Gromov hyperbolicity of planar graphs

We prove that under appropriate assumptions adding or removing an infinite amount of edges to a given planar graph preserves its non-hyperbolicity, a result which is shown to be false in general. In particular, we make a conjecture that every tessellation graph of ?² with convex tiles is non-hyperbolic; it is shown that in order to prove this conjecture it suffices to consider tessellation graphs of ?² such that every tile is a triangle and a partial answer to this question is given. A weaker version of this conjecture stating that every tessellation graph of ?² with rectangular tiles is non-hyperbolic is given and partially answered. If this conjecture were true, many tessellation graphs of ?² with tiles which are parallelograms would be non-hyperbolic.     

Using self-similar properties of turbulent premixed flames to downsize chemical tables in high-performance numerical simulations

Detailed chemical mechanisms have to be incorporated in turbulent combustion modelling to predict flame propagation, ignition, extinction or pollutant formation. Unfortunately, hundreds of species and thousands of elementary reactions are involved in hydrocarbon chemical schemes and cannot be handled in practical simulations, because of the related computational costs and the need to model the complexity of their interaction with turbulent motions. Detailed chemistry may be handled using look-up tables, where chemical parameters such as reaction rates and/or species mass fractions are determined from a reduced set of coordinates, progress variables or mixture fractions, as proposed in ILDM, FPI or FGM methods. Nevertheless, these tables may require large computer memory spaces and non-negligible access times. This issue becomes of crucial importance when running on massively parallel computers: to implement these databases in shared memories would induce a large number of data exchanges, reducing the overall code performance; on the other hand duplicating databases in every local processor memory may become impossible either for large databases or small local memories. This work proposes to take advantage of the self-similar behaviour of turbulent premixed flames to reduce the size of these chemical databases, specifically when running on massively parallel machines, under the FPI (Flame Prolongation of ILDM) framework. Several approaches to reduce the database are investigated and discussed both in terms of memory requirements and access times. A very good compromise is obtained for methane–air turbulent premixed flames, where the size of the database is decreased by a factor of 1000, while the access time is reduced by about 60%.     

Dynamic Covalent Identification of an Efficient Heparin Ligand

Despite heparin being the most widely used macromolecular drug, the design of small‐molecule ligands to modulate its effects has been hampered by the structural properties of this polyanionic polysaccharide. Now a dynamic covalent selection approach is used to identify a new ligand for heparin, assembled from extremely simple building blocks. The amplified molecule strongly binds to heparin (K_D in the low μm range, ITC) by a combination of electrostatic, hydrogen bonding, and CH–π interactions as shown by NMR and molecular modeling. Moreover, this ligand reverts the inhibitory effect of heparin within an enzymatic cascade reaction related to blood coagulation. This study demonstrates the power of dynamic covalent chemistry for the discovery of new modulators of biologically relevant glycosaminoglycans.     

Bohr’s strip for vector valued Dirichlet series

Bohr showed that the width of the strip (in the complex plane) on which a given Dirichlet series , converges uniformly but not absolutely, is at most 1/2, and Bohnenblust-Hille that this bound in general is optimal. We prove that for a given infinite dimensional Banach space Y the width of Bohr’s strip for a Dirichlet series with coefficients a _n in Y is bounded by 1 - 1/Cot (Y), where Cot (Y) denotes the optimal cotype of Y. This estimate even turns out to be optimal, and hence leads to a new characterization of cotype in terms of vector valued Dirichlet series. The first, second and third authors were supported by MEC and FEDER Project MTM2005-08210.     

POLYNOMIAL NUMERICAL INDEX FOR SOME COMPLEX VECTOR-VALUED FUNCTION SPACES

We study the relation between the polynomial numerical indicesof a complex vector-valued function space and the ones of itsrange space. It is proved that the spaces C(K, X) and L(µ,X) have the same polynomial numerical index as the complex Banachspace X for every compact Hausdorff space K and every -finitemeasure µ, which does not hold any more in the real case.We give an example of a complex Banach space X such that, forevery k 2, the polynomial numerical index of order k of X isthe greatest possible, namely 1, while the one of X** is theleast possible, namely k^k/(1–k). We also give new examplesof Banach spaces with the polynomial Daugavet property, namelyL(µ, X) when µ is atomless, and C_w(K, X), C_w*(K,X*) when K is perfect.     

The laser-induced discoloration of stonework; a comparative study on its origins and remedies

For understanding the phenomena associated with the discoloration observed in some cases of infrared laser cleaned stonework surfaces, a comparative study of three different types and morphologies of pollution encrustation and stone substrates was undertaken. Fragments originating from monuments with historic and/or artistic value, bearing homogeneous thin soiling on Pentelic marble (Athens, Greece), thick encrustation on Hontoria limestone (Burgos, Spain) and compact thin crust on gypsum decorations (Athens, Greece), have been studied on the basis of their composition and origin, together with the conditions that may induce yellowing effects upon their laser cleaning with IR wavelengths. While irradiation in the UV (i.e. at 355 nm) could not effectively remove the encrustations studied, irradiation at 1,064 nm was found efficient to remove all the studied pollution accumulations. Discoloration towards yellow was evident in all cases and at different levels, including the samples with intentional patination layer. To the limit of Raman detection no chemical alterations were detected on the irradiated areas while the presence of yellow polar compounds in all the pollution crusts studied supports the argument that the discoloration of the stone surfaces upon their IR irradiation may be due to the uncovering of existing yellow layers as result of the migration of these compounds inwards to the original stone surface. To correct and/or prevent such undesired coloration the use of IR and UV radiation both in sequential and synchronous mode was considered, with positive results.     

Understanding the reactivity of captodative ethylenes in polar cycloaddition reactions. A theoretical study

The electrophilic/nucleophilic character of a series of captodative (CD) ethylenes involved in polar cycloaddition reactions has been studied using DFT methods at the B3LYP/6-31G(d) level of theory. The transition state structures for the electrophilic/nucleophilic interactions of two CD ethylenes toward a nucleophilically activated ethylene, 2-methylene-1,3-dioxolane, and an electrophilically activated ethylene, 1,1-dicyanoethyelene, have been studied, and their electronic structures have been characterized using both NBO and ELF methods. Analysis of the reactivity indexes of the CD ethylenes explains the reactivity of these species. While the electrophilicity of the molecules accounts for the reactivity toward nucleophiles, it is shown that a simple index chosen for the nucleophilicity, Nu, based on the HOMO energy is useful explaining the reactivity of these CD ethylenes toward electrophiles.     

Understanding reaction mechanisms in organic chemistry from catastrophe theory applied to the electron localization function topology

Thom's catastrophe theory applied to the evolution of the topology of the electron localization function (ELF) gradient field constitutes a way to rationalize the reorganization of electron pairing and a powerful tool for the unambiguous determination of the molecular mechanisms of a given chemical reaction. The identification of the turning points connecting the ELF structural stability domains along the reaction pathway allows a rigorous characterization of the sequence of electron pair rearrangements taking place during a chemical transformation, such as multiple bond forming/breaking processes, ring closure processes, creation/annihilation of lone pairs, transformations of C-C multiple bonds into single ones. The reaction mechanism of some relevant organic reactions: Diels-Alder, 1,3-dipolar cycloaddition and Cope rearrangement are reviewed to illustrate the potential of the present approach.     

An understanding of the electrophilic/nucleophilic behavior of electro-deficient 2,3-disubstituted 1,3-butadienes in polar diels-alder reactions. A density functional theory study

The electrophilic/nucleophilic behavior of dimethyl 2,3-dimethylenesuccinate 1, an electron-deficient 2,3-disubstituted 1,3-butadiene, in polar Diels-Alder reactions has been studied using DFT methods at the B3LYP/6-31G(d) level of theory. The electronic nature of bonding of the transition structures involved in the cycloaddition reactions of the diene 1 toward the nucleophilically activated dienophile 6 and the strong electrophilically activated dienophile 7 has been carefully examined within the natural bond orbital (NBO) and the topological analysis of the electron localization function (ELF) frameworks. Additionally, a study of the global electrophilicity pattern of the reagents at the ground state was performed. This evidence allows us to rationalize the participation of electron-deficient 2-susbtituted and 2,3-disubstituted 1,3-butadienes as nucleophiles in polar Diels-Alder reactions.