On stability of sampling-reconstruction models

A useful sampling-reconstruction model should be stable with respect to different kind of small perturbations, regardless whether they result from jitter, measurement errors, or simply from a small change in the model assumptions. In this paper we prove this result for a large class of sampling models. We define different classes of perturbations and present a way of quantifying the robustness of a model with respect to them. We also use the theory of localized frames to study the dual frame method for recovering the original signal from its samples.     

Checking oriented matroid isomorphism by means of canonical labeling

In this paper a method for establishing the structural equivalence of sets of planar geometric features composed by points and lines is presented. It is based on oriented matroid theory, a setting in which the combinatorial structural properties of these geometric features, such as incidence, order, partitioning, separation, and convexity, can be represented and analyzed in a coordinate-free manner. Projective transformations in computer vision keep in general the convexity property which implies an invariant oriented matroid representation of the planar geometric features under this class of transformations. As long as points and lines are in general position, the oriented matroid representation is also insensitive to small changes in the geometric image features. However the oriented matroid representation depends on the labeling of its elements. Checking the structural equivalence of the above mentioned geometric features represented by means of oriented matroids implies establishing whether two oriented matroid representations are equivalent up to relabeling of their elements. This is the oriented matroid isomorphism problem which is solved in this paper by means of a canonical labeling of the elements.     

Ferrocene–Carbohydrate Conjugates as Electrochemical Probes for Molecular Recognition Studies

We report two methods that have allowed the attachment of glucose, mannose and lactose to one or both of the cyclopentadienyl rings of ferrocene. The resulting ferrocene–carbohydrate conjugates were synthesised by the reaction of thioglycosides with ferrocenemethanol and 1,1′‐ferrocenedimethanol in acidic media. A second method based on the regiospecific copper(I)‐catalysed cycloaddition of propargyl glycoside, azidomethyl and bis(azidomethyl)ferrocene as well as azidoethyl glycoside and ethynylferrocene was also used and led to the synthesis of 1,2,3‐triazole‐containing glycoconjugates. The electrochemical behaviour of the synthesised glycoconjugates was investigated. In addition, their binding interactions with β‐cyclodextrin were studied by means of NMR spectroscopy, isothermal titration calorimetry, and cyclic and differential pulse voltammetric experiments. These techniques allowed the determination of the thermodynamic parameters of the complexes, the stability constants for the complexes formed with both the neutral and the oxidised states of the ferrocenyl glycoconjugates, the mode of inclusion and the diffusion coefficients for both the glycoconjugates and the complexes.     

Returnability in complex directed networks (digraphs)

The concept of returnability is proposed for complex directed networks (digraphs). It can be seen as a generalization of the concept of reciprocity. Two measures of the returnability are introduced. We establish closed formulas for the calculation of the returnability measures, which are also related to the digraph spectrum. The two measures are calculated for simple examples of digraphs as well as for real-world complex directed networks and are compared with the reciprocity.     

Further New Bis‐cembranoids from the Hainan Soft Coral Sarcophyton tortuosum

Two new bis‐cembranoids, ximaolides F ( 1 ) and G ( 2 ), were isolated from the Hainan soft coral Sarcophyton tortuosum. The structures and relative configurations of the two new compounds were elucidated by the combination of spectroscopic methods, chemical conversion of ximaolide F ( 1 ) into ximaolide G ( 2 ), and comparison with related model compounds.     

Mild and efficient one-pot synthesis of chiral β-chalcogen amides via 2-oxazoline ring-opening reaction mediated by indium metal

A simple and efficient procedure for the synthesis of β-seleno and β-thio amides via the ring-opening reaction of chiral 2-oxazolines in the presence of indium metal has been developed. Features of this method include the following: (i) easily and accessible starting materials; (ii) indium metal is more stable and less expensive then its respective salts; (iii) useful to excellent yields of β-chalcogen amides derivatives.     

Genus 2 Belyĭ surfaces with a unicellular uniform dessin

A bicoloured graph embedded in a compact oriented surface and dividing it into a union of simply connected components (faces) is known as a dessin d’enfant. It is well known that such a graph determines a complex structure on the underlying topological surface, but a given compact Riemann surface may correspond to different dessins. In this paper we deal with all unicellular (one-faced) uniform dessins of genus 2 and their underlying Riemann surfaces. A dessin is called uniform if white vertices, black vertices and faces have constant degree, say p, q and r respectively. A uniform dessin d’enfant of type (p, q, r) on a given surface S corresponds to the inclusion of the torsion-free Fuchsian group K uniformizing S inside a triangle group Δ(p, q, r). Hence the existence of different uniform dessins on S is related to the possible inclusion of K in different triangle groups. The main result of the paper states that two unicellular uniform dessins belonging to the same genus 2 surface must necessarily be isomorphic or obtained by renormalisation. The problem is approached through the study of the face-centers of the dessins. The displacement of such a point by the elements of K must belong to a prescribed discrete set of (hyperbolic) distances determined by the signature (p, q, r). Therefore looking for face-centers amounts to finding points correctly displaced by every element of K.     

Strong localization and macroscopic atoms for directed polymers

In this article, we derive strong localization results for directed polymers in random environment. We show that at “low temperature” the polymer measure is asymptotically concentrated at a few points of macroscopic mass (we call these points -atoms). These results are derived assuming weak conditions on the tail decay of the random environment. Partially supported by CNRS (UMR 7599 “Probabilités et Modèles Aléatoires”).     

Exact solutions for a nonlinear model

In this paper we show new exact solutions for a type of generalized sine-Gordon equation which is obtained by constructing a Lagrange function for a dynamical coupled system of oscillators. We convert it into a nonlinear system by perturbing the potential energy from a point of view of an approach proposed by Fermi [1].