Catégories de Möbius et fonctorialités: un cadre général pour l'inversion de Möbius

This paper proposes a general setting for Möbius inversion which includes the cases of locally finite partially ordered sets and monoids with the finite decomposition property (f.d.p.). The unifying concept is that of categories with the f.d.p., called Möbius categories, which we characterize in four different ways. The established theory of incidence algebras, Möbius functions, product formulas, reduced algebras, etc., is carried over. Furthermore, the study of functors between Möbius categories yields results in two directions: firstly, inspired from the substitution of formal power series is the construction of a homomorphism between incidence algebras which allows the transfer of Möbius inversions; secondly, surjective functors often give rise to a reduced incidence algebra, thus shedding new light on many important reduced algebras in combinatorial theory.     

Emission secondaire de petits agregats NipCn par des carbures de nickel

The intensities of emission of Ni_pC_n⁺(p = 1–3) and NiC_n^? secondary ions given by two alloys: Ni₃C and NiC 5% at. C, show off a saw-toothed behaviour according to the parity of the number n of carbon atoms. Maxima occur when n is odd for NiC_n⁺ ions and when n is even in the other cases (p = 2, 3; negative ions). Besides, the influence of the carbon concentration in the alloy can be observed.The alternations of NiC_n⁺ and Ni₂C_n⁺ ions can be interpreted from Pitzer and Clementi model (the clusters are supposed to be linear). Thus it can be found greater stabilities for NiC_2k+1 and Ni₂C_2k chains than for NiC_2k and Ni₂C_2k+1 chains respectively, which very well agrees with the “correspondence rule” between the emissions of different species of ions and their electronic properties.     

Enhanced two-photon absorption with novel octupolar propeller-shaped fluorophores derived from triphenylamine

[structure: see text] Novel octupolar fluorophores derived from the symmetrical functionalization of a triphenylamine core with strong acceptor peripheral groups via phenylene-ethynylene linkers have been synthesized and shown to exhibit high fluorescence quantum yields, very large TPA cross-sections in the red-NIR region, and suitable photostability.     

Z‐Shaped Pyrrolo[3,2‐b]pyrroles and Their Transformation into π‐Expanded Indolo[3,2‐b]indoles

Sterically hindered 1,4‐dihydropyrrolo[3,2‐b]pyrroles possessing ortho‐(arylethynyl)phenyl substituents at positions‐2 and ‐5 were efficiently synthesized through a sila‐Sonogashira reaction. These unique Z‐shaped dyes showed relatively strong fluorescence in solution. Detailed optimization revealed that, in the presence of InCl₃, these alkynes readily undergo an intramolecular double cyclization to give hexacyclic products bearing an indolo[3,2‐b]indole skeleton in remarkable yields. Steady‐state UV–visible spectroscopy revealed that upon photoexcitation, the prepared Z‐shaped alkynes undergo mostly radiative relaxation leading to high fluorescence quantum yields. In the case of 7,14‐dihydrobenzo[g]benzo[6,7]indolo[3,2‐b]indoles, we believe that the substantial planarization of geometry in the excited state, is the underlying reason for the observed large Stokes shifts. The presence of additional electron‐withdrawing groups makes it possible to further alter the photophysical properties. The two‐photon absorption cross‐section values of both families of dyes were found to be modest and the nature of the excited state responsible for two‐photon absorption appeared to be strongly affected by the presence of peripheral groups. Serendipitous synthesis of unusual double‐Z‐shaped alkyne by Sonogashira and Glaser coupling is also reported.     

Two‐Photon Polarity Probes Built from Octupolar Fluorophores: Synthesis,Structure–Properties Relationships,and Use in Cellular Imaging

A series of octupolar fluorophores built from a triphenylamine (TPA) core connected to electron‐withdrawing (EW) peripheral groups through conjugated spacers has been synthesized. Their photoluminescence, solvatochromism, and two‐photon absorption (2PA) properties were systematically investigated to derive structure–property relationships. All derivatives exhibit two 2PA bands in the 700–1000 nm region: a first band at low energy correlated with a core‐to‐periphery intramolecular charge transfer that leads to an intense 1PA in the blue‐visible range, and a second more intense band at higher energy due to an efficient coupling of the branches through the TPA core. Increasing the strength of the EW end groups or the length of the conjugated spacers and replacing triple‐bond linkers with double bonds induces both enhancement and broadening of the 2PA responses, thereby leading to cross‐sections up to 2100 GM at peak and higher than 1000 GM over the whole 700–900 nm range. All derivatives exhibit intense photoluminescence (PL) in low‐ to medium‐polarity environments (with quantum yields in the 0.5–0.9 range) and display a strong positive solvatochromic behavior (with Lippert–Mataga specific shifts ranging from 15 000 to 27 500 cm^?1), triple bonds, and phenyl moieties in the conjugated spacers, thereby leading to larger sensitivities than those of double bonds and thienyl moieties. More hydrophilic derivatives were also shown to be biocompatible, to retain their 2PA and PL properties in biological conditions, and finally to be suitable as polarity sensors for multiphoton cell imaging.     

Local electrochemical impedance spectroscopy: A window into heterogeneous interfaces

The ability to probe surface reactivity on a local scale has led to a new insight into the comprehension of the electrochemical reactivity in relation with the microstructure of the surface. Among the different techniques developed in recent years, local electrochemical impedance spectroscopy has the advantage of using a transient approach to locally characterize a stationary electrochemical system without the need to add any redox mediator in solution, which is a great advantage for the study of different systems.In this review, particular attention is paid to the different ways of measuring the local impedance, and the technique implementing a local current measurement in solution is deeply discussed. This local electrochemical impedance spectroscopy journey also encompasses a discussion about technical and experimental limitations.     

Synthesis and pharmacological evaluation of N-substituted 4,6-diaryl-3-pyridazinones as analgesic, antiinflammatory and antipyretic agents

The synthesis and the pharmacological evaluation of 19 new 4,6-diaryl-3-pyridazinones are reported. All compounds were screened for analgesic, antiinflammatory and antipyretic activities. Introduction of an arylpiperazinomethyl moiety in the 2-position of the pyridazinone ring resulted in the most potent activities. Compounds 2a, 2b, 2h and 2i exhibited a higher analgesic activity than did aspirin or noramidopyrine in the hot plate test.     

Molecular Hartree-Fock equations for iteration-variation calculations in momentum space

Summary Molecular Hartree-Fock equations for iteration-variation calculations in momentum space based on trial functions expressed as linear combinations of spherical Gaussian functions are obtained. They are applied to the hydrogen molecule to test their validity. The significant improvements brought by a first iteration are accessed through an asymptotic analysis.