Wavelet processing and digital interferometric contrast to improve reconstructions from X‐ray Gabor holograms

In this work, the application of an undecimated wavelet transformation together with digital interferometric contrast to improve the resulting reconstructions in a digital hard X‐ray Gabor holographic microscope is shown. Specifically, the starlet transform is used together with digital Zernike contrast. With this contrast, the results show that only a small set of scales from the hologram are, in effect, useful, and it is possible to enhance the details of the reconstruction.     

Direct Monitoring of Thickness and Refractive Index of Optical Thin Film Deposited on Fiber End-face

We propose a system for depositing thin films on waveguides which enables low-temperature deposition and precise control of the refractive index and film thickness. It is composed of a conventional ion-beam sputtering (IBS) system and a new system for directly monitoring film characteristics during deposition. We controlled refractive indices over a wide range from 1.52 to 1.97 by moving the sputtering targets (SiO₂ and Si₃N₄) in the IBS system. The refractive index or film thickness was in-situ monitored by observing the optical power reflected from the end-face of a monitoring fiber set in the deposition chamber. Antireflection coating films were successfully deposited on a fiber end-face and a laser diode chip facet with low reflectivity from 0.05 to 0.07%. This deposition system is attractive for constructing highly functional optical devices for future photonic networks.     

Congruence properties of Apéry numbers

Apéry introduced a recurrence relation for a proof of the irrationality of ζ(3). Let a_n (n ≥ 0) satisfy the relation n³a_n ? (34n³ ? 51n² + 27n ? 5)a_{n ? 1} + (n ? 1)³a_{n ? 2} = 0. Which values of a₀ and a₁ cause each a_n to be an integer? This question is answered and some congruence properties of the a_n are given.     

On two expressions of the MLE for a special case of the extended growth curve models

An algebraic proof is given on the equivalence between two solutions of MLEs for a special case of the extended growth curve models called the Banken model. One solution given by Verbyla and Venables is an iterative solution in the general case but reduces to a non-iterative one in the case of the Banken model. The other solution given by von Rosen is a closed-form solution specifically targeted at the Banken model. The proof has turned out to be quite challenging yet intriguing as it touches on many aspects of intricate matrix theory involving projection matrices.     

On the necessary and sufficient condition for the extended Wedderburn–Guttman theorem

Let A be a u by v matrix, and let M and N be u by p and v by q matrices, where p may not be equal to q or rank(M^′AN)<min(p,q). Recently, Galantai [A. Galantai, A note on the generalized rank reduction, Acta Math. Hungarica 116 (2007) 239–246] presented what he claimed to be the necessary and sufficient condition for rank(A-AN(M^′AN)^-M^′A)=rank(A)-rank(AN(M^′AN)^-M^′A) to hold. This rank subtractivity formula along with the condition under which it holds is called the extended Wedderburn–Guttman theorem. In this paper, we show that some of Galantai’s assertions are incorrect.     

High oxygen-reduction activity of silk-derived activated carbon

Activated carbon prepared from silk fibroin, which is free of metal elements, showed a high catalytic activity for the oxygen-reduction reaction (ORR). The activated carbon had a very high onset potential of E_onset = 0.83 V (vs. RHE) in oxygen-saturated 0.5 M H₂SO₄ at 60 °C. The ORR on the activated carbon proceeded by a four-electron process in the high-electrode-potential region; this gradually decreased to a 3.5-electron reaction below about 0.6 V (vs. RHE). Only about 1% of nitrogen atoms (mostly quaternary) remained in the activated carbon by heat-treatment at up to 1200 °C are responsible for the high catalytic activity. The open circuit voltage of a polymer electrolyte fuel cell using the activated carbon as the cathode and a platinum/carbon black anode under pure oxygen and hydrogen gases, respectively, both at one atmosphere, was 0.96 V at 27 °C.     

Binding enhancements of nicotinic acid to water-soluble zinc porphyrins based on triple attractions of coordination, Coulomb, and CH-pi interactions

The binding of amines to artificial zinc-porphyrin receptors 1-4 was examined in basic aqueous solutions. For nicotinic acid and 3,5-dicarboxypyridine, substantial binding enhancements were observed compared to other amines with no pi system or carboxyl group. This observation suggested that interligand attractions of Coulomb and CH-pi interactions in addition to N-atom coordination can act effectively as recognition factors. The differences in the Coulomb interaction between carboxylate and sulfonate anions were also discussed.