The structure of Gelfand-Levitan-Marchenko type equations for Delsarte transmutation operators of linear multi-dimensional differential operators and operator pencils. Part 1

An analog of Gelfand-Levitan-Marchenko integral equations for multi- dimensional Delsarte transmutation operators is constructed by means of studying their differential-geometric structure based on the classical Lagrange identity for a formally conjugated pair of differential operators. An extension of the method for the case of affine pencils of differential operators is suggested.Comment: 12 page

Light Curves and Period Changes of Type II Cepheids in the Globular Clusters M3 and M5

Light curves in the B, V, and I_c passbands have been obtained for the type II Cepheids V154 in M3 and V42 and V84 in M5. Alternating cycle behavior, similar to that seen among RV Tauri variables, is confirmed for V84. Old and new observations, spanning more than a century, show that V154 has increased in period while V42 has decreased in period. V84, on the other hand, has shown large, erratic changes in period that do not appear to reflect the long term evolution of V84 through the HR diagram.Comment: 28 pages, 12 figure

Toward a Comprehensive Approach to the Collection and Analysis of Pica Substances, with Emphasis on Geophagic Materials

Pica, the craving and subsequent consumption of non-food substances such as earth, charcoal, and raw starch, has been an enigma for more than 2000 years. Currently, there are little available data for testing major hypotheses about pica because of methodological limitations and lack of attention to the problem.In this paper we critically review procedures and guidelines for interviews and sample collection that are appropriate for a wide variety of pica substances. In addition, we outline methodologies for the physical, mineralogical, and chemical characterization of these substances, with particular focus on geophagic soils and clays. Many of these methods are standard procedures in anthropological, soil, or nutritional sciences, but have rarely or never been applied to the study of pica.Physical properties of geophagic materials including color, particle size distribution, consistency and dispersion/flocculation (coagulation) should be assessed by appropriate methods. Quantitative mineralogical analyses by X-ray diffraction should be made on bulk material as well as on separated clay fractions, and the various clay minerals should be characterized by a variety of supplementary tests. Concentrations of minerals should be determined using X-ray fluorescence for non-food substances and inductively coupled plasma-atomic emission spectroscopy for food-like substances. pH, salt content, cation exchange capacity, organic carbon content and labile forms of iron oxide should also be determined. Finally, analyses relating to biological interactions are recommended, including determination of the bioavailability of nutrients and other bioactive components from pica substances, as well as their detoxification capacities and parasitological profiles.This is the first review of appropriate methodologies for the study of human pica. The comprehensive and multi-disciplinary approach to the collection and analysis of pica substances detailed here is a necessary preliminary step to understanding the nutritional enigma of non-food consumption