A holistic model for biological mass exchange
type: Item
instance of: scholarly article
title: A holistic model for biological mass exchange
zbMATH Open document ID: 0671.92007
DOI: 10.1016/0895-7177(88)90176-8
published in: Mathematical and Computer Modelling
publication date: 1988-01-01T00:00:00Z
review text: 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.
reviewed by: J.Peil
Mathematics Subject Classification ID: 92Cxx
Mathematics Subject Classification ID: 15A99
Mathematics Subject Classification ID: 76Z05
zbMATH DE Number: 4099100
zbMATH Keywords: holistic modelling of flow processes
zbMATH Keywords: organismic systems
zbMATH Keywords: mass exchanges
zbMATH Keywords: chemical reactions
zbMATH Keywords: vectrix
zbMATH Keywords: kidney
zbMATH Keywords: polydrix
zbMATH Keywords: vinis
zbMATH Keywords: obliteration operator
zbMATH Keywords: Hadamard product
zbMATH Keywords: contracted product
author: Selmo Tauber
MaRDI profile type: Publication
full work available at URL: 0895-7177(88)90176-8
OpenAlex ID: W2073389031
Wikidata QID: Q113881659
cites work: Lumped parameters and scators
cites work: Q5731897
cites work: An application of the Hadamard product to air pollution
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description: scientific article; zbMATH DE number 4099100