Related papers: Reduced algebraic conditions for plane/axial tenso…
We establish a convenient necessary and sufficient condition for a multiaffine real polynomial to be stable, and use it to verify that the half-plane property holds for seven small matroids that resisted the efforts of Choe, Oxley, Sokal,…
In this paper, we propose second-order sufficient optimality conditions for a very general nonconvex constrained optimization problem, which covers many prominent mathematical programs.Unlike the existing results in the literature, our…
We derive conditions under which random sequences of polarizations (two-point symmetrizations) converge almost surely to the symmetric decreasing rearrangement. The parameters for the polarizations are independent random variables whose…
We study the Dirac equation in 3+1 dimensions with a general combination of scalar, vector and tensor interactions with arbitrary strengths, all of them described by central Coulomb potentials acting on a particular plane of motion. For the…
In this paper, we introduce the point-exact condition for a Koszul algebra $A$, which is useful for characterizing the (G1) condition of $A$ in the sense of Mori. Let $B = A/(f)$, where $f \in A_2$ is a regular normal element. We show that…
Only a severely restricted class of tensor fields can provide classical spacetime geometries, namely those that can carry matter field equations that are predictive, interpretable and quantizable. These three conditions on matter translate…
We study polynomial Poisson algebras with some regularity conditions. Linear (Lie-Berezin-Kirillov) structures on dual spaces of semi-simple Lie algebras, quadratic Sklyanin elliptic algebras of \cite{FO1},\cite{FO2} as well as polynomial…
New boundary conditions for integrable nonlinear lattices of the XXX type, such as the Heisenberg chain and the Toda lattice are presented. These integrable extensions are formulated in terms of a generic XXX Heisenberg magnet interacting…
Using Lie symmetry methods for differential equations we have investigated the symmetries of a Lagrangian for a plane symmetric static spacetime. Perturbing this Lagrangian we explore its approximate symmetries. It has a non-trivial…
We introduce a third-order differential condition, analogous to nonzero torsion of a curve, which guarantees a submanifold of Euclidean space is totally skew in a small neighborhood. This condition is used to construct improved totally skew…
Constrained Hamiltonian systems fall into the realm of presymplectic geometry. We show, however, that also Poisson geometry is of use in this context. For the case that the constraints form a closed algebra, there are two natural Poisson…
We discuss various compatibility criteria for overdetermined systems of PDEs generalizing the approach to formal integrability via brackets of differential operators. Then we give sufficient conditions that guarantee that a PDE possessing a…
We obtain a necessary and sufficient condition for the existence of equivariant real structures on complex symmetric spaces for semisimple groups and discuss how to determine the number of equivalence classes for such structures.
An optimal control problem for a semilinear elliptic equation of divergence form is considered. Both the leading term and the semilinear term of the state equation contain the control. The well-known Pontryagin type maximum principle for…
The present article includes the enumeration of $n$-polygons with a certain symmetry property: For an even number $n$ of vertices, we count the $n$-polygons with $\frac{n}{2}$ symmetry axes. In addition, if $n$ is a power of 2, we show the…
We derive a necessary condition for the existence of marginally stable circular orbits of test particles in stationary axisymmetric spacetimes which possess a refection symmetry with respect to the equatorial plane; photon orbits are also…
In this paper, we consider p-biharmonic submanifolds of aspace form. We give the necessary and sufficient conditions for a submanifold to be p-biharmonic in a space form. We present some new properties for the stress p-bienergy tensor.
We prove that polyharmonic maps of arbitrary order from complete nonparabolic Riemannian manifolds to arbitrary Riemannian manifolds must be harmonic if certain smallness and integrability conditions hold.
We present quasi-diagonal preconditioners for piecewise polynomial discretizations of pseudodifferential operators of order minus two in any space dimension. Here, quasi-diagonal means diagonal up to a sparse transformation. Considering…
We prove existence of radially symmetric solutions and validity of Euler-Lagrange necessary conditions for a class of variational problems such that neither direct methods nor indirect methods of Calculus of Variations apply. We obtain…