Aging phenomena in polystyrene thin films

The aging behavior is investigated for thin films of atactic polystyrene through measurements of complex electric capacitance. During isothermal aging process the real part of the electric capacitance increases with aging time, while the imaginary part decreases with aging time. This result suggests that the aging time dependence of the real and imaginary parts are mainly associated with change in thickness and dielectric permittivity, respectively. In thin films, the thickness depends on thermal history of aging even above the glass transition. Memory and `rejuvenation' effects are also observed in the thin films.Comment: 4 pages, 2 figure

Toda Molecule and Tomimatsu-Sato Solution ∼\sim Towards the complete proof of Nakamura's conjecture∼\sim

We discuss the Nakamura's conjecture stating that the Tomimatsu-Sato black hole solution with integer deformation parameter $n$ is composed of the special solutions of the Toda molecule equation at the $n$-th lattice site. From the previous work, in which the conjecture was partly analytically proved, we go further towards final full proof by rearranging the rotation parameter. The proof is explicitly performed for the highest and lowest orders. Though the proof for all orders remains still unsolved, the prospect to the full proof becomes transparent and workable by our method.Comment: 16 pages, 1 fifure, Typos corrected, reference adde