Stable hydrocarbon diradical, an analogue of trimethylenemethane

Hydrocarbon diradical 1, a new stable, 3-fold symmetric analogue of trimethylenemethane (TMM) with no heteroatom perturbation, is prepared and studied. Such diradicals should provide new building blocks for high-spin hydrocarbon polyradicals with very strong net ferromagnetic coupling. Magnetic studies (SQUID) and EPR spectroscopy indicate that 1 in tetrahydrofuran-d8 (THF-d8) possesses a triplet (S = 1) ground state, with strong ferromagnetic coupling. After annealing at room temperature, the EPR spectra of 1 (approximately 0.02 M in frozen THF-d8) consist of a single narrow resonance (deltaH(pp) < 1 G), and intermolecular antiferromagnetic coupling is increased by 1 order of magnitude. This behavior is consistent with the presence of exchange narrowing, thus suggesting aggregation of 1 in THF-d8. Blue solutions of 1 in THF-d8 possess a strong UV-vis absorption band at lambda(max) approximately 640 nm. Diradical 1 in THF-d8 is stable (or persistent) at room temperature, with no detectable decomposition for at least 2 days.     

Analysis of detected signal performance in multi-tracks of optical disk memory using convex-shaped recording mark

The possibility of multi-valued optical disk memory by using a convex-shaped recording mark fabricated by two-photon absorption is investigated. We fabricate a numerical model for convex-shaped recording marks and evaluate the signal characteristics in terms of the signal-to-noise ratio (SNR). The numerical results show that 6 bit data can be realized when the acceptable average SNR is 2 and a length of the mark is 4T.     

Real-root property of the spectral polynomial of the Treibich–Verdier potential and related problems

We study the spectral polynomial of the Treibich–Verdier potential. Such spectral polynomial, which is a generalization of the classical Lamé polynomial, plays fundamental roles in both the finite-gap theory and the ODE theory of Heun's equation. In this paper, we prove that all the roots of such spectral polynomial are real and distinct under some assumptions. The proof uses the classical concept of Sturm sequence and isomonodromic theories. We also prove an analogous result for a polynomial associated with a generalized Lamé equation, where we apply a new approach based on the viewpoint of the monodromy data.     

Telluroxide elimination by direct oxidation of alkyl phenyl telluride

Treatment of sec-alkyl phenyl tellurides, except for the cyclohexyl system, with m-chloroperbenzoic acid(MCPBA) in diethyl ether readily afforded the corresponding olefins in good yields presumably via telluroxide elimination together with small amounts of alcohols and ketones. In the pri-alkyl and cyclohexyl cases the adducts between MCPBA and the tellurides were isolated as stable organotellurium(IV) compounds which gave similar elimination products by neat pyrolysis at 220–2500°C.     

Alkyne-coordinating tridentate ligands: structural properties and reactivity of their rhodium complexes

Complexes of novel alkyne-chelating tridentate ligands bound to a rhodium atom were isolated and characterised. The present alkyne-rhodium complex underwent dimerisation simply by heating to afford the unprecedented cyclobutadiene dirhodium complex. It is also found that the ligands at the trans positions influence the π-coordination of alkynes.     

Synthesis of regiocontrolled polymer having 2-naphthol unit by CuCl-amine catalyzed oxidative coupling polymerization

Regiocontrolled polymer (2) having 2-naphthol unit was prepared by oxidative coupling polymerization of bis(2-naphthol) (1). Polymerizations were conducted in dichloromethane in the presence of [di-μ-hydroxo-bis(N,N,N′,N′-tetramethylethylenediamine)copper(II)] chloride [CuCl(OH)TMEDA] under air at room temperature, producing polymers with number-average molecular weights up to 12,000. The structure of polymer 2 was characterized by 270 MHz ¹H–NMR and 68.5 MHz ¹³C–NMR spectroscopies and was estimated to consist almost completely of 1,1′-linkage. The polymer was readily soluble in polar aprotic solvents and tetrahydrofuran at room temperature. Thermogravimetric analysis of polymer 2 showed 10% weight loss at 450°C in nitrogen. The model reactions were studied to clarify the applicability of CuCl(OH)TMEDA for coupling of naphthol derivatives. © 1999 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 37: 3702–3709, 1999     

Stability for non-hyperbolic fixed points of scalar difference equations

We give some new criteria to determine the stability of a non-hyperbolic fixed point of the scalar difference equation

where and f is a sufficient smooth function. Our results are based on higher order derivative at a fixed point of .     

Molecular weight distribution and molecular structure of polyethylene produced by radiation-induced polymerization

The molecular weight distribution of polyethylene produced by radiation was calculated according to a kinetic scheme. The calculated molecular weight distribution was compared with the results deduced from gel-permeation chromatography. The observed distribution curve from GPC was broader and showed a lower degree of polymerization than the calculated one. Discrepancies between observed and calculated curves can be explained if the polymer contains nonsteady-state products and if the reaction mechanism includes chain transfer to dead polymer. By this reaction long-chain branching would occur. Several long-chain branches per polymer molecule were indeed found, as inferred from solution properties.     

Analytic continuation of eigenvalues of the Lamé operator

Eigenvalues of the Lamé operator are studied as complex-analytic functions in period τ of an elliptic function. We investigate the branching of eigenvalues numerically and clarify the relationship between the branching of eigenvalues and the convergent radius of a perturbation series.     

Integral representation of solutions to Fuchsian system and Heun's equation

We obtain integral representations of solutions to special cases of the Fuchsian system of differential equations and Heun's differential equation. In particular, we calculate the monodromy of solutions to the Fuchsian equation that corresponds to Picard's solution of the sixth Painlevé equation, and to Heun's equation.