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A four-vector field in flat space-time, satisfying a gauge-invariant set of second-order differential equations, is considered as a unified field. The model variational principle corresponds to the general covariance idea and gives rise to…

In this paper we study the center algebras of multilinear forms. It is shown that the center of a nondegenerate multilinear form is a finite dimensional commutative algebra and can be effectively applied to its direct sum decompositions. As…

Formulas are presented for the recursive generation of four-body integrals in which the integrand consists of arbitrary integer powers (>= -1) of all the interparticle distances r_ij, multiplied by an exponential containing an arbitrary…

For certain problems involving vector fields, it is possible to find an associated imaginary field that, in conjunction with the first, forms a complex field for which the equation can be solved. This result is generalized to arbitrary…

In this paper we derive some basic results of circuit theory using `Implicit Linear Algebra' (ILA). This approach has the advantage of simplicity and generality. Implicit linear algebra is outlined in [1]. We denote the space of all vectors…

One of the various versions of the classical Lyapunov-Poincar\'e center theorem states that a nondegenerate real analytic center type planar vector field singularity admits an analytic first integral. In a more proof of this result, R.…

We observe that a particular first integral of the partially-averaged system in the secular theory of the three-body problem appears also as an important conserved quantity of integrable Kepler billiards. In this note we illustrate their…

To a finite dimensional representation of a complex Lie group $G$, an associative algebra of adjoint covariant polynomial maps from the direct sum of $m$ copies of the Lie algebra $\mathfrak{g}$ of $G$ into an algebra of complex matrices is…

Let $\mathbb{F}_p$ be the prime field of order $p>0$ and $G$ be an elementary abelian $p$-group.For some $n$-dimensional cohyperplane $G$-representations $V$ over $\mathbb{F}_p$, we show that $\mathbb{F}_p[V\oplus V^*]^G$, the invariant…

We compute Balmer's prime spectrum for the derived category of quiver representations for a finite ordered quiver and show that it does not recover the quiver. We then associate an algebra to every k-linear triangulated tensor category and…

The bivariate difference field provides an algebraic framework for a sequence satisfying a recurrence of order two. Based on this, we focus on sequences satisfying a recurrence of higher order, and consider the multivariate difference…

We consider absolutely free nonassociative algebras and, more generally, absolutely free algebras with (maybe infinitely) many multilinear operations. Such algebras are described in terms of labeled reduced planar rooted trees. This allows…

We consider the one-loop effective action due to a spinor loop coupled to an abelian vector and axial vector field background. After rewriting this effective action in terms of an auxiliary non-abelian gauge connection, we use the De Witt…

We make two observations regarding the invertibility of Keller maps. i.e., polynomial maps for which the determinant of their Jacobian matrix is identically equal to 1. In our first result, we show that if P is a n-dimensional Keller map,…

We introduce a family of nonnegative integer vectors - primitive vectors - defining hyperplanes of the real affine cube over $C^n:=\{-1,1\}^n$ and study their properties with respect to the rectangles of the cube. As a consequence we give a…

By definition, reciprocal matrices are tridiagonal $n$-by-$n$ matrices $A$ with constant main diagonal and such that $a_{i,i+1}a_{i+1,i}=1$ for $i=1,\ldots,n-1$. For $n\leq 6$, we establish criteria under which the numerical range…

Let $\mathcal{A}$ and $\mathcal{B}$ be two factor von Neumann algebras and $\eta$ be a non-zero complex number. A nonlinear bijective map $\phi:\mathcal A\rightarrow\mathcal B$ has been demonstrated to satisfy…

Effective Riemann space effect of vacuum nonlinear electrodynamics is considered in the context of theory for unified gravitation and electromagnetism. The electromagnetic four-vector potential in the scope of Born-Infeld nonlinear…

We first generalize a classical iteration formula for one variable holomorphic mappings to a formula for higher dimensional holomorphic mappings. Then, as an application, we give a short and intuitive proof of a classical theorem, due to H.…

Let F be a finite extension of Qp and G be GL(2,F). When V is the tensor product of three admissible, irreducible, finite dimensional representations of G, the space of G-invariant linear forms has dimension at most one. When a non zero…