Interior penalty discontinuous Galerkin methods with implicit time‐integration techniques for nonlinear parabolic equations

We prove existence and numerical stability of numerical solutions of three fully discrete interior penalty discontinuous Galerkin methods for solving nonlinear parabolic equations. Under some appropriate regularity conditions, we give the l²(H¹) and l^∞(L²) error estimates of the fully discrete symmetric interior penalty discontinuous Galerkin–scheme with the implicit θ ‐schemes in time, which include backward Euler and Crank–Nicolson finite difference approximations. Our estimates are optimal with respect to the mesh size h. The theoretical results are confirmed by some numerical experiments. © 2012 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2013     

Nitric oxide turn-on fluorescent probe based on deamination of aromatic primary monoamines

The stable, water-soluble, and nonfluorescent FA-OMe can sense nitric oxide (NO) and form the intensely fluorescent product dA-FA-OMe via reductive deamination of the aromatic primary amine. The reaction is accompanied by a notable increase of the fluorescent quantum yield from 1.5 to 88.8%. The deamination mechanism of FA-OMe with NO was proposed in this study. The turn-on fluorescence signals were performed by suppression of photoinduced electron transfer (PeT), which was demonstrated by density functional theory (DFT) calculations of the components forming FA-OMe and dA-FA-OMe. Furthermore, FA-OMe showed water solubility and good stability at physiological pHs. Moreover, the selectivity study indicated that FA-OMe had high specificity for NO over other reactive oxygen/nitrogen species. In an endogenously generated NO detection study, increasing the incubation time of FA-OMe with lipopolysaccharide (LPS) pretreated Raw 264.7 murine macrophages could cause an enhanced fluorescence intensity image. In addition, a diffusion/localization cell imaging study showed that FA-OMe could be trapped in Raw 264.7 cells. These cell imaging results demonstrated that FA-OMe could be used as a turn-on fluorescent sensor for the detection of endogenously generated NO.     

Mass Spectra of Substituted N-Alkylpyrroles and Related Compounds

Under El conditions, substituents on N-alkylpyrroles affect fragmentation of the alkyl groups. The electron-withdrawing character of the cyano group retarded formation of a N-methylene cation, and a labile substituent, i.e., -CHO, -CH₂COOMe, competed with an N-alkyl group to be a initial fragmentation center, MNDO calculation of the heat of formation of possible fragment ions showed that protonated pyridine is the most stable among the isobaric ions.     

Nucleophilic aromatic substitution of activated cationic groups by 18F-labeled fluoride. A useful route to no-carrier-added (NCA) 18F-labeled aryl fluorides

A method is described for the rapid preparation of no-carrier-added (NCA) ¹⁸F-labeled aryl fluorides by treatment of the corresponding aryltrimethylammonium perchlorates with ¹⁸F-labeled fluoride in DMSO. The basic features of the ¹⁸F-for-⁺NMe₃ displacement process are evaluated as a function of the experimental variables and compared with related substitution routes to NCA ¹⁸F-labeled aryl fluorides. The relative nucleofugicity of the ammonium group in the nucleophilic substitution reactions surpasses that of the best neutral leaving groups, including NO₂ and F itself. In contrast, radiofluoride incorporation into aromatic rings $\text{via}$ other cationic substrates, such as aryldimethylsulfonium perchlorates, is prevented by the fast methyl group transfer from the starting compound to the nucleophiles present. The use of the ammonium function as a leaving group in nucleophilic substitutions by ¹⁸F^? may give access to the rapid preparation of novel NCA ¹⁸F-radiopharmaceuticals by facilitating the synthesis and the purification of their labeled precursors.     

Facile, one-pot synthesis of phosphinate-substituted bisphenol A and its alkaline-stable diglycidyl ether derivative

A new phosphinate-substituted bisphenol A, 1,1-bis(4-hydroxyphenyl)-1-(6-oxido-6H-dibenz <c,e> <1,2> oxaphosphorin-6-yl)ethane (1), was prepared by a facile, one-pot procedure. In addition, a reaction mechanism for the preparation of (1) was proposed. Based on (1), a diglycidyl ether derivative (2) was prepared and cured by commercially-available curing agents. The structures of (1-2) were confirmed by IR, high-resolution mass, 1-D and 2-D NMR spectra. Properties such as glass transition temperature, coefficient of thermal expansion, thermal decomposition temperature, and flame retardancy of the resulting thermosets were evaluated and compared with those of the thermosets of diglycidyl ether of bisphenol A. The resulting epoxy thermosets show high T_g, low thermal expansion, good thermostability and excellent flame retardancy.     

Synthesis and characterization of new polyamides containing adamantyl and diamantyl moieties in the main chain

This work synthesized a series of new polyamides by direct polycondensation of 1,3-bis[4-(4-carboxyphenoxy)phenyl]adamantane ( I ) with various diamines. The diacid I was synthesized from 1,3-bis(4-hydroxyphenyl)adamantane in two steps. Polyamides III were soluble in N-methyl-2-pyrrolidone (NMP), N,N-dimethylacetamide (DMAc), and pyridine. The polyamides had medium inherent viscosities of 0.30–0.55 dL/g and number-average molecular weights (M_n) of 22,000–36,000. The polyamides III _a and III _b had tensile strengths of 59.8 and 77.5 MPa, elongation to breakage values of 5.8 and 7.6%, and initial moduli of 1.9 and 1.8 GPa, respectively. Their glass transition temperatures were found to be 219–295°C by means of differential scanning calorimetry (DSC). Dynamic mechanical analysis (DMA) reveals that the incorporation of rigid and bulky diamantane into polyamides III _a and III _b leads to high glass transition temperatures (T_gs), at 299 and 286°C, respectively. The decomposition temperatures of polyamides III at a 5% weight loss ranged from 388 to 416°C in air and from 408 to 435°C in N₂ atmosphere. © 1998 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 36: 785–792, 1998     

Design of zoom lens by optimization technique

A method was developed for solving zoom lens layout. It can be used to solve both the optically and the mechanically compensated zoom systems. The number of moving components is not limited by this method. The damped least squares method is used for finding the solution of zoom lens and the polynomial equations are used for fitting zoom run during the optimization process. Several constraints are also used for smoothing and minimizing the sensitivity of the zoom system. The principles of the method are described, together with some examples that are given to confirm the techniques.     

Minimization of low-temperature microbending losses in initially curved tightly jacketed double-coated optical fibres

Thermally induced microbending losses in initially curved tightly jacketed double-coated optical fibres at low temperature are investigated. The initial deflections are described by a more general formula. The deflections in an initially curved fibre increase gradually with increasing thermally induced compressive axial force, and result in an increase of microbending loss. In order to minimize such a microbending loss, the Young's modulus and Poisson's ratio of the primary coating should be increased. The best value of the Poisson's ratio of the primary coating is 0.5. On the other hand, the thickness of the primary coating, the Young's modulus and effective thermal expansion coefficient of the secondary coating, and the thickness, Young's modulus and effective thermal expansion coefficient of the jacket should be decreased. These results are compared to those of double-coated optical fibres. Thermally induced lateral pressure in the glass fibre can also produce microbending loss. When the effects of axial force and lateral pressure on the microbending losses are both considered, the optimum selection of polymeric coatings is to let the lateral pressure be less than zero, and the magnitude of lateral pressure and the ratio of the final-initial deflection be as small as possible. When the material properties of polymeric coatings and their thicknesses are selected, there are two ways to achieve the optimum design.     

A convenient one-step synthesis of 6-selenoxo-9-(β-D-ribofuranosyl)purine 3′,5′-cyclic phosphate and related compounds

A useful, facile procedure for preparing seleno-heterocyclic compounds is reported. Treatment of cAMP, AMP, adenosine, 2-aminoadenosine, adenine arabinoside and formycin with hydrogen selenide in aqueous pyridine at 65° for 1.5-5 days gave the corresponding seleno compounds in good yield, while these compounds were relatively inert to hydrogen sulfide. A reaction mechanism is proposed.