The universe constructed from a sequence of ordinals

We prove that if where is an -sequence of ordinals then the GCH holds. Received January 1, 1993     

Chemical repercussions of orbital interactions through bond and through space. Effect of remote substituents on the addition of nitrenes to bicyclic olefins

The reactivity of a series of bicyclic olefins with nitrenes is profoundly influenced by the nature of remote functional groups. There is a marked lack of reactivity for reactions with carboethoxynitrene as compared to phthalimidonitrene which is distinctly nucleophilic in character. An explanation for the reluctance to form aziridines is offered in terms of orbital interactions between the distant groups and the olefinic bond, making the latter remarkably electron deficient as evidenced by UV-photoelectron spectrosoopy. Because of the complexity of the spectra, identification of the Ip associated with the reactive π-centre was made by recourse to ab initio configuration interaction calculations for key members of the series.     

Internal energy transfer in laser desorption/ionization from silicon nanowires

Laser-induced desorption/ionization from silicon nanowires (SiNW) is an emerging method for mass spectrometry of small to medium-size molecules. In this new technique, we examined the internal energy transfer to seven benzylpyridinium thermometer ions and extracted the corresponding internal energy distributions. To explore the effect of the energy-deposition rate on the internal energy transfer, two lasers with significantly different pulse lengths (4 ns vs 22 ps) were utilized as excitation sources. A comparison of ion yields indicated that the SiNW substrates required 5-8 times less laser fluence for ion production than either matrix-assisted laser desorption/ionization (MALDI) or desorption/ionization on silicon (DIOS). In contrast however, the survival yield (SY) values showed that the internal energy transferred to the thermometer ions was more than (ps laser) or comparable to (ns laser) MALDI but it was significantly less than in DIOS. The internal energy transfer was only slightly dependent on laser fluence and on wire density. These effects were rationalized in terms of the confinement of thermal energy in the nanowires and of unimpeded three-dimensional plume expansion. Unlike in MALDI from CHCA and in perfluorophenyl-derivatized DIOS, for desorption from SiNWs the effect of laser pulse length on the internal energy transfer was found to be negligible.     

Direct probing of sorbent-solvent interactions for amylose tris(3,5-dimethylphenylcarbamate) using infrared spectroscopy, X-ray diffraction, solid-state NMR, and DFT modeling

The sorbent-solvent interactions for amylose tris(3, 5-dimethylphenylcarbamate) (ADMPC) with five commonly used solvents, hexane, methanol, ethanol, 2-propanol (IPA), and acetonitrile (ACN), are studied using attenuated total reflection infrared spectroscopy (ATR-IR) of thin sorbent films, X-ray diffraction (XRD) of thin films, (13)C cross polarization/magic angle spinning (CP/MAS) and MAS solid state NMR of polymer-coated silica beads (commercially termed "Chiralpak AD"), and DFT modeling. The ADMPC-polymer-coated silica beads are used commercially for analytical and preparative scale separations of chiral enantiomers. The polymer forms helical rods with intra- and inter-rod hydrogen bonds (H-bonds). There are various nm-sized cavities formed between the polymer side-chains and rods. The changes in the H-bonding states of the C=O and NH groups of the polymer upon absorption of each of the five solvents at 25 degrees C are determined with ATR-IR. The IR wavenumbers, the H-bonding interaction energies, and the H-bonding distances of the polymer side-chains with each of the solvent molecules are predicted using the DFT/B3LYP/6-311+g(d,p) level of theory. The changes in the polymer crystallinity upon absorption of each solvent are characterized with XRD. The changes in the polymer crystallinity and the H-bonding states of C=O groups are also probed with (13)C CP/MAS solid-state NMR. The changes in the polymer side-chain mobility are detected using (13)C MAS solid-state NMR. The H-bonding states of the polymer change upon absorption of each polar solvent and usually result in an increase in the polymer crystallinity and the side-chain mobility. The polymer rods are reorganized upon solvent absorption, and the distance between the rods increases with the increase in the solvent molecular size. These results have implications for understanding the role of the solvent in modifying the structure and behavior of the polymer sorbents.     

Polyhydroxy fullerenes

Characterization of C₆₀ polyhydroxyfullerenes (PHF) prepared in alkaline media, preparation facilitated by phase-transfer catalyst, presents challenges in determining the chemical structure resulting from the possibility of multiple isomers or analogs with greater or fewer hydroxyl groups from a single reaction mixture. This paper presents the utilization of analytical methods employed in tandem, especially X-ray photoelectron spectroscopy, nuclear magnetic resonance spectroscopy, Fourier transform infrared spectroscopy for semi-quantitative analysis on the number of hydroxyl groups present in PHF. Capillary Electrophoresis was used for purity estimation of the material. Multiple spectra and electropherograms were analyzed using a new simultaneous curve fitting method. The most accurate estimate of hydroxyl groups for C₆₀ polyhydroxy fullerenes obtained is between 16 and 18 allylic hydroxyl groups by combining analytical methods’ results with 5 % accuracy. High precision (reproducibility) of the experiments is observed. Purity of 98 % is estimated by capillary electrophoresis. The size of PHF nanoparticles or aggregates has been determined by atomic force microscopy to be 7.4–14.2 nm. According to the elemental analysis the average probable empirical formula for the most pure PHF at pH 7.1 is C₆₀O₁₇H₁₂Na₅(NaHCO₃)₃(H₂O)₁₃ and the average formula weight is 1,605.9 g/mol. This is the first thorough characterization of PHF in terms of purity.