Quasiconformal and harmonic mappings between Jordan domains

Let Ω and Ω₁ be Jordan domains, let μ ∈ (0, 1], and let be a harmonic homeomorphism. The object of the paper is to prove the following results: (a) If f is q.c. and ∂Ω, ∂Ω₁ ∈ C ^1,μ , then f is Lipschitz; (b) if f is q.c., ∂Ω, ∂Ω₁ ∈ C ^1,μ and Ω₁ is convex, then f is bi-Lipschitz; and (c) if Ω is the unit disk, Ω₁ is convex, and ∂Ω₁ ∈ C ^1,μ , then f is quasiconformal if and only if its boundary function is bi-Lipschitz and the Hilbert transform of its derivative is in L ^∞. These extend the results of Pavlović (Ann. Acad. Sci. Fenn. 27:365–372, 2002).      

Circuit-Cocircuit Reversing Systems in Regular Matroids

We consider that two orientations of a regular matroid are equivalent if one can be obtained from the other by successive reorientations of positive circuits and/or positive cocircuits. We study the inductive deletion-contraction structure of these equivalence classes in the set of orientations, and we enumerate these classes as evaluations of the Tutte polynomial. This generalizes the results in digraphs from a previous paper. Received January 10, 2006     

Enantioselective transfer hydrogenation of ketones with planar chiral ruthenocene-based phosphinooxazoline ligands

1,2-Disubstituted planar chiral ruthenocene-based phosphinooxazoline ligands (Rc-PHOX, 3 and 4) were synthesized easily and applied in the transfer hydrogenation of ketones to chiral alcohols using 2-propanol as a source of hydrogen with excellent enantioselectivity and high catalytic activity.     

Synthesis, properties and structures of methyldiphenylphosphonium 1-indenylide, 1-C9H6PMePh2, and its chiral tricarbonylchromium(0) complex Cr(η-1-C9H6PMePh2)(CO)3

The hitherto unknown indenyl-derived ylide, methyldiphenylphosphonium 1-indenylide, 1-C₉H₆PMePh₂ (1) and its chromium(0) complex, Cr(η⁵-1-C₉H₆PMePh₂)(CO)₃ (2) have been synthesized and characterized spectroscopically and crystallographically. The structures and properties of 1 and 2 are compared with those of the analogous C₅H₄PMePh₂ and its chromium complex, Cr(η⁵-C₅H₄PMePh₂)(CO)₃. Compound 2, obtained as a racemic mixture, exhibits planar chirality resulting from coordination of the prochiral aromatic ligand.     

Thickness and outerthickness for embedded graphs

We prove new upper bounds for the thickness and outerthickness of a graph in terms of its orientable and nonorientable genus by applying the method of deleting spanning disks of embeddings to approximate the thickness and outerthickness. We also show that every non-planar toroidal graph can be edge partitioned into a planar graph and an outerplanar graph. This implies that the outerthickness of the torus (the maximum outerthickness of all toroidal graphs) is 3. Finally, we show that all graphs embeddable in the double torus have thickness at most 3 and outerthickness at most 5.     

Realization of optoelectronic integrated transmitter and receiver for POF Applications

The optoelectronic integrated transmitter and receiver for 650 nm plastic optical fiber (POF) communication applications realized in 0.5 μm BCD (Biplor, CMOS and DMOS) process is first described in this paper. The 650 nm resonant cavity light emitting diode (RCLED) is used as light source. It is first proposed for optoelectronic integration of the transmitter by bonding RCLED to the driver chip. Temperature compensation technology is employed in the driver circuit to compensate for the modulation current. In the monolithic optoelectronic integrated receiver, large area multi-finger PIN photodetector (PD) that is compatible with standard IC process, transimpedance amplifier and post amplifier are presented. Measurement results show that the responsivity and capacitance of PD is 0.25 A/W and 5 pF, respectively. The sensitivity of receiver is −14.6 dBm at 180 Mb/s and BER is less than 10⁻⁹ for 650 nm input light by POF. A clear eye diagram is demonstrated for 180 Mb/s PRBS. These indicate that optoelectronic integrated chips can be employed in high-speed POF-based Fast Ethernet systems for broadband access network applications.     

Gold Nanoparticle‐labeled Electrochemical Immunoassay Using Open Circuit Potential for Human Chorionic Gonadotropin Detection

This study presents a new approach for an electrochemical immunoassay using gold nanoparticle (AuNP)‐labeled antibodies and pre‐oxidation and reduction processes, followed by open circuit potential (OCP) measurement. Detection of the pregnancy marker, human chorionic gonadotropin hormone (hCG), was used as a model. After preparation of a sandwich‐type immunosystem, the pre‐oxidation and reduction processes were applied, followed by OCP detection. The applied potential and time period were studied for the optimization of pre‐oxidation and reduction processes. We observed that the pre‐oxidation potential of 1.2 V for 60 s and reduction potential of −0.2 V for 30 s provided the highest OCP signal. The detection limit was 79 pg/mL using the optimal conditions. This system could be applied to a simplified and miniaturized diagnostic system for integration in compact analytical devices.     

A characterization of planar partial cubes

Partial cubes as well as planar graphs have been extensively investigated. In this note we introduce an additional topological kind of condition to the Chepoi’s expansion procedure that characterizes planar partial cubes. As a consequence we obtain a characterization of some other planar subclasses of partial cubes.     

Total Colorings of Planar Graphs without Small Cycles

Let G be a planar graph with maximum degree Δ. It is proved that if Δ ≥ 8 and G is free of k-cycles for some k ∈ {5,6}, then the total chromatic number χ′′(G) of G is Δ + 1. This work is supported by a research grant NSFC(60673047) and SRFDP(20040422004) of China. Received: February 27, 2007. Final version received: December 12, 2007.     

不含4-9圈的平面图的L(p,q)-标号

令p≥q是两个正整数.用△(G)和λp,q(G)分别记平面图G的最大度和L(p,q)-标号数.文章证明了若G为不含i-圈,4≤i≤9的平面图,则λp,q(G)≤(2q- 1)Δ(G)+8p-4.这一结果推出x (G2)≤△(G)+5.因此对于这样一类图部分地证实了Wegner的猜想[2].