Enthalpies of reaction of bis(triphenylphosphine)(trans-stilbene)platinum(0) with diphenylcyclopropenone and benzocyclobutenedione

Enthalpies, ΔH(1) ?94.8 ± 6.0 and ΔH(6) ?57.1 ± 5.1 kJ mol^?1, of the following reactions have been measured calorimetrically [Pt(trans-stilbene)(PPh₃)₂](s) + dpcp(g) → (PPh₃)₂Pt(dpcb)(s) + trans-stilbene(g) (1) [Pt(trans-stilbene)(PPh₃)₂](s) + bcbd(g) → (PPh₃)₂Pt(bcpd)(s) + trans-stilbene (g) (6) where dpcp is diphenylcyclopropenone, (PPh₃)₂Pt(dpcb) is (1,1-bistriphenylphosphine)platinadiphenylcyclobutenone, (PPh₃)₂$\text{PtC(Ph)C(Ph)C}$O, bcbd is benzocyclobutene-1,2-dione and (PPh₃)₂Pt(bcpd) is (1,1-bistriphenylphosphine)platinabenzocyclopentanedione,

. It is concluded that the five-membered platinacyclo ring system in (PPh₃)₂Pt(dpcb) is not heavily strained.     

Adsorption and interaction of CO and NO on Pt(410): I. TPD studies

NO and CO adsorption and the NO/CO reaction on Pt(410) are studied by TPD. NO is found to dissociate on Pt(410) at 120 K, but it reacts to form N₂O at higher exposures. The N₂O desorbs in two peaks at 135 and 150 K. CO adsorbs molecularly, and desorbs in 5 peaks at 550, 500, 450, 380 and about 130 K. CO is also found to dissociate upon heating, leaving a carbon residue on the surface which changes the TPD spectra. The NO/CO reaction shows a surface explosion at 360 K. These results provide additional evidence that Pt(410) has unusual reactivity, as predicted by Banholzer, Park, Mak and Masel, Surface Sci. 128 (1983) 176.     

Existence of infinitely many stationary solutions of the L2-subcritical and critical NLSE on compact metric graphs

We investigate the existence of stationary solutions for the nonlinear Schrödinger equation on compact metric graphs. In the $L^2$-subcritical setting, we prove the existence of an infinite number of such solutions, for every value of the mass. In the critical regime, the existence of infinitely many solutions is established if the mass is lower than a threshold value, while global minimizers of the NLS energy exist if and only if the mass is lower or equal to the threshold. Moreover, the relation between this threshold and the topology of the graph is characterized. The investigation is based on variational techniques and some new versions of Gagliardo–Nirenberg inequalities.     

Powers of the Vertex Cover Ideal of a Chordal Graph

In this article, Cohen–Macaulay chordal graphs and generalized star graphs are studied to show that all powers of the vertex cover ideal of such graphs have linear quotients. Moreover, it is shown that the Alexander dual of the clique complex of any chordal graph is vertex decomposable.     

A New Construction for Cohen–Macaulay Graphs

Let G be a finite simple graph on a vertex set V(G) = {x ₁₁,…, x _n1}. Also let m ₁,…, m _n  ≥ 2 be integers and G ₁,…, G _n be connected simple graphs on the vertex sets V(G _i ) = {x _i1,…, x _{im i} }. In this article, we provide necessary and sufficient conditions on G ₁,…, G _n for which the graph obtained by attaching the G _i to G is unmixed or vertex decomposable. Then we characterize Cohen–Macaulay and sequentially Cohen–Macaulay graphs obtained by attaching the cycle graphs or connected chordal graphs to arbitrary graphs.     

Empirical analysis on temporal statistics of human correspondence patterns

Recently, extensive empirical evidence shows that the timing of human behaviors obeys non-Possion statistics with heavy-tailed interevent time distribution. In this paper, we empirically study the correspondence pattern of a great Chinese scientist, named Hsue-Shen Tsien. Both the interevent time distribution and response time distributions deviate from the Poisson statistics, showing an approximate power-law decaying. The two power-law exponents are more or less the same (about 2.1), which strongly support the hypothesis in [A. Vázquez, J.G. Oliveira, Z. Dezsö, K.-I. Goh, I. Kondor, A.-L. Barabási, Phys. Rev. E 73 (2006) 036127] that the response time distribution of the tasks could in fact drive the interevent time distribution, and both the two distributions should decay with the same exponent. Our result is against the claim in [A. Vázquez, J.G. Oliveira, Z. Dezsö, K.-I. Goh, I. Kondor, A.-L. Barabási, Phys. Rev. E 73 (2006) 036127], which suggests the human correspondence pattern belongs to a universality class with exponent 1.5.