A construction of chromatic index critical graphs

We prove that if K is an undirected, simple, connected graph of even order which is of class one, regular of degree p ≥ 2 and such that the subgraph induced by any three vertices is either connected or null, then any graph G obtained from K by splitting any vertex is p-critical. We find that various constructions of critical graphs by S. Fiorini are special cases of a corollary of this result.     

Protein micropatterning using surfaces modified by self-assembled polystyrene microspheres

A technique for micropatterning of proteins on a nonplanar surface to improve the coverage and functionality of biomolecules is demonstrated. A nonplanar microstructure is created by the self-assembly of polystyrene microspheres into an array of microwells on a silicon wafer to allow the integration of a nonplanar spot on a planar chip. After the microspheres were deposited into the microwells, they were conjugated with proteins. The curve surfaces of the microspheres present more surface area for attaching biomolecules which will increase the density of biomolecules and, hence, the sensitivity for detection. Moreover, proteins immobilized on a curved surface can retain their native structures and function better than on a planar surface because of a smaller area of interaction between the protein and the substrate. Patterning of biomolecules was tested with two model fluorescent proteins. The results show that precise patterning of biomolecules on a nonplanar spot can be achieved with this technique.     

Abiotic metallofoldamers as electrochemically responsive molecules

Described are the design, synthesis, and study of nonbiological molecules based on salophen and salen ligands that fold into single-stranded helices in the presence of either Ni(II) or Cu(II). X-ray diffraction studies show that the materials fold into helical structures in the solid state, and a series of NMR studies provide strong evidence that the folded structures are conserved in solution. Metal coordination is required for folding, as NMR and X-ray show that the free ligands do not adopt helical structures. Two of the racemic metallofoldamers spontaneously resolve during crystallization from CHCl3/acetonitrile, and CD spectroscopy and optical rotation show that the resolved, crystalline materials racemize quickly when dissolved at 5 degrees C. This shows that the secondary structures can reorganize easily and can, therefore, provide the basis for responsive materials. By comparison, an analogue from enantiomerically pure (R,R)-(-)-trans-cyclohexanediamine showed a strong CD signal and a large specific rotation. Electrochemical experiments show that a structural reorganization occurs upon metal-centered reduction of a Cu(II)-containing foldamer. When the reduction is carried out in the presence of coordinating ligands, it is proposed that apical binding of those ligands gives square pyramidal complexes. Semiempirical (AM1) calculations support that the helical structure would be disrupted by the reduction to Cu(I) with concomitant reorganization to a square pyramidal complex.     

Effect of oxygen fraction on local entropy generation in a hydrogen–air burner

This study considers numerical simulation of the combustion of hydrogen with air, including oxygen and nitrogen, in a burner and the numerical solution of local entropy generation rate due to the high temperature and velocity gradients in the combustion chamber. The effects of equivalence ratio (ϕ) and oxygen percentage (γ) on the combustion and entropy generation rate are investigated for different ϕs (from 0.5 to 1.0) and γs (from 10 to 30%). The combustion is simulated for the fuel mass flow rate providing the same heat transfer rate to the combustion chamber in the each case. The numerical calculation of combustion is performed individually for all cases with the help of the Fluent CFD code. Furthermore, a computer program has been developed to calculate numerically the volumetric entropy generation rate distributions and the other thermodynamic parameters by using the results of the calculations performed with the FLUENT code. The calculations bring out that the increase of ϕ (or the decrease of λ) reduces significantly the reaction rate levels. The average temperatures in the combustion chamber increase about 70 and 23% with the increases of γ (from 10 to 30%) and ϕ (from 0.5 to 1.0), respectively. With the increase of γ from 10 to 30%, the volumetric local entropy generation rates decrease about 9 and 4% in the cases of ϕ=0.5 and 1.0, respectively, and while the total entropy generation rates decrease exponentially, the merit numbers increase. The useful energy transfer rate to irreversibility rate therefore improves as the oxygen percentage increases.     

Evolutionary snowdrift game incorporating costly punishment in structured populations

The role of punishment and the effects of a structured population in promoting cooperation are important issues. Within a recent model of snowdrift game (SG) incorporating a costly punishing strategy (P), we study the effects of a population connected through a square lattice. The punishers, who carry basically a cooperative (C) character, are willing to pay a cost α$\alpha$ so as to punish a non-cooperative (D) opponent by β$\beta$. Depending on α$\alpha$, β$\beta$, the cost-to-benefit ratio r$r$ in SG, and the initial conditions, the system evolves into different phases that could be homogeneous or inhomogeneous. The spatial structure imposes geometrical constraint on how one agent is affected by neighboring agents. Results of extensive numerical simulations, both for the steady state and the dynamics, are presented. Possible phases are identified and discussed, and isolated phases in the r–β$r\text{–}\beta$ space are identified as special local structures of strategies that are stable due to the lattice structure. In contrast to a well-mixed population where punishers are suppressed due to the cost of punishment, the altruistic punishing strategy can flourish and prevail for appropriate values of the parameters, implying an enhancement in cooperation by imposing punishments in a structured population. The system could evolve to a phase corresponding to the coexistence of C, D, and P strategies at some particular payoff parameters, and such a phase is absent in a well-mixed population. The pair approximation, a commonly used analytic approach, is extended from a two-strategy system to a three-strategy system. We show that the pair approximation can, at best, capture the numerical results only qualitatively. Due to the improper way of including spatial correlation imposed by the lattice structure, the approximation does not give the frequencies of C, D, and P accurately and fails to give the homogeneous AllD and AllP phases.     

Synthesis and structure of two tetranuclear osmium carbonyl isotopomers: a crystallographic isotope effect

A synthetic route to [Os4(mu-H)(mu-OH)(mu-CO)(CO)12] ( 1) has been devised through the activation of [Os4(CO)14] with Me3NO. The pyrolysis and photolysis of the reactant in the presence of a trace amount of water produces 1 in low yield. The solid-state structure of [Os4(mu-H)(mu-OH)(mu-CO)(CO)12 x H2O] (1 x H2O) reveals a butterfly Os4 skeleton with bridging H, OH and CO ligands as well as hydrogen-bonded molecules of water in the crystal lattice. A low-temperature 13C{1H} NMR spectroscopic study revealed a merry-go-round exchange of CO ligands around the Os3 plane containing the asymmetric bridging CO. The exposure of 1 x H2O to D2O yielded [Os4(mu-H)(mu-OD)(mu-CO)(CO)12]2. Although the solid-state, intramolecular structure of 2 closely matched that of 1 x H2O, the intermolecular structure did not: its crystal lattice contained no water of crystallization, a previously unreported crystallographic isotope effect.     

Synthesis and thermal chemistry of copper (I) guanidinates

Copper (I) guanidinate dimers were generated by a salt metathesis route and structurally characterized. The guanidinates differed from the known amidinate dimers because of a large torsion of the dimer ring. This had a direct effect on their thermal chemistry. The thermal reactivity was investigated by several methods, including a novel temperature-resolved, gas-phase method that was monitored by mass spectrometry. The copper guanidinates underwent carbodiimide deinsertion to produce copper metal at temperatures between 225 -and 250 degrees C in the gas phase and at 125 degrees C in solution. The amidinate investigated also showed copper deposition at 190 degrees C in the gas phase, and 135 degrees C in solution, but without carbodiimide deinsertion. The guanidinate compounds deposited crystalline copper at 225 degrees C in a simple chemical vapor deposition experiment.