ON THE COHOMOLOGY OF GENERALIZED RESTRICTED LIE ALGEBRAS

0.IntroductionThispaperisaimedatdevelopingthecohomologytheoryofmodularLiealgebrasandthendeterminingthefirstcohomologygroupsofCartantypeLiealgebras.AsgeneralizationoftheconceptofrestrictedLiealgebras,ageneralizedrestrictedLiealgebra(GRLiealgebra)wasintroducedin[21],whichisassociatedwithabasisandamappingofthebasisintotheLiealgebrasatisfyingthegeneralized-restrictednessconditions.Generalizedrestrictedrepresentations(GRrepresentations)werethenintroduced,whichcanbereducedtotherepresentationsofa…     

Mapping properties of wave and scattering operators for two-body Schrödinger operators

The modified wave and scattering operators are shown to be bounded between weighted L ²-spaces for two-body Schrödinger operators with long range potentials.     

Image Displaying Method of Ground-Based Millimeter Wave Radiometric Imaging System

The image displaying methods used in a millimeter wave radiometric imaging system have great influence on its imaging quality. In order to obtain high quality millimeter wave radiometric images, intensive studies on the image displaying methods are needed. This paper describes the image displaying method of Ground-based 8mm Millimeter Wave Radiometric Imaging (GMWRI) system and compares two different image displaying methods. The experimental results prove the unequal size element arc displaying method fits GMWRI system better.     

Synthesis of grafted poly(p‐phenyleneethynylene) with energy donor–acceptor architecture via atom transfer radical polymerization: Towards nonaggregating and hole‐facilitating light‐emitting material

In this contribution, we demonstrate a new effective methodology for constructing highly efficient and durable poly(p‐phenyleneethynylene) (PPE) containing emissive material with nonaggregating and hole‐facilitating properties through the introduction of hole‐transporting blocks into the PPE system as the grafting coils as well as building the energy donor–acceptor architecture between the grafting coils and the PPE backbone. Poly(2‐(carbazol‐9‐yl)ethyl methacrylate) (PCzEMA), herein, is chosen as the hole‐transporting blocks, and incorporated into the PPE system as the grafting coils via atom transfer radical polymerization. The chemical structure of the resultant copolymer, PPE‐g‐PCzEMA, was characterized by NMR and gel permeation chromatography, showing that the desirable copolymer was obtained with the narrow polydispersity. The increased thermal stability of PPE‐g‐PCzEMA was confirmed by thermogravimetric analysis and differential scanning calorimetry along with its macroinitiator. The optoelectronic properties of this copolymer were studied in detail by ultraviolet‐visible absorption, photoluminescence emission and excitation spectra, and cyclic voltammogram (CV). The results indicate that PPE‐g‐PCzEMA exhibits the solid‐state luminescent property dominated by individual lumophores, and also the energy transfer process from the PCzEMA blocks to the PPE backbone with a relatively higher energy transfer efficiency in the solid‐state compared to that of the solution state. Additionally, the hole‐injection property is greatly facilitated due to the presence of PCzEMA, as confirmed by CV profiles. All these data indicate that PPE‐g‐PCzEMA is a good candidate for use in optoelectronic devices. © 2007 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 3776–3787, 2007     

Pd (II)‐catalyzed vinyl addition polymerization of novel functionalized norbornene bearing dimethyl carboxylate groups

Three novel functionalized polynorbornenes (PNB) with pendant dimethyl carboxylate group (carboxylates—acetate, propionate, and butyrate) are synthesized as a vinyl‐type with a palladium (II) catalyst in high yield. The effects of size of substitutents, molar ratio of monomer to catalyst, solvent polarity, reaction time, and temperature on the polymerization of exo‐norbornene dimethyl propionate were systematically investigated. The low molar ratio and temperature, as well as high polarity of solvent, and long reaction time, are favorable for the enhancement of the monomer conversion, especially, the solvent have an obvious effect on the catalyst activity. The resulting poly(cis‐norbornene‐exo‐2,3‐dimethyl carboxylates) (PNB‐dimethyl carboxylates) show good solubility in common organic solvent and high thermal stability up to 360 °C. The glass transition temperature was detected by DMA at 331, 324, and 318 °C for acetate, propionate, and butyrate, respectively. © 2007 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 3391–3399, 2007     

Phase-Only Encryption and Single Path Decryption System Using Phase-Encoded Exclusive-OR Rules in Fourier Domain

A phase-only encryption scheme using phase-encoded exclusive-OR (XOR) rules in a Fourier plane and a single path decryption system are presented. To generate phase-only encrypted data, a zero-padded original image, multiplied by a random phase image, is Fourier transformed and its real-valued data is encrypted with key data by using phase-encoded XOR rules. Since the original information is encrypted on the Fourier plane, the proposed encryption is more tolerant to loss of key information by scratching or cutting than previous XOR encryption in a space domain. A decryption is simply performed based on 2-f setup with spatial filter by Fourier transform for multiplication phase-only encrypted data with phase-only key data. Due to single path architecture without a reference wave, the proposed system is resistant to mechanical vibrations and fluctuation. Numerical simulations have confirmed the validity of the proposed encryption scheme and simple decryption architecture.     

Codes Over the p-adic Integers

We study codes over the p-adic integers and correct errors in the existing literature. We show that MDS codes exist over the p-adics for all lengths, ranks and p. We show that self-dual codes exist over the 2-adics if and only if the length is a multiple of 8 and that self-dual codes exist over the p-adics with p odd if and only if the length is 0 (mod 4) for p ≡ 3 (mod 4) and 0 (mod 2) for p ≡ 1 (mod 4).     

Synthesis and light emitting properties of polyacetylenes having pendent fluorene groups

Five novel fluorene‐containing polymers, poly[(9,9‐dimethylfluoren‐2‐yl)acetylene] ( PFA1 ), poly[(1‐pentyl‐2‐(9,9‐dimethylfluoren‐2‐yl)acetylene) ( PFA2 ), poly[1‐decyl‐2‐(9,9‐dimethylfluoren‐2‐yl)acetylene] ( PFA3 ), poly[1‐phenyl‐2‐(9,9‐dimethylfluoren‐2‐yl)acetylene] ( PFA4 ), and poly[1‐(3,4‐difluorophenyl)‐2‐(9,9‐dimethylfluoren‐2‐yl)acetylene] ( PFA5 ) were synthesized by the polymerization of the corresponding fluorene‐substituted acetylenic monomers ( M1–M5), using WCl₆, MoCl_5, and TaCl₅ as catalysts and n‐Bu₄Sn as a cocatalyst. The synthesized polymers were thermally stable and readily soluble in common organic solvents. The degradation temperatures for a 5% weight loss of the polymers were ∼352–503 °C under nitrogen. PFA1–PFA5 show emission peaks from 402 to 590 nm. Besides, their electroluminescent properties were studied in heterostructure light‐emitting diodes (LEDs), using PFA2–PFA5 as an emitting layer. The PFA5 device revealed an orange‐red emission peak at 602 nm with a maximum luminescence of 923 cd/m² at 8 V. A device with the ITO/PEDOT/ a mixture of PFA2 (98 wt %) and PFA5 (2 wt %)/Ca/Al showed near white emission. Its maximum luminance and current efficiency are 450 cd/m² at 15 V and 1.3 cd/A, respectively. © 2005 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 519–531, 2006     

In‐line monitoring of UV photopolymerization with a quartz crystal resonator

An in‐line monitoring device using a quartz crystal resonator for thin film polymerization was proposed, and its performance has been evaluated by implementing in the UV polymerization of 2‐hydroxyethyl methacrylate with a photoinitiator of 1‐chloroanthraquinone. Because the variation of resonant resistance of the resonator is proportional to the square root of viscosity change that is closely related to the polymerization degree, the resistance can be used as a measure of the polymerization degree. The resistance measurements were compared with the outcome of instrumental analyses of polymerization degree using an FTIR spectrometer and a gel permeation chromatograph. The experimental results showed that the resistance measurements were consistent with the experimental outcome of the instrumental analyses, and this indicates the effectiveness of the proposed device. Owing to the simplicity and availability of the resonator system, its wide utilization in the monitoring of a variety of film polymerization processes, including photoresistor application, is expected. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 2428–2439, 2006