4 problems

Necessity conjecture. If $V$ is surjective on $S$, then there exists a sequence j_n_{n\geq1}\subset\mathbb N such that

Let $V\in\tilde{\mathcal V}^-$ and let $\frak{f}(V)=(a_{ki})$. For ${\mathbf{x}}\in S$, write $\operatorname{supp}({\mathbf{x}})$ for its support, let ${\mathbf e}_j$ denote the…

Let ${\mathcal E}_1$ and ${\mathcal E}_2$ be two $n$-dimensional isomorphic Volterra evolution algebras, and let the corresponding Volterra quadratic stochastic operators be the op…

Let $S^2$ be the two-dimensional simplex, and let $W_\alpha:S^2\to S^2$ be the quadratic stochastic operator defined in the source by equation $W_\alpha$. Assume…