A generalization of the weighted Strichartz estimates for wave equations and an application to self‐similar solutions

Weighted Strichartz estimates with homogeneous weights with critical exponents are proved for the wave equation without a support restriction on the forcing term. The method of proof is based on expansion by spherical harmonics and on the Sobolev space over the unit sphere, by which the required estimates are reduced to the radial case. As an application of the weighted Strichartz estimates, the existence and uniqueness of self‐similar solutions to nonlinear wave equations are proved on up to five space dimensions. © 2006 Wiley Periodicals, Inc.     

A sphere as a surface which contains many circles II

A sphereM inE ³ is characterized as a simply connected complete smooth surface which contains a circle through each pointp M contained in a normal plane ofM atp.The author would like to thank Professor K. Ogiue for his valuable suggestions.     

On the correlation between NQR frequency and bond length in I3−

A linear correlation between the NQR frequency of the terminal iodine atom and the corresponding I-I bond length in I₃^? was found in several compounds containing triiodide anions. A simple extended Huckel MO calculation suggested that such a correlation can be used to check the validity of wavefunctions of iodine.     

Radiocarbon dating of an ancient Japanese document “Minamoto no Yoritomo Sodehan Migyosho” by accelerator mass spectrometry

We measured radiocarbon age of an ancient document “Minamoto no Yoritomo Sodehan Migyosho”. The content tells that it was issued in 1189 by “Minamoto no Yoritomo” known as the virtually first shogun in Japan to grant “Matsugi” family the privilege of controlling craftsmen of foundry industry. Paleographical views, however, suggested that it can be a counterfeit. The radiocarbon dating clarified that the document was written not in the 12th but after the 16th century.