Stability of Generalized Transition Fronts

We study the qualitative properties of the generalized transition fronts for the reaction–diffusion equations with the spatially inhomogeneous nonlinearity of the ignition type. We show that transition fronts are unique up to translation in time and are globally exponentially stable for the solutions of the Cauchy problem. The results hold for reaction rates that have arbitrary spatial variations provided that the rate is uniformly positive and bounded from above.     

Dichloro and alkylchloro gallium derivatives of dichalcogenoimidodiphosphinate ligands: isolation of a spirogallium cation

Dichloro and chloromethyl Ga(III) complexes of general formulae [XClGa-eta2-{R2P(E)NP(E'R'2-E,E'}](X = Cl, R, R'= Ph, E, E'= O (1), S (2), Se (3); R = Ph, R'= OEt, E = O, E'= S (4); R = Me, R'= Ph, E, E'= S (5) and X = Me, E, E'= O (6), S (7), Se (8)) were synthesised by either metathesis reactions between GaCl3 and the potassium salt of the ligand (X = Cl) or by methane eliminations from in situ prepared GaMe2Cl and the protonated ligands LH (X = Me). Redistribution reaction of (3) in either CDCl3 or THF afforded the solvent-free tetracoordinate gallium spirocycle cation [Ga-{eta2-{Ph2P(Se)NP(Se)Ph2-Se,Se'})2]+ (9+). The molecular structures of complexes 2, 4, 5, 7 and 9(+) show non-planar gallacycle rings.     

Existence et prolongement des solutions holomorphes des équations aux dérivées partielles

Sans résumé     

H-bond relays in proton-coupled electron transfers. Oxidation of a phenol concerted with proton transport to a distal base through an OH relay

Four molecules comprising a phenol moiety and a distal pyridine base connected by an intermediary H-bonding and an H-bonded alcohol group have been synthesized and their electrochemistry has been investigated by means of cyclic voltammetry. The molecules differ by the substituent at the alcohol functional carbon and by methyl groups on the pyridine. The reaction follows a concerted proton-electron transfer pathway as confirmed by the observation of a significant H/D kinetic isotope effect in all four cases. The standard rate constants characterizing each of the four compounds are analyzed in terms of reorganization energy and pre-exponential factor. Intramolecular and solvent reorganization energies appear as practically constant in the series, in which a previously investigated aminophenol is included, whereas significantly different pre-exponential factors are observed. That the latter, which is a measure of the efficiency of proton tunneling concerted with electron transfer, be substantially smaller with the H-bond relay molecules than with the aminophenol is related to the fact that two protons are moved in the first case instead of one in the second. Within the H-bond relay molecules, the pre-exponential factor varies with the substituent present at the alcohol functional carbon in the order CF(3) > H > CH(3), presumably as the result of a fine tuning of the balance between the H-bond accepting and H-bond donating properties of the central OH group. The kinetic H/D kinetic isotope effect increases accordingly in the same order.     

Self-assembled monolayer gold electrode for surfactant analysis

A gold electrode coated with a self-assembled monolayer of octane-thiol (SAM/Au) has been used as an amperometric detector for the determination of surfactants. This detector operated in the presence of a high percentage of organic solvent and was adapted to an HPLC System. At the SAM/Au, the electrochemical response of an electroactive tracer (potassium ferricyanide) was completely inhibited, but, in the presence of a cationic surfactant, the electrochemical reduction was progressively restored. In flow injection analysis, using the SAM/Au in an amperometric flow-through detector polarised at 0.0 V vs Ag/AgCl, a linear response (i=f{[surfactant]}) was observed for cationic surfactants e.g. cetylpyridinium chloride in the concentration range 2 × 10⁻⁶–1 × 10⁻³ M. The electrochemical data along with the determination of the ion pair stoichiometry between the redox tracer and the surfactant suggest an electrochemical response related to ion pair formation and governed by electron transfer by tunneling effect. Received: 28 January 1997 / Accepted: 7 March 1997     

Spectral properties of a tight binding Hamiltonian with period doubling potential

We study a one dimensional tight binding hamiltonian with a potential given by the period doubling sequence. We prove that its spectrum is purely singular continuous and supported on a Cantor set of zero Lebesgue measure, for all nonzero values of the potential strength. Moreover, we obtain the exact labelling of all spectral gaps and compute their widths asymptotically for small potential strength.     

On a perturbed anisotropic equation with a critical exponent

Abstract We study a perturbed anisotropic equation without using the knowledge of the limiting problem. This provides a different method from that introduced by Brézis and Nirenberg [4]. Our arguments use some tools recently developed in [5, 6]. Keywords: Anisotropic critical exponent, Critical level, Compactness, Nehari manifold Mathematics Subject Classification (2000): 35J25, 35J60, 35J65     

Theoretical spectroscopy of the calcium dimer in the A 1Sigma(u)+, c3Pi(u), and a3Sigma(u)+ manifolds: an ab initio nonadiabatic treatment

Nonadiabatic theory of molecular spectra of diatomic molecules is presented. It is shown that in the fully nonadiabatic framework, the rovibrational wave functions describing the nuclear motions in diatomic molecules can be obtained from a system of coupled differential equations. The rovibrational wave functions corresponding to various electronic states are coupled through the relativistic spin-orbit coupling interaction and through different radial and angular coupling terms, while the transition intensities can be written in terms of the ground state rovibrational wave function and bound rovibrational wave functions of all excited electronic states that are electric dipole connected with the ground state. This theory was applied in the nearly exact nonadiabatic calculations of energy levels, line positions, and intensities of the calcium dimer in the A (1)Sigma(u) (+)(1 (1)S+1 (1)D), c (3)Pi(u)(1 (3)P+1 (1)S), and a (3)Sigma(u) (+)(1 (3)P+1 (1)S) manifolds of states. The excited state potentials were computed using a combination of the linear response theory within the coupled-cluster singles and doubles framework for the core-core and core-valence electronic correlations and of the full configuration interaction for the valence-valence correlation, and corrected for the one-electron relativistic terms resulting from the first-order many-electron Breit theory. The electric transition dipole moment governing the A (1)Sigma(u) (+)<--X (1)Sigma(g) (+) transitions was obtained as the first residue of the frequency-dependent polarization propagator computed with the coupled-cluster method restricted to single and double excitations, while the spin-orbit and nonadiabatic coupling matrix elements were computed with the multireference configuration interaction wave functions restricted to single and double excitations. Our theoretical results explain semiquantitatively all the features of the observed Ca(2) spectrum in the A (1)Sigma(u) (+)(1 (1)S+1 (1)D), c (3)Pi(u)(1 (3)P+1 (1)S), and a (3)Sigma(u) (+)(1 (3)P+1 (1)S) manifolds of states.     

5G meets satellite: Non-terrestrial network architecture and 3GPP

With 3GPP Release-17, global 5G standards now support non-terrestrial mobile networks comprising radio access network, terminals, and core network. This enables multi-vendor interoperability as well as interoperability with 3GPP-compliant 5G systems. This paper describes the key features enabling the NG-RAN architecture defined for 5G to support non-terrestrial networks. Starting from a general overview of NG-RAN and of the new paradigms of NTN, we introduce the NTN functionality in NG-RAN specifications with respect to feeder link switchover, cell handling, terminal registration, and OAM aspects. We also discuss different scenarios combining satellite access with 3GPP-defined core networks. We also describe some further enhancements expected to be seen in the next 3GPP release (Rel-18). We believe current and upcoming 3GPP work for NTN represents a solid basis on which 5G satellite networks can be built in the upcoming future.