Molecular design of ambipolar redox-active molecules II: closed-shell systems

This mini-review highlights key structural features that should be taken into account when creating ambipolar redox-active closed-shell metal-free molecules. This type of compound is strongly required for the fabrication of all-organic ‘poleless’ batteries and semiconductors. The suggested strategies aimed at stabilization of both oxidized (cationic) and reduced (anionic) redox-states are based on the comprehensive analysis of the most successful structures taken from the recent publications.     

Stability of O3 + N2, O3 + O2 and O3 + CO2 double hydrates: DFT study

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Quantum discreteness effects and flicker fluctuations in tunneling conductivity

An analysis of events in the tunneling junction shows that the interaction of one-electron processes in a many-electron system may be a source of scale-invariant low-frequency fluctuations of conductivity (the interaction consists in that the quantum probability of an electron transition depends on fast random changes in the environment in the course of the transition, including the changes caused by analogous transitions). The theory relates flicker fluctuations in the tunneling conductivity to the discrete character of the spectrum of electron states and explains the nonlinearity of the noise-current characteristic observed in nanocomposites.     

Remarks on exact controllability for Stokes and Navier–Stokes systems

This Note deals with the controllability of Stokes and Navier–Stokes systems with distributed controls with support in possibly small subdomains. We first present a new global Carleman inequality for the solutions to Stokes-like systems that leads to the null controllability at any time T>0. Then, we present a local result concerning exact controllability to trajectories of the Navier–Stokes system. To cite this article: E. Fernández-Cara et al., C. R. Acad. Sci. Paris, Ser. I 338 (2004).     

On Oscillation Criteria of Fourth Order Linear Differential Equations

The paper deals with oscillation criteria of fourth order linear differential equations with quasi-derivatives.     

Modulation of the phase difference between polarization modes in single-mode fibers

Mechanisms of polarization modulation in a single-mode fiber that modulate the phase difference between polarization modes without affecting their amplitudes are considered. A coefficient that characterizes the efficiency of cylindrical piezoceramic modulators and is independent of their resonant properties is introduced. Analytical expressions for this coefficient for different modulation mechanisms are derived. The lateral pressure on the fiber is shown to provide the highest efficiency. For isotropic fibers, a modulator with a squeezing covering, which increases significantly its efficiency, is studied. For anisotropic fibers, the most appropriate way of phase difference modulation is longitudinal extension, in which case the birefringence axes do not have to be matched. In most cases, the measured and predicted efficiencies are in good correspondence.     

Seizure warning algorithm based on optimization and nonlinear dynamics

There is growing evidence that temporal lobe seizures are preceded by a preictal transition, characterized by a gradual dynamical change from asymptomatic interictal state to seizure. We herein report the first prospective analysis of the online automated algorithm for detecting the preictal transition in ongoing EEG signals. Such, the algorithm constitutes a seizure warning system. The algorithm estimates STL_max, a measure of the order or disorder of the signal, of EEG signals recorded from individual electrode sites. The optimization techniques were employed to select critical brain electrode sites that exhibit the preictal transition for the warning of epileptic seizures. Specifically, a quadratically constrained quadratic 0-1 programming problem is formulated to identify critical electrode sites. The automated seizure warning algorithm was tested in continuous, long-term EEG recordings obtained from 5 patients with temporal lobe epilepsy. For individual patient, we use the first half of seizures to train the parameter settings, which is evaluated by ROC (Receiver Operating Characteristic) curve analysis. With the best parameter setting, the algorithm applied to all cases predicted an average of 91.7% of seizures with an average false prediction rate of 0.196 per hour. These results indicate that it may be possible to develop automated seizure warning devices for diagnostic and therapeutic purposes.Mathematics Subject Classification (1991):20E28, 20G40, 20C20     

Joint extension of two theorems of Kotzig on 3-polytopes

The weight of an edge in a graph is the sum of the degrees of its end-vertices. It is proved that in each 3-polytope there exists either an edge of weight at most 13 for which both incident faces are triangles, or an edge of weight at most 10 which is incident with a triangle, or else an edge of weight at most 8. All the bounds 13, 10, and 8 are sharp and attained independently of each other.