Spectral Estimates for Two-Dimensional Schrödinger Operators with Application to Quantum Layers

A logarithmic type Lieb-Thirring inequality for two-dimensional Schrödinger operators is established. The result is applied to prove spectral estimates on trapped modes in quantum layers.     

Exact Connections between Current Fluctuations and the Second Class Particle in a Class of Deposition Models

We consider a large class of nearest neighbor attractive stochastic interacting systems that includes the asymmetric simple exclusion, zero range, bricklayers’ and the symmetric K-exclusion processes. We provide exact formulas that connect particle flux (or surface growth) fluctuations to the two-point function of the process and to the motion of the second class particle. Such connections have only been available for simple exclusion where they were of great use in particle current fluctuation investigations. MSC: 60K35, 82C41     

Optical Implementation of Precise Color Classification Using Computer Controlled Set of Light Emitting Diodes

Accurate color classification by vector subspace method was implemented by simple optical system including computer controlled set of light-emitting diodes and a photo-receiver operating in the integration regime. The technique is capable for fast and precise classification of color distribution within two-dimensional frame with high spatial resolution. The feasibility of the proposed system is shown by a test of four metameric colors, which were correctly distinguished.     

Variational data-analysis method for combining laboratory-measured light-scattering phase functions and forward-scattering computations

A method is developed based on the variational data-analysis formalism to combine laboratory-measured scattering phase functions with forward-scattering phase function computations based on independent size distribution (SD) measurements. The algorithm yields an optimal estimate of the true phase function of the system that is not only based on the measurements and the computational results but also on all available information of the error variances and, if applicable, error covariances of the measured and computed phase functions. The high flexibility of the method is demonstrated by applying it to phase functions of feldspar and fly ash aerosols. Further, the algorithm is employed to determine the asymmetry parameter g of nine different mineral aerosol samples at two different optical wavelengths, and to assess the relative importance of different error sources in the determination of g. It is found that the use of spherical model particles in simulations of g can result in errors on the same order of magnitude as the uncertainty of the refractive index. The use of spherical model particles in computations of forward scattering, however, is found to be only a minor error source.     

Fractional Josephson vortices: oscillating macroscopic spins

Photon-induced band bending changes and subsequent relaxation at the buried insulator/semiconductor interface of BaF₂/Si(001) have been investigated. This is achieved by creating free charge carriers through absorption of a visible pump laser pulse (λ=532 nm, E=2.33 eV) in the silicon, followed by time resolved photoelectron spectroscopy using vacuum-ultraviolet synchrotron radiation (E=18 eV) as a probe of the BaF₂ valence band (VB). Since the excitation takes place in the semiconductor and the probe photoemission signal originates from the BaF₂, the relaxation at the interface has been probed. PACS 41.60.Ap; 33.60.Cv; 79.60.Jv; 73.40.Qv     

Different aspects of the monotonicity of a function

In this paper, we investigate which aspects are overriding in the concept images of monotonicity of Finnish tertiary mathematics students, i.e., on which aspects of monotonicity they base their argument in different types of exercises related to that concept. Further, we examine the relationship between the quality of principal aspects and the success in solving monotonicity exercises and a few other standard problems in calculus. Our findings indicate that a mathematics student's conception about monotone functions is often restricted to continuous or differentiable functions and the algebraic aspect – the nearest one to the formal definition of monotonicity – is rare.     

A Multiobjective Exploratory Procedure for Regression Model Selection

Variable selection is recognized as one of the most critical steps in statistical modeling. The problems encountered in engineering and social sciences are commonly characterized by over-abundance of explanatory variables, nonlinearities, and unknown interdependencies between the regressors. An added difficulty is that the analysts may have little or no prior knowledge on the relative importance of the variables. To provide a robust method for model selection, this article introduces the multiobjective genetic algorithm for variable selection (MOGA-VS) that provides the user with an optimal set of regression models for a given dataset. The algorithm considers the regression problem as a two objective task, and explores the Pareto-optimal (best subset) models by preferring those models over the other which have less number of regression coefficients and better goodness of fit. The model exploration can be performed based on in-sample or generalization error minimization. The model selection is proposed to be performed in two steps. First, we generate the frontier of Pareto-optimal regression models by eliminating the dominated models without any user intervention. Second, a decision-making process is executed which allows the user to choose the most preferred model using visualizations and simple metrics. The method has been evaluated on a recently published real dataset on Communities and Crime Within the United States.     

Theory of parametric amplification in superlattices

We consider a high-frequency response of electrons in a single miniband of superlattice subject to dc and ac electric fields. We show that Bragg reflections in miniband result in a parametric resonance which is detectable using ac probe field. We establish theoretical feasibility of phase-sensitive THz amplification at the resonance. The parametric amplification does not require operation in conditions of negative differential conductance. This prevents a formation of destructive domains of high electric field inside the superlattice.