The lower algebraicK-theory of virtually infinite cyclic groups

This paper gives a proof of a conjecture of W.-C. Hsiang for the negativeK-theory of integral grouprings , when the group is a subgroup of a uniform lattice in a Lie group. The authors' earlier paper reduced this result to the very special cases where either is finite or is virtually infinite cyclic. The finite case was done much earlier by Carter extending results of Bass and Murthy. The major work of the present paper consists of proving the conjecture when is virtually infinite cyclic.Both authors were supported in part by the National Science Foundation.     

A structural hierarchy in the hydrogen‐bonded adduct N,N′‐di­methyl­piperazine–tartaric acid–water (1/2/2): an N‐component N‐dimensional structure (N = 3) with substructures having N = 1 and 2

In the hydrated adduct N,N′‐di­methyl­piperazine‐1,4‐diium bis(3‐carboxy‐2,3‐di­hydroxy­propanoate) dihydrate, [MeNH(CH₂CH₂)₂NHMe]²⁺·2(C₄H₅O₆)^?·2H₂O or C₆H₁₆N₂²⁺·2C₄H₅O₆^?·2H₂O, formed between racemic tartaric acid and N,N′‐di­methyl­piperazine (triclinic P, Z′ = 0.5), the cations lie across centres of inversion. The anions alone form chains, and anions and water mol­ecules together form sheets; the sheets are linked by the cations to form a pillared‐layer framework. The supramolecular architecture thus takes the form of a family of N‐dimensional N‐component structures having N = 1, 2 or 3.     

Synthesis, characterization, and reactivity of trans-[PtCl(R'R'SO)(A)2]NO3 (R'R'SO = Me2SO, MeBzSO, MePhSO; A= NH3, py, pic). Crystal structure of trans-[PtCl(Me2SO)(py)2]+

Trans complexes such as trans-[PtCl(2)(NH(3))(2)] have historically been considered therapeutically inactive. The use of planar ligands such as pyridine greatly enhances the cytotoxicity of the trans geometry. The complexes trans-[PtCl(R'R'SO)(A)(2)]NO(3) (R'R'SO = substituted sulfoxides such as dimethyl (Me(2)SO), methyl benzyl (MeBzSO), and methyl phenyl sulfoxide (MePhSO) and A = NH(3), pyridine (py) and 4-methylpyridine or picoline (pic)) were prepared for comparison of the chemical reactivity between ammine and pyridine ligands. The X-ray crystal structure determination for trans-[PtCl(Me(2)SO)(py)(2)]NO(3) confirmed the geometry with S-bound Me(2)SO. The crystals are orthorhombic, space group P2(1)2(1)2(1), with cell dimensions a = 7.888(2) A, b = 14.740(3) A, c =15.626(5) A, and Z = 4. The geometry around the platinum atom is square planar with l(Pt-Cl) = 2.304(4) A, l(Pt-S) = 2.218(5) A, and l(Pt-N) = 2.03(1) and 2.02(1) A. Bond angles are normal with Cl-Pt-S = 177.9(2) degrees, Cl-Pt-N(1) = 88.0(4) degrees, Cl-Pt-N(2) = 89.3(5) degrees, S-Pt-N(1) = 93.8(4) degrees, S-Pt-N(2) = 88.9(4) degrees, and N(1)-Pt-N(2) = 177.2(6) degrees. The intensity data were collected with Mo Kalpha radiation with lambda = 0.710 69 A. Refinement was by full-matrix least-squares methods to a final R value of 3.80%. Unlike trans-[PtCl(2)(NH(3))(2)], trans-[PtCl(2)(A)(2)] (A = py or pic) complexes do not react with Me(2)SO. The solvolytic products of cis-[PtCl(2)(A)(2)] (A = py or pic) were characterized. Studies of displacement of the sulfoxide by chloride were performed using HPLC. The sulfoxide was displaced faster for the pyridine complex relative to the ammine complex. Chemical studies comparing the reactivity of trans-[PtCl(R'R'SO)(amine)(2)]NO(3) with a model nucleotide, guanosine 5'-monophosphate (GMP), showed that the reaction gave two principal products: the species [Pt(R'R'SO)(amine)(2)(N7-GMP)], which reacts with a second equivalent of GMP, forming [Pt(amine)(2)(N7-GMP)(2)]. The reaction pathways were different, however, for the pyridine complexes in comparison to the NH(3) species, with sulfoxide displacement again being significantly faster for the pyridine case.     

Critical dynamics of dimers: implications for the glass transition

The Adam-Gibbs view of the glass transition relates the relaxation time to the configurational entropy, which goes continuously to zero at the so-called Kauzmann temperature. We examine this scenario in the context of a dimer model with an entropy-vanishing phase transition and stochastic loop dynamics. We propose a coarse-grained master equation for the order parameter dynamics which is used to compute the time-dependent autocorrelation function and the associated relaxation time. Using a combination of exact results, scaling arguments, and numerical diagonalizations of the master equation, we find nonexponential relaxation and a Vogel-Fulcher divergence of the relaxation time in the vicinity of the phase transition. Since in the dimer model the entropy stays finite all the way to the phase transition point and then jumps discontinuously to zero, we demonstrate a clear departure from the Adam-Gibbs scenario. Dimer coverings are the "inherent structures" of the canonical frustrated system, the triangular Ising antiferromagnet. Therefore, our results provide a new scenario for the glass transition in supercooled liquids in terms of inherent structure dynamics.     

Simulating cardiac electrophysiology using anisotropic mesh adaptivity

The simulation of cardiac electrophysiology requires small time steps and a fine mesh in order to resolve very sharp, but highly localized, wavefronts. The use of very high resolution meshes containing large numbers of nodes results in a high computational cost, both in terms of CPU hours and memory footprint. In this paper an anisotropic mesh adaptivity technique is implemented in the Chaste physiological simulation library in order to reduce the mesh resolution away from the depolarization front. Adapting the mesh results in a reduction in the number of degrees of freedom of the system to be solved by an order of magnitude during propagation and 2–3 orders of magnitude in the subsequent plateau phase. As a result, a computational speedup by a factor of between 5 and 12 has been obtained with no loss of accuracy, both in a slab-like geometry and for a realistic heart mesh with a spatial resolution of 0.125 mm.     

Obstructions to fibering a manifold

Given a map f : M → N of closed topological manifolds we define torsion obstructions whose vanishing is a necessary condition for f being homotopy equivalent to a projection of a locally trivial fiber bundle. If N = S ¹, these torsion obstructions are identified with the ones due to Farrell (Indiana Univ Math J 21:315–346, 1971/1972).     

Repeat‐pulse 13CO2 labeling of canola and field pea: implications for soil organic matter studies

Both the quantity and quality of plant residues can impact soil properties and processes. Isotopic tracers can be used to trace plant residue decomposition if the tracer is homogeneously distributed throughout the plant. Continuous labeling will homogeneously label plants but is not widely accessible because elaborate equipment is needed. In order to determine if the more accessible repeat‐pulse labeling method could be used to trace plant residue decomposition, this labeling procedure was employed using ¹³CO₂ to enrich field pea and canola plants in a controlled environment. Plants were exposed weekly to pulses of 33 atom% ¹³CO₂ and grown to maturity. The distribution of the label throughout the plant parts (roots, stem, leaves, and pod) and biochemical fractions (ADF and ADL) was determined. The label was not homogeneously distributed throughout the plant; in particular, the pod fractions were less enriched than other fractions indicating the importance of continuing labeling well into plant maturity for pod‐producing plants. The ADL fraction was also less enriched than the ADF fraction. Because of the heterogeneity of the label throughout the plant, caution should be applied when using the repeat‐pulse method to trace the fate of ¹³C‐labeled residues in the soil. However, root contributions to below‐ground C were successfully determined from the repeat‐pulse labeled root material, as was ¹³C enrichment of soil within the top 15 cm. Canola contributed more above‐ and below‐ground residue C than field pea; however, canola was also higher in ADF and ADL fractions indicating a more recalcitrant residue. Copyright © 2010 John Wiley & Sons, Ltd.     

Automotive fuels and internal combustion engines: a chemical perspective

Commercial transportation fuels are complex mixtures containing hundreds or thousands of chemical components, whose composition has evolved considerably during the past 100 years. In conjunction with concurrent engine advancements, automotive fuel composition has been fine-tuned to balance efficiency and power demands while minimizing emissions. Pollutant emissions from internal combustion engines (ICE), which arise from non-ideal combustion, have been dramatically reduced in the past four decades. Emissions depend both on the engine operating parameters (e.g. engine temperature, speed, load, A/F ratio, and spark timing) and the fuel. These emissions result from complex processes involving interactions between the fuel and engine parameters. Vehicle emissions are comprised of volatile organic compounds (VOCs), CO, nitrogen oxides (NO(x)), and particulate matter (PM). VOCs and NO(x) form photochemical smog in urban atmospheres, and CO and PM may have adverse health impacts. Engine hardware and operating conditions, after-treatment catalysts, and fuel composition all affect the amount and composition of emissions leaving the vehicle tailpipe. While engine and after-treatment effects are generally larger than fuel effects, engine and after-treatment hardware can require specific fuel properties. Consequently, the best prospects for achieving the highest efficiency and lowest emissions lie with optimizing the entire fuel-engine-after-treatment system. This review provides a chemical perspective on the production, combustion, and environmental aspects of automotive fuels. We hope this review will be of interest to workers in the fields of chemical kinetics, fluid dynamics of reacting flows, atmospheric chemistry, automotive catalysts, fuel science, and governmental regulations.