Invariant subspaces with no generator and a problem of H. Helson

In the almost periodic context, any $H_0^2-$space cannot be generated by one of its elements. Together with cocycle argument, this derives that there exist all kinds of invariant subspaces without single generator, from which we can answer some questions on invariant subspace theory.Comment: 19 page

Another proof of the corona theorem

Let $H^\infty(\Delta)$ be the uniform algebra of bounded analytic functions on the open unit disc $\Delta$, and let $\mathfrak{M}(H^\infty)$ be the maximal ideal space of $H^\infty(\Delta)$. By regarding $\Delta$ as an open subset of $\mathfrak{M}(H^\infty)$, the corona problem asks whether $\Delta$ is dense in $\mathfrak{M}(H^\infty)$, which was solved affirmatively by L. Carleson. Extending the cluster value theorem to the case of finitely many functions, we provide a direct proof of the corona theorem: Let $\phi$ be a homomorphism in $\mathfrak{M}(H^\infty)$, and let $f_1, f_2, \dots, f_N$ be functions in $H^\infty(\Delta)$. Then there is a sequence $\{\zeta_j\}$ in $\Delta$ satisfying$f_k(\zeta_j) \rightarrow \phi(f_k)$ for $k=1, 2, \dots, N$. On the other hand, the corona problem remains unsolved in many general settings, for instance, certain plane domains, polydiscs and balls, our approach is so natural that it may be possible to deal with such cases from another point of view.Comment: 19pages, no figur

Measurements of Charmed Meson Lifetimes and Search for D0D^0-D‾0\overline{D}^0 Mixing with the Belle Experiment

The lifetimes of charmed mesons have been measured using 11.1fb$^{-1} of data collected with the Belle detector at KEKB. Each candidate is fully reconstructed to identify the flavor of the charmed meson. The lifetimes are measured to be$\tau(D^0)=(414.5\pm1.7)$fs,$\tau(D^+)=(1029\pm12)$fs and$\tau(D_s^+)=(488.4^{+7.8}_{-7.7})$fs, where the error is statistical only. The mixing parameter$y_{CP}$is also measured to be$y_{CP}=(1.16^{+1.67}_{-1.65}(stat.))%$through the lifetime difference of$D^0$ mesons decaying into CP-mixed states and CP eigenstates.Comment: 4 pages, 10 figures, BCP4, Ise-Shima, Japan, 19-23 February 200

Private Provision of Public Goods between Families

We consider a two-stage voluntary provision model where individuals in a family contribute to a pure public good and/or a household public good, and, at the same time, the parent makes private transfers to her child within the same family. We show not only that Warr’s neutrality holds regardless of the different timings of parent-to-child transfers, but also that there is a continuum of Nash equilibria in the sense that individuals’ contributions and parental transfers are indeterminate, although the allocation of each’s private consumption and total public good provision is uniquely determined. We further show that, even in the presence of impure altruism or productivity difference in supplying public goods, neutrality and uniqueness of the equilibrium allocation may persist.

Effects of gelation concentration on cyclic deformation behavior of κ-carrageenan hydrogels

The aim of this study is to elucidate the relationship between the network structure of κ-carrageenan hydrogels and their mechanical properties. First κ-carrageenan hydrogels have been prepared at different gelation concentrations, and then the mechanical behavior during four cyclic deformations has been examined at the same κ-carrageenan concentration. Young's modulus is higher for the gel prepared at 5 gL⁻¹ (C05) compared to that for the gel prepared at 30 gL⁻¹ (C30). C30 shows almost linear relation between the stress and the strain like an ideal rubber, while a residual strain appears in each cyclic deformation for C05. The extent of the residual strain depends on the maximum strain and the deformation speed, indicating that C05 deforms plastically to some extent. The residual strain for C05 decreases gradually even after a cyclic deformation and disappears in the case of a small strain as if there were a memory of the structure. The effects of the gelation concentration on the mechanical properties have been explained based on the network structure specific to κ-carrageenan hydrogels. The higher modulus for C05 has been attributed to the higher helix content and the plastic deformation of C05 to the loosely-aggregated crosslinks

Electrochemical generation of silver acetylides from terminal alkynes with a Ag anode and integration into sequential Pd-catalysed coupling with arylboronic acids

An electro-oxidative method for generating silver acetylides from acetylenes with a Ag anode was developed. The reaction could be integrated into a Pd-catalysed electrochemical Sonogashira-type reaction. In the presence of the catalytic amount of Pd(OAc)(2) and 4-BzO-TEMPO, electro-generated silver acetylides reacted immediately with arylboronic acids to afford the corresponding coupling adducts in high yields

Study on acoustical physical constants of ZnO single crystal using the ultrasonic microspectroscopy technology

2008 IEEE International Ultrasonics Symposium Proceeding