Singularities of maximal surfaces

We show that the singularities of spacelike maximal surfaces in Lorentz–Minkowski 3-space generically consist of cuspidal edges, swallowtails and cuspidal cross caps. The same result holds for spacelike mean curvature one surfaces in de Sitter 3-space. To prove these, we shall give a simple criterion for a given singular point on a surface to be a cuspidal cross cap. Dedicated to Yusuke Sakane on the occasion of his 60th birthday.     

Evaluating the ability of polyhydroxyalkanoate synthase mutants to produce P(3HB-co-3HA) from soybean oil

Polyhydroxyalkanoate (PHA) synthase from Pseudomonas sp 61-3 (PhaC1(Ps)) is able to synthesize P(3HB-co-3HA), consisting of a 3HB unit and medium-chain-length 3HA units of 6-12 carbon atoms. Expression vectors encoding 76 PhaC1(Ps) mutants with an amino acid replacement at position 130, 325, 477 or 481 were individually introduced into Ralstonia eutropha. The mutant enzyme genes were evaluated in terms of their abilities to synthesize P(3HB-co-3HA) using soybean oil as a carbon source. 20 mutants showed significantly high accumulation levels of PHA exceeding 30 wt.-% and as high as 57 wt.-%. It was found that hydrophobic amino acids at the positions are more likely to enhance accumulation of PHA in R. eutropha.     

On commutator of generalized Aluthge transformations and Fuglede–Putnam theorem

Let \(A=U|A|\) be the polar decomposition of A on a complex Hilbert space \({\mathscr {H}}\) and \(0<s,t\). Then \({\widetilde{A}}_{s, t}=|A|^sU|A|^t\) and \({\widetilde{A}}_{s, t}^{(*)}=|A^*|^sU|A^*|^t\) are called the generalized Aluthge transformation and generalized \(*\)-Aluthge transformation of A, respectively. A pair (A, B) of operators is said to have the Fuglede–Putnam property (breifly, the FP-property) if \(AX=XB\) implies \(A^*X=XB^*\) for every operator X. We prove that if (A, B) has the FP-property, then \(({\widetilde{A}}_{s, t},{\widetilde{B}}_{s, t})\) and \((({\widetilde{A}}_{s, t})^{*},({\widetilde{B}}_{s, t})^{*})\) has the FP-property for every \(s,t>0\) with \(s+t=1\). Also, we prove that \(({\widetilde{A}}_{s, t},{\widetilde{B}}_{s, t})\) has the FP-property if and only if \((({\widetilde{A}}_{s, t})^{*},({\widetilde{B}}_{s, t})^{*})\) has the FP-property, where A, B are invertible and \( 0 < s, t \) with \( s + t =1\). Moreover, we prove that if \(0 < s, t\) and \({\widetilde{A}}_{s, t}\) is positive and invertible, then \(\left\| {\widetilde{A}}_{s, t}X-X{\widetilde{A}}_{s, t}\right\| \le \left\| A\right\| ^{2t}\left\| ({\widetilde{A}}_{s, t})^{-1}\right\| \left\| X\right\| \) for every operator X. Also, if \( 0 <s, t\) and X is positive, then \(\left\| |{\widetilde{A}}_{s, t}|^{2r} X-X|{\widetilde{A}}_{s, t}|^{2r}\right\| \le \frac{1}{2}\left\| |A|\right\| ^{2r}\left\| X\right\| \) for every \(r>0\).     

p-Phenylenediamine Epoxy Resin Film for Redox Enzyme Detection

Summary: Phenylenediamine derivatives (PDs) are environmentally hazardous, though very useful for chemical analysis. To minimize release into the environment, a PD-containing epoxy resin film was developed that retained redox enzyme activity. p-Phenylenediamine and 2,2-bis(4-glycidyloxyphenyl)-propane were cured to produce a violet film. This film was reactive against peroxidase, a redox enzyme that oxidizes phenylenediamine to afford an imine. Enzymatic oxidation caused the film to change color from violet to deep green. The film exhibited fluorescence at 394 nm under excitation at 350 nm, and the fluorescent intensity decreased with greater oxidation. Thus, the film could be used to detect redox enzyme activity.     

Performance of the micro‐PIC gaseous area detector in small‐angle X‐ray scattering experiments

The application of a two‐dimensional photon‐counting detector based on a micro‐pixel gas chamber (µ‐PIC) to high‐resolution small‐angle X‐ray scattering (SAXS), and its performance, are reported. The µ‐PIC is a micro‐pattern gaseous detector fabricated by printed circuit board technology. This article describes the performance of the µ‐PIC in SAXS experiments at SPring‐8. A dynamic range of >10⁵ was obtained for X‐ray scattering from a polystyrene sphere solution. A maximum counting rate of up to 5 MHz was observed with good linearity and without saturation. For a diffraction pattern of collagen, weak peaks were observed in the high‐angle region in one accumulation of photons.     

Efficient refractive-index modification of fused silica by a resonance-photoionization-like process using F(2) and KrF excimer lasers

Novel materials processing by a multiwavelength excitation process using F(2) and KrF excimer lasers for high-efficiency and high-speed refractive-index modification of fused silica is demonstrated. We find this process to be essentially superior to single-wavelength F(2) -laser processing: The multiwavelength excitation process achieves more than twice the diffraction efficiency of fused silica modified by a F(2) laser at the same total number of photons in each irradiated laser beam supplied to the fused-silica substrate. This superiority is attributed to a resonance-photoionization-like process based on excited-state absorption.     

Ring conformations of d-glucose derivatives possessing two bulky silyl protecting groups at the 3,4-positions; the first observation of a stable full-axial chair conformer without bridge structures

The ring conformations of 3,4-bis-O-tert-butyldimethylsilyl- and 3,4-bis-O-tert-butyldiphenylsilyl-d-glucopyranoses as well as the corresponding phenyl 1-thio-d-glucopyranosides were investigated. Observations showed that the introduction of the two tert-butyldiphenylsilyl groups can flip the pyranose-ring into the ¹C₄ conformation possessing more axial substituents. All the substituents of the 3,4-bis-O-tert-butyldiphenylsilyl-β-d-glucopyranose were axially oriented.     

PHOTOREVERSIBLE Ca2+-DEPENDENT AGGREGATION OF PURIFIED PHYTOCHROME FROM ETIOLATED PEA AND RYE SEEDLINGS

The aggregation of phytochrome purified from etiolated pea ( Pisum satirum cv. Alaska) and rye ( Secale cereale cv. Cougar) tissues was investigated by centrifugation and turbidimetry. Purified pea phytochrome (A₆₆₉/A₂₈₀= 0.88), if irradiated with red light, became precipitable in the presence of CaCl₂. The precipitation upon red-light irradiation was optimal at a Ca^2- or Mg²⁺ concentration of 10–20 m M , was greater at increased phytochrome concentration or lower pH values, and was inhibited by 0.1 M KG. The precipitated phytochrome slowly became soluble after far-red light exposure.
Turbidity of pea phytochrome solutions after red-light irradiation also increased rapidly in the presence of either Ca²⁺ or Mg²⁺. Far-red light exposure after the red light cancelled the turbidity increase. Rye phytochrome showed less turbidity increase than pea phytochrome and occurred only in the presence of Ca²⁺. Partially degraded pea phytochrome produced by endogenous proteases in the extract did not show the turbidity increase. Undegraded pea phytochrome also associated with microsomal fractions under conditions similar to those described above, but the partially degraded phytochrome did not.