In the paper, the problem of simultaneous approximation of a pair of analytic functions by a pair of discrete shifts of the periodic and periodic Hurwitz zeta-function is considered. The above shifts are defined by using the sequence of imaginary parts of non-trivial zeros of the Riemann zeta-function. For the proof of approximation theorems, a weak form of the Montgomery pair correlation conjecture is applied.

In the paper, we obtain universality theorems and a lower estimate for the number of zeros for the composition F ζ (s, α; a, b) , where F is an operator in the space of analytic functions satisfying the Lipschitz type condition, and ζ (s, α; a, b) is a collection consisting of periodic and periodic Hurwitz zeta-functions.

In the paper, we obtain that certain linear and more general combinations of Dirichlet L-functions and Hurwitz zeta-functions have infinitely many zeros in the critical strip. For the proof, universality of those combinations is applied.

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In many fields of human activities such as economics, sustainable development, construction, human resources management etc., dichotomous tests are employed to measure some observed property, for example knowledge level in a specific field or applicant’s eligibility for a job position. Fuzzy classification method for dichotomous test items is proposed in this paper. Depending on the observed property, each test item may well differentiate all testees or only the testees who are strong or weak at that property. Also, the test item may badly differentiate all testees and be inappropriate for that purpose. The method presented in the paper may be applied for small groups of testees with known estimates of the investigated property, for example raw test scores. The proposed method for dichotomous test item classification is based on the fuzzy set theory. Though the tests were originally constructed for knowledge measurement, their mathematical models can be applied for social indicators and wide range of other areas.