Faber-hypercyclic operators

Let Ω be a bounded domain of the complex plane whose boundary is a closed Jordan curve and (F _n ) _n≥0 the sequence of Faber polynomials of Ω. We say that a bounded linear operator T on a separable Banach space X is Ω-hypercyclic if there exists a vector x of X such that {F _n (T)x: n ≥ 0} is dense in X. We show that many of the results in the spectral theory of hypercyclic operators involving the unit disk or its boundary have Ω-hypercyclic counterparts which involve the domain Ω or its boundary. The influence of the geometry of Ω or the smoothness of its boundary on Faber-hypercyclicity is also discussed.     

Can density functional theory (DFT) be used as an aid to a deeper understanding of tandem mass spectrometric fragmentation pathways?

Prediction of tandem mass spectrometric (MS/MS) fragmentation for non‐peptidic molecules based on structure is of immense interest to the mass spectrometrist. If a reliable approach to MS/MS prediction could be achieved its impact within the pharmaceutical industry could be immense. Many publications have stressed that the fragmentation of a molecular ion or protonated molecule is a complex process that depends on many parameters, making prediction difficult. Commercial prediction software relies on a collection of general heuristic rules of fragmentation, which involve cleaving every bond in the structure to produce a list of ‘expected’ masses which can be compared with the experimental data. These approaches do not take into account the thermodynamic or molecular orbital effects that impact on the molecule at the point of protonation which could influence the potential sites of bond cleavage based on the structural motif. A series of compounds have been studied by examining the experimentally derived high‐resolution MS/MS data and comparing it with the in silico modelling of the neutral and protonated structures. The effect that protonation at specific sites can have on the bond lengths has also been determined. We have calculated the thermodynamically most stable protonated species and have observed how that information can help predict the cleavage site for that ion. The data have shown that this use of in silico techniques could be a possible way to predict MS/MS spectra. Copyright © 2009 John Wiley & Sons, Ltd.     

Preparation and characterization of 1,2,3‐triazole‐cured polymers from endcapped azides and alkynes

Fourteen commercial polyols have been characterized by GPC, NMR spectroscopy, and elemental analysis. From these, eight corresponding tosylates, six nitrate esters, seven mesylates, 13 alkynes, and 14 azides have been prepared and all these derivatives have been fully characterized. Five alkyne monomers and eight azide monomers were also prepared. Twelve alkynes and 13 azides (functionality 2–4) were combined in 1,3‐dipolar cycloaddition reactions under neat conditions to prepare triazole‐cured polymers, avoiding any heavy metal catalyst. Characterization by NMR spectroscopy, elemental analysis, and gel permeation chromatography indicated triazole polymers 14 , 22 , 23 , 28 , and 30 with degrees of polymerization of 17–28 to be the best candidates for future work. © 2007 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 46: 238–256, 2008     

Use of diagnostic neutral losses for structural information on unknown aromatic metabolites: an experimental and theoretical study

This work presents the use of neutral losses (NL) for the identification of compounds related to the metabolism of tyrosine. The mass spectra of all the studied compounds, recorded at several collision energies, are compared. The fragmentation mechanism of protonated molecules, MH⁺, is explained by combining collision‐induced dissociation (CID) mass spectra and density functional theory (DFT) calculations. The results show that the first fragmentation is the elimination from MH⁺ of a neutral molecule including a functional group of the linear chain. Three primary neutral losses are observed: 17 u (NH₃), 18 u (H₂O) and 46 u (H₂O+CO) characterizing amino, hydroxyl and carboxylic functions on the linear chain. The presence and abundance of ions corresponding to these losses are dependent on (i) the position of the functional group on the linear chain, (ii) the initial localisation of the protonating hydrogen, and (iii) the substitution of the aromatic ring. For compounds including a functional group on the benzylic carbon atom, the investigation of the other functions requires the knowledge of secondary fragmentations. Among these secondary fragmentations we have retained the loss of NH₃ from [MH–18u]⁺ and the loss of ketene from [MH–17u]⁺. Experimentally these fragmentations are detected using losses of 35 u and 59/73 u. In other words, NL35 identifies hydroxy and amino compounds and NL 46 and/or NL59/73 identify carboxylic acids. The search for characteristic neutral losses is used for the analysis of compounds in a mixture and the analysis of biological fluid. We show that selective search of several neutral losses allows also the unambiguous differentiation of isomers and gives the opportunity to identify compounds in biological fluids. Copyright © 2008 John Wiley & Sons, Ltd.     

A stochastic evolution model for residue Insertion-Deletion Independent from Substitution

We develop here a new class of stochastic models of gene evolution based on residue Insertion-Deletion Independent from Substitution (IDIS). Indeed, in contrast to all existing evolution models, insertions and deletions are modeled here by a concept in population dynamics. Therefore, they are not only independent from each other, but also independent from the substitution process. After a separate stochastic analysis of the substitution and the insertion-deletion processes, we obtain a matrix differential equation combining these two processes defining the IDIS model. By deriving a general solution, we give an analytical expression of the residue occurrence probability at evolution time t as a function of a substitution rate matrix, an insertion rate vector, a deletion rate and an initial residue probability vector. Various mathematical properties of the IDIS model in relation with time t are derived: time scale, time step, time inversion and sequence length. Particular expressions of the nucleotide occurrence probability at time t are given for classical substitution rate matrices in various biological contexts: equal insertion rate, insertion-deletion only and substitution only. All these expressions can be directly used for biological evolutionary applications. The IDIS model shows a strongly different stochastic behavior from the classical substitution only model when compared on a gene dataset. Indeed, by considering three processes of residue insertion, deletion and substitution independently from each other, it allows a more realistic representation of gene evolution and opens new directions and applications in this research field.     

Expanded Pyridiniums: Bis‐cyclization of Branched Pyridiniums into Their Fused Polycyclic and Positively Charged Derivatives—Assessing the Impact of Pericondensation on Structural,Electrochemical, Electronic,and Photophysical Features

This study evaluates the impact of the extension of the π‐conjugated system of pyridiniums on their various properties. The molecular scaffold of aryl‐substituted expanded pyridiniums (referred to as branched species) can be photochemically bis‐cyclized into the corresponding fused polycyclic derivatives (referred to as pericondensed species). The representative 1,2,4,6‐tetraphenylpyridinium ( 1^H ) and 1,2,3,5,6‐pentaphenyl‐4‐(p‐tolyl)pyridinium ( 2^Me ) tetra‐ and hexa‐branched pyridiniums are herein compared with their corresponding pericondensed derivatives, the fully fused 9‐phenylbenzo[1,2]quinolizino[3,4,5,6‐def]phenanthridinium ( 1^H f ) and the hitherto unknown hemifused 9‐methyl‐1,2,3‐triphenylbenzo[h]phenanthro[9,10,1‐def]isoquinolinium ( 2^Me f ). Combined solid‐state X‐ray crystallography and solution NMR experiments showed that stacking interactions are barely efficient when the pericondensed pyridiniums are not appropriately substituted. The electrochemical study revealed that the first reduction process of all the expanded pyridiniums occurs at around ?1 V vs. SCE, which indicates that the lowest unoccupied molecular orbital (LUMO) remains essentially localized on the pyridinium core regardless of pericondensation. In contrast, the electronic and photophysical properties are significantly affected on going from branched to pericondensed pyridiniums. Typically, the number of absorption bands increases with extended activity towards the visible region (down to ca. 450 nm in MeCN), whereas emission quantum yields are increased by three orders of magnitude (at ca. 0.25 on average). A relationship is established between the observed differential impact of the pericondensation and the importance of the localized LUMO on the properties considered: predominant for the first reduction process compared with secondary for the optical and photophysical properties.     

Perfect extinction in subwavelength dual metallic transmitting gratings

We investigate the strong electromagnetic coupling that settles in dual metallic grating structures. This coupling is evidenced to lead to a perfect optical extinction in the transmission spectrum. The behavior of this perfect extinction that strongly depends on the longitudinal space and the lateral displacement between the two gratings can be explained by a simple model that describes the interference between a propagating mode and a couple of evanescent modes. The results show that the electromagnetic transmission of the structure can be tuned by controlling the position of this perfect transmission extinction and thus pave the way to new types of infrared tunable filters.