ν-Stable τ-Tilting Modules

Inspired by τ-tilting theory [3 Adachi , T. , Iyama , O. , Reiten , I. ( 2014 ). τ-tilting theory . Compos. Math. 150 ( 3 ): 415 – 452 .[Crossref], [Web of Science ®] , [Google Scholar]], we introduce the notion of ν-stable support τ-tilting modules. For any finite dimensional selfinjective algebra Λ, we give bijections between two-term tilting complexes in K ^b (proj Λ), ν-stable support τ-tilting Λ-modules, and ν-stable functorially finite torsion classes in modΛ. Moreover, these objects correspond bijectively to selfinjective cluster tilting objects in 𝒞 if Λ is a 2-CY tilted algebra associated with a Hom-finite 2-CY triangulated category 𝒞. We also study some properties of support τ-tilting modules over 2-CY tilted algebras, and we give a necessary condition such that algebras are 2-CY tilted in terms of support τ-tilting modules.     

Difference equations arising from cluster algebras

Journal of Algebraic Combinatorics - We characterize Y/T-system-type difference equations arising from cluster algebras by triples of matrices, which we call T-data, that have a certain symplectic...     

Coherent storage of photoexcited triplet states using 29Si nuclear spins in silicon

Pulsed electron paramagnetic resonance spectroscopy of the photoexcited, metastable triplet state of the oxygen-vacancy center in silicon reveals that the lifetime of the m(s)=±1 sublevels differs significantly from that of the m(s)=0 state. We exploit this significant difference in decay rates to the ground singlet state to achieve nearly ~100% electron-spin polarization within the triplet. We further demonstrate the transfer of a coherent state of the triplet electron spin to, and from, a hyperfine-coupled, nearest-neighbor (29)Si nuclear spin. We measure the coherence time of the (29)Si nuclear spin employed in this operation and find it to be unaffected by the presence of the triplet electron spin and equal to the bulk value measured by nuclear magnetic resonance.     

Chromatic aberration free liquid crystal adaptive optics for flood illuminated retinal camera

A high-resolution, flood-illumination retinal camera using liquid crystal (LC) adaptive optics (AO) is presented. The retinal camera uses light at 780 nm for ocular aberration measurement while light at 655 nm and 593 nm for retinal imaging. In order to avoid chromatic aberrations due to wavelength dependence of LC, we adopt an open-loop technique, in which dynamic correction of aberrations is applied only to the imaging light. A compensation pattern projected on the LC wavefront corrector is adjusted to provide phase wrapping of 2 π for illumination light. We confirmed feasibility of this technique by performing in vivo retinal imaging experiments. Photoreceptors were clearly revealed at both imaging light at 655 nm and 593 nm. Feasibility of the technique was also supported by comparison of the retinal images taken by the present open-loop technique with those taken by the conventional closed-loop one and by analysis of the spatial distribution of the photoreceptors.     

Persistent hole-burning of perylene microcrystallites dispersed in PVA

A persistent hole-burning is observed in β-perylene microcrystallites, which were embedded in poly-vinyl alcohol. By laser light excitation at 22,535 cm⁻¹ and at 10 K, the hole is found at the excitation photon energy. The mechanism of the persistent hole-burning is interpreted in terms of the resolution of microcrystallites into smaller microcrystallites. This is a novel observation of the persistent hole-burning in aromatic microcrystallites. When the specimen, which includes a hole, is annealed at high temperatures, the resolved microcrystallites restore back to the old position as had been. The β-perylene microcrystallite specimen that we have grown was as small as 1.5 nm in average diameter. They are one order smaller in number of molecules included, compared to those that have been reported on aromatic microcrystallites, anthracene for example. Due to this, we were able to observe the 0-0 transition energy, which varied according as the number of molecules involved in the microcrystallites. We also observed the 0-0 absorption (excitation) spectrum, which depends on the molecular arrays in the microcrystallites. The 0-0 transition of a single molecule in poly-vinyl alcohol matrix is anticipated to be located at 22,885 cm⁻¹.     

Permutation complexity via duality between values and orderings

We study the permutation complexity of finite-state stationary stochastic processes based on a duality between values and orderings between values. First, we establish a duality between the set of all words of a fixed length and the set of all permutations of the same length. Second, on this basis, we give an elementary alternative proof of the equality between the permutation entropy rate and the entropy rate for a finite-state stationary stochastic processes first proved in [J.M. Amigó, M.B. Kennel, L. Kocarev, The permutation entropy rate equals the metric entropy rate for ergodic information sources and ergodic dynamical systems, Physica D 210 (2005) 77-95]. Third, we show that further information on the relationship between the structure of values and the structure of orderings for finite-state stationary stochastic processes beyond the entropy rate can be obtained from the established duality. In particular, we prove that the permutation excess entropy is equal to the excess entropy, which is a measure of global correlation present in a stationary stochastic process, for finite-state stationary ergodic Markov processes.     

Local structure analysis of smoky and colorless topaz using single crystal Al NMR

The angular dependence of the ²⁷Al NMR spectrum was measured for single crystals of smoky and colorless topaz, Al₂SiO₄(F,OH)₂. Smoky topaz was obtained by irradiating high energy neutrons to colorless topaz. The quadrupole coupling constant e²Qq/h and the asymmetry parameter η were obtained from the analysis of the angular dependences of quadrupole splitting of the ²⁷Al NMR spectrum. The local structures around the aluminum atoms in smoky and colorless topaz were discussed from the magnitude and the direction of the electric field gradient. The directions of principal axes of the EFG tensor of ²⁷Al were close to the directions of Al-O and Al-F bonds. The difference in the bond lengths between Al(1)-F(1) and Al(1)-F(2) was found to affect the x and y components of the EFG tensor.     

Structural and electrical properties of crystalline (1−x)Ta2O5−xTiO2 thin films fabricated by metalorganic decomposition

Polycrystalline (1−x)Ta₂O₅−xTiO₂ thin films were formed on Si by metalorganic decomposition (MOD) and annealed at various temperatures. As-deposited films were in the amorphous state and were completely transformed to crystalline after annealing above 600 °C. During crystallization, a thin interfacial SiO₂ layer was formed at the (1−x)Ta₂O₅−xTiO₂/Si interface. Thin films with 0.92Ta₂O₅–0.08TiO₂ composition exhibited superior insulating properties. The measured dielectric constant and dissipation factor at 1 MHz were 9 and 0.015, respectively, for films annealed at 900 °C. The interface trap density was 2.5×10¹¹ cm⁻² eV⁻¹, and flatband voltage was −0.38 V. A charge storage density of 22.8 fC/μm² was obtained at an applied electric field of 3 MV/cm. The leakage current density was lower than 4×10⁻⁹ A/cm² up to an applied electric field of 6 MV/cm.     

The RATIO method for time‐resolved Laue crystallography

A RATIO method for analysis of intensity changes in time‐resolved pump–probe Laue diffraction experiments is described. The method eliminates the need for scaling the data with a wavelength curve representing the spectral distribution of the source and removes the effect of possible anisotropic absorption. It does not require relative scaling of series of frames and removes errors due to all but very short term fluctuations in the synchrotron beam.