11 problems

A left-unilateral matrix equation is an equation … where the coefficients $a_r$ and the unknown $x$ are square matrices of the same order, with all coefficients on the left. An ite…

Symmetrized trace conjecture. For matrices of higher degree, the trace of $Q$ is given by the symmetrized-trace expression proposed in the continuation of the source passage.

Let $u=u^{(0)}+u^{(1)}+\ldots+u^{(N)}$ be the order-$N$ approximative standing-wave solution obtained by the iterative procedure, and let $D_b u=0$ denote the Born–Infeld equation,…

Consider the action functional leading to Born–Infeld nonlinear electromagnetism. It is duality-rotation invariant off shell and is known to be a root of an algebraic equation of f…

Finite-origin solution conjecture. There may exist solutions of these field equations that remain finite at $r=0$. The conjecture is motivated by the strong nonlinearity of the fie…

Hidden identity conjecture. The hypergeometric function has the closed form

Fix a time $t$ and let $\phi_1(t,{\boldsymbol{{ q}} })$ and $\pmb{{\cal A}}_1(t,{\boldsymbol{{ q}} })$ be the scalar and vector electromagnetic potentials used in the Hamilton–Jaco…

Let the Maxwell–Born–Infeld fields be generated by generic smooth subluminal point-source motions, and let their electromagnetic potentials be represented in the Lorenz–Lorentz gau…

Let the Maxwell–Born–Infeld field equations have point charge sources, and let (P), (W), (M), (E), and (D) denote the properties specified earlier in the paper. Consider generic sm…

Let the BI manifold be the $6$-dimensional submanifold of $(h,Q,D,B)\in R^{10}$ defined by … The augmented Born–Infeld (ABI) system is the $10\times 10$ system obtained by adjoinin…

Let $p$ and $q$ be the matrices defined by … and let $Q$ be determined perturbatively by … Here ${\cal S}_{p,q}$ denotes the operation that reorders each term of a power-series exp…