Fourier transform and smoothness of solutions of a class of semilinear elliptic degenerate equations with double characteristics

This paper is a continuation of our earlier note [V. T. T. Hien and N. M. Tri, “Analyticity of Solutions of Semililnear Equations with Double Characteristics,” J. Math. Anal. Appl. 337, 1249–1260 (2008)]. Here we prove the analyticity of solutions of a class of semilinear elliptic degenerate equations with double characteristics by using the Fourier transform.     

Regular conjugated terpolymers comprising two different acceptors and bithiophene donor in repeating group: Effect of strong and weak acceptors on semiconducting properties

Diketopyrrolopyrrole (DPP)‐based terpolymers—P(DPP‐TPyT) and P(DPP‐T3MTT)—bearing bithiophene donating groups and weak accepting units such as pyridine (Py) or methyl thiophene‐3‐carboxylate (3MT), in the polymer backbone, were successfully synthesized. Although the two polymers had similar physical and electrochemical properties, grazing incidence X‐ray diffraction patterns of P(DPP‐TPyT) and P(DPP‐T3MTT) showed mixed and edge‐on orientations, respectively, in thermally annealed films. Accordingly, the P(DPP‐T3MTT) showed twice the hole mobility of P(DPP‐TPyT) in a thin‐film transistor, and a blended film of P(DPP‐T3MTT) and [6,6]‐phenyl‐C71‐butyric acid methyl ester (PC₇₁BM) showed better power conversion efficiency in a polymer solar cell. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2016 , 54, 1339‐1347     

Metallabis(phosphonate) als Chelatliganden. II. Synthese und Reaktivität ein- und zweikerniger Palladiumbis(phosphonat)-Komplexe mit OHO- und OBF2O-Brückenbindungen

Metallabisphosphonates as Chelating Ligands. II. Synthesis and Reactivity of Mono- and Binuclear Palladiumbisphosphonate Complexes Containing OHO and OBF₂O Bridges The complexes C₅H₅Pd[{P(OR)₂O}₂H] ( 1 : R = Me; 2 : R = Et) are formed either by reaction of C₅H₅Pd(2-MeC₃H₄) with dimethyl- and diethylphosphite or by reaction of [ClPd{P(OR)₂O}₂H]₂ ( 3 : R = Me; 4 : R = Et) with TlC₅H₅. With excess HP(O)(OMe)₂, the π-allyl complex (2-MeC₃H₄)Pd[{P(OMe)₂O}₂H] ( 5 ) is also formed (besides 1 ) from C₅H₅Pd(2-MeC₃H₄). The ¹H and ³¹P n.m.r. spectra indicate that in 1 – 5 the PdP₂O₂H chelate ring presumably contains a symmetrical OHO-hydrogen bond. The reaction of 3 with BF₃ etherate leads to the binuclear complex [ClPd{P(OMe)₂O}₂BF₂]₂ ( 6 ) which reacts with TlC₅H₅ to yield C₅H₅Pd[{P(OMe)₂O}₂BF₂] ( 7 ). From C₅H₅Pd[{P(OR)₂O}₂H] ( 1 , 2 ) and NH₃ the bisamminepalladium bisphosphonates(NH₃)₂Pd[P(OR)₂O]₂ ( 8 , 9 ) are formed which probably possess a trans-configuration. The reaction of 8 , 9 with CF₃COOH does not lead to a corresponding Pd[{P(OR)₂O}₂H] chelate complex but instead gives by elimination of NH₃ polymeric palladium bisphosphonates [Pd{P(OR)₂O}₂]_n ( 10 , 11 ). 1 reacts with thallium acetylacetonate to give C₅H₅Pd[P(OMe)₂O]₂Tl ( 12 ).     

On convection in a fluid filling the cavity of a moving solid body

The problem of simultaneous motion about a fixed point O of a solid body and unevenly heated viscous incompressible fluid completely filling a finite cavity of the body is considered in linear formulation. The center of mass of the system body plus fluid in the state of mechanical equilibrium is assumed to coincide with point O. The theorem on solvability of the Cauchy problem for small unsteady equilibrium perturbations is proved, and normal perturbations and the spectrum of the problem arising in the analysis of such perturbations are investigated. It is shown that the whole spectrum consists of normal eigenvalues and lies in some half-band containing the real axis. It is shown that the respective system of root vectors is complete. Properties of the spectrum and the dependence on Rayleigh numbers are investigated. Rayleigh numbers for which the real parts of eigenvalues are positive,i.e. when the generated oscillating normal perturbations are damped in time, are evaluated in the case of the fluid being heated from below and above.     

Thermally switchable and discretely tunable comb filter with a linearly chirped fiber Bragg grating

We propose and experimentally demonstrate a novel switchable and discretely tunable comb filter based on a thermally induced linearly chirped fiber Bragg grating. Experimentally we achieved a thermally induced optical bandpass filter that has eight switchable passband peaks with peak separations of 1.6 and 3.2 nm, a very narrow bandwidth (as small as 10 pm) of each peak, a tunable range of 16.5 nm, and a greater than 25 dB rejection ratio. Two spectral peaks separated by only 0.8 nm were also obtained with this comb filter. This filter provides the unique advantages of an all-fiber structure, switchable spectral peaks, independent tuning of the center wavelength and wavelength spacing of the spectral peaks, low polarization sensitivity, simple structure, ease of fabrication, and low cost.     

Room-temperature multiwavelength erbium-doped fiber ring laser employing sinusoidal phase-modulation feedback

An effective method for achieving a room-temperature multiwavelength erbium-doped fiber ring laser is presented. Simultaneous multiwavelength lasing with 0.5-nm intervals is achieved both experimentally and theoretically by addition of sinusoidal phase modulation in the ring cavity to prevent single-wavelength oscillation.     

Poly(trialkylsilyl methacrylate)s: A family of hydrolysable polymers with tuneable erosion profiles

Polymers containing hydrolytically labile trialkylsilyl ester side groups were synthesised via a conventional and a controlled radical polymerization. The trialkylsilyl methacrylate monomer unit was chosen for its capacity to hydrolyse into basic, acid or sea water varying the hydrophilic character of the resulting polymer backbone with time. The hydrolysis or saponification reaction of the ester bond of the trialkylsilyl methacrylate was monitored through a ¹H NMR study showing the formation of siloxane side-products. Several copolymers and polymer blends were prepared as matrixes for controlled erodible systems. Their capacity to hydrolyse was demonstrated through SEM investigations with selective dissolution of free films containing hydrolysable copolymers and PMMA blends. Well-defined random and diblock copolymers with methyl methacrylate were investigated to show the effect of the microstructure on the erosion properties of the corresponding coatings. Poly(methyl methacrylate-b-tert-butyldimethylsilyl methacrylate) diblock copolymers synthesised through the RAFT process showed a better control of the erosion with a constant erosion rate over a long-time service in sea water at pH = 8.2. In addition, experiments showed that the erosion rate could be modulated by varying the molar proportion of hydrolysable side groups onto the copolymer backbone and the weight amount of copolymers mixed with PMMA in toluene solution.     

Synthesis of amorphane and cadinane sesquiterpenes from fabiana imbricata

The monoterpene (−)-isopulegol (7) has been used as a starting material for the total synthesis in eight/nine steps of two sesquiterpenes which were recently isolated from the medicinal plant Fabiana imbricata. Use of this approach has shown that a structure proposed as 3,11-amorphadiene (3) should be revised to that of 4,11-cadinadiene (18) and confirmed the structure proposed for the natural product 4-amorphen-1 1-ol (1).