Sentence examples similar to multi dimensional operators from inspiring English sources

This paper presents the "quasi-inverse" technique (QIT), which combines optimizations of one-dimensional spectral differentiation matrices with Kronecker matrix products to build efficient multi-dimensional operators.

We also give applications to self-adjoint, multi-dimensional diffusion operators.

In this paper we use classical results from complex analysis that give us a new class of trace formulae for the spectrum of discrete multi-dimensional Scrödinger operators with complex-valued potentials.

In [8], Simirnitskii and Sobolevskii considered the difference operator (A_{1h}^{x}) which is an elliptic difference operator of an arbitrary high order of accuracy approximating the multi-dimensional elliptic operator (A_{1}^{x} =B^{x}+delta I).

So it was a multi dimensional challenge.

Poverty is multi dimensional.

In the present paper, the positivity of a multi-dimensional difference operator in the half-space is considered.

Danelich in [12] considered the positivity of a difference analog A h x of the 2m th-order multi-dimensional elliptic operator A x with dependent coefficients on semi-spaces R + × R n − 1.

We consider a particular class of families of multi-dimensional lattice Schrödinger operators with deterministic (e.g., quasi-periodic) potentials generated by the "hull" given by an orthogonal series over the Haar wavelet basis on the torus of arbitrary dimension, with expansion coefficients considered as independent parameters.

In order to evolve fluxes along the cell interfaces we use multi-dimensional approximate evolution operator.

In the present article, the structure of the fractional spaces (E_{alpha }(dot{C} ( mathbb{R}_{hn}^ ),A_{h}^{x})) generated by the multi-dimensional elliptic difference operator (A_{h}^{x}) is investigated.