Unconditional Bases, the Matrix Muckenhoupt Condition, and Carleson Series in a Spectrum

Two families of functions constructed by a system of n scalar Muckenhoupt weights are studied. Criteria are given under which these families are unconditional bases. From the point of view of the spectral operator theory, the problem is reduced to the study of the structure of n-dimensional perturbations of the integration operator. Weighted estimates for the Hilbert transform in the spaces of vector-functions are applied to construct an operator mapping functions of the studied families to vector-valued rational functions. The concept of the Carleson series is used in the study of the following problem: when do vector-valued rational functions form an unconditional basis? Bibliography: 8 titles.     

Effect of trapping centers of luminescent properties of bismuth orthogermanate

Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 54, No. 6, pp. 970–975, June, 1991.     

Self-transparency effect in a twisted nematic liquid crystal cell

In a twisted nematic liquid crystal cell we report and study the self-transparency effect induced by the creation of an isotropic droplet. A simple theoretical model is presented and good agreement with experimental data is found. In a two beams configuration transistor-like behavior is observed and theoretically discussed.     

Isolation of singularities in the density and the kernel of a two-dimensional integral equation for complex boundary surfaces

We consider the solution of integral equations in problems of three-dimensional electromagnetic fields in piecewise-homogeneous media. An algorithm is proposed for analytical isolation of singularities in the kernel and the density of the integral equation of potential theory for the case of complex boundary surfaces.Translated from Vychislitel'naya i Prikladnaya Matematika, No. 56, pp. 14–17, 1985     

Applications of coupled LC-GC: A review

Although coupled liquid chromatographygas chromatography (LC-GC) was first demonstrated ten years ago, only in the last few years has there been a sudden surge of interest in the technique. Approximately 70% of the total number of LC-GC applications have been published in the last two years (1987–88) alone. This review categorizes LC-GC publications into four main application areas: fossil fuels, foods, environmental samples, biologiical/pharmaceutical samples, and miscellaneous samples. Multidimensional separations carried out using other coupled-column chromatographic techniques (such as supercritical fluid chromatography (SFC) with GC, and on-line trace enrichment-GC) have also been included in this review.     

Fluorescence spectra of different configurations of the diphenyl molecule in solid paraffin solutions

Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 51, No. 2, pp. 212–217, August, 1989.     

A Recursive Algorithm for Order Cycle-time that Minimizes Logistics Cost

A firm's logistics cost, including shipping and inventory-carrying, is a substantial percentage of its sales. Nevertheless, typical inventory-control methods ignore or insufficiently represent the shipping cost. This paper describes a recursive algorithm that determines the reorder cycle-time that minimizes total logistics cost. It allows for a realistic accounting of shipping cost, which is modelled here as a function of shipping distance and weight. The algorithm uses a relaxation procedure to identify a suitable initial approximation to the optimal order cycle-time and then, through a series of recursive steps, moves to the optimal result. We demonstrate the algorithm with a single item, with a group of items that share a common order cycle, and with multi-items when item demands are random variables. Experience with this algorithm indicates that it converges to the optimal result in a very few steps.