An Explicit Derivation of the Möbius Function for Bruhat Order

We give an explicit nonrecursive complete matching for the Hasse diagram of the strong Bruhat order of any interval in any Coxeter group. This yields a new derivation of the Möbius function, recovering a classical result due to Verma.     

Temperature and composition dependent structural investigation of the defect perovskite series Sr1−xTi1−2xNb2xO3, 0≤x≤0.2

The crystal structure of the defect perovskite series Sr_1−xTi_1−2xNb_2xO₃ has been investigated over a range of temperatures using high-resolution synchrotron X-ray diffraction, neutron diffraction and electron diffraction. Three distinct regions were observed: 0<x≤0.125 was a solid solution of Sr_1−xTi_1−2xNb_2xO₃ with minor SrTiO₃ intergrowth, 0.125<x≤0.2 was a pure Sr_1−xTi_1−2xNb_2xO₃ solid solution adopting the cubic perovskite type structure (Pm3¯m) and for x>0.2 Sr_0.8Ti_0.6Nb_0.4O₃ and Sr₃TiNb₄O₁₅ formed a two phase region. The cubic structure for Sr_0.8Ti_0.6Nb_0.4O₃ was stable over the temperature range 90-1248 K and the thermal expansion co-efficient was determined to be 8.72(9)×10⁻⁶ K⁻¹. Electron diffraction studies revealed diffuse scattering due to local scale Ti/Nb displacements and slightly enhanced octahedral rotations that did not lead to long range order. The octahedral rotations were observed to ‘lock-in’ at temperatures below ∼75 K resulting in a tetragonal structure (I4/mcm) with anti-phase octahedral tilting about the c-axis.     

Fabrication of catalyst-coated membrane by modified decal transfer technique

A decal transfer method based on colloidal ink was developed for the fabrication of membrane electrode assemblies (MEAs). The new method requires fewer steps and utilizes H⁺ form of membrane compared to conventional decal method based on solution ink utilizing Na⁺ form of membrane. The structural features of the electrodes made by the modified decal method were investigated by scanning electron microscopy (SEM). The performance of fabricated electrode was evaluated for oxygen reduction reaction in a proton exchange membrane fuel cell. The results indicate that the modified decal method has the potential to be a facile method of fabricating electrodes with high performance.     

Synthesis of orthogonally protected (R)- and (S)-2-methylcysteine via an enzymatic desymmeterization and Curtius rearrangement

A synthesis of differentially protected (R)- and (S)-2-methylcysteines is described. Monomethylation of dimethylmalonate followed by alkylation with tert-butylchloromethyl sulfide gave an achiral diester. Desymmeterization by selective hydrolysis of one ester with pig-liver esterase gave the acid in 97% chemical yield and 91% enantiomeric excess. Heating this acid with diphenylphosphoryl azide followed by 4-methoxybenzyl alcohol gave protected (R)-2-methylcysteine. Alternately, the acid and ester groups were interchanged and heated with diphenylphosphoryl azide followed by 4-methoxybenzyl alcohol, giving protected (S)-2-methylcysteine.     

Reactivity of nitrovinylquinones with cyclic and acyclic enol ethers

The nitrovinyl-substituted quinones 2-(2-nitrovinyl)-1,4-benzoquinone and 2-(2-nitrovinyl)-1,4-naphthoquinone react with a variety of cyclic and acyclic enol ethers via two competing pathways. In one pathway, the nitrovinylquinone acts as an inverse electron-demand [4 + 2] diene. This gives quinoid carbocycles, which readily tautomerize to their hydroquinone form. The other pathway involves conjugate (Michael) addition of the enol ether to the nitrovinylquinone, followed by ring closure. This gave dihydrobenzofurans, which can eliminate an alcohol to give benzofurans. Hindered enol ethers tended to favor the conjugate addition pathway, while less hindered enol ethers favored cycloaddition.     

Exo-selective Diels-Alder reactions of vinylazepines. Origin of divergent stereoselectivity in Diels-Alder reactions of vinylazepines, vinylpiperideines, and vinylcycloalkenes

Diels-Alder reactions of vinylazepines with N-phenylmaleimide afforded exclusively the exo cycloadduct, while high endo stereoselectivity was observed, as previously reported, in analogous reactions of vinylpiperideines. This curious contrast was confirmed by X-ray analysis of cycloadducts not susceptible to epimerization. The stereoselectivity of Diels-Alder reactions of vinylazepines, vinylpiperideines, and vinylcycloalkenes exhibits surprising divergence depending on the detailed diene structure, and DFT calculations (Becke3LYP) were undertaken to shed light on these observations. The model calculations correctly predict the major stereoisomers in these reactions, though they tend to significantly underestimate the stereoselectivity. The results suggest some general considerations in predicting or controlling the stereochemistry of this class of Diels-Alder reactions.     

Tricarbonyl (η6 arene) chromium(0) complex derived from 8-phenylmenthol chiral auxiliary

(—)-8-Phenylmenthol was prepared and converted to the corresponding tricarbonyl (⁶-arene) chromium(0) complex. Derivitization as the acrylate ester (1) and subsequent X-ray analysis revealed a 1:1 mix of s-cis and s-trans acrylate in the unit cell, and geometric proximity to support a through-space stacking interaction in the case of the s-trans isomer. The dihedral angle between the best planes through the chromium-bound aryl ring and the acrylate group is 19.9° for the s-trans isomer and 34.4° for the s-cis isomer. Crystal data for (1): C₂₂H₂₆O₅Cr, monoclinic, P2₁ (No. 4), a = 10.269(1), b = 10.482(1), c = 19.787(2), = 95.85(1), Z = 4, and D _calc = 1.32 g cm^–3.     

Chitosan‐based hydrogels: A new polymer‐based system with excellent laser‐damage threshold properties

Two types of chitosan hydrogel systems have been prepared that have a laser damage threshold (LDT) up to 35 times higher than commercial PMMA bulk materials. For these samples, the LDT increases with increasing water content. The mechanism of laser damage and the contribution of water to their high laser damage resistance have been examined. DSC measurements indicate water within the hydrogels exist in various states, each with different laser damage resistance properties. These various states play a key role in determining the LDT by controlling the dissipation of laser energy and providing a mechanism for self‐healing. This preliminary research shows that polymer hydrogels have potential for high power laser applications because they combine good mechanical integrity due to the polymer frame and good energy dissipation and healing characteristics due to the molecular mobility of water. These two traits allow for bulk shape‐retaining films with high laser damage thresholds and potential reversibility in damage processes. © 1999 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 37: 769–778, 1999     

Level density fluctuations and characterization of chaos in the realistic model spectra for odd-odd nuclei

Statistical properties of the realistic energy spectra of the odd-odd nuclei ¹⁰⁶Ag, ¹⁹⁸Au, ¹³⁴Cs, ⁴⁰K and ⁹⁴Rb, calculated within the Interacting Boson Fermion Fermion Model, are investigated by means of the Δ₃ statistics and the Nearest Neighbor Spacing Distribution method. New probability distribution function, which describes well the calculated results and enables the characterization of chaos with a physically meaningfull parameter, is proposed. Level spacing fluctuations of the examined nuclei exhibit the transitional behavior between Poisson and GOE limits, revealing different degrees of chaoticity in their dynamics.     

Relative Cl 2p:P 2s photoionization intensities in transition metal complexes

X-ray photoelectron spectra of the Cl 2p_{$\text{1}\text{2}$, $\text{3}\text{2}$}, P 2s region were obtained for nine transition metal complexes. The Cl:P atom ratios ranged from 1:3 to 3:2 and exhibited a linear relationship with the Cl 2p_{$\text{1}\text{2}$, $\text{3}\text{2}$} : P 2s intensities. Using AlKα radiation, the ratio of the Cl 2p: P 2s photoionization intensities was found to be 2.5: 1.0 with the McPherson ESCA-36 Photoelectron Spectrometer operated in its standard configuration.