The purpose of this paper is to review basic radiation biology and associated terminology to impart a better understanding of the importance of basic concepts of ionizing radiation interactions with living tissue. As health care workers in a field that utilizes ionizing radiation, nuclear medicine technologists are concerned about the possible acute and chronic effects of occupational radiation...

QCD coherence effects in initial state radiation at small x in deep inelastic scattering in HERA kinematics are studied with the help of the Monte Carlo model SMALLX. Theoretical assumptions based on the CCFM evolution equation are reviewed and the basic properties of the partonic final states are investigated. The results are compared with those obtained in the conventional DGLAP evolution sch...

The effect of UV beam, which has been emitted from a natural or a manmade source on cells has been studied in previous studies for several times. Radiation of this beam can have different effects on DNA of the cell, cytotoxicity, the structure of cellular proteins and their mechanical properties based on radiation period or frequency. The effect of radiation of two types of beams, namely UVB an...

In this talk basic general properties of f -divergences, including their axiomatic, and some important classes of f -divergences are presented. Without essential loss of insight we restrict ourselves to discrete probability distributions and note that the extension to the general case relies strongly on the Lebesgue-Radon-Nikodym Theorem.

This technical report summarized facts from the basic theory of generalized closure spaces and gives detailed proofs for them. Many of the results collected here are well known for various types of spaces. We have made no attempt to find the original proofs. 1. Set-Valued Set-Functions 1.1. Closure, Interior, Neighborhood, and Convergent. In this section, which in part generalizes the results o...

We use the following convention: x, t, t1, t2, r, a, b are real numbers and F , G are partial functions from R to R. Let F be a partial function from R to R and let t be a real number. We say that t is a period of F if and only if: (Def. 1) t 6= 0 and for every x holds x ∈ domF iff x+t ∈ domF and if x ∈ domF, then F (x) = F (x+ t). Let F be a partial function from R to R. We say that F is perio...

In this work, we define angles between vectors and between three points. Building on this, we prove basic geometric properties of triangles, such as the Isosceles Triangle Theorem, the Law of Sines and the Law of Cosines, that the sum of the angles of a triangle is π, and the congruence theorems for triangles. The definitions and proofs were developed following those by John Harrison in HOL Lig...

Convex polytopes are fundamental geometric objects that have been investigated since antiquity. The beauty of their theory is nowadays complemented by their importance for many other mathematical subjects, ranging from integration theory, algebraic topology, and algebraic geometry (toric varieties) to linear and combinatorial optimization. In this chapter we try to give a short introduction, pr...