Release of nitrosating species in the course of reduction of benzo-1,2,3,4-tetrazine 1,3-dioxides

[reaction: see text] The reduction of benzo-1,2,3,4-tetrazine 1,3-dioxides (BTDOs) 1 with Na(2)S(2)O(4) or SnCl(2) is suggested to proceed via intermediate N-nitrosobenzotriazoles 3 to afford benzotriazoles 2. The (15)N-labeling experiments exhibit that the N-3 atom of the tetrazine ring is incorporated into the nitroso group of 3 that is ultimately released into solution. It is possible that the biological activity of BTDOs is due to their ability to release nitrosating species, i.e., N-nitrosotriazol 3 or HNO(2), in the course of reduction.     

Selectivity of complex heterogeneous catalytic reactions over energetically nonuniform surfaces

The selectivity in parallel and consecutive heterogeneous catalytic reactions over nonuniform surfaces has been analyzed within the framework of the surface electron gas model. Equations for the selectivity are derived in the case of slow adsorption (no rate-limiting steps). Conditions when the nonuniform character of real catalytic surfaces should be taken into account in modeling of the selectivity behavior are discussed.     

Averaging of nonlinearity-managed pulses

We consider the nonlinear Schrodinger equation with the nonlinearity management which describes Bose-Einstein condensates under Feshbach resonance. By using an averaging theory, we derive the Hamiltonian averaged equation and compare it with other averaging methods developed for this problem. The averaged equation is used for analytical approximations of nonlinearity-managed solitons.     

Devil's staircase of incompressible electron states in a nanotube

It is shown that a periodic potential applied to a nanotube can lock electrons into incompressible states. Depending on whether electrons are weakly or tightly bound to the potential, excitation gaps open up either due to the Bragg diffraction enhanced by the Tomonaga-Luttinger correlations, or via pinning of the Wigner crystal. Incompressible states can be detected in a Thouless pump setup, in which a slowly moving periodic potential induces quantized current, with a possibility to pump on average a fraction of an electron per cycle as a result of interactions.     

Full current statistics of incoherent "cold electrons"

We evaluate the full current statistics (FCS) in the low-dimensional (1D and 2D) diffusive conductors in the incoherent regime eV>E(Th)=D/L(2), E(Th) being the Thouless energy. It is shown that the Coulomb interaction substantially enhances the probability of big current fluctuations for short conductors with E(Th)>1/tau(E), tau(E) being the energy relaxation time, leading to the exponential tails in the current distribution. The current fluctuations are most strong for low temperatures, provided E(Th) approximately [(eV)(2)/Dnu(2)(1)](1/3) for 1D and E(Th) approximately (eV/g)ln(g for 2D, where g is a dimensionless conductance and nu(1) is a 1D density of states. The FCS in the "hot electron" regime is also discussed.     

A molecular dynamics simulation study of the alpha-relaxation in a 1,4-polybutadiene melt as probed by the coherent dynamic structure factor

The dynamic coherent structure factor Scoh(q,t) for a 1,4-polybutadiene (PBD) melt has been investigated using atomistic molecular dynamics simulations. The relaxation of Scoh(q,t) at q = 1.44 angstroms(-1) and q = 2.72 angstroms(-1), corresponding to the first and second peaks in the static structure factor for PBD, was studied in detail over a wide range of temperature. It was found that time-temperature superposition holds for the alpha-relaxation for both q values over a wide temperature range and that the alpha-relaxation can be well described by a stretched (Kohlrauch-William-Watts) exponential with temperature independent but q dependent amplitude and stretching exponent. The alpha-relaxation times for both q values were found to exhibit the same non-Arrhenius temperature dependence, indicating that the same physical processes are responsible for relaxation on both length scales. The alpha-relaxation time was found to depend strongly upon the dynamical range of data utilized in determining the relaxation time, accounting for qualitative discrepancies between alpha-relaxation times reported here and those extracted for PBD from experimentally measured Scoh(q,t).     

Poisson deformations of symplectic quotient singularities

We establish a connection between smooth symplectic resolutions and symplectic deformations of a (possibly singular) affine Poisson variety.In particular, let V be a finite-dimensional complex symplectic vector space and G⊂Sp(V) a finite subgroup. Our main result says that the so-called Calogero-Moser deformation of the orbifold V/G is, in an appropriate sense, a versal Poisson deformation. That enables us to determine the algebra structure on the cohomology of any smooth symplectic resolution X?V/G (multiplicative McKay correspondence). We prove further that if is an irreducible Weyl group and , then no smooth symplectic resolution of V/G exists unless G is of types .     

On the intersection of null spaces for matrix substitutions in a non-commutative rational formal power series

For a rational formal power series in N non-commuting indeterminates, with matrix coefficients, we establish the formula which relates the intersection of the null spaces of coefficients to the intersection of the null spaces of values of this series at N-tuples of $n\times n$ matrices, for n large enough. As an application, we formulate the criteria of observability, controllability, and minimality for a recognizable formal power series representation in terms of matrix substitutions. To cite this article: D. Alpay, D.S. Kalyuzhny??-Verbovetzki??, C. R. Acad. Sci. Paris, Ser. I 339 (2004).     

Delay differential equations for mode-locked semiconductor lasers

We propose a new model for passive mode locking that is a set of ordinary delay differential equations. We assume a ring-cavity geometry and Lorentzian spectral filtering of the pulses but do not use small gain and loss and weak saturation approximations. By means of a continuation method, we study mode-locking solutions and their stability. We find that stable mode locking can exist even when the nonlasing state between pulses becomes unstable.