A Generalized Quasi-Likelihood Estimator for Nonstationary Stochastic Processes−Asymptotic Properties and Examples

2010 Mathematics Subject Classification: 62F12, 62M05, 62M09, 62M10, 60G42.

Existence of Solutions for a Class of Quasi-Linear Singular Integro-Differential Equations

2000 Mathematics Subject Classification: 45F15, 45G10, 46B38.

On Nilpotent Subsemigroups in some Matrix Semigroups

2000 Mathematics Subject Classification: 20M20, 20M10.

Spatio-temporal generation regimes in quasi-CW Raman fiber lasers

We present experimental measurements of intensity spatiotemporal dynamics in quasi-CW Raman fiber laser. Depending on the power, the laser operates in different spatio-temporal regimes varying from partial mode-locking near the generation threshold to almost stochastic radiation and a generation of short-lived pulses at high power. The transitions between the generation regimes are evident in intensity spatio-temporal dynamics. Two-dimensional auto-correlation functions provide an additional insight into temporal and spatial properties of the observed regimes.

On Quasi-Normality of Two-Sided Multiplication

2000 Mathematics Subject Classification: 47B47, 47B10, 47A30.

Normal and Normally Outer Automorphisms of Free Metabelian Nilpotent Lie Algebras

2000 Mathematics Subject Classification: 17B01, 17B30, 17B40.

Oscillation Criteria of Second-Order Quasi-Linear Neutral Delay Difference Equations

2000 Mathematics Subject Classification: 39A10.

Ginzburg-Landau turbulence in quasi-CW Raman fiber lasers

Fiber lasers operating via Raman gain or based on rare-earth-doped active fibers are widely used as sources of CW radiation. However, these lasers are only quasi-CW: their intensity fluctuates strongly on short time scales. Here the framework of the complex Ginzburg-Landau equations, which are well known as an efficient model of mode-locked fiber lasers, is applied for the description of quasi-CW fiber lasers. The vector Ginzburg-Landau model of a Raman fiber laser describes the experimentally observed turbulent-like intensity dynamics, as well as polarization rogue waves. Our results open debates about the common underlying physics of operation of very different laser types - quasi-CW lasers and passively mode-locked lasers. Fiber lasers operating via Raman gain or based on rare-earth-doped active fibers are widely used as sources of CW radiation. However, these lasers are only quasi-CW: their intensity fluctuates strongly on short time scales. Here the framework of the complex Ginzburg-Landau equations, which are well known as an efficient model of mode-locked fiber lasers, is applied for the description of quasi-CW fiber lasers. The vector Ginzburg-Landau model of a Raman fiber laser describes the experimentally observed turbulent-like intensity dynamics, as well as polarization rogue waves. Our results open debates about the common underlying physics of operation of very different laser types - quasi-CW lasers and passively mode-locked lasers.

Quantization of the Inhomogeneous Bianchi I model:quasi-Heisenberg picture

The quantization scheme is suggested for a spatially inhomogeneous 1+1 Bianchi I model. The scheme consists in quantization of the equations of motion and gives the operator (so called quasi-Heisenberg) equations describing explicit evolution of a system. Some particular gauge suitable for quantization is proposed. The Wheeler-DeWitt equation is considered in the vicinity of zero scale factor and it is used to construct a space where the quasi-Heisenberg operators act. Spatial discretization as a UV regularization procedure is suggested for the equations of motion.

Synergistic synthesis of quasi-monocrystal CdS nanoboxes with high-energy facets

Hollow nanostructures with a highly oriented lattice structure and active facets are promising for catalytic applications, while their preparation via traditional approaches contains multiple steps and is time and energy consuming. Here, we demonstrate a new one-step strategy involving two complementary reactions which promote each other; it is capable of producing unique hollow nanoparticles. Specifically, we apply synergic cooperation of cation exchange and chemical etching to attack PbS nanosized cubes (NCs) and produce CdS quasi-monocrystal nanoboxes (QMNBs) which possess the smallest dimensions reported so far, a metastable zinc-blende phase, a large specific surface area, and particularly high-energy {100} facets directly visualized by aberration-corrected scanning transmission electron microscopy. These properties in combination allow the nanoboxes to acquire exceptional photocatalytic activities. As an extension of the approach, we use the same strategy to prepare Co9S8 and Cu7.2S4 single-crystal hollow nanooctahedrons (SCHNOs) successfully. Hence, the synergic reaction synthesis strategy exhibits great potential in engineering unique nanostructures with superior properties.

Extreme value statistics in quasi-CW Raman fiber lasers

It is found that rare extreme events are generated in a Raman fiber laser. The mechanism of the extreme events generation is a turbulent-like four-wave mixing of numerous longitudinal generation modes. © 2012 OSA.

Radiation build-up in laminar and turbulent regimes in quasi-CW Raman fiber laser

We study the radiation build-up in laminar and turbulent generation regimes in quasi-CW Raman fiber laser. We found the resulted spectral shape and generation type is defined by the total spectral broadening/narrowing balance over laser cavity round-trip, which is substantially different in different regimes starting from first round-trips of the radiation build-up. In turbulent regime, the steady-state is reached only after a few round-trips, while in the laminar regime the laser approaches the equilibrium spectrum shape asymptotically.

Computation of rare transitions in the barotropic quasi-geostrophic equations

We investigate the theoretical and numerical computation of rare transitions in simple geophysical turbulent models. We consider the barotropic quasi-geostrophic and two-dimensional Navier–Stokes equations in regimes where bistability between two coexisting large-scale attractors exist. By means of large deviations and instanton theory with the use of an Onsager–Machlup path integral formalism for the transition probability, we show how one can directly compute the most probable transition path between two coexisting attractors analytically in an equilibrium (Langevin) framework and numerically otherWe adapt a class of numerical optimization algorithms known as minimum action methods to simple geophysical turbulent models. We show that by numerically minimizing an appropriate action functional in a large deviation limit, one can predict the most likely transition path for a rare transition between two states. By considering examples where theoretical predictions can be made, we show that the minimum action method successfully predicts the most likely transition path. Finally, we discuss the application and extension of such numerical optimization schemes to the computation of rare transitions observed in direct numerical simulations and experiments and to other, more complex, turbulent systems.

Langevin dynamics, large deviations and instantons for the quasi-geostrophic model and two-dimensional Euler equations

We investigate a class of simple models for Langevin dynamics of turbulent flows, including the one-layer quasi-geostrophic equation and the two-dimensional Euler equations. Starting from a path integral representation of the transition probability, we compute the most probable fluctuation paths from one attractor to any state within its basin of attraction. We prove that such fluctuation paths are the time reversed trajectories of the relaxation paths for a corresponding dual dynamics, which are also within the framework of quasi-geostrophic Langevin dynamics. Cases with or without detailed balance are studied. We discuss a specific example for which the stationary measure displays either a second order (continuous) or a first order (discontinuous) phase transition and a tricritical point. In situations where a first order phase transition is observed, the dynamics are bistable. Then, the transition paths between two coexisting attractors are instantons (fluctuation paths from an attractor to a saddle), which are related to the relaxation paths of the corresponding dual dynamics. For this example, we show how one can analytically determine the instantons and compute the transition probabilities for rare transitions between two attractors.