We investigate non-equilibrium particle transport in a system consisting of a geometric scatterer and two leads coupled to heat baths with different chemical potentials. We derive an expression for the corresponding current, the carriers of which are fermions, and analyze numerically its dependence on the model parameters in examples where the scatterer has a rectangular or triangular shape.

Parametric option pricing models are widely used in finance. These models capture several features of asset price dynamics; however, their pricing performance can be significantly enhanced when they are combined with nonparametric learning approaches that learn and correct empirically the pricing errors. In this article we propose a new nonparametric method for pricing derivatives assets. Our method relies on the state price distribution instead of the state price density, because the former is easier to estimate nonparametrically than the latter. A parametric model is used as an initial estimate of the state price distribution. Then the pricing errors induced by the parametric model are fitted nonparametrically. This model-guided method, called automatic correction of errors (ACE), estimates the state price distribution nonparametrically. The method is easy to implement and can be combined with any model-based

The paper is devoted to a model of a mesoscopic system consisting of a pair of parallel planar waveguides separated by an infinitely thin semitransparent boundary modeled by a transverse interaction. We develop the BirmanSchwinger theory for the corresponding generalized Schrdinger operator. The spectral properties become nontrivial if the barrier coupling is not invariant with respect to longitudinal translations, in particular, there are bound states if the barrier is locally more transparent in the mean and the coupling parameter reaches the same asymptotic value in both directions along the guide axis. We derive the weak-coupling expansion of the ground-state eigenvalue for the cases when the perturbation is small in the supremum and the <b>L</b>¹-norms. The last named result applies to the situation when the support of the leaky part shrinks: the obtained asymptotics differs from that of a double guide divided

In the paper [4], the authors proposed a derivative-free descent algorithm for the nonlinear complementarity problems (NCPs) by the generalized Fischer-Burmeister merit function: p (a, b)= 1

The mutual intensity and its equivalent phase-space representations quantify an optical field's state of coherence and are important tools in the study of light propagation and dynamics, but they can only be estimated indirectly from measurements through a process called coherence retrieval, otherwise known as phase-space tomography. As practical considerations often rule out the availability of a complete set of measurements, coherence retrieval is usually a challenging high-dimensional ill-posed inverse problem. In this paper, we propose a trace-regularized optimization model for coherence retrieval and a provably convergent adaptive accelerated proximal gradient algorithm for solving the resulting problem. Applying our model and algorithm to both simulated and experimental data, we demonstrate an improvement in reconstruction quality over previous models as well as an increase in convergence speed compared to existing first-order methods.