Schmitt mathematics

HS] V. Hutson and K. Schmitt (1992), Permanence in dynamical systems, Mathematical Biosciences 111 1-71. 

The kinetics and mechanisms of chemical reactions in soils have been broadly studied, and comprehensive mathematical models for the particular soil conditions have been presented (Bolt 1979, Huang 2000, Sauve 2001, Schmitt and Sticher 1991, Sparks 1999, Tan 1998). The diversity of ionic species of trace elements and their various affinities to complex inorganic and organic ligands make possible the dissolution of each element over a relatively wide range of pH and Eh. In most soil conditions the effect of pH on the solubility of trace cations is more significant than that of redox potential (Chuang et al. 1996). However, redox potentials of soils also have a crucial impact on the behavior of trace elements (Bartlett 1999). 

It was a long way to go before the genesis of the surface potential differences caused by action potentials deep in the thorax was understood. It was the work of Einthoven and the lead concept that paved the way. It was Burger and van Milaan who introduced the lead vector, making it possible to find the direction to go. Richard McFee replaced the lead vector by the lead field, defined as the electric field set up in the body by a unit current applied to the pick up electrode pair. Otto Schmitt reintroduced the old Helmholtz concept about reciprocity and introduced the concept of transfer impedance already known from the use of four-electrode technique. And it was David Geselowitz who finally put it in the elegant mathematical form. A certain similarity with the Faraday—Maxwell intellectual process runs in our minds. 

Since our model recognizes the separate intracellular and interstitial domains that characterize cardiac tissue, it adopts the formal structure known as the biodomain model (Tung, 1978 Miller and Gezelowitz, 1978). In this model both intracellular and interstitial spaces are assumed to be continuous and congruent ( interpenetrating ) (Schmitt, 1969) but separated everywhere by the cell membrane. These ideas are made more concrete in the following mathematical description. 

Stefan Jebens and Rudiger Weiner, Helmut Podhaisky and Bernhard A. Schmitt, Explicit multi-step peer methods for special second-order differential equations. Applied Mathematics and Computation, 2008, 202, 803-813. 

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