Fixed-edge theorem for graphs with loops

Let G be an undirected graph without multiple edges and with a loop at every vertex—the set of edges of G corresponds to a reflexive and symmetric binary relation on its set of vertices. Then every edge-preserving map of the set of vertices of G to itself fixes an edge [{f(a), f(b)} = {a, b} for some edge (a, b) of G] if and only if (i) G is connected, (ii) G contains no cycles, and (iii) G contains no infinte paths. The proof is conerned with those subgraphs H of a graph G for which there is an edge-preserving map f of the set of vertices of G onto the set of vertices of H and satisfying f(a) = a for each vertex a of H.     

On the Location of Roots of Independence Polynomials

The independence polynomial of a graph G is the function i(G, x) = _k0 i _k x ^k, where i _k is the number of independent sets of vertices in G of cardinality k. We prove that real roots of independence polynomials are dense in (–, 0], while complex roots are dense in , even when restricting to well covered or comparability graphs. Throughout, we exploit the fact that independence polynomials are essentially closed under graph composition.     

Roots of Independence Polynomials of Well Covered Graphs

Let G be a well covered graph, that is, all maximal independent sets of G have the same cardinality, and let i_k denote the number of independent sets of cardinality k in G. We investigate the roots of the independence polynomial i(G, x) = i_kx^k. In particular, we show that if G is a well covered graph with independence number , then all the roots of i(G, x) lie in in the disk |z| (this is far from true if the condition of being well covered is omitted). Moreover, there is a family of well covered graphs (for each ) for which the independence polynomials have a root arbitrarily close to –.     

Homography of central points for optical distortion compensation

The paper presents a novel radial lens distortion modelling method for vision systems. It is based on single images of chessboard planar pattern, in which calibration points (corners of chessboard squares) are localised. The points, which are situated near the image centre, where the distortion is negligible, are used to determine undistorted grid of calibration points by the estimation of homographic matrix. The differences in the localisation of undistorted and distorted points are used to find parameters of radial model by the linear least square method. Having the distortion model, the dense compensation is performed with support of bilinear interpolation and a sparse compensation by Newton iterative scheme providing subpixel accuracy.     

Chip firing and all-terminal network reliability bounds

The (all-terminal) reliability of a graph G is the probability that all vertices are in the same connected component, given that vertices are always operational but edges fail independently each with probability p. Computing reliability is #P-complete, and hence is expected to be intractable. Consequently techniques for efficiently (and effectively) bounding reliability have been the major thrust of research in the area. We utilize a deep connection between reliability and chip firings on graphs to improve previous bounds for reliability.     

Application of a multi-component Eulerian approach to capture interface evolution and vorticity generation in compressible multiphase flow

The hyperbolic Eularian model is used as a mathematical framework for compressible multiphase flows. The formulation was obtained after an averaging process of the single phase Navier-Stokes equations. The closure of multi-component system leads to the volume fraction equation containing a non-conservative term and a pressure equilibrium condition. As a result the model equations cannot be written in a conservative form. To solve the equations a finite volume Godunov type computational approach is developed which uses an approximate Riemann solver combined with a numerical scheme to tackle the non-conservative terms. The approach accounts for pressure non-equilibrium. It enables resolving interfaces separating compressible fluids and captures the baroclinic source of vorticity generation. The computations are performed for various initial conditions and compared with theoretical and experimental data for a shock-bubble interaction problem. The investigated cases include acoustic wave transmission through isolated bubbles of helium and krypton. The numerical results illustrate the characteristic features of the evolving interfaces. The impulsively generated flow perturbations are dominated by the reflection and refraction of the shock and by the vorticity generation within the media. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

TSQ (6-methoxy-8-p-toluenesulfonamido-quinoline), a common fluorescent sensor for cellular zinc, images zinc proteins

Zn(2+) is a necessary cofactor for thousands of mammalian proteins. Research has suggested that transient fluxes of cellular Zn(2+) are also involved in processes such as apoptosis. Observations of Zn(2+) trafficking have been collected using Zn(2+) responsive fluorescent dyes. A commonly used Zn(2+) fluorophore is 6-methoxy-8-p-toluenesulfonamido-quinoline (TSQ). The chemical species responsible for TSQ's observed fluorescence in resting or activated cells have not been characterized. Parallel fluorescence microscopy and spectrofluorometry of LLC-PK(1) cells incubated with TSQ demonstrated punctate staining that concentrated around the nucleus and was characterized by an emission maximum near 470 nm. Addition of cell permeable Zn-pyrithione resulted in greatly increased, diffuse fluorescence that shifted the emission peak to 490 nm, indicative of the formation of Zn(TSQ)(2). TPEN (N,N,N'N'-tetrakis(-)[2-pyridylmethyl]-ethylenediamine), a cell permeant Zn(2+) chelator, largely quenched TSQ fluorescence returning the residual fluorescence to the 470 nm emission maximum. Gel filtration chromatography of cell supernatant from LLC-PK(1) cells treated with TSQ revealed that TSQ fluorescence (470 nm emission) eluted with the proteome fractions. Similarly, addition of TSQ to proteome prior to chromatography resulted in 470 nm fluorescence emission that was not observed in smaller molecular weight fractions. It is hypothesized that Zn-TSQ fluorescence, blue-shifted from the 490 nm emission maximum of Zn(TSQ)(2), results from ternary complex, TSQ-Zn-protein formation. As an example, Zn-carbonic anhydrase formed a ternary adduct with TSQ characterized by a fluorescence emission maximum of 470 nm and a dissociation constant of 1.55 × 10(-7) M. Quantification of TSQ-Zn-proteome fluorescence indicated that approximately 8% of cellular Zn(2+) was imaged by TSQ. These results were generalized to other cell types and model Zn-proteins.     

On the assignment of proton hyperfine splitting constants in benzo[cd]pyrenyl

The assignment of proton hyperfine splitting constants in benzo[cd] pyrenyl has been discussed with the aid of some variants of McLachlan's method and McConnell's relationship.     

Die Hemmwirkung von Spurenmengen Fe3+-Ionen im H2O2-Zerfall

Zusammenfassung In einer Lösung von basischem Magnesiumcarbonat rufen Fe³⁺-Ionen eine Hemmung des H₂O₂-Zerfalls hervor, was besonders deutlich in Gegenwart der in diesem System sonst aktiven Cu²⁺-Ionen zu erkennen war.