Synthesis and properties of new soluble triphenylamine‐based aromatic poly(amine amide)s derived from N,N′‐bis(4‐carboxyphenyl)‐N,N′‐diphenyl‐1,4‐phenylenediamine

A new triphenylamine‐containing aromatic dicarboxylic acid, N,N′‐bis(4‐carboxyphenyl)‐N,N′‐diphenyl‐1,4‐phenylenediamine, was synthesized by the condensation of N,N′‐diphenyl‐1,4‐phenylenediamine with 4‐fluorobenzonitrile, followed by the alkaline hydrolysis of the intermediate dinitrile compound. A series of novel triphenylamine‐based aromatic poly(amine amide)s with inherent viscosities of 0.50–1.02 dL/g were prepared from the diacid and various aromatic diamines by direct phosphorylation polycondensation. All the poly(amine amide)s were amorphous in nature, as evidenced by X‐ray diffractograms. Most of the poly(amine amide)s were quite soluble in a variety of organic solvents and could be solution‐cast into transparent, tough, and flexible films with good mechanical properties. They had useful levels of thermal stability associated with glass‐transition temperatures up to 280 °C, 10% weight‐loss temperatures in excess of 575 °C, and char yields at 800 °C in nitrogen higher than 60%. © 2002 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 41: 94–105, 2003     

Computation of reference Bayesian inference for variance components in longitudinal studies

Generalized linear mixed models (GLMMs) have been applied widely in the analysis of longitudinal data. This model confers two important advantages, namely, the flexibility to include random effects and the ability to make inference about complex covariances. In practice, however, the inference of variance components can be a difficult task due to the complexity of the model itself and the dimensionality of the covariance matrix of random effects. Here we first discuss for GLMMs the relation between Bayesian posterior estimates and penalized quasi-likelihood (PQL) estimates, based on the generalization of Harville’s result for general linear models. Next, we perform fully Bayesian analyses for the random covariance matrix using three different reference priors, two with Jeffreys’ priors derived from approximate likelihoods and one with the approximate uniform shrinkage prior. Computations are carried out via the combination of asymptotic approximations and Markov chain Monte Carlo methods. Under the criterion of the squared Euclidean norm, we compare the performances of Bayesian estimates of variance components with that of PQL estimates when the responses are non-normal, and with that of the restricted maximum likelihood (REML) estimates when data are assumed normal. Three applications and simulations of binary, normal, and count responses with multiple random effects and of small sample sizes are illustrated. The analyses examine the differences in estimation performance when the covariance structure is complex, and demonstrate the equivalence between PQL and the posterior modes when the former can be derived. The results also show that the Bayesian approach, particularly under the approximate Jeffreys’ priors, outperforms other procedures.     

Crystallization of poly(aryl ether ketone ketone) copolymers containing terephthalate/isophthalate moieties

In a previous study, we have investigated the structure, crystallization, and morphology of poly(aryl ether ketone ketone), PEKK, copolymers prepared from diphenyl ether (DPE), terephthalic acid (T), and isophthalic acid (I) with T/I ratios from 100/0 to 50/50. These materials were considered as having -DPE-T-DPE-T- (TT) and/or -DPE-T-DPE-I- (TI) “phthalate diads.” In this work, we continue the study of this copolymer series with six different T/I ratios (40/60, 30/70, 20/80, 15/85, 10/90, and 0/100), which are viewed as having TI and/or -DPE-I-DPE-I- (II) “diads.” The I moieties (1,3-linked isomers) were always found to be incorporated in the crystals and acted as “entropy or symmetry” defects that effectively decreased the equilibrium melting temperature T_m^o and the rate of crystallization. However, the retardation of crystallization in PEKK 0/100 (the homopolymer with pure II diads) was significantly less than expected, which was attributed to the segregation of I moieties between the chains leading to a reduction of total entropy in the unit cells. The evidence of segmental segregation in PEKK 0/100 was seen in x-ray diffraction patterns, where several extra reflections were seen that could only be indexed by the published unit cell modified with a larger c-axis dimension (3.048 nm, corresponding to the length of six phenyl residues or 1.524 nm, the length of three phenyl residues). The composition of 15/85 was found to have the lowest value of T_m^o and the slowest crystallization rate. Upon heating, the “II” crystals (T/I from 30/70 to 0/100) exhibited the conventional double-melting behavior rather than the triple-melting behavior as in the “TI” crystals (50/50 to 40/60). No indication of the second polymorph form 2 was found in “II” crystals. © 1994 John Wiley & Sons, Inc.     

Stable methods for an inverse problem in acoustic scattering by an obstacle and an inhomogeneous medium

We consider (in two-dimensional Euclidean space) the scattering of a plane, time-harmonic acoustic wave by an inhomogeneous medium Ω with compact support and a bounded obstacle D lying completely outside of the inhomogeneous medium. We show that one may determine the shape of D and the local speed of sound in Ω from a knowledge of the asymptotic behavior of the scattered wave (i.e. the far field). This is done by considering a constrained optimization problem and employing integral equation and conformal mapping techniques. By assuming a priori that the functions which determine the shape of D and the local speed of sound in Ω lie in given compact sets, we show that the problem is stable, in the sense that the solution of the inverse scattering problem depends continuously on the far field data.     

Boundary integral equations for the Helmholtz equation: The third boundary value problem

In this paper we study the application of boundary integral equation methods for the solution of the third, or Robin, boundary value problem for the exterior Helmholtz equation. In contrast to earlier work, the boundary value problem is interpreted here in a weak sense which allows data to be specified in L_∞ (?D), ?D being the boundary of the exterior domain which we assume to be Lyapunov of index 1. For this exterior boundary value problem, we employ Green's theorem to derive a pair of boundary integral equations which have a unique simultaneous solution. We then show that this solution yields a solution of the original exterior boundary value problem.     

An optically thin radiating gas jet

A radiating gas jet near the optically thin limit is examined. The gas is assumed to be inviscid, optically grey, and in the state of chemical equilibrium or to obey the ideal gas law. The jet is assumed to be plane-symmetric or axi-symmetric and is fully expanded. Under these conditions and by the method of quasi-one-dimensional flow, the problem is analyzed. In addition to this, numerical examples are also included to illustrate the radiative effects.

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Zusammenfassung Es wird ein strahlender Gasstrahl untersucht, nahe zum optisch dünnen Grenzfall. Das Gas wird reibungsfrei, optisch grau und im chemischen Gleichgewicht (oder als ideales Gas) vorausgesetzt. Der Strahl wird eben oder axisymmetrisch angenommen und ist voll expandiert. Unter diesen Voraussetzungen und mit der Methode der fast-eindimensionalen Strömung wird das Problem analysiert. Zudem sind numerische Beispiele angegeben, um den Strahlungseffekt zu veranschaulichen.

     

Design of low-loss tapered waveguide by applying photonic-crystal-based microlenses in telescopic structure

In this paper, the design of low-loss tapered waveguides by applying photonic-crystal-based microlenses is presented. The microlenses are realized by using two-dimensional photonic crystal (PhC) structures with a hexagonal periodic lattice of air-holes. In order to make the PhC structures behave as homogeneous and isotropic microlenses, the PhC structures are designed to operate in the low-frequency domain with light wavelength sufficiently larger than the PhC lattice constant. The effective indices of the PhC are calculated and the structures are properly arranged in microlenslike shapes. By monolithically integrating the effective microlenses in the tapered area between the two optical waveguides with different core dimensions, the wavefront of the eigenmode can be coupled from the larger core to the smaller core effectively and also the radiation loss in the tapered area between the two connected optical waveguides can be effectively suppressed. The results show that the PhC-based microlens in the telescopic structure can serve as an optical element in the tapered waveguide with the advantages of low loss, high efficiency and compactness.     

One-pot synthesis of hollow Au3Cu1 spherical-like and biomineral botallackite Cu2(OH)3Cl flowerlike architectures exhibiting antimicrobial activity

A new form of Au3Cu1 hollow nanostructure was prepared by the reaction of Cu nanoparticles with HAuCl4. Following a course of aging, the biomineral botallackite Cu2(OH)3Cl nanoflowers were developed with the aid of Au3Cu1 hollow nanostructures at room temperature. It was proposed that the hollow nanospheres could serve as active centers for heterogeneous nucleation and mediated a mineralization process. Scanning electron microscopy and high-resolution transmission electron microscopy indicated that the nanoflowers are three-dimensional in appearance with a range of 500 nm-- to 1 microm in size and made of several nanopetals with about 25 nm in thickness. In addition, we found that the shape separation could be achieved by using cationic cetyltrimethylammonium bromide to filter the different morphology spherical- and flowerlike structures due to the negative charge of hollow nanospheres. Both hollow nanospheres and nanoflowers presented antimicrobial activity toward Streptococcus aureus with MIC50 at 39.6 and 127.2 microg/mL, respectively.