The main value of amaranth lies in its ability to accumulate a large amount protein seeds and leaves. With seed content 15-18%, surpasses wheat (12-14%), rice (7-10%), maize (9-10%), other grain crops. purpose this study was establish the optimal sowing rates for under conditions Western Ukrainian Forest-Steppe zone. employed general scientific methods such as analysis, synthesis, experimentati...

In 1961 Youla published his paper 'On the factorization of rational matrices'. He proved that any proper rational parahermitian matrix, positive definite on the imaginary axis can be factorized as the product of a proper rational matrix, stable with respect to the closed right half plane, and its adjoint. In this paper I prove that for any positive definite, nonstrictly proper matrix this facto...

Let Ω ⊂ R be a bounded domain with smooth boundary, and let K : [0,+∞[→ R be a given continuous function. If n ≥ 2, we denote by A the class of all Carathéodory functions φ : Ω×R → R such that sup (x,t)∈Ω×R |φ(x, t)| 1 + |t|q < +∞ , where 0 < q < n+2 n−2 if n > 2 and 0 < q < +∞ if n = 2. While, when n = 1, we denote by A the class of all Carathéodory functions φ : Ω ×R → R such that, for each r...

The concept of multivariate bijective map of an affine space K over commutative Ring K was already used in Cryptography. We consider the idea of nonbijective multivariate polynomial map Fn of K n into K represented as ”partially invertible decomposition” F (1) n F (2) n . . . F (k) n , k = k(n), such that knowledge on the decomposition and given value u = F (v) allow to restore a special part v...