STRUCTION OF MATHEMATICAL MODEL IN CHANGES OF NUMBERS RED BLOOD CELLS IN PRESERVED BLOOD OF ANIMALS BY SAVING

Abstract

In the work we can see a problem of building mathematical model in changes of numbers red blood cells in preserved blood of animals by saving, which is based on the results of experimental work. Red blood cell are playing very important role in metabolic processes of animal structure. And that's why, its important condition for getting new researches by learning dynamics of numbers red blood cells and their functional state. Mathematical model of any process including biochemical, allows to get information what we need without making a great experiment, often predetermined complexity of method and expensively of experimental researches. For building mathematical model of dependence save mend red blood cells in preserved blood in type preserving environment and it used some elements of mathematical statistics, namely: structure equation of regression, which is based on analysis of received results. The line and also graphs, which are built in a system of rectangular coordinates based on empirical dates.

Therefore, we can express form of communication by the equation:

         where: a - the value of resultant variable, x - value of factor variable, b - desired parameters.

         Regression coefficient will have positive value, in direct connection between correlated signs at the back - negative.

         If the value of effective signs y changing strictly proportional to the change of factor sing x, then the expected value y_i could accurately calculated by the set value x_i. In real terms the observed values x_i will differ from expected values y_i by an amount ε_i. That we get some distribution abnormalities:

         As the difference is smaller then pattern emerges link between the signs is clearer. Therefore, in determining the options is to find a form of communication that would ensure minimum deviations. Since the deviation have different signs, that are required to provide a minimum sum of squared deviations:

where n - number of investigated values, n > 2.

         Method of least squares in the method which include unknown parameters are selected to meet the requirements.

         Of the value of ε apply the theory of extremes, we get the conditions necessary for the determination of unknown parameters a and b:

         The equations called normal equations (the number of normal equations equals the number of parameters).

         Let's do determining the parameters of the linear dependents equation of a, b by method of least squares. To determine the unknown parameters equation           y = ax + b we should build a system of two equations and solve it in relation to the unknown a, b.

         The system of normal equations will be as follows:

 (1)

         Solution system (1) is:

A built equation of regression allows to predict changes, which are stating in this biological system with large degree of probability and it allows to see quantitative measure of power that or another factor (or complex) on results.

Numerical example is given.