Vibrations and chemical states of iron ions in soda‐lime glasses determined by element‐specific X‐ray analyses

We systematically study medium‐range structures including more than three neighboring atoms around iron ions (Fe²⁺ and Fe³⁺) in soda‐lime glass samples with low iron oxide concentrations (M_Fe2O3) and a wide number ratio of Fe²⁺ to all iron ions (Fe²⁺/Σ_nFe). The precise medium‐range structures around iron ions in glass have not yet been revealed because of a lack of the appropriate measurement methods. To avoid this problem, we used element‐specific nuclear resonant inelastic scattering (NRIS) with synchrotron X‐rays to observe the vibrations of iron ions (⁵⁷Fe). The vibrations are related to medium‐range structures with more than three neighboring atoms and to the potential asymmetry and the coordination environment, around iron ions. The NRIS method has high sensitivity and can measure over a wide concentration range. Linear combination fitting of the X‐ray absorption fine structure spectra, which measures only the first neighbors but is a faster than using the NRIS method, was also used additionally. A systematically produced set of glasses with 0.015–5 wt% M_Fe2O3 and 0–0.85 Fe²⁺/Σ_nFe was measured with these methods. It was found that the soda‐lime glass possessed two different medium‐range structures with different iron ion valences (~2+ or ~3+), which were determined by the Fe²⁺/Σ_nFe, and that these structures were generated during production of the glass. Moreover, these medium‐range structures were the same from 0.015 to 5 wt% M_Fe2O3.     

Simultaneous imaging for surface and internal structure of polymer blend thin films

A novel experimental technique for three-dimensional (3D) visualization of phase-separated structure of polymer blend thin film was proposed. Polystyrene/poly(methyl methacrylate) (PS/PMMA) blend thin films with the thickness of approximately 100 nm were cut at extremely low angle by utilizing surface and interface cutting analysis system (SAICAS), and the cross-section was exposed as gradient surface with the width of approximately 2.5 μm. SFM investigation for the grazing cross-section imaged the detailed internal and surface phase separated structure of the (PS/PMMA) blend thin films on one image.     

Improved omnibus test statistic for normality

We propose a new omnibus test statistic for normality based on the Jarque–Bera test statistic. We give the exact first four moments of the null distribution for the statistic using a computer algebra system. Our proposed statistic is an improvement of Jarque–Bera test statistic. Then the cumulants of the standardized statistic satisfy the Cornish–Fisher assumption. We give a normalizing transformation of the statistic based on the Wilson–Hilferty transformation.     

The codes and the lattices of Hadamard matrices

It has been observed by Assmus and Key as a result of the complete classification of Hadamard matrices of order 24, that the extremality of the binary code of a Hadamard matrix H of order 24 is equivalent to the extremality of the ternary code of H^T. In this note, we present two proofs of this fact, neither of which depends on the classification. One is a consequence of a more general result on the minimum weight of the dual of the code of a Hadamard matrix. The other relates the lattices obtained from the binary code and the ternary code. Both proofs are presented in greater generality to include higher orders. In particular, the latter method is also used to show the equivalence of (i) the extremality of the ternary code, (ii) the extremality of the Z₄-code, and (iii) the extremality of a lattice obtained from a Hadamard matrix of order 48.     

Parallel computing of radiative transfer in relativistic jets using Monte Carlo method

We present numerical attempts of radiative transfer in a relativistic scattering flow that can produce gamma rays using a three-dimensional Monte Carlo code. We prepared an initial background flowfield obtained from hydrodynamical simulation of a relativistic jet in which Thomson scattering dominates compared to absorption, and solved the radiative transfer equation for the background evolved by a simple expansion model. Since a large number of sample particles is required for an accurate computation, we have parallelized the Monte Carlo code in order to obtain solutions in a practical computational time even for a long-term simulation coupled with a time-dependent flowfield. Using this code, higher parallel efficiency is achieved with larger number of particles. The obtained light curve from the simple model shows a signal of the transition from the opaque post-shock flow to the transparent regime as the flow expands, and the high-energy photons are generated by not only the Doppler boosting but also the inverse Compton scattering.     

AIC for the non-concave penalized likelihood method

Annals of the Institute of Statistical Mathematics - Non-concave penalized maximum likelihood methods are widely used because they are more efficient than the Lasso. They include a tuning parameter...     

AF Embeddability of Crossed Products of AT Algebras by the Integers and Its Application

We will show that the crossed products of unital simple real rank zero AT algebras by the integers are AF embeddable. This is a generalization of Brown's AF embedding theorem. As an application, we will prove the AF embeddability of crossed product algebras arising from certain minimal dynamical systems induced by two commuting homeomorphisms.     

Prethick Subcategories of Modules and Characterizations of Local Rings

This article studies characterizing local rings in terms of homological dimensions. The key tool is the notion of a prethick subcategory which we introduce in this article. Our methods recover the theorems of Salarian, Sather-Wagstaff, and Yassemi.     

Efficient estimation of stable Lévy process with symmetric jumps

Efficient estimation of a non-Gaussian stable Lévy process with drift and symmetric jumps observed at high frequency is considered. For this statistical experiment, the local asymptotic normality of the likelihood is proved with a non-singular Fisher information matrix through the use of a non-diagonal norming matrix. The asymptotic normality and efficiency of a sequence of roots of the associated likelihood equation are shown as well. Moreover, we show that a simple preliminary method of moments can be used as an initial estimator of a scoring procedure, thereby conveniently enabling us to bypass numerically demanding likelihood optimization. Our simulation results show that the one-step estimator can exhibit quite similar finite-sample performance as the maximum likelihood estimator.