6 problems

Let $\mathcal{E}$ be a complex evolution algebra. An element $u\in\mathcal{E}$ is an idempotent if $u^2=u$. If $\mathcal{E}$ has natural basis $\{e_1,\dots,e_n\}$ and structure mat…

Let $n\in\mathbb{N}$. A field $\mathbb{K}$ is an $n$-FSEANI if the parametric family of systems of equations given by (EE) has a non-zero solution in $\mathbb{K}$ for every choice…

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…

Graph evolution-algebra isomorphism conjecture.

Let $E$ be an $n$-dimensional non-nilpotent evolution algebra satisfying condition $P$. Let $ES_1$ denote the one-dimensional evolution algebra used in the source, let…

Let $A=(a_{i,j})_{1\leq i,j\leq n}$ be a complex invertible matrix, and let $x_1,\dots,x_n$ be complex variables. Nonvanishing solution conjecture. The system … has a solution…