Colourings of cubic graphs inducing isomorphic monochromatic subgraphs

A -bisection of a bridgeless cubic graph is a -colouring of its vertex set such that the colour classes have the same cardinality and all connected components in the two subgraphs induced by the colour classes ( monochromatic components in what follows) have order at most . Ban and Linial Conjectured that every bridgeless cubic graph admits a -bisection except for the Petersen graph. A similar problem for the edge set of cubic graphs has been studied: Wormald conjectured that every cubic graph with has a -edge colouring such that the two monochromatic subgraphs are isomorphic linear forests (ie, a forest whose components are paths). Finally, Ando conjectured that every cubic graph admits a bisection such that the two induced monochromatic subgraphs are isomorphic. In this paper, we provide evidence of a strong relation of the conjectures of Ban-Linial and Wormald with Ando's Conjecture. Furthermore, we also give computational and theoretical evidence in their support. As a result, we pose some open problems stronger than the above-mentioned conjectures. Moreover, we prove Ban-Linial's Conjecture for cubic-cycle permutation graphs. As a by-product of studying -edge colourings of cubic graphs having linear forests as monochromatic components, we also give a negative answer to a problem posed by Jackson and Wormald about certain decompositions of cubic graphs into linear forests.     

Quaternary ammonium compounds in roots and leaves of Capparis spinosa L. from Saudi Arabia and Italy: investigation by HPLC-MS and 1H NMR

Capparis spinosa L. is a perennial plant typical of the Mediterranean flora and a multipurpose plant used for curing various human ailments. Quaternary ammonium compounds (QACs), as constituents of Capparaceae, play important roles in protecting against abiotic stress. Aim of this work was to determine QACs in root and leaves of caper from two proveniences. The presence of stachydrine, choline, glycine betaine and homo-stachydrine has been confirmed by high resolution MS, while ¹H NMR was applied to quantify the main QACs in the aqueous extracts. Stachydrine was quantified at 20.2 mg/g and 32.3 mg/g on dry leaves from South of Italy and Saudi Arabia, respectively, while a minor content was in dry roots (from 10.4 to 12.5 mg/g). Choline was considerably lower both in leaves and roots (from 0.3 to 1.2 mg/g). To our knowledge, this is the first report on the determination of QACs both in root and leaves of C. spinosa.     

Preparation and Characterisation of a Bis-μ-Hydroxo-NiIII2 Complex

Hydroxide-bridged high-valent oxidants have been implicated as the active oxidants in methane monooxygenases and other oxidases that employ bimetallic clusters in their active site. To understand the properties of such species, bis-μ-hydroxo-Ni^II₂ complex ( 1 ) supported by a new dicarboxamidate ligand (N,N′-bis(2,6-dimethyl-phenyl)-2,2-dimethylmalonamide) was prepared. Complex 1 contained a diamond core made up of two Ni^II ions and two bridging hydroxide ligands. Titration of the 1 e⁻ oxidant (NH₄)₂[Ce^IV(NO₃)₆] with 1 at −45 °C showed the formation of the high-valent species 2 and 3 , containing Ni^IINi^III and Ni^III₂ diamond cores, respectively, maintaining the bis-μ-hydroxide core. Both complexes were characterised using electron paramagnetic resonance, X-ray absorption, and electronic absorption spectroscopies. Density functional theory computations supported the spectroscopic assignments. Oxidation reactivity studies showed that bis-μ-hydroxide-Ni^III₂ 3 was capable of oxidizing substrates at −45 °C at rates greater than that of the most reactive bis-μ-oxo-Ni^III complexes reported to date.     

Direct meta-C−H Perfluoroalkenylation of Arenes Enabled by a Cleavable Pyrimidine-Based Template

The development of efficient and mild methods for the synthesis of organofluorine compounds is of foremost interest in various fields of chemistry. A direct pyrimidine-based selective meta-C−H perfluoroalkenylation of arenes involving several commercially available perfluoroolefins is described. The synthetic versatility of the protocol is demonstrated by an extensive substrate scope including different benzylsulfonyl, alkylarene and phenylacetic acid scaffolds. The generality of this methodology including the meta-C−H perfluoroalkenylation of Ibuprofen, the facile cleavage of the directing group and gram-scale reactions are presented.     

Development of a Novel Microwave Distillation Technique for the Isolation of Cannabis sativa L. Essential Oil and Gas Chromatography Analyses for the Comprehensive Characterization of Terpenes and Terpenoids,Including Their Enantio-Distribution

A microwave distillation method was optimized for the extraction and isolation of cannabis essential oil from fresh and dried hemp inflorescences. The developed method enabled us to obtain a distilled product rich in terpenes and terpenoid compounds, responsible of the typical and unique smell of the cannabis plant. The distillate from different hemp cultivars, including Kompolti, Futura 75, Carmagnola, Felina 32 and Finola were characterized by using a gas chromatograph equipped with both mass spectrometer and flame ionization detectors. In a single chromatographic run, the identity and absolute amounts of distilled compounds were determined. Peak assignment was established using a reliable approach based on the usage of two identification parameters, named reverse match, and linear retention index filter. Absolute quantification (mg g⁻¹) of the analytes was performed using an internal standard method applying the flame ionization detector (FID) response factors according to each chemical family. An enantio-GC-MS method was also developed in order to evaluate the enantiomeric distribution of chiral compounds, an analytical approach commonly utilized for establishing the authenticity of suspicious samples.     

To Sandwich Technetium: Highly Functionalized Bis-Arene Complexes [99mTc(η6-arene)2]+ Directly from Water and [99mTcO4]−

The labeling of (bio)molecules with metallic radionuclides such as ^99mTc demands conjugated, multidentate chelators. However, this is not always necessary since phenyl rings can directly serve as integrated, organometallic ligands. Bis-arene sandwich complexes are generally prepared by the Fischer–Hafner reaction. In extension of this, we show that [^99mTc(η⁶-C₆R₆)₂]⁺-type complexes are directly accessible from water and [^99mTcO₄]⁻, even using arenes incompatible with Fischer–Hafner conditions. To unambiguously confirm the nature of these unprecedented ^99mTc complexes, their rhenium homologous have been prepared by substituting naphthalene ligands in [Re(η⁶-C₁₀H₈)₂]⁺ with the corresponding phenyl groups. The ease with which highly stable [^99mTc(η⁶-C₆R₆)₂]⁺ complexes are formed under standard labeling conditions enables a multitude of new potential imaging agents based on commercial pharmaceuticals or lead structures.     

Isolated resonances and nonlinear damping

We analyze isolated resonance curves (IRCs) in single-degree-of-freedom systems possessing nonlinear damping. Through the combination of singularity theory and the averaging method, the onset and merging of IRCs, which coincide to isola and simple bifurcation singularities, respectively, can be analytically predicted. Numerical simulations confirm the accuracy of the analytical developments. Another important finding of this paper is that we unveil a geometrical connection between the topology of the damping force and IRCs. Specifically, we demonstrate that extremas and zeros of the damping force correspond to the appearance and merging of IRCs. Considering a damping force possessing several minima and maxima confirms the general validity of the analytical result. It also evidences a very complex scenario for which different IRCs are created, co-exist and then merge together to form a super IRC which eventually merges with the main resonance peak.     

Maltodextrin as stabilizer for emulsion polymerization: Adsorption and grafting behavior

Emulsion polymerization of the three-monomer system butyl acrylate–styrene–methacrylic acid was performed in batch using a commercial maltodextrin derived from starch degradation as stabilizer. Stable latexes with narrow particle size distributions were obtained in all examined cases. A method was developed to analyze and quantify the partitioning of the maltodextrin between the continuous phase (supernatant) and the particle phase. Significant differences between the polysaccharides adsorbed onto particles with or without emulsion polymerization reaction were observed. The possible reactions of maltodextrin in presence of a radical initiator were studied in aqueous phase, thus confirming maltodextrin degradation. The formation of copolymers involving the original monomers and the stabilizer according to two different reactive pathways was also confirmed. In terms of adsorbed maltodextrin, two different contributions were observed: maltodextrin physically adsorbed and maltodextrin chemically grafted and/or physically incorporated into the polymer.