Ionic conductivity in borate glasses with three types of mixed alkali cations

We have investigated the temperature- and frequency-dependent ionic conductivity in (Li_0.67 ? xNa_0.33 Rb_x)₂B₄O₇ (LNRBO) glasses with x = 0, 0.07, 0.2, 0.33, 0.47, and 0.6. The mixed alkali effect of the ternary mixed alkali system LNRBO is compared with that of the binary mixed alkali systems (Li_1 ? xNa_x)₂B₄O₇ (LNBO), (Li_1 ? xRb_x)₂B₄O₇ (LRBO) and the single alkali glass Rb₂B₄O₇ (RBO). From the results of the dc conductivity and dc activation energy, we observe that the LNRBO system exhibits the combined characteristic of binary mixed alkali systems LNBO and LRBO. It is found that the power-law exponent n for binary alkali glass is the same as that for ternary alkali glass but it is lower than that for single alkali glass. This indicates that the dimensionality of conducting pathway in the mixed alkali glasses of LNBO, LRBO and LNRBO is lower than that in the single alkali RBO. We discuss the concentration dependence of the dc conductivity and dc activation energy in the framework of the bond valence technique to reverse Monte Carlo produced structural model [Phys. Rev. Lett. 90, 155507 (2003)].     

Differential structure on the κ-Minkowski spacetime from twist

We study four-dimensional κ  -Minkowski spacetime constructed by the twist deformation of U(igl(4,R))$U(\mathit{igl}(4,R))$. We demonstrate that the differential structure of such twist-deformed κ-Minkowski spacetime is closed in four dimensions contrary to the construction of κ-Poincaré bicovariant calculus which needs an extra fifth dimension. Our construction holds in arbitrary dimensional spacetimes.     

Carleson Measures via BMO

We obtain new characterizations of Carleson measures via uniform boundedness of BMO norms of certain mass functions associated with the given measure in a natural way. This research was performed during M. Stessin’s visit to Korea University. He thanks the Mathematics Department of Korea University and the “Brain Pool” program for their hospitality and support. The first two authors were supported by the Korea Research Foundation Grant funded by the Korean Government (KRF-2008-314-C00012).     

Composite‐Assisted Phase‐Matching: Efficient Wavelength Conversion in Nonlinear Optical Composite Materials Containing Metal Nanoparticles

A novel phase‐matching scheme which is based on the dispersion compensation in the nonlinear optical composite materials containing metal nanoparticles is proposed. Anomalous dispersion originating from the plasmon resonance in metal nanoparticles compensates the dispersion of the host nonlinear material, leading to the perfect phase‐matching and high efficiency of nonlinear optical wavelength conversion. The effectiveness of this approach is theoretically demonstrated, taking third‐order nonlinear processes such as the direct third‐harmonic generation and four‐wave mixing in ZnO composites containing silica‐core–silver‐shell nanoparticles as examples. The results show that with the proposed phase‐matching scheme, unprecedentedly high conversion efficiency can be obtained compared with preceding results in third‐order nonlinear optical solid‐state materials.     

Estimates of Marcinkiewicz Integrals with Bounded Homogeneous Kernels of Degree Zero

Under the cancellation property and a certain Dini-type condition on kernels, we prove that Marcinkiewicz integrals with kernels which are homogeneous functions of degree zero, are bounded from to , from to , and from to for .     

Composition operators acting on holomorphic Sobolev spaces

We study the action of composition operators on Sobolev spaces of analytic functions having fractional derivatives in some weighted Bergman space or Hardy space on the unit disk. Criteria for when such operators are bounded or compact are given. In particular, we find the precise range of orders of fractional derivatives for which all composition operators are bounded on such spaces. Sharp results about boundedness and compactness of a composition operator are also given when the inducing map is polygonal.

     

High energy femtosecond supercontinuum light generation in large mode area photonic crystal fiber

A large mode area photonic crystal fiber (LMA PCF) with an effective area of 180 μm² is used to generate a high energy, micro-joule range, flat, octave spanning supercontinuum (SC) extending from ~ 600 nm to ~ 1720 nm. A train of femtosecond pulses from a widely-tunable parametric amplifier pumped by a Ti:Sapphire regenerative amplifier system are coupled into a 20 cm length of LMA PCF generating a SC of 1.4 μJ energy. We present an experimental study of the high energy SC as a function of the input power and the pumping wavelength. The spectrum obtained at a pump wavelength of 1260 nm presents spectral flatness variation less than 12 dB over more than 1.1 octave bandwidth. The physical processes behind the SC formation are described in the normal and the anomalous dispersion regions. Our experimental results are successfully compared with the numerical solution of the nonlinear Schrödinger equation.     

ESIPT-Inspired Dual-Mode Photoswitches with Fast Molecular Isomerization in the Solid State

Photoswitchable materials have attracted considerable attention in various fields. Developing excellent solid-state dual-mode photoswitches is an important but challenging task. Herein, we propose a new strategy to construct an excited-state intramolecular proton transfer (ESIPT) inspired photoswitch ( DiAH-pht ) that possesses aggregation-induced emission (AIE) features and displays a fast molecular isomerization process characterized by dual-mode behavior in the solid state. Mechanistic studies indicate that introduction of a bulky group can create a folded molecular conformation that provides adequate volume to facilitate photoisomerization and the enhanced ESIPT effect can boost the isomerization process. The feasibility of our strategy was further demonstrated by the activated photoisomerization performance of the Schiff base derivatives. Furthermore, DiAH-pht shows good performance in the fields of dual-mode information encryption and high-density data storage.     

Lexicographic α-robustness: An alternative to min–max criteria

Robustness in Operations Research/Decision Aid is often associated with min–max and min–max regret criteria. This common approach to determine robust solutions consists in finding a solution which minimizes the maximal cost or regret. Nevertheless, these criteria are known to be too conservative. In this paper, we present and study a new robustness approach, called lexicographic α-robustness, which compensates for this major drawback and many others. Furthermore, we establish a link between lexicographic α-robustness and a third robustness approach called p-robustness.     

A Tetrairon Dication Featuring Tetraethynylbenzene Bridging Ligand: A Molecular Prototype of Quantum Dot Cellular Automata

The unprecedented tetrairon dication [{Cp*(dppe)FeC≡C-}₄-μ-(1,2,4,5-C₆H₂)](PF₆)₂ ( 1 ) was obtained through a sequence of three reactions from 1,2,4,5-tetraethynylbenzene, Cp*(dppe)FeCl (Cp*=C₅Me₅, dppe=1,2-bis(diphenylphosphino)-ethane), KOtBu, and ferrocenium hexafluorophosphate. The cyclic voltammogram of the target molecule, isolated in 77 % yield, exhibits four well separated and reversible redox events showing that 1 is thermodynamically stable with respect to disproportionation (Kc>10⁶). The tetranuclear dication 1 was characterized by XRD on single crystal, IR and NMR spectroscopies and Mössbauer spectrometry. The experimental data show that 1 behaves as a class II mixed-valence complex with the positive charges preferentially disposed on antipodal positions. This new molecule can be regarded as a potential molecular prototype of quantum dot cellular automata.