Noncolliding Squared Bessel Processes

We consider a particle system of the squared Bessel processes with index $\nu > -1$ conditioned never to collide with each other, in which if $-1 < \nu < 0$ the origin is assumed to be reflecting. When the number of particles is finite, we prove for any fixed initial configuration that this noncolliding diffusion process is determinantal in the sense that any multitime correlation function is given by a determinant with a continuous kernel called the correlation kernel. When the number of particles is infinite, we give sufficient conditions for initial configurations so that the system is well defined. There the process with an infinite number of particles is determinantal and the correlation kernel is expressed using an entire function represented by the Weierstrass canonical product, whose zeros on the positive part of the real axis are given by the particle-positions in the initial configuration. From the class of infinite-particle initial configurations satisfying our conditions, we report one example in detail, which is a fixed configuration such that every point of the square of positive zero of the Bessel function $J_{\nu}$ is occupied by one particle. The process starting from this initial configuration shows a relaxation phenomenon converging to the stationary process, which is determinantal with the extended Bessel kernel, in the long-term limit.Comment: v3: LaTeX2e, 26 pages, no figure, corrections made for publication in J. Stat. Phy

Experimental assessment of absorbed dose to mineralized bone tissue from internal emitters: An electron paramagnetic resonance study

EPR resonances attributable to radiation-induced centers in hydroxyapatite were not detectable in bone samples supplied by the USTUR. These centers are the basis for imaging and dose assessment. Presumable, the short range of the alpha particles emitted precluded the formation of appreciable amounts of hydroxyapatite centers. However, one bone sample did offer a suggestion of hydroxyapatite centers and newly-developed methods to extract this information will be pursued

Current issues on EPR dose reconstruction in tooth enamel.

This paper focuses on the opportunities to gain risk assessment information from populations exposed to ionizing radiation. Details are presented on the scale of the nuclear events in several areas within the former Soviet Union. An overview of the issues associated with dose reconstruction by electron paramagnetic resonance (EPR) is given. Principles and outline of the EPR tooth enamel dose assessment are described. Technical details, the latest achievements and the problems of each procedural step are analyzed. In addition, the present accuracy of the EPR dose reconstruction, its problems and cost are discussed