Related papers: Obtaining the multiple Debever null directions
We introduce tensor numerical techniques for solving optimal control problems constrained by elliptic operators in $\mathbb{R}^d$, $d=2,3$, with variable coefficients, which can be represented in a low rank separable form. We construct a…
The very definition of an Einstein metric implies that all its geometry is encoded in the Weyl tensor. With this in mind, in this paper we derive higher-order Bochner type formulas for the Weyl tensor on a four dimensional Einstein…
Tensor networks provide compact and scalable representations of high-dimensional data, enabling efficient computation in fields such as quantum physics, numerical partial differential equations (PDEs), and machine learning. This paper…
We present a new rank-adaptive tensor method to compute the numerical solution of high-dimensional nonlinear PDEs. The method combines functional tensor train (FTT) series expansions, operator splitting time integration, and a new…
Building on an insight due to Avramidi, we provide a system of transport equations for determining key fundamental bi-tensors, including derivatives of the world-function, \sigma(x,x'), the square root of the Van Vleck determinant,…
A non-classical Weyl theory is developed for skew-self-adjoint Dirac systems with rectangular matrix potentials. The notion of the Weyl function is introduced and direct and inverse problems are solved. A Borg-Marchenko type uniqueness…
In [8], some exact splittings are proposed for inhomogeneous quadratic differential equations including, for example, transport equations, kinetic equations, and Schr{\"o}dinger type equations with a rotation term. In this work, these exact…
Ideas from deformation quantization are applied to deform the expression of elements of an algebra. Extending these ideas to certain transcendental elements implies that $\frac{1}{i\h}uv$ in the Weyl algebra is naturally viewed as an…
Time-dependent Partial Differential Equations with given initial conditions are considered in this paper. New differentiation techniques of the unknown solution with respect to time variable are proposed. It is shown that the proposed…
This paper deals with sheaves of differential operators on noncommutative algebras. The sheaves are defined by quotienting a the tensor algebra of vector fields (suitably deformed by a covariant derivative) to ensure zero curvature. As an…
In this paper, we investigate spacetime characterized by a hidden symmetry defined by a given Killing tensor. To exhibit this hidden symmetry, the inverse metric must commute with the Killing tensor under the Schouten-Nijenhuis bracket,…
A new multivariate density estimator for stationary sequences is obtained by Fourier inversion of the thresholded empirical characteristic function. This estimator does not depend on the choice of parameters related to the smoothness of the…
New formulas on the inverse problem for the continuous skew-self-adjoint Dirac type system are obtained. For the discrete skew-self-adjoint Dirac type system the solution of a general type inverse spectral problem is also derived in terms…
Higher-order tensors appear in various areas of mechanics as well as physics, medicine or earth sciences. As these tensors are highly complex, most are not well understood. Thus, the analysis and the visualization process form a highly…
The so-called Weyl transform is a linear map from a commutative algebra of functions to a noncommutative algebra of linear operators, characterized by an action on Cartesian coordinate functions of the form $(x, y) \mapsto (X, Y)$ such that…
Inverse eigenvalue and singular value problems have been widely discussed for decades. The well-known result is the Weyl-Horn condition, which presents the relations between the eigenvalues and singular values of an arbitrary matrix. This…
Algorithms for the computation of the real zeros of hypergeometric functions which are solutions of second order ODEs are described. The algorithms are based on global fixed point iterations which apply to families of functions satisfying…
Braided differential operators $\del^i$ are obtained by differentiating the addition law on the braided covector spaces introduced previously (such as the braided addition law on the quantum plane). These are affiliated to a Yang-Baxter…
A new method for the construction of conformally invariant equations in an arbitrary four dimensional (pseudo-) Riemannian space is presented. This method uses the Weyl geometry as a tool and exploits the natural conformal invariance we can…
The problem of obtaining an explicit representation for the fourth invariant of geodesic motion (generalized Carter constant) of an arbitrary stationary axisymmetric vacuum spacetime generated from an Ernst Potential is considered. The…