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An original approach is proposed to solve rather complex probabilistic problems of the readout of random discrete-point fields; these problems lack an exact analytical solution. Schemes are proposed for the direct, iterative, and combinatorially recursive analytical calculation of multidimensional integral expressions that describe the partial solutions of… (More)
The novelty and originality of the presented studies consists of the fact that the rigorous mathematical proof of one of relationships that describe the probability of an error-free reading of random discrete images contained in them was previously found by the authors using specially created programs for computer analytical calculations.
A way to use an algorithm for compensating for linear distortions for solving a set of linear algebraic equations with a band matrix is examined. The relationships needed for step-by-step finding of a solution are generated, and the framework in which the relationships are correct is determined.
Original programming, combinatorial, and geometric schemes are presented. They have been developed and used by the authors to calculate exact analytical formulas that describe the probability of the formation of local groups of a given size in random point images. Formulas, which will be discussed below, arise in the assessment of the reliability detection… (More)