Reactive resonance in a polyatomic reaction

In the course of an extensive investigation aimed at understanding the detailed mechanisms of a prototypical polyatomic reaction, several remarkable observations were uncovered. To interpret these findings, we surmise the existence of a reactive resonance in this polyatomic reaction. The reaction of concern is F+CH4-->HF+CH3, and the abnormal attributes were revealed only near the reaction threshold. The discovery of reactive resonance in a polyatomic reaction is more than just an extension from a typical atom+diatom reaction. As shown here, it holds great promise to disentangle the elusive intramolecular vibrational dynamics of transient collision complex in the critical transition-state region.     

On Some Three-Color Ramsey Numbers

 In this paper we study three-color Ramsey numbers. Let K _i,j denote a complete i by j bipartite graph. We shall show that (i) for any connected graphs G ₁, G ₂ and G ₃, if r(G ₁, G ₂)≥s(G ₃), then r(G ₁, G ₂, G ₃)≥(r(G ₁, G ₂)−1)(χ(G ₃)−1)+s(G ₃), where s(G ₃) is the chromatic surplus of G ₃; (ii) (k+m−2)(n−1)+1≤r(K _1,k , K _1,m , K _n )≤ (k+m−1)(n−1)+1, and if k or m is odd, the second inequality becomes an equality; (iii) for any fixed m≥k≥2, there is a constant c such that r(K _k,m , K _k,m , K _n )≤c(n/logn), and r(C _2m , C _2m , K _n )≤c(n/logn) ^m/(m−1) for sufficiently large n. Received: July 25, 2000 Final version received: July 30, 2002 RID="*" ID="*" Partially supported by RGC, Hong Kong; FRG, Hong Kong Baptist University; and by NSFC, the scientific foundations of education ministry of China, and the foundations of Jiangsu Province Acknowledgments. The authors are grateful to the referee for his valuable comments. AMS 2000 MSC: 05C55     

<Emphasis Type="Italic">k</Emphasis>-factors in regular graphs

Plesnik in 1972 proved that an （m - 1）-edge connected m-regular graph of even order has a 1-factor containing any given edge and has another 1-factor excluding any given m - 1 edges. Alder et al. in 1999 showed that if G is a regular （2n ＋ 1）-edge-connected bipartite graph, then G has a 1-factor containing any given edge and excluding any given matching of size n. In this paper we obtain some sufficient conditions related to the edge-connectivity for an n-regular graph to have a k-factor containing a set of edges and （or） excluding a set of edges, where 1 ≤ k ≤n/2. In particular, we generalize Plesnik＇s result and the results obtained by Liu et al. in 1998, and improve Katerinis＇ result obtained 1993. Furthermore, we show that the results in this paper are the best possible.     

One-pot conditional self-assembly of multicopper metallacycles

The self-assembly of supramolecular metallacycles via the coordination-driven directional bonding approach can be modified to produce some unexpected structural variations. The combination of a flexible ligand-capped dinuclear transition-metal acceptor like [Cu(2)(dppm)(2)(NCMe)(2)]X(2) (1X(2); dppm = Ph(2)PCH(2)PPh(2); X(-) = BF(4)(-), PF(6)(-), or BPh(4)(-)) with monodentate-bidentate donors like 2-, 3-, and 4-pyridylcarboxylates produced oligomeric compounds [{Cu(2)(dppm)(2)}(μ-(2-PyCO(2)))](2)X(2) (2X(2)), [{Cu(2)(dppm)(2)}(μ-(3-PyCO(2)))](2)X(2) (3X(2)), and [{Cu(2)(dppm)(2)}(μ-(4-PyCO(2)))](4)X(4) (4X(4)), respectively, as the thermodynamically stable products in one-pot reactions. However, the modified self-assembly is still subject to steric hindrance. The reaction of complex 1(BF(4))(2) with 6-Me-3-PyCO(2)H did not produce a polygonal dimeric metallacycle but a simple dinuclear complex, [Cu(2)(dppm)(2)(6-Me-3-PyCO(2))](BF(4)) (5(BF(4))). The crystal structures of complexes 2(PF(6))(2), 3(PF(6))(2), 4(BF(4))(4), and 5(BF(4)) were determined using X-ray diffraction.     

Counting Simsun Permutations by Descents

We count in the present work simsun permutations of length n by their number of descents. Properties studied include the recurrence relation and real-rootedness of the generating function of the number of n-simsun permutations with k descents. By means of generating function arguments, we show that the descent number is equidistributed over n-simsun permutations and n-André permutations. We also compute the mean and variance of the random variable X _n taking values the descent number of random n-simsun permutations, and deduce that the distribution of descents over random simsun permutations of length n satisfies a central and a local limit theorem as n ?? +???.     

Scanning photoemission spectromicroscopic study of 4-nm ultrathin SiO(3.4) protrusions probe-induced on the native SiO(2) layer

Atomic force microscopy probe-induced large-area ultrathin SiO(x) (x ≡ O/Si content ratio and x > 2) protrusions only a few nanometers high on a SiO(2) layer were characterized by scanning photoemission microscopy (SPEM) and X-ray photoemission spectroscopy (XPS). SPEM images of the large-area ultrathin SiO(x) protrusions directly showed the surface chemical distribution and chemical state specifications. The peak intensity ratios of the XPS spectra of the large-area ultrathin SiO(x) protrusions provided the elemental quantification of the Si 2p core levels and Si oxidation states (such as the Si(4+), Si(3+), Si(2+), and Si(1+) species). The O/Si content ratio (x) was evidently determined by the height of the large-area ultrathin SiO(x) protrusions.     

Graphs whose critical groups have larger rank

The critical group C(G) of a graph G is a refinement of the number of spanning trees of the graph and is closely connected with the Laplacian matrix. Let r(G) be the minimum number of generators (i.e., the rank) of the group C(G) and β(G) be the number of independent cycles of G. In this paper, some forbidden induced subgraphs are given for r(G) = n − 3 and all graphs with r(G) = β(G) = n − 3 are characterized.