Abstract

Equations related to the sums of the products of multivariate polynomials are studied. One set of polynomials is considered as determined and the other is sought. In the general case of defining polynomials, a series of relationships is obtained for the degrees of polynomials and determinants of matrices composed of polynomial coefficients. On the basis of these relationships and the continuity equation, a number of variants of covariant vectors of limited current density are presented. The results can definitely be considered correct if the accelerations are not too large. The case where the current vector depends on the variable whose value at transition to the stationary state is dictated by the conditions under which such a transition is treated (if these conditions are unknown, then particular elements of uncertainty are possible in the stationary states).

中文翻译：

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多元多项式和协变有界电流向量的构造

摘要

研究了与多元多项式乘积之和有关的方程。一组多项式被认为是确定的，而另一组被寻求。在定义多项式的一般情况下，针对多项式的阶数和由多项式系数组成的矩阵的行列式获得一系列关系。基于这些关系和连续性方程，提出了电流密度受限的协变矢量的许多变体。如果加速度不是太大，则可以肯定认为结果正确。当前向量取决于变量的情况，该变量在过渡到稳态时的值取决于处理这种过渡的条件（如果这些条件未知，