On totally *-paranormal operators

In this paper we study some properties of a totally *-paranormal operator (defined below) on Hilbert space. In particular, we characterize a totally *-paranormal operator. Also we show that Weyl’s theorem and the spectral mapping theorem hold for totally *-paranormal operators through the local spectral theory. Finally, we show that every totally *-paranormal operator satisfies an analogue of the single valued extension property for W ²(D, H) and some of totally *-paranormal operators have scalar extensions.     

Phenothiazine‐S,S‐dioxide‐ and fluorene‐based light‐emitting polymers: Introduction of e−‐deficient S,S‐dioxide into e−‐rich phenothiazine

A novel series of poly(10‐hexyl‐phenothiazine‐S,S‐dioxide‐3,7‐diyl) and poly(9,9′‐dioctyl‐fluorene‐2,7‐diyl‐alt‐10‐hexyl‐3,7‐phenothiazine‐S,S‐dioxide) (PFPTZ‐SS) compounds were synthesized through Ni(0)‐mediated Yamamoto polymerization and Pd(II)‐catalyzed Suzuki polymerization. The synthesized polymers were characterized by ¹H NMR spectroscopy and elemental analysis and showed higher glass transition temperatures than that of pristine polyfluorene. In terms of photoluminescence (PL), the PFPTZ‐SS compounds were highly fluorescent with bright blue emissions in the solid state. Light‐emitting devices were fabricated with these polymers in an indium tin oxide/poly(3,4‐ethylene dioxythiophene):poly(styrene sulfonate)/polymer/Ca/Al configuration. The electroluminescence (EL) of the copolymers differed from the PL characteristics: the EL device exhibited a redshifted greenish‐blue emission in contrast to the blue emission observed in the PL. Additionally, this unique phenothiazine‐S,S‐dioxide property, triggered by the introduction of an electron‐deficient SO₂ unit into the electron‐rich phenothiazine, gave rise to improvements in the brightness, maximum luminescence intensity, and quantum efficiency of the EL devices fabricated with PFPTZ‐SS. © 2007 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 1236–1246, 2007     

Hydroxyl chain‐end functionalization of polymeric organolithium compounds with oxetane

Hydroxyl chain‐end functionalizations of polymeric organolithium compounds with oxetane (trimethylene oxide) were studied in benzene at 25 °C. Functionalizations of poly(styryl)lithium and polystyrene‐oligo‐butadienyllithium proceed efficiently to form the corresponding ω‐hydroxypropyl‐functionalized polymers in 98 and 97% isolated yields, respectively. No nonfunctional polymer (≤1–2%) was detected by thin layer chromatography (TLC) analysis for either polymer. All functionalized polymers were characterized by ¹³C and ¹H NMR analyses; no evidence for oxetane oligomerization at the chain end was observed. The MALDI‐TOF mass spectrum of ω‐hydroxypropylpolystyrene was consistent with the expected structure without any detectable oligomerization of oxetane. A small, but detectable series of peaks corresponding to nonfunctional polystyrene was also observed in the MALDI‐TOF mass spectrum. The functionalization of the adduct of 1,1‐diphenylethylene and PSLi produced the corresponding ω‐hydroxypropyl‐functionalized polymer in only 86% isolated yield. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 2684–2693, 2006     

Microwave-assisted synthesis of (η-arene)tricarbonylchromium complexes

We have undertaken a study of the microwave-assisted synthesis of (η⁶-arene)tricarbonylchromium complexes. Under microwave irradiation, the reactions of hexacarbonylchromium with arenes gave high yields of (η⁶-arene)chromium tricarbonyl complexes.     

Buckling instabilities in coupled nano-layers

We study the dynamic buckling of a pair of dissimilar Euler-Bernoulli beams subject to compressive edge loading whose transverse displacements are coupled through non-linear interactions, a problem motivated by the mechanics of graphene layers. The transverse coupling models van der Waals interaction and is derived from a Lennard-Jones 12-6 potential. The beams are assumed to be a fixed distance apart at their ends, although this distance is not necessarily equal to the equilibrium distance as identified from the Lennard-Jones potential. Therefore, the equilibrium configuration is not necessarily straight. Via a Galerkin method, the governing equations are reduced to a system that can be used to calculate equilibrium configurations as well as the stability of these configurations. We show that the buckling instability in this model is significantly affected by the presence of the interaction force as well as the separation of the graphene layers at the boundaries.     

Generic initial ideals of Artinian ideals having Lefschetz properties or the strong Stanley property

For a standard Artinian k-algebra A=R/I, we give equivalent conditions for A to have the weak (or strong) Lefschetz property or the strong Stanley property in terms of the minimal system of generators of gin(I). Using the equivalent condition for the weak Lefschetz property, we show that some graded Betti numbers of gin(I) are determined just by the Hilbert function of I if A has the weak Lefschetz property. Furthermore, for the case that A is a standard Artinian k-algebra of codimension 3, we show that every graded Betti number of gin(I) is determined by the graded Betti numbers of I if A has the weak Lefschetz property. And if A has the strong Lefschetz (respectively Stanley) property, then we show that the minimal system of generators of gin(I) is determined by the graded Betti numbers (respectively by the Hilbert function) of I.     

White electroluminescence from a single polyfluorene containing bis‐DCM units

A series of fluorene‐based copolymers composed of blue‐ and orange‐light‐emitting comonomers were synthesized through palladium‐catalyzed Suzuki coupling reactions. 9,9‐Dihexylfluorene and 2‐(2,6‐bis‐{2‐[1‐(9,9‐dihexyl‐9H‐fluoren‐2‐yl)‐1,2,3,4‐tetrahydroquinolin‐6‐yl]‐vinyl}‐pyran‐4‐ylidene)‐malononitrile (DCMF) were used as the blue‐ and orange‐light‐emitting chromophores, respectively. The resulting single polymers exhibited simultaneous blue (423/450 nm) and orange (580–600 nm) emissions from these two chromophores. By adjusting the fluorene and DCMF contents, white light emission could be obtained from a single polymer; a device with an ITO/PEDOT:PSS/polymer/Ca/Al configuration was found to exhibit pure white electroluminescence with Commission Internationale de L'Eclairage (CIE) coordinates of (0.33, 0.31), a maximum brightness of 1180 cd/m², and a current efficiency of 0.60 cd/A. Furthermore, the white light emission of this device was found to be very stable with respect to variation of the driving voltage. The CIE coordinates of the device were (0.32, 0.29), (0.32, 0.29), and (0.33, 0.31) for driving voltages of 7, 8, and 10 V, respectively. © 2007 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 3380–3390, 2007     

Crystallinity and morphology dependent luminescence of Li-doped Y2−xGdxO3:Eu thin film phosphors

The influence of lithium doping on the crystallization, the surface morphology, and the luminescent properties of pulsed laser deposited Y_2−xGd_xO₃:Eu³⁺ thin film phosphors was investigated. The crystallinity, the surface morphology, and the photoluminescence (PL) of films depended highly on the Li-doping and the Gd content. The relationship between the crystalline and morphological structures and the luminescent properties was studied, and Li⁺ doping was found to effectively enhance not only the crystallinity but also the luminescent brightness of Y_2−xGd_xO₃:Eu³⁺ thin films. In particular, the incorporation of Li and Gd into the Y₂O₃ lattice could induce remarkable increase in the PL. The highest emission intensity was observed Li-doped Y_1.35Gd_0.6O₃:Eu³⁺ thin films whose brightness was increased by a factor of 4.6 in comparison with that of Li-doped Y₂O₃:Eu³⁺ thin films.     

High-accuracy surface position sensor based on a two-lens system

Two optical lenses are used to compose a surface position measuring system. A measurand is positioned near the front focal point of the first lens. At the output end of the other lens, a beam splitter is used to split the beam into two paths. One photodetector is positioned before the focal point of the lens in one path and another after the focal point in the other so that the intensities falling onto the two detectors can be adjusted to be equal when the first lens is in focus. This device provides a compact and high-accuracy surface sensor. In this paper, the design and experimental study of the sensor system is described. It is shown that such a sensor embodiment can lead to a resolution of 1 μm.     

Students' Retention of Mathematical Knowledge and Skills in Differential Equations

This study investigates students' retention of mathematical knowledge and skills in two differential equations classes. Posttests and delayed posttests after 1 year were administered to students in inquiry‐oriented and traditional classes. The results show that students in the inquiry‐oriented class retained conceptual knowledge, as seen by their performance on modeling problems, and retained equal proficiency in procedural problems, when compared with students in the traditionally taught classes. The results of this study add additional support to the claim that teaching for conceptual understanding can lead to longer retention of mathematical knowledge.