Fractional maximal operators with weighted Hausdorff content

Positivity - Let $$n\ge 2$$ be the spatial dimension. The purpose of this note is to obtain some weighted estimates for the fractional maximal operator $${{\mathfrak {M}}}_{\alpha }$$ of order...     

Polymorphism of 4-Fluorophenylpyruvic Acid Studied by X-Ray Crystallography and Vibrational Spectroscopy

Two polymorphic forms (I and II) of 4-fluorophenylpyruvic acid (F-PPA) were obtained by crystallization from different solvents, showing a melting point at 163.2 and 171.0 °C. Crystal structures of polymorphs I and II were determined by X-ray crystallography. IR and Raman spectra of the two polymorphs were measured and the spectral characteristics were compared with those of phenylpyruvic acid. the two polymorphs show similar molecular and crystal structures to each other, except for the molecular geometries of the enol and the carboxylic acid moieties. Distinct IR spectral differences which result from the crystal field splitting were observed between the two polymorphs.     

Reflectivity measurements of superionic conductors for Li ion secondary battery materials

The reflection measurements of superionic conductors LiCoO₂ and Li_1-xCoO₂, which are already in use for the positive electrode material of 4 V rechargeable lithium batteries, have been performed in the millimeter wave region from 6 to 60 cm⁻¹ using the electron storage ring facilities of Institute of Molecular Science in Okazaki. The increase of the reflectivity has been observed in the low wavenumber region below 10 cm^-1 above 300 K in Li_1-xCoO₂ for the first time, while the reflectivity of LiCoO₂ has almost the constant value in all observed temperature region between 77 to 380 K. The results will be discussed in connection with our previous results of LiNiO₂.     

An NC Parallel Algorithm for Edge-Coloring Series–Parallel Multigraphs

Many combinatorial problems can be efficiently solved in parallel for series–parallel multigraphs. The edge-coloring problem is one of a few combinatorial problems for which no NC parallel algorithm has been obtained for series–parallel multigraphs. This paper gives an NC parallel algorithm for the problem on series–parallel multigraphsG. It takesO(log n) time withO(Δn/log n) processors, wherenis the number of vertices and Δ is the maximum degree ofG.     

An active resonator system for CW-ESR measurement operating at 700 MHz

An active resonator system operating at 700 MHz, which can attain a high Q for CW-ESR measurements of a high loss sample, was developed. This system consisted of a loop-gap resonator (LGR), a receiver coil, an excitation coil, and a phase tunable amplifier. A part of the RF power at the LGR was picked up by the receiver coil, amplified, and irradiated to the LGR again by the excitation coil, which made up a feedback circuit. Because the feedback circuit provided the energy that canceled the loss in the resonator, the Q of the active resonator system increased. When a sample tube (inner diameter, 20 mm; axial length, 31 mm) containing a nitroxide radical and physiological saline solution was placed in the resonator, the Q could be varied from 55 to 4000. It was possible to obtain a Q of the active resonator system with sample that was higher than that of the value of the LGR without a sample in a no-feedback condition. The ESR signal intensity increased up to 7 times with the increase in Q. The sensitivity increased up to 50%, which was a much smaller advance than that of the Q, because the noise level also increased with the increase in signal intensity.     

Simultaneous determination of D-glucose and 3-hydroxybutyrate by chemiluminescence detection with immobilized enzymes in a flow injection system.

A chemiluminometric flow-through sensor for the simultaneous determination of glucose (Glu) and 3-hydroxybutyrate (HB) in a single sample has been developed. Coimmobilized 3-hydroxybutyrate dehydrogenase/NADH oxidase/peroxidase, a support material, and coimmobilized glucose dehydrogenase/NADH oxidase/peroxidase were packed sequentially in a transparent PTFE tube. The tube was then placed in front of a photomultiplier tube as a flow cell. A two-peak recording was obtained by one injection of the sample solution. The peak heights of the first and second peaks were dependent on the concentrations of HB and Glu, respectively. The calibration graphs for HB and Glu were linear at 0.05-10 and 0.1-30 microM, respectively. The maximum sample throughput was 30 h(-1). The sensor was stable for two weeks.     

Synthesis of Al–Cr decagonal quasicrystal nanoparticles and their temperature of phase transformation to stable crystal phase

The synthesis of Al–Cr single quasicrystal (QC) nanoparticles of the decagonal phase was achieved by introducing an advanced gas flow evaporation method. By obtaining successive electron diffraction patterns for single-QC nanoparticles, the phase transformation temperature of a single-QC nanoparticle was determined to be 700 °C. It was also determined that part of the QC nanoparticle decomposed into hex-Al₈Cr₅ and Al during the phase transformation. Since the grain growth did not occur during the phase transformation in the present experiment, the inherent phase transformation temperature could be measured.     

Peroxidase-dependent fluorescence decrease of carboxyfluorescein and its enhancement by liposome encapsulation

The fluorescence intensity of 5(6)-carboxyfluorescein (CF) was decreased by addition of horseradish peroxidase (HRP) and hydrogen peroxide (H₂O₂). The reaction inside a liposome containing CF and HRP on addition of H₂O₂ was measured fluorometrically after destruction of the liposome with Triton X-100. The reaction efficiency was higher than that without liposome because CF and HRP were concentrated inside the latter. The determination of H₂O₂ can be performed with a smaller amount of HRP by liposome encapsulation.     

Side-chain relaxation in stereoregular poly(isobutyl methacrylate)

The effects of stereoregularity on the low-temperature relaxation processes were studied by dynamic mechanical measurements on isotactic and syndiotactic polyisobutyl methacrylates (iso-PiBMA and syn-PiBMA). The α, β, and γ relaxation processes were observed in both stereoregular forms. Both the α, and β loss peaks were at lower temperatures for iso-PiBMA than for syn-PiBMA. The γ loss peak was observed at about ?155°C at 30 Hz for both forms, and the apparent activation energy of this process was same for both samples within experimental error (6.7 ± 0.5 kcal/mole). It was reduced from these results that the α and β processes are both considerably influenced by the isotactic configuration but the γ process is not.