Transversality family of expanding rational semigroups

We study finitely generated expanding semigroups of rational maps with overlaps on the Riemann sphere. We show that if a d$d$-parameter family of such semigroups satisfies the transversality condition, then for almost every parameter value the Hausdorff dimension of the Julia set is the minimum of 2 and the zero of the pressure function. Moreover, the Hausdorff dimension of the exceptional set of parameters is estimated. We also show that if the zero of the pressure function is greater than 2$2$, then typically the 2-dimensional Lebesgue measure of the Julia set is positive. Some sufficient conditions for a family to satisfy the transversality conditions are given. We give non-trivial examples of families of semigroups of non-linear polynomials with the transversality condition for which the Hausdorff dimension of the Julia set is typically equal to the zero of the pressure function and is less than 2$2$. We also show that a family of small perturbations of the Sierpinski gasket system satisfies that for a typical parameter value, the Hausdorff dimension of the Julia set (limit set) is equal to the zero of the pressure function, which is equal to the similarity dimension. Combining the arguments on the transversality condition, thermodynamical formalisms and potential theory, we show that for each a∈C$a\in \mathbb{C}$ with |a|≠0,1$\left|a\right|\ne 0,1$, the family of small perturbations of the semigroup generated by {z²,az²}$\{z^2,a{z}^2\}$ satisfies that for a typical parameter value, the 2-dimensional Lebesgue measure of the Julia set is positive.     

Development of high resolution resonance ionization mass spectrometry for trace analysis of 93mNb

⁹³Nb(n, n′)^93mNb reaction allows retrospective estimation of integrated fast neutron dose in nuclear reactor. We proposed isomer-selective trace analysis of ^93mNb by Resonance Ionization Mass Spectrometry (RIMS) combined with a gas-jet atomic source and an injection locked Ti:Sapphire laser system operated at several kHz. Resonant ionization spectroscopy of Nb in gas-jet using Ti:Sapphire laser was demonstrated.     

Flame Emission Spectrometry Using Atomic Absorption Apparatus (I) Determination of Sr In Sea Water

Flame emission determination of Sr in sea water is studied using an ordinary atomic absorption apparatus. The analytical line 4607 A is used with background correction at 4616 A. The ionization is found to be negligible in air acetylene flame with sea water, and the interference of H₂SO₄ is elimentated using the higher part of the flame.     

Study of Strangeness Photoproduction on the Neutron in the Threshold Region

Photoproduction of the neutral kaon on the deuteron has been investigated at the Research Center for Electron Photon Science, Tohoku University. We constructed the Neutral Kaon Spectrometer-2 for the detection of charged particles from the decay of the neutral kaon and the hyperon. We obtained a momentum distribution of K ⁰ with the inclusive measurement. It was consistent with the previous measurement. The total cross section of γ + d → K ⁰ + Λ + p was estimated from the measured integral cross section of γ + d → Λ + X. The total cross section with respect to the photon energy was compared with the theoretical calculations. It favored the Saclay-Lyon A model calculation with the ratio of the neutral to charged coupling constants of the axial-vector meson, K ₁, as ~ ?1.5. The energy dependence and the magnitude of the total cross section were similar to the total cross section of γ + p → K ⁺ Λ.     

Asymptotics for functionals of self-normalized residuals of discretely observed stochastic processes

The purpose of this paper is to derive the stochastic expansion of self-normalized-residual functionals stemming from a class of diffusion type processes observed at high frequency, where total observing period may or may not tend to infinity. The result enables us to construct some explicit statistics for goodness of fit tests, consistent against “presence of a jump component” and “diffusion-coefficient misspecification”; then, the acceptance of the null hypothesis may serve as a collateral evidence for using the correctly specified diffusion type model. Especially, our asymptotic result clarifies how to remove the bias caused by plugging in a diffusion-coefficient estimator.     

Carboxylic acid recognition of diamidine having a fluorescent 1,8-diphenylanthracene unit and its detection of amidinium-carboxylate and amidinium formation

A diphenylanthracene-based diamidine (1a) fluorescent probe for the detection of dicarboxylic acids has been designed and synthesized, which has an extended π-conjugation rather than a simple anthracene ring, in order to observe highly different fluorescence wavelengths after complex formation with dicarboxylic acids. The fluorescence spectra of the mixed solution of the diamidine 1a and carboxylic acids showed two different fluorescence bands, which corresponded to the complex formation (amidinium-carboxylate formation, λ_em?=?450?nm, light blue color) and dissociated amidinium formation (λ_em?=?510?nm as a broad band, green color). The complexed and dissociated states were confirmed by DOSY NMR and TD-DFT calculations. These different fluorescence wavelengths may come from the differences in the dihedral angles between the phenyl rings at the 1,8-position and anthracene ring (difference in π-conjugation) of 1a under complex formation and dissociated amidinium formation. The proposed mechanism for the observation of the different fluorescence wavelengths (complex formation and amidinium formation) was also confirmed by the fluorescence study of diamidine 1b which causes restricted rotation of the phenyl rings by substitution of the steric methyl groups, and observed the same fluorescence spectra for the complex formation and amidinium formation (400, 420, 450?nm as a vibrational structure of anthracene ring). These fluorescence characteristics of the diamidine 1a are also applicable for the detection of α,ω?dicarboxylic acids.     

Synthetic study of a moss-produced oxylipin and its structural revision

The proposed structure for a moss-produced acetylenic oxylipin (10-keto-type structure) was synthesized from a known glycidol derivative by an 11-step sequence involving epoxide ring opening with a terminal acetylene and enzymatic hydrolysis of a methyl ester intermediate. The NMR spectra of the proposed structure was, however, different from those of the natural oxylipin, which prompted us to synthesize its 9-epi-isomer and two diastereomeric 12-keto-type positional isomers. Comparison of the NMR spectra of the three isomers with those of the natural oxylipin indicated that the natural oxylipin was actually a mixture of the two diastereomeric positional isomers.     

Optical resolution via catalytic generation of chiral auxiliary

A new catalytic method for separating enantiomers of racemic compounds is proposed. Catalytic asymmetric addition of racemic trans-2-substituted cyclohexanols to imines provided diastereomeric mixtures of aminals, and the subsequent separation of the enantiomers by silica-gel column chromatography and the hydrolysis of the aminals produced the alcohols in an optically active form.     

Structure Switching and Modulation of the Magnetic Properties in Diarylethene‐Bridged Metallosupramolecular Compounds by Controlled Coordination‐Driven Self‐Assembly

We report three self‐assembled iron complexes that comprised an anti‐parallel open form (o‐ L _anti), a parallel open form (o‐ L _syn), and a closed form (c‐ L ) of diarylethene conformers. Under kinetic control, Fe^II₂(o‐ L _anti)₃ was isolated, which exhibited a dinuclear structure with diamagnetic properties. Under light‐irradiation control, Fe^II₂(c‐ L )₃ was prepared and exhibited paramagnetism and spin‐crossover behaviour. Under thermodynamic control and in the presence of indispensable [Fe^III(Tp*)(CN)₃]^?, Fe^II₂(o‐ L _anti)₃ and Fe^II₂(c‐ L )₃ transformed into tetranuclear Fe^III₂Fe^II₂(o‐ L _syn)₂, which exhibited complete spin‐crossover behaviour at T_1/2=353 K.     

Characteristics of ZnO epilayer on the post-annealed buffer layer on GaN/sapphire substrate by pulsed laser deposition

We employed epi-GaN substrates for ZnO film growth, and studied the deposition and post-annealing effects. ZnO films were grown by pulsed laser deposition (PLD) method. The as-grown films were annealed for one hour under atmospheric pressure air. ZnO morphologies after annealing were investigated and the post-annealed ZnO films grown at T _g =700^oC have very smooth surfaces and the rms with roughness is about 0.5 nm. Finally, ZnO post-annealed buffer layer was inserted between ZnO epilayer and GaN/sapphire substrates. It is confirmed by AFM that growth temperature of 700^oC helps the films grow in step-flow growth mode. It is observed by cathode luminescence spectrum that the ZnO film grown at 700^oC has very low visible luminescence, indicating the decrease of the deep level defects. It is also revealed by Hall measurements that carrier concentration is decreased by increasing the growth temperatures. It is suggested that low temperature buffer layer growth and post-annealing technique can be used to fabricate ZnO hetero-epitaxy.