For the Landauâ??Lifshitzâ??Gilbert (LLG) equation of micromagnetics we study linearly implicit backward difference formula (BDF) time discretizations up to order $5$ combined with higher-order non-conforming finite element space discretizations, which are based on weak formulation due Alouges but use approximate tangent spaces that defined by $L^2$-averaged instead nodal orthogonality constrai...

In this paper we study the orthogonality conditions satisfied by Jacobi polynomials P (α,β) n when the parameters α and β are not necessarily > −1. We establish orthogonality on a generic closed contour on a Riemann surface. Depending on the parameters, this leads to either full orthogonality conditions on a single contour in the plane, or to multiple orthogonality conditions on a number of con...

Abstract. In this paper we study the orthogonality conditions satisfied by Jacobi polynomials P (α,β) n when the parameters α and β are not necessarily > −1. We establish orthogonality on a generic closed contour on a Riemann surface. Depending on the parameters, this leads to either full orthogonality conditions on a single contour in the plane, or to multiple orthogonality conditions on a num...

The joint bidiagonalization (JBD) method has been used to compute some extreme generalized singular values and vectors of a large regular matrix pair . We make numerical analysis the underlying JBD process establish relationships between it two mathematically equivalent Lanczos bidiagonalizations in finite precision. Based on results analysis, we investigate convergence approximate show that, u...

This letter studies the performance of a single gateway LoRa system in presence different interference considering imperfect orthogonality effect. It utilizes concepts stochastic geometry to present low-complexity approximate closed-form model for computing success and coverage probabilities under these challenging conditions. Monte Carlo simulation results have shown that is not as theoretical...

We provide a few natural applications of the analytic newvectors, initiated in \cite{JN} arXiv:1911.01880, to some questions automorphic forms for $\mathrm{PGL}_n(\mathbb{Z})$ with $n\ge 2$, archimedean conductor aspect. prove an orthogonality result Fourier coefficients, density estimate non-tempered forms, equidistribution Satake parameters respect Sato--Tate measure, and second moment centra...

Notions of orthogonality and convolution are explored with the use Kontorovich–Lebedev transform its convolution. New classes corresponding orthogonal polynomials functions investigated. Integral representations, relations explicit expressions established.

A very simple and extremely computationally efficient algorithm for blind separation of two speech sources from two mixtures is presented in this paper. The algorithm exploits the approximate W-disjoint orthogonality of speech signals and assumes specific sensors (microphones) setting that allows the sources to possess a feature we call cross high-low diversity. Two sources are said to be cross...

The paper deals with robust direction of arrival (DOA) estimation based on independent component analysis (ICA) in the presence of sensor gain perturbation and unknown noise fields. It has been shown that the noise subspace based estimator suffers from the drawback of being very sensitivity to orthogonality between the estimated noise subspace and true signal subspace. However, no single subspa...