Novel time-harmonic beam fields have been recently obtained by utilizing a non-orthogonal coordinate system which is a priori matched to the field’s planar linearly-phased Gaussian aperture distribution. These waveobjects were termed tilted Gaussian beams. The present investigation is concerned with parameterization of these time-harmonic tilted Gaussian beams and of the wave phenomena associat...

A Lagrangian multiform structure is established for a generalisation of the Darboux system describing orthogonal curvilinear coordinate systems. It has been shown in past that this coupled PDEs fact an encoding entire Kadomtsev-Petviashvili (KP) hierarchy terms so-called Miwa variables. Thus, providing description multidimensionally consistent amounts to new 3-form continuous KP system. matrix ...

ABSTRACT The linear mixing model (LMM) is a well-known and useful method for decomposing spectra in a hyperspectral image into the sum of their constituents, or endmembers. Mathematically, if the spectra are represented as n-dimensional vectors, then the LMM implies that the set of endmembers defines a basis or coordinate system for the set of spectra. Because the endmembers themselves are gene...

Let K be a symmetric convex body in R. It is well-known that for every θ ∈ (0, 1) there exists a subspace F of R with dimF = [(1− θ)n] such that (∗) PF (K) ⊇ c √ θ MK Dn ∩ F, where PF denotes the orthogonal projection onto F . Consider a fixed coordinate system in R. We study the question whether an analogue of (∗) can be obtained when one is restricted to choose F among the coordinate subspace...

The following article presents a new isometric transformation algorithm based on the transformation in the newly normed Hilbert type space. The presented method is based on so-called virtual translations, already known in advance, of two relative oblique orthogonal coordinate systems-interior and exterior orientation of sensors-to a common, known in both systems, point. Each of the systems is t...

the purpose of this paper is to present a 2d depth-averaged model for simulating and examining unsteady flow patterns in open channel bends. in particular, this paper proposes a 2d depth-averaged model that takes into account the influence of the secondary flow phenomenon through calculation of the dispersion stresses. the dispersion terms which arose from the integration of the product of the ...

We address the poor scalability of learning algorithms for orthogonal recurrent neural networks via use stochastic coordinate descent on group, leading to a cost per iteration that increases linearly with number states. This contrasts cubic dependency typical feasible such as Riemannian gradient descent, which prohibits big network architectures. Coordinate rotates successively two columns matr...