Ion pairs formed by alkali metals. Complex of caesium with 4-nitropyridine

The ESR spectra of the 4-nitropyridine/caesium system in dimethoxyethane have been measured in the range of temperature between ?100 and +20°C. These spectra are drastically different from those of the ion pairs obtained with the lighter alkali metals, and an interpretation is offered.     

The influence of solvation on the mechanism of ethylene and benzene methylation

By means of the MINDO/3 method, elcctrophilic attack of CH⁺₃ and CH⁺₃OH⁺₂ on ethylene and benzene has been studied in order to discuss the timing or desolvalion. Partial desolvation at the transition stale is found. The implications of this fact are analyzed.     

Positive Solutions of Nonlocal Boundary Value Problems: A Unified Approach

We give a unified approach for studying the existence of multiplepositive solutions of nonlinear differential equations of theform where g, f are non-negativefunctions, subject to various nonlocal boundary conditions.We study these problems via new results for a perturbed integralequation, in the space C[0, 1], of the form where [u], ß[u] are linear functionalsgiven by Stieltjes integrals but are not assumed to be positivefor all positive u. This means we actually cover many more differentialequations than the simple equation written above. Previous resultshave studied positive functionals only, but even for positivefunctionals our methods give improvements on previous work.The well-known m-point boundary value problems are special casesand we obtain sharp conditions on the coefficients, which allowssome of them to have opposite signs. We also use some optimalassumptions on the nonlinear term.     

Laplace equations,Lefschetz properties and line arrangements

In this note we extend the main result in [6] on artinian ideals failing Lefschetz properties, varieties satisfying Laplace equations and existence of suitable singular hypersurfaces. Moreover we characterize the minimal generation of ideals generated by powers of linear forms by the configuration of their dual points in the projective plane and we use this result to improve some propositions on line arrangements and Strong Lefschetz Property at range 2 in [6]. The starting point was an example in [3]. Finally we show the equivalence among failing SLP, Laplace equations and some unexpected curves introduced in [3].     

A new family of time-space harmonic polynomials with respect to Lévy processes

By means of a symbolic method, a new family of time-space harmonic polynomials with respect to Lévy processes is given. The coefficients of these polynomials involve a formal expression of Lévy processes by which many identities are stated. We show that this family includes classical families of polynomials such as Hermite polynomials. Poisson–Charlier polynomials result to be a linear combinations of these new polynomials, when they have the property to be time-space harmonic with respect to the compensated Poisson process. The more general class of Lévy–Sheffer polynomials is recovered as a linear combination of these new polynomials, when they are time-space harmonic with respect to Lévy processes of very general form. We show the role played by cumulants of Lévy processes, so that connections with boolean and free cumulants are also stated.     

Theory and experiment of large numerical aperture objective Raman microscopy: application to the stress‐tensor determination in strained cubic materials

We present the theory underlying the large numerical aperture objective micro‐Raman backscattering experiment and apply it to the elaboration of a characterization methodology for the determination of the stress tensor in strained cubic semiconductor structures. The presented stress characterization technique consists in monitoring the variations of the stress‐sensitive optical phonon peak position and linewidth while rotating stepwise the sample about its normal. The practical application of the technique is illustrated on a silicon‐on‐insulator (SOI) microelectronic structure demonstrating a plane stress‐tensor determination. Copyright © 2008 John Wiley & Sons, Ltd.     

Raman spectroscopy shows interchain through space charge delocalization in a mixed valence oligothiophene cation and in its pi-dimeric biradicaloid dication

The vibrational Raman spectra of a decathiophene are provided in three relevant oxidations states: for the radical cation, its class III mixed valence system and its "frozen, -170 degrees C" class II MV analogue; for the dication, its singlet biradical pi-dimer and its "hot, +70 degrees C" magnetically active triplet excited state. Everything is compatible with interpentathiophene charge delocalization occurring at distances of 4-5 A similar to those found in the crystals of pi-stacked oligothiophenes. This stresses the interest of this spectroscopic tool for the analyses of electronic processes in crystals or in thin films of conjugated organic molecules.     

A speciality theorem for curves in P<Superscript>5</Superscript>

Let be an integral projective curve. One defines the speciality index e(C) of C as the maximal integer t such that , where ω _C denotes the dualizing sheaf of . Extending a classical result of Halphen concerning the speciality of a space curve, in the present paper we prove that if is an integral degree d curve not contained in any surface of degree  < s, in any threefold of degree  < t, and in any fourfold of degree  < u, and if , then Moreover equality holds if and only if C is a complete intersection of hypersurfaces of degrees u, , and . We give also some partial results in the general case , .