Partial characterizations of clique-perfect and coordinated graphs: Superclasses of triangle-free graphs

A graph G is clique-perfect if the cardinality of a maximum clique-independent set of H equals the cardinality of a minimum clique-transversal of H, for every induced subgraph H of G. A graph G is coordinated if the minimum number of colors that can be assigned to the cliques of H in such a way that no two cliques with non-empty intersection receive the same color equals the maximum number of cliques of H with a common vertex, for every induced subgraph H of G. Coordinated graphs are a subclass of perfect graphs. The complete lists of minimal forbidden induced subgraphs for the classes of clique-perfect and coordinated graphs are not known, but some partial characterizations have been obtained. In this paper, we characterize clique-perfect and coordinated graphs by minimal forbidden induced subgraphs when the graph is either paw-free or {gem, W₄, bull}-free, both superclasses of triangle-free graphs.     

Weighted Composition Operators from H ∞ to the Bloch Space of a Bounded Homogeneous Domain

Let D be a bounded homogeneous domain in ℂ ⁿ . In this paper, we study the bounded and the compact weighted composition operators mapping the Hardy space H ^∞(D) into the Bloch space of D. We characterize the bounded weighted composition operators, provide operator norm estimates, and give sufficient conditions for compactness. We prove that these conditions are necessary in the case of the unit ball and the polydisk. We then show that if D is a bounded symmetric domain, the bounded multiplication operators from H ^∞(D) to the Bloch space of D are the operators whose symbol is bounded.     

Homothetic transformations and geometric loci: properties of triangles and quadrilaterals

In this paper, we use geometric transformations to find some interesting properties related with geometric loci. In particular, given a triangle or a cyclic quadrilateral, the locus generated by the centroid or by the orthocentre (for triangles) or by the anticentre (for cyclic quadrilaterals) when one vertex moves on the circumcircle of the figure are considered. These loci are studied in paragraphs 3 and 4. By means of the homothetic transformations some properties of triangles and quadrilaterals are found. The study of these properties can be used, with profit, in a classroom activity supported by Dynamic Geometry System.     

NP-completeness results for edge modification problems

The aim of edge modification problems is to change the edge set of a given graph as little as possible in order to satisfy a certain property. Edge modification problems in graphs have a lot of applications in different areas, and many polynomial-time algorithms and NP-completeness proofs for this kind of problems are known. In this work we prove new NP-completeness results for these problems in some graph classes, such as interval, circular-arc, permutation, circle, bridged, weakly chordal and clique-Helly graphs.     

Bergman Spaces and Carleson Measures on Homogeneous Isotropic Trees

Hastings studied Carleson measures for non-negative subharmonic functions on the polydisk and characterized them by a certain geometric condition relative to Lebesgue measure σ. Cima & Wogen and Luecking proved analogous results for weighted Bergman spaces on the unit ball and other open subsets of \(\mathbb {C}^{n}\). We consider a similar problem on a homogeneous tree, and study how the characterization and properties of Carleson measures for various function spaces depend on the choice of reference measure σ.     

Reactivity of a phosphinito-bridged PtI-PtI complex with nucleophiles: substitution versus addition

As a result of the strong electrophilic character of the Pt bound to O, the phosphinito-bridged PtI complex [(PHCy2)Pt(micro-PCy2){kappa2P,O-micro-P(O)Cy2}Pt(PHCy2)](Pt-Pt) (1) undergoes attack at the O-bound Pt atom by molecules such as di- and tricyclohexylphosphane, dicyclohexylphosphane oxide, and dicyclohexylphosphane sulfide. Thus, reaction of 1 with PHCy2 gives the symmetric PtI dimer [(PHCy2)Pt(micro-PCy2)]2(Pt-Pt) (2), while the hydrido-bridged complex syn-[(PHCy2){kappaP-P(O)Cy2}Pt(micro-PCy2)(micro-H)Pt(PHCy2){kappaP-P(O)Cy2}](Pt-Pt) (4) is obtained from reaction of 1 with P(O)HCy2; the thiophosphinito complex [(PHCy2)Pt(micro-PCy2){kappa2P,S-micro-P(S)Cy2}Pt(PHCy2)](Pt-Pt) (8) forms selectively in reaction of 1 with P(S)HCy2. For comparison, the reaction with PCy3 results only in ligand substitution, affording [(PCy3)Pt(micro-PCy2){kappa2P,O-micro-P(O)Cy2}Pt(PHCy2)](Pt-Pt) (5). DFT studies confirmed the remarkable electrophilicity of the oxygen-bound Pt and shed light on the nature of the metal-metal bond in Pt dimers.     

Portable X-ray fluorescence device reveals the artistic palette of Carlo Bononi,Baroque artist from Ferrara

The principal aim of the in situ X-ray fluorescence (XRF) analysis on the canvas “The Coronation of the Virgin” was to characterise the colour palette of Carlo Bononi (Ferrara, 1580–1632), a lesser-known artist of the early Baroque period in Ferrara. More than 100 points were collected by means of an XRF spectrometer, but the presence of many overlapping painted layers left some doubts about the preparation and the background layers. The scanning electron microscopy with energy dispersive spectrometer analysis on two samples resolved some of these doubts. The results obtained indicate the use of typical 17th century pigments, such as lead white, vermilion, azurite and a copper-based green. For yellow pigments, the artist used the yellow ochre in some cases, while in others he used lead-tin yellow. We also individuated at least three different shades of umber. Almost all the pigments have been identified and they are the first step in establishing the technical apparatus necessary to understand the modus operandi of the Ferrarese artist.