On a property specific to the tent map

Let a set {X_λ; λ  Λ} of subspaces of a topological space X be a cover of X. Mathematical conditions are proposed for each subspace X_λ to define a map g_Xλ:X_λ→X which has the following property specific to the tent map known in the baker’s transformation. Namely, for any infinite sequence ω₀, ω₁, ω₂, … of X_λ, λ  Λ, we can find an initial point x₀  ω₀ such that g_ω0(x₀)ω₁,g_ω1(g_ω0(x₀))ω₂,…. The conditions are successfully applied to a closed cover of a weak self-similar set.     

A prediction problem in

For a nonnegative integrable weight function on the unit circle , we provide an expression for , in terms of the series coefficients of the outer function of , for the weighted distance , where is the normalized Lebesgue measure and ranges over trigonometric polynomials with frequencies in , , . The problem is open for .

     

Temperature sensitivity of Ge-B-SiO(2) waveguide Bragg gratings on a crystallized glass substrate

Waveguide Bragg gratings were fabricated by plasma-enhanced chemical-vapor deposition followed by irradiation with KrF excimer laser light through a phase mask. The period of the Bragg grating was 0.53 mum, and the Bragg wavelength was ~1.53 mum . The temperature dependence of the Bragg wavelength was 11 pm/ degrees C for a 10GeO(2) -90SiO(2)(mol.%) core waveguide on a Si substrate, and the Bragg wavelength shift was successfully reduced to 5.0pm/ degrees C by use of a 14GeO(2)-12B(2)O(3)-74SiO(2) (mol.%) core and a crystallized glass substrate with a thermal-expansion coefficient of -2.0x10(-6)(/ degrees C) .     

Remarks on Herz-Type Hardy Spaces

Basic properties of the Herz-type Hardy spaces , such as the boundedness of singular integral operators and the fractional integration operators, atomic decomposition, dense subspaces, etc., are established in the full range 0 < q < ∞. Partly supported by the Grants-in-Aid for Scientific Research (A)(1)11304009, (B)(1)10440046, Japan Society for the Promotion of Science.     

Photoluminescence properties of selectively grown InN microcrystals

We investigated the photoluminescence (PL) properties of regularly arranged N‐polar InN microcrystals with m ‐plane sidewall facets. We observed narrow PL emission at 0.678 eV with a linewidth of ～14 meV at 4 K and a clear band‐filling effect with increasing excitation power. We also observed a normal red shift of the PL peak energy as large as 51 meV (～150 nm) with increasing temperature from 4 to 300 K, similar to that observed for non‐degenerated semiconductors. The integrated PL intensity ratio I_300K/I_4K was measured to be 6.1%. These results indicate that InN microcrystals have a low residual carrier density and excellent optical properties without being adversely affected by surface electron accumulation, despite their relatively high surface area. (© 2012 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Dynamic self-organization of migrating cells under constraints by spatial confinement and epithelial integrity

The European Physical Journal E - We consider a microscopic field theoretical approach for interacting active nematic particles. With only steric interactions the self-propulsion strength in such...     

Simultaneous Measurement of Individual ATPase and Mechanical Reactions by a Single Myosin Molecule at Work

Based on techniques for single molecule imaging and nanomanipulation by optical tweezers, we have developed a new technique that allows simultaneous measurement of individual ATPase and mechanical reactions from a single myosin molecule during force generation. We show how the ATPase reaction couples to the mechanical reaction directly at the single molecule level. The results show that the myosin head can produce force even after releasing the bound nucleotide, probably ADP, suggesting that the chemical energy driven by ATP hydrolysis can be hysteretically stored in the myosin molecule. This view does not support a widely accepted hypothesis in which the force generation is tightly coupled to ligand dissociation.This paper was originally presented as an invited paper at the seventh Meeting on Near Field Optics, which was held on July 1, 1998 at Nagoya University, Nagoya, organized by the Research Group on Near Field Optics of the Optical Society of Japan, an affiliate of the Japan Society of Applied Physics.     

Partial autocorrelation functions of the fractional ARIMA processes with negative degree of differencing

Let be a fractional ARIMA(p,d,q) process with partial autocorrelation function α(·). In this paper, we prove that if d∈(−1/2,0) then |α(n)|∼|d|/n as n→∞. This extends the previous result for the case 0<d<1/2.