Hyperbolic mean growth of bounded holomorphic functions in the ball

We consider the hyperbolic Hardy class , . It consists of holomorphic in the unit complex ball for which and

where denotes the hyperbolic distance of the unit disc. The hyperbolic version of the Littlewood-Paley type -function and the area function are defined in terms of the invariant gradient of , and membership of is expressed by the property of the functions. As an application, we can characterize the boundedness and the compactness of the composition operator , defined by , from the Bloch space into the Hardy space .

     

The class number one problem for some non-abelian normal CM-fields of degree 48

We prove that there is precisely one normal CM-field of degree 48 with class number one which has a normal CM-subfield of degree 16: the narrow Hilbert class field of with .

     

Quasi-elastic scattering of the proton drip line nucleus 17F on 12C at 60 MeV

The quasi-elastic scattering angular distribution of the proton drip line nucleus ¹⁷F on a ¹²C target was measured at 60 MeV. The experimental data have been compared with the theoretical analysis based onto optical model and continuum discretized coupled channels (CDCC). The couplings between breakup and elastic scattering channels, and between inelastic and elastic scattering channels resulted very weak. In order to explore the breakup effects the total reaction cross-section was deduced from the angular distribution of the quasi-elastic scattering data, and then compared with the existing data for the other weakly and tightly bound nuclei on ¹²C target using a universal function. From this comparison, we concluded that the breakup effect is not important for weakly bound projectiles on the light target as obtained also with the CDCC analysis.     

ZnO–SnO2 branch–stem nanowires based on a two-step process: Synthesis and sensing capability

ZnO–SnO₂ branch–stem nanostructures were realized on a basis of a two-step process. In step 1, SnO₂-stem nanowires were synthesized. In step 2, ZnO-branch nanowires were successfully grown on the SnO₂-stem nanowires through a simple evaporation technique. We have pre-deposited thin Au layers on the surface of SnO₂ nanowire stems and subsequently evaporated Zn powders on the nanowires. The ZnO branches, which sprouted from the SnO₂ stems, had diameters in a range of 30–35 nm. As-synthesized branches were of single crystalline hexagonal ZnO structures. Since the branch tips were comprised of Au-containing nanoparticles, the Au-catalyzed vapor–liquid–solid growth mechanism was more likely to control the growth process of the ZnO branches. To test a potential use of ZnO–SnO₂ branch–stem nanostructures in chemical gas sensors, their sensing performances with respect to NO₂ gas were investigated, showing the promising potential in chemical gas sensors.     

Fabrication of textured KNNT ceramics by reactive template grain growth using NN templates

Lead-free non-stoichiometric (K_0.470Na_0.545)(Nb_0.55Ta_0.45)O₃ (KNNT) textured ceramics were prepared by a reactive templated grain growth method using NaNbO₃ (NN) templates. The Plate-like NaNbO₃ (NN) templates were synthesized from bismuth layer-structured Bi_2.5Na_3.5Nb₅O₁₈ (BNN) particles by a topochemical microcrystal conversion (TMC) method. Using 5 wt% of NN templates, textured KNNT ceramics were fabricated, and their crystal structure, microstructure, dielectric and piezoelectric properties were compared with non-textured KNNT ceramics prepared by a conventional solid state reaction method. The textured KNNT ceramics exhibited high grain orientation and high dielectric constant. In addition, piezoelectric properties of textured KNNT ceramics were improved, giving a high piezoelectric coefficient d₃₃ = 390 pC/N and piezoelectric coupling coefficient k_p = 0.60.     

Non-equilibrium stochastic model for stock exchange market

We study the effect of the topology of industrial relationship (IR) between the companies in a stock exchange market on the universal features in the market. For this we propose a stochastic model for stock exchange markets based on the behavior of technical traders. From the numerical simulations we measure the return distribution, P(R)$P\left(R\right)$, and the autocorrelation function of the volatility, C(T)$C\left(T\right)$, and find that the observed universal features in real financial markets are originated from the heterogeneity of IR network topology. Moreover, the heterogeneous IR topology can also explain Zipf–Pareto’s law for the distribution of market value of equity in the real stock exchange markets.