Geometric indices and the Alexander polynomial of a knot

It is well-known that any Laurent polynomial satisfying and is the Alexander polynomial of a knot in . We show that can be realized by a knot which has the following properties simultaneously: (i) tunnel number 1; (ii) bridge index 3; and (iii) unknotting number 1.

     

Excitation of Intra-4f Shell Luminescence of Rare Earth Ions (Er3+ and Yb3+) by the Energy Transfer from Si Nanocrystals

Photoluminescence (PL) properties of SiO₂ films containing Si nanocrystals (nc-Si) and Er³⁺ (Yb³⁺) were studied. PL peaks attributable to the recombination of electron–hole pairs in nc-Si (1.5eV) and the intra-4f shell transition of Er³⁺ (0.81eV) (Yb³⁺ (1.26eV)) were observed simultaneously at room temperature. Correlation of the two peaks was studied as a function of nanocrystalline size. It was found that the intensity of the Er³⁺-related (Yb³⁺-related) peak increases drastically as the size of nc-Si decreases. Temperature dependence of PL spectra was studied. In the case of Yb-doped samples, temperature quenching of the PL became small as the size decreased, while in the case of Er-doped samples, no remarkable temperature dependence was observed. Two major features of the quantum size effects of nc-Si, i.e., the band-gap widening and the increase in the PL efficiency with decreasing the size, are thought to contribute to the improvement of room temperature PL efficiency of Er³⁺ (Yb³⁺).     

Aerial imaging steganography method for aerial imaging by retro-reflection with dual acrylic ball

Optical Review - This paper proposes a novel steganography method to show an aerial image that is formed with aerial imaging by retro-reflection by use of dual transparent balls made of acrylic...     

Evolution of the Kondo effect in a quantum dot probed by shot noise

We measure the current and shot noise in a quantum dot in the Kondo regime to address the nonequilibrium properties of the Kondo effect. By systematically tuning the temperature and gate voltages to define the level positions in the quantum dot, we observe an enhancement of the shot noise as temperature decreases below the Kondo temperature, which indicates that the two-particle scattering process grows as the Kondo state evolves. Below the Kondo temperature, the Fano factor defined at finite temperature is found to exceed the expected value of unity from the noninteracting model, reaching 1.8±0.2.     

Nonlinear optical characteristics of CdS and ZnS nanoparticles implanted into zirconium oxide thin films

The nonlinear refractive indices γ and nonlinear absorption coefficients of ZrO₂ films doped with CdS or ZnS nanoparticles, as well as with various metals, are measured. The effects of semiconductor and metal nanoparticles and annealing on the nonlinear optical properties of films are studied. The structural parameters of films, determined by electron microscopy and x-ray dispersion spectroscopy, are compared to the optical and nonlinear optical characteristics of these media. The high magnitude of γ of the films ((3±0.6)×10^?11 cm² W^{? 1}) is attributed to the surface enhancement effect in semiconductor nanoparticles. On the basis of Z-scan data obtained at different intensities of radiation, it is shown that the variations in γ of the ZrO₂:CdS(Cr) and ZrO₂:ZnS(Mn) films are related to the generation of free carriers.