2- and 2,7-Substituted para-N-Methylpyridinium Pyrenes: Syntheses,Molecular and Electronic Structures,Photophysical, Electrochemical,and Spectroelectrochemical Properties and Binding to Double-Stranded (ds) DNA

Two N-methylpyridinium compounds and analogous N-protonated salts of 2- and 2,7-substituted 4-pyridyl-pyrene compounds were synthesised and their crystal structures, photophysical properties both in solution and in the solid state, electrochemical and spectroelectrochemical properties were studied. Upon methylation or protonation, the emission maxima are significantly bathochromically shifted compared to the neutral compounds, although the absorption maxima remain almost unchanged. As a result, the cationic compounds show very large apparent Stokes shifts of up to 7200 cm⁻¹. The N-methylpyridinium compounds have a single reduction at ca. −1.5 V vs. Fc/Fc⁺ in MeCN. While the reduction process was reversible for the 2,7-disubstituted compound, it was irreversible for the mono-substituted one. Experimental findings are complemented by DFT and TD-DFT calculations. Furthermore, the N-methylpyridinium compounds show strong interactions with calf thymus (ct)-DNA, presumably by intercalation, which paves the way for further applications of these multi-functional compounds as potential DNA-bioactive agents.     

α'β-Elimination and wittig rearrangement of the carbanion from benzyl cyclooctyl ether

Beside the Wittig rearrangement and the migration of the cyclooctyl radical to the para position, the title carbanion gives rise to an elimination in a syn process.     

Contractually stable networks

We consider situations where players are part of a network and belong to coalitions in a given coalition structure. We propose the concept of contractual stability to predict the networks that are going to emerge at equilibrium when the consent of coalition partners is needed for adding or deleting links. Two different decision rules for consent are analyzed: simple majority and unanimity. We characterize the coalition structures that make the strongly efficient network contractually stable under the unanimity decision rule and the coalition structures that sustain some critical network as contractually stable under the simple majority decision rule and under any decision rule requiring the consent of any proportion of coalition partners. Requiring the consent of coalition members may help to reconcile stability and efficiency in some classical models of network formation.     

Counting Function of Characteristic Values and Magnetic Resonances

We consider the meromorphic operator-valued function I ? K(z) = I ? A(z)/z where A is holomorphic on the domain 𝒟 ? ?, and has values in the class of compact operators acting in a given Hilbert space. Under the assumption that A(0) is a selfadjoint operator which can be of infinite rank, we study the distribution near the origin of the characteristic values of I ? K, i.e. the complex numbers w ≠ 0 for which the operator I ? K(w) is not invertible, and we show that generically the characteristic values of I ? K converge to 0 with the same rate as the eigenvalues of A(0).

We apply our abstract results to the investigation of the resonances of the operator H = H ₀ + V where H ₀ is the shifted 3D Schrödinger operator with constant magnetic field of scalar intensity b > 0, and V: ?³ → ? is the electric potential which admits a suitable decay at infinity. It is well known that the spectrum σ(H ₀) of H ₀ is purely absolutely continuous, coincides with [0, + ∞[, and the so-called Landau levels 2bq with integer q ≥ 0, play the role of thresholds in σ(H ₀). We study the asymptotic distribution of the resonances near any given Landau level, and under generic assumptions obtain the main asymptotic term of the corresponding resonance counting function, written explicitly in the terms of appropriate Toeplitz operators.     

Spacetime Causality in the Study of the Hankel Transform

We study Hilbert space aspects of the Klein-Gordon equation in two-dimensional spacetime. We associate to its restriction to a spacelike wedge a scattering from the past light cone to the future light cone, which is then shown to be (essentially) the Hankel transform of order zero. We apply this to give a novel proof, solely based on the causality of this spatio-temporal wave propagation, of the theorem of de Branges and V. Rovnyak concerning Hankel pairs with a support property. We recover their isometric expansion as an application of Riemann’s general method for solving Cauchy-Goursat problems of hyperbolic type. Communicated by Vincent Rivasseau Submitted: October 28, 2005; Accepted: February 17, 2006     

Confidence intervals for the Hurst parameter of a fractional Brownian motion based on finite sample size

In this paper, we show how concentration inequalities for Gaussian quadratic form can be used to propose confidence intervals of the Hurst index parametrizing a fractional Brownian motion. Both cases where the scaling parameter of the fractional Brownian motion is known or unknown are investigated. These intervals are obtained by observing a single discretized sample path of a fractional Brownian motion and without any assumption on the Hurst parameter H.     

Convergence of Discrete Snakes

The discrete snake is an arborescent structure built with the help of a conditioned Galton-Watson tree and random i.i.d. increments Y. In this paper, we show that if and , then the discrete snake converges weakly to the Brownian snake (this result was known under the hypothesis ). Moreover, if this condition fails, and the tails of Y are sufficiently regular, we show that the discrete snake converges weakly to an object that we name jumping snake. In both case, the limit of the occupation measure is shown to be the integrated super-Brownian excursion. The proofs rely on the convergence of the codings of discrete snake with the help of two processes, called tours.     

Some properties of the range of super-Brownian motion

We consider a super-Brownian motion X. Its canonical measures can be studied through the path-valued process called the Brownian snake. We obtain the limiting behavior of the volume of the ɛ-neighborhood for the range of the Brownian snake, and as a consequence we derive the analogous result for the range of super-Brownian motion and for the support of the integrated super-Brownian excursion. Then we prove the support of X _t is capacity-equivalent to [0, 1]² in ℝ^d, d≥ 3, and the range of X, as well as the support of the integrated super-Brownian excursion are capacity-equivalent to [0, 1]⁴ in ℝ^d, d≥ 5. Received: 7 April 1998 / Revised version: 2 October 1998