b-colouring outerplanar graphs with large girth

A b-colouring of a graph is a colouring of its vertices such that every colour class contains a vertex that has a neighbour in all other classes. The b-chromatic number of a graph is the largest integer $k$ such that the graph has a $b$-colouring with $k$ colours. We show here how to compute in polynomial time the $b$-chromatic number of an outerplanar graph of girth at least $8$. This generalizes the seminal result of Irving and Manlove on trees.     

The diagnonal multivariate natural exponential families and their classification

A natural exponential family (NEF)F in ? ⁿ ,n>1, is said to be diagonal if there existn functions,a ₁,...,a _n , on some intervals of ?, such that the covariance matrixV _F (m) ofF has diagonal (a ₁(m ₁),...,a _n (m _n )), for allm=(m ₁,...,m _n ) in the mean domain ofF. The familyF is also said to be irreducible if it is not the product of two independent NEFs in ? ^k and ? ^n-k , for somek=1,...,n?1. This paper shows that there are only six types of irreducible diagonal NEFs in ? ⁿ , that we call normal, Poisson, multinomial, negative multinomial, gamma, and hybrid. These types, with the exception of the latter two, correspond to distributions well established in the literature. This study is motivated by the following question: IfF is an NEF in ? ⁿ , under what conditions is its projectionp(F) in ? ^k , underp(x ₁,...,x _n )∶=(x ₁,...,x _k ),k=1,...,n?1, still an NEF in ? ^k ? The answer turns out to be rather predictable. It is the case if, and only if, the principalk×k submatrix ofV _F (m ₁,...,m _n ) does not depend on (m _k+1,...,m _n ).     

X‐ray absorption study of the local structure at the NiO/oxide interfaces

This work reports an X‐ray absorption near‐edge structure (XANES) spectroscopy study at the Ni K‐edge in the early stages of growth of NiO on non‐ordered SiO₂, Al₂O₃ and MgO thin films substrates. Two different coverages of NiO on the substrates have been studied. The analysis of the XANES region shows that for high coverages (80 Eq‐ML) the spectra are similar to that of bulk NiO, being identical for all substrates. In contrast, for low coverages (1 Eq‐ML) the spectra differ from that of large coverages indicating that the local order around Ni is limited to the first two coordination shells. In addition, the results also suggest the formation of cross‐linking bonds Ni—O—M (M = Si, Al, Mg) at the interface.     

Passivation of aluminium–n+ silicon contacts for solar cells by ultrathin Al2O3 and SiO2 dielectric layers

Ultra‐thin thermally grown SiO₂ and atomic‐layer‐deposited (ALD) Al₂O₃ films are trialled as passivating dielectrics for metal–insulator–semiconductor (MIS) type contacts on top of phosphorus diffused regions applicable to high efficiency silicon solar cells. An investigation of the optimum insulator thickness in terms of contact recombination factor J_{0_cont} and contact resistivity ρ_c is undertaken on 85 Ω/□ and 103 Ω/□ diffusions. An optimum ALD Al₂O₃ thickness of ～22 Å produces a J_{0_cont} of ～300 fAcm^–2 whilst maintaining a ρ_c lower than 1 mΩ cm² for the 103 Ω/□ diffusion. This has the potential to improve the open‐circuit voltage by a maximum 15 mV. The thermally grown SiO₂ fails to achieve equivalently low J_{0_cont} values but exhibits greater thermal stability, resulting in slight improvements in ρ_c when annealed for 10 minutes at 300 °C without significant changes in J_{0_cont}. The after‐anneal J_{0_cont} reaches ～600 fAcm^–2 with a ρ_c of ～2.5 mΩ cm² for the 85 Ω/□ diffusion amounting to a maximum gain in open‐circuit voltage of 6 mV. (© 2013 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

A θ-stable approximations of abstract Cauchy problems

Summary We study the approximation of linear parabolic Cauchy problems by means of Galerkin methods in space andA -stable multistep schemes of arbitrary order in time. The error is evaluated in the norm ofL _t ² (H _x ¹ ) L _t (L _x ² ).     

Validation and generalization of DEA and its uses

Summary Rapidly expanding uses of DEA have been accompanied by developments which have enhanced its power and enlarged its utility for additional applications. Developments covered in the present paper include simulation studies comparing DEA with competing forms of statistical regressions. Other studies covered show how these two approaches can be combined in complementary fashion. Another part of this paper deals with Chance Constrained Programming formulations which incorporate probabilistic elements into DEA. Included also are discussions of statistical characterizations with accompanying tests of statistical significance for DEA efficiency evaluations. This paper concludes with uses of DEA in “discovery processes”-processes that need strengthening (and encouragemnt) in contemporary social science and management science research. Suggestions are made for additional research on further developments which extend to uses of DEA to provide new approaches in economics (including econometrics), management and psychology and an Appendix introduces new or recently developed efficiency measures for use in DEA. Invited by J. T. Pastor     

Homology of proof-nets

This work defines homology groups for proof-structures in multiplicative linear logic (see [Gir1], [Gir2], [Dan]). We will show that these groups characterize proof-nets among arbitrary proof-structures, thus obtaining a new correctness criterion and of course a new polynomial algorithm for testing correctness. This homology also bears information on sequentialization. An unexpected geometrical interpretation of the linear connectives is given in the last section. This paper exclusively focuses onabstract proof-structures, i.e. paired-graphs. The relation with actual proofs is investigated in [Gir1], [Gir2], [Dan], [Ret] and [Tro].     

The diameter of random regular graphs

We give asymptotic upper and lower bounds for the diameter of almost everyr-regular graph onn vertices (n → ∞).     

Long paths in sparse random graphs

We consider random graphs withn labelled vertices in which edges are chosen independently and with probabilityc/n. We prove that almost every random graph of this kind contains a path of length ≧(1 −α(c))n where α(c) is an exponentially decreasing function ofc. Dedicated to Tibor Gallai on his seventieth birthday