Homomorphisms to oriented cycles

We discuss the existence of homomorphisms to oriented cycles and give, for a special class of cyclesC, a characterization of those digraphs that admit, a homomorphism toC. Our result can be used to prove the multiplicativity of a certain class of oriented cycles, (and thus complete the characterization of multiplicative oriented cycles), as well as to prove the membership of the corresponding decision problem in the classNPcoNP. We also mention a conjecture on the existence of homomorphisms to arbitrary oriented cycles.     

Sol-gel derived carbon ceramic electrode containing methylene blue-intercalated α-zirconium phosphate micro particles

Methylene blue-intercalated alpha-zirconium phosphate (MBZrP) micro particles in deionized water were deposited onto the surface of graphite powder to prepare graphite powder-supported MBZrP, which was subsequently dispersed into methyltrimethoxysilane-derived gels to yield a conductive composite. The composite was used as electrode material to fabricate a surface-renewable, rigid, leak-free carbon ceramic composite electrode, bulk-modified with methylene blue (MB). In the configuration, alpha-zirconium phosphate was employed as a solid host for MB, which acted as a catalyst. Graphite powder ensured conductivity by percolation, the silicate provided a rigid porous backbone and the methyl groups endowed hydrophobicity and thus limited the wetting section of the modified electrode. Peak currents of the MBZrP-modified electrode were surface-confined at low scan rates but diffusion-controlled at high scan rates. Square-wave voltammetric study revealed that MBZrP immobilized in carbon ceramic matrix presented a two-electron, three-proton redox process in acidic aqueous solution with pH ranged from 0.44 to 2.94. In addition, the chemically modified electrode showed an electrocatalytic activity toward nitrite reduction at +0.15 V ( vs. Ag/AgCl) in acidic aqueous solution (pH=0.44). The linear range and detection limit are 1x10(-6)-4x10(-3) mol x L(-1) and 1.5x10(-7) mol x L(-1), respectively.     

Influence of the water molecule on cation-pi interaction: ab initio second order Møller-Plesset perturbation theory (MP2) calculations

The influence of introducing water molecules into a cation-pi complex on the interaction between the cation and the pi system was investigated using the MP2/6-311++G method to explore how a cation-pi complex changes in terms of both its geometry and its binding strength during the hydration. The calculation on the methylammonium-benzene complex showed that the cation-pi interaction is weakened by introducing H(2)O molecules into the system. For example, the optimized interaction distance between the cation and the benzene becomes longer and longer, the transferred charge between them becomes less and less, and the cation-pi binding strength becomes weaker and weaker as the water molecule is introduced one by one. Furthermore, the introduction of the third water molecule leads to a dramatic change in both the complex geometry and the binding energy, resulting in the destruction of the cation-pi interaction. The decomposition on the binding energy shows that the influence is mostly brought out through the electrostatic and induction interactions. This study also demonstrated that the basis set superposition error, thermal energy, and zero-point vibrational energy are significant and needed to be corrected for accurately predicting the binding strength in a hydrated cation-pi complex at the MP2/6-311++G level. Therefore, the results are helpful to better understand the role of water molecules in some biological processes involving cation-pi interactions.