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.     

Additions of enantiopure alpha-sulfinyl carbanions to (S)-N-sulfinimines: asymmetric synthesis of beta-amino sulfoxides and beta-alphamino alcohols

The addition of the lithium anions derived from (R)- and (S)-methyl and -ethyl p-tolyl sulfoxides to (S)-N-benzylidene-p-toluenesulfinamide provides an easy access route to enantiomerically pure beta-(N-sulfinyl)amino sulfoxides. Stereoselectivity can be achieved when the configurations at the sulfur atoms of the two reagents are opposite (matched pair), thus resulting in only one diastereoisomer, even for the case in which two new chiral centers are created. The N-sulfinyl group primarily controls the configuration of the carbon bonded to the nitrogen, whereas the configuration of the alpha-sulfinyl carbanion seems to be responsible for the level of asymmetric induction, as well as for the configuration of the new stereogenic C-SO carbon in the reactions with ethyl p-tolyl sulfoxides. An efficient method for transforming the obtained beta-(N-sulfinyl)amino sulfoxides into optically pure beta-amino alcohols, based on the stereoselective non-oxidative Pummerer reaction, is also reported.     

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.     

(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.     

α-CGRP disrupts amylin fibrillization and regulates insulin secretion: implications on diabetes and migraine

Despite being relatively benign and not an indicative signature of toxicity, fibril formation and fibrillar structures continue to be key factors in assessing the structure–function relationship in protein aggregation diseases. The inability to capture molecular cross-talk among key players at the tissue level before fibril formation greatly accounts for the missing link toward the development of an efficacious therapeutic intervention for Type II diabetes mellitus (T2DM). We show that human α-calcitonin gene-related peptide (α-CGRP) remodeled amylin fibrillization. Furthermore, while CGRP and/or amylin monomers reduce the secretion of both mouse Ins1 and Ins2 proteins, CGRP oligomers have a reverse effect on Ins1. Genetically reduced Ins2, the orthologous version of human insulin, has been shown to enhance insulin sensitivity and extend the life-span in old female mice. Beyond the mechanistic insights, our data suggest that CGRP regulates insulin secretion and lowers the risk of T2DM. Our result rationalizes how migraine might be protective against T2DM. We envision the new paradigm of CGRP : amylin interactions as a pivotal aspect for T2DM diagnostics and therapeutics. Maintaining a low level of amylin while increasing the level of CGRP could become a viable approach toward T2DM prevention and treatment.

CGRP concentration is elevated in migraine conditions. The protective effect of migraine against type 2 diabetes is attributed to the ability of CGRP to remodel human amylin aggregation and to suppress the secretion of mouse insulin 2 (the orthologue of human insulin).     

Heteroatom derivatives of indene: V. Vibrational spectra of benzimidazole

Infrared and Raman measurements for benzimidazole are presented and discussed, including its argon-matrix infrared spectrum. To assist in the assignment, benzimidazole's harmonic force fields for the 321G* and 631G* levels were scaled by scaled factors derived by fitting the respective computed force fields of other indene derivatives to previously reported experimental vibrational frequencies. Comparison to the best set of experimental wavenumbers, usually taken from the matrix, shows mean 321G* and 631G* deviations of 7.0 and 5.8 cm⁻¹ for the planar modes, and 14.0 and 6.8 cm⁻¹ for the nonplanar modes, respectively, with much of the error residing in imino-hydrogen group modes. Standard entropies are derived with the matrix wavenumbers and the methods of statistical mechanics. An attempt to determine standard entropies by calorimetric methods was unsuccessful. The triple-point temperature T_tp and enthalpy of fusion Δ¹_crH_m only are reported.     

Enantiomerically pure alpha-amino acid synthesis via hydroboration-suzuki cross-coupling

The Garner aldehyde-derived methylene alkene 5 and the corresponding benzyloxycarbonyl compound 25 undergo hydroboration with 9-BBN-H followed by palladium-catalyzed Suzuki coupling reactions with aryl and vinyl halides. After one-pot hydrolysis-oxidation, a range of known and novel nonproteinogenic amino acids were isolated as their N-protected derivatives. These novel organoborane homoalanine anion equivalents are generated and transformed under mild conditions and with wide functional group tolerance: electron-rich and -poor aromatic iodides and bromides (and a vinyl bromide) all undergo efficient Suzuki coupling. The extension of this methodology to prepare meso-DAP, R,R-DAP, and R,R-DAS is also described.