On the Automorphism Group of the Kohn-Nirenberg Domain

In this paper, we prove that there are no automorphism orbits of the Kohn-Nirenberg domain accumulating at the origin.     

Riesz potential estimates for a class of double phase problems

A double phase problem with a bounded Borel measure on the right hand side is studied. We prove an optimal pointwise gradient estimate for such a measure data problem via Riesz potentials of the measure under log-Dini continuity assumption on the modulating coefficients. As a consequence, we find an optimized $C^1$ regularity criterion.     

A two-point in situ method for simultaneous analysis of radioactivity in seawater and sediment

A new in situ radioactivity analysis method was developed to determine the fractional contributions of gamma-ray emitters in seawater and sediment from total measured counts. A semi-empirical formula to determine the fractional count contributions was derived using the variation characteristics of the gamma-ray attenuation rate and geometrical efficiency with the measurement points. The proposed method was employed to make in situ gamma-ray measurements using a CeBr₃ detector for radioactivity analysis of seawater and sediment at a coastal area with a relatively high tidal range. The full energy peak efficiency of the detector at measurement site was obtained using the GEANT4 simulation code. The radioactivity concentration of ⁴⁰K in seawater and sediment was determined using the proposed method and laboratory analysis with sampling. The MDA of the in situ measurement for ¹³⁷Cs and ¹³¹I was also estimated assuming they were deposited on the sediment surface-layer. The validation of this method was demonstrated by comparing with the sampling analysis results.

     

Optical measurement of neural activity using surface plasmon resonance

We demonstrate that surface plasmon resonance (SPR) is applicable to the optical detection of neural signals. A low-noise SPR sensor was developed as a label- and artifact-free method for the extracellular recording of neural activity. The optical responses obtained from a rat sciatic nerve were highly correlated with simultaneously recorded electrical responses. Additional studies with stimulation intensity and lidocaine further confirmed that the optically measured signals originated from neural activities.     

Regularity results of the thin obstacle problem for the p(x)-Laplacian

We study thin obstacle problems involving the energy functional with $p(x)$-growth. We prove higher integrability and Hölder regularity for the gradient of minimizers of the thin obstacle problems under the assumption that the variable exponent $p(x)$ is Hölder continuous.     

Pulse-amplitude equalization using a polarization-maintaining laser resonator

For the first time to our knowledge, pulse-amplitude equalization of rational-harmonically mode-locked fiber ring laser pulses has been experimentally demonstrated using a polarization-maintaining laser resonator without any additional device. The pulse-amplitude distribution of the laser pulses was controlled by the modulator driving power, and stable pulse-amplitude-equalized pulses with repetition rates of 20, 30, and 40 GHz have been obtained in the linear region of the modulator.     

Quality properties of sausage made with gamma irradiated natural casing from intestine of pork or lamb

Quality properties in emulsion-type sausage stuffed into irradiated natural casing were studied. The numbers of total aerobic bacteria, Enterococci and coliform bacteria in the sausage prepared with irradiated natural pork and lamb casing were significantly decreased or eliminated compared to those prepared with the nonirradiated control. The 2-thiobarbituric acid reactive substances (TBARS) value in the sausage with irradiated natural casing did not change significantly during storage with minor exceptions. The total working force of shear of the sausages were decreased in both irradiated casings but the sensory evaluation showed no difference. Therefore, the gamma irradiation was a useful technique to sanitize the natural pork and lamb casings and to extend the shelf-life of the sausage made with natural casings during distribution.     

Electron transfer behavior at polyoxometalate-adsorbed alkanethiol self-assembled monolayers

The interaction between polyoxometalate (POM) anions, SiMo₁₂O₄₀⁴⁻, and a self-assembled monolayer (SAM) of dodecanethiol (DT) on Au surfaces was investigated using electrochemical methods, X-ray photoelectron spectroscopy, and scanning probe microscopy. The SiMo₁₂O₄₀⁴⁻ ions adsorb on the SAM of DT on Au to form a composite organic-inorganic hybrid layer. The adsorbed SiMo₁₂O₄₀⁴⁻ ion on the SAM layer shows its characteristic redox waves with an electron transfer rate slower than that on a bare Au electrode. The electron transfer behavior at DT−SAM could be regulated by the adsorption of SiMo₁₂O₄₀⁴⁻ depending on the charge of the investigated electroactive species: a significant increase toward a positively charged Ru(NH₃)₆³⁺ ion, a moderate increase toward a neutral 1,1′-ferrocenedimethanol molecule and a slight decrease toward a negatively charged Fe(CN)₆³⁻ ion. The effect of the chain length of alkanethiols on the adsorption of SiMo₁₂O₄₀⁴⁻ ion was also investigated: as the chain length decreases, the amount of the adsorbed POM increases and the electron transfer rate through the composite layers increases. The nature of SiMo₁₂O₄₀⁴⁻ ions adsorbed on the SAMs of alkanethiols on Au is discussed in detail.     

Global gradient estimates for non-uniformly elliptic equations

We consider a nonlinear and non-uniformly elliptic problem in divergence form on a bounded domain. The problem under consideration is characterized by the fact that its ellipticity rate and growth radically change with the position, which provides a model for describing a feature of strongly anisotropic materials. We establish the global Calderón–Zygmund type estimates for the distributional solution in the case that the boundary of the domain is of class \(C^{1,\beta }\) for some \(\beta >0\).