Square-free-preserving and primitive-preserving homomorphisms

The aim of this paper is to investigate homomorphisms which reserve square-free languages or primitive languages. A characterization of square-free-preserving homomorphisms is presented. We show that every square-free-preserving homomorphism is primitive-preserving. Strongly cube-free-preserving homomorphisms are also studied.     

On L(d,1)-labelings of graphs

Given a graph G and a positive integer d, an L(d,1)-labeling of G is a function f that assigns to each vertex of G a non-negative integer such that if two vertices u and v are adjacent, then |f(u)−f(v)|d; if u and v are not adjacent but there is a two-edge path between them, then |f(u)−f(v)|1. The L(d,1)-number of G, λ_d(G), is defined as the minimum m such that there is an L(d,1)-labeling f of G with f(V){0,1,2,…,m}. Motivated by the channel assignment problem introduced by Hale (Proc. IEEE 68 (1980) 1497–1514), the L(2,1)-labeling and the L(1,1)-labeling (as d=2 and 1, respectively) have been studied extensively in the past decade. This article extends the study to all positive integers d. We prove that λ_d(G)Δ²+(d−1)Δ for any graph G with maximum degree Δ. Different lower and upper bounds of λ_d(G) for some families of graphs including trees and chordal graphs are presented. In particular, we show that the lower and the upper bounds for trees are both attainable, and the upper bound for chordal graphs can be improved for several subclasses of chordal graphs.     

Effects of substituent and solvent on the structure and spectral properties of maleimide derivatives

The maximum absorption wavelength , emission wavelength (λ_em) and the related oscillator strength (f) of the maleimides in the ground and first excited states were calculated by using the DFT, CIS and the time-dependent density functional theory (TD-DFT) methods, where the molecular structures were optimized by DFT/B3LYP/6-31G^* calculation. Solvent effects on the maleimides were examined using the PCM simulation at DFT/B3LYP level with the 6-31G^* basis set. For N-substituted maleimide, the substituent gives only a slight influence on the maleimide chromophore, while planar conformation of PhMLH leads to the improvement in π-delocalization from substituent to maleimide unit. For 3,4-substituted maleimide, the steric repulsion between substituent and maleimide chromophore influences the extent of π-delocalization and the molecular conformation. The calculated and λ_em of maleimides are in good agreement with the experimental data. In the gas phase, both absorption and emission peaks are red-shift as compared to the non-substituted maleimide. Under solvent environment, the more planar conformation of PhMLH shows a blue-shift in the calculated and λ_em as compared with other N-substituted maleimides. For 3,4-substituted maleimides, the effect of substitution produces the most significant spectral red-shift as compared to other maleimides.     

Reactivity and electronic property of decaphenylmetallocenes of Mo and W atoms

The perphenylmetallocene complexes (η⁵-C₅Ph₅)₂W (1), [(η⁵-C₅Ph₅)₂W]⁺I₃⁻ (1⁺I₃), (η⁵-C₅Ph₅)₂Mo (2) and [(η⁵-C₅Ph₅)₂Mo]⁺I₃⁻ (2⁺I₃) have been prepared. Hydrogenation of 1 in THF produces (η⁵-C₅Ph₅)₂WH₂ (4), while (η⁵-C₅Ph₅)₂WHCl (3) is afforded in 1,2-dichloroethane solvent. Carbonylation of 1 produces (η⁵-C₅Ph₅)₂W(CO) (5). Treatment of 1 with the strong acid CF₃SO₃H leads to the dicationic species [(η⁵-C₅Ph₅)₂W]⁺²[CF₃SO₃]⁻₂ (1⁺²Tf₂) after crystallization. The structures of 2⁺I₃ and 1⁺²Tf₂ have been determined by an X-ray diffraction study. The magnetic susceptibility study indicates a ³E_2g ground-state for 1 and 2, and a ⁴A_2g ground-state for 1⁺ and 2⁺.     

Determination of unbound cefamandole in rat blood by microdialysis and microbore liquid chromatography

To analyze unbound cefamandole in rat blood, a method combing microdialysis with microbore liquid chromatography has been developed. A microdialysis probe was inserted into the jugular vein/right atrium of male Sprague-Dawley rats to examine the unbound cefamandole level in the rat blood following cefamandole administration (50 mg/kg, i.v.). The dialysates were directly submitted to a liquid chromatographic system. Samples were eluted with a mobile phase containing acetonitrile-methanol-100 mM monosodium phosphate (pH 5.0; 15:20:65, v/v). The UV wavelength was set at 270 nm for monitoring the analyte. Using the retrograde method, at infusion concentrations of 1 microg/mL of cefamandole, the in vivo microdialysis recoveries were 55.44% for the rat blood (n = 6). Intra- and inter-assay accuracy and precision of the analyses were < or = 10% in the range of 0.1-10 microg/mL. Pharmacokinetic parameters were calculated from the recovery-corrected dialysate concentrations of cefamandole vs time data. The elimination half-life (t1/2,beta) was 21.6 +/- 1.6 min. The results suggest that the pharmacokinetics of unbound cefamandole in blood following cefamandole administration (50 mg/kg, i.v., n = 5) fit best to the two-compartmental model.     

A Traveling Wave Ion Mobility Spectrometry (TWIMS) Study of the Robo1-Heparan Sulfate Interaction

Roundabout 1 (Robo1) interacts with its receptor Slit to regulate axon guidance, axon branching, and dendritic development in the nervous system and to regulate morphogenesis and many cell functions in the nonneuronal tissues. This interaction is known to be critically regulated by heparan sulfate (HS). Previous studies suggest that HS is required to promote the binding of Robo1 to Slit to form the minimal signaling complex, but the molecular details and the structural requirements of HS for this interaction are still unclear. Here, we describe the application of traveling wave ion mobility spectrometry (TWIMS) to study the conformational details of the Robo1-HS interaction. The results suggest that Robo1 exists in two conformations that differ by their compactness and capability to interact with HS. The results also suggest that the highly flexible interdomain hinge region connecting the Ig1 and Ig2 domains of Robo1 plays an important functional role in promoting the Robo1-Slit interaction. Moreover, variations in the sulfation pattern and size of HS were found to affect its binding affinity and selectivity to interact with different conformations of Robo1. Both MS measurements and CIU experiments show that the Robo1-HS interaction requires the presence of a specific size and pattern of modification of HS. Furthermore, the effect of N-glycosylation on the conformation of Robo1 and its binding modes with HS is reported.

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N-Doped, porous TiO2 with rutile phase and visible light sensitive photocatalytic activity

Nitrogen-doped, porous rutile has been prepared by hydrothermal reaction of TiN in nitric acid, with the nitrogen atoms present in the interstitial sites and in the form of adsorbed nitrate ions. The N-rutile powder exhibits outstanding photocatalytic activity toward degradation of adsorbed methylene blue under visible light irradiation.