Ink transfer onto the printed surface is provided by parameters as follows: dampening solution in ink emulsification level, dampening solution parameters as long as its ingredients and their exact dosing, dampening solution transfer features between fountain rollers, blanket and printing plate and printed material surface characteristics, thickness and volume of ink on the printing plate, level of ink setting on the imprint. Deviations in transfer from the optimal parameters cause the negative consequences. On the other hand there are hardly any new approaches in explanations of mutual influence of the technological environment parameters in the printing contact which results in lowering the printing process effectiveness while printing with minimal layers of ink-water emulsion. In this article the mutual influence correlations of the printing contact technological environment characteristics are revealed, allowing operating the minimal layers of ink-water emulsion on high-productive machines while normalizing the color reproduction and imprints' quality.

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The mathematical model using the field theory had been used to correct the supply values of the printing ink to set the printing press up for the optimal ink transfer to the imprint. Determining the optimal values of controlling ink supply is figured to be more critical rather than controlling the dampening solution supply, through it availability to be supplied zonally and due to various printing elements area on the printing form. Modelling the process allows to forecast the use of causeconsequential ties in order to achieve the stability of the printing process from the printing machine setup through the print run to the printing finish. Through the vector field with the means of integral calculus the ink transfer to the imprint had been researched. The ink layer thickness had been determined as the cylindrical surface height, with taking into the account its optimal maximal transfer to the printed surface. Gained equations are showcasing the growth of previously con ducted research and allow the more exact understanding of the inktransfer me chanism in the offset printing while utilizing the realistic environment of dampening solution zonal supply adjustment absence. Based on the divergence definition, and also based on the experimentally obtained data, the research of ink optical densities had been conducted, also the colour deviations were researched along the whole imprint's surface in dynamics.

The stochasticity of the ink-water balance in the offset printing process is actually a fact. We have only the rotating speed of the duct dampening roller adjustment to apply the water to the printing plate, and against we have the ink zones which can be opened differently depending on the printing elements quantity. This means that in any way of settings we will definitely have a certain constant amount of water emulsified in a different quantity of ink. This should be so far acceptable as long as we have the wide-latitude inks in terms of tackiness, water acceptance and other rheological properties. As nowadays all modern inks are a little changed in terms of ISO 12647-2 dot gain requirements and they are now more sensitive to the very exact ink/water regulations. If looking in the very idle printing element we can consider it as a figure filled with ink-water emulsion. The water-ink flow can be described with the Ostrogradsky-Gauss formulae: ν ν Ω. A divergence parameter shows the flow density in the field ν which is limited by Ω 1 and Ω 2 surfaces on the continuously-differentiated vector-function which should be determinative in this very point of the field. In terms of vector field flow we can explain the ink/water emulsion transfer from the printing plate to the blanket and afterwards to the imprint using also the theory of mathematical delays concerning the instability of regulations feedback. Therefore we can predict the outcome for ink emulsification in the very exact point in the printing plate and in general also.