Jensen’s functional equation on the symmetric group S<Subscript>n</Subscript>

Two natural extensions of Jensen’s functional equation on the real line are the equations f(xy) + f(xy ⁻¹) =  2f(x) and f(xy) + f(y ⁻¹ x) =  2f(x), where f is a map from a multiplicative group G into an abelian additive group H. In a series of papers (see Ng in Aequationes Math 39:85–99, 1990; Ng in Aequationes Math 58:311–320, 1999; Ng in Aequationes Math 62:143–159, 2001), Ng solved these functional equations for the case where G is a free group and the linear group GL_n(R), R=\mathbbZ,\mathbbR{{GL_n(R), R=\mathbb{Z},\mathbb{R}}} , is a quadratically closed field or a finite field. He also mentioned, without a detailed proof, in the above papers and in (see Ng in Aequationes Math 70:131–153, 2005) that when G is the symmetric group S _n , the group of all solutions of these functional equations coincides with the group of all homomorphisms from (S _n , ·) to (H, + ). The aim of this paper is to give an elementary and direct proof of this fact.     

Combination of Raman, Infrared, and X-Ray Energy-Dispersion Spectroscopies and X-Ray Diffraction to Study a Fossilization Process

X-ray diffraction was combined with X-ray energy-dispersion, Fourier-transform infrared, and Raman spectroscopies to study the fossilization of a Cretaceous specimen of the plant Brachyphyllum castilhoi, a fossil from the Ipubi Formation, in the Araripe Sedimentary Basin, Northeastern Brazil. Among the possible fossilization processes, which could involve pyrite, silicon oxide, calcium oxide, or other minerals, we were able to single out pyritization as the central mechanism producing the fossil, more than 100 million years ago. In addition to expanding the knowledge of the Ipubi Formation, this study shows that, when combined with other experimental techniques, Raman spectroscopy is a valuable tool at the paleontologist’s disposal.     

Specific molecular and cellular events induced by irradiated X‐ray photoactivatable drugs raise the problem of co‐toxicities: particular consequences for anti‐cancer synchrotron therapy

Synchrotrons are capable of producing intense low‐energy X‐rays that enable the photoactivation of high‐Z elements. Photoactivation therapy (PAT) consists of loading tumors with photoactivatable drugs and thereafter irradiating them at an energy, generally close to the K‐edge of the element, that enhances the photoelectric effect. To date, three major photoactivatable elements are used in PAT: platinum (cisplatin and carboplatin), iodine (iodinated contrast agents and iododeoxyuridine) and gadolinium (motexafin gadolinium). However, the molecular and cellular events specific to PAT and the radiobiological properties of these photoactivatable drugs are still misknown. Here, it is examined how standard and synchrotron X‐rays combined with photoactivatable drugs impact on the cellular response of human endothelial cells. These findings suggest that the radiolysis products of the photoactivatable drugs may participate in the synergetic effects of PAT by increasing the severity of radiation‐induced DNA double‐strand breaks. Interestingly, subpopulation of highly damaged cells was found to be a cellular pattern specific to PAT. The data show that the efficiency of emerging anti‐cancer modalities involving synchrotron photoactivation strongly depends on the choice of photoactivatable drugs, and important series of experiments are required to secure their clinical transfer before applying to humans.     

Discrimination between Olfactory Receptor Agonists and Non‐agonists

A joint approach combining free‐energy calculations and calcium‐imaging assays on the broadly tuned human 1G1 olfactory receptor is reported. The free energy of binding of ten odorants was computed by means of molecular‐dynamics simulations. This state function allows separating the experimentally determined eight agonists from the two non‐agonists. This study constitutes a proof‐of‐principle for the computational deorphanization of olfactory receptors.     

An Easy Route to (Hetero)arylboronic Acids

An unprecedented spontaneous reactivity between diazonium salts and diboronic acid has been unveiled, leading to a versatile arylboronic acid synthesis directly from (hetero)arylamines. This fast reaction (35 min overall) tolerates a wide range of functional groups and is carried out under very mild conditions. The radical nature of the reaction mechanism has been investigated.     

A Multifunctional Photoswitch: 6π Electrocyclization versus ESIPT and Metalation

A terthiazole‐based molecular switch associating 6π electrocyclization, excited state intramolecular proton transfer (ESIPT), and strong metal binding capability was prepared. The photochemical and photophysical properties of this molecule and of the corresponding nickel and copper complexes were thoroughly investigated by steady‐state and ultrafast absorption spectroscopy and rationalized by DFT/TDDFT calculations. The switch behaves as a biphotochrome with time‐dependent photochemical outcome and displays efficient ESIPT‐based fluorescence photoswitching. Both photochemical reactions are suppressed by nickel or copper metalation, and the main factors contributing to the quenching of the electrocyclization are discussed.     

Combining electronic properties and virtual screening for the development of new antioxidants: Trolox-like compounds as application example

Oxidative stress is an imbalance between the production of free radicals and the antioxidant defenses of the organism. Heart diseases, anemia, inflammation, and neurodegenerative disorders have been associated with this biological condition. Trolox is a notable antioxidant drug similar to vitamin E, and it is used to decrease the oxidative stress or repair the damage caused by it. In this work, the virtual screening technique is applied to identify compounds with antioxidant activities similar to Trolox. The antioxidant activity of these compounds was assessments by the mechanisms of hydrogen atom transfer and single electron transfer. Properties such as bond dissociation enthalpy, adiabatic ionization potential, Gibbs free reaction energy, spin density, highest occupied molecular orbital (HOMO), and GAP (HOMO-LUMO) energies, obtained from the DFT approach, point out to the predominance of the HAT mechanism for the antioxidant action of these compounds. The obtained results contribute to a better understanding of the chemical and physical properties responsible for antioxidant activity and the design of new antioxidant agents.     

Interaction soliton–sable dans un canal en eau peu profonde

Interaction between solitons and a sandy bed in shallow water is investigated. In our experiments, solitons are generated on the background of a harmonic wave, in a wave flume used in resonant mode. It is found that the sand ripples formed by the solitons propagation induce a significant decrease of solitons amplitude and of the phase shift between the soliton and the harmonic wave. However, the amplitude of the harmonic wave is approximately constant. The possible physical processes of such behaviour for the soliton amplitude and for the harmonic wave amplitude are discussed. To cite this article: F. Marin et al., C. R. Mecanique 333 (2005).     

Sharp Sobolev Asymptotics for Critical Anisotropic Equations

We investigate blow-up theory and prove sharp Sobolev asymptotics for a general class of anisotropic critical equations in bounded domains of .     

Nonbonded P···P and P···Se Interactions in Naphthalene 1,8-Positions: Role of Lone-Pair Orbitals

The lone pair-lone pair repulsion plays an important role in the nonbonded P;;;P interaction in naphthalene 1,8-positions. The conformations around P and Se in 8-(PhSe)-1-(Ph 2 P=O)C 10 H 6 are determined by the attractive O;;;Se--C 3c-4e type interaction. The P;;;Se interaction in the 1,8-positions is also discussed.