Some recent developments in the transmutation operator approach

This is a brief overviewof some recent developments in the transmutation operator approach to practical solution of mathematical physics problems. It introduces basic notions and results of transmutation theory, and gives a brief historical survey with some important references. Mainly applications to linear ordinary and partial differential equations and to related boundary value and spectral problems are discusse

On some generalizations of the properties of the multidimensional generalized Erdélyi-Kober operators and their applications

In this paper we investigate the composition of a multidimensional generalized Erdélyi-Kober operator with differential operators of high order. In particular, with powers of the differential Bessel operator. Applications of proved properties to solving the Cauchy problem for a multidimensional polycaloric equation with a Bessel operator are show

Transmutation operators as a solvability concept of abstract singular equations

One of the methods of studying differential equations is the transmutation operators method. Detailed study of the theory of transmutation operators with applications may be found in the literature. Application of transmutation operators establishes many important results for different classes of differential equations including singular equations with Bessel operato

Fractional Bessel integrals and derivatives on semi-axes

In this paper we study fractional powers of the Bessel differential operator. The fractional powers are defined explicitly in the integral form without use of integral transforms in its definitions. Some general properties of the fractional powers of the Bessel differential operator are proved and some are listed. Among them are different variations of definitions, relations with the Mellin and Hankel transforms, group property, evaluation of resolvent integral operator in terms of the Wright or generalized Mittag-Leffler function

Concentrations of 90Sr in the tooth tissues 60 years after intake : results of TL measurements and applications for Techa River dosimetry

This article focuses on the study of 90Sr in the tooth tissues of Techa riverside residents 60 years after intake. The Techa River was contaminated by radioactive wastes in the 1950s. Contamination of the river system, including water, bottom sediment, floodplain soil, and grass, depended on the distance from the source of releases. Therefore, the average 90Sr intake was different in different settlements located downstream the river. An additional factor influencing 90Sr accumulation in the teeth is the rate of tissue mineralization at the time of intake which depended on the donor\u2019s age at the time of releases. Measurements of 90Sr concentration in various dental tissues (enamel, crown, and root dentin) of 166 teeth were performed about 60 years after the main intake using the method of thermoluminescence passive beta detection. The paper presents the current levels of tooth tissue contamination, and the tooth-to-tooth variability of 90Sr concentration in tooth tissues was assessed for the tissues which were matured at the time of massive liquid radioactive waste releases into the Techa River. A model describing the expected levels of 90Sr in matured dental tissues depending on age and intake has been elaborated for the population under study. The results obtained will be used for calculation of internal dose in enamel and for interpretation of tooth doses measured by means of the electron paramagnetic resonance method, among the population of the Techa River region