Palladium-catalyzed allylic oxidation of olefins by t-butyl hydroperoxide and tellurium(IV) oxide

Treatment of several cyclic olefins, β-pinene, allylbenzene, and estragole with palladium(II) salt in acetic acid in the presence of t-butyl hydroperoxide and tellurium(IV) oxide afforded mainly the corresponding allylic acetates. The reaction proceeded catalytically with palladium(II) salt, t-BuOOH working as a reoxidizing agent.     

The multiplicity of abelian covers of splice quotient singularities

From a resolution graph with certain conditions, Neumann and Wahl constructed an equisingular family of surface singularities called splice quotients. For this class some fundamental analytic invariants have been computed from their resolution graph. In this paper we give a method to compute the multiplicity of an abelian covering of a splice quotient from its resolution graph and the Galois group.     

On equivalence of L p -norms related to Schrödinger type operators on Riemannian manifolds

In this paper, we study Schrödinger type operator on a Riemannian manifold. Under some assumptions on a potential function, we characterize the domain of the square root of the Schrödinger type operator on L ^p space. In the proof, the defective intertwining properties and the Littlewood-Paley inequalities play important roles.     

Functional monomers and polymers. LXXI. Conformation and interaction studies of poly-L-lysine derivatives with pendant nucleic acid bases

Copolymers of L -lysine and L -lysine derivatives which contained nucleic acid bases substituted on the N^ε position were synthesized by grafting nucleic acid derivatives onto poly-L -lysine. The conformation and interaction of these copolymers in solution were studied by using spectroscopic measurements. They existed in helical conformation at neutral pH values, and the polymer complex formation among them was examined by ultraviolet (UV) measurements in organic solvents. A decrease in the nucleic acid base content of the copolymers resulted in a decrease in helical structures and also in interactions with the polymer-containing complementary bases.     

Determination of threo and erythro configurations of 3-fluorophenylalanine for verifying stereochemical aspects of recently reported syntheses

Determination of threo and erythro configurations of both diastereoisomers of 3-fluorophenylalanine on the basis of chemical transformation and X-ray analysis has confirmed that the aziridine ring opening reaction gives the threo isomer stereoselectively, whereas the fluorodehydroxylation reaction affords both isomers nonselectively.     

Regioselective lithiation of II-(arene)chromium tricarbonyl complexes

Chromium tricarbonyl complexes of 3-methoxybenzyl alcohol and related compounds were selectively lithiated at the 4-position in contrast to the corresponding metal free arene compounds. The resulting 4-lithio complexes were converted to the 4-substituted arene compounds in moderate to excellent yields through the reactions with proper electrophiles and subsequent demetalation.     

Several contributions to soil compactibility induced by cyclic loading test

To investigate the soil compactibility during the cyclic loading, three different kinds of paddy field soils were prepared so as to clarify interrelationships among stress amplitude ratio, bulk density, soil water content and pore water pressure. The presetting values of specimen include the soil water content(percent dry basis) and bulk density of 25% d.b. and 1.1 Mg/m³ respectively. The relation between the number of cyclic loading and axial strain exhibited an asymptotically increasing trend, converging toward a specific value for each experimental condition. Possible effect caused by elastic–plastic characteristics could be recognized, when axial strain for 0.5 Hz excitation becomes greater than the one of 1.0 Hz under same stress amplitude ratio. When the stress amplitude ratio took 0.1, the absolute value of axial strain of 0.5 Hz was greater than the one of 1.0 Hz, whereas its decreasing trend was recognized in the sequence of silt, clay and silty sand. The qualitative relations between pore water pressure and number of cyclic loading were also examined to scrutinize the effect of effective water pressure to the soil compactibility.     

Energy-Preserving $H^1$--Galerkin Schemes for the Hunter-Saxton Equation

We consider the numerical integration of the Hunter–Saxton equation, which models the propagation of weakly nonlinear orientation waves. For the equation, we present two weak forms and their Galerkin discretizations. The Galerkin schemes preserve the Hamiltonian of the equation and can be implemented with cheap H~1 elements. Numerical experiments confirm the effectiveness of the schemes.     

On Symmetric Stable-Type Processes with Degenerate/Singular Lévy Densities

Journal of Theoretical Probability - We consider symmetric stable-type processes with degenerate/singular Lévy densities via Dirichlet form theory. We give conditions of some global path...     

A COCR method for solving complex symmetric linear systems

The Conjugate Orthogonal Conjugate Gradient (COCG) method has been recognized as an attractive Lanczos-type Krylov subspace method for solving complex symmetric linear systems; however, it sometimes shows irregular convergence behavior in practical applications. In the present paper, we propose a Conjugate A$A$-Orthogonal Conjugate Residual (COCR) method, which can be regarded as an extension of the Conjugate Residual (CR) method. Numerical examples show that COCR often gives smoother convergence behavior than COCG.