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.     

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.     

A velocity program using the Kanade–Lucas–Tomasi feature-tracking algorithm with demonstration for pressure and electroosmosis conditions

Investigating microfluidic flow profiles is of interest in the microfluidics field for the determination of various characteristics of a lab-on-a-chip system. Microparticle tracking velocimetry uses computational methods upon recording video footage of microfluidic flow to ultimately visualize motion within a microfluidic system across all frames of a video. Current methods are computationally expensive or require extensive instrumentation. A computational method suited to microparticle tracking applications is the robust Kanade–Lucas–Tomasi (KLT) feature-tracking algorithm. This work explores a microparticle tracking velocimetry program using the KLT feature-tracking algorithm. The developed program is demonstrated using pressure-driven and EOF and compared with the respective mathematical fluid flow models. An electrostatics analysis of EOF conditions is performed in the development of the mathematical using a Poisson's Equation solver. This analysis is used to quantify the zeta potential of the electroosmotic system. Overall, the KLT feature-tracking algorithm presented in this work proved to be highly reliable and computationally efficient for investigations of pressure-driven and EOF in a microfluidic system.     

Synthesis and Characterization of Polymers Derived from the Copolymerization of 1,1′-Dihydroxyethyl-2,2′-Biimidazole and the Diglycidyl Ether of Bisphenol A

Abstract

1,1′-Dihydroxyethyl-2,2′-biimidazole has been used as a copolymerizing monomer with the diglycidyl ether of bisphenol A in the preparation of biimidazole-containing epoxy polymers. Polymerization reactions were studied in bulk, with and without catalyst, and in N,N-dimethylforma-mide and anisole solvents, with and without catalyst. FT-IR and NMR spectra, molecular weight, thermal and solubility characteristics were obtained. Polymers isolated as amorphous light brown solids were found to be only sparingly soluble in THF or in highly polar nitrogen-containing solvents (DMF, NMP, pyridine). These materials exhibited molecular weights up to 37 000 for SnC1₄-catalyzed polymerization carried out in DMF. A glass-transition temperature of 391°C was observed for polymers obtained under uncatalyzed solventless conditions. The glass transition temperature was 373°C for product obtained under SnC1₄-catalyzed, solventless conditions. Thermogravimetric analysis in air of polymers obtained under varying solvent and catalyst conditions showed less than 25% weight loss below 330°C and greater than 75% weight loss above 400°C.