Approximation of the basic characteristics of the auditory analyzer

Empirical approximating formulas describing the most important psychophysiological properties of the human auditory analyzer are derived.     

Predictive control of periodic-review production inventory systems with deteriorating items

In this paper a predictive control strategy is applied to a periodic-review dynamic inventory system with deteriorating items. Given the current inventory level, we determine the optimal production rates to be implemented at the beginning of each of the following periods over the control horizon. The effectiveness of this approach is the use of future information of the inventory target level and the desired production rate, which are available, along the fixed horizon. The deterioration coefficient may be known or unknown and both cases are considered. In the case where it is unknown, the self-tuning predictive control is applied. The proposed control algorithms are illustrated by simulations.     

Applying Cognition-Based Assessment to Elementary School Students' Development of Understanding of Area and Volume Measurement

As part of a discussion of cognition-based assessment (CBA) for elementary school mathematics, I describe assessment tasks for area and volume measurement and a research-based conceptual framework for interpreting students' reasoning on these tasks. At the core of this conceptual framework is the notion of levels of sophistication. I provide details on an integrated set of levels for area and volume measurement that (a) starts with the informal, preinstructional reasoning typically possessed by students, (b) ends with the formal mathematical concepts targeted by instruction, and (c) indicates cognitive plateaus reached by students in moving from (a) to (b).     

Symmetry of internal dynamics of the tetrahydrofuran molecule

A noninvariant geometrical group characterizing the internal dynamics of the tetrahydrofuran molecule C₄H₈O with allowance for the clearly pronounced pseudorotation effect is constructed. On this basis, some qualitative features of the energy spectrum of the molecule following from the analysis of high-resolution spectroscopic data are explained.     

Recording dynamic holograms in a semiconductor crystal CdF<Subscript>2</Subscript>:In

The kinetics of decay of a phase hologram in a semiconductor CdF₂ crystal with bistable In centers is studied. Kinetic constants of the hologram decay are found, and the potential relief of the bistable center is plotted. The resolving power of the crystal is evaluated and recording of a transparency is demonstrated.     

Electronic excitation energy transfer between dye molecules in H<Subscript>2</Subscript>O and D<Subscript>2</Subscript>O solutions in the micellar phase

Processes of electronic excitation energy transfer (EEET) in H₂O+D₂O solutions within reversed micelles with different degrees of hydration were studied. It is ascertained that the structure of solutions forms a cluster distribution of interacting molecules having a fractal dimensionality. As a result, in regions with a locally high concentration of the dye molecules, an increase in the EEET efficiency is observed. Solubilization by reversed micelles leads to destruction of the cluster structure of the water system, with the dependence of the EEET efficiency on the degree of hydration being nonmonotonic. As the degree of hydration increases, the inhomogeneities of the structure inherent in bulk water are restored.     

Effective Values of Variable Components of the Refractive Index upon Nonlinear Recording of Phase Holograms

The diffraction of a plane wave incident on a thick hologram at the first and second Bragg angles in the process of nonlinear recording is analyzed using the coupled-wave equations. It is shown that, in this case, the two-wave approximation with the use of effective modulation amplitudes of the refractive index, n _1ef and n _2ef, can be applied. Analytical dependences of n _1ef and n _2ef on the modulation amplitudes of the refractive index n ₁ and n ₂ at the fundamental and doubled spatial frequencies are obtained and the criteria of their applicability are determined. The dependences found are used to calculate the parameters of gratings recorded in a photopolymeric material.     

Absorption of electromagnetic radiation by an inhomogeneous spherical particle

The cross section of absorption of electromagnetic radiation by an inhomogeneous spherical particle is calculated. The general case of an arbitrary value of the ratio of the particle radius to the radius of the dielectric core is considered. The condition of diffuse reflection of electrons from the inner and outer surfaces of the metal layer of the particle is taken as the boundary condition of the problem. The limiting cases are considered and the results obtained are discussed.     

Computer processing of electronic absorption spectra of rare-earth elements in inorganic laser media

Algorithms and program modules are developed for calculation of the Judd-Ofelt parameters on modern computers. These programs can be used to perform numerical analysis of the energy absorption by rareearth ions in laser media.