Random orderings of the integers and card shuffling

In this paper we study random orderings of the integers with a certain invariance property. We describe all such orders in a simple way. We define and represent random shuffles of a countable set of labels and then give an interpretation of these orders in terms of a class of generalized riffle shuffles.     

Liquid crystalline hexa-amides and side chain polysiloxanes of azacrown [18]-N6

The hexa-4-dodecyloxybenzoyl derivative 1 of azacrown [18]-N₆ was originally reported to have a 'tubular' mesophase on the basis of its large central ring and 6-fold symmetry. Starting in the mesophase, annealing of 1 under a cover slip results in formation of a new crystalline phase that melts directly to an isotropic liquid at the temperature previously observed for the mesophase to isotropic transition. Thus the phase behaviour of 1 is kinetically controlled. The analogous hexa-3,4-bisdodecyloxybenzoyl derivative 2 of azacrown [18]-N₆ has no kinetic limitations to its phase changes and has an enantiotropic columnar liquid crystalline phase. We have synthesized side chain copolysiloxanes with a (CH₂)₁₁ spacer and 75-84 per cent by weight of the same 4-dodecyloxybenzoyl-[18]-N₆ mesogen. The polysiloxanes also display a liquid crystalline phase.     

Production of slow muonic hydrogen isotopes in vacuum

Muonic hydrogen isotopes (μ⁻ p, μ⁻ d, and μ⁻t) are simple quantum mechanical systems ideally suited for studies of numerous fundamental phenomena in electroweak and strong interactions as well as in applied areas such as muon chemistry or muon catalyzed fusion. Emission of muonic hydrogen isotopes into vacuum helps to overcome the limitations which are normally imposed on conventional investigations with gaseous and liquid targets. A proof of principle experiment for this new technique was performed at TRIUMF last year. Negative muons with 30 MeV/c momentum were stopped in a thin film of solid hydrogen and produced very low energy μ⁻d in vacuum. The distribution center of the normal velocity components of emitted μ⁻d atoms was measured to be ∼1 cm/μs. The yield of μ⁻d in vacuum is an increasing function of H₂ film thickness δ up to a value of δ≥1 mm.     

The Spirit Is Willing: Nonlinearity, Bifurcations, and Mental Control

In recent years there has been considerable interest in the construction of nonlinear models of the dynamics of human behavior. In this exploratory article we argue that attempts at controlling problematic thoughts, emotions, or behaviors can lead to nonlinearity in mental/behavioral dynamics. We illustrate our model by fitting threshold autoregression models to self-recorded time series of the daily highs in intensity of anxiety and obsessive ruminations, kept by an individual in therapy for this problem. In our discussion, we raise the possibility that bifurcations that occur in this nonlinear model may offer insight into mental control paradoxes.     

Monitoring the transformation of colloidal crystals by styrene vapor using atomic force microscopy

The stages of transformation of a colloidal crystalline film of latex spheres to a new periodic structure were imaged by atomic force microscopy. Colloidal crystalline films were prepared with 320 nm diameter poly(styrene-co-2-hydroxyethyl methacrylate) (PSt/HEMA) spheres. The hexagonally ordered surfaces of the colloidal crystalline films were transformed with styrene vapor at room temperature to a new morphology having holes in the surface and the same periodicity as the original films. The surfaces of colloidal crystals and the transformed films have a raspberry-like texture superposed on the 320 nm hexagonal periodicity. Both height images and phase images reveal that the latex spheres shrink and the transformation proceeds by an order-disorder-order sequence. The final structure is an interconnected colloidal array with smaller polystyrene particles dispersed in a continuous PSt/HEMA matrix.     

Peak area measurements of cross-polarization magic-angle-spinning 13C-NMR spectra of crosslinked polystyrenes

Cross-polarization magic-angle-spinning ¹³C-NMR spectra of polystyrenes crosslinked with 1–20% of methine vinyl carbon ¹³C-labeled p-divinylbenzene and of Friedel–Crafts crosslinked poly(chloromethylstyrene)s have been obtained with both glossy solid and CDCl₃-swollen gel samples. The spectra of natural abundance, uncrosslinked, glassy polystyrene, and the spectra of the solid labeled networks give aliphatic and aromatic peak areas only 0.7 times as large per ¹³C atom as that of poly(oxymethylene). Similarly the crosslinked poly(chloromethylstyrene) gave peak areas about 0.6 times that of internal poly(oxymethylene). The labeled gels give peak areas 0.2–0.6 times as large per ¹³C atom as glassy polystyrene, and the peak areas in spectra of gels increase with the divinylbenzene content     

Kinetics of the thermal unimolecular decomposition of hex-1-ene-3-yne. Heat of formation and resonance stabilization energy of the 3-ethenylpropargyl radical

The thermal unimolecular decomposition of hex-1-ene-3-yne (HEY) has been investigated over the temperature range 949–1230 K using the technique of very low-pressure pyrolysis (VLPP). One reaction pathway is the expected C₅? C₆ bond fission to form the resonance-stabilized 3-ethenylpropargyl radical. There is a concurrent process producing molecular hydrogen which probably occurs via the intermediate formation of hexatrienes and cyclohexa-1,3-diene. RRKM calculations yield the extrapolated high-pressure rate parameters at 1100 K given by the expressions 10^16.0±0.3 exp(?300.4 ± 12.6 kJ mol^?1/RT) s^?1 for bond fission and 10^13.2+0.4 exp(?247.7 ± 8.4 kJ mol^?1/RT) for the overall formation of hydrogen. The A factors were assigned from the results of previous studies of related alkynes, alkenes, and alkadienes. The activation energy for the bond fission reaction leads to ΔH [H₂CCHCC?H₂] = 391.9, DH [H₂CCHCCCH₂? H] = 363.3, and a resonance stabilization energy of 56.9 ± 14.0 kJ mol^?1 for the 3-ethenylpropargyl radical, based on a value of 420.2 kJ mol^?1 for the primary C? H bond dissociation energy in alkanes. Comparison with the revised value of 46.6 kJ mol^?1 for the resonance energy of the unsubstituted propargyl radical indicates that the ethenyl substituent (CH₂?CH) on the terminal carbon atom has only a small effect on the propargyl resonance energy. © John Wiley & Sons, Inc.     

Some reactions of 1-alkyl-1,2,3,4-tetrahydropyridines with organic azides. Synthesis of 1-alkylpiperidylidene-2-sulfonamides

The 1,3-dipolar cycloaddition reaction of 1-substituted-1,2,3,4-tetrahydropyridines 4a-d with organic azides 5 afforded the respective 1-substituted-piperidylidene-2-sulfonamides 6 . In contrast, the reaction of (E)-1-(1-propenyl)-1,2,3,4-tetrahydropyridine ( 4e ) with 4-chlorobenzenesulfonyl azide yielded 6m as well as 1-(4-chlorophenyl)sulfonimine-1,2,3,4-tetrahydropyridine ( 7 ) arising from addition of the azide to the (E)-1-(1-propenyl) substituent of 4e .     

Two-Photon Excitation of 4'-Hydroxymethyl-4,5',8-Trimethylpsoralen

Abstract— Psoralens are a class of pharmaceutical agents commonly used to treat several cutaneous disorders. When irradiated with a mode-locked titanium: sapphire (Ti: sapphire) laser tuned to 730 nm, an aqueous solution of 4'-hydroxymethyl-4,5',8-trimethylpsoralen (HMT) emits blue light. The emission spectrum is centered at 452 nm and is identical to that obtained by one-photon excitation with UVA excitation, and its magnitude depends quad-ratically on the intensity of laser excitation. These results suggest that two-photon excitation occurs to a potentially photochemically active state. To estimate the two-photon absorption cross section, it was first necessary to measure the emission quantum yield of HMT using 365 nm excitation at room temperature that resulted in a value of 0.045 ± 0.007. The two-photon absorption cross section of HMT at 730 nm is therefore estimated to be 20 ± 10⁻⁵⁰ cm⁴ s (20 Göppert-Mayer). The excited-state photophysics and photochemistry of psoralens suggest potential applications to cutaneous phototherapy in diseases such as psoriasis and dystrophic epidermolysis bullosa.