Let Î± > 1 be an algebraic number and Î¾ > 0. Denote the fractional parts of Î¾Î±n by {Î¾Î±n}. In this paper, we estimate a lower bound for the number Î»N (Î±, Î¾) of integers n with 0 â‰¤ n < N and {Î¾Î±} â‰¥ minâ€¦ (More)

Let Î± > 1 be an algebraic number and Î¾ a nonzero real number. In this paper, we compute the range of the fractional parts {Î¾Î±n} (n = 0, 1, . . .). In particular, we estimate the maximal and minimalâ€¦ (More)

We study the limit shape of successive coronas of a tiling, which models the growth of crystals. We define basic terminologies and discuss the existence and uniqueness of corona limits, and thenâ€¦ (More)

2-Phenylquinoline (1) degraded proteins under photo-irradiation with long-wavelength UV light without additives and under neutral conditions. We designed and synthesized a 2-phenylquinoline-estrogenâ€¦ (More)

Solid-phase affinity labeling of a target protein, peanut agglutinin (PNA), with the specifically designed chemical tool 1 selectively and effectively furnished the labeled PNA. Furthermore, thisâ€¦ (More)

The influence of a thin carbonate-containing hydroxyapatite (CA) coating to tetragonal zirconia polycrystal (TZP) on osteoblastlike cell response was investigated. TZP disks were subjected toâ€¦ (More)

OBJECTIVE
Periodontal pathogens in dental plaque are the main causative agents of periodontitis and peri-implantitis. Detection of the presence of such periodontal pathogens early would serve as aâ€¦ (More)