On the chromatic number of set systems

An (r, l)‐system is an r‐uniform hypergraph in which every set of l vertices lies in at most one edge. Let m_k(r, l) be the minimum number of edges in an (r, l)‐system that is not k‐colorable. Using probabilistic techniques, we prove that where b_{r, l} is explicitly defined and a_{r, l} is sufficiently small. We also give a different argument proving (for even k) where a′_{r, l}=(r?l+1)/r(2^r?1re)^?l/(l?1). Our results complement earlier results of Erd?s and Lovász [10] who mainly focused on the case l=2, k fixed, and r large. © 2001 John Wiley & Sons, Inc. Random Struct. Alg., 19: 87–98, 2001     

Large induced forests in sparse graphs

For a graph G, let a(G) denote the maximum size of a subset of vertices that induces a forest. Suppose that G is connected with n vertices, e edges, and maximum degree Δ. Our results include: (a) if Δ ≤ 3, and G ≠ K₄, then a(G) ≥ n ? e/4 ? 1/4 and this is sharp for all permissible e ≡ 3 (mod 4); and (b) if Δ ≥ 3, then a(G) ≥ α(G) + (n ? α(G))/(Δ ? 1)². Several problems remain open. © 2001 John Wiley & Sons, Inc. J Graph Theory 38: 113–123, 2001     

Application of principal component analysis to gas sensing characteristics of Cr0.8Fe0.2NbO4 thick film array

The transient changes in resistances of Cr_0.8Fe_0.2NbO₄ thick film sensors towards specified concentrations of H₂, NH₃, acetonitrile, acetone, alcohol, cyclohexane and petroleum gas at different operating temperatures were recorded. The analyte-specific characteristics such as slopes of the response and retrace curves, area under the curve and sensitivity deduced from the transient curve of the respective analyte gas have been used to construct a data matrix. Principal component analysis (PCA) was applied to this data and the score plot was obtained. Distinguishing one reducing gas from the other is demonstrated based on this approach, which otherwise is not possible by measuring relative changes in conductivity. This methodology is extended for three Cr_0.8Fe_0.2NbO₄ thick film sensor array operated at different temperatures.     

Technical Notes on Volume Averaging in Porous Media I: How to Choose a Spatial Averaging Operator for Periodic and Quasiperiodic Structures

This paper is a first of a series aiming at revisiting technical aspects of the volume averaging theory. Here, we discuss the choice of the spatial averaging operator for periodic and quasiperiodic structures. We show that spatial averaging must be defined in terms of a convolution and analyze the properties of a variety of kernels, with a particular focus on the smoothness of average fields, the ability to attenuate geometrical fluctuations, Taylor series expansions, averaging of periodic fields and resilience to perturbations of periodicity. We conclude with a set of recommendations regarding kernels to use in the volume averaging theory.     

Quadruple systems with independent neighborhoods

A 4-graph is odd if its vertex set can be partitioned into two sets so that every edge intersects both parts in an odd number of points. Let

     

Ni(II) complexes featuring non-metallated pincer-type ligands

Attempts to prepare pincer-type Ni complexes from the ligands (i-Pr(2)POCH(2))(2)CH(2) and (pz*CH(2))(2)CH(2) (pz* = 3,5-dimethylpyrazol-1-yl) gave instead the complexes cis-{kappa(P),kappa(P')-(i-Pr(2)POCH(2))(2)CH(2)}NiCl(2) and {kappa(N),kappa(N')-(pz*CH(2))(2)CH(2)}NiBr(2). X-Ray diffraction studies confirmed that these potentially pincer-type ligands have not undergone metallation, serving instead as chelating ligands in essentially square-planar or tetrahedral complexes. Heating of these compounds failed to induce metallation of the coordinated ligands.     

Estimating local bonding/antibonding character of canonical molecular orbitals from their energy derivatives. The case of coordinating lone pair orbitals

According to Koopmans theorem, the derivative of the energy of a canonical molecular orbital (MO) with respect to nuclear coordinates quantifies its bonding/antibonding character. This quantity allows predictions of bond length variation on ionisation in a panel of 19 diatomic species. In polyatomic molecules, the derivative of a MO energy with respect to a given bond length reveals the nature and the degree of the bonding/antibonding contribution of this MO with respect to this bond. Accordingly, the HOMO “lone pairs” of CO and CN^? and the HOMO‐2 of CH₃CN are found to be antibonding with respect to the C? X bond (X = N, O), whereas the HOMO of N₂ is found to be bonding. With the same approach, the variation of the bonding character in the MOs of CO and CH₃CN on interaction with an electron acceptor (modeled through the approach of a proton) or by applying an electric field was studied. © 2016 Wiley Periodicals, Inc.     

On the Size‐Ramsey Number of Hypergraphs

The size‐Ramsey number of a graph G is the minimum number of edges in a graph H such that every 2‐edge‐coloring of H yields a monochromatic copy of G. Size‐Ramsey numbers of graphs have been studied for almost 40 years with particular focus on the case of trees and bounded degree graphs. We initiate the study of size‐Ramsey numbers for k‐uniform hypergraphs. Analogous to the graph case, we consider the size‐Ramsey number of cliques, paths, trees, and bounded degree hypergraphs. Our results suggest that size‐Ramsey numbers for hypergraphs are extremely difficult to determine, and many open problems remain.