Miniature open channel scrubbers for gas collection

An open channel scrubber is proposed as a miniature fieldable gas collector. The device is 100 mm in length, 26 mm in width and 22 mm in thickness. The channel bottom is rendered hydrophilic and liquid flows as a thin layer on the bottom. Air sample flows atop the appropriately chosen flowing liquid film and analyte molecules are absorbed into the liquid. There is no membrane at the air-liquid interface: they contact directly each other. Analyte species collected over a 10 min interval are determined by fluorometric flow analysis or ion chromatography. A calculation algorithm was developed to estimate the collection efficiency a priori; experimental and simulated results agreed well. The characteristics of the open channel scrubber are discussed in this paper from both theoretical and experimental points of view. In addition to superior collection efficiencies at relatively high sample air flow rates, this geometry is particularly attractive that there is no change in collection performance due to membrane fouling. We demonstrate field use for analysis of ambient SO₂ near an active volcano. This is basic investigation of membraneless miniature scrubber and is expected to lead development of an excellent micro-gas analysis system integrated with a detector for continuous measurements.     

Total colorings and list total colorings of planar graphs without intersecting 4-cycles

Suppose that G is a planar graph with maximum degree Δ and without intersecting 4-cycles, that is, no two cycles of length 4 have a common vertex. Let χ^″(G), and denote the total chromatic number, list edge chromatic number and list total chromatic number of G, respectively. In this paper, it is proved that χ^″(G)=Δ+1 if Δ≥7, and and if Δ(G)≥8. Furthermore, if G is a graph embedded in a surface of nonnegative characteristic, then our results also hold.     

Linear coloring of planar graphs with large girth

A proper vertex coloring of a graph G is linear if the graph induced by the vertices of any two color classes is the union of vertex-disjoint paths. The linear chromatic number of the graph G is the smallest number of colors in a linear coloring of G. In this paper we prove that every planar graph G with girth g and maximum degree Δ has if G satisfies one of the following four conditions: (1) g≥13 and Δ≥3; (2) g≥11 and Δ≥5; (3) g≥9 and Δ≥7; (4) g≥7 and Δ≥13. Moreover, we give better upper bounds of linear chromatic number for planar graphs with girth 5 or 6.     

A generalization of Tutte’s theorem on Hamiltonian cycles in planar graphs

In 1956, W.T. Tutte proved that a 4-connected planar graph is hamiltonian. Moreover, in 1997, D.P. Sanders extended this to the result that a 4-connected planar graph contains a hamiltonian cycle through any two of its edges. We prove that a planar graph G has a cycle containing a given subset X of its vertex set and any two prescribed edges of the subgraph of G induced by X if |X|≥3 and if X is 4-connected in G. If X=V(G) then Sanders’ result follows.     

New families of perfect nonlinear polynomial functions

A new class of almost perfect nonlinear (APN) polynomial functions has been recently introduced. We give some generalizations of these functions and deduce new families of perfect nonlinear (PN) functions. We show that these PN functions are CCZ-inequivalent to the known perfect nonlinear functions.     

A quadratic system with two parallel straight-line-isoclines

In this paper, a quadratic system with two parallel straight-line-isoclines is considered. This system corresponds to the system of class II in the classification of Ye Yanqian [Ye Yanqian et al., Theory of Limit Cycles, Transl. Math. Monogr., vol. 66, American Mathematical Society, Providence, RI, 1986]. Using the field rotation parameters of the constructed canonical system and geometric properties of the spirals filling the interior and exterior domains of its limit cycles, we prove that the maximum number of limit cycles in a quadratic system with two parallel straight-line-isoclines and two finite singular points is equal to two. Besides, we obtain the same result in a different way: applying the Wintner–Perko termination principle for multiple limit cycles and using the methods of global bifurcation theory developed in [V.A. Gaiko, Global Bifurcation Theory and Hilbert’s Sixteenth Problem, Kluwer, Boston, 2003].     

Uniqueness of some cyclic projective planes

For n < 41 and for {121, 125, 128, 169, 256, 1024}, every cyclic projective plane of order n is desarguesian.      

Undirected power graphs of semigroups

The undirected power graph G(S) of a semigroup S is an undirected graph whose vertex set is S and two vertices a,b∈S are adjacent if and only if a≠b and a ^m =b or b ^m =a for some positive integer m. In this paper we characterize the class of semigroups S for which G(S) is connected or complete. As a consequence we prove that G(G) is connected for any finite group G and G(G) is complete if and only if G is a cyclic group of order 1 or p ^m . Particular attention is given to the multiplicative semigroup ℤ _n and its subgroup U _n , where G(U _n ) is a major component of G(ℤ _n ). It is proved that G(U _n ) is complete if and only if n=1,2,4,p or 2p, where p is a Fermat prime. In general, we compute the number of edges of G(G) for a finite group G and apply this result to determine the values of n for which G(U _n ) is planar. Finally we show that for any cyclic group of order greater than or equal to 3, G(G) is Hamiltonian and list some values of n for which G(U _n ) has no Hamiltonian cycle.     

无符号拉普拉斯谱半径的新上界

如果一个图存在定向满足其最大出度△~＋不超过最大度△的一半,则通过估计图的半边路径（semi-edge walk）的个数,得到了该图的无符号拉普拉斯谱半径的一个新上界.进而根据D.Goncalves对平面图边分解的结果,得到了平面图无符号拉普拉斯谱半径的一个新上界.     

Dual-core leaky optical waveguide as an integrated-optic polarizer

We present a design of a dual-core leaky waveguide that can be used as an integrated-optic polarizer. The proposed polarizer works on the principle of mode filtering. The structure is characterized by two cores, namely core-1 and core-2 and a high index layer in the upper-most region, such a structure supports leaky modes. The leakage losses of the modes have been calculated by using the transfer matrix method (TMM). Single polarization operation is ensured by high differential leakage loss between fundamental TE and TM modes. We show TE-pass operation with 0.5 dB/mm loss in TE₀ mode and 13 dB/mm loss in TM₀ mode, and TM-pass operation with 0.36 dB/mm loss in TM₀ mode and 7.45 dB/mm loss in TE₀ mode. Besides single-polarization operation, single-mode operation of the structure is ensured by high leakage loss of all the other higher-order modes.