We study the total generalised variation regularisation of symmetric tensor fields from medical applications, namely diffusion tensor regularisation. We study the effect of the pointwise positivity constraint on the tensor field, as well as the difference between direct denoising of the tensor field first solved from the Stejskal-Tanner equation, as was done in our earlier work, and of incorpor...

Based on the higher-order restricted flows, first type of integrable deformed fourth-order matrix NLS equations, that is, equations with self-consistent sources (FMNLSSCS), is derived. By virtue $${\bar{\partial }}$$ -dressing method, second called NLS–Maxwell–Bloch system (FMNLS-MB) presented. We prove equivalence FMNLSSCS and FMNLS-MB successfully. Furthermore, N-soliton solutions are explici...

This article makes use of simultaneous decomposition four quaternion matrixes to investigate some Sylvester-like matrix equation systems. We present useful necessary and sufficient conditions for the consistency system equations in terms equivalence form block matrixes. also derive general solution according partition coefficient As an application system, we practical a ϕ-Hermitian provide when...

This paper presents preconditioned Galerkin and minimal residual algorithms for the solution of Sylvester equations AX XB = C. Given two good preconditioner matricesM and N for matrices A and B, respectively, we solve the Sylvester equations MAXN MXBN =MCN. The algorithms use the Arnoldi process to generate orthonormal bases of certain Krylov subspaces and simultaneously reduce the order of Syl...

This paper deals with the finite element solution of the convection diffusion equation in one and two dimensions. Two main techniques are adopted and compared. The first one includes Petrov-Galerkin based on Lagrangian tensor product elements in conjunction with streamlined upwinding. The second approach represents Bubnov/Petrov-Galerkin schemes based on a new group of exponential elements. It ...

In this paper we make a comparison between the two-scale asymptotic expansion method for periodic homogenization and the so-called Bloch wave method. It is wellknown that the homogenized tensor coincides with the Hessian matrix of the first Bloch eigenvalue when the Bloch parameter vanishes. In the context of the two-scale asymptotic expansion method, there is the notion of high order homogeniz...