The determination of silicon in airborne particulate matter by XRF and LA-ICP-MS

This study reports the analysis of Si in airborne particulate matter by laser ablation inductively coupled plasma mass spectrometry (LA-ICP-MS) as well as X-ray fluorescence (XRF). It was found that Si concentration in airborne particulates collected on PTFE-membrane filters could be accurately determined with a laser beam operated at 160 mJ free running mode, 6.5 mm defocusing distance and 0.8 l/min carrier gas flow rate during the LA-ICP-MS measurement. Standard filters prepared by NIST SRM 1648 urban particulates were used for both XRF and LA-ICP-MS not only to establish the calibration curves of Si, but also to examine the proposed method's effectiveness. The capability of applying both methods for natural sample analysis was also examined. Particulate loaded filter samples collected from a heavily polluted metropolitan area of Kaoshiung, Taiwan were initially measured by XRF, then by LA-ICP-MS. An intercomparison between them was thus performed. As a result, both XRF and LA-ICP-MS proved to be the valid analytical methods for directly determining Si concentrations in airborne particulates on PTFE membrane filters.     

Crown Ether Phase Transfer Catalysts for An Ionic Polymerization of Bisphenol A / 4,4′‐Dichlorodiphenyl Sulfone

Various crown ethers were prepared and applied as phase transfer catalysts for the an ionic copolymerization of bisphenol A and 4,4′‐dichlorodiphenyl sulfone monomers with alkali salts, e.g., NaNH₂, NaOH and KOH, as initiators. The catalytic abilities of various crown ethers for the an ionic polymerization of bisphenol A / 4,4′‐dichlorodiphenyl sulfone were found to be in the order: 15‐crown‐5 ? monobenzo‐15‐crown‐5 > 18‐crown‐6 > Dicyclohexano‐18‐crown‐6 > Dibenzo‐18‐crown‐6 > 12‐crown‐4 with sodium amide (NaNH₂) as initiator. Sodium amide was shown to be a better initiator than NaOH or KOH with monobenzo‐ 15‐crown‐5 as a catalyst. Effects of solvents and temperature on the crown ether catalytic polymerization were also investigated. Dimethyl sulfoxide (DMSO) exhibited much better for the polymerization than other organic solvents, e.g., toluene, p‐xylene, dimethyl formamide and dioxane. Higher polymerization was found at higher temperatures and about 100% yield of poly(bisphenol A / sulfone) was obtained at 125 °C in 3 hr. The molecular weight of poly(bisphenol A / sulfone) as a function of reaction time was determined with gel permeation chromatography. Concentration effects of crown ether on % yield and molecular weight of poly(bisphenol A / sulfone) were also investigated and discussed.     

An Iron‐Catalyzed Cascade Approach to Benzo[b]carbazole Synthesis Followed by 1,4‐Sulfonyl Migration

A simple and straightforward approach was developed to construct 5H‐benzo[b]carbazole derivatives by iron catalysis in a cascade sequence. The notable features of this work include an atom‐economical cascade sequence, unprecedented 1,4‐sulfonyl migration, tolerance of a variety of functional groups, good yields, and an economical catalytic system.     

Fixed point theorems for multifunctions having KKM property on almost convex sets

In this paper, for two nonempty subsets X and Y of a linear space E, we define the class KKM(X,Y) and investigate the fixed point problem for T∈KKM(X,X) with X an almost convex subset of a locally convex space. Our fixed point theorem contains Lassonde fixed point theorem for Kakutani factorizable multifunctions as special case.     

Two-grid discretization schemes for nonlinear Schrödinger equations

We study efficient two-grid discretization schemes with two-loop continuation algorithms for computing wave functions of two-coupled nonlinear Schrödinger equations defined on the unit square and the unit disk. Both linear and quadratic approximations of the operator equations are exploited to derive the schemes. The centered difference approximations, the six-node triangular elements and the Adini elements are used to discretize the PDEs defined on the unit square. The proposed schemes also can compute stationary solutions of parameter-dependent reaction–diffusion systems. Our numerical results show that it is unnecessary to perform quadratic approximations.     

Asymmetric Polymer Particles with Anisotropic Curvatures by Annealing Polystyrene Microspheres on Poly(vinyl alcohol) Films

Anisotropic polymer particles such as Janus particles have attracted significant attention in recent years because of their unique properties and unusual self‐assembly behavior. Most anisotropic polymer particles synthesized so far, however, only have different chemical regions compartmentalized on the particles. It remains a great challenge to fabricate anisotropic polymer particles with different shapes within a single particle. A novel approach is developed to prepare anisotropic polymer particles that contain two hemispheres with different curvatures by annealing polystyrene microspheres on poly(vinyl alcohol) films. During the annealing process, the polymer microspheres gradually sink into the polymer films and transform to asymmetric polymer particles, driven by the surface and interfacial tensions of the polymers. Selective removal techniques are also used to confirm the morphologies of the asymmetric particles.

     

Algebraic methods for the solution of linear functional equations

The equation

$$\sum^{n}_ {i=0} a_{i}f(b_{i}x + (1 - b_{i})y) = 0$$

belongs to the class of linear functional equations. The solutions form a linear space with respect to the usual pointwise operations. According to the classical results of the theory they must be generalized polynomials. New investigations have been started a few years ago. They clarified that the existence of non-trivial solutions depends on the algebraic properties of some related families of parameters. The problem is to find the necessary and sufficient conditions for the existence of non-trivial solutions in terms of these kinds of properties. One of the earliest results is due to Z. Daróczy [1]. It can be considered as the solution of the problem in case of n = 2. We are going to take more steps forward by solving the problem in case of n = 3.

     

Continuation and stability analysis for Bloch waves of the Gross-Pitaevskii equation

We describe a two-parameter continuation algorithm for computing Bloch waves of Bose-Einstein condensates (BEC) in optical lattices which is governed by the Gross-Pitaevskii equation (GPE). The Fourier collocation method and fourth-order Adini’s elements with penalty are used to discretize the GPE. We propose two different approaches so that the two-parameter continuation algorithm can be modified to compute closed tubes at the four corners of the Bloch band. We also study linear stability analysis for the GPE. We show that all the discrete steady-state solutions are numerically neutrally stable. Numerical results show that the four edges of the Bloch waves are surrounded by closed loops if the coefficient of the cubic nonlinear term is greater than that of the periodic potential. Moreover, closed tubes at the four corners of the Bloch band are obtained. The numerical results display superfluidity of BEC.     

Numerical simulation of Taylor Couette flow of Bingham fluids

The Bingham fluid flow between two concentric cylinders is studied using numerical simulation. The cylinders are assumed to rotate independently, and with an imposed axial sliding. The flow field is decomposed with linearity arguments of the base circular Couette shear flow and corresponding deviation field. The numerical methods are based on the expression of the deviation field in terms of complete sets of orthogonal functions and Chebyshev series. The Galerkin projection method is used with the pressure term being eliminated. The Adams Bashforth scheme is adopted for time marching. The results show that the vortices are squeezed toward the inner cylinder due to the effect of yield stress. When the outer cylinder is held stationary, the yield stress plays a role in weakening the vortex flow. However, for the co-rotation situation, the vortex flow is initially strengthened with an increase of yield stress, and then weakened as the yield stress is raised large enough. The annular unyielded regions emerge and stick to the outer cylinder. In case of Taylor Couette flow with an imposed axial sliding, a spiral vortex flow is visible with spiral unyielded region being obtained.