Infinite,highly connected digraphs with no two arc-disjoint spanning trees

We present a construction of countably infinite, highly connected graphs and digraphs, which shows that several basic connectivity results on finite graphs, including Edmondsapos;s branching theorem, cannot be extended to the infinite case.     

The Hadwiger number of infinite vertex-transitive graphs

We prove that every infinite, locally finite 3-connected, almost 4-connected, almost transitive, nonplanar graph, which contains infinitely many pairwise disjoint infinite paths belonging to the same end, can be contracted into an infinite complete graph. This implies that every infinite, locally finite, connected, nonplanar vertex-transitive graph with only one end can be contracted into an infinite complete graph. This problem was raised by L. Babai.     

Determination of 1-(2-methoxyphenyl)piperazine derivatives of isocyanates at low concentrations by temperature-programmed miniaturized liquid chromatography

A temperature-programmed packed capillary LC method with large-volume injection on-column focusing has been developed for screening and determination of 1-(2-methoxyphenyl)piperazine derivatives of airborne toluene-2,4-diisocyanate, toluene-2,6-diisocyanate, hexamethylenediisocyanate and methylenebisphenyl-4,4-diisocyanate, based on sampling methods described in MDHS 25/3. Injection volumes up to 100 microl were successfully loaded onto the 250x0.32 mm I.D. capillary column packed with 3 microm Hypersil ODS particles. The isocyanate derivatives were loaded at 10 degrees C and eluted by a three-step temperature program starting at 10 degrees C for 10 min, followed by a temperature ramp of 2.5 degrees C min(-1) to 45 degrees C and then 9.9 degrees C min(-1) to 90 degrees C. The mobile phase consisted of acetonitrile-acetate buffer (3% triethylamine, pH 4.5) (45:55, v/v). The isocyanate derivatives were dissolved in acetonitrile-acetate buffer (3% triethylamine, pH 4.5) (30:70, v/v) to achieve sufficient focusing. The concentration limit of detection of the individual derivatives utilizing an "U" shaped flow cell with a 8.0 mm light path and an injection volume of 100 microl was 44, 87, 43 and 210 pg ml(-1) for toluene-2,6-diisocyanate, hexamethylenediisocyanate, toluene-2,4-diisocyanate and methylenebisphenyl-4,4-diisocyanate, respectively. Within the investigated concentration range, 10-500 ng ml(-1), the linear calibration curves gave correlation coefficients ranging from 0.994 to 0.998. The repeatability of the method with regard to retention time and peak height ranged from 0.3 to 1.1% and 1.1 to 2.3% (n=9) relative standard deviation, respectively. The average recovery of the method, with regard to toluene-2,4-diisocyanate, was 97.7+/-1.6% (n=9).     

Short and long term stability of the elemental composition of human body fluid reference materials and their use as master lots

Summary Studies have been made of both short and long term stability of trace elements in lyophilized human body fluid reference materials, as well as the stability of mercury in reconstituted urine solutions. No detectable concentration changes for mercury, lead and aluminium occurred during the 5-year period. There are large differences in the amounts of mercury loss among different reconstituted materials. Addition of traces of gold to the solutions minimized the mercury loss and increased the useable time of the reconstituted material from hours to 8 days. A certification process based on direct determinations by reference laboratories and by comparison against master lots of the same material and against similar certified reference materials is presented. Values for calcium, copper and mercury obtained from reference laboratories and using the data transfer principle have been assigned in new batches of urine and serum.     

The cover-index of infinite graphs

We show that the cover-index of an infinite graph can be expressed in terms of colouring properties of its finite subgraphs when the minimum degree of the graph is finite. We prove that every simple graph with infinite minimum degree contains a tree which is regular of degree and use this to prove that every graph with minimum degree can be decomposed into mutually edge-disjoint spanning subgraphs without ioslated vertices. In particular, the cover-index of a graph equals the minimum degree, when this is infinite.     

The number of k-colorings of a graph on a fixed surface

We prove that, for every fixed surface S, there exists a largest positive constant c such that every 5-colorable graph with n vertices on S has at least c·2ⁿ distinct 5-colorings. This is best possible in the sense that, for each sufficiently large natural number n, there is a graph with n vertices on S that has precisely c·2ⁿ distinct 5-colorings. For the sphere the constant c is , and for each other surface, it is a finite problem to determine c. There is an analogous result for k-colorings for each natural number k>5.     

Decompositions of highly connected graphs into paths of length 3

We prove that a 171‐edge‐connected graph has an edge‐decomposition into paths of length 3 if and only its size is divisible by 3. It is a long‐standing problem whether 2‐edge‐connectedness is sufficient for planar triangle‐free graphs, and whether 3‐edge‐connectedness suffices for graphs in general. © 2008 Wiley Periodicals, Inc. J Graph Theory 58: 286–292, 2008     

Activated carbon as adsorbent for alkyllead in air

A method is described for the determination of alkyllead in air with activated carbon as adsorbent. The main factor affecting the adsorption capacity of the activated carbon for alkyllead was the concentration of hydrocarbons in the sampled air, as these were also adsorbed. Particulate inorganic lead was collected on a membrane filter in front of the adsorbent. The alkyllead was extracted from the adsorbent into hot nitric acid, and the concentration determined by electrothermal atomic absorption spectrometry. The detection limit was 0.002 μg Pb m^?3 (sample volume 1 m³), and precision was 9.5% r.s.d. at 2.1 μg Pb m^?3 alkyllead. The method was used to monitor exposure of gasoline tank truck drivers to alkyllead. During the filling of tank trucks with leaded gasoline, alkyllead concentrations from 1 to 750 μg Pb m^?3 were found in the drivers' breathing zone, but most were well below the Norwegian TLV of 75 μg Pb m^?3.     

Determination of total, organic solvent extractable, volatile and tetraalkyllead in fish, vegetation, sediment and water samples

Procedures for the determination of total, hexane extractable, volatile and tetraalkyllead in fish, vegetation, sediment and water samples are given. Detection limits, better than those obtainable by any other published methods, are in the range of 10–50 ppb-total Pb, 2-ppb-hexane extractable Pb, 0.5–1.5 ppb-volatile Pb and 0.5 ppb-tetraalkyllead. Standard reference samples from National Bureau of Standards were used as controls where applicable and satisfactory agreement was obtained between accepted values and values obtained by the proposed procedure.     

Rectangular and visibility representations of infinite planar graphs

We provide a new method for extending results on finite planar graphs to the infinite case. Thus a result of Ungar on finite graphs has the following extension: Every infinite, planar, cubic, cyclically 4‐edge‐connected graph has a representation in the plane such that every edge is a horizontal or vertical straight line segment, and such that no two edges cross. A result of Tamassia and Tollis extends as follows: Every countably infinite planar graph is a subgraph of a visibility graph. Furthermore, every locally finite, 2‐connected, planar graph is a visibility graph. © 2006 Wiley Periodicals, Inc. J Graph Theory 52: 257–265, 2006