Critical exponent and critical blow-up for quasilinear parabolic equations

B ₂-groups are special (torsion-free) abelian Butler groups. The interest in this class of groups comes from representation theory. A particular functor, also called Butler functor, connects algebraic properties of the category of free abelian groups with (a few) distinguished subgroups with these Butler groups. This helps to understand Butler groups and caused lots of activities on Butler groups. Butler groups were originally defined for finite rank, however a homological connection discovered by Bican and Salce opened the investigation of Butler groups of infinite rank. Despite the fact that classifications of Butler groups are possible under restriction even for infinite rank (see a forthcoming paper by Files and Göbel [Mathematische Zeitschrift]), general structure theorems are impossible. This is supported by the following very special case of the Main Theorem of this paper, showing that any ring with a free additive group is an endomorphism ring of a Butler group. The result implies the existence of large indecomposable or of large superdecomposable Butler groups as well as the existence of counter-examples for Kaplansky’s test problems.     

Achievement of a 920-MHz high resolution NMR

We have developed a 920-MHz NMR system and performed the proton NMR measurement of H(2)O and ethylbenzene using the superconducting magnet operating at 21.6 T (920 MHz for proton), which is the highest field produced by a superconducting NMR magnet in the persistent mode. From the NMR measurements, it is verified that both homogeneity and stability of the magnet have a specification sufficient for a high resolution NMR.     

Cluster Categories Coming from Cyclic Posets

Cyclic posets are generalizations of cyclically ordered sets. In this article, we show that any cyclic poset gives rise to a Frobenius category over any discrete valuation ring R. The stable category of a Frobenius category is always triangulated and has a cluster structure in many cases. The continuous cluster categories of [14 Igusa , K. , Todorov , G. ( 2013 ). Continuous Frobenius categories . Proceedings of the Abel Symposium 2011 : 115 – 143 .[Crossref] , [Google Scholar]], the infinity-gon of [12 Holm , T. , Jøot rgensen , P. ( 2012 ). On a cluster category of infinite Dynkin type, and the relation to triangulations of the infinity-gon . Math. Z. 270 : 277 – 295 .[Crossref], [Web of Science ®] , [Google Scholar]], and the m-cluster category of type A _∞ (m ≥ 3) [13 Holm , T. , Jøot rgensen , P. ( 2015 ). Cluster tilting vs. weak cluster tilting in Dynkin type A infinity . Forum Math. 27 : 1117 – 1137 .[Crossref], [Web of Science ®] , [Google Scholar]] are examples of this construction as well as some new examples such as the cluster category of ?². An extension of this construction and further examples are given in [16 Igusa, K., Todorov, G. Continuous Cluster Categories of Type D. arXiv:1309.7409 . [Google Scholar]].     

Optical current transducers using flint glass fiber as the faraday sensor element

This paper describes development of the optical current transducers using flint glass fiber as the Faraday effect sensing element. Excellent polarization properties of the fiber with low birefringence are described, and the design and test data of a current transducer using the fiber manufactured for use in electric power facilities are reviewed. Experimental results on flexible characteristics of a scheme with round trip light transmission in the fiber is also reported.     

Nanoparticles in Emissions and Atmospheric Environment: Now and Future

Journal of Nanoparticle Research -     

Nanometric summation architecture based on optical near-field interaction between quantum dots

A nanoscale data summation architecture is proposed and experimentally demonstrated based on the optical near-field interaction between quantum dots. Based on local electromagnetic interactions between a few nanometric elements via optical near fields, we can combine multiple excitations at a certain quantum dot, which allows construction of a summation architecture. Summation plays a key role for content-addressable memory, which is one of the most important functions in optical networks.     

Magneto-Optical Properties of Silica Gel Containing Magnetite Fine Particles

The magnetic composite materials that consist of transparent matrix and magnetic fine particles are expected to have large residual magnetization and coercive force because of their fine magnetic domain structure, and also to show magneto-optical effects. Silica gels containing magnetite (Fe₃O₄) fine particles were prepared by sol-gel method. The magnetic, optical and magneto-optical properties of the composites were investigated by measurements of magnetization curves, UV-visible spectra and Faraday rotation in visible range. The saturation magnetization of the composite was almost as same as that expected from the amount of magnetite fine particles in it. Although the composites had large and broad absorption at around 400 nm, they still maintained their transparency. The origins of decrement of transparency attributed to the optical absorption of magnetite and scattering due to magnetite fine particles. The whole composites showed positive Faraday rotation under external static magnetic field due to the large contribution of diamagnetic silica gel matrix. Magnetite contributed negative Faraday rotation with maximum at around 470–480 nm to the magneto-optical spectra of the composites.     

Boron 1s photoelectron spectrum of 11BF3: vibrational structure and linewidth

The boron 1s photoelectron spectrum of (11)BF(3) has been measured at a photon energy of 400 eV and a resolution of about 55 meV. The pronounced vibrational structure seen in the spectrum has been analyzed to give the harmonic and anharmonic vibrational frequencies of the symmetric stretching mode, 128.1 and 0.15 meV, as well as the change in equilibrium BF bond length upon ionization, -5.83 pm. A similar change in bond length has been observed for PF(3) and SiF(4), but a much smaller change for CF(4). Theoretical calculations for BF(3) that include the effects of electron correlation give results that are in reasonable accord with the experimental values. The Lorentzian (lifetime) width of the boron 1s core hole in BF(3) is found to be 72 meV, comparable to the value of 77 meV that has been reported for CF(4).     

Fluorescent behavior of 2‐(3,4,5,6‐tetrafluoro‐2‐hydroxyphenyl)imidazo‐[1,2‐a]pyridine in the presence of metal perchlorate

2‐(3,4,5,6‐Tetrafluoro‐2‐hydroxyphenyl)imidazo[1,2‐a]pyridine ( 1 ) emits long wavelength light around 540 nm both in polar and in nonpolar solvents. Zn²⁺ perchlorate in acetonitrile causes the intermediate wavelength emission around 430 nm, which is ascribed to the species where the imidazole nitrogen atom and the phenolate oxygen atom bridge Zn²⁺. In the presence of Hg²⁺ and Al³⁺ perchlorates, short wavelength emission around 370 nm is strongly increased and this fluorescent enhancement is attributable not to the coordination of Hg²⁺ and Al³⁺ to 1 but to the formation of the salt of perchloric acid of 1 .