An Additive Problem with Primes in Arithmetic Progressions

In this paper, we extend a classical result of Hua to arithmetic progressions with large moduli. The result implies the Linnik Theorem on the least prime in an arithmetic progression.     

Low Cost, High Efficiency, Gain Flattened L Band EDFA Using FBGs as C Band Seed Generators

A low cost, coolerless 980nm diode pumped, gain flattened L band EDFA with fast transient control, high pump efficiency and gain clamping effect was realized by using FBGs as C band seed generators.     

Well-dispersed gold nanowire suspension for assembly application

A method for fabricating well-dispersed nanowire suspension has been demonstrated in the paper. Thin gold nanowires were prepared by template synthesis, and then functionalized with sulphonate group-terminated thiols before suspended in different solvents. The degree of aggregation of the obtained suspension was evaluated with transmission electron microscopy (TEM) and UV-vis spectroscopy. It was found that the degree of aggregation was predominated by the solvents, and the best degree of dispersion was obtained when isopropyl alcohol (IPA) was used as the solvent. The gold nanowires from the suspension can be selectively assembled onto chemically patterned substrates. This well-dispersed nanowire suspension is potentially useful for fabricating novel nanodevices.     

Two-Frequency Brillouin Fiber Laser Based on Bragg Grating Fabry-Perot Cavity

A novel and simple two-frequency Brillouin fiber laser is presented. It is based on a fiber Fabry-Perot cavity with fiber Bragg gratings as reflectors. The model of stimulated Brillouin scattering in fiber grating-based Fabry-Perot resonator is investigated. The laser allows conversion efficiency of close to 100% and suppresses the higher-order Stokes waves. The theoretical prediction is presented and the experimental demonstration is realized.     

Facile modifications of a polyimide via chloromethylation. I. Novel synthesis of a new photosensitive polyimide

A soluble aromatic polyimide was chloromethylated via a reaction with chloromethyl methyl ether in the presence of tin(IV) chloride to produce a new starting material for the modification of aromatic polyimides. The chemical structure of the resulting polymer was confirmed by ¹H NMR and Fourier transform infrared spectroscopy. The maximum number of chloromethyl groups per repeat unit was 1.81. The chloromethylated polyimide was stable up to 250 °C and soluble in both chloroform and tetrahydrofuran. So that its utilization for further modification could be demonstrated, cinnamic acid was reacted with the formed polyimide, and it produced a new photosensitive polyimide with a cinnamoyl side chain. The photosensitivity of the resulting polyimide was investigated with ultraviolet spectroscopic methods. © 2002 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 41: 22–29, 2003     

Least‐squares meshfree method for incompressible Navier–Stokes problems

A least‐squares meshfree method based on the first‐order velocity–pressure–vorticity formulation for two‐dimensional incompressible Navier–Stokes problem is presented. The convective term is linearized by successive substitution or Newton's method. The discretization of all governing equations is implemented by the least‐squares method. Equal‐order moving least‐squares approximation is employed with Gauss quadrature in the background cells. The boundary conditions are enforced by the penalty method. The matrix‐free element‐by‐element Jacobi preconditioned conjugate method is applied to solve the discretized linear systems. Cavity flow for steady Navier–Stokes problem and the flow over a square obstacle for time‐dependent Navier–Stokes problem are investigated for the presented least‐squares meshfree method. The effects of inaccurate integration on the accuracy of the solution are investigated. Copyright © 2004 John Wiley & Sons, Ltd.     

Synthesis and structural characterization of novel,fluorinated poly(phthalazinone ether)s containing perfluorophenylene moieties

The synthesis and structural characterization of a series of novel, fluorinated poly(phthalazinone ether)s containing perfluorophenylene moieties are described. The monomers, 4‐(4′‐hydroxyaryl)phthalazin‐1(2H)‐ones ( 2a – 2d ), were conveniently and efficiently synthesized from phenols and phthalic anhydride in two steps via 2‐(4′‐hydroxybenzoyl)benzoic acids, which were first obtained by the Friedel–Crafts reaction in good yields and with high stereoselectivity and were then converted into 2a – 2d by fusion with hydrazine. All the polymers were prepared by nucleophilic aromatic substitution (S_NAr) polycondensation between the compounds perfluorobiphenyl and 4‐(4′‐hydroxyaryl)phthalazin‐1(2H)‐ones ( 2a ‐ 2d ). The resulting fluorinated polymers were readily soluble in common organic solvents (e.g., CHCl₃, tetrahydrofuran, dimethylformamide, dimethyl sulfoxide, N‐methylpyrrolidone, etc.) at room temperature. Their weight‐average molecular weights and the polydispersities ranged from (7.96–18.25) × 10³ to 1.31–2.71, respectively. Their glass‐transition temperatures varied from 213 to 263 °C. They were all stable up to 390 °C both in air and in argon. The 5% weight‐loss temperatures of these polymers in air and argon ranged from 393–487 to 437–509 °C, respectively. Wide‐angle X‐ray diffraction studies indicated they were all amorphous and could be attributed to the presence of kink nonplanar moiety, phenyl phthalazinone along the polymer backbone. © 2004 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 925–932, 2004     

Soluble,saturated‐red‐light‐emitting poly(p‐phenylenevinylene) containing triphenylamine units and cyano groups

A conjugated poly(p‐CN‐phenylenevinylene) (PCNPV) containing both electron‐donating triphenylamine units and electron‐withdrawing cyano groups was prepared via Knoevenagel condensation in a good yield. Gel permeation chromatography suggested that the soluble polymer had a very high weight‐average molecular weight of 309,000. A bright and saturated red emission was observed under UV excitation in solution and film. Cyclic voltammetry showed that the polymer presented quasi‐reversible oxidation with a relatively low potential because of the triphenylamine unit. A single‐layer indium tin oxide/PCNPV/Mg–Ag device emitted a bright red light (633 nm). © 2004 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 3947–3953, 2004     

Mutual influence of the morphology and capillary rheological properties in nylon/glass‐fiber/liquid‐crystalline‐polymer blends

Nylon‐6/glass‐fiber (GF)/liquid‐crystalline‐polymer (LCP) ternary blends with different viscosity ratios were prepared with three kinds of nylon‐6 with different viscosities as matrices. The rheological behaviors of these blends were characterized with capillary rheometry. The morphology was observed with scanning electron microscopy and polarizing optical microscopy. This study showed that although LCP did not fibrillate in binary nylon‐6/LCP blends, LCP fibrillated to a large aspect ratio in some ternary blends after GF was added. The addition of 5 wt % LCP significantly reduced the melt viscosity of nylon‐6/GF blends to such an extent that some nylon‐6/GF/LCP blends had quite low viscosities, not only lower than those of neat resins and nylon‐6/GF blends but also lower than those of corresponding nylon‐6/LCP blends. The mutual influence of the morphology and rheological properties was examined. The great reduction of the melt viscosity was considered the result of LCP fibrillation. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 1619–1627, 2004     

Segmental and secondary dynamics in hydrogen‐bonded poly(4‐vinylphenol)/poly(methyl methacrylate) blends

Broadband dielectric spectroscopy was used to study the segmental (α) and secondary (β) relaxations in hydrogen‐bonded poly(4‐vinylphenol)/poly(methyl methacrylate) (PVPh/PMMA) blends with PVPh concentrations of 20–80% and at temperatures from ?30 to approximately glass‐transition temperature (T_g) + 80 °C. Miscible blends were obtained by solution casting from methyl ethyl ketone solution, as confirmed by single differential scanning calorimetry T_g and single segmental relaxation process for each blend. The β relaxation of PMMA maintains similar characteristics in blends with PVPh, compared with neat PMMA. Its relaxation time and activation energy are nearly the same in all blends. Furthermore, the dielectric relaxation strength of PMMA β process in the blends is proportional to the concentration of PMMA, suggesting that blending and intermolecular hydrogen bonding do not modify the local intramolecular motion. The α process, however, represents the segmental motions of both components and becomes slower with increasing PVPh concentration because of the higher T_g. This leads to well‐defined α and β relaxations in the blends above the corresponding T_g, which cannot be reliably resolved in neat PMMA without ambiguous curve deconvolution. The PMMA β process still follows an Arrhenius temperature dependence above T_g, but with an activation energy larger than that observed below T_g because of increased relaxation amplitude. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 3405–3415, 2004