Rings of normal and nonnormal numbers

We construct an uncountable ring of real numbers all of whose nonzero elements are normal to baseb and nonnormal to baseab, wherea, b are and pair of integers greater than one with (a,b)=1. To the memory of Gerold Wagner     

Superconvergence of the iterated collocation methods for Hammerstein equations

In this paper, we analyse the iterated collocation method for Hammerstein equations with smooth and weakly singular kernels. The paper expands the study which began in [16] concerning the superconvergence of the iterated Galerkin method for Hammerstein equations. We obtain in this paper a similar superconvergence result for the iterated collocation method for Hammerstein equations. We also discuss the discrete collocation method for weakly singular Hammerstein equations. Some discrete collocation methods for Hammerstein equations with smooth kernels were given previously in [3, 18].     

Development of a new traceless aniline linker for solid-phase synthesis of azomethines. Application to parallel synthesis of a rod-shaped liquid crystalline library

A new traceless linker was developed to synthesize a library of 42 compounds possessing an azomethine linkage using combinatorial solid-phase parallel synthesis. The loading of the substrates on a solid support and cleavage from the solid support were performed by an imine synthesis and by imine-exchanged process under mild conditions, respectively. Thioesters with a hydroxy group on the central core exhibited liquid crystalline properties with the widest transition temperatures in the library.     

Real-time spectroscopy of Frenkel exciton system

We performed selective excitations of the first- and second-excited Frenkel exciton states (Q- and B-excitons) with use of sub-40-fs and sub-5-fs visible laser pulses. The transient absorption signals exhibit oscillatory features associated with molecular vibrations. From an analysis of the spectral profiles of the phase and amplitude of the oscillation, the experimental result is well explained by the modulated transition dipole moment, which is caused by the dynamic intensity borrowing from the intense B-transition to the weak Q-transition.     

Synthesis of polymers by using divalent metal salts of mono(hydroxyethyl) phthalate: Metal-containing polyurethanes

As difunctional compounds containing an ionic bond in the molecule, divalent metal salts (I) of mono(hydroxyethyl) phthalate were prepared in high purity and high yield. Mg and Ca were selected as divalent metal. Metal-containing polyurethanes containing ionic links in the main chain were synthesized by the polyaddition reaction of I or, I–glycols with diisocyanates. The polyurethane obtained were glassy materials or white powders, depending on the species of diisocyanates and glycols. Close agreement between observed and calculated values of metal content of the polyurethanes were obtained. The viscosities (in dimethyl-formamide) of the polyurethanes decreased markedly with increasing of metal content. Moreover, the decomposition temperatures were lowered by introduction of metals into the polyurethanes. However, the decomposition rates of metal-containing polyurethanes were lower than those of polyurethanes not containing metal.     

Some results on odd factors of graphs

A {1, 3, …,2n ? 1}-factor of a graph G is defined to be a spanning subgraph of G, each degree of whose vertices is one of {1, 3, …, 2n ? 1}, where n is a positive integer. In this paper, we give a sufficient condition for a graph to have a {1, 3, …, 2n ? 1}-factor.