On the Differential Polynomial of a Graph

We introduce the differential polynomial of a graph. The differential polynomial of a graph G of order n is the polynomial B(G; x) :=∑?(G)k=-nB_k(G) x~(n+k), where B_k(G) denotes the number of vertex subsets of G with differential equal to k. We state some properties of B(G;x) and its coefficients.In particular, we compute the differential polynomial for complete, empty, path, cycle, wheel and double star graphs. We also establish some relationships between B(G; x) and the differential polynomials of graphs which result by removing, adding, and subdividing an edge from G.     

Exploring the Volatiles Released from Roots of Wild and Domesticated Tomato Plants under Insect Attack

Plants produce volatile organic compounds that are important in communication and defense. While studies have largely focused on volatiles emitted from aboveground plant parts upon exposure to biotic or abiotic stresses, volatile emissions from roots upon aboveground stress are less studied. Here, we investigated if tomato plants under insect herbivore attack exhibited a different root volatilome than non-stressed plants, and whether this was influenced by the plant’s genetic background. To this end, we analyzed one domesticated and one wild tomato species, i.e., Solanum lycopersicum cv Moneymaker and Solanum pimpinellifolium, respectively, exposed to leaf herbivory by the insect Spodoptera exigua. Root volatiles were trapped with two sorbent materials, HiSorb and PDMS, at 24 h after exposure to insect stress. Our results revealed that differences in root volatilome were species-, stress-, and material-dependent. Upon leaf herbivory, the domesticated and wild tomato species showed different root volatile profiles. The wild species presented the largest change in root volatile compounds with an overall reduction in monoterpene emission under stress. Similarly, the domesticated species presented a slight reduction in monoterpene emission and an increased production of fatty-acid-derived volatiles under stress. Volatile profiles differed between the two sorbent materials, and both were required to obtain a more comprehensive characterization of the root volatilome. Collectively, these results provide a strong basis to further unravel the impact of herbivory stress on systemic volatile emissions.     

Stereoisomeric Tris-BINOL-Menthol Bulky Monophosphites: Synthesis,Characterisation and Application in Rhodium-Catalysed Hydroformylation

Four stereoisomeric monoether derivatives, based on axially chiral (R)- or (S)-BINOL bearing a chiral (+)- or (−)-neomenthyloxy group were synthesised and fully characterised by NMR spectroscopy and X-ray crystallography. The respective tris-monophosphites were thereof prepared and fully characterised. The coordination ability of the new bulky phosphites with Rh(CO)₂(acac), was attested by ³¹P NMR, which presented a doublet in the range of δ = 120 ppm, with a ¹J(¹⁰³Rh-³¹P) coupling constant of 290 Hz. The new tris-binaphthyl phosphite ligands were further characterised by DFT computational methods, which allowed us to calculate an electronic (CEP) parameter of 2083.2 cm⁻¹ and an extremely large cone angle of 345°, decreasing to 265° upon coordination with a metal atom. Furthermore, the monophosphites were applied as ligands in rhodium-catalysed hydroformylation of styrene, leading to complete conversions in 4 h, 100% chemoselectivity for aldehydes and up to 98% iso-regioselectivity. The Rh(I)/phosphite catalytic system was also highly active and selective in the hydroformylation of disubstituted olefins, including (E)-prop-1-en-1-ylbenzene and prop-1-en-2-ylbenzene.     

Theoretical and empirical approaches to understanding the effect of phosphonate groups on the thermal degradation for two chemically modified PMMA

The influence of phosphonated groups on thermal degradation and flammability has been investigated in the case of two chemically modified PMMA. Thermogravimetric analysis as well as pyrolysis combustion flow calorimetry have been used to define the efficiency of phosphorus in both condensed and vapor phases. A theoretical study was also performed to determine the contribution of phosphonated groups to the effective heat of combustion, residue content and heat release capacity. Empirical and theoretical approaches agreed to highlight that PMMA modified with monophosphonated comonomer is more efficient in both condensed and vapor phases in terms of flammability and char formation. These results were attributed to the ability of phosphonate groups to interact with ester groups and also to the weakness of the P–C–N bonds. Moreover, this study proposes a method for designing the chemical environment of phosphonate group in polymers to achieve better flame retardancy.     

Directed ortho-lithiation of unprotected diphenylphosphinic acids

Directed ortho lithiation of diphenylphosphinic acid and subsequent electrophilic trapping provides mono ortho-functionalized derivatives including enantiopure γ-aminophosphinic acids in moderate yields. Copper catalyzed coupling of the ortho anion leads to biphenyl-2,2′-diylbis(phenylphosphinic acid), a phosphorus analogue of biphenyl-2,2′-dicarboxylic acid. Preliminary studies of the metal-binding abilities of this O,O-chelating ligand towards a series of metal cations are included.     

A theoretical NMR study of the structure of benzynes and some of their carbocyclic and heterocyclic analogs

This work reports the theoretical study of the aromaticity of a series of carbocycles (benzene, cyclohexane, bent and planar cyclooctatetraene) and heterocycles (pyridine, furan, thiophene, pyrrole) and their didehydro forms (arynes and hetarynes). As aromaticity probe Schleyer's NICS were used and represented in two 3D isosurfaces of the electron density. The spatial 3D representation of the NICS is shown to be a powerful tool to visualize the aromaticity (or its absence) of different molecules.     

Nanostructures of sodium titanate/zirconium oxide

In this work is reported the synthesis of nanotubes and nanoribbons from mixed oxides (Ti_1−x Zr _x O₂·nH₂O), employing hydrothermal treatment in a highly alkaline medium. The morphology and crystal structure of the products obtained via hydrothermal treatment depend on the value of x. For example, for x equal to 0 and 0.50 were observed the presence of nanotubes (diameter around 9 nm) and nanoribbons (diameter around 200 nm), respectively. However, for x values above 0.50, there was no morphological change. Regarding the crystalline structure of these samples, for x equal to 0 was observed the sodium titanate phase; already for x values up to 0.50, we observed the presence of two crystalline phases: sodium titanate and tetragonal ZrO₂. For x values above 0.50, only tetragonal ZrO₂ was observed. Furthermore, only the product obtained from x equal to 0.15 was observed the presence of three-dimensional flower-like arrangements. The results obtained by the characterization techniques showed the segregation of zirconium after hydrothermal treatment of precursors with x less or equal to 0.50. Thus, we describe the important role that Ti/Zr molar ratio of the precursor plays on the morphology and crystalline phase of the products formed by hydrothermal treatment.     

Effect of 1-Aminoanthracene (1-AMA) Binding on the Structure of Three Lipocalin Proteins,the Dimeric β Lactoglobulin,the Dimeric Odorant Binding Protein and the Monomeric α<Subscript>1</Subscript>-Acid Glycoprotein. Fluorescence Spectra and Lifetimes Studies

We studied effect of 1-aminoanthracene (1-AMA) binding on the structures of dimeric β lactoglobulin, dimeric odorant binding protein (OBP) and monomeric α₁-acid glycoprotein (lipocalin family proteins) by monitoring fluorescence excitation spectra and measuring fluorescence lifetimes of the tryptophan residues of the proteins. Results show that binding of 1-AMA to β lactoglobulin and OBP modifies their conformation even at low probe concentration compared to that of the proteins. Structural modification induces a red shift of the fluorescence excitation spectra maximum of tryptophan residues accompanied with an increase of the third fluorescence lifetime and a decrease of its pre-exponential factor. These effects were not observed for α₁-acid glycoprotein, probably as the result of carbohydrate presence. These data raise doubts concerning use of 1-AMA as a probe to study biological properties of β lactoglobulin and OBP.