Monochromatic and Heterochromatic Subgraphs in Edge-Colored Graphs - A Survey

Nowadays the term monochromatic and heterochromatic (or rainbow, multicolored) subgraphs of an edge-colored graph appeared frequently in literature, and many results on this topic have been obtained. In this paper, we survey results on this subject. We classify the results into the following categories: vertex-partitions by monochromatic subgraphs, such as cycles, paths, trees; vertex partition by some kinds of heterochromatic subgraphs; the computational complexity of these partition problems; some kinds of large monochromatic and heterochromatic subgraphs. We have to point out that there are a lot of results on Ramsey type problem of monochromatic and heterochromatic subgraphs. However, it is not our purpose to include them in this survey because this is slightly different from our topics and also contains too large amount of results to deal with together. There are also some interesting results on vertex-colored graphs, but we do not include them, either. Supported by NSFC, PCSIRT and the “973” program.     

Porphyrin-cyclodextrin supramolecular complexes as myoglobin model in water

This mini-review reports supramolecular system composed of O-methylated β-cyclodextrins and metalloporphyrins that mimic the functions of myoglobin (Mb) in aqueous solution. Although many Mb functional models have been demonstrated so far, most models can bind dioxygen only in organic solvents such as toluene. Recently, we prepared the model systems composed of O-methylated β-cyclodextrin dimers having pyridine and imidazole linkers and tetrakis(4-sulfonatophenyl)porphinato iron(II) (hemoCD and Fe(II)PImCD). HemoCD binds dioxygen reversibly in aqueous solution, and the dioxygen adduct of hemoCD is very stable (a half-lifetime is 30 h at pH 7). Although the dioxygen affinity of Fe(II)PImCD is much higher than hemoCD, the stability and the reversibility of this system is lower. This review compares the functions of these model systems with those in biological systems. This review was written to dedicate to Professor Janos H. Fendler on the occasion of his 70th birthday. He gave me a chance to study biomimetic chemistry when he was a professor of Texas A&M University.     

Local fields in Co and Mn Co-doped ZnO

The magnetic properties of ZnO co-doped with 5 at. % Co and 5 at. % Mn(Zn_0.90Co_0.05Mn_0.05O) synthesized by a solid-state reaction were investigated by means of ⁵⁷Co emission Mössbauer spectroscopy. The majority of the probe ions (80 %) residing in defect-free substitutional Zn sites take the oxidation state of ⁵⁷Fe ²⁺, and the others presumably form local defects taking the state of ⁵⁷Fe ³⁺ at room temperature. Both components show doublets, and RT ferromagnetism was thus absent in the sample. For the measurement at 10 K, spectral broadening was observed, implying a possible presence of a weak magnetic component.     

Fructose/dioxygen biofuel cell based on direct electron transfer-type bioelectrocatalysis

One-compartment biofuel cells without separators have been constructed, in which d-fructose dehydrogenase (FDH) from Gluconobacter sp. and laccase from Trametes sp. (TsLAC) work as catalysts of direct electron transfer (DET)-type bioelectrocatalysis in the two-electron oxidation of d-fructose and four-electron reduction of dioxygen as fuels, respectively. FDH adsorbs strongly and stably on Ketjen black (KB) particles that have been modified on carbon papers (CP) and produces the catalytic current with the maximum density of about 4 mA cm(-2) without mediators at pH 5. The catalytic wave of the d-fructose oxidation is controlled by the enzyme kinetics. The location and the shape of the catalytic waves suggest strongly that the electron is directly transferred to the KB particles from the heme c site in FDH, of which the formal potential has been determined to be 39 mV vs. Ag|AgCl|sat. KCl. Electrochemistry of three kinds of multi-copper oxidases has also been investigated and TsLAC has been selected as the best one of the DET-type bioelectrocatalyst for the four-electron reduction of dioxygen in view of the thermodynamics and kinetics at pH 5. In the DET-type bioelectrocatalysis, the electron from electrodes seems to be transferred to the type I copper site of multi-copper oxidases. TsLAC adsorbed on carbon aerogel (CG) particles with an average pore size of 22 nm, that have been modified on CP electrodes, produces the catalytic reduction current of dioxygen with a density of about 4 mA cm(-2), which is governed by the mass transfer of the dissolved dioxygen. The FDH-adsorbed KB-modified CP electrodes and the TsLAC-adsorbed CG-modified CP electrodes have been combined to construct one-compartment biofuel cells without separators. The open-circuit voltage was 790 mV. The maximum current density of 2.8 mA cm(-2) and the maximum power density of 850 microW cm(-2) have been achieved at 410 mV of the cell voltage under stirring.     

An efficient unnatural base pair for PCR amplification

Expansion of the genetic alphabet by an unnatural base pair system provides a powerful tool for modern biotechnology. As an alternative to previous unnatural base pairs, we have developed a new pair between 7-(2-thienyl)imidazo[4,5-b]pyridine (Ds) and 2-nitropyrrole (Pn), which functions in DNA amplification. Pn more selectively pairs with Ds in replication than another previously reported pairing partner, pyrrole-2-carbaldehyde (Pa). The nitro group of Pn efficiently prevented the mispairing with A. High efficiency and selectivity of the Ds-Pn pair in PCR amplification were achieved by using a substrate mixture of the gamma-amidotriphosphate of Ds and the usual triphosphates of Pn and the natural bases, with Vent DNA polymerase as a 3' to 5' exonuclease-proficient polymerase. After 20 cycles of PCR, the total mutation rate of the Ds-Pn site in an amplified DNA fragment was approximately 1%. PCR amplification of DNA fragments containing the unnatural Ds-Pn pair would be useful for expanded genetic systems in DNA-based biotechnology.     

Straight-Line Embeddings of Two Rooted Trees in the Plane

We prove the following theorem: Let T ₁ and T ₂ be two disjoint rooted trees with roots v ₁ and v ₂ , respectively, and let P be a set of |T₁ T₂| points in the plane in general position containing two specified points p ₁ and p ₂ . Then the union T ₁ $\cup$ T ₂ can be straight-line embedded onto P such that v ₁ and v ₂ correspond to p ₁ and p ₂ , respectively. Moreover, we give a O(n ² log n) time algorithm for finding such an embedding, where n is the number of vertices contained in T ₁ $\cup$ T ₂ . Received July 3, 1997, and in revised form February 25, 1998.     

[2,3]‐Wittig Rearrangement of Enantiomerically Enriched 3‐Substituted 1‐Propenyloxy‐1‐phenyl‐2‐propen‐1‐yl Carbanions: Effect of Heteroatoms and Conjugating Groups on Planarization of an α‐Oxy‐Benzylcarbanion through a Double Bond

Don't get trapped : The effect of conjugating electron‐withdrawing groups and α‐anion‐stabilizing heteroatom substituents on configurational stability of chiral carbanions through a double bond was examined on the basis of extent of chirality transfer in intramolecular trapping in [2,3]‐Wittig rearrangement of chiral 3‐substituted 1‐propenyloxy‐1‐phenyl‐2‐propen‐1‐yl carbanions (see scheme).