The embeddings of a graph—A survey

Topological graph theory seeks to find answers to the question of how graphs map into surfaces. This paper surveys the information now available about the range of a graph, namely, the set of surfaces on which the graph can be “neatly” embedded. Several other closely related topics, such as irreducible graphs, coloring problems, and crossing numbers, are ignored. As is quite often the case with mathematical theories, this discipline developed in a rather haphazard manner. Many isolated results existed before the practitioners became aware of the fact that they were developing a theory. The turning point occurred in 1968, when Ringel and Youngs completed their proof of the Heawood conjecture. Their proof, in addition to settling an old unsolved problem, also reinforced the significance of the rotation systems. It is the author's belief that these rotation systems, together with the generalized embedding schemes can, and should, become the main tool in all investigations concerning the embeddings of a graph. This survey is written from that point of view. After defining the scope of the area surveyed, this paper proceeds to discuss the significance of the rotation systems and embedding schemes. Several theorems of a general nature are listed. Attention is then focused on the maximum and minimum genera of a graph. Discussion of the first of these is deferred to another survey article by R. Ringeisen to appear in a subsequent issue. The various methods developed by researchers in this area for determining the (minimum) genus are then described. This is followed by a listing of all the theoretical information that is available about the genus parameter. The paper includes two tables that exhibit most of the graphs with known genus.     

Zur Chemie von Polyhalocyclopentadienen, 22. Mitt.: Über die Herstellung von 1,4,5,6,7,7-Hexachlorbicyclo[2.2.1]hepten-(5)-bishydroxymethylen-(2,3)

Zusammenfassung 1,4,5,6,7,7-Hexachlor-bicyclo[2.2.1]hepten-(5)-bis-hydroxymethylen-(2,3) (I) läßt sich sowohl durch direkte Umsetzung von Hexachlorcyclopentadien (II) und Buten-(2)-diol-(1,4) (III) wie auch durch LiAlH₄-Reduktion von 1,4,5,6,7,7-Hexachlor-bicyclo[2.2.1]hepten-(5)-dicarbonsäure-(2,3) (IV), IV-Anhydrid oder IV-Estern in guter Ausbeute gewinnen.Auf Wunsch der Autoren erscheint diese Abhandlung erst im Herbst 1961.21. Mitt., Dtsch. Bund. Pat. 1 081 886 vom 2. 5. 1958.     

Plexin B3 promotes neurite outgrowth,interacts homophilically,and interacts with Rin

Background  

Plexins, known to date as receptors of semaphorins, are implicated in semaphorin-mediated axon repulsion and growth cone collapse. However, subtype-specific functions of the majority of the nine members of the mammalian plexin family are largely unknown. In order to investigate functional properties of B-plexins, we analyzed the expression of human and murine plexin B3 and expressed full-length human plexins B2 (B2) and B3 (B3) in NIH-3T3 cells.     

Comparison of measurements of phase velocity in human calcaneus to Biot theory

Biot's theory for elastic propagation in porous media has previously been shown to be useful for modeling the dependence of phase velocity on porosity in bovine cancellous bone in vitro. In the present study, Biot's theory is applied to measurements of porosity-dependent phase velocity in 53 human calcanea in vitro. Porosity was measured using microcomputed tomography for some samples (n = 23) and estimated based on bone mineral densitometry for the remaining samples (n = 30). The phase velocity at 500 kHz was measured in a water tank using a through-transmission technique. Biot's theory performed well for the prediction of the dependence of sound speed on porosity. The trend was quasilinear, but both the theory and experiment show similar slight curvature. The root mean square error (RMSE) of predicted versus measured sound speed was 15.8 m/s.     

Water dimer diffusion on Pd[111] assisted by an H-bond donor-acceptor tunneling exchange

Based on the results of density functional theory calculations, a novel mechanism for the diffusion of water dimers on metal surfaces is proposed, which relies on the ability of H bonds to rearrange through quantum tunneling. The mechanism involves quasifree rotation of the dimer and exchange of H-bond donor and acceptor molecules. At appropriate temperatures, water dimers diffuse more rapidly than water monomers, thus providing a physical explanation for the experimentally measured high diffusivity of water dimers on Pd[111] [Science 297, 1850 (2002)]].     

Charm Safe-Level beta-Lactam Test for amoxicillin, ampicillin, ceftiofur, cephapirin, and penicillin G in raw commingled milk

The Charm Safe-Level beta-Lactam Test was evaluated by a U.S. Food and Drug Administration (FDA) test protocol administered by the AOAC-Research Institute. The sensitivity and selectivity of the test were evaluated with >800 negative raw commingled and drug-fortified milk samples by the manufacturer and an independent laboratory. Probit analysis by the independent laboratory determined the following 90% positive levels with 95% confidence: amoxicillin, 5.6 ppb; ampicillin, 8.5 ppb; cephapirin, 13.7 ppb; ceftiofur, 46.2 ppb; and penicillin G, 3.6 ppb. These values were within a range of +/- 20% of the manufacturer's data. Selection of negative samples met confidence specifications. Ruggedness parameters were studied and defined, and the stability of frozen milk was verified. There were no interferences from somatic cells (1,000,000 somatic cell count/mL) or bacteria (300,000 colony-forming units/mL), or from 27 other non-beta-lactam animal drugs. Test performance with raw milk samples containing incurred penicillin, ampicillin, and amoxicillin was consistent with the dose responses determined with fortified milk samples. Incurred cephalosporin in raw milk samples was detected at lower levels than was cephalosporin in fortified milk samples, presumably because of the presence of metabolite, as verified by other test methods. Quality control data support consistency in manufacture between batches and the stability of refrigerated test reagents for up to 1 year. Successful fulfillment of these criteria led to FDA certification of the test when used with a reader in U.S. milk testing programs.     

New insights into the intercalation chemistry of Al(OH)3

This paper reports a number of recent developments in the intercalation chemistry of Al(OH)(3). From Rietveld refinement and solid-state NMR, it has been possible to develop a structural model for the recently reported [M(II)Al(4)(OH)(12)](NO(3))(2)·yH(2)O family of layered double hydroxides (LDHs). The M(2+) cations occupy half of the octahedral holes in the Al(OH)(3) layers, and it is thought that there is complete ordering of the metal ions while the interlayer nitrate anions are highly disordered. Filling the remainder of the octahedral holes in the layers proved impossible. While the intercalation of Li salts into Al(OH)(3) is facile, it was found that the intercalation of M(II) salts is much more capricious. Only with Co, Ni, Cu, and Zn nitrates and Zn sulfate were phase-pure LDHs produced. In other cases, there is either no reaction or a phase believed to be an LDH forms concomitantly with impurity phases. Reacting Al(OH)(3) with mixtures of M(II) salts can lead to the production of three-metal M(II)-M(II)'-Al LDHs, but it is necessary to control precisely the starting ratios of the two M(II) salts in the reaction gel because Al(OH)(3) displays selective intercalation of M nitrate (Li > Ni > Co ≈ Zn). The three-metal M(II)-M(II)'-Al LDHs exhibit facile ion exchange intercalation, which has been investigated in the first energy dispersive X-ray diffraction study of a chemical reaction system performed on Beamline I12 of the Diamond Light Source.     

Polypyrrole electrodeposition on inorganic semiconductors CuInSe2 and CuInS2 for photovoltaic applications

Thin polypyrrole (PPy) layers with an average thickness of about 0.5 μm were deposited, using potentiostatic and galvanostatic techniques, on CuInSe₂ (CISe) structures prepared electrochemically on glass/ITO substrates and on CuInS₂ (CIS) structures fabricated on Cu tape substrates. The polymer layer of p-type is considered as an alternative to the traditional buffer layer and window layer in the conventional cell structure. The deposition proceeded from an aqueous solution containing sodium naphthalene-2-sulfonate as a dopant. In order to prepare stable PPy films of high quality with a good adherence to the surface of inorganic semiconductors CIS and CISe, the optimal concentrations of reagents, current densities and electrodepositing potentials were selected experimentally. Electrochemical polymerization of pyrrole to PPy on CIS surfaces is faster under white light irradiation and the polymerisation starts at lower potential than in the dark. Significant photovoltage and photocurrent of the fabricated CISe/PPy and CIS/PPy structures have been observed under standard white light illumination.     

Synthesis, NMR Characterization, and a Simple Application of Lithium Borotritide

LiBH(4) is a powerful and selective reagent for regiospecific reduction reactions. A simple synthesis of LiB(3)H(4) at near theoretical specific radioactivity is reported. We have treated Li(3)H synthesized from tritium gas ((3)H(2), approximately 98%) with BBr(3) to produce LiB(3)H(4) (specific activity = 4120 GBq/mmol = 110 Ci/mmol. The maximum theoretical specific activity of LiB(3)H(4) is 4252 GBq/mmol = 115.04 Ci/mmol; 1 matom of (3)H = 1063 GBq = 28.76 Ci.) The tritium labeling performance of the reagent was tested by an exemplary reduction of 2-naphthaldehyde to 2-naphthalenemethanol. LiB(3)H(4) and the reduction products were characterized by a combination of (1)H, (3)H, and (11)B NMR techniques, as appropriate.     

Silicon nitride/silicon oxide interlayers for solar cell passivating contacts based on PECVD amorphous silicon

This Letter demonstrates improved passivating contacts for silicon solar cells consisting of doped silicon films together with tunnelling dielectric layers. An improvement is demonstrated by replacing the commonly used silicon oxide interfacial layer with a silicon nitride/silicon oxide double interfacial layer. The paper describes the optimization of such contacts, including doping of a PECVD intrinsic a‐Si:H film by means of a thermal POCl₃ diffusion process and an exploration of the effect of the refractive index of the SiN_x. The n⁺ silicon passivating contact with SiN_x /SiO_x double layer achieves a better result than a single SiN_x or SiO_x layer, giving a recombination current parameter of ～7 fA/cm² and a contact resistivity of ～0.005 Ω cm², respectively. These self‐passivating electron‐selective contacts open the way to high efficiency silicon solar cells. (© 2015 WILEY‐VCH Verlag GmbH &Co. KGaA, Weinheim)