Magnesium complexes incorporated by sulfonate phenoxide ligands as efficient catalysts for ring‐opening polymerization of ε‐caprolactone and trimethylene carbonate

Two novel sulfonate phenol ligands—3,3′‐di‐tert‐butyl‐2′‐hydroxy‐5,5′,6,6′‐tetramethyl‐biphenyl‐2‐yl 4‐X‐benzenesulfonate (X?CF₃, L^CF3 ‐H, and X?OCH₃, L^OMe ‐H)—were prepared through the sulfonylation of 3,3′‐di‐tert‐butyl‐5,5′,6,6′‐tetramethylbiphenyl‐2,2′‐diol with the corresponding 4‐substituted benzenesulfonyl chloride (1 equiv.) in the presence of excess triethylamine. Magnesium (Mg) complexes supported by sulfonate phenoxide ligands were synthesized and characterized structurally. The reaction of MgⁿBu₂ with L‐H (2 equiv.) produces the four‐coordinated monomeric complexes ( L^CF3 )₂Mg ( 1 ) and ( L^OMe )₂Mg ( 2 ). Complexes 1 and 2 are efficient catalysts for the ring‐opening polymerization of ε‐caprolactone (ε‐CL) and trimethylene carbonate (TMC) in the presence of 9‐anthracenemethanol; complex 1 catalyzes the polymerization of ε‐CL and TMC in a controlled manner, yielding polymers with the expected molecular weights and narrow polydispersity indices (PDIs). In ε‐CL polymerization, the activity of complex 1 is greater than that of complex 2 , likely because of the greater Lewis acidity of Mg²⁺ metal caused by the electron‐withdrawing substitute trifluoromethyl (? CF₃) at the 4‐position of the benzenesulfonate group. © 2010 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 48: 3564–3572, 2010     

Adjustable picosecond pulse duration in a LD end pumped SESAM passively mode-locked Nd:YVO<Subscript>4</Subscript> laser

With adjustable pulse durations, a semiconductor saturable absorber mirror (SESAM) passively mode-locked picosecond Nd:YVO₄ laser was studied. The pulse duration was adjustable from 20 to 80 ps by using intracavity etalons of different thicknesses.     

A multinomial tree model for pricing credit default swap options

Among the traded credit derivatives, the market interest in credit default swap options (CDSwaptions) is enormous. We propose a multinomial tree model to price Bermudan CDSwaptions. Our basic rationale is that we distribute the occurring probability for each node in a branch proportional to the probability density function of the assumed (normal) distribution. Through this approach, without the need of solving a large number of equations simultaneously, only the first four moments are required to build an arbitrarily large N-branches tree. We also demonstrate the detailed model implementation procedure including the valuation and the estimation of critical prices through an empirical example in Tucker and Wei (J Fixed Income 15(1):88–95, 2005). Numerical results show that, in the valuation, the proposed multinomial tree model is accurate and can significantly save pricing time under the same degree of accuracy as the binomial tree model. In the estimation of critical prices, the results are less accurate than those in the valuation, but the relative errors are acceptable.     

Extension of the GHJW theorem for operator ensembles

The Gisin-Hughston-Jozsa-Wootters theorem plays an important role in analyzing various theories about quantum information, quantum communication, and quantum cryptography. It means that any purifications on the extended system which yield indistinguishable state ensembles on their subsystem should have a specific local unitary relation. In this Letter, we show that the local relation is also established even when the indistinguishability of state ensembles is extended to that of operator ensembles.     

Readily Accessible and Predictable Naphthalene‐Based Two‐Photon Fluorophore with Full Visible‐Color Coverage

Herein we report 22 acedan‐derived, two‐photon fluorophores with synthetic feasibility and full coverage of visible wavelength emission. The emission wavelengths were predicted by computational analysis, which enabled us to visualize multicolor images by two‐photon excitation with single wavelength, and to design a turn‐on, two‐photon fluorescence sensor for endogenous H₂O₂ in Raw 264.7 macrophage and rat brain hippocampus ex vivo.     

Monolayer Co3O4 Inverse Opals as Multifunctional Sensors for Volatile Organic Compounds

Monolayers of periodic porous Co₃O₄ inverse opal (IO) thin films for gas‐sensor applications were prepared by transferring cobalt‐solution‐dipped polystyrene (PS) monolayers onto sensor substrates and subsequent removal of the PS template by heat treatment. Monolayer Co₃O₄ IO thin films having periodic pores (d≈500 nm) showed a high response of 112.9 to 5 ppm C₂H₅OH at 200 °C with low cross‐responses to other interfering gases. Moreover, the selective detection of xylene and methyl benzenes (xylene+toluene) could be achieved simply by tuning the sensor temperature to 250 and 275 °C, respectively, so that multiple gases can be detected with a single chemiresistor. Unprecedentedly high ethanol response and temperature‐modulated control of selectivity with respect to ethanol, xylene, and methyl benzenes were attributed to the highly chemiresistive IO nanoarchitecture and to the tuned catalytic promotion of different gas‐sensing reactions, respectively. These well‐ordered porous nanostructures could have potential in the field of high‐performance gas sensors based on p‐type oxide semiconductors.     

PROPERTIES AND CALCULATION OF PAIRED HAAR TRANSFORM

Different properties of recently introduced Paired Haar transform have been shown. Nonpolynomial Haar Pxpansion of incompletely specified Boolean functions has been presented. Based on the above properties and expansion some applications of Paired Haar spectrum have been proposed. Algorithm for the calculation of Haar Pair spectrum from disjoint cubes for systems of incompletely specified Boolean functions has also been developed.