Abstract Plant protection products are currently the main part of crop cultivation technologies not only in Krasnoyarsk territory, but also around world. The most promising way to protect plants from pests is an integrated system that involves use chemical control agents cases where pest population exceeds economic threshold, and effectiveness increase natural mechanisms for regulating number c...

In this paper we present an effective method for computing certain real coefficients λn which appear in a criterion for the Riemann hypothesis proved by Xian-Jin Li. With the use of this method a sequence of two-thousand λn’s has been calculated. This sequence reveals a peculiar and unexpected behavior: it can be split into a strictly growing trend and some tiny oscillations superimposed on thi...

In this note we begin by resolving (in the negative) a question posed by Paz [6, Open Problem 1, p. 65] concerning the existence of an effective procedure for determining whether a recursively specified "probabilistie input-output relation" is of finite rank. To show that such an algorithm does not exist, it is enough to prove the undecidability of the corresponding problem for "probabilistic w...

Let h(x, y) be a non-degenerate binary cubic form with integral coefficients, and let S be an arbitrary finite set of prime numbers. By a classical theorem of Mahler, there are only finitely many pairs of relatively prime integers x, y such that h(x, y) is an S-unit. In the present paper, we reverse a well-known argument, which seems to go back to Shafarevich, and use the modularity of elliptic...