An algebraic characterization of planar graphs

A cycle in a graph is a set of edges that covers each vertex an even number of times. A cocycle is a collection of edges that intersects each cycle in an even number of edges. A bicycle is a collection of edges that is both a cycle and a cocycle. The cycles, cocycles, and bicycles each form a vector space over the integers modulo two when addition is defined as symmetric difference of sets. In this paper we examine the relationship between the left-right paths in a planar graph and the cycle space, cocylce space, and bicycle space. We show that planar graphs are characterized by the existence of a diagonal—a double cover by tours that interacts with the cycle space, cocycle space, and bicycle space in a special manner. This generalizes a result of Rosenstiehl and Read that characterized those planar graphs with no nonempty bicycles. © 1995 John Wiley & Sons, Inc.     

On webs of maximum rank

This paper contains two results on webs of maximal rank. First, we show that at each point, the web normals for a codimension-r web of maximum r-rank are (r−1)-dimensional generators of a rational normal scroll in the projectivized tangent space to the web domain, an extension of a theorem of Chern and Griffiths in the case r=2 [5]. We use this statement to deduce that webs of maximum rank are almost-Grassmannizable in the sense of Akivis [1]. Second, we show that there are exceptional (that is, maximum rank, but not algebraizable) webs W(2n, n, 2) for all n≥2. The construction relies on the properties of zero-cycles on algebraic K3 surfaces.     

Investigation of operational parameters for an industrial CFB combustor of coal, biomass and sludge

The combustion of coal and/or biomass （sludge, wood waste, RDF, etc.） in a circulating fluidized bed has been a commercial topper for over 20 years, and references to principles and applications are numerous and widespread although few data are presented concerning the operation of large scale CFB-units. The authors studied the CFB-combustion at UPM-Kymmene （Ayr）, a major paper mill relying for its steam production upon the combustion of coal （80-85 %）, wood bark （5-10%） and wastewater treatment sludge （5-10%）. The maximum capacity of the CFB is 58 MWth. A complete diagnostic of the operation was made, and additional tests were performed to assess the operating mode. The plant schematics, relevant dimensions and process data are given. To assess the operation of the UPM-CFB, it is important to review essential design parameters and principles of CFB combustors, which will be discussed in detail to include required data, heat balance and flowrates, operating versus transport velocity, kinetics and conversion （including the possible effect of the Bouduard reaction if carbon is present）. Since the residence time in the riser and the cyclone efficiency determine the burnout of circulating fuel-particles, the UPM-CFB was subjected to a stimulus response technique using nickel oxide as tracer. Results illustrate the efficiency of the cyclone separation and the number of recycle loops for particles of a given size. Results will also be used to assess the cyclone operation and efficiency and to comment upon expected and measured carbon conversion.     

Bounded Direction–Length Frameworks

A direction–length framework is a pair (G,p) where G=(V;D,L) is a ‘mixed’ graph whose edges are labelled as ‘direction’ or ‘length’ edges and p is a map from V to ℝ ^d for some d. The label of an edge uv represents a direction or length constraint between p(u) and p(v). Let G ⁺ be obtained from G by adding, for each length edge e of G, a direction edge with the same end vertices as e. We show that (G,p) is bounded if and only if (G ⁺,p) is infinitesimally rigid. This gives a characterization of when (G,p) is bounded in terms of the rank of the rigidity matrix of (G ⁺,p). We use this to characterize when a mixed graph is generically bounded in ℝ ^d . As an application we deduce that if (G,p) is a globally rigid generic framework with at least two length edges and e is a length edge of G then (G∖e,p) is bounded.     

Selective anion binding by a cofacial binuclear zinc complex of a Schiff-base pyrrole macrocycle

The synthesis of the new cofacial binuclear zinc complex [Zn(2)(L)] of a Schiff-base pyrrole macrocycle is reported. It was discovered that the binuclear microenvironment between the two metals of [Zn(2)(L)] is suited for the encapsulation of anions, leading to the formation of [K(THF)(6)][Zn(2)(μ-Cl)(L)]·2THF and [Bu(n)(4)N][Zn(2)(μ-OH)(L)] which were characterized by X-ray crystallography. Unusually obtuse Zn-X-Zn angles (X = Cl: 150.54(9)° and OH: 157.4(3)°) illustrate the weak character of these interactions and the importance of the cleft preorganization to stabilize the host. In the absence of added anion, aggregation of [Zn(2)(L)] was inferred and investigated by successive dilutions and by the addition of coordinating solvents to [Zn(2)(L)] solutions using NMR spectroscopy as well as isothermal microcalorimetry (ITC). On anion addition, evidence for deaggregation of [Zn(2)(L)], combined with the formation of the 1:1 host-guest complex, was observed by NMR spectroscopy and ITC titrations. Furthermore, [Zn(2)(L)] binds to Cl(-) selectively in THF as deduced from the ITC analyses, while other halides induce only deaggregation. These conclusions were reinforced by density functional theory (DFT) calculations, which indicated that the binding energies of OH(-) and Cl(-) were significantly greater than for the other halides.     

Quantum dynamics of hydrogen interacting with single-walled carbon nanotubes: multiple H-atom adsorbates

In a previous paper [J. L. McAfee and B. Poirier, J. Chem. Phys. 130, 064701 (2009)], using spin-polarized density functional theory (DFT), the authors reported a binding energy of 0.755 eV, for a single hydrogen atom adsorbed on a pristine (unrelaxed) (5,5) single-walled carbon nanotube (SWNT) substrate. A full three-dimensional (3D) potential energy surface (PES) for the SWNT-H system was also developed, and used in a quantum dynamics calculation to compute all rovibrational bound states, and associated equatorial and longitudinal adsorbate migration rates. A highly pronounced preference for the latter migration pathway at ambient temperatures was observed. In this work, we extend the aforementioned study to include multiple H-atom adsorbates. Extensive DFT calculations are performed, in order to ascertain the most relevant dynamical pathways. For two adsorbates, the SWNT-H-H system is found to exhibit highly site-specific binding, as well as long-range correlation and pronounced binding energy enhancement. The latter effect is even more pronounced in the full-hydrogenation limit, increasing the per-adsorbate binding energy to 2.6 eV. To study migration dynamics, a single-hole model is developed, for which the binding energy drops to 2.11 eV. A global 3D PES is developed for the hole migration model, using 40 radial × 18 cylindrical ab initio geometries, fit to a Fourier basis with radially dependent expansion coefficients (rms error 4.9 meV). As compared with the single-adsorbate case, the hole migration PES does not exhibit separate chemisorption and physisorption wells. The barrier to longitudinal migration is also found to be much lower. Quantum dynamics calculations for all rovibrational states are then performed (using a mixed spectral basis/phase-space optimized discrete variable representation), and used to compute longitudinal migration rates. Ramifications for the use of SWNTs as potential hydrogen storage materials are discussed.