The Conormal Derivative Problem for Elliptic Equations with BMO Coefficients on Reifenberg Flat Domains

We study the inhomogeneous conormal derivative problem for thedivergence form elliptic equation, assuming that the principalcoefficients belong to the BMO space with small BMO semi-normsand that the boundary is -Reifenberg flat. These conditionsfor the W^{1, p}-theory not only weaken the requirements on thecoefficients but also lead to a more general geometric conditionon the domain. In fact, the Reifenberg flatness is the minimalregularity condition for the W^{1, p}-theory. 2000 MathematicsSubject Classification 35R05 (primary), 35J15 (secondary).     

Constructing the Kähler and the symplectic structures from certain spinors on 4-manifolds

We show that, on an oriented Riemannian 4-manifold, existence of a non-zero parallel spinor with respect to a spin structure implies that the underlying smooth manifold admits a Kähler structure. A similar but weaker condition is obtained for the 4-manifold to admit a symplectic structure. We also show that the structure in which the non-zero parallel spinor lives is equivalent to the canonical spin structure associated to the Kähler structure.

     

A Three-Dimensional Porous Organic Semiconductor Based on Fully sp2-Hybridized Graphitic Polymer

Dimensionality plays an important role in the charge transport properties of organic semiconductors. Although three-dimensional semiconductors, such as Si, are common in inorganic materials, imparting electrical conductivity to covalent three-dimensional organic polymers is challenging. Now, the synthesis of a three-dimensional π-conjugated porous organic polymer (3D p-POP) using catalyst-free Diels–Alder cycloaddition polymerization followed by acid-promoted aromatization is presented. With a surface area of 801 m² g⁻¹, full conjugation throughout the carbon backbone, and an electrical conductivity of 6(2)×10⁻⁴ S cm⁻¹ upon treatment with I₂ vapor, the 3D p-POP is the first member of a new class of permanently porous 3D organic semiconductors.     

Semi-analytical study of meniscus oscillation in an electrospray under AC voltage

In this paper, the oscillation of the meniscus in an electrospray with AC voltage is semi-analytically investigated. The electric field is achieved using the charge simulation method and the mutual interaction between the electric field and hydrodynamics is iteratively explored to investigate the oscillation. After determining the static meniscus shape on a nozzle, the meniscus oscillation is simulated under sinusoidal AC voltage. The semi-analytic simulation can offer the oscillating meniscus shapes and contours of the electric field outside the meniscus according to the applied frequency. Furthermore, the velocity profile of the liquid inside the meniscus is achieved.     

Bulk heterojunction polymer solar cells based on binary and ternary blend systems

Polymer solar cells (PSCs) were fabricated using a ternary blend film consisting two conjugated polymers and a soluble fullerene derivative as the donor and acceptor materials, respectively. And, to compare ternary blend system, the single‐component copolymers consisting of the repeating units of each of the copolymers, used in ternary blend solar cells, were designed and synthesized for use as the electron donor materials in binary blend solar cells. We systematically investigated the field‐effect carrier mobilities and the optical, electrochemical, and photovoltaic properties of the copolymers. Under optimized conditions, the binary blend polymer systems showed power conversion efficiencies (PCEs) for the PSCs in the range 3.87–4.16% under AM 1.5 illumination (100 mW cm^?2). All polymers exhibited similar PCEs that did not depend on the ratio of repeating units. The binary blend solar cell containing a single‐component copolymer as the electron donor material performed better than the ternary blend solar cell in this work. © 2011 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2011     

W 1, p(·)-Regularity for Elliptic Equations with Measurable Coefficients in Nonsmooth Domains

We establish global W ^{1, p(·)}-estimates for second order elliptic equations in divergence form under the natural assumption that p(·) is log-Hölder continuous. To this end, we assume that the coefficients are measurable in one variable and have small BMO semi-norms in the other variables and the boundary of the domain is Reifenberg flat. Our work is an optimal and natural extension of W ^1,p -regularity for such equations with merely measurable coefficients beyond Lipschitz domains.     

Direct catalytic C–H arylation of imidazo[1,2-a]pyridine with aryl bromides using magnetically recyclable Pd–Fe3O4 nanoparticles

The direct C–H arylation of a heteroarene with aryl bromides has been achieved under the catalysis of magnetic nanoparticles. In the presence of bimetallic Pd–Fe₃O₄ heterodimer nanocrystals (1 mol % in palladium), the reaction of imidazo[1,2-a]pyridine with various aryl bromides gives the corresponding arylated products with exclusive C3-selectivity. The highly regioselective method is applicable to a wide range of aryl bromides with varying electronic and steric properties. The Pd–Fe₃O₄ nanocrystals can be recoverable by simple magnetic separation and have been recycled ten times without loss of catalytic activity.     

Heck and Sonogashira cross-coupling reactions using recyclable Pd–Fe3O4 heterodimeric nanocrystal catalysts

We have developed a convenient Pd–Fe₃O₄ heterodimeric nanocrystal catalyst system for Heck and Sonogashira reactions. This catalyst offers an environment-friendly, atom-efficient, and robust catalytic system for both reactions. Furthermore the nanocrystal catalyst could be easily separated by an external magnet and recycled six times without losing its catalytic activity.