A holistic model for biological mass exchange (Q1119501)

For a holistic modelling of flow processes in organismic systems which are accompanied by mass exchanges as well as by chemical reactions new algebraic structures are constructed. To represent the changes in such a flow (for instance the flow of blood, i.e. a solution of chemicals in a vessel between two points) the algebraic structure of a so-called vectrix (contraction of vector-matrix) is proposed. To model the organic exchange processes in an exchange organ, like the kidney, or in a group of connected organs more refined, the whole input-output system consisting of a multitude of such reacting and exchanging flows will be described by a more complex structure which is called by the author ``polydrix'', and by operations on it. After introduction of vinis (vectors in integers) and of an obliteration operator the definition of polydrix by its elements is given. For the practical applications considered in the paper polydrices of dimension one, called monodrix, of dim. two, called didrix, and of dim. 3, called tridrix, are of interest. (A monodrix is simply a vector, a didrix a matrix in the usual sense.) Operations on polydrices (equality, addition, scalar multiplication, the Hadamard product of two polydrices and a so-called contracted product of two polydrices) and the operation of reduction of order are explained.