (that bearing the lone electron pair) in the predominant rotamer being the favored one. The regioselectivity is also completely controlled by the cyano group. Additionally, the reactivity of compound 1 as well as its endo-selectivity are both higher than those observed for the corresponding (Z)-3-sulfinylacrylates, thus proving the potential of sulfinylnitriles as chiral dienophiles.